Advance Validation Guide-Volume I - Graitec · 2020. 8. 21. · ADVANCE VALIDATION GUIDE 3 INTRODUCTION The Advance Design Validation Guide 2021 outlines a vast set of practical test

VALIDATION GUIDE

Advance Design

Validation Guide Volume I

Version: 2021

Tests passed on: 29 July 2020

Number of tests: 918

ADVANCE VALIDATION GUIDE

3

INTRODUCTION

The Advance Design Validation Guide 2021 outlines a vast set of practical test cases showing the behavior of Advance Design 2021 in various areas and various conditions. The tests cover a wide field of expertise:

Modeling

Combinations Management according to Eurocode 0, CR 0-2012, CISC and AISC

Climatic Load Generation according to Eurocode 1, CR1-1-3/2012, CR1-1-4/2012,

NTC 2008, NV2009, NBC 2015 and ASCE 7-10

Meshing

Finite Element Calculation

Reinforced Concrete Design according to Eurocode 2, NTC 2008 and CSA

Steel Member Design according to Eurocode 3, NTC 2008, AISC and CSA

Timber Member Design according to Eurocode 5

Seismic Analysis according to Eurocode 8, PS92, RPA99/2003, RPS 2011

Report generation

Import / Export procedures

User Interface Behavior

Such tests are generally made of a reference (independent of the specific software version tested), a transformation (a calculation or a data-processing scenario), a result (given by the specific software version tested) and a difference, usually measured in percentage as a drift from a specific set of reference values. Depending on the cases, the used reference can be a theoretical calculation performed manually, a sample taken from the technical literature, or the result of a previous version considered as accurate by experience.

In the field of structural analysis and design, software users must always keep in mind that the results depend, to a great extent, on the modeling (especially when dealing with finite elements) and on the settings of the numerous assumptions and options available in the software. A software package cannot entirely replace engineers’ experience and analysis. Despite all the efforts we have made in terms of quality management, we cannot guaranty the correct behavior and the validity of the results issued by Advance Design in any given situation.

This complex validation process is carried out along with and in addition to manual testing and beta testing, in order to attain the "operational version" status. Its final outcome is the present guide, which contains a thorough description of the automatic tests, highlighting both the theoretical background and the results that our validation experts have obtained by using the current software release. We hope that this guide will highly contribute to the knowledge and the confidence you keep placing in Advance Design.

Ionel DRAGU

Graitec Innovation CTO


4

– 1 FINITE ELEMENT METHOD ......................................................................................... 11

1.1 System of two bars with three hinges (01-0002SSLLB_FEM) ............................................................. 12

1.2 Cantilever rectangular plate (01-0001SSLSB_FEM) ............................................................................ 15

1.3 Circular plate under uniform load (01-0003SSLSB_FEM) ................................................................... 17

1.4 Thin lozenge-shaped plate fixed on one side (alpha = 0 °) (01-0007SDLSB_FEM) ............................. 20

1.5 Thin circular ring fixed in two points (01-0006SDLLB_FEM)............................................................... 22

1.6 Tied (sub-tensioned) beam (01-0005SSLLB_FEM) .............................................................................. 25

1.7 Thin lozenge-shaped plate fixed on one side (alpha = 15 °) (01-0008SDLSB_FEM) ........................... 29

1.8 Thin lozenge-shaped plate fixed on one side (alpha = 45 °) (01-0010SDLSB_FEM) ........................... 31

1.9 Vibration mode of a thin piping elbow in plane (case 1) (01-0011SDLLB_FEM) ................................. 33

1.10 Thin circular ring hanged on an elastic element (01-0014SDLLB_FEM) ............................................ 35

1.11 Vibration mode of a thin piping elbow in plane (case 3) (01-0013SDLLB_FEM) ................................ 38

1.12 Double fixed beam with a spring at mid span (01-0015SSLLB_FEM) ................................................ 40

1.13 Slender beam with variable section (fixed-free) (01-0004SDLLB_FEM) ............................................. 43

1.14 Thin lozenge-shaped plate fixed on one side (alpha = 30 °) (01-0009SDLSB_FEM) .......................... 46

1.15 Vibration mode of a thin piping elbow in plane (case 2) (01-0012SDLLB_FEM) ................................ 48

1.16 Short beam on simple supports (eccentric) (01-0018SDLLB_FEM) ................................................... 51

1.17 Rectangular thin plate simply supported on its perimeter (01-0020SDLSB_FEM) ............................ 55

1.18 Annular thin plate fixed on a hub (repetitive circular structure) (01-0022SDLSB_FEM) ................... 58

1.19 Slender beam on two fixed supports (01-0024SSLLB_FEM) ............................................................. 60

1.20 Short beam on simple supports (on the neutral axis) (01-0017SDLLB_FEM).................................... 64

1.21 Cantilever beam in Eulerian buckling (01-0021SFLLB_FEM) ............................................................. 67

1.22 Bending effects of a symmetrical portal frame (01-0023SDLLB_FEM) .............................................. 69

1.23 Fixed thin arc in planar bending (01-0027SSLLB_FEM) ..................................................................... 72

1.24 Fixed thin arc in out of plane bending (01-0028SSLLB_FEM)............................................................ 75

1.25 Double fixed beam (01-0016SDLLB_FEM) .......................................................................................... 77

1.26 Thin square plate fixed on one side (01-0019SDLSB_FEM) ............................................................... 80

1.27 Slender beam on three supports (01-0025SSLLB_FEM) .................................................................... 83

1.28 Bimetallic: Fixed beams connected to a stiff element (01-0026SSLLB_FEM) ................................... 86

1.29 Truss with hinged bars under a punctual load (01-0031SSLLB_FEM)............................................... 89

1.30 Beam on elastic soil, free ends (01-0032SSLLB_FEM) ...................................................................... 91

1.31 Caisson beam in torsion (01-0037SSLSB_FEM) ................................................................................ 94

1.32 Portal frame with lateral connections (01-0030SSLLB_FEM)............................................................. 97

1.33 EDF Pylon (01-0033SFLLA_FEM) ..................................................................................................... 100

1.34 Square plate under planar stresses (01-0039SSLSB_FEM) ............................................................. 104

1.35 Stiffen membrane (01-0040SSLSB_FEM) ......................................................................................... 107

1.36 Beam on elastic soil, hinged ends (01-0034SSLLB_FEM) ............................................................... 110


5

1.37 Double hinged thin arc in planar bending (01-0029SSLLB_FEM) .....................................................113

1.38 Simply supported square plate (01-0036SSLSB_FEM) .....................................................................116

1.39 Thin cylinder under a uniform radial pressure (01-0038SSLSB_FEM) .............................................118

1.40 Thin cylinder under its self weight (01-0044SSLSB_MEF)................................................................120

1.41 Thin cylinder under a hydrostatic pressure (01-0043SSLSB_FEM) .................................................122

1.42 Simply supported square plate under a uniform load (01-0051SSLSB_FEM) ..................................125

1.43 Spherical dome under a uniform external pressure (01-0050SSLSB_FEM) .....................................127

1.44 Beam on two supports considering the shear force (01-0041SSLLB_FEM) ....................................130

1.45 Torus with uniform internal pressure (01-0045SSLSB_FEM) ...........................................................132

1.46 Spherical shell with holes (01-0049SSLSB_FEM) .............................................................................134

1.47 Simply supported rectangular plate under a uniform load (01-0053SSLSB_FEM)...........................136

1.48 Simply supported rectangular plate under a uniform load (01-0052SSLSB_FEM)...........................138

1.49 Thin cylinder under a uniform axial load (01-0042SSLSB_FEM) ......................................................140

1.50 Spherical shell under internal pressure (01-0046SSLSB_FEM)........................................................143

1.51 Pinch cylindrical shell (01-0048SSLSB_FEM) ...................................................................................146

1.52 A plate (0.01 m thick), fixed on its perimeter, loaded with a uniform pressure (01-0057SSLSB_FEM)148

1.53 Triangulated system with hinged bars (01-0056SSLLB_FEM) ..........................................................150


1.55 A plate (0.01 m thick), fixed on its perimeter, loaded with a punctual force (01-0062SSLSB_FEM) 154

1.56 A plate (0.01333 m thick), fixed on its perimeter, loaded with a uniform pressure (01-0058SSLSB_FEM) ........................................................................................................................................156




1.60 Shear plate perpendicular to the medium surface (01-0055SSLSB_FEM) .......................................164

1.61 Simply supported rectangular plate loaded with punctual force and moments (01-0054SSLSB_FEM)166


1.63 A plate (0.01333 m thick), fixed on its perimeter, loaded with a punctual force (01-0063SSLSB_FEM)170

1.64 Vibration mode of a thin piping elbow in space (case 2) (01-0068SDLLB_FEM) ..............................172

1.65 Reactions on supports and bending moments on a 2D portal frame (Rafters) (01-0077SSLPB_FEM)174

1.66 Plane portal frame with hinged supports (01-0089SSLLB_FEM) ......................................................176

1.67 Slender beam of variable rectangular section (fixed-fixed) (01-0086SDLLB_FEM) ..........................178


1.69 Short beam on two hinged supports (01-0084SSLLB_FEM) ............................................................183


1.71 Double fixed beam in Eulerian buckling with a thermal load (01-0091HFLLB_FEM) .......................188

1.72 Double fixed beam in Eulerian buckling with a thermal load (01-0091HFLLB_FEM) .......................190

1.73 A plate (0.1 m thick), fixed on its perimeter, loaded with a punctual force (01-0066SSLSB_FEM) ..192


6

1.74 Reactions on supports and bending moments on a 2D portal frame (Columns) (01-0078SSLPB_FEM) ........................................................................................................................................ 194

1.75 Slender beam of variable rectangular section with fixed-free ends (ß=5) (01-0085SDLLB_FEM) ... 196

1.76 Fixed/free slender beam with eccentric mass or inertia (01-0096SDLLB_FEM) .............................. 201

1.77 Membrane with hot point (01-0099HSLSB_FEM) ............................................................................. 205

1.78 Beam on 3 supports with T/C (k = 0) (01-0100SSNLB_FEM) ............................................................ 208

1.79 A 3D bar structure with elastic support (01-0094SSLLB_FEM) ....................................................... 211

1.80 Fixed/free slender beam with centered mass (01-0095SDLLB_FEM) .............................................. 218

1.81 Simple supported beam in free vibration (01-0098SDLLB_FEM) ..................................................... 223

1.82 Beam on 3 supports with T/C (k = -10000 N/m) (01-0102SSNLB_FEM) ............................................ 226

1.83 Linear system of truss beams (01-0103SSLLB_FEM) ...................................................................... 229

1.84 BAEL 91 (concrete design) - France: Linear element in combined bending/tension - without compressed reinforcements - Partially tensioned section (02-0158SSLLB_B91) ...................................... 232

1.85 Cantilever beam in Eulerian buckling with thermal load (01-0092HFLLB_FEM).............................. 237

1.86 Double cross with hinged ends (01-0097SDLLB_FEM) .................................................................... 239

1.87 Beam on 3 supports with T/C (k -> infinite) (01-0101SSNLB_FEM).................................................. 242

1.88 BAEL 91 (concrete design) - France: Design of a concrete floor with an opening (03-0208SSLLG_BAEL91) .................................................................................................................................. 245

1.89 CM66 (steel design) - France: Design of a 2D portal frame (03-0207SSLLG_CM66) ....................... 253

1.90 BAEL 91 (concrete design) - France: Linear element in simple bending - without compressed reinforcement (02-0162SSLLB_B91) ........................................................................................................... 260

1.91 CM66 (steel design) - France: Design of a Steel Structure (03-0206SSLLG_CM66) ........................ 264

1.92 PS92 - France: Study of a mast subjected to an earthquake (02-0112SMLLB_P92) ........................ 273

1.93 Non linear system of truss beams (01-0104SSNLB_FEM) ............................................................... 278

1.94 Generating planar efforts before and after selecting a saved view (TTAD #11849) ......................... 281

1.95 Verifying forces for triangular meshing on planar element (TTAD #11723)..................................... 281

1.96 Verifying stresses in beam with "extend into wall" property (TTAD #11680) .................................. 281

1.97 Verifying the displacement results on linear elements for vertical seism (TTAD #11756) .............. 281

1.98 Verifying constraints for triangular mesh on planar elements (TTAD #11447) ................................ 281

1.99 Verifying diagrams after changing the view from standard (top, left,...) to user view (TTAD #11854)282

1.100 Verifying forces results on concrete linear elements (TTAD #11647) ............................................ 282

1.101 Generating results for Torsors NZ/Group (TTAD #11633) .............................................................. 282

1.102 Verifying Sxx results on beams (TTAD #11599) ............................................................................. 282

1.103 Verifying diagrams for Mf Torsors on divided walls (TTAD #11557) .............................................. 282

1.104 EC8 / NF EN 1998-1 - France: Verifying the level mass center (TTAD #11573, TTAD #12315) ....... 283

1.105 Verifying results on punctual supports (TTAD #11489) ................................................................. 283

1.106 Verifying nonlinear analysis results for frames with semi-rigid joints and rigid joints (TTAD #11495) ........................................................................................................................................................ 283

1.107 Generating a report with torsors per level (TTAD #11421) ............................................................. 283

1.108 Verifying tension/compression supports on nonlinear analysis (TTAD #11518)........................... 283


7

1.109 Verifying tension/compression supports on nonlinear analysis (TTAD #11518) ...........................284

1.110 Verifying the main axes results on a planar element (TTAD #11725) .............................................284

1.111 Verifying the display of the forces results on planar supports (TTAD #11728)..............................284

1.112 Verifying the internal forces results for a simple supported steel beam .......................................284

1.113 Verifying forces on a linear elastic support which is defined in a user workplane (TTAD #11929)285

1.114 Verifying torsors on a single story coupled walls subjected to horizontal forces .........................285

1.115 Calculating torsors using different mesh sizes for a concrete wall subjected to a horizontal force (TTAD #13175) ..............................................................................................................................................285

1.116 Verifying results of a steel beam subjected to dynamic temporal loadings (TTAD #14586) ..........286

1.117 Verifying a simply supported concrete slab subjected to temperature variation between top and bottom fibers ................................................................................................................................................289

1.118 FEM Results - United Kingdom: Simply supported laterally restrained (from P364 Open Sections Example 2) ....................................................................................................................................................290

1.119 Verifying the correct use of symmetric steel cross sections (eg. IPE300S) ...................................292

1.120 Temperature load: SD frame with elements under tempertature gradient, applied on separate systems ........................................................................................................................................................292

1.121 Verifying displacements of a prestressed cable structure with results presented in Tibert, 1999.292

1.122 Checks the bending moments in the central node of a steel frame with two beams having a rotational stiffness of 42590 kN/m. ..............................................................................................................292

1.123 Verifies the ultimate factored gravity loads acting on elements of a structure ..............................293

1.124 Verifies the response spectrum analysis results for a 2D frame ....................................................297

1.125 Verifying results for prestressed steel cables (Sxx 10MPa) ...........................................................302

1.126 Imposed displacement, support settlement (d=30mm) ..................................................................302

1.127 Plane strain behavior - dam cross-section supporting earth/water pressure of 0.7 and 1 MPa ....302

1.128 Spectral/Seismic analysis for rigid diaphragm (membrane) subjected to bidirectional seismic action .........................................................................................................................................................302

1.129 Modal analysis of a structure with ”membrane” type element .......................................................303

1.130 Modal analysis of a structure with rigid diaphragm .......................................................................303

1.131 Time history analysis on concrete membrane subjected to dynamic punctual load .....................303

1.132 Modal analysis of a structure with “bar” type elements .................................................................304

1.133 Modal analysis of a structure with planar elastic supports (global coordinate system)................308

1.134 Modal analysis of a structure with an elastic linear support (global coordinate system) ..............313

1.135 Generalized buckling analysis on bending rigid structure made of short beam elements ............317

1.136 Generalized buckling analysis on bending rigid structure made of variable section beams ........319

1.137 Modal analysis of a structure with an elastic linear support (local coordinate system) ................321

1.138 Modal analysis of a structure with elastic releases on linear elements .........................................325

1.139 Generalized buckling analysis on membrane element ...................................................................329

1.140 Generalized buckling analysis on windwall defined as rigid diaphragm element ..........................331

1.141 Generalized buckling analysis on column with elastic support in global coordinate system .......333

1.142 Modal analysis of a structure with elastic punctual supports (local coordinate system) ..............335

1.143 Modal analysis of a structure with releases on beam elements .....................................................340


8

1.144 Generalized buckling analysis on 2D truss structure made of bar elements. ............................... 344

1.145 Generalized buckling analysis on shell with planar elastic support in global coordinate system 346

1.146 Generalized buckling analysis on shell with linear elastic support in global coordinate system . 348

1.147 Dynamic analysis - Verifies displacements on beam with point mass subject to seismic load.... 350

1.148 Dynamic analysis - Verifies modal mass participation percentages on a model with point mass subject to seismic load ............................................................................................................................... 352

1.149 Generalized buckling analysis on shell with linear elastic support in local coordinate system ... 354

1.150 Generalized buckling analysis on beams with elastic releases ..................................................... 356

1.151 Dynamic analysis – Verifies the displacements of a sloped frame rafter subject to horizontal seismic action.............................................................................................................................................. 359

1.152 Dynamic analysis – Verifies the envelope of node displacement on linear element with elastic releases subject to Dynamic Temporal Load .............................................................................................. 361

1.153 Dynamic analysis – Verifies the displacements of a sloped frame rafter with elastic releases subject to horizontal seismic action ........................................................................................................... 363

1.154 Generalized buckling analysis on column with elastic support, in local coordinate system ........ 365

1.155 Generalized buckling analysis on model with beam elements with specific releases .................. 367

1.156 Dynamic analysis – Verifies the envelope of node displacement on linear element under Dynamic Temporal Load............................................................................................................................................. 369

1.157 Time history analysis – Verifies the displacements on a column with elastic punctual support (local coordinate system) subject to dynamic temporal load at the top .................................................... 371

1.158 Time history analysis – Verifying the displacements on a cantilever column connected to a steel plate on elastic support in global coordinate system ................................................................................. 373

1.159 Time history analysis – Verifies displacements, forces and bending moments for beam elements structure subject to dynamic temporal loads ............................................................................................. 375

1.160 Time history analysis - Verifies displacements, forces and bending moments for variable beam elements structure subject to dynamic temporal loads ............................................................................. 377

1.161 Time history analysis – Verifies the displacements on a column with elastic punctual support (global coordinate system) subject to dynamic temporal load at the top .................................................. 379

1.162 Time history analysis – Verifies the displacements on shell element with linear elastic support (local coordinate system) subject to point dynamic temporal load............................................................ 381

1.163 NL static analysis on T/C point supports – Verifies displacements on linear elements and forces on supports operating in compression with elastic stiffness defined in local coordinate system............ 383

1.164 NL static analysis on T/C point supports – Verifies displacements on linear elements and forces on supports operating in compression with elastic stiffness defined in global coordinate system ......... 383

1.165 Time history analysis – Verifies displacements for a rigid membrane model subject to time history analysis load case ....................................................................................................................................... 384

1.166 Time history analysis – Verifies the displacements on a column with fixed support subject to dynamic temporal load at the top ................................................................................................................ 386

1.167 Time history analysis – Verifies displacements and forces for bar elements subject to dynamic temporal load ............................................................................................................................................... 388

1.168 Time history analysis - Verifies displacements, forces and bending moments for S beam elements structure subject to dynamic temporal loads ............................................................................................. 390

1.169 NL static analysis on T/C linear supports – Verifies displacements on planar elements and torsors on linear supports operating in compression with elastic stiffness defined in global coordinate system 392

1.170 NL static analysis on T/C linear supports – Verifies displacements on planar elements and torsors on linear supports operating in tension with elastic stiffness defined in local coordinate system ........... 392


9

1.171 NL static analysis on T/C point supports – Verifies displacements on linear elements and forces on supports operating in tension with elastic stiffness defined in local coordinate system .....................392

1.172 NL static analysis on T/C linear supports – Verifies displacements on planar elements and torsors on linear supports operating in compression with elastic stiffness defined in local coordinate system ..393

1.173 NL static analysis on T/C linear supports – Verifies displacements on planar elements and torsors on linear supports operating in tension with elastic stiffness defined in global coordinate system .........393

1.174 NL static analysis on T/C planar supports – Verifies displacements on elements and torsors on supports operating in compression with elastic stiffness defined in global coordinate system ...............393

1.175 NL static analysis on T/C planar supports – Verifies displacements on elements and torsors on supports operating in compression with elastic stiffness defined in local coordinate system .................394

1.176 NL static analysis on T/C planar supports – Verifies displacements on elements and torsors on supports operating in tension with elastic stiffness defined in local coordinate system ..........................394

1.177 NL static analysis on T/C point supports – Verifies displacements on linear elements and forces on supports operating in tension with elastic stiffness defined in global coordinate system ...................394

1.178 Time history analysis – Verifies displacements and bending moments for a plate type element subject to dynamic temporal load case .......................................................................................................395

1.179 NL static analysis on T/C planar supports – Verifies displacements on elements and torsors on supports operating in tension with elastic stiffness defined in global coordinate system ........................397

1.180 Elastic punctual (local coordinate system) supports in Linear static analysis – Verifies displacements on a cantilever column (S beam type) .................................................................................398

1.181 T/C planar support (global coordinate system) in Non-Linear static analysis – Verifies displacements on a horizontal plate (shell type) subject to uniform distributed planar load .....................400

1.182 Elastic linear (global coordinate system) support in Linear static analysis – Verifies displacements on a S type beam subject to point force at midspan ..........................................................402

1.183 NL static analysis on strut element type - Verifies nodal displacements and forces in strut after performing NL static analysis ......................................................................................................................404

1.184 T/C punctual (local coordinate system) supports in Non-Linear static analysis – Verifies displacements on a cantilever column (S beam type) .................................................................................405

1.185 Elastic linear (local coordinate system) support in Linear static analysis – Verifies displacements on a S type beam subject to point force at midspan ...................................................................................407

1.186 T/C linear (local coordinate system) support in Non-Linear static analysis – Verifies displacements on a S type beam subject to point force at midspan ..........................................................409

1.187 T/C linear (global coordinate system) support in Non-Linear static analysis – Verifies displacements on a S type beam subject to point force at midspan ..........................................................410

1.188 NL static analysis on membrane – Verifies nodal displacements and forces in the planar element after performing NL static analysis..............................................................................................................412

1.189 Elastic planar support (global coordinate system) in Linear static analysis – Verifies displacements on a horizontal plate (shell type) subject to uniform distributed planar load .....................413

1.190 NL static analysis on variable beam steel frame - Verifies nodes displacements after performing NL static analysis .........................................................................................................................................415

1.191 Verify the behavior of elastic displacement release on one end of a beam in static analysis (200kN/m) .....................................................................................................................................................418

1.192 Torsors/Groups of walls with rotated local axes, z+ and z- (load 10kN/m at top on z direction) - check MX, MY / Group ..................................................................................................................................418

1.193 Nonlinear static analysis on 3D model with rigid diaphragm defined as shell with DOF constraint subjected to horizontal and gravitational loads ..........................................................................................419

1.194 NL static analysis on 3D model with windwall defined as rigid diaphragm subject to horizontal and gravitational loads........................................................................................................................................423


10

1.195 Torsors/Groups of walls with rotated local axes, z+ and z- (load 10kN/m at top on z direction) - check MX, TY / Group, Mf and Tyz .............................................................................................................. 423

1.196 Torsors/Groups of walls with rotated local axes, z+ and z- (load 10kN at top in the walls plane) - check MX, TY / Group, Mz and Txy .............................................................................................................. 423

1.197 Torsors/Groups of walls with rotated local axes, z+ and z- (load 10kN/m at top on z direction) - check MY, TX, Mf and Tyz............................................................................................................................ 424

1.198 Verify the behavior of elastic rotational releases on both ends of a beam in static analysis (100kNm/deg) ............................................................................................................................................... 424

1.199 Torsors/Groups of walls with rotated local axes, z+ and z- (load 10kN at top in the walls plane) - check MY, TX / Group, Mz, Txy .................................................................................................................... 424

1.200 Torsors/Groups of walls with rotated local axes, z+ and z- (load 10kN at top at angle with walls plane) - check Mz, Mf, Txy, Tyz.................................................................................................................... 424

1.201 Verifying the resultant forces on single walls ................................................................................ 425

1.202 Verifying the sum of actions on supports ...................................................................................... 425

1.203 Pushover Analysis - Verifies the Pushover load distribution - Concentrated ............................... 425

1.204 Pushover Analysis - Verifies the Pushover load distribution - Triangular..................................... 425

1.205 Pushover Analysis - Verifies the Pushover load distribution - Uniform ........................................ 426

1.206 Pushover Analysis: Verifying the Pushover Analysis on a converted model (Advance Design 2020.2) ........................................................................................................................................................ 426

1.207 EC3/ NF EN1993-1-1/NA France: Pushover Analysis - Verifies the limit states and status of a steel EC8-3 flexural plastic hinge ........................................................................................................................ 427

1.208 EC3/ NF EN 1993-1-1/NA - France: Pushover Analysis - Verifies the status of a steel FEMA flexural plastic hinge ................................................................................................................................................ 427

1.209 Verifying the resultant forces on a group of walls ......................................................................... 428

1.210 AISC: Pushover Analysis - Verifies the status of a steel FEMA flexural plastic hinge .................. 433

1.211 Time history analysis – Verifies the displacements on shell element with linear elastic support (global coordinate system) subject to point dynamic temporal load ......................................................... 434

1.212 AISC: Pushover Analysis - Verifies the status of a steel EC8-3 flexural plastic hinge .................. 436

1.213 Pushover Analysis - Verifies the Pushover load distribution - Parabolic ...................................... 436

1 Finite Element Method


12

1.1 System of two bars with three hinges (01-0002SSLLB_FEM)

Test ID: 2434

Test status: Passed

1.1.1 Description

On a system of two bars (AC and BC) with three hinges, a punctual load in applied in point C. The vertical displacement in point C and the tensile stress on the bars are verified.

1.1.2 Background

1.1.2.1 Model description

■ Reference: Structure Calculation Software Validation Guide, test SSLL 09/89;

■ Analysis type: linear static;

■ Element type: linear.

System of two bars with three hinges Scale =1/33

0002SSLLB_FEM

Units

I. S.

Geometry

■ Bars angle relative to horizontal: = 30°,

■ Bars length: l = 4.5 m,

■ Bar section: A = 3 x 10-4

m2.

Materials properties

■ Longitudinal elastic modulus: E = 2.1 x 1011

Pa.

Boundary conditions

■ Outer: Hinged in A and B,

■ Inner: Hinge on C

Effel2001 - Structure - 10.1

Système de deux barres à trois rotules

Ech=1/33

01-0002SSLLB_MEF

4 . 5 0 0 m

3 0 °

3 0 °

4 . 5 0 0 m

AA

BB

CC

FF

X

Y

Z X

Y

Z


13

Loading

■ External: Punctual load in C: F = -21 x 103 N.

■ Internal: None.

1.1.2.2 Displacement of the model in C

Reference solution

uc = -3 x 10-3 m

Finite elements modeling

■ Linear element: beam, imposed mesh,

■ 21 nodes,

■ 20 linear elements.

Displacement shape


Displacement in C 0002SSLLB_FEM

1.1.2.3 Bars stresses

Reference solutions

AC bar = 70 MPa

BC bar = 70 MPa



■ 21 nodes,



14

1.1.2.4 Shape of the stress diagram


Bars stresses 0002SSLLB_FEM

1.1.2.5 Theoretical results

Solver Result name Result description Reference value

CM2 DZ Vertical displacement in point C [cm] -0.30

CM2 Sxx Tensile stress on AC bar [MPa] 70

CM2 Sxx Tensile stress on BC bar [MPa] 70

1.1.3 Calculated results

Result name Result description Value Error

DZ Vertical displacement in point C [cm] -0.299954 cm 0.02%

Sxx Tensile stress on AC bar [MPa] 69.9998 MPa 0.00%

Sxx Tensile stress on BC bar [MPa] 69.9998 MPa 0.00%


15

1.2 Cantilever rectangular plate (01-0001SSLSB_FEM)

Test ID: 2433

Test status: Passed

1.2.1 Description

Verifies the vertical displacement on the free extremity of a cantilever rectangular plate fixed on one side. The plate is 1 m long, subjected to a uniform planar load.

1.2.2 Background


■ Reference: Structure Calculation Software Validation Guide, test SSLS 01/89.

■ Analysis type: linear static.

■ Element type: planar.

Cantilever rectangular plate Scale =1/4

01-0001SSLSB_FEM

Units

S.I.

Geometry

■ Thickness: e = 0.005 m,

■ Length: l = 1 m,

■ Width: b = 0.1 m.



Pa,

■ Poisson's ratio: = 0.3.


16

Boundary conditions

■ Outer: Fixed at end x = 0,

■ Inner: None.

Loadings

■ External: Uniform load p = -1700 Pa on the upper surface,

■ Internal: None.

1.2.2.2 Displacement of the model in the linear elastic range

Reference solution

The reference displacement is calculated for the unsupported end located at x = 1m.

u = bl

4p

8EIz =

0.1 x 14 x 1700

8 x 2.1 x 1011

x 0.1 x 0.005

3

12

= -9.71 cm


■ Planar element: plate, imposed mesh,

■ 1100 nodes,

■ 990 surface quadrangles.

Deformed shape

Deformed cantilever rectangular plate Scale =1/4

01-0001SSLSB_FEM



CM2 DZ Vertical displacement on the free extremity [cm] -9.71



DZ Vertical displacement on the free extremity [cm] -9.58696 cm 1.27%


17

1.3 Circular plate under uniform load (01-0003SSLSB_FEM)

Test ID: 2435

Test status: Passed

1.3.1 Description

On a circular plate of 5 mm thickness and 2 m diameter, an uniform load, perpendicular on the plan of the plate, is applied. The vertical displacement on the plate center is verified.

1.3.2 Background


■ Reference: Structure Calculation Software Validation Guide, test SSLS 03/89;



Circular plate under uniform load Scale =1/10

01-0003SSLSB_FEM

Units

I. S.

Geometry

■ Circular plate radius: r = 1m,

■ Circular plate thickness: h = 0.005 m.



Pa,


Boundary conditions

■ Outer: Plate fixed on the side (in all points of its perimeter),

For the modeling, we consider only a quarter of the plate and we impose symmetry conditions on some nodes (see the following model; yz plane symmetry condition):translation restrained nodes along x and rotation restrained nodes along y and z: translation restrained nodes along x and rotation restrained nodes along y and z:

■ Inner: None.


18

Loading

■ External: Uniform loads perpendicular on the plate: pZ = -1000 Pa,

■ Internal: None.

1.3.2.2 Vertical displacement of the model at the center of the plate

Reference solution

Circular plates form:

u = pr

4

64D =

-1000 x 14

64 x 2404 = - 6.50 x 10

-3 m

with the plate radius coefficient: D = Eh

3

12(1-2) =

2.1 x 1011

x 0.0053

12(1-0.32)

D = 2404



■ 70 nodes,

■ 58 planar elements.

Circular plate under uniform load Scale =1.5

Meshing 01-0003SSLSB_FEM

Deformed shape

Circular plate under uniform load Scale =1.5

Deformed 01-0003SSLSB_FEM


19



CM2 DZ Vertical displacement on the plate center [mm] -6.50



DZ Vertical displacement on the plate center [mm] -6.47032 mm 0.46%


20

1.4 Thin lozenge-shaped plate fixed on one side (alpha = 0 °) (01-0007SDLSB_FEM)

Test ID: 2439

Test status: Passed

1.4.1 Description

Verifies the eigen modes frequencies for a 10 mm thick lozenge-shaped plate fixed on one side, subjected to its own weight only.

1.4.2 Background


■ Reference: Structure Calculation Software Validation Guide, test SDLS 02/89;

■ Analysis type: modal analysis;


Thin lozenge-shaped plate fixed on one side Scale =1/10

01-0007SDLSB_FEM

Units

I. S.

Geometry

■ Thickness: t = 0.01 m,

■ Side: a = 1 m,

■ = 0°

■ Points coordinates:

► A ( 0 ; 0 ; 0 )

► B ( a ; 0 ; 0 )

► C ( 0 ; a ; 0 )

► D ( a ; a ; 0 )



Pa,

■ Poisson's ratio: = 0.3,

■ Density: = 7800 kg/m3.


21

Boundary conditions

■ Outer: AB side fixed,

■ Inner: None.

Loading

■ External: None,

■ Internal: None.

1.4.2.2 Eigen mode frequencies relative to the angle

Reference solution

M. V. Barton formula for a side "a" lozenge, leads to the frequencies:

fj = 2a2

1i

2

)1(12

Et2

2

where i = 1,2, and i

2 = g().

3.492

8.525

M.V. Barton noted the sensitivity of the result relative to the mode and the angle. He acknowledged that the i values were determined with a limited development of an insufficient order, which led to consider a reference value that is based on an experimental result, verified by an average of seven software that use the finite elements calculation method.



■ 61 nodes,


Eigen mode shapes



CM2 Eigen mode Eigen mode 1 frequency [Hz] 8.7266



Result description Value Error

Eigen mode 1 frequency [Hz] 8.67 Hz -0.65%



22

1.5 Thin circular ring fixed in two points (01-0006SDLLB_FEM)

Test ID: 2438

Test status: Passed

1.5.1 Description

Verifies the first eigen modes frequencies for a thin circular ring fixed in two points, subjected to its own weight only.

1.5.2 Background


■ Reference: Structure Calculation Software Validation Guide, test SDLL 12/89;

■ Analysis type: modal analysis, plane problem;


Thin circular ring fixed in two points Scale =1/2

01-0006SDLLB_FEM

Units

I. S.

Geometry

■ Average radius of curvature: OA = OB = R = 0.1 m,

■ Angular spacing between points A and B: 120° ;

■ Rectangular straight section:

► Thickness: h = 0.005 m,

► Width: b = 0.010 m,

► Section: A = 5 x 10-5 m

2,

► Flexure moment of inertia relative to the vertical axis: I = 1.042 x 10-10

m4,

■ Point coordinates:

► O (0 ;0),

► A (-0.05 3 ; -0.05),

► B (0.05 3 ; -0.05).


23



Pa



Boundary conditions

■ Outer: Fixed at A and B,

■ Inner: None.

Loading

■ External: None,

■ Internal: None.

1.5.2.2 Eigen mode frequencies

Reference solutions

The deformation of the fixed ring is calculated from the deformations of the free-free thin ring

■ Symmetrical mode:

► u’i = i cos(i)

► v’i = sin (i)

► ’i = 1-i

2

R sin (i)

■ Antisymmetrical mode:

► u’i = i sin(i)

► v’i = -cos (i)

► ’i = 1-i

2

R cos (i)

From Green’s method results:

fj = 2

1j

2R

h

12

E

with a support angle of 120°.

i 1 2 3 4

Symmetrical mode 4.8497 14.7614 23.6157

Antisymmetrical mode 1.9832 9.3204 11.8490 21.5545


■ Linear element: beam, without meshing,

■ 32 nodes,


Eigen mode shapes


24

1.5.2.3 Theoretic results


CM2 Eigen mode Eigen mode 1 frequency - 1 antisymmetric 1 [Hz] 235.3

CM2 Eigen mode Eigen mode 2 frequency - 2 symmetric 1 [Hz] 575.3




CM2 Eigen mode Eigen mode 6 frequency - 6 antisymmetric 4 [Hz] 2557




Eigen mode 1 frequency - 1 antisymmetric 1 [Hz] 236.32 Hz 0.43%

Eigen mode 2 frequency - 2 symmetric 1 [Hz] 578.52 Hz 0.56%



Eigen mode 5 frequency - 5 symmetric 2 [Hz] 1760 Hz 0.51%


Eigen mode 7 frequency - 7 symmetric 3 [Hz] 2777.43 Hz -0.86%


25

1.6 Tied (sub-tensioned) beam (01-0005SSLLB_FEM)

Test ID: 2437

Test status: Passed

1.6.1 Description

Verifies the tension force on a beam reinforced by a system of hinged bars, subjected to a uniform linear load.

1.6.2 Background



■ Analysis type: static, thermoelastic (plane problem);


Tied (sub-tensioned) beam Scale =1/37

01-0005SSLLB_FEM

Units

I. S.

Geometry

■ Length:

► AD = FB = a = 2 m,

► DF = CE = b = 4 m,

► CD = EF = c = 0.6 m,

► AC = EB = d = 2.088 m,

► Total length: L = 8 m,

■ AD, DF, FB Beams:

► Section: A = 0.01516 m2,

► Shear area: Ar = A / 2.5,

► Inertia moment: I = 2.174 x 10-4

m4,

■ CE Bar:


26

► Section: A1 = 4.5 x 10-3

m2,

■ AC, EB bar:

► Section: A2 = 4.5 x 10-3

m2,

■ CD, EF bars:

► Section: A3 = 3.48 x 10-3 m

2.


■ Isotropic linear elastic material,


Pa,

■ Shearing module: G = 0.4x E.

Boundary conditions

■ Outer: Hinged in A, support connection in B (blocked vertical translation),

■ Inner: Hinged at bar ends: AC, CD, EF, EB.

Loading

■ External: Uniform linear load p = -50000 N/ml,

■ Internal: Shortening of the CE tie of = 6.52 x 10-3

m (dilatation coefficient: CE = 1 x 10-5

/°C and temperature

variation T = -163°C).

1.6.2.2 Compression force in CE bar

Reference solution

The solution is established by considering the deformation effects due to the shear force and normal force:

= 1 - 4

3 x

a

L

k = A

Ar = 2.5

t = I

A

= (L/c)2 x (1+ (A/A1) x (b/L) + 2 x (A/A2) x (d/a)

2 x (d/L) + 2 x (A/A3) (c/a)

2 x (c/L)

= k x [(2Et2) / (GaL)]

= + +

0 = 1 – (a/L)2 x (2 – a/L)

0 = 6k x (E/G) x (t/L)2 x (1 + b/L)

0 = 0 + 0

NCE = - (1/12) x (pL2/c) x (0 /) + (EI/(Lc

2)) x (/) = 584584 N


Linear element: without meshing,

■ AD, DF, FB: S beam (considering the shear force deformations),

■ AC, CD, EF, EB: bar,

■ CE: beam,

■ 6 nodes.


27

Force diagrams


Compression force in CE bar

1.6.2.3 Bending moment at point H

Reference solution

MH = - (1/8) x pL2 x [1- (2/3) x (0/)] – (EI/(Lc)) x (/p) = 49249.5 N


Linear element: without meshing,

■ AD, DF, FB: S beam (considering the shear force deformations),

■ AC, CD, EF, EB: bar,

■ CE: beam,

■ 6 nodes.

Shape of the bending moment diagram


Mz bending moment


28

1.6.2.4 Vertical displacement at point D

Reference solution

The reference displacement vD provided by AFNOR is determined by averaging the results of several software with implemented finite elements method.

vD = -0.5428 x 10-3 m


■ Linear element: without meshing,

► AD, DF, FB: S beam (considering the shear force deformations),

► AC, CD, EF, EB: bar,

► CE: beam,

■ 6 nodes.

Deformed shape


Deformed



CM2 FX Tension force on CE bar [N] 584584



Fx Tension force on CE bar [N] 584580 N 0.00%


29


Test ID: 2440

Test status: Passed

1.7.1 Description


1.7.2 Background






01-0008SDLSB_FEM

Units

I. S.

Geometry


■ Side: a = 1 m,

■ = 15°


► A ( 0 ; 0 ; 0 )

► B ( a ; 0 ; 0 )

► C ( 0.259a ; 0.966a ; 0 )

► D ( 1.259a ; 0.966a ; 0 )



Pa,




30

Boundary conditions


■ Inner: None.

Loading

■ External: None,

■ Internal: None.

1.7.2.2 Eigen modes frequencies function by angle

Reference solution

M. V. Barton formula for a lozenge of side "a" leads to the frequencies:

fj = 2a2

1i

2

)1(12

Et2

2

where i = 1,2, or i

2 = g().

3.601

8.872

M. V. Barton noted the sensitivity of the result relative to the mode and the angle. He acknowledged that the i values were determined with a limited development of an insufficient order, which led to consider a reference value that is based on an experimental result, verified by an average of seven software that use the finite elements calculation method.



■ 961 nodes,


Eigen mode shapes










31


Test ID: 2442

Test status: Passed

1.8.1 Description


1.8.2 Background






01-0010SDLSB_FEM

Units

I. S.

Geometry


■ Side: a = 1 m,

■ = 45°


► A ( 0 ; 0 ; 0 )

► B ( a ; 0 ; 0 )

► C ( 2

2a ;

2

2 a ; 0 )

► D (2

22 a ;

2

2a ; 0 )



Pa,




32

Boundary conditions


■ Inner: None.

Loading

■ External: None,

■ Internal: None.


Reference solution


fj = 2a2

1i

2

)1(12

Et2

2

where i = 1,2, or i

2 = g().

4.4502

10.56




■ 961 nodes,


Eigen mode shapes







Eigen mode 1 frequency [Hz] 11.31 Hz 1.70%



33

1.9 Vibration mode of a thin piping elbow in plane (case 1) (01-0011SDLLB_FEM)

Test ID: 2443

Test status: Passed

1.9.1 Description

Verifies the vibration modes of a thin piping elbow (1 m radius) with fixed ends and subjected to its self weight only.

1.9.2 Background



■ Analysis type: modal analysis (plane problem);


Vibration mode of a thin piping elbow in plane Scale = 1/7

Case 1 01-0011SDLLB_FEM

Units

I. S.

Geometry

■ Average radius of curvature: OA = R = 1 m,

■ Straight circular hollow section:

■ Outer diameter: de = 0.020 m,

■ Inner diameter: di = 0.016 m,

■ Section: A = 1.131 x 10-4 m

2,

■ Flexure moment of inertia relative to the y-axis: Iy = 4.637 x 10-9

m4,

■ Flexure moment of inertia relative to z-axis: Iz = 4.637 x 10-9

m4,

■ Polar inertia: Ip = 9.274 x 10-9

m4.

■ Points coordinates (in m):

► O ( 0 ; 0 ; 0 )

► A ( 0 ; R ; 0 )

► B ( R ; 0 ; 0 )


34



Pa,



Boundary conditions

■ Outer: Fixed at points A and B ,

■ Inner: None.

Loading

■ External: None,

■ Internal: None.


Reference solution

The Rayleigh method applied to a thin curved beam is used to determine parameters such as:

■ in plane bending:

fj = 2

2

i

R2

A

EIz

where i = 1,2,


■ Linear element: beam,

■ 11 nodes,


Eigen mode shapes



CM2 Eigen mode Eigen mode frequency in plane 1 [Hz] 119




Eigen mode frequency in plane 1 [Hz] 120.09 Hz 0.92%



35

1.10 Thin circular ring hanged on an elastic element (01-0014SDLLB_FEM)

Test ID: 2446

Test status: Passed

1.10.1 Description

Verifies the first eigen modes frequencies of a circular ring hanged on an elastic element, subjected to its self weight only.

1.10.2 Background



■ Analysis type: modal analysis, plane problem;


Thin circular ring hang from an elastic element Scale = 1/1

01-0014SDLLB_FEM

Units

I. S.

Geometry

■ Average radius of curvature: OB = R = 0.1 m,

■ Length of elastic element: AB = 0.0275 m ;

■ Straight rectangular section:

► Ring

Thickness: h = 0.005 m,

Width: b = 0.010 m,

Section: A = 5 x 10-5 m

2,

Flexure moment of relative to the vertical axis: I = 1.042 x 10-10

m4,

► Elastic element


36

Thickness: h = 0.003 m,

Width: b = 0.010 m,

Section: A = 3 x 10-5 m

2,

Flexure moment of inertia relative to the vertical axis: I = 2.25 x 10-11

m4,


► O ( 0 ; 0 ),

► A ( 0 ; -0.0725 ),

► B ( 0 ; -0.1 ).



Pa,



Boundary conditions

■ Outer: Fixed in A,

■ Inner: None.

Loading

■ External: None,

■ Internal: None.


Reference solutions

The reference solution was established from experimental results of a mass manufactured aluminum ring.



■ 43 nodes,


Eigen mode shapes


37



CM2 Eigen mode Eigen mode 1 Asymmetrical frequency [Hz] 28.80

CM2 Eigen mode Eigen mode 2 Symmetrical frequency [Hz] 189.30



CM2 Eigen mode Eigen mode 5 Symmetrical frequency [Hz] 682.00




Eigen mode 1 Asymmetrical frequency [Hz] 28.81 Hz 0.03%

Eigen mode 2 Symmetrical frequency [Hz] 189.69 Hz 0.21%



Eigen mode 5 Symmetrical frequency [Hz] 683.9 Hz 0.28%



38


Test ID: 2445

Test status: Passed

1.11.1 Description

Verifies the vibration modes of a thin piping elbow (1 m radius) extended by two straight elements of length L, subjected to its self weight only.

1.11.2 Background





Vibration mode of a thin piping elbow Scale = 1/12


Units

I. S.

Geometry





■ Section: A = 1.131 x 10-4 m

2,


m4,


m4,


m4.


► O ( 0 ; 0 ; 0 )

► A ( 0 ; R ; 0 )

► B ( R ; 0 ; 0 )

► C ( -L ; R ; 0 )

► D ( R ; -L ; 0 )


39



Pa,



Boundary conditions

■ Outer:

► Fixed at points C and Ds,

► At A: translation restraint along y and z,

► At B: translation restraint along x and z,

■ Inner: None.

Loading

■ External: None,

■ Internal: None.


Reference solution



fj = 2

2

i

R2

A

EIz

where i = 1,2,



■ 41 nodes,


Eigen mode shapes



CM2 Eigen mode Eigen mode frequency in plane 1 [Hz] 25.300

CM2 Eigen mode Eigen mode frequency in plane 2 [Hz] 27.000



Eigen mode frequency in plane 1 [Hz] 24.96 Hz -1.34%

Eigen mode frequency in plane 2 [Hz] 26.71 Hz -1.07%


40

1.12 Double fixed beam with a spring at mid span (01-0015SSLLB_FEM)

Test ID: 2447

Test status: Passed

1.12.1 Description

Verifies the vertical displacement on the middle of a beam consisting of four elements of length "l", having identical characteristics. A punctual load of -10000 N is applied.

1.12.2 Background


■ Reference: internal GRAITEC test;



Units

I. S.

Geometry

■ = 1 m

■ S = 0.01 m2

■ I = 0.0001 m4



Pa,


Boundary conditions

■ Outer:

■ Fixed at ends x = 0 and x = 4 m,

■ Elastic support with k = EI/ rigidity

■ Inner: None.

Loading

■ External: Punctual load P = -10000 N at x = 2m,

■ Internal: None.


Reference solution

The reference vertical displacement v3, is calculated at the middle of the beam at x = 2 m.


41

Rigidity matrix of a plane beam:

EIEIEIEI

EIEIEIEI

EIEIEIEI

EIEIEIEI

460

260

6120

6120

00l

ES00

ES

260

460

6120

6120

00ES

-00ES

K

22

2323

22

2323

e

Given the symmetry / X and load of the structure, it is unnecessary to consider the degrees of freedom associated with normal work (u2, u3, u4).

The same symmetry allows the deduction of:

■ v2 = v4

■ 2 = -4

■ 3 = 0

6

5

4

3

2

1

0

0

0

0

0

4626

612612

2680

26

6120

24612

2680

26

6120

124612

2680

26

6120

24612

2646

612612

5

5

1

1

5

5

4

4

3

3

2

2

1

1

22

22

22

22

22

22

22

22

22

22

M

R

P

M

R

v

v

v

v

v

EI

33

333

333

333

33

The elementary rigidity matrix of the spring in its local axis system, )(

)(

11

11

6

3

5U

UEIk

, must be expressed in

the global axis system by means of the rotation matrix (90° rotation):

6

6

6

3

3

3

5

000000

010010

000000

000000

010010

000000

v

u

v

u

EIK

344332 4

3 0

826vv


42

34433233

2 024612

vvvv

y)unnecessar(usually 026826

244423222vvvv

(3)

m 10 11905.03

612124612 03

2

3

34243332223

EIl

Pv

EI

Pvvv



■ 6 nodes,

■ 4 linear elements + 1 spring,

Deformed shape

Double fixed beam with a spring at mid span

Deformed

Note: the displacement is expressed here in m



CM2 Dz Vertical displacement on the middle of the beam [mm] -0.11905



Dz Vertical displacement on the middle of the beam [mm] -0.119048 mm 0.00%


43

1.13 Slender beam with variable section (fixed-free) (01-0004SDLLB_FEM)

Test ID: 2436

Test status: Passed

1.13.1 Description

Verifies the first eigen mode frequencies for a slender beam with variable section, subjected to its own weight.

1.13.2 Background





Slender beam with variable section (fixed-free) Scale =1/4

01-0004SDLLB_FEM

Units

I. S.

Geometry

■ Beam length: l = 1.00 m,

■ Initial section (in A):

► Height: h1 = 0.04 m,

► Width: b1 = 0.04 m,

► Section: ,

► Flexure moment of inertia relative to z-axis: Iz1 = 2.1333 x 10-7 m

4,

■ Final section (in B):

► Height: h2 = 0.01 m,

► Width: b2 = 0.01 m,

► Section:

► Flexure moment of inertia relative to z-axis: Iz2 = 8.3333 x 10-10

m4.


44


■ Longitudinal elastic modulus: E = 2 x 1011

Pa,

■ Density: 7800 kg/m3.

Boundary conditions

■ Outer: Fixed in A,

■ Inner: None.

Loading

■ External: None,

■ Internal: None.


Reference solutions

Precise calculation by numerical integration of the differential equation of beams bending (Euler-Bernoulli theories):

2

x2 (EIz

2v

x2 ) = -A

2v

x2 where Iz and A vary with the abscissa.

The result is: = 1

2 i

h2

l2

E

12

1 2 3 4 5

23.289 73.9 165.23 299.7 478.1


■ Linear element: variable beam, imposed mesh,

■ 31 nodes,


Eigen mode shapes


45
















46


Test ID: 2441

Test status: Passed

1.14.1 Description


1.14.2 Background






01-0009SDLSB_FEM

Units

I. S.

Geometry


■ Side: a = 1 m,

■ = 30°


► A ( 0 ; 0 ; 0 )

► B ( a ; 0 ; 0 )

► C ( 0.5a ; 3

2 a ; 0 )

► D ( 1.5a ; 3

2 a ; 0 )



Pa,




47

Boundary conditions


■ Inner: None.

Loading

■ External: None,

■ Internal: None.


Reference solution


fj = 2a2

1i

2

)1(12

Et2

2

where i = 1,2, or i

2 = g().

3.961

10.19




■ 961 nodes,


Eigen mode shapes










48


Test ID: 2444

Test status: Passed

1.15.1 Description

Verifies the vibration modes of a thin piping elbow (1 m radius) extended by two straight elements of length L, subjected to its self weight only.

1.15.2 Background







Units

I. S.

Geometry


■ L = 0.6 m,


■ Outer diameter de = 0.020 m,

■ Inner diameter di = 0.016 m,

■ Section: A = 1.131 x 10-4 m

2,


m4,


m4,


m4.



49

► O ( 0 ; 0 ; 0 )

► A ( 0 ; R ; 0 )

► B ( R ; 0 ; 0 )

► C ( -L ; R ; 0 )

► D ( R ; -L ; 0 )



Pa,



Boundary conditions

■ Outer:

► Fixed at points C and D



■ Inner: None.

Loading

■ External: None,

■ Internal: None.


Reference solution



fj = 2

2

i

R2

A

EIz

where i = 1,2,



■ 23 nodes,


Eigen mode shapes


50










51

1.16 Short beam on simple supports (eccentric) (01-0018SDLLB_FEM)

Test ID: 2450

Test status: Passed

1.16.1 Description

Verifies the first eigen mode frequencies of a short beam on simple supports (the supports are eccentric relative to the neutral axis).

1.16.2 Background



■ Analysis type: modal analysis, (plane problem);


Short beam on simple supports (eccentric) Scale = 1/5

01-0018SDLLB_FEM

Units

I. S.

Geometry

■ Height: h = 0.2m,


■ Width: b = 0.1 m,

■ Section: A = 2 x 10-2 m

4,


m4.



Pa,




52

Boundary conditions

■ Outer:

► Hinged at A (null horizontal and vertical displacements),

► Simple support at B.

■ Inner: None.

Loading

■ External: None.

■ Internal: None.

1.16.2.2 Eigen modes frequencies

Reference solution

The problem has no analytical solution, the solution is determined by averaging several software: Timoshenko model with shear force deformation effects and rotation inertia. The bending modes and the traction-compression are coupled.


■ Linear element: S beam, imposed mesh,

■ 10 nodes,


Eigen modes shape

Short beam on simple supports (eccentric)

Mode 1


Mode 2


53


Mode 3


Mode 4


Mode 5


54
















55

1.17 Rectangular thin plate simply supported on its perimeter (01-0020SDLSB_FEM)

Test ID: 2452

Test status: Passed

1.17.1 Description

Verifies the first eigen mode frequencies of a thin rectangular plate simply supported on its perimeter.

1.17.2 Background





Rectangular thin plate simply supported on its perimeter Scale = 1/8

01-0020SDLSB_FEM

Units

I. S.

Geometry

■ Length: a = 1.5 m,

■ Width: b = 1 m,


■ Points coordinates in m:

► A (0 ;0 ;0)

► B (0 ;1.5 ;0)

► C (1 ;1.5 ;0)

► D (1 ;0 ;0)


56



Pa,



Boundary conditions

■ Outer:

► Simple support on all sides,

► For the modeling: hinged at A, B and D.

■ Inner: None.

Loading

■ External: None.

■ Internal: None.


Reference solution

M. V. Barton formula for a rectangular plate with supports on all four sides, leads to:

fij = 2

[ (

a

i)2 + (

b

j)2]

)1(12

Et2

2

where:

i = number of half-length of wave along y ( dimension a)

j = number of half-length of wave along x ( dimension b)


■ Planar element: shell,

■ 496 nodes,


Eigen mode shapes


57



CM2 Eigen mode Eigen mode “i" - “j” frequency, for i = 1; j = 1. [Hz] 35.63








Eigen mode "i" - "j" frequency, for i = 1; j = 1 (Mode 1) [Hz] 35.58 Hz -0.14%


Eigen mode "i" - "j" frequency, for i = 1; j = 2 (Mode 3) [Hz] 109.98 Hz 0.33%





58

1.18 Annular thin plate fixed on a hub (repetitive circular structure) (01-0022SDLSB_FEM)

Test ID: 2454

Test status: Passed

1.18.1 Description

Verifies the eigen mode frequencies of a thin annular plate fixed on a hub.

1.18.2 Background




■ Element type: planar element.

Annular thin plate fixed on a hub (repetitive circular structure) Scale = 1/3

01-0022SDLSB_FEM

Units

I. S.

Geometry

■ Inner radius: Ri = 0.1 m,

■ Outer radius: Re = 0.2 m,

■ Thickness: t = 0.001 m.

Material properties


Pa,



Boundary conditions

■ Outer: Fixed on a hub at any point r = Ri.


59

■ Inner: None.

Loading

■ External: None.

■ Internal: None.


Reference solution

The solution of determining the frequency based on Bessel functions leads to the following formula:

fij = 1

2Re2 ij

2

Et2

12(1-2)

where:

i = the number of nodal diameters

j = the number of nodal circles

and ij2 such as:

j \ i 0 1 2 3

0 13.0 13.3 14.7 18.5

1 85.1 86.7 91.7 100


■ Planar element: plate,

■ 360 nodes,



















Eigen mode “i" - “j” frequency, for i = 2; j = 1 (Mode 22) [Hz] 555.51 Hz -0.64%




60

1.19 Slender beam on two fixed supports (01-0024SSLLB_FEM)

Test ID: 2456

Test status: Passed

1.19.1 Description

A straight slender beam with fixed ends is loaded with a uniform load, several punctual loads and a torque. The shear force, bending moment, vertical displacement and horizontal reaction are verified.

1.19.2 Background





Slender beam on two fixed supports Scale = 1/4

01-0024SSLLB_FEM

Units

I. S.

Geometry

■ Length: L = 1 m,

■ Beam inertia: I = 1.7 x 10-8

m4.



Pa.

Boundary conditions


■ Inner: None.

Loading

■ External:


61

► Uniformly distributed load from A to B: py = p = -24000 N/m,

► Punctual load at D: Fx = F1 = 30000 N,

► Torque at D: Cz = C = -3000 Nm,

► Punctual load at E: Fx = F2 = 10000 N,

► Punctual load at E: Fy = F = -20000 N.

■ Internal: None.

1.19.2.2 Shear force at G

Reference solution

Analytical solution:

■ Shear force at G: VG

VG = 0.216F – 1.26 L

C



■ 5 nodes,


Results shape


Shear force

1.19.2.3 Bending moment in G

Reference solution


■ Bending moment at G: MG


62

MG = pL

2

24 - 0.045LF – 0.3C



■ 5 nodes,


Results shape


Bending moment

1.19.2.4 Vertical displacement at G

Reference solution


■ Vertical displacement at G: vG

vG = pl

4

384EI +

0.003375FL3

EI +

0.015CL2

EI



■ 5 nodes,



63

Results shape


Deformed

1.19.2.5 Horizontal reaction at A

Reference solution


■ Horizontal reaction at A: HA

HA = -0.7F1 –0.3F2



■ 5 nodes,




CM2 Fz Shear force in point G. [N] -540

CM2 My Bending moment in point G. [Nm] -2800

CM2 Dz Vertical displacement in point G. [cm] -4.90

CM2 Fx Horizontal reaction in point A. [N] 24000



Fz Shear force in point G [N] -540 N 0.00%

My Bending moment in point G [Nm] -2800 N*m 0.00%

DZ Vertical displacement in point G [cm] -4.90485 cm -0.10%

Fx Horizontal reaction in point A [N] 24000 N 0.00%


64

1.20 Short beam on simple supports (on the neutral axis) (01-0017SDLLB_FEM)

Test ID: 2449

Test status: Passed

1.20.1 Description

Verifies the first eigen mode frequencies of a short beam on simple supports (the supports are located on the neutral axis), subjected to its own weight only.

1.20.2 Background




Short beam on simple supports on the neutral axis Scale = 1/6

01-0017SDLLB_FEM

Units

I. S.

Geometry

■ Height: h = 0.2 m,


■ Width: b = 0.1 m,

■ Section: A = 2 x 10-2 m

4,


m4.



Pa,




65

Boundary conditions

■ Outer:

► Hinged at A (null horizontal and vertical displacements),

► Simple support in B.

■ Inner: None.

Loading

■ External: None.

■ Internal: None.


Reference solution

The bending beams equation gives, when superimposing, the effects of simple bending, shear force deformations and rotation inertia, Timoshenko formula.

The reference eigen modes frequencies are determined by a numerical simulation of this equation, independent of any software.

The eigen frequencies in tension-compression are given by:

fi =

l2

i

E where i =

2

)1i2(


■ Linear element: S beam, imposed mesh,

■ 10 nodes,


Eigen mode shapes


66


















67

1.21 Cantilever beam in Eulerian buckling (01-0021SFLLB_FEM)

Test ID: 2453

Test status: Passed

1.21.1 Description

Verifies the critical load result on node 5 of a cantilever beam in Eulerian buckling. A punctual load of -100000 is applied.

1.21.2 Background


■ Reference: internal GRAITEC test (Euler theory);

■ Analysis type: Eulerian buckling;


Units

I. S.

Geometry

■ L= 10 m

■ S=0.01 m2

■ I = 0.0002 m4



N/m2,


Boundary conditions


■ Inner: None.

Loading

■ External: Punctual load P = -100000 N at x = L,

■ Internal: None.

1.21.2.2 Critical load on node 5

Reference solution

The reference critical load established by Euler is:

98696.0100000

98696N 98696

L4

EIP

2

2

critique


68


■ Planar element: beam, imposed mesh,

■ 5 nodes,

■ 4 elements.

Deformed shape



CM2 Fx Critical load on node 5. [N] -98696



Fx Critical load on node 5 (mode 1) [N] -100000 N -1.32%


69

1.22 Bending effects of a symmetrical portal frame (01-0023SDLLB_FEM)

Test ID: 2455

Test status: Passed

1.22.1 Description

Verifies the first eigen mode frequencies of a symmetrical portal frame with fixed supports.

1.22.2 Background





Bending effects of a symmetrical portal frame Scale = 1/5

01-0023SDLLB_FEM

Units

I. S.

Geometry

■ Straight rectangular sections for beams and columns:

■ Thickness: h = 0.0048 m,

■ Width: b = 0.029 m,

■ Section: A = 1.392 x 10-4 m

2,


m4,


A B C D E F

x -0.30 0.30 -0.30 0.30 -0.30 0.30

y 0 0 0.36 0.36 0.81 0.81


70



Pa,



Boundary conditions


■ Inner: None.

Loading

■ External: None.

■ Internal: None.


Reference solution

Dynamic radius method (slender beams theory).



■ 60 nodes,


Deformed shape

Bending effects of a symmetrical portal frame Scale = 1/7

Mode 13


71



CM2 Eigen mode Eigen mode 1 antisymmetric frequency [Hz] 8.8


CM2 Eigen mode Eigen mode 3 symmetric frequency [Hz] 43.8







CM2 Eigen mode Eigen mode 10 antisymmetric frequency [Hz] 206


CM2 Eigen mode Eigen mode 12 antisymmetric frequency [Hz] 320

CM2 Eigen mode Eigen mode 13 symmetric frequency [Hz] 335



Eigen mode 1 antisymmetric frequency [Hz] 8.78 Hz -0.23%

Eigen mode 2 antisymmetric frequency [Hz] 29.43 Hz 0.10%

Eigen mode 3 symmetric frequency [Hz] 43.85 Hz 0.11%










Eigen mode 13 symmetric frequency [Hz] 334.96 Hz -0.01%


72

1.23 Fixed thin arc in planar bending (01-0027SSLLB_FEM)

Test ID: 2459

Test status: Passed

1.23.1 Description

Arc of a circle fixed at one end, subjected to two punctual loads and a torque at its free end. The horizontal displacement, vertical displacement and rotation about Z-axis are verified.

1.23.2 Background



■ Analysis type: static linear (plane problem);


Fixed thin arc in planar bending Scale = 1/24

01-0027SSLLB_FEM

Units

I. S.

Geometry

■ Medium radius: R = 3 m ,

■ Circular hollow section:

► de = 0.02 m,

► di = 0.016 m,

► A = 1.131 x 10-4 m

2,

► Ix = 4.637 x 10-9 m

4.


Longitudinal elastic modulus: E = 2 x 1011

Pa.

Boundary conditions

■ Outer: Fixed in A.

■ Inner: None.

Loading

■ External:


73

At B:

► punctual load F1 = Fx = 10 N,

► punctual load F2 = Fy = 5 N,

► bending moment about Oz, Mz = 8 Nm.

■ Internal: None.

1.23.2.2 Displacements at B

Reference solution

At point B:

■ displacement parallel to Ox: u = R

2

4EI [F1R + 2F2R + 4Mz]

■ displacement parallel to Oy: v = R

2

4EI [2F1R + (3 - 8)F2R + 2( - 2)Mz]

■ rotation around Oz: = R

4EI [4F1R + 2( - 2)F2R + 2Mz]



■ 31 nodes,


Results shape


Deformed


74



CM2 DX Horizontal displacement in point B [m] 0.3791

CM2 DZ Vertical displacement in point B [m] 0.2417

CM2 RY Rotation about Z-axis in point B [rad] -0.1654



DX Horizontal displacement in point B [m] 0.378914 m -0.05%

DZ Vertical displacement in point B [m] 0.241738 m 0.02%

RY Rotation about Z-axis in point B [rad] -0.165362 Rad 0.02%


75

1.24 Fixed thin arc in out of plane bending (01-0028SSLLB_FEM)

Test ID: 2460

Test status: Passed

1.24.1 Description

An arc of a circle fixed at one end is loaded with a punctual force at its free end, perpendicular to the plane. The out of plane displacement, torsion moment and bending moment are verified.

1.24.2 Background



■ Analysis type: static linear;


Fixed thin arc in out of plane bending Scale = 1/6

01-0028SSLLB_FEM

Units

I. S.

Geometry



► de = 0.02 m,

► di = 0.016 m,

► A = 1.131 x 10-4 m

2,

► Ix = 4.637 x 10-9 m

4.


76



Pa,


Boundary conditions

■ Outer: Fixed at A.

■ Inner: None.

Loading

■ External: Punctual force in B perpendicular on the plane: Fz = F = 100 N.

■ Internal: None.

1.24.2.2 Displacements at B

Reference solution

Displacement out of plane at point B:

uB = FR

3

EIx [

4 +

EIx

KT (

3

4 - 2)]

where KT is the torsional rigidity for a circular section (torsion constant is 2Ix).

KT = 2GIx = EIx

1 + uB =

FR3

EIx [

4 + (1 + ) (

3

4 - 2)]



■ 46 nodes,


1.24.2.3 Moments at = 15°

Reference solution

■ Torsion moment: Mx’ = Mt = FR(1 - sin)

■ Bending moment: Mz’ = Mf = -FRcos



■ 46 nodes,




CM2 D Displacement out of plane in point B [m] 0.13462

CM2 Mx Torsion moment in = 15° [Nm] 74.1180

CM2 Mz Bending moment in = 15° [Nm] -96.5925



D Displacement out of plane in point B [m] 0.135156 m 0.40%

Mx Torsion moment in Theta = 15° [Nm] 74.103 N*m -0.02%

Mz Bending moment in Theta = 15° [Nm] 96.5925 N*m 0.00%


77

1.25 Double fixed beam (01-0016SDLLB_FEM)

Test ID: 2448

Test status: Passed

1.25.1 Description

Verifies the eigen modes frequencies and the vertical displacement on the middle of a beam consisting of eight elements of length "l", having identical characteristics. A punctual load of -50000 N is applied.

1.25.2 Background


■ Reference: internal GRAITEC test (beams theory);

■ Analysis type: static linear, modal analysis;


Units

I. S.

Geometry


■ Axial section: S=0.06 m2

■ Inertia I = 0.0001 m4



N/m2,


■ Density: = 7850 kg/m3

Boundary conditions

■ Outer: Fixed at both ends x = 0 and x = 8 m,

■ Inner: None.

Loading

■ External: Punctual load P = -50000 N at x = 4m,

■ Internal: None.


Reference solution

The reference vertical displacement v5, is calculated at the middle of the beam at x = 2 m.

m 05079.00001.0111.2192

1650000

192

33

5

EEI

Plv


78



■ 9 nodes,

■ 8 elements.

Deformed shape

Double fixed beam

Deformed

1.25.2.3 Eigen mode frequencies of the model in the linear elastic range

Reference solution

Knowing that the first four eigen mode frequencies of a double fixed beam are given by the following formula:

S

IE

Lf n

n.

.

..2 2

2

where for the first 4 eigen modes frequencies

Hz 26.228=f 8.199

Hz 15.871=f 9.120

Hz 8.095=f 67.61

Hz 2.937=f 37.22

424

323

222

121



■ 9 nodes,

■ 8 elements.

Modal deformations

Double fixed beam

Mode 1


79

Double fixed beam

Mode 2

Double fixed beam

Mode 3

Double fixed beam

Mode 4



CM2 Dz Vertical displacement on the middle of the beam [m] -0.05079







Dz Vertical displacement on the middle of the beam [m] -0.0507937 m -0.01%






80

1.26 Thin square plate fixed on one side (01-0019SDLSB_FEM)

Test ID: 2451

Test status: Passed

1.26.1 Description

Verifies the first eigen modes frequencies of a thin square plate fixed on one side.

1.26.2 Background





Thin square plate fixed on one side Scale = 1/6

01-0019SDLSB_FEM

Units

I. S.

Geometry

■ Side: a = 1 m,

■ Thickness: t = 1 m,


► A (0 ;0 ;0)

► B (1 ;0 ;0)

► C (1 ;1 ;0)

► D (0 ;1 ;0)



Pa,


81



Boundary conditions

■ Outer: Edge AD fixed.

■ Inner: None.

Loading

■ External: None.

■ Internal: None.


Reference solution

M. V. Barton formula for a square plate with side "a", leads to:

fj = 2a2

1

i

2

)1(12

Et2

2

where i = 1,2, . . .

i 1 2 3 4 5 6

i 3.492 8.525 21.43 27.33 31.11 54.44



■ 959 nodes,


Eigen mode shapes

Thin square plate fixed on one side

Mode 1


82


Mode 2


Mode 3


















83

1.27 Slender beam on three supports (01-0025SSLLB_FEM)

Test ID: 2457

Test status: Passed

1.27.1 Description

A straight slender beam on three supports is loaded with two punctual loads. The bending moment, vertical displacement and reaction on the center are verified.

1.27.2 Background



■ Analysis type: static (plane problem);


Slender beam on three supports Scale = 1/49

01-0025SSLLB_FEM

Units

I. S.

Geometry


■ Beam inertia: I = 6.3 x 10-4

m4.


Longitudinal elastic modulus: E = 2.1 x 1011

Pa.

Boundary conditions

■ Outer:


84

► Hinged at A,

► Elastic support at B (Ky = 2.1 x 106 N/m),

► Simple support at C.

■ Inner: None.

Loading

■ External: 2 punctual loads F = Fy = -42000N.

■ Internal: None.

1.27.2.2 Bending moment at B

Reference solution

The resolution of the hyperstatic system of the slender beam leads to:

k = Ky3L

EI6

■ Bending moment at B: MB

MB = ± 2

L

)k8(

F)k26(



■ 5 nodes,


Results shape

Slender beam on three supports Scale = 1/49

Bending moment

1.27.2.3 Reaction in B

Reference solution

■ Compression force in the spring: VB

VB = -11F

8 + k


85



■ 5 nodes,


1.27.2.4 Vertical displacement at B

Reference solution

■ Deflection at the spring location: vB

vB = 11F

Ky(8 + k)



■ 5 nodes,


Results shape

Slender beam on three supports

Deformed



CM2 My Bending moment in point B. [Nm] -63000

CM2 DZ Vertical displacement in point B. [cm] -1.00

CM2 Fz Reaction in point B. [N] -21000



My Bending moment in point B [Nm] -63000 N*m 0.00%

DZ Vertical displacement in point B [cm] -1 cm 0.00%

Fz Reaction in point B [N] -21000 N 0.00%


86

1.28 Bimetallic: Fixed beams connected to a stiff element (01-0026SSLLB_FEM)

Test ID: 2458

Test status: Passed

1.28.1 Description

Two beams fixed at one end and rigidly connected to an undeformable beam is loaded with a punctual load. The deflection, vertical reaction and bending moment are verified in several points.

1.28.2 Background





Fixed beams connected to a stiff element Scale = 1/10

01-0026SSLLB_FEM

Units

I. S.

Geometry

■ Lengths:

► L = 2 m,

► l = 0.2 m,

■ Beams inertia moment: I = (4/3) x 10-8

m4,

■ The beam sections are squared, of side: 2 x 10-2 m.



Pa.


87

Boundary conditions

■ Outer: Fixed in A and C,

■ Inner: The tangents to the deflection of beams AB and CD at B and D remain horizontal; practically, we restraint translations along x and z at nodes B and D.

Loading

■ External: In D: punctual load F = Fy = -1000N.

■ Internal: None.

1.28.2.2 Deflection at B and D

Reference solution

The theory of slender beams bending (Euler-Bernouilli formula) leads to a deflection at B and D:

The resolution of the hyperstatic system of the slender beam leads to:

vB = vD = FL

3

24EI



■ 4 nodes,


Results shape

Fixed beams connected to a stiff element Scale = 1/10

Deformed

1.28.2.3 Vertical reaction at A and C

Reference solution

Analytical solution.



■ 4 nodes,



88

1.28.2.4 Bending moment at A and C

Reference solution




■ 4 nodes,

■ 3 linear elements



CM2 D Deflection in point B [m] 0.125

CM2 D Deflection in point D [m] 0.125

CM2 Fz Vertical reaction in point A [N] -500

CM2 Fz Vertical reaction in point C [N] -500

CM2 My Bending moment in point A [Nm] 500

CM2 My Bending moment in point C [Nm] 500



D Deflection in point B [m] 0.125376 m 0.30%

D Deflection in point D [m] 0.125376 m 0.30%

Fz Vertical reaction in point A [N] -500 N 0.00%

Fz Vertical reaction in point C [N] -500 N 0.00%

My Bending moment in point A [Nm] 500.083 N*m 0.02%

My Bending moment in point C [Nm] 500.083 N*m 0.02%


89

1.29 Truss with hinged bars under a punctual load (01-0031SSLLB_FEM)

Test ID: 2463

Test status: Passed

1.29.1 Description

Verifies the horizontal and the vertical displacement in several points of a truss with hinged bars, subjected to a punctual load.

1.29.2 Background





Truss with hinged bars under a punctual load Scale = 1/10

01-0031SSLLB_FEM

Units

I. S.

Geometry

Elements Length (m) Area (m2)

AC 0.5 2 2 x 10-4

CB 0.5 2 2 x 10-4

CD 2.5 1 x 10-4

BD 2 1 x 10-4



Pa.

Boundary conditions

■ Outer: Hinge at A and B,

■ Inner: None.


90

Loading

■ External: Punctual force at D: Fy = F = - 9.81 x 103 N.

■ Internal: None.

1.29.2.2 Displacements at C and D

Reference solution

Displacement method.



■ 4 nodes,


Displacements shape

Truss with hinged bars under a punctual load Scale = 1/9

Deformed



CM2 DX Horizontal displacement in point C [mm] 0.26517

CM2 DX Horizontal displacement in point D [mm] 3.47902

CM2 DZ Vertical displacement in point C [mm] 0.08839

CM2 DZ Vertical displacement in point D [mm] -5.60084



DX Horizontal displacement in point C [mm] 0.264693 mm -0.18%

DX Horizontal displacement in point D [mm] 3.47531 mm -0.11%

DZ Vertical displacement in point C [mm] 0.0881705 mm -0.25%

DZ Vertical displacement in point D [mm] -5.595 mm 0.10%


91

1.30 Beam on elastic soil, free ends (01-0032SSLLB_FEM)

Test ID: 2464

Test status: Passed

1.30.1 Description

A beam under 3 punctual loads lays on a soil of constant linear stiffness. The bending moment, vertical displacement and rotation about z-axis on several points of the beam are verified.

1.30.2 Background





Beam on elastic soil, free ends Scale = 1/21

01-0032SSLLB_FEM

Units

I. S.

Geometry

■ L = ( 10 )/2,

■ I = 10-4 m

4.



Pa.

Boundary conditions

■ Outer:

► Free A and B extremities,

► Constant linear stiffness of soil ky = K = 840000 N/m2.

■ Inner: None.


92

Loading

■ External: Punctual load at A, C and B: Fy = F = - 10000 N.

■ Internal: None.

1.30.2.2 Bending moment and displacement at C

Reference solution

= 4

K/(4EI)

= L/2

= sh (2) + sin (2)

■ Bending moment:

MC = (F/(4))(ch(2) - cos (2) – 8sh()sin())/

■ Vertical displacement:

vC = - (F/(2K))( ch(2) + cos (2) + 8ch()cos() + 2)/



■ 72 nodes,


Bending moment diagram

Beam on elastic soil, free ends Scale = 1/20

Bending moment

1.30.2.3 Displacements at A

Reference solution


vA = (2F/K)( ch()cos() + ch(2) + cos(2))/

■ Rotation about z-axis

A = (-2F2/K)( sh()cos() - sin()ch() + sh(2) - sin(2))/


93



■ 72 nodes,




CM2 My Bending moment in point C [Nm] 5759

CM2 Dz Vertical displacement in point C [m] -0.006844

CM2 Dz Vertical displacement in point A [m] -0.007854

CM2 RY Rotation about z-axis in point A [rad] -0.000706



My Bending moment in point C [Nm] 5779.54 N*m 0.36%

Dz Vertical displacement in point C [m] -0.00684369 m 0.00%

Dz Vertical displacement in point A [m] -0.00786073 m -0.09%

RY Rotation Theta about z-axis in point A [rad] -0.000707427 Rad -0.20%


94

1.31 Caisson beam in torsion (01-0037SSLSB_FEM)

Test ID: 2468

Test status: Passed

1.31.1 Description

A torsion moment is applied on the free end of a caisson beam fixed on one end. For both ends, the displacement, the rotation about Z-axis and the stress are verified.

1.31.2 Background





Caisson beam in torsion Scale = 1/4

01-0037SSLSB_FEM

Units

I. S.

Geometry

■ Length; L = 1m,

■ Square section of side: b = 0.1 m,

■ Thickness = 0.005 m.



Pa,


Boundary conditions

■ Outer: Beam fixed at end x = 0;

■ Inner: None.


95

Loading

■ External: Torsion moment M = 10N.m applied to the free end (for modeling, 4 forces of 50 N).

■ Internal: None.

1.31.2.2 Displacement and stress at two points

Reference solution

The reference solution is determined by averaging the results of several calculation software with implemented finite elements method.

Points coordinates:

■ A (0,0.05,0.5)

■ B (-0.05,0,0.8)

Note: point O is the origin of the coordinate system (x,y,z).



■ 90 nodes,


Deformed shape

Caisson beam in torsion Scale = 1/4

Deformed


96



CM2 D Displacement in point A [m] -0.617 x 10-6

CM2 D Displacement in point B [m] -0.987 x 10-6

CM2 RY Rotation about Z-axis in point A [rad] 0.123 x 10-4

CM2 RY Rotation about Z-axis in point B [rad] 0.197 x 10-4

CM2 sxy_mid xy stress in point A [MPa] -0.11

CM2 sxy_mid xy stress in point B [MPa] -0.11



D Displacement in point A [µm] 0.615911 µm -0.18%

D Displacement in point B [µm] 0.986809 µm -0.02%

RY Rotation about Z-axis in point A [rad] -1.23211e-05 Rad -0.17%

RY Rotation about Z-axis in point B [rad] -1.97173e-05 Rad -0.09%

sxy_mid Sigma xy stress in point A [MPa] -0.100038 MPa -0.04%

sxy_mid Sigma xy stress in point B [MPa] -0.100213 MPa -0.21%


97

1.32 Portal frame with lateral connections (01-0030SSLLB_FEM)

Test ID: 2462

Test status: Passed

1.32.1 Description

Verifies the rotation about z-axis and the bending moment on a portal frame with lateral connections.

1.32.2 Background





Portal frame with lateral connections Scale = 1/21

01-0030SSLLB_FEM

Units

I. S.

Geometry

Beam Length Moment of inertia

AB lAB = 4 m IAB =

64

3 x 10

-8 m

4

AC lAC = 1 m IAC =

1

12 x 10

-8 m

4

AD lAD = 1 m IAD =

1

12 x 10

-8 m

4

AE lAE = 2 m IAE =

4

3 x 10

-8 m

4

■ G is in the middle of DA.

■ The beams have square sections:

► AAB = 16 x 10-4

m

► AAD = 1 x 10-4 m

► AAC = 1 x 10-4 m


98

► AAE = 4 x 10-4

m


Longitudinal elastic modulus: E = 2 x 1011

Pa,

Boundary conditions

■ Outer:

► Fixed at B, D and E,

► Hinge at C,

■ Inner: None.

Loading

■ External:

► Punctual force at G: Fy = F = - 105 N,

► Distributed load on beam AD: p = - 103 N/m.

■ Internal: None.

1.32.2.2 Displacements at A

Reference solution

Rotation at A about z-axis:

We say: kAn = EIAn

lAn where n = B, C, D or E

K = kAB + kAD + kAE + 3

4 kAC

rAn = kAn

K

C1 = FlAD

8 -

plAB2

12

= C1

4K



■ 6 nodes,


Displacements shape

Portal frame with lateral connections

Deformed


99

1.32.2.3 Moments in A

Reference solution

■ MAB = plAB

2

12 + rAB x C1

■ MAD = - FlAD

8 + rAD x C1

■ MAE = rAE x C1

■ MAC = rAC x C1



■ 6 nodes,




CM2 RY Rotation about z-axis in point A [rad] -0.227118

CM2 My Bending moment in point A (MAB) [Nm] 11023.72

CM2 My Bending moment in point A (MAC) [Nm] 113.559

CM2 My Bending moment in point A (MAD) [Nm] 12348.588

CM2 My Bending moment in point A (MAE) [Nm] 1211.2994



RY Rotation Theta about z-axis in point A [rad] -0.227401 Rad -0.12%

My Bending moment in point A (Moment AB) [Nm] 11021 N*m -0.02%

My Bending moment in point A (Moment AC) [Nm] 113.704 N*m 0.13%

My Bending moment in point A (Moment AD) [Nm] 12347.5 N*m -0.01%

My Bending moment in point A (Moment AE) [Nm] 1212.77 N*m 0.12%


100

1.33 EDF Pylon (01-0033SFLLA_FEM)

Test ID: 2465

Test status: Passed

1.33.1 Description

Verifies the displacement at the top of an EDF Pylon and the dominating buckling results. Three punctual loads corresponding to wind loads are applied on the main arms, on the upper arm and on the lower horizontal frames of the pylon.

1.33.2 Background


■ Reference: Internal GRAITEC test;

■ Analysis type: static linear, Eulerian buckling;

■ Element type: linear

Units

I. S.

Geometry



Pa,


Boundary conditions

■ Outer:

► Hinged support,

► For the modeling, a fixed restraint and 4 beams were added at the pylon supports level.

■ Inner: None.


101

Loading

■ External:

Punctual loads corresponding to a wind load.

► FX = 165550 N, FY = - 1240 N, FZ = - 58720 N on the main arms,

► FX = 50250 N, FY = - 1080 N, FZ = - 12780 N on the upper arm,

► FX = 11760 N, FY = 0 N, FZ = 0 N on the lower horizontal frames

■ Internal: None.


Reference solution


102

Software ANSYS 5.3 NE/NASTRAN 7.0

Max deflection (m) 0.714 0.714

dominating mode 2.77 2.77



■ 402 nodes,

■ 1034 elements.

Deformed shape


103

Buckling modal deformation (dominating mode)



CM2 D Displacement at the top of the pylon [m] 0.714

CM2 Dominating buckling - critical , mode 4 [Hz] 2.77



D Displacement at the top of the pylon [m] 0.71254 m -0.20%

Dominating buckling - critical Lambda - mode 4 [Hz] 2.83 Hz 2.17%

D Displacement at the top of the pylon [m] m

Dominating buckling - critical Lambda - mode 4 [Hz] Hz


104

1.34 Square plate under planar stresses (01-0039SSLSB_FEM)

Test ID: 2470

Test status: Passed

1.34.1 Description

Verifies the vertical displacement and the stresses on a square plate of 2 x 2 m, fixed on 3 sides with a uniform surface load on its surface.

1.34.2 Background




■ Element type: planar (membrane).

Square plate under planar stresses Scale = 1/19

Modeling

1;1,

Units

I. S.

Geometry

■ Thickness: e = 1 m,

■ 4 square elements of side h = 1 m.



Pa,


Boundary conditions

■ Outer: Fixed on 3 sides,

■ Inner: None.


105

Loading

■ External: Uniform load p = -1. 108 N/ml on the upper surface,

■ Internal: None.


Reference solution

The reference displacements are calculated on nodes 7 and 9.

v9 = -6ph(3 + )(1 -

2)

E(8(3 - )2 - (3 + )

2) = -0.1809 x 10

-3 m,

v7 = 4(3 - )

3 + v9 = -0.592 x 10

-3 m,

For element 1.4:

(For the stresses calculated above, the abscissa point (x = 0; y = 0) corresponds to node 8.)

yy = E

1 - 2

(v9 - v7)

2h (1 + ) for

xx = yy for

xy = E

1 + (v9 + v7) + (v9 - v7)

4h (1 + ) for


■ Planar element: membrane, imposed mesh,

■ 9 nodes,


= -1 ; yy = 0

= 0 ; yy = -47.44 MPa

= 1 ; yy = -94.88 MPa

= -1 ; xx = 0

= 0 ; xx = -14.23 MPa

= 1 ; xx = -28.46 MPa

= -1 ; = 0 ; xy = -47.82 MPa

= 0 ; = 0 ; xy = -31.21 MPa

= 1 ; = 0 ; xy = -14.61 MPa


106

Deformed shape



CM2 DZ Vertical displacement on node 7 [mm] -0.592

CM2 DZ Vertical displacement on node 5 [mm] -0.1809

CM2 sxx_mid xx stresses on Element 1.4 in x = 0 m [MPa] 0

CM2 sxx_mid xx stresses on Element 1.4 in x = 0.5 m [MPa] -14.23

CM2 sxx_mid xx stresses on Element 1.4 in x = 1 m [MPa] -28.46

CM2 syy_mid yy stresses on Element 1.4 in x = 0 m [MPa] 0

CM2 syy_mid yy stresses on Element 1.4 in x = 0.5 m [MPa] -47.44

CM2 syy_mid yy stresses on Element 1.4 in x = 1 m [MPa] -94.88

CM2 sxy_mid xy stresses on Element 1.4 in y = 0 m [MPa] -14.66

CM2 sxy_mid xy stresses on Element 1.4 in y = 1 m [MPa] -47.82



DZ Vertical displacement on node 7 [mm] -0.59203 mm -0.01%

DZ Vertical displacement on node 5 [mm] -0.180898 mm 0.00%

sxx_mid Sigma xx stresses on Element 1.4 in x = 0 m [MPa] 1.86265e-15 MPa 0.00%

sxx_mid Sigma xx stresses on Element 1.4 in x = 0.5 m [MPa] -14.2315 MPa -0.01%

sxx_mid Sigma xx stresses on Element 1.4 in x = 1 m [MPa] -28.463 MPa -0.01%

syy_mid Sigma yy stresses on Element 1.4 in x = 0 m [MPa] 2.23517e-14 MPa 0.00%

syy_mid Sigma yy stresses on Element 1.4 in x = 0.5 m [MPa] -47.4383 MPa 0.00%

syy_mid Sigma yy stresses on Element 1.4 in x = 1 m [MPa] -94.8767 MPa 0.00%

sxy_mid Sigma xy stresses on Element 1.4 in y = 0 m [MPa] -14.611 MPa 0.33%

sxy_mid Sigma xy stresses on Element 1.4 in y = 1 m [MPa] -47.8178 MPa 0.00%


107

1.35 Stiffen membrane (01-0040SSLSB_FEM)

Test ID: 2471

Test status: Passed

1.35.1 Description

Verifies the horizontal displacement and the stress on a plate (8 x 12 cm) fixed in the middle on 3 supports with a punctual load at its free node.

1.35.2 Background


■ Reference: Klaus-Jürgen Bathe - Finite Element Procedures in Engineering Analysis, Example 5.13;


■ Element type: planar (membrane).

1;1,

Units

I. S.

Geometry

■ Thickness: e = 0.1 cm,

■ Length: l = 8 cm,

■ Width: B = 12 cm.


■ Longitudinal elastic modulus: E = 30 x 106 N/cm

2,


Boundary conditions

■ Outer: Fixed on 3 sides,

■ Inner: None.

Loading

■ External: Uniform load Fx = F = 6000 N at A,

■ Internal: None.


108

1.35.2.2 Results of the model in the linear elastic range

Reference solution

Point B is the origin of the coordinate system used for the results positions.

MPa 96.17N/cm 1796 ;1

MPa 98.8N/cm 898 ;0

0 ;1

for 181

MPa 55.11N/cm 1155 ;1

MPa 77.5N/cm 577 ;0

0 ;1

for

MPa 49.38N/cm 3849 ;1

MPa 24.19N/cm 1924 ;0

0 ;1

for 121

3410.97510.367410.2

6000

21

1

1

2

3

2

xy1

2

xy1

xy1

1

2

yy1

2

yy1

yy1

11

2

xx1

2

xx1

xx1

21

4

66

222

b

uE

a

uE

cm

a

ES

ba

eabE

F

K

Fu

Axy

xxyy

Axx

A


■ Planar element: membrane, imposed mesh,

■ 6 nodes,

■ 2 quadrangle planar elements and 1 bar.

Deformed shape


109



CM2 DX Horizontal displacement Element 1 in A [cm] 9.340000

CM2 sxx_mid xx stress Element 1 in y = 0 cm [MPa] 38.490000

CM2 sxx_mid xx stress Element 1 in y = 6 cm [MPa] 0

CM2 syy_mid yy stress Element 1 in y = 0 cm [MPa] 11.550000

CM2 syy_mid yy stress Element 1 in y = 6 cm [MPa] 0

CM2 sxy_mid xy stress Element 1 in x = 0 cm [MPa] 0

CM2 sxy_mid xy stress Element 1 in x = 4 cm [MPa] -8.980000

CM2 sxy_mid xy stress Element 1 in x = 8 cm [MPa] -17.960000



DX Horizontal displacement Element 1 in A [µm] 9.33999 µm 0.00%

sxx_mid Sigma xx stress Element 1 in y = 0 cm [MPa] 38.489 MPa 0.00%

sxx_mid Sigma xx stress Element 1 in y = 6 cm [MPa] -5.92119e-15 MPa 0.00%

syy_mid Sigma yy stress Element 1 in y = 0 cm [MPa] 11.5467 MPa -0.03%

syy_mid Sigma yy stress Element 1 in y = 6 cm [MPa] -7.40149e-16 MPa 0.00%

sxy_mid Sigma xy stress Element 1 in x = 0 cm [MPa] -7.27596e-15 MPa 0.00%

sxy_mid Sigma xy stress Element 1 in x = 4 cm [MPa] -8.98076 MPa -0.01%

sxy_mid Sigma xy stress Element 1 in x = 8 cm [MPa] -17.9615 MPa -0.01%


110

1.36 Beam on elastic soil, hinged ends (01-0034SSLLB_FEM)

Test ID: 2466

Test status: Passed

1.36.1 Description

A beam under a punctual load, a distributed load and two torques lays on a soil of constant linear stiffness. The rotation around z-axis, the vertical reaction, the vertical displacement and the bending moment are verified in several points.

1.36.2 Background





Beam on elastic soil, hinged ends Scale = 1/27

01-0034SSLLB_FEM

Units

I. S.

Geometry

■ L = ( 10 )/2,

■ I = 10-4 m

4.



Pa.

Boundary conditions

■ Outer:

► Free A and B ends,

► Soil with a constant linear stiffness ky = K = 840000 N/m2.

■ Inner: None.


111

Loading

■ External:

► Punctual force at D: Fy = F = - 10000 N,

► Uniformly distributed force from A to B: fy = p = - 5000 N/m,

► Torque at A: Cz = -C = -15000 Nm,

► Torque at B: Cz = C = 15000 Nm.

■ Internal: None.

1.36.2.2 Displacement and support reaction at A

Reference solution

= 4

K/(4EI)

= L/2

= ch(2) + cos(2)

■ Vertical support reaction:

VA = -p(sh(2) + sin(2)) - 2Fch()cos() + 22C(sh(2) - sin(2)) x

1

2

■ Rotation about z-axis:

A = p(sh(2) – sin(2)) + 2Fsh()sin() - 22C(sh(2) + sin(2)) x

1

(K/)



■ 50 nodes,


Deformed shape


Deformed

1.36.2.3 Displacement and bending moment at D

Reference solution


vD = 2p( - 2ch()cos()) + F(sh(2) – sin(2)) - 82Csh()sin() x

1

2K


112

■ Bending moment:

MD = 4psh()sin() + F(sh(2) + sin(2)) - 82Cch()cos() x

1

42



■ 50 nodes,


Bending moment diagram


Bending moment



CM2 RY Rotation around z-axis in point A [rad] 0.003045

CM2 Fz Vertical reaction in point A [N] -11674

CM2 Dz Vertical displacement in point D [cm] -0.423326

CM2 My Bending moment in point D [Nm] -33840



RY Rotation around z-axis in point A [rad] 0.00304333 Rad -0.05%

Fz Vertical reaction in point A [N] -11709 N -0.30%

Dz Vertical displacement in point D [cm] -0.423297 cm 0.01%

My Bending moment in point D [Nm] -33835.9 N*m 0.01%


113

1.37 Double hinged thin arc in planar bending (01-0029SSLLB_FEM)

Test ID: 2461

Test status: Passed

1.37.1 Description

Verifies the rotation about Z-axis, the vertical displacement and the horizontal displacement on several points of a double hinged thin arc in planar bending.

1.37.2 Background





Double hinged thin arc in planar bending Scale = 1/8

01-0029SSLLB_FEM

Units

I. S.

Geometry



► de = 0.02 m,

► di = 0.016 m,

► A = 1.131 x 10-4 m

2,

► Ix = 4.637 x 10-9 m

4.



Pa,



114

Boundary conditions

■ Outer:

► Hinge at A,

► At B: allowed rotation along z, vertical displacement restrained along y.

■ Inner: None.

Loading

■ External: Punctual load at C: Fy = F = - 100 N.

■ Internal: None.

1.37.2.2 Displacements at A, B and C

Reference solution

■ Rotation about z-axis

A = - B = (

2 - 1)

FR2

2EI

■ Displacement;

Vertical at C: vC =

8 FR

EA + (

3

4 - 2)

FR3

2EI

Horizontal at B: uB = FR

2EA -

FR3

2EI



■ 37 nodes,


Displacements shape


Deformed


115



CM2 RY Rotation about Z-axis in point A [rad] 0.030774

CM2 RY Rotation about Z-axis in point B [rad] -0.030774

CM2 DZ Vertical displacement in point C [cm] -1.9206

CM2 DX Horizontal displacement in point B [cm] 5.3912



RY Rotation about Z-axis in point A [rad] 0.0307785 Rad 0.01%

RY Rotation about Z-axis in point B [rad] -0.0307785 Rad -0.01%

DZ Vertical displacement in point C [cm] -1.92019 cm 0.02%

DX Horizontal displacement in point B [cm] 5.386 cm -0.10%


116

1.38 Simply supported square plate (01-0036SSLSB_FEM)

Test ID: 2467

Test status: Passed

1.38.1 Description

Verifies the vertical displacement in the center of a simply supported square plate.

1.38.2 Background





Simply supported square plate Scale = 1/9

01-0036SSLSB_FEM

Units

I. S.

Geometry

■ Side = 1 m,

■ Thickness h = 0.01m.



Pa,



Boundary conditions

■ Outer:

► Simple support on the plate perimeter,

► For the modeling, we add a fixed support at B.

■ Inner: None.


117

Loading

■ External: Self weight (gravity = 9.81 m/s2).

■ Internal: None.

1.38.2.2 Vertical displacement at O

Reference solution

According to Love- Kirchhoff hypothesis, the displacement w at a point (x,y):

w(x,y) = wmnsinmxsinny

where wmn = 192g(1 -

2)

mn(m2 + n

2)

6Eh

2



■ 441 nodes,


Deformed shape

Simply supported square plate Scale = 1/6

Deformed



CM2 Dz Vertical displacement in point O [m] -0.158



Dz Vertical displacement in point O [µm] -0.164899 µm -4.37%


118

1.39 Thin cylinder under a uniform radial pressure (01-0038SSLSB_FEM)

Test ID: 2469

Test status: Passed

1.39.1 Description

Verifies the stress, the radial deformation and the longitudinal deformation of a cylinder loaded with a uniform internal pressure.

1.39.2 Background



■ Analysis type: static elastic;


Thin cylinder under a uniform radial pressure Scale = 1/18

01-0038SSLSB_FEM

Units

I. S.

Geometry


■ Radius: R = 1 m,

■ Thickness: h = 0.02 m.



Pa,


Boundary conditions

■ Outer:


119

► Free conditions

► For the modeling, only ¼ of the cylinder is considered and the symmetry conditions are applied. On the other side, we restrained the displacements at a few nodes in order to make the model stable.

■ Inner: None.

Loading

■ External: Uniform internal pressure: p = 10000 Pa,

■ Internal: None.

1.39.2.2 Stresses in all points

Reference solution

Stresses in the planar elements coordinate system (x axis is parallel with the length of the cylinder):

■ xx = 0

■ yy = pR

h



■ 209 nodes,


1.39.2.3 Cylinder deformation in all points

■ Radial deformation:

R = pR2

Eh

■ Longitudinal deformation:

L = -pRL

Eh



CM2 syy_mid yy stress in all points [Pa] 500000.000000

CM2 Dz L radial deformation of the cylinder in all points [µm] 2.380000

CM2 DY L longitudinal deformation of the cylinder in all points [µm] -2.860000



syy_mid Sigma yy stress in all points [Pa] 499521 Pa -0.10%

Dz Delta R radial deformation of the cylinder in all points [µm] 2.39214 µm 0.51%

DY Delta L longitudinal deformation of the cylinder in all points [µm]

-2.85445 µm 0.19%


120

1.40 Thin cylinder under its self weight (01-0044SSLSB_MEF)

Test ID: 2475

Test status: Passed

1.40.1 Description

Verifies the stress, the longitudinal deformation and the radial deformation of a thin cylinder subjected to its self weight only.

1.40.2 Background



■ Analysis type: static, linear elastic;


A cylinder of R radius and L length subject of self weight only.

Thin cylinder under its self weight Scale = 1/24

01-0044SSLSB_FEM

Units

I. S.

Geometry



■ Radius: R = 1 m.



Pa,


■ Density: = 7.85 x 104 N/m

3.


121

Boundary conditions

■ Outer:

► Null axial displacement at z = 0,

► For the modeling, we consider only a quarter of the cylinder, so we impose the symmetry conditions on the nodes that are parallel with the cylinder’s axis.

■ Inner: None.

Loading

■ External: Cylinder self weight,

■ Internal: None.

1.40.2.2 Stresses

Reference solution

x axis of the local coordinate system of planar elements is parallel to the cylinders axis.

xx = z

yy = 0


■ Planar element: shell, imposed mesh,

■ 697 nodes,


1.40.2.3 Cylinder deformation

Reference solution

■ L longitudinal deformation of the cylinder:

L = z

2

2E

■ R radial deformation of the cylinder:

R = -Rz

E



CM2 sxx_mid xx stress for z = L [Pa] -314000.000000

CM2 DY L longitudinal deformation for z = L [mm] 0.002990

CM2 Dz R radial deformation for z = L[mm] -0.000440

* To obtain this result, you must generate a calculation note “Planar elements stresses by load case in neutral fiber" with results on center.



sxx_mid Sigma xx stress for z = L [Pa] -309143 Pa 1.55%

DY Delta L longitudinal deformation for z = L [mm] 0.00298922 mm -0.03%

Dz Delta R radial deformation for z = L [mm] -0.000443587 mm -0.82%


122

1.41 Thin cylinder under a hydrostatic pressure (01-0043SSLSB_FEM)

Test ID: 2474

Test status: Passed

1.41.1 Description

Verifies the stress, the longitudinal deformation and the radial deformation of a thin cylinder under a hydrostatic pressure.

1.41.2 Background





Thin cylinder under a hydrostatic pressure Scale = 1/25

01-0043SSLSB_FEM

Units

I. S.

Geometry






Pa,


Boundary conditions

■ Outer: For the modeling, we consider only a quarter of the cylinder, so we impose the symmetry conditions on the nodes that are parallel with the cylinder’s axis.

■ Inner: None.


123

Loading

■ External: Radial internal pressure varies linearly with the "p" height, p = p0 z

L ,

■ Internal: None.

1.41.2.2 Stresses

Reference solution


xx = 0

yy = p0Rz

Lh



■ 209 nodes,



Reference solution


L = -p0Rz

2

2ELh

■ L radial deformation of the cylinder:

R = p0R2z

ELh



■ 209 nodes,



124

Deformation shape

Thin cylinder under a hydrostatic pressure

Deformed



CM2 syy_mid yy stress in z = L/2 [Pa] 500000.000000

CM2 DY L longitudinal deformation of the cylinder at the inferior extremity [mm]

-0.002860

CM2 Dz L radial deformation of the cylinder in z = L/2 [mm] 0.002380



syy_mid Sigma yy stress in z = L/2 [Pa] 504489 Pa 0.90%

DY Delta L longitudinal deformation of the cylinder at the inferior extremity [mm]

-0.00285442 mm 0.20%

Dz Delta L radial deformation of the cylinder in z = L/2 [mm]

0.00238372 mm 0.16%


125

1.42 Simply supported square plate under a uniform load (01-0051SSLSB_FEM)

Test ID: 2481

Test status: Passed

1.42.1 Description

A square plate simply supported is subjected to a uniform load. The vertical displacement and the bending moments at the plate center are verified.

1.42.2 Background





Simply supported square plate under a uniform load Scale = 1/9

01-0051SSLSB_FEM

Units

I. S.

Geometry

■ Side: a =b = 1 m,



■ Longitudinal elastic modulus: E = 1.0 x 107 Pa,


Boundary conditions

■ Outer: Simple support on the plate perimeter (null displacement along z-axis),

■ Inner: None


126

Loading

■ External: Normal pressure of plate p = pZ = -1.0 Pa,

■ Internal: None.

1.42.2.2 Vertical displacement and bending moment at the center of the plate

Reference solution

Love-Kirchhoff thin plates theory.



■ 361 nodes,


1.42.2.3 Theoretical result


CM2 DZ Vertical displacement at plate center [m] -4.43 x 10-3

CM2 Mxx MX bending moment at plate center [Nm] 0.0479

CM2 Myy MY bending moment at plate center [Nm] 0.0479



DZ Vertical displacement at plate center [m] -0.00435847 m 1.61%

Mxx Mx bending moment at plate center [Nm] 0.0471381 N*m -1.59%

Myy My bending moment at plate center [Nm] 0.0471381 N*m -1.59%


127

1.43 Spherical dome under a uniform external pressure (01-0050SSLSB_FEM)

Test ID: 2480

Test status: Passed

1.43.1 Description

A spherical dome of radius (a) is subjected to a uniform external pressure. The horizontal displacement and the external meridian stresses are verified.

1.43.2 Background





Spherical dome under a uniform external pressure

01-0050SSLSB_FEM

Units

I. S.

Geometry

■ Radius: a = 2.54 m,


■ Angle: = 75°.


128



Pa,


Boundary conditions

■ Outer: Fixed on the dome perimeter,

■ Inner: None.

Loading

■ External: Uniform pressure p = 0.6897 x 106 Pa,

■ Internal: None.

1.43.2.2 Horizontal displacement and exterior meridian stress

Reference solution

The reference solution is determined by averaging the results of several calculation software with implemented finite elements method. 2% uncertainty about the reference solution.



■ 401 nodes,


Deformed shape


129



CM2 DX Horizontal displacements in = 15° 1.73 x 10-3

CM2 DX Horizontal displacements in = 45° -1.02 x 10-3

CM2 syy_mid yy external meridian stresses in = 15° -74

CM2 sxx_mid XX external meridian stresses in = 45° -68



DX Horizontal displacements in Psi = 15° [mm] 1.73064 mm 0.04%

DX Horizontal displacements in Psi = 45° [mm] -1.01367 mm 0.62%

syy_mid Sigma yy external meridian stresses in Psi = 15° [MPa] -72.2609 MPa 2.35%

sxx_mid Sigma XX external meridian stresses in Psi = 45° [MPa] -68.9909 MPa -1.46%


130

1.44 Beam on two supports considering the shear force (01-0041SSLLB_FEM)

Test ID: 2472

Test status: Passed

1.44.1 Description

Verifies the vertical displacement on a 300 cm long beam, consisting of an I shaped profile of a total height of 20.04 cm, a 0.96 cm thick web and 20.04 cm wide / 1.46 cm thick flanges.

1.44.2 Background





Units

I. S.

Geometry

l = 300 cm

h = 20.04 cm

b= 20.04 cm

tw = 1.46 cm

tf = 0.96 cm

Sx= 74.95 cm2

Iz = 5462 cm4

Sy = 16.43 cm2


■ Longitudinal elastic modulus: E = 2285938 daN/cm2,

■ Transverse elastic modulus G = 879207 daN/cm2


Boundary conditions

■ Outer:

► Simple support on node 11,


131

► For the modeling, put an hinge at node 1 (instead of a simple support).

■ Inner: None.

Loading

■ External: Vertical punctual load P = -20246 daN at node 6,

■ Internal: None.

1.44.2.2 Vertical displacement of the model in the linear elastic range

Reference solution

The reference displacement is calculated in the middle of the beam, at node 6.


■ Planar element: S beam, imposed mesh,

■ 11 nodes,


Deformed shape



CM2 DZ Vertical displacement at node 6 [cm] -1.017



DZ Vertical displacement at node 6 [cm] -1.01722 cm -0.02%


132

1.45 Torus with uniform internal pressure (01-0045SSLSB_FEM)

Test ID: 2476

Test status: Passed

1.45.1 Description

Verifies the stress and the radial deformation of a torus with uniform internal pressure.

1.45.2 Background





Torus with uniform internal pressure

01-0045SSLSB_FEM

Units

I. S.

Geometry


■ Transverse section radius: b = 1 m,

■ Average radius of curvature: a = 2 m.



Pa,



133

Boundary conditions

■ Outer: For the modeling, only 1/8 of the cylinder is considered, so the symmetry conditions are imposed to end

nodes.

■ Inner: None.

Loading

■ External: Uniform internal pressure p = 10000 Pa

■ Internal: None.

1.45.2.2 Stresses

Reference solution

(See stresses description on the first scheme of the overview)

If a – b r a + b

11 = pb

2h r + a

r

22 = pb

2h



■ 361 nodes,



Reference solution

■ R radial deformation of the torus:

R = pb

2Eh (r - (r + a))



■ 361 nodes,




CM2 syy_mid 11 stresses for r = a - b [Pa] 7.5 x 105

CM2 syy_mid 11 stresses for r = a + b [Pa] 4.17 x 105

CM2 sxx_mid 22 stress for all r [Pa] 2.50 x 105

CM2 Dz L radial deformations of the torus for r = a - b [m] 1.19 x 10-7

CM2 Dz L radial deformations of the torus for r = a + b [m] 1.79 x 10-6



syy_mid Sigma 11 stresses for r = a - b [Pa] 742770 Pa -0.96%

syy_mid Sigma 11 stresses for r = a + b [Pa] 415404 Pa -0.38%

sxx_mid Sigma 22 stress for all r [Pa] 250331 Pa 0.13%

Dz Delta L radial deformations of the torus for r = a - b [mm] -0.000117352 mm 1.38%

Dz Delta L radial deformations of the torus for r = a + b [mm]

0.00180274 mm 0.71%


134

1.46 Spherical shell with holes (01-0049SSLSB_FEM)

Test ID: 2479

Test status: Passed

1.46.1 Description

A spherical shell with holes is subjected to 4 forces, opposite 2 by 2. The horizontal displacement is verified.

1.46.2 Background





Spherical shell with holes

01-0049SSLSB_FEM

Units

I. S.

Geometry

■ Radius: R = 10 m


■ Opening angle of the hole: 0 = 18°.





135

Boundary conditions

■ Outer: For modeling, we consider only a quarter of the shell, so we impose symmetry conditions (nodes in the vertical yz plane are restrained in translation along x and in rotation along y and z. Nodes on the vertical xy plane are restrained in translation along z and in rotation along x and y),

■ Inner: None.

Loading

■ External: Punctual loads F = 1 N, according to the diagram,

■ Internal: None.

1.46.2.2 Horizontal displacement at point A

Reference solution




■ 99 nodes,


Deformed shape

Spherical shell with holes Scale = 1/79

Deformed

1.46.2.3 Theoretical background


CM2 DX Horizontal displacement at point A(R,0,0) [mm] 94.0



DX Horizontal displacement at point A(R,0,0) [mm] 92.6751 mm -1.41%


136

1.47 Simply supported rectangular plate under a uniform load (01-0053SSLSB_FEM)

Test ID: 2483

Test status: Passed

1.47.1 Description

A rectangular plate simply supported is subjected to a uniform load. The vertical displacement and the bending moments at the plate center are verified.

1.47.2 Background





Simply supported rectangular plate under a uniform load Scale = 1/25

01-0053SSLSB_FEM

Units

I. S.

Geometry

■ Width: a = 1 m,

■ Length: b = 5 m,





Boundary conditions


■ Inner: None.


137

Loading


■ Internal: None.


Reference solution




■ 793 nodes,




CM2 DZ Vertical displacement at plate center [m] 1.416 x 10-2

CM2 Mxx MX bending moment at plate center [Nm] 0.1246

CM2 Myy MY bending moment at plate center [Nm] 0.0375



DZ Vertical displacement at plate center [cm] -1.40141 cm 1.03%

Mxx Mx bending moment at plate center [Nm] -0.124082 N*m 0.42%

Myy My bending moment at plate center [Nm] -0.0375624 N*m -0.17%


138

1.48 Simply supported rectangular plate under a uniform load (01-0052SSLSB_FEM)

Test ID: 2482

Test status: Passed

1.48.1 Description

A rectangular plate simply supported is subjected to a uniform load. The vertical displacement and the bending moments at the plate center are verified.

1.48.2 Background





Simply supported rectangular plate under a uniform load Scale = 1/11

01-0052SSLSB_FEM

Units

I. S.

Geometry

■ Width: a = 1 m,

■ Length: b = 2 m,





Boundary conditions


■ Inner: None.


139

Loading


■ Internal: None.


Reference solution




■ 435 nodes,


1.48.2.3 Theoretical background


CM2 DZ Vertical displacement at plate center [m] -1.1060 x 10-2

CM2 Mxx MX bending moment at plate center [Nm] -0.1017

CM2 Myy MY bending moment at plate center [Nm] -0.0464



DZ Vertical displacement at plate center [cm] -1.10238 cm 0.33%

Mxx Mx bending moment at plate center [Nm] -0.101737 N*m -0.04%

Myy My bending moment at plate center [Nm] -0.0462457 N*m 0.33%


140

1.49 Thin cylinder under a uniform axial load (01-0042SSLSB_FEM)

Test ID: 2473

Test status: Passed

1.49.1 Description

Verifies the stress, the longitudinal deformation and the radial deformation of a cylinder under a uniform axial load.

1.49.2 Background



■ Analysis type: static elastic;


Thin cylinder under a uniform axial load Scale = 1/19

01-0042SSLSB_FEM

Units

I. S.

Geometry






Pa,


Boundary conditions

■ Outer:

► Null axial displacement at the left end: vz = 0,

► For the modeling, only a ¼ of the cylinder is considered.

■ Inner: None.


141

Loading

■ External: Uniform axial load q = 10000 N/m

■ Inner: None.

1.49.2.2 Stress in all points

Reference solution


xx = q

h

yy = 0



■ 697 nodes,


1.49.2.3 Cylinder deformation at the free end

Reference solution


L = qL

Eh

■ R radial deformation of the cylinder:

R = -qR

Eh



■ 697 nodes,


Deformation shape

Thin cylinder under a uniform axial load Scale = 1/22

Deformation shape


142



CM2 sxx_mid xx stress at all points [Pa] 5 x 105

CM2 syy_mid yy stress at all points [Pa] 0

CM2 DY L longitudinal deformation at the free end [m] 9.52 x 10-6

CM2 Dz R radial deformation at the free end [m] -7.14 x 10-7



sxx_mid Sigma xx stress at all points [Pa] 500000 Pa 0.00%

syy_mid Sigma yy stress at all points [Pa] -2.11463e-09 Pa 0.00%

DY Delta L longitudinal deformation at the free end [mm] -0.00952381 mm -0.04%

Dz Delta R radial deformation at the free end [mm] 0.000710887 mm -0.44%


143

1.50 Spherical shell under internal pressure (01-0046SSLSB_FEM)

Test ID: 2477

Test status: Passed

1.50.1 Description

A spherical shell is subjected to a uniform internal pressure. The stress and the radial deformation are verified.

1.50.2 Background





Spherical shell under internal pressure

01-0046SSLSB_FEM

Units

I. S.

Geometry


■ Radius: R2 = 1 m,

■ = 90° (hemisphere).


144



Pa,


Boundary conditions

■ Outer:

Simple support (null displacement along vertical displacement) on the shell perimeter.

For modeling, we consider only half of the hemisphere, so we impose symmetry conditions (DOF restrains placed in the vertical plane xy in translation along z and in rotation along x and y). In addition, the node at the top of the shell is restrained in translation along x to assure the stability of the structure during calculation).

■ Inner: None.

Loading

■ External: Uniform internal pressure p = 10000 Pa

■ Internal: None.

1.50.2.2 Stresses

Reference solution

(See stresses description on the first scheme of the overview)

If 0° 90°

11 = 22 = pR2

2

2h



■ 343 nodes,



Reference solution

■ R radial deformation of the calotte:

R = pR22 (1 - ) sin

2Eh



■ 343 nodes,



145

Deformed shape

Spherical shell under internal pressure Scale = 1/11

Deformed



CM2 sxx_mid 11 stress for all [Pa] 2.50 x 105

CM2 syy_mid 22 stress for all [Pa] 2.50 x 105

CM2 Dz R radial deformations for = 90° [m] 8.33 x 10-7



sxx_mid Sigma 11 stress for all Theta [Pa] 250202 Pa 0.08%

syy_mid Sigma 22 stress for all Theta [Pa] 249907 Pa -0.04%

Dz Delta R radial deformations for Theta = 90° [mm] 0.000832794 mm -0.02%


146

1.51 Pinch cylindrical shell (01-0048SSLSB_FEM)

Test ID: 2478

Test status: Passed

1.51.1 Description

A cylinder of length L is pinched by 2 diametrically opposite forces (F). The vertical displacement is verified.

1.51.2 Background





A cylinder of length L is pinched by 2 diametrically opposite forces (F).

Pinch cylindrical shell

01-0048SSLSB_FEM

Units

I. S.

Geometry

■ Length: L = 10.35 m (total length),

■ Radius: R = 4.953 m,

■ Thickness: h = 0.094 m.


147




Boundary conditions

■ Outer: For the modeling, we consider only half of the cylinder, so we impose symmetry conditions (nodes in the horizontal xz plane are restrained in translation along y and in rotation along x and z),

■ Inner: None.

Loading

■ External: 2 punctual loads F = 100 N,

■ Internal: None.

1.51.2.2 Vertical displacement at point A

Reference solution




■ 777 nodes,


1.51.2.3 Theoretical result


CM2 DZ Vertical displacement in point A [m] -113.9 x 10-3



DZ Vertical displacement in point A [mm] -113.301 mm 0.53%


148

1.52 A plate (0.01 m thick), fixed on its perimeter, loaded with a uniform pressure (01-0057SSLSB_FEM)

Test ID: 2487

Test status: Passed

1.52.1 Description

Verifies the vertical displacement for a square plate (0.01 m thick), of side "a", fixed on its perimeter, loaded with a uniform pressure.

1.52.2 Background


■ Reference: Structure Calculation Software Validation Guide, test SSLV 09/89;

■ Analysis type: static;


Units

I. S.

Geometry

■ Side: a = 1 m,


■ Slenderness: = a

h = 100.


■ Reinforcement,


Pa,


Boundary conditions

■ Outer:

Fixed sides: AB and BD,

For the modeling, we impose symmetry conditions at the CB side (restrained displacement along x and restrained rotation around y and z) and CD side (restrained displacement along y and restrained rotation around x and z),

■ Inner: None.

Loading

■ External: 1 MPa uniform pressure,

■ Internal: None.


149

1.52.2.2 Vertical displacement at C

Reference solution

This problem has a precise analytical solution only for thin plates. Therefore we propose the solutions obtained with Serendip elements with 20 nodes or thick plate elements of 4 nodes. The expected result should be between these

values at 5%.



■ 289 nodes,




CM2 Dz Vertical displacement in point C [m] -6.639 x 10-2



Dz Vertical displacement in point C [cm] -6.56563 cm 1.11%


150

1.53 Triangulated system with hinged bars (01-0056SSLLB_FEM)

Test ID: 2486

Test status: Passed

1.53.1 Description

A truss with hinged bars is placed on three punctual supports (subjected to imposed displacements) and is loaded with two punctual forces. A thermal load is applied to all the bars. The traction force and the vertical displacement are verified.

1.53.2 Background



■ Analysis type: static (plane problem);


Units

I. S.

Geometry

■ = 30°,

■ Section A1 = 1.41 x 10-3

m2,

■ Section A2 = 2.82 x 10-3

m2.


■ Longitudinal elastic modulus: E =2.1 x 1011

Pa,

■ Coefficient of linear expansion: = 10-5

°C-1

.

Boundary conditions

■ Outer:

► Hinge at A (uA = vA = 0),

► Roller supports at B and C ( uB = v’C = 0),

■ Inner: None.

Loading

■ External:

► Support displacement: vA = -0.02 m ; vB = -0.03 m ; v’C = -0.015 m ,

► Punctual loads: FE = -150 KN ; FF = -100 KN,

► Expansion effect on all bars for a temperature variation of 150° in relation with the assembly temperature (specified geometry),


151

■ Internal: None.

1.53.2.2 Tension force in BD bar

Reference solution

Determining the hyperstatic unknown with the section cut method.


■ Linear element: S beam, automatic mesh,

■ 11 nodes,

■ 17 S beams + 1 rigid S beam for the modeling of the simple support at C.

1.53.2.3 Vertical displacement at D

Reference solution

vD displacement was determined by several software with implemented finite elements method.



■ 11 nodes,

■ 17 S beams + 1 rigid S beam for the modeling of simple support at C.

Deformed shape

Triangulated system with hinged bars

01-0056SSLLB_FEM



CM2 Fx FX traction force on BD bar [N] 43633

CM2 DZ Vertical displacement on point D [m] -0.01618



Fx Fx traction force on BD bar [N] 42892.3 N -1.70%

DZ Vertical displacement on point D [m] -0.016236 m -0.35%


152


Test ID: 2491

Test status: Passed

1.54.1 Description


1.54.2 Background





Units

I. S.

Geometry

■ Side: a = 1 m,



h = 10.


■ Reinforcement,


Pa,


Boundary conditions

■ Outer:

Fixed edges: AB and BD,


■ Inner: None.

Loading


■ Internal: None.


153


Reference solution

This problem has a precise analytical solution only for thin plates. Therefore we propose the solutions obtained with Serendip elements with 20 nodes or thick plate elements of 4 nodes. The expected result should be between these values at ± 5%.



■ 289 nodes,







Dz Vertical displacement in point C [mm] -0.0781846 mm 0.61%


154

1.55 A plate (0.01 m thick), fixed on its perimeter, loaded with a punctual force (01-0062SSLSB_FEM)

Test ID: 2492

Test status: Passed

1.55.1 Description

Verifies the vertical displacement for a square plate (0.01 m thick), of side "a", fixed on its perimeter, loaded with a punctual force in the center.

1.55.2 Background





Square plate of side "a".

0.01 m thick plate fixed on its perimeter Scale = 1/5

01-0062SSLSB_FEM

Units

I. S.

Geometry

■ Side: a = 1 m,



h = 100.


■ Reinforcement,


Pa,



155

Boundary conditions

■ Outer: Fixed edges,

■ Inner: None.

Loading

■ External: Punctual force applied on the center of the plate: FZ = -106 N,

■ Internal: None.

1.55.2.2 Vertical displacement at point C (center of the plate)

Reference solution




■ 961 nodes,




CM2 DZ Vertical displacement in point C [m] -0.29579



DZ Vertical displacement in point C [m] -0.292146 m 1.23%


156


Test ID: 2488

Test status: Passed

1.56.1 Description


1.56.2 Background





Square plate of side "a", for the modeling, only a quarter of the plate is considered.

Units

I. S.

Geometry

■ Side: a = 1 m,



h = 75.


■ Reinforcement,


Pa,


Boundary conditions

■ Outer:

Fixed sides: AB and BD,


■ Inner: None.

Loading


■ Internal: None.


157


Reference solution




■ 289 nodes,









158


Test ID: 2490

Test status: Passed

1.57.1 Description


1.57.2 Background





Units

I. S.

Geometry

■ Side: a = 1 m,



h = 20.


■ Reinforcement,


Pa,


Boundary conditions

■ Outer:



■ Inner: None.

Loading


■ Internal: None.


159


Reference solution




■ 289 nodes,









160


Test ID: 2495

Test status: Passed

1.58.1 Description


1.58.2 Background






01-0065SSLSB_FEM

Units

I. S.

Geometry

■ Side: a = 1 m,


■ Slenderness: = 20.


■ Reinforcement,


Pa,



161

Boundary conditions

■ Outer: Fixed sides,

■ Inner: None.

Loading

■ External: Punctual force applied at the center of the plate: FZ = -106 N,

■ Internal: None.

1.58.2.2 Vertical displacement at point C center of the plate)

Reference solution




■ 961 nodes,




CM2 DZ Vertical displacement in point C [m] -0.2595 x 10-2





162


Test ID: 2494

Test status: Passed

1.59.1 Description


1.59.2 Background






01-0064SSLSB_FEM

Units

I. S.

Geometry

■ Side: a = 1 m,




■ Reinforcement,


Pa,



163

Boundary conditions


■ Inner: None.

Loading

■ External: punctual force applied in the center of the plate: FZ = -106 N,

■ Internal: None.

1.59.2.2 Vertical displacement at point C (the center of the plate)

Reference solution




■ 961 nodes,









164

1.60 Shear plate perpendicular to the medium surface (01-0055SSLSB_FEM)

Test ID: 2485

Test status: Passed

1.60.1 Description

Verifies the vertical displacement of a rectangular shear plate fixed at one end, loaded with two forces.

1.60.2 Background





Shear plate Scale = 1/50

01-0055SSLSB_FEM

Units

I. S.

Geometry


■ Width: l = 1 m,





Boundary conditions

■ Outer: Fixed AD edge,

■ Inner: None.


165

Loading

■ External:

► At B: Fz = -1.0 N,

► At C: FZ = 1.0 N,

■ Internal: None.


Reference solution




■ 497 nodes,


Deformed shape

Shear plate Scale = 1/35

Deformed



CM2 Dz Vertical displacement in point C [m] 35.37 x 10-3



Dz Vertical displacement in point C [m] 35.6655 mm 0.84%


166

1.61 Simply supported rectangular plate loaded with punctual force and moments (01-0054SSLSB_FEM)

Test ID: 2484

Test status: Passed

1.61.1 Description

A rectangular plate simply supported is subjected to a punctual force and moments. The vertical displacement is verified.

1.61.2 Background





Simply supported rectangular plate loaded with punctual force and moments

01-0054SSLSB_FEM

Units

I. S.

Geometry

■ Width: DA = CB = 20 m,

■ Length: AB = DC = 5 m,

■ Thickness: h = 1 m,


■ Longitudinal elastic modulus: E =1000 Pa,


Boundary conditions

■ Outer: Punctual support at A, B and D (null displacement along z-axis),

■ Inner: None.


167

Loading

■ External:

► In A: MX = 20 Nm, MY = -10 Nm,

► In B: MX = 20 Nm, MY = 10 Nm,

► In C: FZ = -2 N, MX = -20 Nm, MY = 10 Nm,

► In D: MX = -20 Nm, MY = -10 Nm,

■ Internal: None.


Reference solution




■ 867 nodes,


Deformed shape

Simply supported rectangular plate loaded with punctual force and moments

Deformed



CM2 Dz Vertical displacement in point C [m] -12.480



Dz Vertical displacement in point C [m] -12.6677 m -1.50%


168


Test ID: 2489

Test status: Passed

1.62.1 Description


1.62.2 Background





Units

I. S.

Geometry

■ Side: a = 1 m,



h = 50.


■ Reinforcement,


Pa,


Boundary conditions

■ Outer:



■ Inner: None.

Loading


■ Internal: None.


169


Reference solution




■ 289 nodes,









170


Test ID: 2493

Test status: Passed

1.63.1 Description


1.63.2 Background






01-0063SSLSB_FEM

Units

I. S.

Geometry

■ Side: a = 1 m,



h = 75.


■ Reinforcement,


Pa,



171

Boundary conditions

■ Outer: Fixed sides,

■ Inner: None.

Loading

■ External: Punctual force applied on the center of the plate: FZ = -106 N,

■ Internal: None.

1.63.2.2 Vertical displacement at point C (the center of the plate)

Reference solution




■ 961 nodes,









172

1.64 Vibration mode of a thin piping elbow in space (case 2) (01-0068SDLLB_FEM)

Test ID: 2498

Test status: Passed

1.64.1 Description

Verifies the eigen mode transverse frequencies for a thin piping elbow with a radius of 1 m, extended with two straight elements (0.6 m long) and subjected to its self weight only.

1.64.2 Background



■ Analysis type: modal analysis (in space);



01-0068SDLLB_FEM

Units

I. S.

Geometry


■ L = 0.6 m,




■ Section: A = 1.131 x 10-4 m

2,


m4,


m4,


m4.


► O ( 0 ; 0 ; 0 )

► A ( 0 ; R ; 0 )

► B ( R ; 0 ; 0 )

► C ( -L ; R ; 0 )


173

► D ( R ; -L ; 0 )



Pa,



Boundary conditions

■ Outer:


► In A: translation restraint along y and z,

► In B: translation restraint along x and z,

■ Inner: None.

Loading

■ External: None,

■ Internal: None.


Reference solution


■ transverse bending:

fj = i

2

2 R2

GIpA

where i = 1,2.



■ 23 nodes,


Eigen mode shapes



CM2 Eigen mode Eigen mode Transverse 1 frequency [Hz] 33.4

CM2 Eigen mode Eigen mode Transverse 2 frequency [Hz] 100



Eigen mode Transverse 1 frequency [Hz] 33.19 Hz -0.63%



174

1.65 Reactions on supports and bending moments on a 2D portal frame (Rafters) (01-0077SSLPB_FEM)

Test ID: 2500

Test status: Passed

1.65.1 Description

Moments and actions on supports calculation on a 2D portal frame. The purpose of this test is to verify the results of Advance Design for the M. R. study of a 2D portal frame.

1.65.2 Background


■ Reference: Design and calculation of metal structures.



1.65.2.2 Moments and actions on supports M.R. calculation on a 2D portal frame.

RDM results, for the linear load perpendicular on the rafters, are:

2

qLVV EA

H

fh3f3k²h

f5h8

32

²qLHH EA

HhMM DB fhH8

²qLMC


175


Comparison between theoretical results and the results obtained by Advance Design for a linear load perpendicular on the chords


CM2 Fz Vertical reaction V in A [DaN] -1000

CM2 Fz Vertical reaction V in E [DaN] -1000

CM2 Fx Horizontal reaction H in A [DaN] -332.9

CM2 Fx Horizontal reaction H in E [DaN] -332.9

CM2 My Moment in node B [DaNm] 2496.8

CM2 My Moment in node D [DaNm] -2496.8

CM2 My Moment in node C [DaNm] -1671



Fz Vertical reaction V on node A [daN] -1000 daN 0.00%

Fz Vertical reaction V on node E [daN] -1000 daN 0.00%

Fx Horizontal reaction H on node A [daN] -332.665 daN 0.07%

Fx Horizontal reaction H on node E [daN] -332.665 daN 0.07%

My Moment in node B [daNm] 2494.99 daN*m -0.07%

My Moment in node D [daNm] -2494.99 daN*m 0.07%

My Moment in node C [daNm] -1673.35 daN*m -0.14%


176

1.66 Plane portal frame with hinged supports (01-0089SSLLB_FEM)

Test ID: 2505

Test status: Passed

1.66.1 Description

Calculation of support reactions of a 2D portal frame with hinged supports.

1.66.2 Background





Units

I. S.

Geometry


■ I1 = 5.0 x 10-4

m4

■ a = 4 m

■ h = 8 m

■ b = 10.77 m

■ I2 = 2.5 x 10-4

m4


■ Isotropic linear elastic material.

■ E = 2.1 x 1011

Pa

Boundary conditions

Hinged base plates A and B (uA = vA = 0 ; uB = vB = 0).


177

Loading

■ p = -3 000 N/m

■ F1 = -20 000 N

■ F2 = -10 000 N

■ M = -100 000 Nm

1.66.2.2 Calculation method used to obtain the reference solution

■ K = (I2/b)(h/I1)

■ p = a/h

■ m = 1 + p

■ B = 2(K + 1) + m

■ C = 1 + 2m

■ N = B + mC

■ VA = 3pl/8 + F1/2 – M/l + F2h/l

■ HA = pl²(3 + 5m)/(32Nh) + (F1l/(4h))(C/N) + F2(1-(B + C)/(2N)) + (3M/h)((1 + m)/(2N))

1.66.2.3 Reference values

Point Magnitudes and units Value

A V, vertical reaction (N) 31 500.0

A H, horizontal reaction (N) 20 239.4

C vc (m) -0.03072



CM2 Fz Vertical reaction V in point A [N] -31500

CM2 Fx Horizontal reaction H in point A [N] -20239.4

CM2 DZ vc displacement in point C [m] -0.03072



Fz Vertical reaction V in point A [N] -31500 N 0.00%

Fx Horizontal reaction H in point A [N] -20239.3 N 0.00%

DZ Displacement in point C [m] -0.0307191 m 0.00%


178

1.67 Slender beam of variable rectangular section (fixed-fixed) (01-0086SDLLB_FEM)

Test ID: 2504

Test status: Passed

1.67.1 Description

Verifies the eigen modes (flexion) for a slender beam with variable rectangular section (fixed-fixed).

1.67.2 Background





Units

I. S.

Geometry

■ Length: L = 0.6 m,

■ Constant thickness: h = 0.01 m

■ Initial section:

► b0 = 0.03 m

► A0 = 3 x 10-4 m²

■ Section variation:

► with ( = 1)

► b = b0e-2x

► A = A0e-2x


■ E = 2 x 1011

Pa

■ = 0.3

■ = 7800 kg/m3

Boundary conditions

■ Outer:

► Fixed at end x = 0,

► Fixed at end x = 0.6 m.

■ Inner: None.

Loading

■ External: None,

■ Internal: None.


179

1.67.2.2 Reference results

Calculation method used to obtain the reference solution

i pulsation is given by the roots of the equation:

0rlsinslshrs2

²r²sslchrlcos1

with

0²²s;²r;EI

A 2i

si2i

2i

zo

2i04

i

Therefore, the translation components of i(x) mode, are:

))sx(rsh)rxsin(s(

)rlsin(s)sl(rsh

)sl(ch)rlcos(sxchrxcosex x

i

Uncertainty about the reference: analytical solution:

Reference values

Eigen mode order

Frequency (Hz) Eigen mode i(x)*

x = 0 0.1 0.2 0.3 0.4 0.5 0.6

1 143.303 0 0.237 0.703 1 0.859 0.354 0

2 396.821 0 -0.504 -0.818 0 0.943 0.752 0

3 779.425 0 0.670 0.210 -0.831 0.257 1 0

4 1289.577 0 -0.670 0.486 0 -0.594 1 0

* i(x) eigen modes* standardized to 1 at the point of maximum amplitude.

Eigen modes


180



CM2 Eigen mode Frequency of eigen mode 1 [Hz] 143.303






Frequency of eigen mode 1 [Hz] 145.88 Hz 1.80%





181


Test ID: 2497

Test status: Passed

1.68.1 Description

Verifies the eigen mode transverse frequencies for a thin piping elbow with a radius of 1 m, fixed on its ends and subjected to its self weight only.

1.68.2 Background



■ Analysis type: modal analysis (space problem);



01-0067SDLLB_FEM

Units

I. S.

Geometry





■ Section: A = 1.131 x 10-4 m

2,


m4,


m4,


m4.


► O ( 0 ; 0 ; 0 )

► A ( 0 ; R ; 0 )

► B ( R ; 0 ; 0 )


182



Pa,



Boundary conditions

■ Outer: Fixed at points A and B,

■ Inner: None.

Loading

■ External: None,

■ Internal: None.


Reference solution



fj = i

2

2 R2

GIpA

where i = 1,2.



■ 11 nodes,


Eigen mode shapes




CM2 Eigen mode Eigen mode Transverse 2 frequency [Hz] 125






183

1.69 Short beam on two hinged supports (01-0084SSLLB_FEM)

Test ID: 2502

Test status: Passed

1.69.1 Description

Verifies the deflection magnitude on a non-slender beam with two hinged supports.

1.69.2 Background


■ Reference: Structure Calculation Software Validation Guide, test SSLL 02/89



Units

I. S.

Geometry

■ Length: L = 1.44 m,

■ Area: A = 31 x 10-4 m²

■ Inertia: I = 2810 x 10-8

m4

■ Shearing coefficient: az = 2.42 = A/Ar


■ E = 2 x 1011

Pa

■ = 0.3

Boundary conditions

■ Hinge at end x = 0,

■ Hinge at end x = 1.44 m.

Loading

Uniformly distributed force of p = -1. X 105 N/m on beam AB.



The deflection on the middle of a non-slender beam considering the shear force deformations given by the Timoshenko function:

GA8

pl

EI

pl

384

5v

r

24

where

12

EG and

zr a

AA

where "Ar" is the reduced area and "az" the shear coefficient calculated on the transverse section.


184


Reference values

Point Magnitudes and units Value

C V, deflection (m) -1.25926 x 10-3



CM2 Dz Deflection magnitude in point C [m] -0.00125926



Dz Deflection magnitude in node C [m] -0.00125926 m 0.00%


185


Test ID: 2499

Test status: Passed

1.70.1 Description

Verifies the eigen mode transverse frequencies for a thin piping elbow with a radius of 1 m, extended with two straight elements (2 m long) and subjected to its self weight only.

1.70.2 Background



■ Analysis type: modal analysis (space problem);



01-0069SDLLB_FEM

Units

I. S.

Geometry


■ L = 2 m,




■ Section: A = 1.131 x 10-4 m

2,


m4,


m4,


m4.


► O ( 0 ; 0 ; 0 )

► A ( 0 ; R ; 0 )

► B ( R ; 0 ; 0 )


186

► C ( -L ; R ; 0 )

► D ( R ; -L ; 0 )



Pa,



Boundary conditions

■ Outer:




■ Inner: None.

Loading

■ External: None,

■ Internal: None.


Reference solution



fj = i

2

2 R2

GIpA

where i = 1,2 with i = 1,2:



■ 41 nodes,


Eigen mode shapes


187


Reference









188

1.71 Double fixed beam in Eulerian buckling with a thermal load (01-0091HFLLB_FEM)

Test ID: 2506

Test status: Passed

1.71.1 Description

Verifies the normal force on the nodes of a double fixed beam in Eulerian buckling with a thermal load.

1.71.2 Background


■ Reference: Euler theory;



Units

I. S.

Geometry

L= 10 m

Cross Section Sx m² Sy m² Sz m² Ix m4 Iy m4 Iz m4 Vx m3 V1y m3 V1z m3 V2y m3 V2z m3

IPE200 0.002850 0.001400 0.001799 0.0000000646 0.0000014200 0.0000194300 0.00000000 0.00002850 0.00019400 0.00002850 0.00019400


■ Longitudinal elastic modulus: E= 2.1 x 1011

N/m2,


■ Coefficient of thermal expansion: = 0.00001

Boundary conditions


■ Inner: None.


189

Loading

■ External: Punctual load FZ = 1 N at = L/2 (load that initializes the deformed shape),

■ Internal: T = 5°C corresponding to a compression force of:


Reference solution


Observation: in this case, the thermal load has no effect over the critical coefficient



■ 11 nodes,

■ 10 elements.

Deformed shape of mode 1



CM2 Fx Normal Force on Node 6 - Case 101 [kN] -29.925




Fx Normal Force Fx on Node 6 - Case 101 [kN] -29.904 kN 0.07%

Fx Normal Force Fx on Node 6 - Case 102 [kN] -118.081 kN -0.30%


190

1.72 Double fixed beam in Eulerian buckling with a thermal load (01-0091HFLLB_FEM)

Test ID: 2506

Test status: Passed

1.72.1 Description

Verifies the normal force on the nodes of a double fixed beam in Eulerian buckling with a thermal load.

1.72.2 Background





Units

I. S.

Geometry

L= 10 m

Cross Section Sx m² Sy m² Sz m² Ix m4 Iy m4 Iz m4 Vx m3 V1y m3 V1z m3 V2y m3 V2z m3

IPE200 0.002850 0.001400 0.001799 0.0000000646 0.0000014200 0.0000194300 0.00000000 0.00002850 0.00019400 0.00002850 0.00019400



N/m2,


■ Coefficient of thermal expansion: = 0.00001

Boundary conditions


■ Inner: None.


191

Loading

■ External: Punctual load FZ = 1 N at = L/2 (load that initializes the deformed shape),

■ Internal: T = 5°C corresponding to a compression force of:


Reference solution





■ 11 nodes,

■ 10 elements.

Deformed shape of mode 1







Fx Normal Force Fx on Node 6 - Case 101 [kN] -29.904 kN 0.07%

Fx Normal Force Fx on Node 6 - Case 102 [kN] -118.081 kN -0.30%


192


Test ID: 2496

Test status: Passed

1.73.1 Description


1.73.2 Background






01-0066SSLSB_FEM

Units

I. S.

Geometry

■ Side: a = 1 m,




■ Reinforcement,


Pa,


Boundary conditions


■ Inner: None.


193

Loading

■ External: punctual force applied in the center of the plate: FZ = -106 N,

■ Internal: None.

1.73.2.2 Vertical displacement at point C (center of the plate)

Reference solution




■ 961 nodes,




CM2 DZ Vertical displacement in point C [m] -0.42995 x 10-3



DZ Vertical displacement in point C [mm] -0.412094 mm 4.15%


194

1.74 Reactions on supports and bending moments on a 2D portal frame (Columns) (01-0078SSLPB_FEM)

Test ID: 2501

Test status: Passed

1.74.1 Description

Moments and actions on supports calculation on a 2D portal frame. The purpose of this test is to verify the results of Advance Design for the M. R. study of a 2D portal frame.

1.74.2 Background


■ Reference: Design and calculation of metal structures.




195

1.74.2.2 Moments and reactions on supports M.R. calculation on a 2D portal frame.

RDM results, for the linear load perpendicular on the column, are:

L2

²qhVV EA

fh3f3k²h

fh26kh5

16

²qhHE

qhHH EA

hHqh

M EB 2

² fhH

4

²qhM EC hHM ED



CM2 Fz Vertical reaction V in A [DaN] 140.6

CM2 Fz Vertical reaction V in E [DaN] -140.6

CM2 Fx Horizontal reaction H in A [DaN] 579.1

CM2 Fx Horizontal reaction H in E [DaN] 170.9

CM2 My Moment in B [DaNm] -1530.8

CM2 My Moment in D [DaNm] -1281.7

CM2

CM2

My Moment in C [DaNm] 302.7



Fz Vertical reaction V on node A [daN] 140.625 daN 0.02%

Fz Vertical reaction V on node E [daN] -140.625 daN -0.02%

Fx Horizontal reaction H on node A [daN] 579.169 daN 0.01%

Fx Horizontal reaction H on node E [daN] 170.831 daN -0.04%

My Moment in node B [daNm] -1531.27 daN*m -0.03%

My Moment in node D [daNm] -1281.23 daN*m 0.04%

My Moment in node C [daNm] 302.063 daN*m -0.21%


196

1.75 Slender beam of variable rectangular section with fixed-free ends (ß=5) (01-0085SDLLB_FEM)

Test ID: 2503

Test status: Passed

1.75.1 Description

Verifies the eigen modes (bending) for a slender beam with variable rectangular section (fixed-free).

1.75.2 Background





Units

I. S.

Geometry


■ Straight initial section:

► h0 = 0.04 m

► b0 = 0.05 m

► A0 = 2 x 10-3 m²

■ Straight final section

► h1 = 0.01 m

► b1 = 0.01 m

► A1 = 10-4

m²


■ E = 2 x 1011

Pa

■ = 7800 kg/m3

Boundary conditions

■ Outer:

► Fixed at end x = 0,

► Free at end x = 1

■ Inner: None.

Loading

■ External: None,

■ Internal: None.


197



Precise calculation by numerical integration of the differential equation of beams bending (Euler-Bernoulli theories):

²t

²A

²x

²EIz

x2

2

where Iz and A vary with the abscissa.

The result is:

12

E²l

1h,i

2

1fi with

51b

b

41h

h

1 2 3 4 5

= 5 24.308 75.56 167.21 301.9 480.4


Reference values

Eigen mode type Frequency (Hz)

Flexion

1 56.55

2 175.79

3 389.01

4 702.36

5 1117.63

MODE 1 Scale = 1/4


198

MODE 2 Scale = 1/4

MODE 3 Scale = 1/4


199

MODE 4 Scale = 1/4

MODE 5 Scale = 1/4


200


Result name Result description Reference value

Eigen mode Frequency of eigen mode 1 [Hz] 56.55









Frequency of eigen mode 3 [Hz] 388.85 Hz -0.04%




201

1.76 Fixed/free slender beam with eccentric mass or inertia (01-0096SDLLB_FEM)

Test ID: 2510

Test status: Passed

1.76.1 Description

Fixed/free slender beam with eccentric mass or inertia.

Tested functions: Eigen mode frequencies, straight slender beam, combined bending-torsion, plane bending, transverse bending, punctual mass.

1.76.2 Background





■ Tested functions: Eigen mode frequencies, straight slender beam, combined bending-torsion, plane bending, transverse bending, punctual mass..

1.76.2.2 Problem data

Units

I. S.

Geometry

■ Outer diameter: de= 0.35 m,

■ Inner diameter: d i = 0.32 m,

■ Beam length: l = 10 m,

■ Distance BC: lBC = 1 m

■ Area: A =1.57865 x 10-2 m2

■ Inertia: Iy = Iz = 2.21899 x 10-4m

4

■ Polar inertia: Ip = 4.43798 x 10-4m

4

■ Punctual mass: mc = 1000 kg


202


■ Longitudinal elasticity modulus of AB element: E = 2.1 x 1011

Pa,

■ Density of the linear element AB: = 7800 kg/m3

■ Poisson's ratio =0.3(this coefficient was not specified in the AFNOR test , the value 0.3 seems to be the more appropriate to obtain the correct frequency value of modes No. 4 and 5 with NE/NASTRAN:

■ Elastic modulus of BC element: E = 1021

Pa

■ Density of the linear element BC: = 0 kg/m3

Boundary conditions

Fixed at point A, x = 0,

Loading

None for the modal analysis

1.76.2.3 Reference frequencies

Reference solutions

The different eigen frequencies are determined using a finite elements model of Euler beam (slender beam).

fz + t0 = flexion x,z + torsion

fy + tr = flexion x,y + traction

Mode Units Reference

1 (fz + t0) Hz 1.636

2 (fy + tr) Hz 1.642

3 (fy + tr) Hz 13.460

4 (fz + t0) Hz 13.590

5 (fz + t0) Hz 28.900

6 (fy + tr) Hz 31.960

7 (fz + t0) Hz 61.610

1 (fz + t0) Hz 63.930

Uncertainty about the reference solutions

The uncertainty about the reference solutions: 1%


■ Linear element AB: Beam

■ Imposed mesh: 50 elements.

■ Linear element BC: Beam

■ Without meshing

Modal deformations


203



CM2 Frequency Eigen mode 1 frequency (fz + t0) [Hz] 1.636

CM2 Frequency Eigen mode 2 frequency (fy + tr) [Hz] 1.642







Note:

fz + t0 = flexion x,z + torsion

fy + tr = flexion x,y + traction

Observation: because the mass matrix of Advance Design is condensed and not consistent, the torsion modes obtained are not taking into account the self rotation mass inertia of the beam.


204












205

1.77 Membrane with hot point (01-0099HSLSB_FEM)

Test ID: 2513

Test status: Passed

1.77.1 Description

Membrane with hot point.

Tested functions: Stresses.

1.77.2 Background


■ Reference: NAFEMS, Test T1

■ Analysis type: static, thermo-elastic;

■ Tested functions: Stresses.

Observation: the units system of the initial NAFEMS test, defined in mm, was transposed in m for practical reasons. However, this has no influence on the results values.

Units

I. S.

Geometry / meshing

A quarter of the structure is modeled by incorporating the terms of symmetries.

Thickness: 1 m


206



Pa,


■ Elongation coefficient = 0.00001.

Boundary conditions

■ Outer:

► For all nodes in y = 0, uy =0;

► For all nodes in x = 0, ux =0;

■ Inner: None.

Loading

■ External: None,

■ Internal: Hot point, thermal load T = 100°C;

1.77.3 yy stress at point A:

Reference solution:


207

Reference value: yy = 50 MPa in A


■ Planar elements: membranes,

■ 28 planar elements,

■ 39 nodes.



CM2 syy_mid yy in A [MPa] 50

Note: This value (50.87) is obtained with a vertical cross section through point A. The value represents yy at the left end of the diagram.

With CM2, it is essential to display the results with the “Smooth results on planar elements” option deactivated.



syy_mid Sigma yy in A [MPa] 50.8666 MPa 1.73%


208

1.78 Beam on 3 supports with T/C (k = 0) (01-0100SSNLB_FEM)

Test ID: 2514

Test status: Passed

1.78.1 Description

Verifies the rotation, the displacement and the moment on a beam consisting of two elements of the same length and identical characteristics with 3 T/C supports (k = 0).

1.78.2 Background



■ Analysis type: static non linear;

■ Element type: linear, T/C.

Units

I. S.

Geometry

■ L= 10 m

■ Section: IPE 200, Iz = 0.00001943 m4



N/m2,


Boundary conditions

■ Outer:

► Support at node 1 restrained along x and y (x = 0),

► Support at node 2 restrained along y (x = 10 m),

► T/C stiffness ky = 0,

■ Inner: None.

Loading

■ External: Vertical punctual load P = -100 N at x = 5 m,

■ Internal: None.

1.78.2.2 References solutions

ky being null, the non linear model behaves the same way as the structure without support 3.


209

Displacements

rad 000153.0Lk2EI3EI32

LkEI6PL

m 00153.0Lk2EI316

PL3v


LkEI3PL


LkEI2PL3

3yzz

3yz

2

3

3yz

3

3

3yzz

3yz

2

2

3yzz

3yz

2

1

Mz Moments

N.m 2502

MM

4

PL)m5x(M

0Lk2EI316

PLk3M

0M

1z2zz

3yz

4y

2z

1z



■ 3 nodes,

■ 2 linear elements + 1 T/C.

Deformed shape


210

Moment diagrams



CM2 RY Rotation Ry in node 1 [rad] 0.000153

CM2 RY Rotation Ry in node 2 [rad] -0.000153

CM2 DZ Displacement V in node 3 [m] 0.00153


CM2 My Moment M in node 1 [Nm] 0

CM2 My Moment M - middle span 1 [Nm] -250



RY Rotation Ry in node 1 [rad] 0.000153175 Rad 0.11%

RY Rotation Ry in node 2 [rad] -0.000153175 Rad -0.11%

DZ Displacement V in node 3 [m] 0.00153175 m 0.11%

RY Rotation Ry in node 3 [rad] -0.000153175 Rad -0.11%

My Moment M in node 1 [Nm] 1.42709e-13 N*m 0.00%

My Moment M - middle span 1 [Nm] -250 N*m 0.00%


211

1.79 A 3D bar structure with elastic support (01-0094SSLLB_FEM)

Test ID: 2508

Test status: Passed

1.79.1 Description

A 3D bar structure with elastic support is subjected to a vertical load of -100 kN. The V2 magnitude on node 5, the normal force magnitude, the reaction magnitude on supports and the action magnitude are verified.

1.79.2 Background


■ Reference: Internal GRAITEC;



Units

I. S.

Geometry

For all bars:

■ H = 3 m

■ B = 3 m

■ S = 0.02 m2

Element Node i Node j

1 (bar) 1 5

2 (bar) 2 5

3 (bar) 3 5

4 (bar) 4 5

5 (spring) 5 6


■ Isotropic linear elastic materials

■ Longitudinal elastic modulus: E = 2.1 E8 N/m2,


212

Boundary conditions

■ Outer: At node 5: K = 50000 kN/m ;

■ Inner: None.

Loading

■ External: Vertical load at node: P = -100 kN,

■ Internal: None.


System solution

2

22 B

HL . Also, U1 = V1 = U5 = U6 = V6 = 0

■ Stiffness matrix of bar 1

1L

2x= where

.12

1.1

2

1)(.).1()(

jiji uuuuL

xu

L

xxu

in the local coordinate system:

)(

)(

)(

)(

0000

0101

0000

0101

)(

)(

11

11

4

1

4

14

1

4

12

=

2

2

1

2

1

2

12

1

1

1

1

101

j

j

i

i

j

i

L T

e

T

v

v

u

v

u

L

ES

u

u

L

ESd

L

ES

dL

ESdxBBESdVBHBk

e


213

where

)v(

)u(

)v(

)u(

0000

0101

0000

0101

L

ESk

5

5

1

1

1

The elementary matrix ek expressed in the global coordinate system XY is the following: ( angle allowing

the transition from the global base to the local base):

22

22

22

22

e

eee

T

ee

sinsincossinsincos

sincoscossincoscos

sinsincossinsincos

sincoscossincoscos

L

ESK

cossin00

sincos00

00cossin

00sincos

Ravec RkRK

Knowing that L

Hsin and

2cos

L

B, then:

2

2

22

2

22

L2

HBcossin

L

Hsin

L2

Bcos

)(

)(

)(

)(

22

2222

22

2222

:)D

H(arctan =5,1 nodes 1element for

5

5

1

1

22

22

22

22

31

V

U

V

U

HHB

HHB

HBBHBB

HHB

HHB

HBBHBB

L

ESK

■ Stiffness matrix of spring support 5

)(

)(

)(

)(

0000

0101

0000

0101

)(

)(

11

11 :system coordinate local in the

4

KKsay We

5

j

j

i

i

j

i

v

u

v

u

Ku

uKk

)(

)(

)(

)(

1010

0000

1010

0000

':90=6,5 nodes 5element for

6

6

5

5

5

V

U

V

U

KK


214

■ System FQK

6Y

6X

5X

1Y

1X

6

6

5

5

1

1

2

33

2

33

3

2

33

2

3

2

33

2

33

3

2

33

2

3

R

R

P

R

R

R

V

U

V

U

V

U

K0K000

000000

K0KHL

ES

2

HB

L

ESH

L

ES

2

HB

L

ES

002

HB

L

ES

2

B

L

ES

2

HB

L

ES

2

B

L

ES

00HL

ES

2

HB

L

ESH

L

ES

2

HB

L

ES

002

HB

L

ES

2

B

L

ES

2

HB

L

ES

2

B

L

ES

If U1 = V1 = U5 = U6 = V6 = 0, then:

m 001885.0

4

KH

L

ES4

P

KHL

ES4

P

V2

3

2

3

5

And

N 23563V4

KRN 1436VH

L

ESR

0RN 1015V2

HB

L

ESRN 1015V

2

HB

L

ESR

56Y52

31Y

6X535X531X

Note:

■ The values on supports specified by Advance Design correspond to the actions,

■ RY6 calculated value must be multiplied by 4 in relation to the double symmetry,

■ x1 value is similar to the one found by Advance Design by dividing this by 2

Effort in bar 1:

1759

1759

11

11 and

200

200

002

002

5

1

5

1

5

5

1

1

5

5

1

1

N

N

u

u

L

ES

V

U

V

U

L

B

L

HL

H

L

BL

B

L

HL

H

L

B

v

u

v

u

5

1

5

1

5

5

1

1

5

5

1

1

11

11 and

cossin00

sincos00

00cossin

00sincos

N

N

u

u

L

ES

V

U

V

U

v

u

v

u


215

Reference values

Point Magnitude Units Value

5 V2 m -1.885 10-3

All bars Normal force N -1759

Supports 1, 3, 4 and 5 Fz action N -1436

Supports 1, 3, 4 and 5 Action Fx=Fy N 7182/1015

Support 6 Fz action N 23563 x 4=94253


■ Linear element: beam, automatic mesh,

■ 5 nodes,


Deformed shape


216

Normal forces diagram


217

1.79.2.3 Reference values


CM2 D V2 magnitude on node 5 [m] -1.885 10-3

CM2 Fx Normal force magnitude on bar 1 [N]

-1759

CM2

CM2

Fx Normal force magnitude on bar 2 [N]

-1759


-1759


-1759

CM2 Fz Fz reaction magnitude on support 1 [N] 1436




CM2 Fx Action Fx magnitude on support 1 [N] -718

CM2 Fx Action Fx magnitude on support 3 [N] 718

CM2

CM2

Fx Action Fx magnitude on support 4 [N] 718

CM2 Fx Action Fx magnitude on support 5 [N] -718

CM2 Fy Action Fy magnitude on support 1 [N] -718

CM2 Fy Action Fy magnitude on support 3 [N] -718

CM2 Fy Action Fy magnitude on support 4 [N] 718

CM2 Fy Action Fy magnitude on support 5 [N] 718

CM2 Fz Fz reaction magnitude on support 6 [N] 23563 x 4=94253



D Displacement on node 5 [mm] 1.88508 mm 0.00%

Fx Normal force magnitude on bar 1 [N] -1759.4 N -0.02%




Fy Fz reaction magnitude on support 1 [N] 1436.55 N 0.04%




Fx Action Fx magnitude on support 1 [N] -718.274 N -0.04%

Fx Action Fx magnitude on support 2 [N] 718.274 N 0.04%

Fx Action Fx magnitude on support 3 [N] 718.274 N 0.04%

Fx Action Fx magnitude on support 4 [N] -718.274 N -0.04%

Fz Action Fy magnitude on support 1 [N] -718.274 N -0.04%

Fz Action Fy magnitude on support 2 [N] -718.274 N -0.04%

Fz Action Fy magnitude on support 3 [N] 718.274 N 0.04%

Fz Action Fy magnitude on support 4 [N] 718.274 N 0.04%

Fy Action Fy magnitude on support 6 [N] 94253.8 N 0.00%


218

1.80 Fixed/free slender beam with centered mass (01-0095SDLLB_FEM)

Test ID: 2509

Test status: Passed

1.80.1 Description

Fixed/free slender beam with centered mass.

Tested functions: Eigen mode frequencies, straight slender beam, combined bending-torsion, plane bending, transverse bending, punctual mass.

1.80.2 Background





■ Tested functions: Eigen mode frequencies, straight slender beam, combined bending-torsion, plane bending, transverse bending, punctual mass.

Units

I. S.

Geometry

■ Outer diameter de = 0.35 m,


■ Beam length: l = 10 m,

■ Area: A =

■ Polar inertia: IP = 4.43798 x 10-4m

4

■ Inertia: Iy = Iz = 2.21899 x 10-4m

4

■ Punctual mass: mc = 1000 kg

■ Beam self-weight: M


219



Pa,


■ Poisson's ratio: =0.3 (this coefficient was not specified in the AFNOR test , the value 0.3 seems to be the more appropriate to obtain the correct frequency value of mode No. 8 with NE/NASTRAN)

Boundary conditions

■ Outer: Fixed at point A, x = 0.00m,

■ Inner: none

Loading



Reference frequency

For the first mode, the Rayleigh method gives the approximation formula

)M24.0m(I

EI3x2/1f

c3

z1

Mode Shape Units Reference

1 Flexion Hz 1.65

2 Flexion Hz 1.65

3 Flexion Hz 16.07

4 Flexion Hz 16.07

5 Flexion Hz 50.02

6 Flexion Hz 50.02

7 Traction Hz 76.47

8 Torsion Hz 80.47

9 Flexion Hz 103.2

10 Flexion Hz 103.2

Comment: The mass matrix associated with the beam torsion on two nodes, is expressed as:

12/1

2/11

3

Il P

And to the extent that Advance Design uses a condensed mass matrix, the value of the torsion mass inertia

introduced in the model is set to: 3

Il p

Uncertainty about the reference frequencies

■ Analytical solution mode 1,

■ Other modes: 1%,


■ Linear element AB: Beam,

■ Beam meshing: 20 elements.


220

Modal deformations


221

Observation: the deformed shape of mode No. 8 that does not really correspond to a torsion deformation, is actually the display result of the translations and not of the rotations. This is confirmed by the rotation values of the corresponding mode.

Eigen modes vector 8

Node DX DY DZ RX RY RZ

1 -3.336e-033 6.479e-031 -6.316e-031 1.055e-022 5.770e-028 5.980e-028 2 -5.030e-013 1.575e-008 -1.520e-008 1.472e-002 6.022e-008 6.243e-008 3 -1.005e-012 6.185e-008 -5.966e-008 2.944e-002 1.171e-007 1.214e-007 4 -1.505e-012 1.365e-007 -1.317e-007 4.416e-002 1.705e-007 1.769e-007 5 -2.002e-012 2.381e-007 -2.296e-007 5.887e-002 2.206e-007 2.289e-007 6 -2.495e-012 3.648e-007 -3.517e-007 7.359e-002 2.673e-007 2.774e-007 7 -2.983e-012 5.149e-007 -4.963e-007 8.831e-002 3.106e-007 3.225e-007 8 -3.464e-012 6.867e-007 -6.618e-007 1.030e-001 3.506e-007 3.641e-007 9 -3.939e-012 8.785e-007 -8.464e-007 1.177e-001 3.873e-007 4.023e-007

10 -4.406e-012 1.088e-006 -1.049e-006 1.325e-001 4.207e-007 4.371e-007 11 -4.863e-012 1.315e-006 -1.267e-006 1.472e-001 4.508e-007 4.684e-007 12 -5.310e-012 1.556e-006 -1.499e-006 1.619e-001 4.777e-007 4.964e-007 13 -5.746e-012 1.811e-006 -1.744e-006 1.766e-001 5.015e-007 5.210e-007 14 -6.169e-012 2.077e-006 -2.000e-006 1.913e-001 5.221e-007 5.423e-007 15 -6.580e-012 2.353e-006 -2.265e-006 2.061e-001 5.396e-007 5.605e-007 16 -6.976e-012 2.637e-006 -2.539e-006 2.208e-001 5.541e-007 5.755e-007 17 -7.357e-012 2.928e-006 -2.819e-006 2.355e-001 5.658e-007 5.874e-007 18 -7.723e-012 3.224e-006 -3.104e-006 2.502e-001 5.746e-007 5.965e-007 19 -8.072e-012 3.524e-006 -3.393e-006 2.649e-001 5.808e-007 6.028e-007 20 -8.403e-012 3.826e-006 -3.685e-006 2.797e-001 5.844e-007 6.065e-007 21 -8.717e-012 4.130e-006 -3.977e-006 2.944e-001 5.856e-007 6.077e-007

With NE/NASTRAN, the results associated with mode No. 8, are:


222



CM2 Eigen mode 1 frequency [Hz] 1.65









Comment: The difference between the reference frequency of torsion mode (mode No. 8) and the one found by Advance Design may be explained by the fact that Advance Design is using a lumped mass matrix (see the corresponding description sheet).







Eigen mode 5 frequency [Hz] 50 Hz -0.04%

Eigen mode 6 frequency [Hz] 50 Hz -0.04%





223

1.81 Simple supported beam in free vibration (01-0098SDLLB_FEM)

Test ID: 2512

Test status: Passed

1.81.1 Description

Simple supported beam in free vibration.

Tested functions: Shear force, eigen frequencies.

1.81.2 Background


■ Reference: NAFEMS, FV5


■ Tested functions: Shear force, eigen frequencies.

Units

I. S.

Geometry

Full square section:

■ Dimensions: a x b = 2m x 2 m

■ Area: A = 4 m

2

■ Inertia: IP = 2.25 m4

Iy = Iz = 1.333 m4



Pa,




224

Boundary conditions

■ Outer:

► x = y = z = Rx = 0 at A ;

► y = z =0 at B ;

■ Inner: None.

Loading



Mode Shape Units Reference

1 Flexion Hz 42.649

2 Flexion Hz 42.649

3 Torsion Hz 77.542

4 Traction Hz 125.00

5 Flexion Hz 148.31

6 Flexion Hz 148.31

7 Torsion Hz 233.10

8 Flexion Hz 284.55

9 Flexion Hz 284.55

Comment: Due to the condensed (lumped) nature of the mass matrix of Advance Design, the frequencies values of 3 and 7 modes cannot be found by this software. The same modeling done with NE/NASTRAN gave respectively for mode 3 and 7: 77.2 and 224.1 Hz.


■ Straight elements: linear element

■ Imposed mesh: 5 meshes

Modal deformations


225



CM2 Frequency of eigen mode 1 [Hz] 42.649







Comment: The torsion modes No. 3 and 7 that are calculated with NASTRAN cannot be calculated with Advance Design CM2 solver and therefore the mode No. 3 of the Advance Design analysis corresponds to mode No. 4 of the reference. The same problem in the case of No. 7 - Advance Design, that corresponds to mode No. 8 of the reference.











226

1.82 Beam on 3 supports with T/C (k = -10000 N/m) (01-0102SSNLB_FEM)

Test ID: 2516

Test status: Passed

1.82.1 Description

Verifies the rotation, the displacement and the moment on a beam consisting of two elements of the same length and identical characteristics with 3 T/C supports (k = -10000 N/m).

1.82.2 Background





Units

I. S.

Geometry

■ L= 10 m

■ Section: IPE 200, Iz = 0.00001943 m4



N/m2,


Boundary conditions

■ Outer:



► T/C ky Rigidity = -10000 N/m (the – sign corresponds to an upwards restraint),

■ Inner: None.

Loading


■ Internal: None.


227


Displacements


LkEI6PL

m 00058.0Lk2EI316

PL3v


LkEI3PL


LkEI2PL3

3yzz

3yz

2

3

3yz

3

3

3yzz

3yz

2

2

3yzz

3yz

2

1

Mz Moments

N.m 9.2202

MM

4

PL)m5x(M

N.m 15.58Lk2EI316

PLk3M

0M

1z2zz

3yz

4y

2z

1z



■ 3 nodes,


Deformed shape


228

Moment diagram



CM2 RY Rotation Ry in node 1 [rad] -0.000129


CM2 DZ Displacement - node 3 [m] 0.00058


CM2 My M moment - node 1 [Nm] 0

CM2 My M moment - node 2 [Nm] -58.15

CM2 My M moment - middle span 1 [Nm] -220.9




RY Rotation Ry in node 2 [rad] -0.000105646 Rad 0.33%

DZ Displacement - node 3 [m] 0.000581169 m 0.20%

RY Rotation Ry in node 3 [rad] -3.44295e-05 Rad -1.26%

My M moment - node 1 [Nm] -1.42109e-14 N*m 0.00%

My M moment - node 2 [Nm] 58.1169 N*m -0.06%

My M moment - middle span 1 [Nm] -220.942 N*m -0.02%


229

1.83 Linear system of truss beams (01-0103SSLLB_FEM)

Test ID: 2517

Test status: Passed

1.83.1 Description

Verifies the displacement and the normal force for a bar system containing 4 elements of the same length and 2 diagonals.

1.83.2 Background




■ Element type: linear, bar.

Units

I. S.

Geometry

■ L= 5 m

■ Section S = 0.005 m2



N/m2.

Boundary conditions

■ Outer:

► Support at node 1 restrained along x and y,


■ Inner: None.

Loading

■ External: Horizontal punctual load P = 50000 N at node 3,

■ Internal: None.


230


Displacements

m 000108.0ES11

PL5v

m 000541.0ES11

PL25u

m 000129.0ES11

PL6v

m 000649.0ES11

PL30u

4

4

3

3

N normal forces

N 32141P11

25N N 22727P

11

5N

N 38569P11

26N N 27272P

11

6N

N 22727P11

5N 0N

4243

1323

1412


■ Linear element: bar, without meshing,

■ 4 nodes,


Deformed shape


231

Normal forces



CM2 DX u3 displacement on Node 3 [m] 0.000649

CM2 DZ v3 displacement on Node 3 [m] -0.000129


CM2 DZ v4 displacement on Node 4 [m] 0.000108

CM2 Fx N12 normal force on Element 1 [N] 0

CM2 Fx N23 normal force on Element 2 [N] -27272



CM2 Fx N13 normal effort on Element 5 [N] 38569




DX u3 displacement on Node 3 [m] 0.000649287 m 0.04%

DZ v3 displacement on Node 3 [m] -0.000129871 m -0.68%

DX u4 displacement on Node 4 [m] 0.000541063 m 0.01%

DZ v4 displacement on Node 4 [m] 0.000108224 m 0.21%

Fx N12 normal force on Element 1 [N] 0 N 0.00%

Fx N23 normal force on Element 2 [N] -27272.9 N 0.00%

Fx N43 normal force on Element 3 [N] 22727.1 N 0.00%

Fx N14 normal force on Element 4 [N] 22727.1 N 0.00%

Fx N13 normal effort on Element 5 [N] 38569.8 N 0.00%

Fx N42 normal force on Element 6 [N] -32140.9 N 0.00%


232

1.84 BAEL 91 (concrete design) - France: Linear element in combined bending/tension - without compressed reinforcements - Partially tensioned section (02-0158SSLLB_B91)

Test ID: 2520

Test status: Passed

1.84.1 Description

Verifies the reinforcement results for a concrete beam with 8 isostatic spans subjects to uniform loads and compression normal forces.

1.84.2 Background


■ Reference: J. Perchat (CHEC) reinforced concrete course



Units

■ Forces: kN

■ Moment: kN.m

■ Stresses: MPa

■ Reinforcement density: cm²

Geometry

■ Beam dimensions: 0.2 x 0.5 ht

■ Length: l = 48 m in 8 spans of 6m,


■ Longitudinal elastic modulus: E = 20000 MPa,

■ Poisson's ratio: = 0.

Boundary conditions

■ Outer:

► Hinged at end x = 0,

► Vertical support at the same level with all other supports

■ Inner: Hinged at each beam end (isostatic)

Loading

■ External:

► Case 1 (DL): uniform linear load g= -5kN/m (on all spans except 8)

Fx = 10 kN at x = 42m: Ng = -10 kN for spans from 6 to 7

Fx = 140 kN at x = 32m: Ng = -150 kN for span 5

Fx = -50 kN at x = 24m: Ng = -100 kN for span 4



Fx = -70 kN at x = 6m: Ng = -30 kN for span 1

► Case 10 (DL): uniform linear load g = -5 kN/m (span 8)

Fx = 10 kN at x = 48m: Ng = -10 kN

Fx = -10 kN at x = 42m

► Case 2 to 8 (LL): uniform linear load q = -9 kN/m (on spans 1, 3 to 7)

uniform linear load q = -15 kN/m (on span 2)


233

Fx = 30 kN at x = 6m (case 2 span 1)

Fx = -50 kN at x = 6m (case 3 span 2)










Fx = -8 kN at x = 36m (case 8 span 7


► Case 9 (ACC): uniform linear load a = -25 kN/m (on 8th span)



Comb BAELUS: 1.35xDL+1.5xLL with duration of more than 24h (comb 101, 104 to 107)

Comb BAEULI: 1.35xDL+1.5xLL with duration between 1h and 24h (comb 102)

Comb BAELUC: 1.35xDL + 1.5xLL with duration of less than 1h (comb 103)

Comb BAELS: 1xDL + 1*LL (comb 108 to 114)

Comb BAELA: 1xDL + 1xACC with duration of less than 1h (comb 115)

■ Internal: None.

Reinforced concrete calculation hypothesis:

All concrete covers are set to 5 cm

BAEL 91 calculation (according to 99 revised version)

Span Concrete Reinforcement Application Concrete Cracking

1 B20 HA fe500 D>24h No Non prejudicial

2 B35 Adx fe235 1h<D<24h No Non prejudicial

3 B50 HA fe 400 D<1h Yes Non prejudicial

4 B25 HA fe500 D>24h Yes Prejudicial

5 B25 HA fe500 D>24h No Very prejudicial

6 B30 Adx fe235 D>24h Yes Prejudicial

7 B40 HA fe500 D>24h Yes 160 MPa

8 B45 HA fe500 D<1h Yes Non prejudicial

1.84.2.2 Reinforcement calculation

Reference solution

Span 1 Span 2 Span 3 Span 4 Span 5 Span 6 Span 7 Span 8

fc28 20 35 50 25 25 30 40 45

ft28 1.8 2.7 3.6 2.1 2.1 2.4 3 3.3

fe 500 235 400 500 500 235 500 500

teta 1 0.9 0.85 1 1 1 1 0.85

gamb 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.15


234


gams 1.15 1.15 1.15 1.15 1.15 1.15 1.15 1

h 1.6 1 1.6 1.6 1.6 1 1.6 1.6

fbu 11.33 22.04 33.33 14.17 14.17 17.00 22.67 39.13

fed 434.78 204.35 347.83 434.78 434.78 204.35 434.78 500.00

sigpreju 250.00 156.67 264.00 250.00 250.00 156.67 160.00 252.76

sigtpreju 200.00 125.33 211.20 200.00 200.00 125.33 160.00 202.21

g 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00

q 9.00 15.00 9.00 9.00 9.00 9.00 9.00 25.00

pu 20.25 29.25 20.25 20.25 20.25 20.25 20.25 30.00

pser 14.00 20.00 14.00 14.00 14.00 14.00 14.00

G -30.00 -100.00 -50.00 -100.00 -150.00 -10.00 -10.00 -10.00

Q -30.00 -50.00 -40.00 -100.00 -100.00 -8.00 -8.00 -8.00

l 6.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00

Mu 91.13 131.63 91.13 91.13 91.13 91.13 91.13 135.00

Nu -85.50 -210.00 -127.50 -285.00 -352.50 -25.50 -25.50 -18.00

Mser 63.00 90.00 63.00 63.00 63.00 63.00 63.00

Nser -60.00 -150.00 -90.00 -200.00 -250.00 -18.00 -18.00

Vu 60.75 87.75 60.75 60.75 60.75 60.75 60.75 90.00

Main reinforcement calculation according to ULS

Mu/A 74.03 89.63 65.63 34.13 20.63 86.03 86.03 131.40

ubu 0.161 0.100 0.049 0.059 0.036 0.125 0.094 0.083

a 0.221 0.133 0.062 0.077 0.046 0.167 0.123 0.108

z 0.410 0.426 0.439 0.436 0.442 0.420 0.428 0.430

Au 6.12 20.57 7.97 8.35 9.18 11.27 5.21 6.46

Main reinforcement calculation with prejudicial cracking according to SLS

Mser/A 51.000 60.000 45.000 23.000 13.000 59.400 59.400 0.000

a 0.4186 0.6678 0.6303 0.4737 0.4737 0.6328 0.6923 0.6157

Mrb 87.53 220.78 302.44 121.16 121.16 182.01 258.82 267.55

A 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

B -3.0000 -3.0000 -3.0000 -3.0000 -3.0000 -3.0000 -3.0000 -3.0000

C -0.4533 -0.8511 -0.3788 -0.2044 -0.1156 -0.8426 -0.8250 0.0000

D 0.4533 0.8511 0.3788 0.2044 0.1156 0.8426 0.8250 0.0000

alpha1 0.238 0.432 0.428

z 0.414 0.385 0.386

Aserp 10.22 10.99 10.75

Main reinforcement calculation with very prejudicial cracking according to SLS

Mser/A 51.00 60.00 45.00 23.00 13.00 59.40 59.40 0.00

a 0.47 0.72 0.68 0.53 0.53 0.68 0.69 0.67

Mrb 96.93 231.67 319.66 132.43 132.43 192.27 258.82 283.60

A 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

B -3.0000 -3.0000 -3.0000 -3.0000 -3.0000 -3.0000 -3.0000 -3.0000

C -0.5667 -1.0638 -0.4735 -0.2556 -0.1444 -1.0532 -0.8250 0.0000

D 0.5667 1.0638 0.4735 0.2556 0.1444 1.0532 0.8250 0.0000

alpha1 0.203

z 0.420

Asertp 14.049

Transverse reinforcement calculation

tu 0.68 0.98 0.68 0.68 0.68 0.68 0.68 1.00

k 0.57 0.40 0.00 -0.14 -0.41 0.00 0.00 0.00

At/st 1.87 7.08 4.31 3.90 4.77 7.34 3.45 4.44


235


Recapitulation

Aflex 6.12 20.57 7.97 10.22 14.05 11.27 10.75 6.46

e0 -0.95 -1.67 -1.43 -3.17 -3.97 -0.29 -0.29 -0.13

Aminfsimp 0.75 2.38 1.86 0.87 0.87 2.11 1.24 1.37

Aminfcomp 0.83 2.54 2.01 0.90 0.90 2.80 1.65 0.30

At 1.87 7.08 4.31 3.90 4.77 7.34 3.45 4.44

Atmin 1.60 3.40 2.00 1.60 1.60 3.40 1.60 1.60


■ Linear elements: beams with imposed mesh

■ 29 nodes,




CM2 Az Inf. main reinf. T1 [cm2] 6.12

CM2 Amin Min. main reinf. T1 [cm2] 0.75

CM2 Atz Trans. reinf. T1 [cm2] 1.87

















CM2 Amin Min. main. reinf. T7 [cm2] 1.24





The "Mu limit" method must be applied in order to achieve the same results.


236



Az Inf. main reinf. T1 [cm²] -6.11718 cm² 0.05%

Amin Min. main reinf. T1 [cm²] 0.7452 cm² -0.64%

Atz Trans. reinf. T1 [cm²] 1.8699 cm² -0.01%



Atz Trans. reinf. T2 [cm²] 7.07943 cm² -0.01%


Amin Min. main reinf. T3 [cm²] 1.863 cm² 0.16%

Atz Trans. reinf. T3 [cm²] 4.3125 cm² 0.06%

Az Inf. main reinf. T4 [cm²] -10.2301 cm² -0.10%










Amin Min. main. reinf. T7 [cm²] 1.242 cm² 0.16%






237

1.85 Cantilever beam in Eulerian buckling with thermal load (01-0092HFLLB_FEM)

Test ID: 2507

Test status: Passed

1.85.1 Description

Verifies the vertical displacement and the normal force on a cantilever beam in Eulerian buckling with thermal load.

1.85.2 Background





Units

I. S.

Geometry

■ L= 10.00 m

■ S=0.01 m2

■ I = 0.0002 m4



N/m2,


■ Coefficient of thermal expansion: = 0.00001.

Boundary conditions


■ Inner: None.

Loading

■ External: Punctual load P = -100000 N at x = L,

■ Internal: T = -50°C (Contraction equivalent to the compression force)

( 5000001.0T0005.001.010.2

100000

ES

N100

)


Reference solution




238



■ 5 nodes,

■ 4 elements.

Deformed shape



CM2 DZ Vertical displacement v5 on Node 5 - Case 101 [cm] -1.0

CM2 Fx Normal Force on Node A - Case 101 [N] -100000

CM2 Fx Normal Force on Node A - Case 102 [N] -98696



DZ Vertical displacement on Node 5 [cm] -1 cm 0.00%

Fx Normal Force - Case 101 [N] -100000 N 0.00%

Fx Normal Force - Case 102 [N] -98699.3 N 0.00%


239

1.86 Double cross with hinged ends (01-0097SDLLB_FEM)

Test ID: 2511

Test status: Passed

1.86.1 Description

Double cross with hinged ends.

Tested functions: Eigen frequencies, crossed beams, in plane bending.

1.86.2 Background


■ Reference: NAFEMS, FV2 test


■ Tested functions: Eigen frequencies, Crossed beams, In plane bending.

Units

I. S.

Geometry

Full square section:

■ Arm length: L = 5 m

■ Dimensions: a x b = 0.125 x 0.125

■ Area: A = 1.563 10-2

m2

■ Inertia: IP = 3.433 x 10-5m

4

Iy = Iz = 2.035 x 10-5m

4



Pa,



240

Boundary conditions

■ Outer: A, B, C, D, E, F, G, H points restraint along x and y;

■ Inner: None.

Loading



Mode Units Reference

1 Hz 11.336

2,3 Hz 17.709

4 to 8 Hz 17.709

9 Hz 45.345

10,11 Hz 57.390

12 to 16 Hz 57.390


■ Linear elements type: Beam

■ Imposed mesh: 4 Elements / Arms

Modal deformations


241



CM2 Frequency Frequency of Eigen Mode 1 [Hz] 11.336


















Frequency of Eigen Mode 1 [Hz] 11.33 Hz -0.05%

















242

1.87 Beam on 3 supports with T/C (k -> infinite) (01-0101SSNLB_FEM)

Test ID: 2515

Test status: Passed

1.87.1 Description

Verifies the rotation, the displacement and the moment on a beam consisting of two elements of the same length and identical characteristics with 3 T/C supports (k -> infinite).

1.87.2 Background





Units

I. S.

Geometry

■ L= 10 m

■ Section: IPE 200, Iz = 0.00001943 m4



N/m2,


Boundary conditions

■ Outer:



► T/C stiffness ky (1.1030

N/m),

■ Inner: None.

Loading


■ Internal: None.


ky being infinite, the non linear model behaves the same way as a beam on 3 supports.


243

Displacements


LkEI6PL

0Lk2EI316

PL3v


LkEI3PL


LkEI2PL3

3yzz

3yz

2

3

3yz

3

3

3yzz

3yz

2

2

3yzz

3yz

2

1

Mz Moments

N.m 13.2032

MM

4

PL)m5x(M

N.m 75.93Lk2EI316

PLk3M

0M

1z2zz

3yz

4y

2z

1z



■ 3 nodes,


Deformed shape


244

Moment diagram



CM2 RY Rotation Ry - node 1 [rad] 0.000115

CM2 RY Rotation Ry - node 2 [rad] -0.000077

CM2 DZ Displacement - node 3 [m] 0

CM2 RY Rotation Ry - node 3 [rad] 0.000038

CM2 My Moment M - node 1 [Nm] 0

CM2 My Moment M - node 2 [Nm] 93.75

CM2 My Moment M - middle span 1 [Nm] -203.13




RY Rotation Ry in node 2 [rad] -7.65875e-05 Rad 0.54%

DZ Displacement - node 3 [m] 9.36486e-30 m 0.00%

RY Rotation Ry in node 3 [rad] 3.81695e-05 Rad 0.45%

My Moment M - node 1 [Nm] 1.3145e-13 N*m 0.00%

My Moment M - node 2 [Nm] 93.6486 N*m -0.11%

My Moment M - middle span 1 [Nm] -203.176 N*m -0.02%


245

1.88 BAEL 91 (concrete design) - France: Design of a concrete floor with an opening (03-0208SSLLG_BAEL91)

Test ID: 2524

Test status: Passed

1.88.1 Description

Verifies the displacements, bending moments and reinforcement results for a 2D concrete slab with supports and punctual loads.

1.88.2 Background


■ Calculation model: 2D concrete slab.

► Slab thickness: 20 cm

► Slab length: 20m

► Slab width: 10m

► The supports (punctual and linear) are considered as hinged.

► Supports positioning (see scheme below)

► 1,50m*2,50m opening => see positioning on the following scheme

■ Materials:

► Concrete B25

► Young module: E= 36000 MPa

■ Load case:

► Permanent loads: 100 kg/m2

► Permanent loads: 200 kg/ml around the opening

► Punctual loads of 2T in permanent loads (see the following definition)

► Usage overloads: 250 kg/m2

■ Mesh density: 0.5 m

Slab geometry


246

Support positions

Positions of punctual loads


247

Global loading overview

Load Combinations

Code Numbers Type Title

BAGMAX 1 Static Permanent loads + self weight

BAQ 2 Static Usage overloads

BAELS 101 Comb_Lin Gmax+Q

BAELU 102 Comb_Lin 1.35Gmax+1.5Q


248

1.88.2.2 Effel Structure Results

SLS max displacements (load combination 101)

Mx bending moment for ULS load combination


249

My bending moment for ULS load combination

Mxy bending moment for ULS load combination

1.88.2.3 Effel RC Expert Results

Main hypothesis

■ Top and bottom concrete covers: 3 cm

■ Slightly dangerous cracking

■ Concrete B25 => Fc28= 25 MPa

■ Reinforcement calculation according to Wood method.

■ Calculation starting from non averaged forces.


250

Axi reinforcements

Ayi reinforcements


251

Axs reinforcements

Ays reinforcements


252


Solver

Result name

Result description Reference value

CM2 D Max displacement for SLS (load combination 101) [cm] 0.176

CM2 Myy Mx and My bending moments for ULS (load combination 102) Max(Mx) [kN.m] 25.20

CM2 Myy Mx and My bending moments for ULS (load combination 102) Min(Mx) [kN.m] -15.71

CM2 Mxx Mx and My bending moments for ULS (load combination 102) Max(My) [kN.m] 31.17

CM2 Mxx Mx and My bending moments for ULS (load combination 102) Min(My) [kN.m] -18.79

CM2 Mxy Mx and My bending moments for ULS (load combination 102) Max (Mxy) [kN.m] 10.26

CM2 Mxy Mx and My bending moments for ULS (load combination 102) Min (Mxy) [kN.m] -10.14

CM2 Axi Theoretic reinforcements Axi [cm2] 3.84

CM2 Axs Theoretic reinforcements Axs [cm2] 3.55

CM2 Ayi Theoretic reinforcements Ayi [cm2] 3.75

CM2 Ays Theoretic reinforcements Ays [cm2] 4.53

These values are obtained from the maximum values from the mesh.



D Max displacement for SLS (load combination 101) [cm] 0.174641 cm -0.77%

Myy Mx and My bending moments for ULS (load combination 102) Max(Mx) [kNm]

25.2594 kN*m 0.24%

Myy Mx and My bending moments for ULS (load combination 102) Min(Mx) [kNm]

-15.6835 kN*m 0.17%

Mxx Mx and My bending moments for ULS (load combination 102) Max(My) [kNm]

31.2449 kN*m 0.24%

Mxx Mx and My bending moments for ULS (load combination 102) Min(My) [kNm]

-18.7726 kN*m 0.09%

Mxy Mx and My bending moments for ULS (load combination 102) Max (Mxy) [kNm]

-10.1558 kN*m 1.02%

Mxy Mx and My bending moments for ULS (load combination 102) Min (Mxy) [kNm]

10.2508 kN*m 1.09%

Axi Theoretic reinforcements Axi [cm2] 3.83063 cm² -0.24%

Axs Theoretic reinforcementsAxs [cm2] 3.629 cm² 2.23%

Ayi Theoretic reinforcements Ayi [cm2] 3.72879 cm² -0.57%

Ays Theoretic reinforcements Ays [cm2] 4.61909 cm² 1.97%


253

1.89 CM66 (steel design) - France: Design of a 2D portal frame (03-0207SSLLG_CM66)

Test ID: 2523

Test status: Passed

1.89.1 Description

Verifies the steel calculation results (displacement at ridge, normal forces, bending moments, deflections, stresses, buckling lengths, lateral torsional buckling lengths and cross section optimization) for a 2D metallic portal frame, according to CM66.

1.89.2 Background


■ Calculation model: 2D metallic portal frame.

► Column section: IPE500

► Rafter section: IPE400

► Base plates: hinged.

► Portal frame width: 20m

► Columns height: 6m

► Portal frame height at the ridge: 7.5m

■ Load case:

► Permanent loads: 150 kg/m on the roof + elements self weight.

► Usage overloads: 800 kg/ml on the roof

■ Mesh density: 1m

Model preview

Combinations

Code Numbers Type Title

CMP 1 Static Permanent load + self weight

CMS 2 Static Usage overloads

CMCFN 101 Comb_Lin 1.333P

CMCFN 102 Comb_Lin 1.333P+1.5S

CMCFN 103 Comb_Lin P+1.5S

CMCD 104 Comb_Lin P+S


254

1.89.2.2 Effel Structure Results

Ridge displacements (combination 104)

Diagram of normal force envelope


255

Envelope of bending moments diagram

1.89.2.3 Effel Expert CM results

Main hypotheses

For columns

■ Deflections: 1/150

Envelopes deflections calculation.

■ Buckling: XY plane: Automatic calculation of the structure on fixed nodes

XZ plane: Automatic calculation of the structure on fixed nodes

Ka-Kb Method

■ Lateral-torsional buckling: Ldi automatic calculation: no restraints

Lds imposed value: 2 m

For the rafters



■ Buckling: XY plane: Automatic calculation of the structure on fixed nodes


Ka-Kb Method

■ Lateral-torsional buckling: Ldi automatic calculation: No restraints

Lds imposed value: 1.5m

Optimization criteria

■ Work ratio optimization between 90 and 100%

■ Labels optimization (on Advance Design templates)


256

Deflection verification

Ratio

CM Stress diagrams

Work ratio

Stresses


257

Buckling lengths

Lfy

Lfz

Lateral-torsional buckling lengths

Ldi


258

Lds

Optimization


259



CM2 D Displacement at the ridge [cm] 9.36

CM2 Fx Envelope normal forces on Columns (min) [T] -15.77

CM2 Fx Envelope normal forces on Rafters (max) [T] -1.02

CM2 My Envelope bending moments on Columns (min) [T.m] -42.41

CM2 My Envelope bending moments on Rafters (max) [T.m] 42.41

CM2 Deflection CM deflections on Columns [%] L / 438 (34%)

CM2 Deflection CM deflections on Rafters [%] L / 111 (180%)

CM2 Stress CM stresses on Columns [MPa] 230.34

CM2 Stress CM stresses on Rafters [MPa] 458.38

CM2 Lfy Buckling lengths on Columns - Lfy [m] 5.84

CM2 Lfz Buckling lengths on Columns - Lfz [m] 6

CM2 Lfy Buckling lengths on Rafters - Lfy [m] 7.08

CM2 Lfz Buckling lengths on Rafters - Lfz [m] 10.11

Warning, the local axes in Effel Structure have different orientation in Advance Design.


CM2 Ldi Lateral-torsional buckling lengths on Columns Ldi [m] 6

CM2 Lds Lateral-torsional buckling lengths on Columns Lds [m] 2

CM2 Ldi Lateral-torsional buckling lengths on Rafters Ldi [m] 10.11

CM2 Lds Lateral-torsional buckling lengths on Rafters Lds [m] 1.5

Solver Result name Result description Rate (%) Final section

CM2 Work ratio IPE500 columns - section optimization 98 IPE500

CM2 Work ratio IPE400 rafters - section optimization 195 IPE550



D Displacement at the ridge [cm] 9.36473 cm 0.05%

Fx Envelope normal forces on Columns (min) [T] -15.7798 T -0.06%

Fx Envelope normal forces on Rafters (max) [T] -1.0161 T 0.38%

My Envelope bending moments on Columns (min) [Tm] 42.4226 T*m 0.03%

My Envelope bending moments on Rafters (max) [Tm] 42.4226 T*m 0.03%

Deflection CM deflections on Columns [adm] 438.077 Adim. 0.02%

Deflection CM deflections on Rafters [adm] 111.325 Adim. 0.29%

Stress CM stresses on Columns [adm] 230.331 MPa 0.00%

Stress CM stresses on Rafters [adm] 458.367 MPa 0.00%

Lfy Buckling lengths on Columns - Lfy [m] 6 m 0.00%

Lfz Buckling lengths on Columns - Lfz [m] 5.84401 m 0.07%

Lfy Buckling lengths on Rafters - Lfy [m] 10.1119 m 0.02%

Lfz Buckling lengths on Rafters - Lfz [m] 7.07904 m -0.01%

Ldi Lateral-torsional buckling lengths on Columns Ldi [m] 6 m 0.00%

Lds Lateral-torsional buckling lengths on Columns Lds [m] 2 m 0.00%

Ldi Lateral-torsional buckling lengths on Rafters Ldi [m] 10.1119 m 0.02%

Lds Lateral-torsional buckling lengths on Rafters Lds [m] 1.5 m 0.00%

Work ratio IPE500 columns - section optimization [adm] 0.980131 Adim. 0.01%

Work ratio IPE400 rafters - section optimization [adm] 1.9505 Adim. 0.03%


260

1.90 BAEL 91 (concrete design) - France: Linear element in simple bending - without compressed reinforcement (02-0162SSLLB_B91)

Test ID: 2521

Test status: Passed

1.90.1 Description

Verifies the reinforcement results for a concrete beam with 8 isostatic spans subjected to uniform loads.

1.90.2 Background


■ Reference: J. Perchat (CHEC) reinforced concrete course



Units

■ Forces: kN

■ Moment: kN.m

■ Stresses: MPa

■ Reinforcement density: cm2

Geometry

■ Beam dimensions: 0.2 x 0.5 ht

■ Length: l = 42 m in 7 spans of 6m,


■ Longitudinal elastic modulus: E = 20000 MPa,

■ Poisson's ratio: = 0.

Boundary conditions

■ Outer:

► Hinged at end x = 0,

► Vertical support at the same level with all other supports

■ Inner: Hinge z at each beam end (isostatic)

Loading

■ External:

► Case 1 (DL): uniform linear load g = -5 kN/m (on all spans except 8)

► Case 2 to 8 (LL): uniform linear load q = -9 kN/m (on spans 1, 3 to 7)

uniform linear load q = -15 kN/m (on span 2)

► Case 9 (ACC): uniform linear load a = -25 kN/m (on 8

th span)

► Case 10 (DL): uniform linear load g = -5 kN/m (on 8

th span)

Comb BAELUS: 1.35xDL+1.5xLL with duration of more than 24h (comb 101, 104 to 107)

Comb BAEULI: 1.35xDL+1.5xLL with duration between 1h and 24h (comb 102)

Comb BAELUC: 1.35xDL + 1.5xLL with duration of less than 1h (comb 103)

Comb BAELS: 1xDL + 1*LL (comb 108 to 114)

Comb BAELUA: 1xDL + 1xACC (comb 115)

■ Internal: None.


261

Reinforced concrete calculation hypothesis:

■ All concrete covers are set to 5 cm

■ BAEL 91 calculation with the revised version 99

Span Concrete Reinforcement Application Concrete Cracking

1 B20 HA fe500 D>24h No Non prejudicial

2 B35 Adx fe235 1h<D<24h No Non prejudicial

3 B50 HA fe 400 D<1h Yes Non prejudicial

4 B25 HA fe500 D>24h Yes Prejudicial

5 B60 HA fe500 D>24h No Very prejudicial

6 B30 Adx fe235 D>24h Yes Prejudicial

7 B40 HA fe500 D>24h Yes 160 MPa

8 B45 HA fe500 D<1h Yes Non prejudicial

1.90.2.2 Reinforcement calculation

Reference solution


fc28 20 35 50 25 60 30 40 45 ft28 1.8 2.7 3.6 2.1 4.2 2.4 3 3.3 fe 500 235 400 500 500 235 500 500

teta 1 0.9 0.85 1 1 1 1 0.85 gamb 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.15 gams 1.15 1.15 1.15 1.15 1.15 1.15 1.15 1

h 1.6 1 1.6 1.6 1.6 1 1.6 1.6

fbu 11.33 22.04 33.33 14.17 34.00 17.00 22.67 39.13 fed 434.78 204.35 347.83 434.78 434.78 204.35 434.78 500.00

sigpreju 250.00 156.67 264.00 250.00 285.15 156.67 160.00 252.76 sigtpreju 200.00 125.33 211.20 200.00 228.12 125.33 160.00 202.21

g 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 q 9.00 15.00 9.00 9.00 9.00 9.00 9.00 25.00 pu 20.25 29.25 20.25 20.25 20.25 20.25 20.25 30.00

pser 14.00 20.00 14.00 14.00 14.00 14.00 14.00 l 6.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00

Mu 91.13 131.63 91.13 91.13 91.13 91.13 91.13 135.00 Mser 63.00 90.00 63.00 63.00 63.00 63.00 63.00 Vu 60.75 87.75 60.75 60.75 60.75 60.75 60.75 90.00

Longitudinal reinforcement calculation according to ELU

ubu 0.199 0.147 0.068 0.159 0.066 0.132 0.099 0.085 a 0.279 0.200 0.087 0.217 0.086 0.178 0.131 0.111 z 0.400 0.414 0.434 0.411 0.435 0.418 0.426 0.430

Au 5.24 15.56 6.03 5.10 4.82 10.67 4.91 6.28

Main reinforcement calculation with prejudicial cracking according to SLS

A 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 B -3.000 -3.000 -3.000 -3.000 -3.000 -3.000 -3.000 -3.000 C -0.56000 -0.89362 -0.87500 D 0.56000 0.89362 0.87500

alpha1 0.367 0.442 0.438 z 0.395 0.384 0.384

Aserp 6.38 10.48 10.25

Main reinforcement calculation with very prejudicial cracking according to SLS

A 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 B -3.00 -3.00 -3.00 -3.00 -3.00 -3.00 -3.00 -3.00 C -0.70 -1.60 -0.66 -0.70 -0.61371 -1.12 -0.88 0.00 D 0.70 1.60 0.66 0.70 0.61371 1.12 0.88 0.00

alpha1 0.381 z 0.393

Asertp 7.030


262


Transversal reinforcement calculation

tu 0.68 0.98 0.68 0.68 0.68 0.68 0.68 1.00 k 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00

At/st 0.69 1.79 4.31 3.45 3.45 7.34 3.45 4.44

Recapitulation

Aflex 5.24 15.56 6.03 6.38 7.03 10.67 10.25 6.28 Aminflex 0.75 2.38 1.86 0.87 1.74 2.11 1.24 1.37

At 0.69 1.79 4.31 3.45 3.45 7.34 3.45 4.44 Atmin 1.60 3.40 2.00 1.60 1.60 3.40 1.60 1.60


■ Linear elements: beams with imposed mesh

■ 29 nodes,



Reference





















CM2 Amin Min. main. reinf. T7 [cm2] 1.24





The "Mu limit" method must be applied to attain the same results.


263






















Amin Min. main. reinf. T7 [cm²] 1.242 cm² 0.16%






264

1.91 CM66 (steel design) - France: Design of a Steel Structure (03-0206SSLLG_CM66)

Test ID: 2522

Test status: Passed

1.91.1 Description

Verifies the steel calculation results (maximum displacement, normal force, bending moment, deflections, buckling lengths, lateral-torsional buckling and cross section optimization) for a simple metallic framework with a concrete floor, according to CM66.

1.91.2 Background


■ Calculation model: Simple metallic framework with a concrete floor.

■ Load case:

► Permanent loads: 150 kg/m² for the floor and 25kg/m² for the roof.

► Overloads: 250 kg/m² on the floor.

► Wind loads on region II for a normal location

► Snow loads on region 2B at an altitude of 750m.

■ CM66 Combinations

Model preview

Structure’s load case

Code No. Type Title

CMP 1 Static SW + Dead loads CMS 2 Static Overloads for usage


265

Structure’s load case

Code No. Type Title

CMV 3 Static Wind overloads along +X in overpressure CMV 4 Static Wind overloads along +X in depression CMV 5 Static Wind overloads along -X in overpressure CMV 6 Static Wind overloads along -X in depression CMV 7 Static Wind overloads along +Z in overpressure CMV 8 Static Wind overloads along +Z in depression CMV 9 Static Wind overloads along -Z in overpressure CMV 10 Static Wind overloads along -Z in depression CMN 11 Static Normal snow overloads

1.91.2.2 Effel Structure results

Displacement Envelope (“CMCD" load combinations)

Envelope of linear element forces

Env. Case No. Max.

location

D DX DY DZ

(cm) (cm) (cm) (cm)

Max(D) 213 148 CENTER 12.115 0.037 12.035 -1.393

Min(D) 188 1.1 START 0.000 0.000 0.000 0.000

Max(DX) 204 72.1 START 3.138 3.099 0.434 0.244

Min(DX) 204 313 END 2.872 -1.872 -0.129 -2.174

Max(DY) 213 148 CENTER 12.115 0.037 12.035 -1.393

Min(DY) 213 61.5 END 9.986 -0.118 -9.985 0.046

Max(DZ) 201 371 CENTER 4.149 -0.006 -0.188 4.145

Min(DZ) 203 370 CENTER 4.124 -0.006 -0.240 -4.118

Envelope of forces on linear elements (“CMCFN” load combinations)

Envelope of linear element forces

Env. Case No. MaxSite Fx Fy Fz Mx My Mz

(T) (T) (T) (T*m) (T*m) (T*m)

Max (Fx) 120 4.1 START 19.423 -4.108 -1.384 -0.003 1.505 7.551

Min (Fx) 138 98 START -41.618 -0.962 -0.192 0.000 0.000 0.000

Max(Fy) 120 57 END -13.473 16.349 -0.016 -0.003 0.002 55.744

Min(Fy) 120 60 START -15.994 -16.112 -0.006 -3E-004 6E-006 53.096

Max(Fz) 177 371 START -3.486 -0.118 2.655 0.000 0.000 0.000

Min(Fz) 187 370 START -3.666 -0.147 -2.658 0.000 0.000 0.000

Max(Mx) 120 111 END 3.933 4.840 0.278 0.028 -4E-005 11.531

Min(Mx) 120 21 END -22.324 13.785 -0.191 -0.028 -0.004 42.562

Max(My) 177 371 CENTER -3.099 -0.118 -0.323 0.000 4.403 -0.500

Min(My) 179 370 CENTER -3.283 -0.155 0.321 0.000 -4.373 -0.660

Max (Mz) 120 57 END -13.473 16.349 -0.016 -0.003 0.002 55.744

Min (Mz) 120 59.2 END -19.455 -8.969 -0.702 -0.003 -0.001 -57.105

Envelope of linear element stresses (“CMCFN” load combinations)

Envelope of linear element stresses

Env. Case No. MaxSite sxxMax sxyMax sxzMax sFxx sMxxMax

(MPa) (MPa) (MPa) (MPa) (MPa)

Max(sxxMax) 120 59.2 END 273.860 -14.696 -1.024 -16.453 290.312

Min(sxxMax) 120 292 START -150.743 0.000 0.000 -150.743 0.000

Max(sxyMax) 120 57 START 262.954 37.139 -0.030 -15.609 278.562

Min(sxyMax) 120 60 END 241.643 -36.595 -0.011 -18.536 260.179

Max(sxzMax) 185 371 START -2.949 -0.183 3.876 -2.949 0.000

Min(sxzMax) 179 370 START -3.104 -0.255 -3.882 -3.104 0.000

Max(sFxx) 120 293 END 161.095 9E-005 -0.002 161.095 0.000

Min(sFxx) 120 292 START -150.743 0.000 0.000 -150.743 0.000

Max(sMxxMax) 120 59.2 END 273.860 -14.696 -1.024 -16.453 290.312

Min(sMxxMax) 1 1.1 START -4.511 3.155 -0.646 -4.511 0.000


266

1.91.2.3 CM66 Effel Expertise results

Hypotheses

For columns



■ Buckling XY plane: Automatic calculation of the structure on displaceable nodes


■ Lateral-torsional buckling: Ldi automatic calculation: hinged restraint

Lds automatic calculation: hinged restraint

For rafters



■ Buckling: XY plane: Automatic calculation of the structure on displaceable nodes


■ Lateral-torsional buckling: Ldi automatic calculation: no restraint


For columns



■ Buckling: XY plane: Automatic calculation of the structure on displaceable nodes

XZ plane: Automatic calculation of the structure on displaceable nodes

■ Lateral-torsional buckling: Ldi automatic calculation: hinged restraint


Optimization parameters

■ Work ratio optimization between 90 and 100%

■ All the sections from the library are available.

■ Labels optimization.

The results of the optimization given below correspond to an iteration of the finite elements calculation.


267

Deflection verification

Ratio

Max values on the element

■ Columns: L / 168

■ Rafter: L / 96

■ Column: L / 924


268

CM Stress diagrams

Work ratio

Stresses

Max values on the element

■ Columns: 375.16 MPa

■ Rafter: 339.79 MPa

■ Column: 180.98 MPa


269

Buckling lengths

Lfy

Lfz


270

Lateral-torsional buckling lengths

Ldi

Lds


271

Optimization



CM2 D Maximum displacement (CMCD) [cm] 12.115

CM2 Fx Envelope normal force (CMCFN) Min (Fx) [T] -41.618

CM2 Fx Envelope normal force (CMCFN) Max (Fx) [T] 19.423

CM2 My Envelope bending moment (CMCFN) Min (Mz) [Tm] -57.105

CM2 My Envelope bending moment (CMCFN) Max (Mz) [Tm] 55.744

Warning, the Mz bending moment of Effel Structure corresponds to the My bending moment of Advance Design.


CM2 Deflection CM deflections on Columns [adm] L / 168 (89%)

CM2 Deflection CM deflections on Rafters [adm] L / 96 (208%)

CM2 Deflection CM deflections on Columns [adm] L / 924 (16%)


CM2 Stress CM stresses on Rafters [MPa] 339.74


CM2 Lfy Buckling lengths on Columns Lfy [m] 8.02

CM2 Lfz Buckling lengths on Columns Lfz [m] 24.07

CM2 Lfy Buckling lengths on Rafters Lfy [m] 1.72

CM2 Lfz Buckling lengths on Rafters Lfz [m] 20.25

CM2CM2

Lfy Buckling lengths on Columns Lfy [m] 4.20

CM2 Lfz Buckling lengths on Columns Lfz [m] 5.67


272

Warning, the local axes in Effel Structure are opposite to those in Advance Design.


CM2 Ldi Lateral-torsional buckling lengths on Columns Ldi [m] 8.5

CM2 Lds Lateral-torsional buckling lengths on Columns Lds [m] 8.5

CM2 Ldi Lateral-torsional buckling lengths on Rafters Ldi [m] 8.61

CM2 Lds Lateral-torsional buckling lengths on Rafters Lds [m] 1.72

CM2 Ldi Lateral-torsional buckling lengths on Columns Ldi [m] 2

CM2 Lds Lateral-torsional buckling lengths on Columns Lds [m] 2

Solver Result name Result description Rate (%) Final section

CM2 Work ratio IPE500 columns - section optimization [adm] 1.59 IPE600

CM2 Work ratio IPE400 rafters - section optimization [adm] 1.45 IPE500

CM2 Work ratio IPE400 columns - section optimization [adm] 0.77 IPE360



D Maximum displacement (CMCD) [cm] 12.138 cm 0.19%

Fx Envelope normal force (CMCFN) Min (Fx) [T] -41.6255 T -0.02%

Fx Envelope normal force (CMCFN) Max (Fx) [T] 19.4736 T 0.26%

My Envelope bending moment (CMCFN) Min (Mz)[Tm] -57.113 T*m -0.01%

My Envelope bending moment (CMCFN) Max (Mz) [Tm] 55.7624 T*m 0.03%

Deflection CM deflections on Columns [adm] 167.595 Adim. -0.24%

Deflection CM deflections on Rafters [adm] 96.0768 Adim. 0.08%

Deflection CM deflections on Columns [adm] 925.218 Adim. 0.13%

Stress CM stresses on Columns [MPa] 374.504 MPa -0.04%

Stress CM stresses on Rafters [MPa] 347.517 MPa 2.29%

Stress CM stresses on Columns [MPa] 180.65 MPa -0.18%

Lfy Buckling lengths on Columns Lfy [m] 7.96718 m -0.66%

Lfz Buckling lengths on Columns Lfz [m] 24.0693 m 0.00%

Lfy Buckling lengths on Rafters Lfy [m] 1.72255 m 0.15%

Lfz Buckling lengths on Rafters Lfz [m] 20.2452 m -0.02%

Lfy Buckling lengths on Columns Lfy [m] 4.19567 m -0.10%

Lfz Buckling lengths on Columns Lfz [m] 5.67211 m 0.04%

Ldi Lateral-torsional buckling lengths on Columns Ldi [m] 8.5 m 0.00%

Lds Lateral-torsional buckling lengths on Columns Lds [m] 8.5 m 0.00%

Ldi Lateral-torsional buckling lengths on Rafters Ldi [m] 8.61187 m 0.02%

Lds Lateral-torsional buckling lengths on Rafters Lds [m] 8.61187 m 0.02%

Ldi Lateral-torsional buckling lengths on Columns Ldi [m] 2 m 0.00%

Lds Lateral-torsional buckling lengths on Columns Lds [m] 2 m 0.00%

Work ratio IPE500 columns - section optimization [adm] 1.59363 Adim. 0.23%

Work ratio IPE400 rafters - section optimization [adm] 1.4788 Adim. 1.99%

Work ratio IPE400 columns - section optimization [adm] 0.768724 Adim. -0.17%


273

1.92 PS92 - France: Study of a mast subjected to an earthquake (02-0112SMLLB_P92)

Test ID: 2519

Test status: Passed

1.92.1 Description

A structure consisting of 2 beams and 2 punctual masses, subjected to a lateral earthquake along X. The frequency modes, the eigen vectors, the participation factors, the displacement at the top of the mast and the forces at the top of the mast are verified.

1.92.2 Background



■ Analysis type: modal and spectral analyses;

■ Element type: linear, mass.

1.92.2.2 Material strength model

Units

I. S.

Geometry

■ Length: L= 35.00 m,

■ Outer radius: Rext= 3.00 m,

■ Inner radius: Rint= 2.80 m,

■ Axial section: S= 3.644 m

2,

■ Polar inertia: Ip= 30.68 m4,

■ Bending inertias: Ix= 15.34 m4,

Iy= 15.34 m4,

Masses

■ M1= 203873.6 kg

■ M2= 101936.8 kg



N/m2,


■ Density: = 25 kN/m3,


274

Boundary conditions

■ Outer: Fixed in X= 0.00m, Y= 0.00 m,

Loading

■ External: Seismic excitation on X direction


Linear element: beam, automatic mesh,

1.92.2.3 Seismic hypothesis in conformity with PS92 regulation

■ Zone: Nice Sophia Antipolis (Zone II) ;

■ Site: S1 (Medium soil, 10m thickness);

■ Construction type class: B;

■ Behavior coefficient: 3;

■ Material damping: 4% (Reinforced concrete).

1.92.2.4 Modal analysis

Eigen periods reference solution

Substract the value of structure’s specific horizontal periods by solving the following equation:

0MKdet 2

2

1

3

M0

0MM

25

516

L7

EI48K

Eigen modes Units Reference

1 Hz 2.085

2 Hz 10.742

Modal vectors

For 1:

055.3

1

U

U0

U

U

M0

0M

25

516

L7

EI48

2

1

1

2

1

12

2

2

11

3

For 2:

655.0

1

U

U

2

1

2

Normalizing relative to the mass

3

4

110842.2

10305.9 ;

3

3

210316.1

1001.2


275

Modal deformations

1.92.2.5 Spectral study

Design spectrum


276

Nominal acceleration:

2n1 sm5411.5a 2.085Hzf

2n2 sm25.6aHz742.01f

Observation: the gap between pulses is greater than 10%, so the modal responses can be regarded as independent.

Reference participation factors

Mii

séismedudirectionladedirecteurVecteur:

Eigen modes Reference

1 479.427

2 275.609

Pseudo-acceleration

iiii a in (m/s2)

4.0

%5

: Damping correction factor,

: Structure damping.

8.2556

2.70261

2.4783-

3.78521

Reference modal displacement

024.814E

021.576E1

045.446E-

048.318E2

Equivalent static forces

058.415E

055.510EF1

052.526E-

057.717EF2

Displacement at the top of the mast

22

1 04E446.502E81.4U

Units Reference

m 4.814 E-02

Shear force at the top of the mast

3

05E526.205E415.8T

22

1

3: Being the behavior coefficient of forces

Units Reference

N 2.929 E+05


277

Moment at the base

Units Reference

N.m 1.578 E+07


Reference


CM2 Frequency Frequency Mode 1 [Hz] 2.085

CM2 Frequency Frequency Mode 2 [Hz] 10.742

CM2 D Displacement at the top of the mast [cm] 4.814

CM2 Fz Forces at the top of the mast [N] 2.929E+05



Frequency Mode 1 [Hz] 2.08 Hz -0.24%

Frequency Mode 2 [Hz] 10.74 Hz -0.02%

D Displacement at the top of the mast [cm] 4.81159 cm -0.05%

Fz Forces at the top of the mast [N] 292677 N -0.08%


278

1.93 Non linear system of truss beams (01-0104SSNLB_FEM)

Test ID: 2518

Test status: Passed

1.93.1 Description

Verifies the displacement and the normal force for a bar system containing 4 elements of the same length and 2 diagonals.

1.93.2 Background




■ Element type: linear, bar, tie.

Units

I. S.

Geometry

■ L= 5 m

■ Section S = 0.005 m2



N/m2.

Boundary conditions

■ Outer:



■ Inner: None.

Loading

■ External: Horizontal punctual load P = 50000 N at node 3,


279

■ Internal: None.


In non linear analysis without large displacement, the introduction of ties for the diagonal bars removes bar 5 (test No. 0103SSLLB_FEM allows finding an compression force in this bar at the linear calculation).

Displacements

0v

m 000238.0ES

PLv

m 001195.0ES11

PL5uu

4

3

43

N normal forces

0N 0N

N 70711P2N N 50000PN

0N 0N

4243

1323

1412


■ Linear element: bar, without meshing,

■ 4 nodes,


Deformed shape


280

Normal forces




CM2 DZ v3 displacement on Node 3 [m] -0.000238


CM2 DZ v4 displacement on Node 4 [m] 0





CM2 Fx N13 normal effort on Element 5 [N] 70711




DX u3 displacement on Node 3 [m] 0.00119035 m -0.39%

DZ v3 displacement on Node 3 [m] -0.000238095 m -0.04%

DX u4 displacement on Node 4 [m] 0.00119035 m -0.39%

DZ v4 displacement on Node 4 [m] 9.94686e-316 m 0.00%


Fx N23 normal force on Element 2 [N] -50000 N 0.00%


Fx N14 normal force on Element 4 [N] 2.08884e-307 N 0.00%

Fx N13 normal effort on Element 5 [N] 70710.7 N 0.00%



281

1.94 Generating planar efforts before and after selecting a saved view (TTAD #11849)

Test ID: 3454

Test status: Passed

1.94.1 Description

Generates efforts for all planar elements before and after selecting the third saved view.

1.95 Verifying forces for triangular meshing on planar element (TTAD #11723)

Test ID: 3463

Test status: Passed

1.95.1 Description

Performs the finite elements calculation, verifies the forces for triangular meshing on a planar element and generates a report for planar elements forces by load case.

The planar element is a square shell (5 m) with a thickness of 20 cm, C20/25 material with a linear rigid support. A linear load of -10.00 kN is applied on FZ direction.

1.96 Verifying stresses in beam with "extend into wall" property (TTAD #11680)

Test ID: 3491

Test status: Passed

1.96.1 Description

Verifies the results on two concrete beams which have the "Extend into the wall" option enabled. One of the beams is connected to 2 walls on both sides and one with a wall and a pole. Generates the linear elements forces by elements report.

1.97 Verifying the displacement results on linear elements for vertical seism (TTAD #11756)

Test ID: 3442

Test status: Passed

1.97.1 Description

Verifies the displacements results on an inclined steel bar for vertical seism according to Eurocodes 8 localization and generates the corresponding report.

The steel bar has a rigid support and IPE100 cross section and is subjected to self weight and seism load on Z direction (vertical).

1.98 Verifying constraints for triangular mesh on planar elements (TTAD #11447)

Test ID: 3460

Test status: Passed

1.98.1 Description

Performs the finite elements calculation, verifies the stresses for triangular mesh on a planar element and generates a report for planar elements stresses in neutral fiber.

The planar element is 20 cm thick, C20/25 material with a linear rigid support. A linear load of 30.00 kN is applied on FX direction.


282

1.99 Verifying diagrams after changing the view from standard (top, left,...) to user view (TTAD #11854)

Test ID: 3539

Test status: Passed

1.99.1 Description

Verifies the results diagrams display after changing the view from standard (top, left,...) to user view.

1.100 Verifying forces results on concrete linear elements (TTAD #11647)

Test ID: 3551

Test status: Passed

1.100.1 Description

Verifies forces results on concrete beams consisting of a linear element and on beams consisting of two linear elements. Generates the linear elements forces by load case report.

1.101 Generating results for Torsors NZ/Group (TTAD #11633)

Test ID: 3594

Test status: Passed

1.101.1 Description

Performs the finite elements calculation on a complex concrete structure with four levels. Generates results for Torsors NZ/Group. Verifies the legend results.

The structure has 88 linear elements, 30 planar elements, 48 windwalls, etc.

1.102 Verifying Sxx results on beams (TTAD #11599)

Test ID: 3595

Test status: Passed

1.102.1 Description

Performs the finite elements calculation on a complex model with concrete, steel and timber elements. Verifies the Sxx results on beams. Generates the maximum stresses report.

The structure has 40 timber linear elements, 24 concrete linear elements, 143 steel elements. The loads applied on the structure: dead loads, live loads, snow loads, wind loads and temperature loads (according to Eurocodes).

1.103 Verifying diagrams for Mf Torsors on divided walls (TTAD #11557)

Test ID: 3610

Test status: Passed

1.103.1 Description

Performs the finite elements calculation and verifies the results diagrams for Mf torsors on a high wall divided in 6 walls (by height).

The loads applied on the model: self weight, two live load cases and seism loads according to Eurocodes 8.


283

1.104 EC8 / NF EN 1998-1 - France: Verifying the level mass center (TTAD #11573, TTAD #12315)

Test ID: 3609

Test status: Passed

1.104.1 Description

Performs the finite elements calculation on a model with two planar concrete elements with a linear support. Verifies the level mass center and generates the "Excited total masses" and "Level modal mass and rigidity centers" reports.

The model consists of two planar concrete elements with a linear fixed support. The loads applied on the model are: self weight, a planar live load of -1 kN and seism loads according to French standards of Eurocodes 8.

1.105 Verifying results on punctual supports (TTAD #11489)

Test ID: 3693

Test status: Passed

1.105.1 Description

Performs the finite elements calculation and generates the punctual supports report, containing the following tables: "Displacements of point supports by load case", "Displacements of point supports by element", "Point support actions by load case", "Point support actions by element" and "Sum of actions on supports and nodes restraints".

The structure consists of concrete, steel and timber linear elements with punctual supports.

1.106 Verifying nonlinear analysis results for frames with semi-rigid joints and rigid joints (TTAD #11495)

Test ID: 3795

Test status: Passed

1.106.1 Description

Verifies the nonlinear analysis results for two frames with one level. One of the frames has semi-rigid joints and the other has rigid joints.

1.107 Generating a report with torsors per level (TTAD #11421)

Test ID: 3774

Test status: Passed

1.107.1 Description

Generates a report with the torsors per level results.

1.108 Verifying tension/compression supports on nonlinear analysis (TTAD #11518)

Test ID: 4198

Test status: Passed

1.108.1 Description

Verifies the behavior of supports with several rigidities fields defined.

Performs the finite elements calculation and generates the "Displacements of linear elements by element" report.

The model consists of a vertical linear element (concrete B20, R20*30 cross section) with a rigid punctual support at the base and a T/C punctual support at the top. A value of 15000.00 kN/m is defined for the KTX and KTZ stiffeners of the T/C support. Two loads of 500.00 kN are applied.


284

1.109 Verifying tension/compression supports on nonlinear analysis (TTAD #11518)

Test ID: 4197

Test status: Passed

1.109.1 Description

Verifies the supports behavior when the rigidity has a high value.

Performs the finite elements calculation and generates the "Displacements of linear elements by element" report.

The model consists of a vertical linear element (concrete B20, R20*30 cross section) with a rigid punctual support at the base and a T/C punctual support at the top. A large value of the KTX stiffener of the T/C support is defined. Two loads of 500.00 kN are applied.

1.110 Verifying the main axes results on a planar element (TTAD #11725)

Test ID: 4310

Test status: Passed

1.110.1 Description

Verifies the main axes results on a planar element.

Performs the finite elements calculation for a concrete wall (20 cm thick) with a linear support. Displays the forces results on the planar element main axes.

1.111 Verifying the display of the forces results on planar supports (TTAD #11728)

Test ID: 4375

Test status: Passed

1.111.1 Description

Performs the finite elements calculation and verifies the display of the forces results on a planar support. The model consists of a concrete vertical element with a planar support.

1.112 Verifying the internal forces results for a simple supported steel beam

Test ID: 4533

Test status: Passed

1.112.1 Description

Performs the finite elements calculation for a horizontal element (S235 material and IPE180 cross section) with two hinge rigid supports at each end. One of the supports has translation restraints on X, Y and Z, the other support has restraints on Y and Z.

Verifies the internal forces My, Fz. Validated according to: Example: 3.1 - Simple beam bending without the stability loss Publication: Steel structures members - Examples according to Eurocodes By: F. Wald a kol.


285

1.113 Verifying forces on a linear elastic support which is defined in a user workplane (TTAD #11929)

Test ID: 4553

Test status: Passed

1.113.1 Description

Verifies forces on a linear elastic support, which is defined in a user workplane, and generates a report with forces for linear support in global and local workplane.

1.114 Verifying torsors on a single story coupled walls subjected to horizontal forces

Test ID: 4804

Test status: Passed

1.114.1 Description

Verifies torsors on a single story coupled walls subjected to horizontal forces

1.115 Calculating torsors using different mesh sizes for a concrete wall subjected to a horizontal force (TTAD #13175)

Test ID: 5088

Test status: Passed

1.115.1 Description

Calculates torsors using different mesh sizes for a concrete wall subjected to a horizontal force.


286

1.116 Verifying results of a steel beam subjected to dynamic temporal loadings (TTAD #14586)

Test ID: 5853

Test status: Passed

1.116.1 Description

Verifies a double-end fixed steel beam subjected to harmonic concentrated loadings.

2 Hz and 3 Hz excitation frequencies are studied.

1.116.2 Background

The harmonic response of a steel beam fixed at both ends is studied. The beam contains 8 elements having the same length and identical characteristics. Harmonic concentrated loadings (a vertical load and a bending moment) are applied in the middle of the beam. Two excitation frequencies are studied: 2.0 and 3.0 Hz.


■ Reference: NE/Nastran V8;



Units

I. S.

Geometry

Below are described the beam cross section characteristics:

■ Beam length: L = 16 m,

■ Square shaped cross section: b = 0.05 m,

■ Section area: A = 0.06 m2,

■ Flexion inertia moment about the y (or z) axis: I = 0.0001 m4.



N/m2,

■ Poisson coefficient: = 0.3,


Boundary conditions

■ Outer:

► Fixed support at start point (x = 0),

► Fixed support at end point (x = 16.00).

■ Inner: None.


287

Loading

■ External:

► Point load at x=8: P = Fz = -50 000 sin (2π f t) N

► Bending moment at x=8: M = My = 10000 sin (2π f t) Nm

■ Internal: None.

1.116.2.2 Harmonic response from NE/Nastran V8

Reference solution

Considering a natural frequency (modal) analysis for a double-end fixed beam, the first four natural frequencies can be determined using the following formula:

A

IE

Lf n

n

2

2

2

The modal response is determined considering 14 modes.

The first four mode shapes and their frequencies are:

12 = 22.37 f1 = 2.937 Hz

22 = 61.67 f2 = 8.095 Hz

32 = 120.9 f3 = 15.871 Hz

42 = 199.8 f4 = 26.228 Hz

The vertical reference displacement is calculated in the middle of the beam at x = 8 m.

Software NE/NASTRAN 8.0

Vertical maximum displacement (f = 2 Hz) in the middle of the beam

0.155 m

Vertical maximum displacement (f = 3 Hz) in the middle of the beam

2.266 m


288

Response in the middle of the beam with f = 2 Hz

Response in the middle of the beam with f = 3 Hz


■ Linear element: beam, imposed mesh

■ 9 nodes,




Deformed – D Vertical maximum displacement in the middle of the beam (2 Hz) [m]

0.155 m

Deformed – D Vertical maximum displacement in the middle of the beam (3 Hz) [m]

2.266 m



D Vertical maximum displacement in the middle of the beam (2 Hz)

15.3783 cm -0.7852 %

D Vertical maximum displacement in the middle of the beam (3 Hz)

211.41 cm -6.7034 %


289

1.117 Verifying a simply supported concrete slab subjected to temperature variation between top and bottom fibers

Test ID: 6239

Test status: Passed

1.117.1 Description

Verifies a simply supported concrete slab subjected to a variation of temperature (8 Celsius degrees outside and 22 Celsius degrees inside).

In this project, global Z axis is oriented downwards.


290

1.118 FEM Results - United Kingdom: Simply supported laterally restrained (from P364 Open Sections Example 2)

Test ID: 6327

Test status: Passed

1.118.1 Description

The 533x210x92 UKB in S275 beam is fully laterally restrained along its length and pinned supports, includes a UDL and point load at the centre.

1.118.2 Background


Reference: SCI PUBLICATION P364, Steel Building Design: Worked Examples - Open Sections. In accordance with Eurocodes and the UK National Annexes, Example 2 - Simply supported laterally restrained beam

■ Analysis type: static linear (plane problem),

■ Element type: linear,

The beam shown in the figure below is fully laterally restrained along its length and has bearing lengths of 50 mm at the unstiffened supports and 75 mm under the point load. Design the beam in S275 steel for the loading shown below.

The design aspects covered in this example are:

■ Calculation of design values of actions for ULS and SLS,

■ Cross section classification,

■ Cross sectional resistance:

► Shear buckling,

► Shear,

► Bending moment,

■ Resistance of web to transverse forces,

■ Vertical deflection of beam at SLS.

Units

Metric System

Geometry

Below are described the column cross section characteristics:

■ Depth: h= 533.1 mm

■ Width: b= 209.3 mm

■ Flange thickness: 15.6 mm

■ Root radius: r= 12.7 mm

■ Depth between flange fillets: d= 476.5 mm

■ Second moment of area, y-y axis:

■ Plastic modulus, y-y ax:

■ Section area: A= 11700

■ Modulus of elasticity:


291


For buildings that will be built in the UK, the nominal values of the yield strength (fy) and the ultimate strength (fu) for structural steel should be those obtained from the product standard. Where a range is given, the lowest nominal value should be used.

For S275 steel and t ≤ 16 mm

■ Yield strength:

1.118.2.2 Shear resistance

Verify that:

For plastic design, is the design plastic shear resistance ( ).

is the shear area and is determined as follows for rolled I and H sections with the load applied parallel to the web.

Therefore,

The design plastic shear resistance is:

Maximum design shear

Therefore the shear resistance of the section is adequate.



Steel Strength - Work ratio - Fz Shear Resistance 30%



My My -539.624 kN*m -0.0230 %

Fz Fz end -269.602 kN -0.0378 %

Fz Fz mid -62.475 kN 0.0400 %


292

1.119 Verifying the correct use of symmetric steel cross sections (eg. IPE300S)

Test ID: 6350

Test status: Passed

1.119.1 Description

This test is verifying if the symmetric steel cross sections are sent correctly, with the inversed cross section characteristics, to the CM2 engine.

1.120 Temperature load: SD frame with elements under tempertature gradient, applied on separate systems

Test ID: 6362

Test status: Passed

1.120.1 Description

The purpose of this test is check the displacements values of a node (hinge node) on a Static determined frame.

All 3 linear elements are subjected to a load from a temperature applies with different gradient values.

All 3 temperature load cases are applied on each element, using the List option from the temperature load case.

1.121 Verifying displacements of a prestressed cable structure with results presented in Tibert, 1999.

Test ID: 6365

Test status: Passed

1.121.1 Description

The model contains 12 prestressed cable elements subjected to a small uniform self-weight and concentrated loads at each cable intersection point.

Note that the cable net is not in equilibrium under its assumed initial configuration.

The displacement at the cable intersection points under the four point loads is compared with results presented in Tibert, 1999.

1.122 Checks the bending moments in the central node of a steel frame with two beams having a rotational stiffness of 42590 kN/m.

Test ID: 6381

Test status: Passed

1.122.1 Description

ECCS-Manual Design of Steel Structures to EC3(2010) L.S da Silva, R Simoes H Gervasio.(page 79-Example 2.2), point a.

It checks the bending moments in the central node of a steel frame with two beams having a rotational stiffness of 42590 kN/m.


293

1.123 Verifies the ultimate factored gravity loads acting on elements of a structure

Test ID: 6421

Test status: Passed

1.123.1 Description

The test verifies the load combination generator according to of the National Building Code of Canada 2010

The ultimate factored gravity loads acting on elements of a structure are evaluated

1.123.2 Background

A building consists of two flat slabs supported by columns and concrete walls (acting also as lateral supports) is subjected to gravity loads (dead loads, live loads and snow loads).

The test verifies the calculation of the factored loads and load combinations as defined by NBCC-2010 carried by an interior column of the building and compares the results returned by the program depending on the fine element meshing type of the slab.


■ Analysis type: linear static analysis – 3D problem

■ Elements type: linear, planar

■ Load cases:

Loads acting on the roof:

Dead load (category D): Fz=-3.0kN/m2; Snow load (category S): Fz=-1.84kN/m

2;

Loads acting on the floor:

Dead load (category D): Fz=-3.6kN/m2; Live load (category L): Fz=-2.4kN/m

2;

Units

Metric System


294

Geometry

■ Cross sections:

Columns: C500 (500x500mm)

Slabs: 200mm thick

Walls: 200mm thick


Concrete Con030(24) is used in this test. The following characteristics are used in relation to this material:

■ Longitudinal rigidity E=26621MPa

■ Transverse rigidity: G=11092.08MPa

■ Poisson’s ratio: ν=0.2

■ Density=2.45T/m3

Boundary conditions

The boundary conditions are described below:

■ The column are fixed at their bases, Restraints: TX, TY, TZ, RX, RY, RZ;

■ Linear rigid support are placed at the base of the supporting walls, Restraints: TX, TY, TZ, RX, RY, RZ;

Loading

The following ultimate load combinations are used in this test:

Case Load Combination

Principal loads Companion loads

1 D4.1 -

2 D25.1 + L5.1 S5.0

3 D25.1 + S5.1 L5.0

Note:

LOAD COMBINATIONS WITHOUT CRANE LOADS FOR ULTIMATE STATES (NBCC2010):

Case Load Combination

Principal loads Companion loads

1 D4.1 -

2 ( D25.1 or D9.0 ) + L5.1 S5.0 or W4.0

3 ( D25.1 or D9.0 ) + S5.1 L5.0 or W4.0

4 ( D25.1 or D9.0 ) + W4.1 L5.0 or S5.0

5 ( D0.1 + E0.1 ) L5.0 + S25.0


Reference solution

The tributary area of the column is: 2755.710 mmmAtributary

COLUMN C:

Unfactored loads:

kNmmkNDC 22575/3)( 22

kNmmkNSC 13875/84.1)( 22


295

Factored load combinations:

COMB1:

kNkNCf 31522540.1

COMB2:

kNkNkNCf 25.3501385.022525.1

COMB3:

kNkNkNCf 25.4881385.122525.1

COLUMN D:

Unfactored loads:

kNmmkNDC 27075/6.3)( 22

kNmmkNLC 18075/40.2)( 22

Factored load combinations:

COMB1:

kNkNkNC f 693)270225(4.1

COMB2:

kNkNkNkNkNCf 75.9571385.01805.1)225270(25.1

COMB3:

kNkNkNkNkNCf 75.9151805.01385.1)225270(25.1

Combination 2 governs the design of the column in this case.


■ Linear element: S beam

■ 5 linear element, 6 planar elements

Combination 101:


296

Combination 103:

Combination 106:


Result name Result description Level of the column Reference value

COMB1 Factored axial load Level 2 315.00kN

Level 1 693.00kN


Level 1 957.75kN


Level 1 915.75kN


297

1.124 Verifies the response spectrum analysis results for a 2D frame

Test ID: 6420

Test status: Passed

1.124.1 Description

The test verifies the response spectrum analysis method results for 2D frame.

The masses are lumped at the middle of each rigid element.

1.124.2 Background

Two storey structure shown in the figure below is subjected to Montreal response spectrum. Using RSA method the test verifies the probable maximum displaced shape of the structure, the maximum shear in the second floor as well as the maximum shear at the base using the SRSS combination. It is assumed that the damping is 5% in each mode of vibration.

Gravity g=9.81m/s

2


■ Analysis type: Dynamic - 2D problem

■ Elements type: linear and masses

■ Modal analysis: The masses used to calculate the lateral first two modes of the structures are defined by only point masses. An imposed seism damping of 5%.

■ The following load case is used:

► Dead load (category D): Self weight

Masses: M1=6.89T; M2=3.45T

Units

Metric System


298

Geometry

Cross sections:

■ Columns Level1: C164.88,

■ Columns Level2: C143.35,

■ Horizontal members: RIGID,

Lengths:

■ Columns height: 5m,


Reinforced concrete Con040(24) is used. The following characteristics are used in relation to this material:

■ Specified compressive strength of concrete f’c=40MPa,

■ Specified yield strength of non-restressed reinforcement or anchor steel fy=500MPa,

■ Longitudinal elastic modulus: E=29602MPa

■ Transverse rigidity: G=12334.17MPa

■ Poisson’s ratio: ν=0.2

■ Density: 2.45T/m3

Boundary conditions


■ Outer:

► All the columns are fixed at their base

■ Inner: None.

Loading

The frame is subjected the following load combination:

■ The ultimate limit state (ULS) combination is: Cmax = 1 x D


Reference solution

a) Spectral responses calculation:

The relative displacement spectral response values i

DS and the spectral acceleration i

AS corresponding to each

mode are obtained from the Response spectrum NBCC2010 of Montreal region (soil C, damping 5%).

The modal analysis of this structure gives :

sT

sT

600.02

231.12

2

2

1

1

Therefore the spectral values are:

Mode T(s) Sa (g) Sv=Sa/ω (m/s) SD=Sv/ ω (m)

1 1.235 0.119 0.228 0.045

2 0.600 0.300 0.281 0.027


299

b) Maximum displacement values for each DDOF:

The maximal displacement for ach DDOF is given by:

jjDj

jASαx

)(max

With j are the participation factors of mode j:

j

Tj

jM

rMAα

jM , the generalized mass calculated for each mode:

jTjj AMAM

838.1

11A

;

089.1

12A

mkNsM /823.18838.1

1

5.30

07838.11 2

1

mNsM /150.11089.1

1

5.30

07089.11 2

2

Thereby:

714.01

1

5.30

07838.11

823.18

11

α

285.01

1

5.30

07089.11

150.11

12

α

1 iα

)(059.0

0321.0

838.1

1045.0714.0

1max2

1max1 m

x

x

)(0084.0

0077.0

089.1

1027.0285.0

2max2

2max1 m

x

x

c) Estimation of maximum modal forces at each level and modal shear forces at the base:

jjxKQ maxmax

;

jAjj

jSαMV

2max

;

Mode1:

kNQ

Q

38.5

85.5

059.0

0321.0

200200

2005501

max2

1max1

kNVbase 202.1181.9119.0714.0823.18 21max

Mode2:

kNQ

Q

22.3

92.5

0084.0

0077.0

200200

2005502

max2

2max1

kNVbase 75.281.93.0285.0150.11 22max


300

d) Estimation of maximum responses by statistical combination of the maximum modal responses (SRSS):

Maximum modal responses are combined with the relatively simple statistical method SRSS:

2 ; 1 ;2

max

)2(2

max

)1(max ,

ixxx iii

;2

max22

max1

max ase, VVVb

Maximal displacements:

)(059.0

033.0

0084.0059.0

0077.00321.022

22

max2

max1m

x

x

Maximal shear at the base:

;535.1175.2202.1122

max ase, kNVb


■ Linear element: S beam, rigid;

■ 8 nodes,

■ 6 linear element.

■ 2 point supports


301



x1max Maximal displacement of the first DDOF 33.01mm

X2max Maximal displacement of the second DDOF 59.59mm

Vbase,max Maximum base shear of the response spectrum analysis 11.535kN


302

1.125 Verifying results for prestressed steel cables (Sxx 10MPa)

Test ID: 6495

Test status: Passed

1.125.1 Description

A reinforced concrete (C25/30) frame with R20*30 cross sections for both columns and the beam is prestressed diagonally with an S235, D5.05 cross section, cable. The reference parameters are the displacement of the upper left corner of the frame (node 21, coord. 0 0 5) and stress Sxx on the cable (linear element no. 4, start end coord. 0 0 5). The prestressed state of the cable is defined as an initial constraint Sxx of 10 MPa.

The reference values are compared with results obtained for an identical model on an independent software.

1.126 Imposed displacement, support settlement (d=30mm)

Test ID: 6496

Test status: Passed

1.126.1 Description

It is given a simple reinforced concrete frame: two beams and one beam. The right side support suffers a settlement of 30mm = an imposed displacement of 30mm is defined. The values for the upper left node displacement, the displaced support displacement and the bending moment in the beam are validated with an independent software.

1.127 Plane strain behavior - dam cross-section supporting earth/water pressure of 0.7 and 1 MPa

Test ID: 6519

Test status: Passed

1.127.1 Description

The model represents a retaining wall behavior under earth/water pressure load. The structure is reduced to a representative cross-section modelled by a plane strain planar element type, made of C25/30 cocrete and fixed at the base. The pressure (0.7 and 1 MPa) acting on the face of the wall is represented by two linear loads: 700 and 1000 kN/m.

The reference values (displacement of planar element report) are compared with results obtained for an identical model on an independent software.

1.128 Spectral/Seismic analysis for rigid diaphragm (membrane) subjected to bidirectional seismic action

Test ID: 6521

Test status: Passed

1.128.1 Description

The test verifies the modal masses and frequencies of the 3D system subjected to bidirectional horizontal seismic action.

The vertical elements are two columns and two shell elements made of C25/30 concrete. The columns have square section of 30x30 cm and the walls have 20 cm thickness with a 5 m height. The columns are fixed at the base while the walls are pinned with linear supports. The slab above the vertical elements is modelled with a load area defined as a rigid diaphragm made of C25/30 concrete with 20 cm thickness. A gravity load uniformly distributed is defined on the rigid diaphragm, with a value of 9.81 kN/m2. The seismic action is defined according to EN 1998-1, having imposed agr/g = 3 and A soil type, using Elastic 1 spectrum. Modal analysis takes into account the masses obtained by combining static loads. Ten modes will be analyzed.


303

1.129 Modal analysis of a structure with ”membrane” type element

Test ID: 6535

Test status: Passed

1.129.1 Description

This test verifies results from the modal analysis for a simple 3D frame structure with horizontal rectangular in plan planar element modeled with using membrane elements type. The model consists in a C25/30 concrete 3D structure made of linear S beams and planar "membrane", with triangular mesh type. The punctual supports are considered to be fixed. Modal analysis includes 10 modes to be verified. Mass definition is from the self-weight of the elements with no masses eccentricity and 0% imposed damping. The results to be verified are the frequencies of the first 10 eigen modes and the excited total masses on UX and UY directions.

1.130 Modal analysis of a structure with rigid diaphragm

Test ID: 6536

Test status: Passed

1.130.1 Description

This test verifies results from the modal analysis for a simple 3D frame structure with horizontal rectangular in plane rigid diaphragm . The diaphragm is modelled by the Load area element. The model consists in a 3D structure made of linear S beams and planar "rigid diaphragm", made from C25/30 concrete. Grid with triangles T3 mesh type.

The punctual supports are considered to be fixed. Modal analysis includes 10 modes to be verified. Mass definition is from the self-weight of the elements with no masses eccentricity and 0% imposed damping. The results to be verified are the frequencies of the first 10 eigen modes and the exited total masses on UX and UY directions.

1.131 Time history analysis on concrete membrane subjected to dynamic punctual load

Test ID: 6522

Test status: Passed

1.131.1 Description

The test verifies the maximum (and @ 10s) displacement of a planar membrane which is subject to a punctual dynamic load of 300 kN on X direction pointed at the top corner of the planar element. The test also verifies the maximum Fxy shear force on the element.

The membrane is fully fixed at the bottom with a linear support. On one side of the membrane there is a concrete column made of C25/30 concrete with 20x30 cm section. The membrane is made of C25/30 concrete with a thickness of 50 mm. The base is 3.0 m with a 6.0 m height. The size of the mesh is 250 mm. The dynamic temporal load is defined as a harmonic solicitation with a pulsation on 10 rad/sec for 20 seconds.


304

1.132 Modal analysis of a structure with “bar” type elements

Test ID: 6534

Test status: Passed

1.132.1 Description

This test verifies results from the modal analysis for a simple tower-shaped structure made from bar linear elements. All linear elements are steel pipes with the same cross-section (D100x5mm) and are defined by using ‘bar’ element type (transferring only axial forces), made of S235 steel.

All four punctual supports are supposed to be pinned. Modal analysis includes 10 modes to be verified. Mass definition is from the self-weight of the elements with no masses eccentricity and 0% imposed damping. The results to be verified are the frequencies of the first 6 eigen modes and the exited total masses on UX and UY directions.

The results are validated with another independent software.

1.132.2 Background


■ 3D structure – linear elements only

■ Element type: Bar

■ Analysis type: Modal analysis

Units

Metric System

Geometry

■ Base length L=4.0 m

■ Base width W=3.0 m

■ Two identical segments with the height 4.0m each

■ Total structure height = 8.0 m

Linear elements

■ Type: bar


305

■ Cross section:

Circular hollow

Diameter: 100.0 mm

Thickness: 5.0 mm


Isotropic material:

■ Mass Density ρ = 7850 kg/m3

■ Young's Modulus E = 210 GPa

■ Poisson's Ratio ν = 0.3

Boundary conditions

■ Punctual supports at 4 points: (0;0;0), (4,0,0), (4,3,0) and (0,3,0)

■ Type: Pinned

■ Coordinate system: Global

Loading

■ None


Modal analysis assumptions

■ Number of modes: 10

■ Masses definition: from the self-weight

■ Imposed damping: 0%

■ Masses eccentricity: Disabled


■ Number of bars: 32

■ Number of nodes: 12

■ All linear elements are ‘bars’ type

Verified results

Verified results are:

■ Frequencies for first 6 eigen modes

■ Excited total masses (on UX and UY directions)


306

Comparison

Results are compared with results coming from the identical model created and calculated by using another independent FEM software with following assumptions to the Modal analysis:

■ Mass matrix type: Lumped without rotations

■ Active mass directions: X,Y,Z

■ Analysis method: Subspace iteration\

■ Dumping: Not active


307

Reference values:

1.132.2.3 Calculated results

Description Unit AD 2018R2 AD 2019 Difference Reference Difference

Eigen mode 1 frequency Hz 18.89 18.89 0.0%

18.88 0.05%

Eigen mode 2 frequency Hz

23.74 23.74 0.0%

23.74 0.0%


29.87 29.87 0.0%

29.86 0.03%


40.34 40.34 0.0%

40.33 0.02%


69.02 69.02 0.0%

69.00 0.03%


70.50 70.50 0.0%

70.49 0.01%


78.97 78.97 0.0%

78.95 0.02%


89.85 89.85 0.0%

89.84 0.01%


98.17 98.17 0.0%

98.15 0.02%


146.09 146.09 0.0%

146.07 0.01%

Excited total masses - UX kg 1358.2 1358.2 0.0%

1358.6 0.03%

Excited total masses - UY kg 1358.2 1358.2 0.0%

1358.6 0.03%

Excited total masses - UZ kg 1358.2 1358.2 0.0%

1358.6 0.03%


308

1.133 Modal analysis of a structure with planar elastic supports (global coordinate system)

Test ID: 6540

Test status: Passed

1.133.1 Description

This test verifies the modal analysis results for a simple 3D structure with planar elastic supports.

Supports are defined in the global coordinate systems. The model consists in a 2D frame (one horizontal beam and two vertical columns) resting on two square planar elements. The planar elements are defined as a shell while the linear are S beams. The planar elements have 20 cm thickness while the linear have 20x30 cm section, made of C25/30 concrete.

Planar elastic supports are defined under the full area of both planar elements (A and B), having elastic characteristics. Supports are defined in the global coordinate systems. Ten modes will be analyzed having mass definition from selfweight with no eccentricity, with 0% imposed damping. The mesh type is Delaunay Q4 quadrangles with 0.5 m dimension.

Frequencies for the first 10 modes and excited total masses will be analyzed and compared with result obtained by modelling the same structure in another independent FEM software.

1.133.2 Background


■ 3D structure – bending rigid structure

■ Element types: Planar – Shell, Linear – S beams


Units

Metric System

Geometry

A 2D frame (one horizontal beam on two columns) is standing on two square planar elements.

■ Length of beam: 5.0m

■ Height of columns: 3.0 m

■ Width x Length of planar elements: 2.0 x 2.0 m

■ Thickness of planar elements: 20 cm

■ Section of linear elements: Rectangular – width 20cm, height 30 cm


309


The same material for linear and planar elements.

Isotropic material (Concrete C25/30):


■ Young's Modulus E = 31475.806 MPa


Boundary conditions

Planar elastic supports are defined under full area of both planar elements (A and B).

Parameters for support on the planar element A (under column no. 1):


■ Stiffness:

KTX 100.0 kN/m/m2

KTY 10.0 kN/m/m2

KTZ 10000.0 kN/m/m2

KRX 0.0 kNm/deg/m2

KRY 0.0 kNm/deg/m2

KRZ 100.0 kNm/deg/m2

Parameters for support on the planar element B (under column no. 2):


■ Stiffness:

KTX 100.0 kN/m/m2

KTY 10000.0 kN/m/m2

KTZ 10.0 kN/m/m2

KRX 0.0 kNm/deg/m2

KRY 0.0 kNm/deg/m2

KRZ 100.0 kNm/deg/m2

Loading

■ None








310


■ Number of linear elements (s beam): 3

■ Number of planar elements (shell): 2

■ Mesh definition is Global

■ Mesh type: Delaunay, only quadrangles

■ FE size: 0.5 m

Verified results



■ Excited total masses (on UX, UY and UZ directions)

Modes 1 and 2:


311

Modes 3 and 4:

Modes 5 and 6:


312

Modes 7 and 8:

Comparison




■ Analysis method: Subspace iteration




Eigen mode 1 frequency Hz 0.814 0.814 0.0% 0,872 6.7%









Eigen mode 10 frequency Hz 15.991 15.991 0.0% 15,991 0,0%

Excited total masses - UX kg 5650.0 5650.0 0.0% 5650.0 0.0%

Excited total masses - UY kg 5650.0 5650.0 0.0% 5650.0 0.0%

Excited total masses - UZ kg 5650.0 5650.0 0.0% 5650.0 0.0%


313

1.134 Modal analysis of a structure with an elastic linear support (global coordinate system)

Test ID: 6541

Test status: Passed

1.134.1 Description

This test verifies results from the modal analysis for a simple 3D frame structure with an elastic linear support. Supports are defined in the global coordinate systems.

The model contains a shell element made of S235 steel with a 2.0 cm thickness. Boundary conditions consist in two linear supports: one is a linear elastic at the top of the shell element and the other is pinned at the bottom.

10 modes will be analyzed with mass definition from self-weight. No masses eccentricity. 0% imposed damping. Mesh is defined as Delaunay only Q4 quadrangles. Frequencies for the first 10 modes and excited total masses will be verified and compared with results obtained by modelling the same structure in another independent FEM software.

1.134.2 Background


■ 3D structure – bending rigid structure,

■ Element type: Shell,

■ Analysis type: Modal analysis,

Units

Metric System

Geometry

A rectangular planar element defined on 4 points:

■ (A) 0,0,5; (B) 0,3,5; (C) 5,0,0; (D) 5,3,0;

■ Thickness: 2.00 cm


Isotropic material (Steel S235):

■ Mass Density ρ= 7850 kg/m3,

■ Young's Modulus E= 210 GPa,

■ Poisson's Ratio = 0.3,


314

Boundary conditions

Linear elastic support between points A and B:


■ Stiffness:

KTX 100.0 kN/m/m

KTY 0.0 kN/m/m

KTZ 10000000.0 kN/m/m

KRX 0.0 kNm/deg/m

KRY 100.0 kNm/deg/m

KRZ 10000000.0 kNm/deg/m

Linear rigid support between points C and D:


■ Type: Pin (free RX,RY,RZ; blocked TX,TY,TZ)

Loading

■ None



■ Number of modes: 10,

■ Masses definition: from the self-weight,

■ Imposed damping: 0%,

■ Masses eccentricity: Disabled,


■ Number nodes: 105,

■ Mesh definition is Global,

■ Mesh type: Delaunay, only quadrangles,

■ FE size: 0.5 m,

Verified results


■ Frequencies for first 10 eigen modes,


315

■ Excited total masses (on UX, UY and UZ directions),

4 first modes:

Comparison

Results are compared with results coming from the identical model created and calculated by using another independent FEM software with the following assumptions to the Modal analysis:

■ Mass matrix type: Lumped without rotations,

■ Active mass directions: X,Y,Z,

■ Analysis method: Subspace iteration,

■ Dumping: Not active,


316













Excited total masses - UX kg 3211,5 3211,5 0.0% 3211,5 0.0%

Excited total masses - UY kg 3211,5 3211,5 0.0% 3211,5 0.0%

Excited total masses - UZ kg 3211,5 3211,5 0.0% 3211,5 0.0%


317

1.135 Generalized buckling analysis on bending rigid structure made of short beam elements

Test ID: 6545

Test status: Passed

1.135.1 Description

The test verifies the results from the generalized buckling analysis (10 modes) for a bending rigid structure made of bar elements. The structure is subject to gravitational point force at midspan. The linear elements are bar type made of IPE200 profile, S235 steel. The truss has one fix point and one with Tx released. Magnification factors from generalized buckling analysis (10 modes) will be verified.

1.135.2 Background

Checking the critical magnification factors from a generalized buckling analysis on a model made of short beam elements.


■ Reference: None

■ Analysis type: Generalized buckling / Bending rigid structure / 3D

■ Element type: Linear (S Beam)

■ Load cases: Live Loads: FZ = -1000 kN

Units

Metric System

Geometry

Cross sections:

■ IPE200 (European Profiles)


Material S235 is used.

Boundary conditions


■ Punctual Support n°1: Pin

■ Punctual Support n°2: TY, TZ and RX restrained


318

Loading

The structure is subjected to the following actions:

■ 1 punctual load: FZ = -1000 kN

■ 1 Generalized buckling analysis (10 modes)

1.135.2.2 Modeling


■ 7 Linear elements (S Beams)

■ 2 Rigid point supports

■ 22 nodes (mesh size = 1m)

■ 1 Point load

1.135.2.3 Results

Description AD 2019 AD 2018R2 Difference

Magnification factor (Mode 1) 0,060 0,060 0%











319

1.136 Generalized buckling analysis on bending rigid structure made of variable section beams

Test ID: 6546

Test status: Passed

1.136.1 Description

The test verifies the results from the generalized buckling analysis (10 modes) for a bending rigid structure made of variable section elements. The structure is subject to gravitational point force at midspan.

The linear elements are made of variable beam (IPE100 to IPE400 cross section), S235 steel. The model has one pin point and one with Ty, Tz and Rx restrained. Magnification factors from generalized buckling analysis (10 modes) will be verified.

1.136.2 Background

Checking the critical magnification factors from a generalized buckling analysis on a model made of variable cross section beam elements.


■ Reference: None,

■ Analysis type: Generalized buckling/ Bending rigid structure/ 3D,

■ Element type: Linear (Variable cross section Beam),

■ Load cases: Live Loads: FZ = -1000 kN,

Units

Metric System

Geometry

Cross sections:

■ Variable cross section beams (IPE 100 to IPE 400) (European Profiles)


320



Boundary conditions


■ Punctual Support n°1: Pin,

■ Punctual Support n°2: TY, TZ and RX restrained,

Loading

The column is subjected to the following load combinations and actions:

■ 1 punctual load: FZ= -1000 kN,

■ 1 Generalized buckling analysis (10 modes),

1.136.2.2 Modeling


■ 7 Linear elements (Variable cross section Beams)

■ 2 Point supports

■ 22 nodes (mesh size = 1.00m)

■ 1 Point load

1.136.2.3 Results













321

1.137 Modal analysis of a structure with an elastic linear support (local coordinate system)

Test ID: 6539

Test status: Passed

1.137.1 Description

This test verifies results from the modal analysis for a simple 3D frame structure with an elastic linear support. Supports are defined in the local coordinate systems. The model contains a shell element made of S235 steel with a 2.0 cm thickness. Boundary conditions consist in two linear supports: one is a linear elastic at the top of the shell element and the other is pinned at the bottom. 10 modes will be analyzed with mass definition from self-weight. No masses eccentricity. 0% imposed damping.

Mesh is defined as Delaunay only Q4 quadrangles. Frequencies for the first 10 modes and excited total masses will be verified and compared with results obtained by modelling the same structure in another independent FEM software.

1.137.2 Background



■ Element type: Shell


Units

Metric System

Geometry

A rectangular planar element defined on 4 points:

■ (A) 0,0,5; (B) 0,3,5: (C) 5,0,0; (C) 5,3,0

■ Thickness: 2.0 cm


Isotropic material (Steel S235):




322


Boundary conditions

Linear elastic support between points A and B:

■ Coordinate system: Local (Plate 1)

■ Stiffness:

KTX 10000000.0 kN/m/m

KTY 0.0 kN/m/m

KTZ 100.0 kN/m/m

KRX 0.0 kNm/deg/m

KRY 100.0 kNm/deg/m

KRZ 0.0 kNm/deg/m

Linear rigid support between points C and D:

■ Coordinate system: Local

■ Type: Pin (free RX,RY,RZ, blocked TX,TY,TZ)

Loading

■ None








■ Number nodes: 105

■ Mesh definition is Global

■ Mesh type: Delaunay, only quadrangles

■ FE size: 0.5 m

Verified results



■ Excited total masses (on UX, UY and UZ directions)


323

4 first modes:

Comparison

Results are compared with results coming from the identical model created and calculated by using an independent commercial FEM software with following assumptions to the Modal analysis:



■ Analysis method: Subspace iteration



324













Excited total masses - UX kg 3211,5 3211,5 0.0% 3196,04 0.5%

Excited total masses - UY kg 3211,5 3211,5 0.0% 3196,04 0.5%

Excited total masses - UZ kg 3211,5 3211,5 0.0% 3196,04 0.5%


325

1.138 Modal analysis of a structure with elastic releases on linear elements

Test ID: 6543

Test status: Passed

1.138.1 Description

This test verifies the modal analysis results for a 2D structure with IPE100 cross section linear elements made from S235 steel.

The model consists of a 2D structure made of linear elements with bending stiffness on plane (XZ). Both columns are fixed at the base. Elastic releases are defined on both ends of the linear elements with ID 5, 6 and 7.

Ten modes will be analyzed with mass definition from self-weight. The masses have no eccentricity. Frequencies for the first 10 modes and excited total masses will be verified and compared with results obtained by modelling the same structure in another independent FEM software.

1.138.2 Background


■ 2D structure - bending rigid structure on plane(XZ),

■ Linear element types: Beam,

■ Analysis type: Modal analysis,

Units

Metric System

Geometry

2D structure on XZ plane - dimensions as on the picture above.

Linear elements

■ Type: Beams,

■ Section: IPE100,


Isotropic material: Steel S235:


326

■ Mass Density: ρ= 7850 kg/m3,

■ Young's Modulus: E= 210 GPa,

■ Poisson's Ratio: = 0.3,

Boundary conditions

■ Punctual supports at the bottom of both columns,

■ Type: Fixed (blocked are all 3 available directions: TX, TZ, RY),

■ Coordinate system: Global,

Releases

Defined elastic releases:

■ Ry (X= 0.00 m, Y= 10 kNm/deg) on both ends of linear elements with number 5,6,7;

■ Tz (X=0.00 m, Y=10 kN/m) on the top (End1) of the linear element number 9;

Loading

■ None



■ Number of modes: 10,

■ Masses definition: from the self-weight,

■ Imposed damping: 0%,

■ Masses eccentricity: Disabled.


■ Number of bars: 11 (type: beam),

■ Number of nodes: 8,

■ Mesh on all linear elements is set as Automatic with the Number set to 10.


327

Verified results


■ Frequencies for first 10 eigen modes,

■ Excited total masses (on UX and UY directions),

Modes 1 and 2:

Modes 3 and 4:


328

Modes 5 and 6:

Comparison


■ Mass matrix type: Lumped without rotations,

■ Active mass directions: X, Y, Z,

■ Analysis method: Subspace iteration,

■ Dumping: Not active,

■ To have identical model (when each linear element is meshed by dividing into 10 parts), all elements have generated 9 additional nodes at equal intervals.
















329

1.139 Generalized buckling analysis on membrane element

Test ID: 6547

Test status: Passed

1.139.1 Description

The test verifies the results from the generalized buckling analysis (10 modes) for a bending rigid structure made of one vertical membrane element. The element is subject to gravitational linear uniform distributed load at the upper edge.

The planar element is made of C25/30 concrete with 5 cm thickness. The membrane is fixed at the bottom edge with a linear support. Delaunay triangles and quadrangles T3-Q4 mesh type is used with 0.5 m element size. Magnification factors from generalized buckling analysis (10 modes) will be verified.

1.139.2 Background

Checking the critical magnification factors from a generalized buckling analysis on a model made of a vertical membrane element.


■ Reference: None

■ Analysis type: Generalized buckling / Bending rigid structure / plane

■ Element type: Planar (Membrane)

■ Load cases: Live Loads: FZ = -100 kN/m

Units

Metric System

Geometry

■ Thickness: 5cm


Material C25/30 is used.


330

Boundary conditions


■ Linear Support: Fixed

Loading

The membrane is subjected to the following load combinations and actions:

■ 1 linear load: FZ = -1000 kN


1.139.2.2 Modeling


■ 1 Planar element (Membrane)

■ 1 Rigid linear support

■ 45 nodes (mesh size = 0.5 m)

■ 1 Linear load

1.139.2.3 Results













331

1.140 Generalized buckling analysis on windwall defined as rigid diaphragm element

Test ID: 6548

Test status: Passed

1.140.1 Description

The test verifies the results from the generalized buckling analysis (4 modes) for a bending rigid structure made of one vertical windwall defined as rigid diaphragm element. The element is subject to gravitational linear uniform distributed load at the upper edge.

The planar element is made of C25/30 concrete with 5 cm thickness. The windwall is fixed at the bottom edge with a linear support. Delaunay triangles and quadrangles T3-Q4 mesh type is used with 0.5 m element size. Magnification factors from generalized buckling analysis (4 modes) will be verified.

1.140.2 Background

Checking the critical magnification factors from a generalized buckling analysis on a model made of a windwall defined as rigid diaphragm element.


■ Reference: None

■ Analysis type: Generalized buckling / Bending rigid structure / plane

■ Element type: Windwall with ‘Rigid diaphragm’ property enabled

■ Load cases: Live Loads: FZ = -100 kN/m

Units

Metric System

Geometry

■ Thickness: 5cm




332

Boundary conditions


■ Linear Support: Fixed

Loading

The membrane is subjected to the following load combinations and actions:

■ 1 linear load: FZ = -100 kN


1.140.2.2 Modeling


■ 1 Windwall defined as rigid diaphragm

■ 1 Rigid linear support

■ 11 nodes (mesh size = 0.5m)

■ 1 Linear load

1.140.2.3 Results







333

1.141 Generalized buckling analysis on column with elastic support in global coordinate system

Test ID: 6549

Test status: Passed

1.141.1 Description

The test verifies the results from the generalized buckling analysis (10 modes) for a bending rigid structure made of one vertical concrete column subject to compressive axial force, defined as beam, in global coordinate system.

The column has 20x50 cm cross section, made of C25/30 concrete with a 10 m height. The column has an elastic point support with stiffness at the base. The column is subject to 1000kN gravitational point load. Magnification factors from generalized buckling analysis (10 modes) and buckling lengths will be verified.

1.141.2 Background

Checking the critical magnification factors from a generalized buckling analysis on a model with elastic punctual supports in global coordinate system. The model consists of a concrete column subject to compressive axial force.


■ Reference: None

■ Analysis type: Generalized buckling / Bending rigid structure / 3D

■ Element type: Linear (Beams)


Units

Metric System


334

Geometry

Cross sections:

■ R20*50



Boundary conditions


■ Elastic point support: KTZ=1000 kN/m, KTX= KTY=1kN/m and KRX= KTRY=KRZ=1 kNm/°

Loading

The model is subjected to the following actions:



1.141.2.2 Modeling


■ 1 Linear element (Beams)

■ 1 Elastic point support

■ 11 nodes (mesh size = 1m)

■ 1 Point load

1.141.2.3 Results













335

1.142 Modal analysis of a structure with elastic punctual supports (local coordinate system)

Test ID: 6537

Test status: Passed

1.142.1 Description

This test verifies results from the modal analysis for a simple 3D frame structure with elastic punctual supports. Supports are defined in the local coordinate systems (compatible with connected linear elements). Linear elements are S beam type 20x30 cm cross section made of C25/30 concrete. Punctual elastic supports are defined on points A and B. Seismic damping is set to 0.0% for all directions for both supports. 10 modes will be analyzed with mass definition from self-weight of the elements with 0% imposed damping and no mass eccentricity. Frequencies and excited total masses will be analyzed and compared with reference results obtained by modelling the same structure in another independent software.

1.142.2 Background



■ Element types: S beam


Units

Metric System

Geometry

2D frame (XZ plane) defined on 3D model.

■ Beam coordinates: (A) 0,0,5; (B) 5,0,3

■ Column coordinates: (B) 5,0,3; (C) 5,0,0

Linear elements

■ Type: S beam

■ section:

Rectangular

Height: 30.0 cm


336

Width: 20.0 cm


Isotropic material (Concrete C25/30):


■ Young's Modulus E = 31475.806 MPa


Boundary conditions

Punctual elastic supports defined on points A and B.

Seismic damping is set to 0.0% for all directions for both supports.

Point A:

■ Coordinate system: Local (Linear element #1)

■ Stiffness:

KTX 100.0 kN/m

KTY 1000000.0 kN/m

KTZ 0.0 kN/m

KRX 0.0 kNm/deg

KRY 0.0 kNm/deg

KRZ 1000000.0 kNm/deg

Point B:

■ Coordinate system: Local (Linear element #2)

■ Stiffness:

KTX 1000000.0 kN/m

KTY 100.0 kN/m

KTZ 1000000.0 kN/m

KRX 0.0 kNm/deg

KRY 100.0 kNm/deg

KRZ 0.0 kNm/deg


337

Loading

■ None








■ Number of bars: 2 (s beams)

■ Mesh definition for linear elements set as Automatic with Size = 0.5 m

Verified results





338

6 first modes:


339

Comparison






■ To have identical model (when each linear element is meshed with 0.5 m), all elements have generated additional node at equal intervals.














Excited total masses - UY kg 1257.77 1257.77 0.0% 1257.77 0.0%



340

1.143 Modal analysis of a structure with releases on beam elements

Test ID: 6542

Test status: Passed

1.143.1 Description

This test verifies results from the modal analysis for a 2D structure with beam linear elements. On ends of selected linear elements total releases are defined. The model consists of a 2D structure – bending rigid structure on plane (XZ) made of beam linear elements. IPE100 cross section S235 steel. The two columns are fixed at the bottom. Linear elements with number 5,6,7 have Ry released and linear element number 9 has Tz released at the top (End1).

10 modes will be analyzed with mass definition from self-weight. No masses eccentricity. 0% imposed damping. Frequencies for the first 10 modes and excited total masses will be verified and compared with results obtained by modelling the same structure in another independent FEM software.

1.143.2 Background


■ 2D structure - bending rigid structure on plane (XZ)

■ Linear element types: Beam


Units

Metric System

Geometry

2D structure on XZ plane - dimensions as on the picture above.

Linear elements

■ Type: Beams

■ Section: IPE100


Isotropic material: Steel S235:


341




Boundary conditions

■ Punctual supports at the bottom of both columns

■ Type: Fixed (blocked are all 3 available directions: TX, TZ, RY)


Releases

Defined total releases:

■ Ry on both ends of linear elements with number 5,6,7

■ Tz on the top (End1) of the linear element number 9

Loading

■ None








■ Number of bars: 11 (type: beam)


■ Mesh on all linear elements is set as Automatic with the Number set to 10.


342

Verified results




Modes 1 and 2:

Modes 3 and 4:


343

Modes 5 and 6:

Comparison



■ Active mass directions: X, Y,Z



■ To have identical model (when each linear element is meshed by dividing into 10 parts), all elements have generated 9 additional nodes at equal intervals.
















344

1.144 Generalized buckling analysis on 2D truss structure made of bar elements.

Test ID: 6544

Test status: Passed

1.144.1 Description

The test verifies the results from the generalized buckling analysis (4 modes) for a 2D truss structure made of bar elements. The structure is subject to gravitational point force at midspan. The linear elements are bar type made of CE505 (Otua) profile, S235 steel. The truss has one pin point and one with Ty, Tz and Rx restrained. Magnification factors from generalized buckling analysis will be verified.

1.144.2 Background

Checking the critical magnification factors from a generalized buckling analysis on a model made of bar elements.


■ Reference: None

■ Analysis type: Generalized buckling / Truss structure / 2D

■ Element type: Linear (Bar)


Units

Metric System

Geometry

Cross sections:

■ CE505 (Otua)



Boundary conditions


■ Punctual Support n°1: Fixed

■ Punctual Support n°2: Tx released


345

Loading

The column is subjected to the following load combinations and actions:



1.144.2.2 Modeling


■ 7 Linear elements (Bars)

■ 2 Rigid point supports

■ 5 nodes

■ 1 Point load

1.144.2.3 Results







346

1.145 Generalized buckling analysis on shell with planar elastic support in global coordinate system

Test ID: 6553

Test status: Passed

1.145.1 Description

The test verifies the results from the generalized buckling analysis (10 modes) for a bending rigid structure made of one vertical planar element defined as shell subject to compressive linear load, supported on a horizontal shell element.

The shell elements are made of C25/30 concrete with 20 cm thickness. The horizontal shell has an elastic planar support with stiffness, defined in global coordinate system. The vertical shell is subject to 200kN/m gravitational linear load. Magnification factors from generalized buckling analysis (10 modes) will be verified.

1.145.2 Background

Checking the critical magnification factors from a generalized buckling analysis on a model with elastic planar supports in global coordinate system. The model contains a vertical shell element supported on a horizontal shell element.




■ Element type: Planar (Shell),

■ Load cases: Live Loads: FZ = -200 kN/m,

Units

Metric System

Geometry

■ Thickness: 20cm


347



Boundary conditions


■ Elastic linear support: KTz=225 kN/m/m2 and KTx= KTz= 1 kN/m/m

2 KRx= KRy=KRz=1 kNm/°/m

2

(global coordinate system – Planar element n°1)

Loading


■ 1 linear load: FZ= -200 kN/m,


1.145.2.2 Modeling


■ 2 Planar element (Shell),

■ 1 Elastic planar support,

■ 95 nodes (mesh size = 1.00m),

■ 1 Linear load,

1.145.2.3 Results













348

1.146 Generalized buckling analysis on shell with linear elastic support in global coordinate system

Test ID: 6551

Test status: Passed

1.146.1 Description

The test verifies the results from the generalized buckling analysis (10 modes) for a bending rigid structure made of one vertical planar element defined as shell subject to compressive linear load. The shell element is made of C25/30 concrete with 20 cm thickness.

The shell has an elastic linear support with stiffness at the base, in global coordinate system. The shell is subject to 200kN/m gravitational linear load. Magnification factors from generalized buckling analysis (10 modes) will be verified.

1.146.2 Background

Checking the critical magnification factors from a generalized buckling analysis on a model with elastic linear supports in global coordinate system. The model contains a planar vertical shell element subject to gravitational linear load.



■ Analysis type: Generalized buckling (10 modes)/ Bending rigid structure/ 3D,



Units

Metric System

Geometry

Cross sections:

■ Thickness: 20cm,


349



Boundary conditions


■ Elastic linear support n°1: KTx=200 kN/m, KTy= KTz=1 kN/m and KRx= KRy=KRz=1 kNm/°

Loading


■ 1 linear load: FZ = -200 kN/m,


1.146.2.2 Modeling



■ 1 Elastic linear support,

■ 66 nodes (mesh size= 1.00m),

■ 1 Linear load,

1.146.2.3 Results













350

1.147 Dynamic analysis - Verifies displacements on beam with point mass subject to seismic load

Test ID: 6556

Test status: Passed

1.147.1 Description

The test verifies displacements of a node on a beam with point mass subject to seismic action. The model consists of two linear elements, one column and one beam made of HEA200 S275 steel. A point mass of Mz=3000kg is positioned at the middle of the beam.

The column is fixed at the base and the beam has restrained Tx, Ty, Tz and Rz at the right end. Dx, Dy and Dz displacements from seismic cases Ex and Ey of node 9 will be analyzed.

1.147.2 Background

Verifies displacements on the central node of a beam on the node on which acts a point mass load under seismic load case EX and EY.


■ Reference: None

■ Analysis type: seismic analysis/ bending rigid structure / 3D


■ Load cases: Dead load, Seism EN 1998-1 EX,EY,EZ.

Units

Metric System

Geometry


■ HEA200 (European profile)

■ Section area: A = 5383 mm2


351


Material S275 is used. The following characteristics are used in relation to this material:


Boundary conditions


■ Outer:

► Puntual support n.1: Fixed

► Puntual support n.2: Restrained TX, TY, TZ and RX

■ Inner: None.

Loading

The rafter is subjected to the following loads:

■ Dead load D (self-weight);

■ Seismic loads EN 1998-1 EX, EY, EZ,

■ Masses definition: point mass and self-weight of elements.

■ Point mass: MZ=3000 kg

1.147.2.2 Finite element modeling


■ 2 Linear elements: S beam

■ 6 nodes, 1 node for mass load


Description Symbol Unit AD 2019 AD 2018R2 Difference

Displacement X in node 9 (EX) DX mm 0.001 0.001 0.0%

Displacement Y in node 9 (EX) DY mm 0.000 0.000 0.0%

Displacement Y in node 9 (EX) DZ mm 0.088 0.088 0.0%

Displacement X in node 9 (EY) DX mm 0.000 0.000 0.0%

Displacement Y in node 9 (EY) DY mm 19.563 19.563 0.0%

Displacement Z in node 9 (EY) DZ mm 0.000 0.000 0.0%



DX Dx (EX) 0.00101995 mm 1.9950 %

DY Dy (EX) 4.49112e-09 mm 0.0000 %

DZ Dz (EX) 0.0884058 mm 0.4611 %

DX Dx (EY) 0 mm 0.0000 %

DY Dy (EY) 19.563 mm 0.0000 %

DZ Dz (EY) 8.53289e-11 mm 0.0000 %


352

1.148 Dynamic analysis - Verifies modal mass participation percentages on a model with point mass subject to seismic load

Test ID: 6557

Test status: Passed

1.148.1 Description

The test verifies modal mass participation percentages on a model with point mass subject to seismic action. The model consists of two linear elements, one column and one beam made of HEA200 S275 steel. A point mass of Mz=300kg is positioned at the middle of the beam.

The column is fixed at the base and the beam has restrained Tx, Ty, Tz and Rz at theright end. Modal mass participation percentages for the first 6 modes will be analyzed.

1.148.2 Background

Verifies the percentage of modal mass on Y direction on a beam subjected a point mass in the middle for EY load case.


■ Analysis type: modal analysis/ bending rigid structure / 3D


■ Mass: MZ = 300 kg

■ Load cases: Dead load D, Seism EN 1998-1 EX, EY, EZ.

Units

Metric System

Geometry


■ HEA200 (European profile)



353


Material 275 is used. The following characteristics are used in relation to this / these material(s):


Boundary conditions


■ Outer:

► Punctual support n.1: Fixed

► Punctual support n.2: Restrained at TX, TY, TZ and RX

■ Inner: None.

Loading

The rafter is subjected to the following loads:

■ Dead load D (self-weight),

■ Punctual mass MZ = 3000 kg,

■ Seismic loads EN 1998-1 EX, EY, EZ,

■ Masses definition: Point masses and self-weight of elements,

■ 6 modes.

1.148.2.2 Modeling


■ 2 Linear elements: S beam,

■ 6 nodes, 1 node for mass load

■ 2 rigid punctual supports.



Modal mass mode nr. 1 Y (%) 74.780 74.780 0.0%

Modal mass mode nr. 2 Y (%) 0 0 0.0%



Modal mass mode nr. 5 Y (%) 0 0 0.0%



354

1.149 Generalized buckling analysis on shell with linear elastic support in local coordinate system

Test ID: 6552

Test status: Passed

1.149.1 Description

The test verifies the results from the generalized buckling analysis (10 modes) for a bending rigid structure made of one vertical planar element defined as shell subject to compressive linear load. The shell element is made of C25/30 concrete with 20 cm thickness. The shell has an elastic linear support with stiffness at the base, in local coordinate system.

The shell is subject to 200kN/m gravitational linear load. Magnification factors from generalized buckling analysis (10 modes) will be verified.

1.149.2 Background

Checking the critical magnification factors from a generalized buckling analysis on a model with elastic linear supports in local coordinate system. The model contains a vertical shell element subject to compressive linear load.



■ Analysis type: Generalized buckling (10 modes)/ Bending rigid structure/ 3D,



Units

Metric System

Geometry

Cross sections:

■ Thickness: 20cm,


355



Boundary conditions


■ Elastic linear support: KTy=200 kN/m, KTx= KTz=1 kN/m and KRx= KRy=KRz=1 kNm/°

(local coordinate system – Planar element n°1)

Loading


■ 1 linear load: FZ = -200 kN/m,


1.149.2.2 Modeling



■ 1 Elastic linear support,


■ 1 Linear load,

1.149.2.3 Results













356

1.150 Generalized buckling analysis on beams with elastic releases

Test ID: 6555

Test status: Passed

1.150.1 Description

The test verifies the results from the generalized buckling analysis (10 modes) for a bending rigid structure made of one vertical concrete column subject to compressive axial force, defined as two beams with elastic releases.

The column has 20x50 cm cross section, made of C25/30 concrete with a 10 m height, composed of two beams with 5m height each. The column has a fix point support at the base. The column is subject to 1000kN gravitational point load.Magnification factors from generalized buckling analysis (10 modes) and buckling lengths will be verified.

1.150.2 Background

Checking the critical magnification factors from a generalized buckling analysis on a model made of Beam elements with elastic releases.




■ Element type: Linear (Beams),



357

Units

Metric System

Geometry

Cross sections:

■ R20*50



Boundary conditions


■ Point support: Fixed,

■ Linear element n°3: Elastic release at extremity n°2:

Loading


■ 1 punctual load: FZ = -1000 kN,


1.150.2.2 Modeling


■ 1 Linear element (Beams),

■ 1 Fixed point support,

■ 11 nodes (mesh size= 1.00m),

■ 1 Point load,


358

1.150.2.3 Results













359

1.151 Dynamic analysis – Verifies the displacements of a sloped frame rafter subject to horizontal seismic action

Test ID: 6559

Test status: Passed

1.151.1 Description

The test verifies the displacement of a sloped frame rafter with pinned extremities subject to horizontal seismic action. The sloped beam is subject to uniform distributed gravitational load (10kN/m).

The columns have HEA200 section while the beam has IPE200 cross section, made of S275 steel. The columns are fixed at the base. The beam has Ry and Rz released at both ends. Displacements from seismic action will be analyzed.

1.151.2 Background

Verifies the displacements on a sloped portal frame rafter (node n.11) with pinned extremities under horizontal seism action (EX and EY).


■ Reference: None

■ Analysis type: Seismic analysis / bending rigid structure / 3D

■ Element type: linear (beams)

■ Load cases: Dead load D, Live load L, Seism EN 1998-1 EX, EY,EZ

:


360

Units

Metric System

Geometry

Rafter section IPE 200:

■ Depth: h = 200 mm

■ Width: b = 100 mm


Column sections HEA 200:



Section area: A = 5383 mm2



Boundary conditions


■ Outer:

► Column fixed at base (Z=0)

► First column fixed at top (Z=5), second column fixed at top (Z=6)

► Rafter released on both extremities on Ry and Rz.

■ Inner: None.

Loading

The rafter is subjected to the following load combinations and actions:

■ Dead load 1-D self-weight,

■ Live linear load 2 L = 10 kN/m,

■ Seism EN 1998-1 EX, EY, EZ,

■ Masses definition: obtained by combining static load cases

1.151.2.2 Modeling


■ Linear element: S beam,

■ 6 nodes for first column, 6 nodes for rafter, 7 nodes for the second column



Description Symbol Unit AD 2019 AD

2018R2 Difference

Displacement X node n.11 (EX) DX mm 57.729 57.729 0.0%

Displacement Y node n.11 (EX) DY mm 0.000 0.000 0.0%

Displacement Z node n.11 (EX) DZ mm 0.002 0.002 0.0%

Displacement X node n.11 (EY) DX mm 0.000 0.000 0.0%

Displacement Y node n.11 (EY) DY mm 54.079 54.079 0.0%

Displacement Z node n.11 (EY) DZ mm 0.000 0.000 0.0%


361

1.152 Dynamic analysis – Verifies the envelope of node displacement on linear element with elastic releases subject to Dynamic Temporal Load

Test ID: 6560

Test status: Passed

1.152.1 Description

The test verifies the envelope of node displacement of nodes situated on linear elements. The beam is subject to dynamic temporal load. The model consists of IPE120 and IPE200 beams made of S275 steel. The main beams are pinned at one end and have Tx, Ty, Tz and Rx restrained at the other end.

The secondary beams have Ry elastic releases at both ends. The secondary beams are subject to dynamic temporal loads at the center of the beam having Fz = -5.00 kN, Fz = -3.00 kN, Fz = -2.00 kN. Envelope of node displacements from the dynamic temporal load case will be analyzed.

1.152.2 Background

Verifies the envelope of the displacement on Z direction of linear element n.5 (on nodes 8, 12, 17, 22, 27, 35) with elastic releases on the ends on Ry.


■ Reference: None

■ Analysis type: Time-history analysis / bending rigid structure/ 3D

■ Element type: Linear (beams)

■ Load cases: Dead load D, Dynamic temporal load DT

Units

Metric System

Geometry

Main beams section HEA 220:




Secondary beams section IPE 120


362






Boundary conditions

The boundary conditions are described below for main beams:

■ Outer:

► Fixed on both the extremities;

► Pinned at extremity 1, Restrained at TX, TY, TZ and RX at extremity 2.

■ Inner: None.

The boundary conditions are described below for secondary beams:

■ Outer:

► Elastic releases Ry on Extremity 1 and Extremity 2;

Loading

The purlin is subjected to the following load combinations and actions:

■ Dead load D

■ Dynamic load DT Fz = -5.00 kN, Fz = -3.00 kN, Fz = -2.00 kN from the center to the edge

1.152.2.2 Modeling


■ Linear element: beams

■ 2 Main beams (11 nodes), 5 secondary beams: (6 nodes)




2018R2 Difference

Envelope of node DZ node n.8 DZ mm 1.715 1.715 0.0%







363

1.153 Dynamic analysis – Verifies the displacements of a sloped frame rafter with elastic releases subject to horizontal seismic action

Test ID: 6562

Test status: Passed

1.153.1 Description

The test verifies the displacement of a sloped frame rafter with elastic releases subject to horizontal seismic action. The sloped beam is subject to uniform distributed gravitational load (10kN/m).

The columns have HEA200 section while the beam has IPE200 cross section, made of S275 steel. The columns are fixed at the base. The beam has Ry elastic released at both ends. Displacements from seismic action will be analyzed.

1.153.2 Background

Verifies the displacements on a sloped portal frame rafter (node n.11) with elastic releases at both ends subject to horizontal seism action.


■ Reference: None

■ Analysis type: Seismic analysis / bending rigid structure / 3D

■ Element type: Linear

■ Load cases: Dead load D, Live load L, Seism EN 1998-1 EX, EY,EZ

:

Units

Metric System


364

Geometry

Rafter section IPE 200:




Column sections HEA 200:



Section area: A = 5383 mm2



Boundary conditions


■ Outer:

► Column fixed at base (Z=0),

► First column fixed at top (Z=5), second column fixed at top (Z=6),

► Rafter with elastic releases at both extremities on Ry.

■ Inner: None.

Loading

The rafter is subjected to the following load combinations and actions:

■ Dead load 1-D self-weight,

■ Live linear load 2-L = 10 kN/m,

■ Seism EN 1998-1 EX, EY, EZ,

■ Masses definition: obtained by combining static load cases.

1.153.2.2 Modeling


■ Linear element: S beam,

■ 6 nodes for first column, 6 nodes for rafter, 7 nodes for the second column




2018R2 Difference

Displacement node n.11 for EX DX mm 38.223 38.223 0.0%

Displacement node n.11 for EX DY mm 0.000 0.000 0.0%

Displacement node n.11 for EX DZ mm 0.046 0.046 0.0%

Displacement node n.11 for EY DX mm 0.000 0.000 0.0%

Displacement node n.11 for EY DY mm 54.559 54.559 0.0%

Displacement node n.11 for EY DZ mm 0.000 0.000 0.0%


365

1.154 Generalized buckling analysis on column with elastic support, in local coordinate system

Test ID: 6550

Test status: Passed

1.154.1 Description

The test verifies the results from the generalized buckling analysis (10 modes) for a bending rigid structure made of one vertical concrete column subject to compressive axial force, defined as beam, in local coordinate system.

The column has 20x50 cm cross section, made of C25/30 concrete with a 10 m height. The column has an elastic point support with stiffness at the base. The column is subject to 1000kN gravitational point load. Magnification factors from generalized buckling analysis (10 modes) and buckling lengths will be verified.

1.154.2 Background

Checking the critical magnification factors from a generalized buckling analysis on a model with elastic punctual supports in local coordinate system. The model consists of a concrete column subject to compressive axial force.



■ Analysis type: Generalized buckling / Bending rigid structure / 3D,



Units

Metric System


366

Geometry

Cross sections:

■ R20*50



Boundary conditions


■ Elastic point support n°1: KTZ=1000 kN/m, KTX= KTY=1kN/m and KRX= KTRY=KRZ=1 kNm/°

(local coordinate system – Linear element n°3)

Loading


■ 1 punctual load: FZ= -1000 Kn,


1.154.2.2 Modeling


■ 1 Linear element (Beams),

■ 1 Elastic point support,

■ 11 nodes (mesh size = 1m),

■ 1 Point load.

1.154.2.3 Results













367

1.155 Generalized buckling analysis on model with beam elements with specific releases

Test ID: 6554

Test status: Passed

1.155.1 Description

The test verifies the results from the generalized buckling analysis (10 modes) for a bending rigid structure made of beam elements with specific releases subject to point load. Cross section of the beams is IPE200 made of S235 steel. The model contains one pinned support and one with Ty, Tz and Rx restrained.

Linear elements 3, 4, 5 are hinged (Ry restrained) on both edges, and linear elements 1 and 7 are hinged (Ry restrained) on one edge. Magnification factors from generalized buckling analysis (10 modes) will be verified.

1.155.2 Background

Checking the critical magnification factors from a generalized buckling analysis on a model made of beam elements with specific releases.





■ Load cases: Live Loads: FZ= -1000 Kn,

Units

Metric System

Geometry

Cross sections:

■ IPE200 (European Profiles)



Boundary conditions


■ Punctual Support n°1: Pin,


368

■ Punctual Support n°2: TY, TZ and RX restrained,

■ Linear elements n°3,4,5 are hinged (Ry) on both edges,

■ Linear elements n°1 and 7 are hinged (Ry) on one edge,

Loading


■ 1 punctual load: FZ= -1000 Kn,


1.155.2.2 Modeling


■ 7 Linear elements (S Beams),

■ 2 Rigid point supports,


■ 1 Point load,

1.155.2.3 Results

Description AD 2019 AD

2018R2 Difference












369

1.156 Dynamic analysis – Verifies the envelope of node displacement on linear element under Dynamic Temporal Load

Test ID: 6558

Test status: Passed

1.156.1 Description

The test verifies the envelope of node displacement of nodes situated on linear element no. 9 on Z direction. The beam is subject to dynamic temporal load. The model consists of IPE120 and IPE200 beams made of S275 steel. The main beams are pinned at one end and have Tx, Ty, Tz and Rx restrained at the other end.

The secondary beams have Ry restrained at both ends. The secondary beams are subject to dynamic temporal loads at the center of the beam having Fz = -5.00 kN, Fz = -3.00 kN, Fz = -2.00 kN. Envelope of node displacements from the dynamic temporal load case will be analyzed.

1.156.2 Background

Verifies the envelopes of the node displacement on Z direction on linear element nr. 9 (nodes nr. 6, 14, 19, 24, 29, 37)


■ Reference: None

■ Analysis type: Time history analysis / bending rigid structure/ 3D

■ Element type: linear (beams)

■ Load cases: Dead load D, Dynamic temporal load DT

Units

Metric System

Geometry

Main beams section IPE 200:




Secondary beams section IPE 120


370






Boundary conditions

The boundary conditions are described below for main beams:

■ Outer:

► Fixed on both the extremities;

► Pinned at extremity 1, Restrained at TX, TY, TZ and RX at extremity 2.

■ Inner: None.

The boundary conditions are described below for secondary beams:

■ Outer:

► Released at Ry on Extremity 1 and Extremity 2;

Loading

The purlin is subjected to the following load combinations and actions:

■ Dead load D

■ Dynamic load DT Fz = -5.00 kN, Fz = -3.00 kN, Fz = -2.00 kN from the center to the edge

1.156.2.2 Modeling


■ Linear element: beams

■ 2 Main beams (11 nodes), 5 secondary beams (6 nodes),




Envelope displacement node 6 DZ mm 16.997 16.997 0.0%







371

1.157 Time history analysis – Verifies the displacements on a column with elastic punctual support (local coordinate system) subject to dynamic temporal load at the top

Test ID: 6565

Test status: Passed

1.157.1 Description

The test verifies displacements of a cantilever column subject to dynamic temporal load. The column has elastic point support at the bottom and is subject to dynamic temporal load of 1.0kN on x direction at the top. The elastic point support is defined in local coordinate system.

Cross section is HEB100 made of S235 steel with a 5m height. Displacements on nodes will be analyzed from the Dynamic temporal load case.

1.157.2 Background


■ Reference: none

■ Analysis type: static linear / 3D


■ Load cases: dynamic temporal load FX = 1,0 kN

Units

Metric System

Geometry

Cross sections:

■ HEB100 (European Profiles)

■ Height 5 m


372


Material S235


■ Elastic Punctual Support n°1 – Stiffness: KTX = 100,0 kN/m

(local coordinate system) KTY = 100,0 kN/m

KTZ = 100,0 kN/m

KRX = 100,0 kN*m/°

KRY = 100,0 kN*m/°

KRZ = 100,0 kN*m/°

1.157.2.2 Modeling


■ 1 Linear element: S beam,

■ 6 nodes,

1.157.2.3 Results


displacement nod 1 Dx mm 9.68 9.68 0,0%







373

1.158 Time history analysis – Verifying the displacements on a cantilever column connected to a steel plate on elastic support in global coordinate system

Test ID: 6568

Test status: Passed

1.158.1 Description

The test verifies the node displacements of a cantilever column connected to a steel plate.

The plate is resting on a planar elastic support. The column is subjected on X direction to a 1 kN dynamic temporal load applied at the top of the column. The column is a HEB100 made of S235 steel with a 5 m height. The plate has 1x1 m dimensions with a 10 cm thickness made of S235 steel. Dx horizontal displacements from the dynamic temporal load case will be analyzed.

1.158.2 Background

Verifies displacements on a cantilever column (S beam type) connected to steel plate. Column is loaded by punctual dynamic temporal load at top 1 kN in X. Support of plate is Elastic planar.


■ Reference: none

■ Analysis type: static linear and planar / 3D

■ Element type: linear, planar

■ Load cases: dynamic temporal load FX = 1,0 kN

Units

Metric System

Geometry:

■ Column cross section HEB100 (European Profiles)

■ Column Height 5 m

■ Plate Length and Width 1x1 m

■ Plate Thickness 0,1 m


374


Material S235


■ Elastic planar Support n°1 – Stiffness: KTX = 100,0 kN/m

(global coordinate system) KTY = 100,0 kN/m

KTZ = 100,0 kN/m

KRX = 100,0 kN*m/°

KRY = 100,0 kN*m/°

KRZ = 100,0 kN*m/°

1.158.2.2 Modeling


■ planar element: shell,


■ 14 nodes

1.158.2.3 Results


displacement nod 3 (bottom) (Dx) mm 3.27 327 0,0%

displacement nod 14 (top) (Dx) mm 4.11 4.11 0,0%


375

1.159 Time history analysis – Verifies displacements, forces and bending moments for beam elements structure subject to dynamic temporal loads

Test ID: 6571

Test status: Passed

1.159.1 Description

The test verifies displacements and forces on a plane truss structure made entirely of “beam” type elements subject to dynamic temporal loads. The beam elements have 75x75 mm square cross section made of G40.21M-350W steel. The truss has one pinned support and one with Tx and Ry restraints released.

The dynamic temporal load is pointed at the top left corner of the truss having Fx=50 kN. The dynamic temporal load is defined as a harmonic function with 2 rad/s pulsation for 20 seconds. Displacements (D), axial force and bending moments resulted from the dynamic temporal load case will be analyzed.

1.159.2 Background

Check the reaction, behavior and internal forces for a truss structure made entirely of “Beam” elements subjected to a dynamic load.


■ Reference: none

■ Analysis type: dynamic / time history / truss structure 2D

■ Element type: linear (beam)

■ Load cases: Dynamic

Units

Metric System

Geometry

Below are described the cross-section characteristics:

■ Depth: h = 75mm

■ Width: b = 75mm


376


Material(s) CSA G40-350W is used.

Boundary conditions


■ Punctual Support 1: pinned

■ Punctual Support 2:

► Tx: free

► Ty: fixed

► Tz: fixed

► Rx: fixed

► Ry: free

► Rz: fixed

Loading

The column is subjected to the following loads:

■ 1 punctual dynamic load of 50kN:

1.159.2.2 Modeling


■ 9 Linear elements: all beam elements

■ 75 nodes

■ 2 rigid point supports

■ 1 punctual dynamic load

1.159.2.3 Results


Displacement (MaxD) D mm 0.664 0.664 0.0%

Displacement (@10s) D mm 0.513 0.513 0.0%

Axial Force (MaxD) Fx kN 54.72 54.72 0.0%

Bending Moment (MaxD) My kN.m 0.20 0.20 0.0%


377

1.160 Time history analysis - Verifies displacements, forces and bending moments for variable beam elements structure subject to dynamic temporal loads

Test ID: 6573

Test status: Passed

1.160.1 Description

The test verifies displacements and forces on a plane truss structure made entirely of “variable beam” type elements subject to dynamic temporal loads. The variable beam elements have 25x52 mm to 25x200mm variable cross section made of G40.21M-350W steel.

The truss has one pinned support and one with Tx and Ry restraints released. The dynamic temporal load is pointed at the top left corner of the truss having Fx=50 kN. The dynamic temporal load is defined as a harmonic function with 2 rad/s pulsation for 20 seconds. Displacements (D), axial force and bending moments resulted from the dynamic temporal load case will be analyzed.

1.160.2 Background

Check the reaction, behavior and internal forces for a truss structure made entirely of “Variable Beam” elements subjected to a dynamic load.


■ Reference: none


■ Element type: linear (variable beam)


Units

Metric System

Geometry


■ Start Cross-Section

Depth: h = 50mm

Width: b = 25mm

■ End Cross-section

Depth: h = 200mm

Width: b = 25mm


378



Boundary conditions




► Tx: free

► Ty: fixed

► Tz: fixed

► Rx: fixed

► Ry: free

► Rz: fixed

Loading



1.160.2.2 Modeling


■ 9 Linear elements: all variable beam elements

■ 75 nodes



1.160.2.3 Results







379

1.161 Time history analysis – Verifies the displacements on a column with elastic punctual support (global coordinate system) subject to dynamic temporal load at the top

Test ID: 6564

Test status: Passed

1.161.1 Description

The test verifies displacements of a cantilever column subject to dynamic temporal load. The column has elastic point support at the bottom and is subject to dynamic temporal load of 1.0kN on x direction at the top. The elastic point support is defined in global coordinate system


1.161.2 Background


■ Reference: none,

■ Analysis type: static linear/ 3D,


■ Load cases: dynamic temporal load FX = 1.00 kN,

Units

Metric System

Geometry

■ Section: HEB100 (European Profiles),

■ Height: 5.00 m.


380


Material S235


■ Elastic Punctual Support n°1 – Stiffness: KTX = 100,0 kN/m,

(global coordinate system) KTY = 100,0 kN/m,

KTZ = 100,0 kN/m,

KRX = 100,0 kN*m/°,

KRY = 100,0 kN*m/°,

KRZ = 100,0 kN*m/°,

1.161.2.2 Modeling



■ 6 nodes,

1.161.2.3 Results









381

1.162 Time history analysis – Verifies the displacements on shell element with linear elastic support (local coordinate system) subject to point dynamic temporal load

Test ID: 6567

Test status: Passed

1.162.1 Description

The test verifies displacements of a cantilever shell element subject to two points dynamic temporal loads. The shell has a linear elastic support at the bottom, defined in local coordinate system. The shell has 5x5m dimensions with 10cm thickness made of S235 steel.

The mesh is defined as Delaunay triangles and quadrangles T3-Q4 with 1m mesh size. The two loads are pointed at the top corner on x and y direction F=1kN. The test verifies the node displacements from the dynamic temporal loads case.

1.162.2 Background

Verifies horizontal displacements on a cantilever wall (shell element type). Wall is subject to two punctual dynamic temporal loads at top 1 kN in X and 1 kN in Y directions. The wall has one linear elastic support, defined in local coordinate system.


■ Reference: none

■ Analysis type: static planar / 3D

■ Element type: planar

■ Load cases: dynamic temporal load FX = 1,0 kN, FY = 1,0 kN

Units

Metric System

Geometry

■ Length 5 m

■ Height 5 m

■ Thickness 0,1 m


382


Material S235


■ Elastic Linear Support n°1 – Stiffness: KTX = 100,0 kN/m

(local coordinate system) KTY = 100,0 kN/m

KTZ = 100,0 kN/m

KRX = 100,0 kN*m/°

KRY = 100,0 kN*m/°

KRZ = 100,0 kN*m/°

1.162.2.2 Modeling



■ 36 nodes,

1.162.2.3 Results


displacement nod 3 (bottom) (D) mm 5.28 5.28 0,0%

displacement nod 36 (top) (D) mm 42.43 42.43 0,0%


383

1.163 NL static analysis on T/C point supports – Verifies displacements on linear elements and forces on supports operating in compression with elastic stiffness defined in local coordinate system

Test ID: 6576

Test status: Passed

1.163.1 Description

The test verifies a two-span frame response from non-linear static analysis. The structure is subject to 50kN/m gravitational uniform distributed load on one span. S beam elements have IPE500 cross section made of S235 steel.

The frame is supported by a fix point in the middle and two T/C point supports with KTx=1000kN/m stiffness. The T/C point supports are operating in compression. The T/C point supports are defined in global coordinate system. Displacements in linear elements and forces in point supports are verified from the non-linear static case.

1.164 NL static analysis on T/C point supports – Verifies displacements on linear elements and forces on supports operating in compression with elastic stiffness defined in global coordinate system

Test ID: 6577

Test status: Passed

1.164.1 Description

The test verifies a two-span frame response from non-linear static analysis. The structure is subject to 50kN/m gravitational uniform distributed load on one span. S beam elements have IPE500 cross section made of S235 steel.

The frame is supported by a fix point in the middle and two T/C point supports with KTx=1000kN/m stiffness. The T/C point supports are operating in compression. The T/C point supports are defined in global coordinate system. Displacements in linear elements and forces in point supports are verified from the non-linear static case.


384

1.165 Time history analysis – Verifies displacements for a rigid membrane model subject to time history analysis load case

Test ID: 6575

Test status: Passed

1.165.1 Description

The test verifies the displacements on a model made of rigid membrane elements resulted from a dynamic temporal load case. The structure is subject to 400kN/m linear load applied at the top. The load is defined as dynamic temporal with a harmonic function. The rigid membranes have 10 cm thickness made of C25/30 concrete. The structure is supported on four pinned linear supports. The mesh is defined as Delaunay triangles and quadrangles T3-Q4 with 0.1 m mesh size.

Displacements resulted from the dynamic temporal load case will be verified.

1.165.2 Background

Check the reaction, behavior and internal forces for a structure made entirely of “rigid membrane” surface elements subjected to a dynamic load.


■ Reference: none

■ Analysis type: dynamic / time history / bending rigid structure 3D

■ Element type: Planar (rigid mebrane)


Units

Metric System


385

Geometry


■ Thickness: 100mm


Material(s) concrete C25/30 is used.

Boundary conditions


■ Linear Support 1: Pinned




The core wall system is subjected to the following loads:

■ 1 linear dynamic load of 400kN/m:

1.165.2.2 Modeling


■ 5 planar elements: rigid membrane

■ 36 nodes

■ 4 rigid linear supports

■ 1 linear dynamic load

1.165.2.3 Results





386

1.166 Time history analysis – Verifies the displacements on a column with fixed support subject to dynamic temporal load at the top

Test ID: 6563

Test status: Passed

1.166.1 Description

The test verifies displacements of a cantilever column subject to dynamic temporal load. The column is fixed at the bottom and is subject to dynamic temporal load of 1.0kN on x direction at the top.


1.166.2 Background



■ Analysis type: static linear/ 3D,


■ Load cases: dynamic temporal load FX = 1.00 kN,

Units

Metric System

Geometry

■Section: HEB100 (European Profiles),

■ Height: H=5.00 m,


387


Material S235


■ Rigid Punctual Support n°1:

1.166.2.2 Modeling



■ 6 nodes,

1.166.2.3 Results


displacement nod 1 Dx mm 0 0 0,0%







388

1.167 Time history analysis – Verifies displacements and forces for bar elements subject to dynamic temporal load

Test ID: 6570

Test status: Passed

1.167.1 Description

The test verifies displacements and forces on a plane truss structure made entirely of “bar” type elements subject to dynamic temporal loads. The bar elements have 75x75 mm square cross section made of G40.21M-350W steel. The truss has one fixed support and one with Tx translations released.

The dynamic temporal load is pointed at the top left corner of the truss having Fx=10 kN. The dynamic temporal load is defined as a harmonic function with 200 rad/s pulsation for 20 seconds. Displacements (D) and axial force resulted from the dynamic temporal load case will be analyzed.

1.167.2 Background


■ Reference: none


■ Element type: linear (bar)


Units

Metric System

Geometry


■ Depth: h = 75mm

■ Width: b = 75mm


389



Boundary conditions


■ Punctual Support 1: Fixed


► Tx: free

► Ty: fixed

► Tz: fixed

► Rx: fixed

► Ry: fixed

► Rz: fixed

Loading



1.167.2.2 Modeling


■ 9 Linear elements: all Bar

■ 6 nodes



1.167.2.3 Results






390

1.168 Time history analysis - Verifies displacements, forces and bending moments for S beam elements structure subject to dynamic temporal loads

Test ID: 6572

Test status: Passed

1.168.1 Description

The test verifies displacements and forces on a plane truss structure made entirely of “S beam” type elements subject to dynamic temporal loads. The S beam elements have 75x75 mm square cross section made of G40.21M-350W steel. The truss has one pinned support and one with Tx and Ry restraints released.

The dynamic temporal load is pointed at the top left corner of the truss having Fx=50 kN. The dynamic temporal load is defined as a harmonic function with 2 rad/s pulsation for 20 seconds. Displacements (D), axial force and bending moments resulted from the dynamic temporal load case will be analyzed.

1.168.2 Background

Check the reaction, behavior and internal forces for a truss structure made entirely of “S Beam” elements subjected to a dynamic load.


■ Reference: none


■ Element type: linear (S beam)


Units

Metric System

Geometry


■ Depth: h = 75mm

■ Width: b = 75mm


391



Boundary conditions




► Tx: free

► Ty: fixed

► Tz: fixed

► Rx: fixed

► Ry: free

► Rz: fixed

Loading



1.168.2.2 Modeling


■ 9 Linear elements: all Sbeam elements

■ 75 nodes



1.168.2.3 Results







392

1.169 NL static analysis on T/C linear supports – Verifies displacements on planar elements and torsors on linear supports operating in compression with elastic stiffness defined in global coordinate system

Test ID: 6581

Test status: Passed

1.169.1 Description

The test verifies a two-span frame response from non-linear static analysis. The structure is subject to 100kN/m gravitational uniform distributed load on one span and 100kN point force on “x” direction.

The model consists in a shell element with 20cm thickness and a short beam Element with 60x60 cm section made of C25/30 concrete. The frame is supported by a fix point in the middle and two T/C linear supports with KTz=1000kN/m stiffness. The T/C linear supports are operating in compression. The T/C linear supports are defined in local coordinate system. 0.5m mesh size. Displacements in planar elements and torsors in linear supports are verified from the non-linear static case.

1.170 NL static analysis on T/C linear supports – Verifies displacements on planar elements and torsors on linear supports operating in tension with elastic stiffness defined in local coordinate system

Test ID: 6584

Test status: Passed

1.170.1 Description


The model consists in a shell element with 20cm thickness and a short beam Element with 60x60 cm section made of C25/30 concrete. The frame is supported by a fix point in the middle and two T/C linear supports with KTz=1000kN/m stiffness. The T/C linear supports are operating in tension.The T/C linear supports are defined in local coordinate system. 0.5m mesh size. Displacements in planar elements and torsors in linear supports are verified from the non-linear static case.

1.171 NL static analysis on T/C point supports – Verifies displacements on linear elements and forces on supports operating in tension with elastic stiffness defined in local coordinate system

Test ID: 6580

Test status: Passed

1.171.1 Description

The test verifies a two-span frame response from non-linear static analysis. The structure is subject to 50kN/m gravitational uniform distributed load on one span.

S beam elements have IPE500 cross section made of S235 steel. The frame is supported by a fix point in the middle and two T/C point supports with KTx=1000kN/m stiffness. The T/C point supports are operating in tension. The T/C point supports are defined in local coordinate system. Displacements in linear elements and forces in point supports are verified from the non-linear static case.


393

1.172 NL static analysis on T/C linear supports – Verifies displacements on planar elements and torsors on linear supports operating in compression with elastic stiffness defined in local coordinate system

Test ID: 6582

Test status: Passed

1.172.1 Description


The model consists in a shell element with 20cm thickness and a short beam Element with 60x60 cm section made of C25/30 concrete. The frame is supported by a fix point in the middle and two T/C linear supports with KTx=1000kN/m stiffness. The T/C linear supports are operating in compression. The T/C linear supports are defined in local coordinate system. 0.5m mesh size.Displacements in planar elements are verified from the non-linear static case.

1.173 NL static analysis on T/C linear supports – Verifies displacements on planar elements and torsors on linear supports operating in tension with elastic stiffness defined in global coordinate system

Test ID: 6583

Test status: Passed

1.173.1 Description


The model consists in a shell element with 20cm thickness and a short beam Element with 60x60 cm section made of C25/30 concrete. The frame is supported by a fix point in the middle and two T/C linear supports with KTz=1000kN/m stiffness. The T/C linear supports are operating in tension. The T/C linear supports are defined in global coordinate system. 0.5m mesh size. Displacements in planar elements and torsors in linear supports are verified from the non-linear static case.

1.174 NL static analysis on T/C planar supports – Verifies displacements on elements and torsors on supports operating in compression with elastic stiffness defined in global coordinate system

Test ID: 6585

Test status: Passed

1.174.1 Description


The model consists in a shell element with 20cm thickness and two short beam element with 60x60 cm (40x60 cm) section made of C25/30 concrete. The frame is supported by a fix point in the middle and two square shell elements which have T/C planar supports with KTz=1000kN/m stiffness. The T/C planar supports are operating in compression. The T/C planar supports are defined in global coordinate system. 0.5m mesh size. Displacements in planar elements and torsors in planar supports are verified from the non-linear static case.


394

1.175 NL static analysis on T/C planar supports – Verifies displacements on elements and torsors on supports operating in compression with elastic stiffness defined in local coordinate system

Test ID: 6586

Test status: Passed

1.175.1 Description


The model consists in a shell element with 20cm thickness and two short beam element with 60x60 cm (40x60 cm) section made of C25/30 concrete. The frame is supported by a fix point in the middle and two square shell elements which have T/C planar supports with KTz=1000kN/m stiffness. The T/C planar supports are operating in compression. The T/C planar supports are defined in local coordinate system. 0.5m mesh size.

Displacements in planar elements and torsors in planar supports are verified from the non-linear static case.

1.176 NL static analysis on T/C planar supports – Verifies displacements on elements and torsors on supports operating in tension with elastic stiffness defined in local coordinate system

Test ID: 6588

Test status: Passed

1.176.1 Description


The model consists in a shell element with 20cm thickness and two short beam element with 60x60 cm (40x60 cm) section made of C25/30 concrete. The frame is supported by a fix point in the middle and two square shell elements which have T/C planar supports with KTz=1000kN/m stiffness. The T/C planar supports are operating in tension. The T/C planar supports are defined in local coordinate system. 0.5m mesh size.


1.177 NL static analysis on T/C point supports – Verifies displacements on linear elements and forces on supports operating in tension with elastic stiffness defined in global coordinate system

Test ID: 6578

Test status: Passed

1.177.1 Description

The test verifies a two-span frame response from non-linear static analysis. The structure is subject to 50kN/m gravitational uniform distributed load on one span.

S beam elements have IPE500 cross section made of S235 steel. The frame is supported by a fix point in the middle and two T/C point supports with KTz=1000kN/m stiffness. The T/C point supports are operating in tension. The T/C point supports are defined in global coordinate system.

Displacements in linear elements and forces in point supports are verified from the non-linear static case.


395

1.178 Time history analysis – Verifies displacements and bending moments for a plate type element subject to dynamic temporal load case

Test ID: 6574

Test status: Passed

1.178.1 Description

The test verifies the displacements and bending moments on a plate type element resulted from a dynamic temporal load. The plate has 2x6 m in plane dimensions with 15 cm thickness made of C25/30 concrete. The plate is supported on four point supports. The plate is subject to 5kN/m2 gravitational uniform distributed load defined as dynamic temporal load. The mesh is defined as Delaunay triangles and quadrangles T3-Q4 with 0.1 m mesh size.

Displacements and bending moments resulted from the dynamic temporal load case will be verified.

1.178.2 Background

Check the reaction, behavior and internal forces for a structure made entirely of “plate” surface elements subjected to a dynamic load.


■ Reference: none

■ Analysis type: dynamic / time history / bending rigid structure 3D

■ Element type: Planar (plate)


Units

Metric System

Geometry


■ Thickness: 150mm


396


Material(s) concrete C25/30 is used.

Boundary conditions


■ Point Support 1:

Tx: fixed

Ty: fixed

Tz: fixed

Rz: fixed


Tz: fixed


Tz: fixed


Tz: fixed

The floor is subjected to the following loads:

■ 1 planar dynamic load of -5kN/m^2:

1.178.2.2 Modeling


■ 1 planar element: plate

■ 1281 nodes (mesh 100mm)

■ 4 point supports

■ 1 planar dynamic load

1.178.2.3 Results




Moment (MaxD) Mxx kN.m 8.99 8.99 0.0%

Moment (MaxD) Myy kN.m 37.30 37.30 0.0%


397

1.179 NL static analysis on T/C planar supports – Verifies displacements on elements and torsors on supports operating in tension with elastic stiffness defined in global coordinate system

Test ID: 6587

Test status: Passed

1.179.1 Description


The model consists in a shell element with 20cm thickness and two short beam element with 60x60 cm (40x60 cm) section made of C25/30 concrete. The frame is supported by a fix point in the middle and two square shell elements which have T/C planar supports with KTz=1000kN/m stiffness. The T/C planar supports are operating in tension. The T/C planar supports are defined in global coordinate system. 0.5m mesh size.



398

1.180 Elastic punctual (local coordinate system) supports in Linear static analysis – Verifies displacements on a cantilever column (S beam type)

Test ID: 6605

Test status: Passed

1.180.1 Description

This test verifies the displacements on a cantilever column subject to horizontal point force and supported on an elastic point support. The column is a HEB100 european profile made of S235 steel with a 5 m height, The elastic point support is defined to have KTx=KTy=KTz=100kN/m and KRx=KRy=KRz=100kNm/° stiffness.

The elastic point support is defined in local coordinate system. Nodes displacements are verified after performing static linear analysis on the model.

1.180.2 Background


■ Reference: none

■ Analysis type: Elastic punctual (local coordinate system) supports in Linear Static analysis


■ Load cases: point load Fx = 1,0 kN

Units

Metric System

Geometry

Cross sections:


■ Height 5 m


Material S235


399


■ Elastic Point Support in local coordinate system

■ Stiffness: (KTX, KTY, KTZ) = 100 kN/m, (KRX, KRY, KRY) =100 kNm/°

1.180.2.2 Modeling


■ 1 Linear element: S beam

■ 6 nodes

1.180.2.3 Results


displacement nod 1 DX mm 10.00 10.00 0.0%






displacement nod 1 DZ mm -10.02 -10.02 0.0%







400

1.181 T/C planar support (global coordinate system) in Non-Linear static analysis – Verifies displacements on a horizontal plate (shell type) subject to uniform distributed planar load

Test ID: 6612

Test status: Passed

1.181.1 Description

This test verifies the displacements on a horizontal shell plate subject to gravitationalplanar uniform distributed load supported on an T/C planar support. The shell has 20cm thickness and is made of C25/30 concrete. The T/C planar support is defined to have KTx=KTy=KTz=100kN/m and KRx=KRy=KRz=100kNm/° stiffness.

The T/C planar support is defined in global coordinate system. Nodes displacements are verified after performing static non-linear analysis on the model.

1.181.2 Background



■ Analysis type: Elastic planar (global coordinate system) supports in NL Static analysis,

■ Element type: plate,

■ Load cases: area load Fz = -1.00 kN/m2.

Units

Metric System

Geometry

Cross sections:

■ Plate thickness: h= 20 cm,

■ Length*width: L*b= 500x500 cm.


Material: C25/30


401


■ Elastic planar (global coordinate system) supports in NL Static analysis,

■ Stiffness: (KTX, KTY, KTZ)= 100 kN/m, (KRX, KRY, KRY) =100 kNm/°,

1.181.2.2 Modeling


■ 1 planar element: plate,

■ 9 nodes.

1.181.2.3 Results












402

1.182 Elastic linear (global coordinate system) support in Linear static analysis – Verifies displacements on a S type beam subject to point force at midspan

Test ID: 6606

Test status: Passed

1.182.1 Description

This test verifies the displacements on a horizontal S type beam subject to gravitational point force and supported on an elastic linear support. The S beam is a HEB100 european profile made of S235 steel with a 5 m length. The elastic linear support is defined to have KTx=KTy=KTz=100kN/m and KRx=KRy=KRz=100kNm/° stiffness.

The elastic linear support is defined in global coordinate system. Nodes displacements are verified after performing static linear analysis on the model.

1.182.2 Background


■ Reference: none

■ Analysis type: Elastic linear (global coordinate system) supports in Linear Static analysis



Units

Metric System

Geometry

Cross sections:


■ Length 5 m


Material S235


■ Elastic linear (global coordinate system) supports in Linear Static analysis


1.182.2.2 Modeling



■ 6 nodes


403

1.182.2.3 Results









404

1.183 NL static analysis on strut element type - Verifies nodal displacements and forces in strut after performing NL static analysis

Test ID: 6617

Test status: Passed

1.183.1 Description

The test verifies the response of a braced frame subject to horizontal point load after performing NL static analysis on the model. The structure consists of S beam to define the frame and a diagonal strut. The frame is fixed at the base by two point supports. Horizontal point force is applied at the beam column intersection.

Horizontal nodes displacements and axial forces in the strut element resulted from the 10 steps load application are verified.


405

1.184 T/C punctual (local coordinate system) supports in Non-Linear static analysis – Verifies displacements on a cantilever column (S beam type)

Test ID: 6609

Test status: Passed

1.184.1 Description

This test verifies the displacements on a cantilever column subject to horizontal point force and supported on an T/C point support defined to operate in compression. The column is a HEB100 european profile made of S235 steel with a 5 m height. The T/C point support is defined to have KTx=KTy=KTz=100kN/m and KRx=KRy=KRz=100kNm/° stiffness.The T/C point support is defined in local coordinate system.

Nodes displacements are verified after performing static non-linear analysis on the model.

1.184.2 Background


■ Reference: none

■ Analysis type: Elastic punctual (local coordinate system) supports in NL Static analysis



Units

Metric System

Geometry

Cross sections:


■ Height 5 m


Material S235


406


■ Elastic T/C point Support in local coordinate system


1.184.2.2 Modeling



■ 6 nodes

1.184.2.3 Results















407

1.185 Elastic linear (local coordinate system) support in Linear static analysis – Verifies displacements on a S type beam subject to point force at midspan

Test ID: 6607

Test status: Passed

1.185.1 Description

This test verifies the displacements on a horizontal S type beam subject to gravitational point force and supported on an elastic linear support. The S beam is a HEB100 european profile made of S235 steel with a 5 m length. The elastic linear support is defined to have KTx=KTy=KTz=100kN/m and KRx=KRy=KRz=100kNm/° stiffness.

The elastic linear support is defined in local coordinate system.Nodes displacements are verified after performing static linear analysis on the model.

1.185.2 Background


■ Reference: none

■ Analysis type: Elastic linear (local coordinate system) supports in Linear Static analysis



Units

Metric System

Geometry

Cross sections:


■ Lenght 5 m


Material S235


■ Elastic linear (local coordinate system) supports in Linear Static analysis


1.185.2.2 Modeling



■ 6 nodes


408

1.185.2.3 Results









409

1.186 T/C linear (local coordinate system) support in Non-Linear static analysis – Verifies displacements on a S type beam subject to point force at midspan

Test ID: 6613

Test status: Passed

1.186.1 Description

This test verifies the displacements on a horizontal S type beam subject to gravitational point force and supported on an T/C linear support. The S beam is a HEB100 european profile made of S235 steel with a 5 m length. The T/C linear support is defined to have KTx=KTy=KTz=100kN/m and KRx=KRy=KRz=100kNm/° stiffness. The T/C linear support is defined in local coordinate system and imposed to operate in compression.



410

1.187 T/C linear (global coordinate system) support in Non-Linear static analysis – Verifies displacements on a S type beam subject to point force at midspan

Test ID: 6610

Test status: Passed

1.187.1 Description

This test verifies the displacements on a horizontal S type beam subject to gravitational point force and supported on an T/C linear support. The S beam is a HEB100 european profile made of S235 steel with a 5 m length. The T/C linear support is defined to have KTx=KTy=KTz=100kN/m and KRx=KRy=KRz=100kNm/° stiffness. The T/C linear support is defined in global coordinate system and imposed to operate in compression.


1.187.2 Background


■ Reference: none

■ Analysis type: Elastic linear (global coordinate system) supports in NL Static analysis



Units

Metric System

Geometry

Cross sections:


■ Lenght 5 m


Material S235


■ Elastic T/C linear (global coordinate system) supports in NL Static analysis



411

1.187.2.2 Modeling



■ 6 nodes

1.187.2.3 Results




displacement nod 3 DZ mm

-4.05 -4.05 0.0%


displacement nod 5 DZ mm

-3.99 -3.99 0.0%



412

1.188 NL static analysis on membrane – Verifies nodal displacements and forces in the planar element after performing NL static analysis

Test ID: 6618

Test status: Passed

1.188.1 Description

The test verifies the response of a membrane subject to uniform distributed load after performing Non-Linear static analysis. The membrane has 20cm thickness and is made of C25/30 concrete and is fixed at the base by a linear support. Uniform distributed load is applied on the top edge with a value of 50kN, gravitationally.

Forces in the membrane and nodal displacements are verified from the Non-Linear static case.


413

1.189 Elastic planar support (global coordinate system) in Linear static analysis – Verifies displacements on a horizontal plate (shell type) subject to uniform distributed planar load

Test ID: 6608

Test status: Passed

1.189.1 Description

This test verifies the displacements on a horizontal shell plate subject to gravitational Planar uniform distributed load supported on an elastic planar support. The shell has 20cm thickness and is made of C25/30 concrete.The elastic planar support is defined to have KTx=KTy=KTz=100kN/m and KRx=KRy=KRz=100kNm/° stiffness. The elastic planar support is defined in global coordinate system.

Nodes displacements are verified after performing static linear analysis on the model.

1.189.2 Background



■ Analysis type: Elastic planar (global coordinate system) supports in Linear Static analysis,

■ Element type: plate,

■ Load cases: area load Fz = -1.00 kN/m2,

Units

Metric System

Geometry

Cross sections:

■ plate thickness: h= 20 cm,

■ Length*width: L*b=500m x 500 cm.


Material C25/30


414


■ Elastic planar (global coordinate system) supports in Linear Static analysis


1.189.2.2 Modeling


■ 1 planar element: plate

■ 9 nodes

1.189.2.3 Results












415

1.190 NL static analysis on variable beam steel frame - Verifies nodes displacements after performing NL static analysis

Test ID: 6614

Test status: Passed

1.190.1 Description

The test verifies the response of a steel frame after performing NL static analysis. The linear elements are "variable beam" type, with doubly symmetric cross section, made of S235 steel. The frame is fixed in two point supports, defined in global coordinate system. Uniform linear load of 10 kN/m on the beam and 5kN point force in x direction in the column-beam node. The nodal displacements from the 10 number load steps are verified.

The results are validated with another independent software.

1.190.2 Background

The test verifies result from Non-Linear analysis for a simple frame structure made of variable beam type elements. The frame is subject to point and uniform distributed load.


■ 2D structure – linear elements only

■ Element type: variable beam

■ Analysis type: Non-Linear analysis

■ Software version: AD2019 build 14030

■ Results are validated with another independent software.

Units

Metric System

Geometry

■ Base length L=5.0 m

■ Height H=5.0 m


416

Linear elements

■ Type: variable beam

■ Cross section (variable beam):

Start point: End point:


Isotropic material:




Boundary conditions

■ Punctual supports;

■ Type: Fixed


Loading

■ Dead load case: Fz=10kN/m2 uniform distributed load; Fx=5kN point load


Non-Linear analysis definition




■ All linear elements are ‘variable beam’ type

Verified results


■ Horizontal displacements for the first 10 load steps:


417

Comparison

Results are compared with results coming from the identical model created and calculated by using another independent FEM software.


Node numbering in AD

Description Symbol Unit AD 2019 Reference Difference

displacement node 21 Dx mm 0.327 0.324 0.92%











418

1.191 Verify the behavior of elastic displacement release on one end of a beam in static analysis (200kN/m)

Test ID: 6620

Test status: Passed

1.191.1 Description

The model comprises of two frames. One frame having elements with default fixed ends and the other having applied an elastic displacement release at the start extremity (1). The cross-section of the linear elements is Rectangular 20x30cm and the material is Reinforced Concrete C25/30. The rigidity applied to the displacement of the beam end node is 200kN/m. Both frames are subjected to a horizontal concentrated load of 100kN at the beams end.

1.192 Torsors/Groups of walls with rotated local axes, z+ and z- (load 10kN/m at top on z direction) - check MX, MY / Group

Test ID: 6621

Test status: Passed

1.192.1 Description

There are 4 walls with rotated local axes and z in same direction in one Group and 4 walls with rotated local axes and z in same direction in the second group, but with z in the opposite sense than the first group. All walls are: 3x5m, 20cm thick shell elements, fixed supported at the base and free on all other edges, loaded at top with a linear 10kN/m load on the local z direction and same sense. All walls are in the same plane, perpendicular to global XOY and at an angle about the XOZ plane.

Check the results for MX/Group and TY/Group (Global coordinate system): should be identical for the two groups, independent of the local axes position on the individual walls.


419

1.193 Nonlinear static analysis on 3D model with rigid diaphragm defined as shell with DOF constraint subjected to horizontal and gravitational loads

Test ID: 6624

Test status: Passed

1.193.1 Description

The test verifies the response of a 3D structure after performing Nonlinear static analysis. The model consists of linear elements and a planar element defined as shell. To simulate the rigid diaphragm effect, a DOF constraint is imposed having master node placed in the center of the shell (center of rigidity) and slave nodes in the mesh points. The master-slave connection is defined to have Tx, Ty and Rz restrained.

The linear elements have 20x30 cm cross section, while the shell has 20 cm thickness. All elements are made of C25/30 concrete. The structure is subjected to horizontal X and Y linear load and gravitational planar load.

Nodes displacements and forces on the linear and planar elements are verified after performing Nonlinear static analysis on the model. Results from 10 steps are verified and compared with results obtained from another independent software.

1.193.2 Background


■ 3D structure – linear and planar elements

■ Element type: shell, S beam

■ Analysis type: Non-Linear analysis

Units

Metric System

Geometry

■ Base length: L = 8.0 m

■ Base width: l = 5.0 m

■ Height: H = 5.0 m

■ Cross sections:


420

columns: beams:


C25/30 concrete:

■ Mass Density: ρ = 2500 kg/m3

■ Young's Modulus: E = 31.47 GPa

■ Poisson's Ratio: ν = 0.2

Boundary conditions

■ Punctual supports;

■ Type: Fixed


Loading

■ Dead load case: Fx = 100 kN/m, Fy = -100 kN/m linear load

■ Dead load case: Fz = -20 kN/m2 planar load

DOF constraint definition:

■ Master node defined in the center of the planar element (center of rigidity)

■ Slave nodes defined on each mesh points (0.5 m mesh size)


Non-Linear analysis definition


421



■ Number of planar elements: 1


Verified results


■ Displacements for the first 10 load steps;

■ Forces in linear elements;

■ Forces in planar elements.

Comparison

Results are compared with results coming from the identical model created and calculated by using another independent FEM software.

Calculated results

Mesh model preview

Description Symbol Unit Step Position AD 2019 Reference Difference

Axial force in column 21 Fx kN

1 top 52.01 52.66 1.25%

Axial force in column 21 Fx kN bottom 53.41 53.41 0.00%


2 top 104.39 105.74 1.29%



3 top 156.77 159.28 1.60%



4 top 209.15 213.26 1.97%



5 top 261.53 267.73 2.37%



6 top 313.91 322.68 2.79%


Axial force in column 21 Fx kN 7 top 366.29 378.15 3.24%


422



8 top 418.67 434.14 3.70%



9 top 471.05 490.68 4.17%



10 top 523.43 547.79 4.65%


Description Step Symbol Unit AD 2019 Reference Difference

Displacement of node 57 10 Dx cm 11.74 11.75 0.09 %

Displacement of node 57 10 Dy cm 36.39 36.42 0.08 %

Displacement of node 57 10 Dz cm 0.14 0.14 0.00 %


423

1.194 NL static analysis on 3D model with windwall defined as rigid diaphragm subject to horizontal and gravitational loads.

Test ID: 6625

Test status: Passed

1.194.1 Description

The test verifies the response of a 3D structure after performing Non-Linear static analysis. The model consists of linear elements and a windwall defined as rigid diaphragm. Self weight is disabled for the windwall. The linear elements have 20x30cm cross section, while the windwall has 20cm thickness. All elements are made of C25/30 concrete. The structure is subject to horizontalX and Y linear load and gravitational planar load.

Nodes displacements and forces on the linear elements are verified after performing Non-Linear static analysis on the model. Results from 10 steps are verified.

1.195 Torsors/Groups of walls with rotated local axes, z+ and z- (load 10kN/m at top on z direction) - check MX, TY / Group, Mf and Tyz

Test ID: 6622

Test status: Passed

1.195.1 Description

There are 4 walls with rotated local axes and z in same direction in one Group and 4 walls with rotated local axes and z in same direction in the second group, but with z in the opposite sense than the first group. All walls are: 3x5m, 20cm thick shell elements, fixed supported at the base and free on all other edges, loaded at top with a linear 10kN/m load on the local z direction and same sense. All walls are in the same plane, perpendicular to global XOY and parallel to the XOZ plane.

Check the results for MX/Group and TY/Group (Global coordinate system), should be identical for the two groups, independent of the local axes position on the individual walls, Mf and Tyz (local coordinate system).

1.196 Torsors/Groups of walls with rotated local axes, z+ and z- (load 10kN at top in the walls plane) - check MX, TY / Group, Mz and Txy

Test ID: 6627

Test status: Passed

1.196.1 Description

There are 4 walls with rotated local axes and z in same direction in one Group and 4 walls with rotated local axes and z in same direction in the second group, but with z in the opposite sense than the first group. All walls are: 3x5m, 20cm thick shell elements, fixed supported at the base and free on all other edges, loaded at top with a concentrated 10kN load in the walls plane. All walls are in the same plane, perpendicular to global XOY and parallel to the YOZ plane.

Check the results for MX/Group and TY/Group (Global coordinate system), should be identical for the two groups, independent of the local axes position on the individual walls, Mz and Txy (local coordinate system).


424

1.197 Torsors/Groups of walls with rotated local axes, z+ and z- (load 10kN/m at top on z direction) - check MY, TX, Mf and Tyz

Test ID: 6628

Test status: Passed

1.197.1 Description

There are 4 walls with rotated local axes and z in same direction in one Group and 4 walls with rotated local axes and z in same direction in the second group, but with z in the opposite sense than the first group. All walls are: 3x5m, 20cm thick shell elements, fixed supported at the base and free on all other edges, loaded at top with a linear 10kN/m load on the local z direction and same sense. All walls are in the same plane, perpendicular to global XOY and parallel to the YOZ plane. Check the results for MY/Group and TX/Group (Global coordinate system), should be identical for the two groups, independent of the local axes position on the individual walls, Mf and Tyz (local coordinate system).

1.198 Verify the behavior of elastic rotational releases on both ends of a beam in static analysis (100kNm/deg)

Test ID: 6619

Test status: Passed

1.198.1 Description

The model comprises of two frames. One frame having elements with default fixed ends and the other having applied an elastic rotational release at both ends. The cross-section of the linear elements is Rectangular 20x30cm and the material is Reinforced Concrete C25/30. The rigidity applied to the rotation of the beam end nodes is 100kNm/degree. Both frames are subjected to a vertical distributed load of -10kN/m.

1.199 Torsors/Groups of walls with rotated local axes, z+ and z- (load 10kN at top in the walls plane) - check MY, TX / Group, Mz, Txy

Test ID: 6623

Test status: Passed

1.199.1 Description

There are 4 walls with rotated local axes and z in same direction in one Group and 4 walls with rotated local axes and z in same direction in the second group, but with z in the opposite sense than the first group. All walls are: 3x5m, 20cm thick shell elements, fixed supported at the base and free on all other edges, loaded at top with a concentrated 10kN load in the walls plane and same sense. All walls are in the same plane, perpendicular to global XOY and parallel to the XOZ plane.

Check the results for MY/Group and TX/Group (Global coordinate system), should be identical for the two groups, independent of the local axes position on the individual walls, Mz and Txy (local coordinate system).

1.200 Torsors/Groups of walls with rotated local axes, z+ and z- (load 10kN at top at angle with walls plane) - check Mz, Mf, Txy, Tyz

Test ID: 6626

Test status: Passed

1.200.1 Description

There are 4 walls with rotated local axes and z in same direction in one Group and 4 walls with rotated local axes and z in same direction in the second group, but with z in the opposite sense than the first group. All walls are: 3x5m, 20cm thick shell elements, fixed supported at the base and free on all other edges, loaded at top with a concentrated 10kN load at angle with the walls plane. All walls are in the same plane, perpendicular to global XOY and at an angle relative to the XOZ plane.

Check the results for MX/Group, MY/Group and TX/Group (Global coordinate system), should be identical for the two groups, independent of the local axes position on the individual walls, Mz, Mf, Txy and Tyz (local coordinate system).


425

1.201 Verifying the resultant forces on single walls

Test ID: 6692

Test status: Passed

1.201.1 Description

The test verifies the sign of the resultant forces generated on single walls. The walls have different local axes.

1.202 Verifying the sum of actions on supports

Test ID: 6694

Test status: Passed

1.202.1 Description

The model consists of a single storey reinforced concrete structure, having 4 column: 2 of 4 meters and 2 of 5 meters. The structure is loaded at the top by two lateral loads, one on each directions. The resulting bending moments on the supports are verified.

1.203 Pushover Analysis - Verifies the Pushover load distribution - Concentrated

Test ID: 6698

Test status: Passed

1.203.1 Description

The model consists of a 3-storeys reinforced concrete structure. The storeys have different areas.

The structure is loaded by dead loads (self weight and applied loads), live loads, wind loads and snow loads. Seismic load cases are also generated.

Two Pushover Load Types are defined:

- Load Type 1 - the distribution is set to "concentrated" and the point of application to "center of mass". The maximum total lateral load is set to "Percentage of the total gravity loads"

- Load Type 2 - the distribution is set to "concentrated" and the point of application to "surface distributed on slab". The maximum total lateral load is set to "Percentage of the total gravity loads"

For each load type, the "Maximum total lateral load" and the loads distributed at each storey are verified wtih analytical results.

1.204 Pushover Analysis - Verifies the Pushover load distribution - Triangular

Test ID: 6700

Test status: Passed

1.204.1 Description




- Load Type 1 - the distribution is set to "triangular" and the point of application to "center of mass". The maximum total lateral load is set to "Percentage of the total gravity loads"

- Load Type 2 - the distribution is set to "triangular" and the point of application to "surface distributed on slab". The maximum total lateral load is set to "Percentage of the total gravity loads"



426

1.205 Pushover Analysis - Verifies the Pushover load distribution - Uniform

Test ID: 6699

Test status: Passed

1.205.1 Description




- Load Type 1 - the distribution is set to "uniform" and the point of application to "center of mass". The maximum total lateral load is set to "Percentage of the total gravity loads"

- Load Type 2 - the distribution is set to "uniform" and the point of application to "surface distributed on slab". The maximum total lateral load is set to "Percentage of the total gravity loads"


1.206 Pushover Analysis: Verifying the Pushover Analysis on a converted model (Advance Design 2020.2)

Test ID: 6718

Test status: Passed

1.206.1 Description

The aim of the test is to verify the generation of Pushover loads and the definition of Plastic Hinges on a model after conversion.

The model consists of a 2 storey structure, made of both reinforced concrete and steel elements.

The structure is loaded by dead loads (8.5 kN/m2) and live loads (6 kN/m2).

During the test:

- the Pushover loads cases are generated:

- 4 - Pushover 1 X+ - Load type 1, the distribution is set to "concentrated", the point of application to "center of mass" and the maximum total load to "percentage of the total gravity loads"

- 5 - Pushover 2 X+ - Load type 1, the distribution is set to "uniform", the point of application to "surface distributed on slab" and the maximum total load to "percentage of the total gravity loads"

- the Plastic Hinges are defined for several steel and reinforced concrete elements

- the Pushover Analysis is run

- the "Flexural plastic hinges status by load case", the "Axial plastic hinges status by load case" and the "Overstrength ratio (Alfa_1/Alfa_u)" reports are generated.


427

1.207 EC3/ NF EN1993-1-1/NA France: Pushover Analysis - Verifies the limit states and status of a steel EC8-3 flexural plastic hinge

Test ID: 6740

Test status: Passed

1.207.1 Description

The model consists of two identical steel S235 linear elements, having an HEB300 cross-section. The elements are fixed supported at both ends.

For both elements an EC8-3 plastic hinge is defined on Ry and Rz DOF''s only at one end in order to prevent instability when the plastic hinge is developed.

For one element the cross-section class is defined as class 1, while for the other it is defined as class 2.

Two Pushover load cases are defined:

- a load case on the X direction with a user defined concentrated load of 5000kN applied at midspan

- a load case on the Y direction with a user defined concentrated load of 2500kN applied at midspan

The Pushover Analysis is defined with 50 steps.

The aim of the test is to verify the limit states, the plastic hinge rotation at each step and the sequence of plastic hinge statuses. The results are validated with an independent software.

During the test, the Pushover analysis is run with and without the Steel design. The "Flexural plastic hinges status by load step" report is generated for each run.

1.208 EC3/ NF EN 1993-1-1/NA - France: Pushover Analysis - Verifies the status of a steel FEMA flexural plastic hinge

Test ID: 6738

Test status: Passed

1.208.1 Description

The model consists of a steel S235 linear element, having an HEB300 cross-section. The element is fixed supported at both ends.

A FEMA plastic hinge is defined on Ry and Rz DOF''s only at one end in order to prevent instability when the plastic hinge is developed.





The aim of the test is to verify the plastic hinge rotation at each step and the sequence of plastic hinge statuses. The results are validated with an independent software.



428

1.209 Verifying the resultant forces on a group of walls

Test ID: 6693

Test status: Passed

1.209.1 Description

The test verifies the generation of the resultant forces on a group of walls. The model consists of two perpendicular reinforced concrete walls. The walls have fixed linear supports at the base and linear loads applied at the top. The resultant forces generated by Advance Design on the group of walls are validated by hand calculation – the resultant forces are derived from the individual forces on each wall.

1.209.2 Background


■ 3D structure

■ Element type: Planar - shell

■ Analysis type: Linear analysis

■ Software version: AD2020 build 15107

■ Results are validated by hand calculation.

Units

Metric System

Geometry

■ Length of wall 1=3.00m

■ Length of wall 2=6.00m

■ Height of wall 1 and 2=5.0 m

Linear elements

■ Type: shell


429

■ Thickness= 20 cm


Isotropic material, C25/30:


■ Young's Modulus E = 31.475 GPa


Boundary conditions

■ Linear supports;

■ Type: Fixed


Loading

■ Live load case: Fz=-3.33kN/m uniform distributed load – top of wall 1 and 2

Fx= 3.33kN/m uniform distributed load – top of wall 2

Fy= 3.33kN/m uniform distributed load – top of wall 1



■ Number of planar elements: 2

■ Number of linear supports: 2

■ Mesh Type: Delauney

■ Mesh element size: 0.75 m

Verified results


■ Resultant forces on the group of walls (wall 1+2)

NZ / Goup resultant axial force and MX / Group -resultant Mx bending moment on the group of walls


430

Description Value Unit

MY / Group up 7.03 kN/m

MY / Group down 91.42 kN/m

MX / Group up -3.59 kN/m

MX / Group down -45.57 kN/m

TY / Group up 10.00 kN

TY / Group down 9.85 kN

TX / Group up 20.00 kN

TX / Group down 19.75 kN

NZ / Group up -29.87 kN

NZ / Group down -29.94 kN

Resultant forces on the group of walls – on global coordinates

Comparison

The resultant forces generated by Advance Design on the group of walls are compared with those obtained by hand calculation – the resultant forces are derived from the individual forces on each wall.


The resultant forces on each wall are used as input data.

NZ axial force and MX bending moment on wall 2 – on global coordinates

Description Wall 1 Wall 2 Unit

MY / up 1.37 3.71 kN/m

MY / down 43.54 25.86 kN/m

MX / up -2.05 -5.43 kN/m

MX / down 1.33 -90.95 kN/m

TY / up 5.76 4.24 kN

TY / down -1.50 11.34

kN

TX / up 9.60 10.40 kN

TX / down 11.77 7.98 kN

NZ / up -11.25 -18.61 kN

NZ / down -24.66 -5.28 kN

Resultant forces on wall 1 and wall 2 – on global coordinates


431

Firstly, the center of weight, about which the resultant forces are computed, for the group of the walls is calculated. Then, the corresponding lever arm for the axial forces of the walls.

Center of weight of the group of walls and lever arm of the axial forces

MY/Group_up = MY/Group_up_wall1 + MY/Group_up_wall1 + NZ_up_wall1*x_w1 + NZ_up_wall2*x_w2 =

= 1.37kN/m + 3.71kN/m - (-)11.25kN *1m + (-)18.61kN * 0.5m = 7.03 kN/m

MX/Group_up= MX/Group_up_wall1 + MX/Group_up_wall1 + NZ_up_wall1*y_w1 + NZ_up_wall2*y_w2

= -2.05kN/m + (-)5.43kN/m - (-11.25)kN*2m + (-)18.61kN/m*1m = -3.59 kN/m

TY/Group_up = TY/Group_up_wall1 + TY/Group_up_wall2 = 5.76kN + 4.24kN = 10 kN

TX/Group_up = TX/Group_up wall1 + TX/Group_up_wall2 = 9.60kN + 10.40kN = 20 kN

NZ/Group_up = NZ/Group_up_wall1 + NZ/Group_up_wall2 = -11.25kN + (-)18.61kN = -29.86kN

Where:

x_w1 = (-1) and is the projection on X of the distance between the resultant axial resultant N on wall 1 (NZ_wall1) and the geometrical centre of the group

x_w2 = 0.5 and is the projection on X of the distance between the resultant axial resultant N on wall 2 (NZ_wall2) and the geometrical centre of the group

y_w1 = (-2) and is the projection on Y of the distance between the resultant axial resultant N on wall 1 (NZ_wall1) and the geometrical centre of the group

y_w2 = 1 and is the projection on Y of the distance between the resultant axial resultant N on wall 2 (NZ_wall2) and the geometrical centre of the group


432

It is done similarly for the base of the group of walls, finally obtaining:

Description AD Hand calculation

Unit Deviation

MY / up 7.03 7.03 kN/m 0.07%

MY / down 91.42 91.42 kN/m 0.00%

MX / up -3.59 -3.59 kN/m

0.00%

MX / down -45.57 -45.58 kN/m -0.02%

TY / up 10.00 10.00 kN 0.00%

TY / down 9.85 9.84 kN 0.10%

TX / up 20.00 20.00 kN

0.00%

TX / down 19.75 19.75 kN 0.00%

NZ / up -29.87 -29.86 kN

0.03%

NZ / down -29.94 -29.94 kN 0.00%

Verification of the resultant forces on a group of walls


433

1.210 AISC: Pushover Analysis - Verifies the status of a steel FEMA flexural plastic hinge

Test ID: 6739

Test status: Passed

1.210.1 Description


A FEMA plastic hinge is defined on Ry and Rz DOF''s only at one end in order to prevent instability when the plastic hinge is developed.








434

1.211 Time history analysis – Verifies the displacements on shell element with linear elastic support (global coordinate system) subject to point dynamic temporal load

Test ID: 6566

Test status: Passed

1.211.1 Description

The test verifies displacements of a cantilever shell element subject to two points dynamic temporal loads. The shell has a linear elastic support at the bottom, defined in global coordinate system. The shell has 5x5m dimensions with 10cm thickness made of S235 steel. The mesh is defined as Delaunay triangles and quadrangles T3-Q4 with 1m mesh size. The two loads are pointed at the top corner on x and y direction F=1kN. The test verifies the node displacements from the dynamic temporal loads case.

1.211.2 Background

Verifies horizontal displacements on a cantilever wall (shell element type). Wall is subject to two punctual dynamic temporal loads at top 1 kN in X and 1 kN in Y directions. The wall has one linear elastic support, defined in global coordinate system.


■ Reference: none

■ Analysis type: static planar / 3D

■ Element type: planar

■ Load cases: dynamic temporal load FX = 1,0 kN, FY = 1,0 kN

Units

Metric System

Geometry

■ Length 5 m

■ Height 5 m

■ Thickness 0,1 m


435


Material S235


■ Elastic Linear Support n°1 – Stiffness: KTX = 100,0 kN/m

(global coordinate system) KTY = 100,0 kN/m

KTZ = 100,0 kN/m

KRX = 100,0 kN*m/°

KRY = 100,0 kN*m/°

KRZ = 100,0 kN*m/°

1.211.2.2 Modeling



■ 36 nodes,

1.211.2.3 Results


displacement nod 3 (bottom) (D) mm 5.28 5.28 0,0%

displacement nod 36 (top) (D) mm 42.43 42.43 0,0%


436

1.212 AISC: Pushover Analysis - Verifies the status of a steel EC8-3 flexural plastic hinge

Test ID: 6741

Test status: Passed

1.212.1 Description


An EC8-3 plastic hinge is defined on Ry and Rz DOF''s only at one end in order to prevent instability when the plastic hinge is developed.






During the test, the Pushover analysis is run with and without the Steel design. The "Flexural plastic hinges status by load step" report is generated for each run

1.213 Pushover Analysis - Verifies the Pushover load distribution - Parabolic

Test ID: 6701

Test status: Passed

1.213.1 Description




- Load Type 1 - the distribution is set to "parabolic" and the point of application to "center of mass". The maximum total lateral load is set to "Percentage of the total gravity loads"

- Load Type 2 - the distribution is set to "parabolic" and the point of application to "surface distributed on slab". The maximum total lateral load is set to "Percentage of the total gravity loads"


Advance Validation Guide-Volume I - Graitec · 2020. 8. 21. · ADVANCE VALIDATION GUIDE 3 INTRODUCTION The Advance Design Validation Guide 2021 outlines a vast set of practical test

Documents