Date

(v3.14)

ArcelorMittal Composite Bridge Predesign

Preliminary design software for composite bridges

PRELIMINARY DESIGN REPORT

Company : Universitatea Tehnica Cluj-NapocaUser name : Petrut MirelaProject name : Structuri compuse otel-betonProject reference :Comment :Date : 31.01.2014

Page 1 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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User name : Petrut Mirela

E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

BRIEF DESCRIPTION OF SOFTWARE

Purpose of software

The ACOBRI software is used for preliminary design of the rolled-steel main beams of a composite steel and concrete bridgesuperstructure. It is intended as a means of checking the feasibility of a design solution, optimizing a preliminary design throughappropriate choice of parameters, and estimating the main quantities involved. It is not intended to produce a construction designcalculation report

Scope of application

The kinds of bridges handled are road bridges, railway bridges, and footbridges with superstructures made up of steel beams supportinga participating reinforced concrete slab or with filler-beam decks. Beams may be simply supported or continuous in the case of multi-spanbridges. Calculations are performed in accordance with the following design codes: French codes (2004), Eurocodes ENV, EurocodesENV + French NAD and DIN Fachberichte (2003).

Method of analysis and design checks

On the basis of a definition of bridge geometry, materials, and loads, the program calculates internal forces and moments in the mainbeams under the effect of: dead load, superimposed dead load and live load; concrete shrinkage; temperature differential; any supportheight adjustment. The analysis is performed with a finite element solver, using a grid model. The structure is discretized by bar elementscorresponding to segments of the main beams, longitudinal and transverse strips of slab, and any crossbeams. For calculating flexuraland torsional stiffnesses, account is taken of creep and any concrete cracking, depending on the type of internal forces or moments.Longitudinal and transverse influence lines are used to determine the position of mobile loads producing extreme effects at the differentcross-sections considered.

To establish preliminary design of beams, the program calculates the main load combinations for the bridge in the in-service phase. Thedesign checks for the serviceability limit state and ultimate limit state concern stresses in the beams and in the longitudinalreinforcement, compressive stresses in the concrete, the ultimate moment resistance, crack control and the vertical deformation andstress variation in beams at the fatigue limit state. The software also calculates reactions at supports and the number of connectorsrequired to transfer shear forces between the beams and the slab. For filler-beam decks, the calculations include a number of specialfeatures in accordance with the specifications of the design codes.

Detailed information on the scope of application of the software, on the assumptions, methods, and approximations used and on thecalculations performed are provided in the users manual and in the on-line help module.

Comments :

The program can deal with straight, unskewed bridges with a horizontal slab of constant thickness. If the bridge to be analyzed does notmatch these assumptions but does not vary substantively from them, the software can be used for an approximate calculation. In thiscase the user will have to use engineering judgment both to determine the adaptations to be made to the data entered and to assess therepresentativity of results given and, as required, adjust or complete the calculations and checks.

The software establishes a preliminary design for the main beams of the bridge under in-service conditions. It does not carry out anychecks for construction phases. Lateral-torsional buckling of beams is not analyzed for the construction phase. Diaphragms and/orbracing may have to be implemented for the construction phase as well as the in-service phase.

ACOBRI is a preliminary design software tool which does not analyze all situations or perform in an exhaustive manner all the verificationcalculations required for construction design.

ACOBRI was developed by CTICM, Centre Technique Industriel de la Construction Mtallique, France.

Copyright : ArcelorMittal - Long Carbon Europe - Research Center.

Page 2 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

Universitatea Tehnica Cluj-Napoca

Project name : Structuri compuse otel-beton

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User name : Petrut Mirela

E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

DATA

ROAD BRIDGE - Conventional beam and slab superstructure

Eurocodes (EN)

2 spans Span length 1 = 15.000 m

Span length 2 = 15.000 m

Slab dimensionsWidth = 10.000 m Thickness = 30.0 cm

Haunch = 15.0 cm

4 beam lines (Distance to left-hand edge of deck slab)

Line 1 : 1.500 mCentre distance = 2.333 m

Line 2 : 3.833 mCentre distance = 2.333 m

Line 3 : 6.167 mCentre distance = 2.333 m

Line 4 : 8.500 m

Shear studs : 19x175

Reinforcement ratio = 3.0 %

Top layer : 70 % Distance to top of slab = 4.0 cm

Bottom layer : 30 % Distance between bottom of slab = 4.0 cm

Propping : No propping of main beams during deck slab concreting.

Overhang : Overhang formwork suspended from the two outermost beams only.

An equivalent superimposed dead load is taken into account in the calculation of the slab weight

Reinforcing steel fy = 500.00 N/mm2

Structural steel S275 (WITH reduction of yield strength with thickness)

Density = 7850 kg/m3

Concrete Class C35/45

Density = 2650 kg/m3

Shrinkage strain = 200.10 -6Temperature difference between slab and beams = 10 C

Page 3 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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Material properties used in calculations

Yield strength of the steel of girders fy = 265.0 MPaYield strength of the reinforcing steel fy = 500.0 MPa

Modulus of elasticity Ecm = 34077 MPaLimit compressive strenght of concretefck = 35 MPa

Page 4 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

Universitatea Tehnica Cluj-Napoca

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User name : Petrut Mirela

E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

Steel sections

span 1 Left-hand edge beam HE 700 B

Intermediate beams HE 700 B

Right-hand edge beam HE 700 B

span 2 Left-hand edge beam HE 700 B

Intermediate beams HE 700 B

Right-hand edge beam HE 700 B

Cracked regions

Support lines LH side (m) RH side (m)C0 - -

P1 2.250 (15 %) 2.250 (15 %)

C2 - -

Footways and restraint systems

LH footway width: 1.500 m

RH footway, width: 1.500 m

LH restraint system, distance to LH edge of deck slab 1.500 m

RH restraint system, distance to RH edge of deck slab 1.500 m

Bridge class : 1

Superimposed dead loads of deck surfacing or ballast, footways or maintenance walkways etc - SDL1

Footways Thickness = 20.0 cm Density = 2000.0 kg/m3LH footway width = 1.50 mRH footway width = 1.50 m

Waterproofing Thickness = 3.0 cm Density = 2400.0 kg/m3

Surfacing Thickness = 8.0 cm Density = 2400.0 kg/m3

Parapets left-hand side x = 0.10 m q = 1.00 kN/mright-hand side x = 0.10 m q = 1.00 kN/m

Restraint system left-hand side x = 1.50 m q = 1.00 kN/mright-hand side x = 1.50 m q = 1.00 kN/m

Live loads on footways Distributed load = 5.00 kN/m 2

Left-hand footway Width of loaded area = 1.50 m Distance to slab edge = 0.00 m

Right-hand footway Width of loaded area = 1.50 m Distance to slab edge = 0.00 m

Page 5 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

Universitatea Tehnica Cluj-Napoca

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E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

Definition of truck load models

Abnormal load : None

Fatigue load model : Load model on LH track / laneMean gross weight of truck : 600. kNNumber of trucks : 2.00 millions per year and slow laneService life (years) : 100

Support height ajustments and settlements

Height adjustments Settlements

Support line No. 0 0 mm 0 mm

Support line No. 1 0 mm 0 mm

Support line No. 2 0 mm 0 mm

Page 6 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

Universitatea Tehnica Cluj-Napoca

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User name : Petrut Mirela

E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

Assumptions for calculation and checks

Calculation coefficients

Diaphragms Coefficient for inertia = 0.10Coefficient for mass = 0.10

Slab elements Coefficient for inertia - longitudinal = 1.00Coefficient for inertia - transverse = 1.00

Serviceability Limit States

Deflection due to live loads limited to 1/ 500 of span length

Partial safety factor for the structural steel M,ser = 1.00Partial safety factor for shear resistance of studs v = 1.25

Ultimate Limit States

Partial safety factors :for sections resistance M0 = 1.00for buckling resistance M1 = 1.10for slab concrete strength c = 1.50for shear resistance of studs M = 1.15

Fatigue Limit States

Partial safety factors for fatigue loading Ff = 1.00Top flange :

Partial safety factor for fatigue strength Mf = 1.15Detail category 80 MPa

Bottom flange :Partial safety factor for fatigue strength Mf = 1.15Detail category 160 MPa

Page 7 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

Universitatea Tehnica Cluj-Napoca

Project name : Structuri compuse otel-beton

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Comment :

User name : Petrut Mirela

E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

Weighting factors for SDL1 :

Increase Reduction

Waterproofing 1.20 0.80

Surfacing 1.40 0.80

Footways 1.00 1.00

Adjustment factors applied to load model 1 (UDL + TS) :

Q1 Qi (i>1) q1 qi(i>1) qrClass 1 1.0 1.0 1.0 1.0 1.0Class 2 1.0 1.0 1.0 1.0 1.0Class 3 1.0 1.0 1.0 1.0 1.0

The class of the bridge is : Class 1

Partial factors for loads - Combination factors :

Partial factors for loads (ULS) :

Permanent loads G = 1.35Traffic loads Q = 1.35Other variable loads Q = 1.50Height adjustments P = 1.00Settlements G,set = 1.20Shrinkage S = 1.00

Combination factors :

0 1 2 '1gr1a TS 0.75 0.75 0.00 0.80

gr1a UDL 0.40 0.40 0.00 0.80gr5 0.00 0.00 0.00 1.00TK 0.60 0.60 0.50

Page 8 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

Universitatea Tehnica Cluj-Napoca

Project name : Structuri compuse otel-beton

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User name : Petrut Mirela

E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

LIST OF LOAD CASES

No. Symbol Name of load case Modular ratio

1 PP Self-weight -

2 SS SDL1 15.54

3 SS+ Increased SDL1 15.54

4 SS- Reduced SDL1 15.54

5 EQ SDL2 15.54

6 TH+DT Simpl. temp. load +DTC 15.72

7 TH-DT Simpl. temp. load -DTC 15.72

8 RE Concrete shrinkage 15.72

9 Eigenmode 6.16

10 UDL Load model 1 UDL 6.16

11 TS Load model 1 TS 6.16

12 TR Load on footways 6.16

Page 9 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

LIST OF ULS COMBINATIONS

Loading subscripts and symbols1 3 4 5 6 7 8 10 11 12

ULS comb. PP SS+ SS- EQ TH+DT TH-DT RE UDL TS TR 1 1.35 1.35 1.35 1.35 1.35 0.68 2 1.35 1.35 1.35 1.35 1.35 0.68 3 1.35 1.35 1.35 1.50 0.54 1.01 0.27 4 1.35 1.35 1.35 1.50 0.54 1.01 0.27 5 1.35 1.35 1.35 1.50 0.54 1.01 0.27 6 1.35 1.35 1.35 1.50 0.54 1.01 0.27 7 1.35 1.35 1.35 1.00 1.35 1.35 0.68 8 1.35 1.35 1.35 1.00 1.35 1.35 0.68 9 1.35 1.35 1.35 1.50 1.00 0.54 1.01 0.27

10 1.35 1.35 1.35 1.50 1.00 0.54 1.01 0.27 11 1.35 1.35 1.35 1.50 1.00 0.54 1.01 0.27 12 1.35 1.35 1.35 1.50 1.00 0.54 1.01 0.27

Page 10 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

Universitatea Tehnica Cluj-Napoca

Project name : Structuri compuse otel-beton

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User name : Petrut Mirela

E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

LIST OF SLS COMBINATIONS

Loading subscripts and symbols1 3 4 5 6 7 8 10 11 12

Characteristics PP SS+ SS- EQ TH+DT TH-DT RE UDL TS TR 1 1.00 1.00 1.00 0.60 1.00 1.00 0.60 2 1.00 1.00 1.00 0.60 1.00 1.00 0.60 3 1.00 1.00 1.00 0.60 1.00 1.00 0.60 4 1.00 1.00 1.00 0.60 1.00 1.00 0.60 5 1.00 1.00 1.00 1.00 0.40 0.75 0.24 6 1.00 1.00 1.00 1.00 0.40 0.75 0.24 7 1.00 1.00 1.00 1.00 0.40 0.75 0.24 8 1.00 1.00 1.00 1.00 0.40 0.75 0.24 9 1.00 1.00 1.00 0.60 1.00 1.00 1.00 0.60

10 1.00 1.00 1.00 0.60 1.00 1.00 1.00 0.60 11 1.00 1.00 1.00 0.60 1.00 1.00 1.00 0.60 12 1.00 1.00 1.00 0.60 1.00 1.00 1.00 0.60 13 1.00 1.00 1.00 1.00 1.00 0.40 0.75 0.24 14 1.00 1.00 1.00 1.00 1.00 0.40 0.75 0.24 15 1.00 1.00 1.00 1.00 1.00 0.40 0.75 0.24 16 1.00 1.00 1.00 1.00 1.00 0.40 0.75 0.24

Page 11 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

Universitatea Tehnica Cluj-Napoca

Project name : Structuri compuse otel-beton

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Comment :

User name : Petrut Mirela

E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

Loading subscripts and symbols1 3 4 5 6 7 8 10 11 12

Frequent PP SS+ SS- EQ TH+DT TH-DT RE UDL TS TR 17 1.00 1.00 1.00 0.50 0.40 0.75 0.24 18 1.00 1.00 1.00 0.50 0.40 0.75 0.24 19 1.00 1.00 1.00 0.50 0.40 0.75 0.24 20 1.00 1.00 1.00 0.50 0.40 0.75 0.24 21 1.00 1.00 1.00 0.50 1.00 0.40 0.75 0.24 22 1.00 1.00 1.00 0.50 1.00 0.40 0.75 0.24 23 1.00 1.00 1.00 0.50 1.00 0.40 0.75 0.24 24 1.00 1.00 1.00 0.50 1.00 0.40 0.75 0.24

Page 12 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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Loading subscripts and symbols1 3 4 5 6 7 8 10 11 12

Quasi-perm. PP SS+ SS- EQ TH+DT TH-DT RE UDL TS TR 25 1.00 1.00 1.00 0.50 26 1.00 1.00 1.00 0.50 27 1.00 1.00 1.00 0.50 28 1.00 1.00 1.00 0.50 29 1.00 1.00 1.00 0.50 1.00 30 1.00 1.00 1.00 0.50 1.00 31 1.00 1.00 1.00 0.50 1.00 32 1.00 1.00 1.00 0.50 1.00

Page 13 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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Loading subscripts and symbols1 3 4 5 6 7 8 10 11 12

Infrequent PP SS+ SS- EQ TH+DT TH-DT RE UDL TS TR 33 1.00 1.00 1.00 0.60 0.80 0.80 0.48 34 1.00 1.00 1.00 0.60 0.80 0.80 0.48 35 1.00 1.00 1.00 0.60 0.80 0.80 0.48 36 1.00 1.00 1.00 0.60 0.80 0.80 0.48 37 1.00 1.00 1.00 0.60 1.00 0.80 0.80 0.48 38 1.00 1.00 1.00 0.60 1.00 0.80 0.80 0.48 39 1.00 1.00 1.00 0.60 1.00 0.80 0.80 0.48 40 1.00 1.00 1.00 0.60 1.00 0.80 0.80 0.48

Page 14 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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ESTIMATED QUANTITIES

Structural steel sections :

Steel grade : S275

Lengths (m)

Position Span Number Profile Nominal On/Under Sum Weight (t) Pre-camber (cm)

1 1 4 HE 700 B 15.00 0.20 15.20 14.623 1.6

2 2 4 HE 700 B 15.00 0.20 15.20 14.623 1.6

29.246

Shear connectors :

Position Span Number Weight (t)

1 1 912 0.391

2 2 906 0.389

0.780

Slab concrete :

Surface of slab : 300.00 m2

Position Span Volume (m3)

1 1 47.7

2 2 47.7

95.4

NB :

- The indicated beam lengths and pre-cambers correspond to span lengths.Supply specifications may differ, depending on the position of any splices.Constraints associated with fabrication, finishing, transport, and handling are to be checked on a case-by-case basis.

- The quantities indicated for beams do not include stiffeners, bearing plates, diaphragms, end plates, etc.These items are to be added in accordance with the features of the structure.

- The number of shear connectors given includes a flat 30% increase over the theoretical quantityto take account of fabrication practice.

Page 15 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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Mass on slab :

Waterproofing (t) Surfacing (t) Footways (t) Subtotal (t)Span 1 7.560 20.160 18.000 45.720

Span 2 7.560 20.160 18.000 45.720

TOTAL 15.120 40.320 36.000 91.440

Page 16 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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NUMBER OF CONNECTORS

19x175 : d = 19.0 mm - h = 175.0 mm

span Row 1 Row 2 Row 3 Row 4 Total Weight (t) 1 244 212 212 244 912 0.391 2 244 209 209 244 906 0.389

1818 0.780

NB : - The number of shear connectors given includes a flat 30% increase over the theoretical quantityto take account of fabrication practice.

Page 17 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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LIST OF CROSS-SECTIONS OF INTEREST

Bridge length : 30.00 m ( 9 cross-sections of interest)

Section No. Position (m) Type span

1 0.00 Origin abutment

2 2.25 Limit of support region 3 7.50 Mid-span 1 4 12.75 Limit of support region

5 15.00 Support

6 17.25 Limit of support region 7 22.50 Mid-span 2 8 27.75 Limit of support region

9 30.00 End abutment

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ArcelorMittal Composite Bridge Predesign (v3.14)

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FACTORS FOR FATIGUE LOADS

Additional dynamic amplification factor : fatReference : EN 1991-2 : 2003 4.6.1 (6)

Cross-section fatn1 1.300

n2 1.188

n3 1.000

n4 1.000

n5 1.000

n6 1.000

n7 1.000

n8 1.188

n9 1.300

Page 19 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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FACTORS FOR FATIGUE LOADS (Continued)

Damage equivalence factor : Reference : EN 1993-2 : 2006 9.5.2

Beam linesS L/R n1 n2 n3 n4

n1 L 2.333 2.333 2.333 2.333

n2 R 2.333 2.333 2.333 2.333

n2 L 2.333 2.333 2.333 2.333

n3 R 2.333 2.333 2.333 2.333

n3 L 2.333 2.333 2.333 2.333

n4 R 2.333 2.333 2.333 2.333

n4 L 1.800 1.800 1.800 1.800

n5 R 1.800 1.800 1.800 1.800

n5 L 1.800 1.800 1.800 1.800

n6 R 1.800 1.800 1.800 1.800

n6 L 2.333 2.333 2.333 2.333

n7 R 2.333 2.333 2.333 2.333

n7 L 2.333 2.333 2.333 2.333

n8 R 2.333 2.333 2.333 2.333

n8 L 2.333 2.333 2.333 2.333

n9 R 2.333 2.333 2.333 2.333

S = Cross-section - R = Right - L = Left

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CROSS-SECTION CHARACTERISTICS

Beam line No. : 1Section No. : 1Node line No. : 1Type of cross-section : SupportPosition : 0.00 m Origin abutment

Effective slab width for internal force and moment calculation (1) : 2.67 m

for stress calculation (2) : 2.22 m

Concrete state Casting Uncracked CrackedLoads Permanent Permanent Live -

Modular ratio - 15.54 15.72 6.16Section modulus of top flange (cm3) (2) -7340. 361574. 383828. 86117. -112727.

Section modulus of bottom fibre (cm3) (2) 7340. 14317. 14298. 15720. 13776.

Section modulus of concrete slab (cm3) (2) -385085. -386349. -282477.

Sect. modulus, top reinforcement layer (cm3) (2) -17673.

Shear area (cm2) 137.10

Plastic moment (M > 0) (kN.m) (2) 5746. 5746. 5746.

Plastic moment (M < 0) (kN.m) (2) 5721.

Plastic neutral axis (M > 0) (mm) (2) 965.42 965.42 965.42

Plastic neutral axis (M < 0) (mm) (2) 700.00

Reduction factor Beta (2) 0.994 0.994 0.994

Elastic neutral axis (mm) (1) 350.00 757.47 755.76 875.89

Bending moment of inertia (cm4) (1) 256887. 1106951. 1103119. 1401531.

Torsional moment of inertia (cm4) (1) 830.94 78042.00 77180.64 195557.40

Cross-sectional area (cm2) (1) 306.38 821.12 815.38 1604.55

Bending moment of inertia (cm4) (2) 256887. 1043475. 1039583. 1346175. 859287.

Elastic neutral axis (mm) (2) 350.00 728.86 727.08 856.32 623.77

Cross-sectional area (cm2) (2) 306.38 734.47 729.70 1386.04 505.98

NB : -Section modulus is positive for fibres below elastic neutral axis. -Section modulus is negative for fibres above elastic neutral axis. -The position of the neutral axis is measured from the bottom fibre of the bottom steel section flange

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ArcelorMittal Composite Bridge Predesign (v3.14)

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INTERNAL FORCES AND MOMENTS IN CROSS-SECTION OF INTEREST

Beam line No. : 1 M : Bending momentSection No. : 1 V : Shear forceNode line No. : 1 d : DeflectionType of cross-section : Support n : Modular ratioPosition : 0.00 m Origin abutment

PERMANENT LOADS

left-hand side right-hand side

Load case n M (kN.m) V (kN) M (kN.m) V (kN) d (cm)Self-weight - -0.01 -127.84 0.00

SDL1 15.54 -0.15 -50.43 0.00

Increased SDL1 15.54 -0.10 -56.60 0.00

Reduced SDL1 15.54 -0.18 -46.86 0.00

SDL2 15.54 -0.10 -10.92 0.00

Simpl. temp. load +DTC 15.72 -261.01 -25.70 0.00

primary effect -261.06

secondary effect 0.06 -25.70

axial force - slab N = 1068.90 kN

Simpl. temp. load -DTC 15.72 261.01 25.70 0.00

primary effect 261.06

secondary effect -0.06 25.70

axial force - slab N = -1068.90 kN

Concrete shrinkage 15.72 522.02 35.37 0.00

primary effect 522.13

secondary effect -0.11 35.37

axial force - slab N = -2137.79 kN

LIVE LOADS Modular ratio = 6.16

left-hand side right-hand side

Mmax Mmin Vmax Vmin Vmax Vmin dLoad case (kN.m) (kN.m) (kN) (kN) (kN) (kN) (cm)

Load model 1 UDL 0.00 0.00 -77.96 11.24 0.00

Load model 1 TS 0.00 0.00 -207.53 28.17 0.00

Load on footways 0.00 0.00 -45.17 4.12 0.00

Fatigue LM3 Left-hand slow lane 0.25 -0.61 -123.64 14.01

Page 22 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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User name : Petrut Mirela

E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

CHECKING CROSS-SECTION OF INTEREST

Beam line No. : 1Section No. : 1Node line No. : 1Type of cross-section : SupportPosition : 0.00 m Origin abutment

SERVICEABILITY LIMIT STATE Value Limit Ratio CombinationDeflections (m) 0.000 0.030 0.00 -

Minimum reinforcement (%) 1.00 3.00 0.33 -

Slab cracking max = 25. mm or emax = 200. mm No.18Concrete compressive stress (MPa) -0.52 21.00 0.02 No.15

Tensile stress in reinforcement (MPa) 7.76 400.00 0.02 No.2

Stress in top fibre of steel section (MPa) -37.29 265.00 0.14 No.16

Stress in bottom fibre of steel section (MPa) 15.42 265.00 0.06 No.15

Concrete compressive stress (MPa) -0.43 15.75 0.03 No.31

Shear stress in steel section (MPa) -38.18 153.00 0.25 No.1

Normal stress / shear interaction (MPa) -66.12 265.00 0.25 No.1

Shear connection (kN/m) 449.34 728.07 0.62 No.1

NB : - The minimum reinforcement for Serviceability Limit States has been checked for the maximum bar diameter :*s = 20 mm.The reinforcement ratio is shown as "Limit" and must be greater than the strength value shown as "Value".

- Tensile stresses are positive; compressive stresses are negative.

ULTIMATE LIMIT STATE Value Limit Ratio CombinationPlastic shear resistance (kN) 679.64 2097.57 0.32 No.1

Sagging, Class 1 or 2 (kN.m) 913.24 5709.69 0.16 No.11

Hogging, Class 1 or 2 (kN.m) 391.90 5720.73 0.07 No.4

Bending / shear interaction (sagging) (kN.m) - - - -

Bending / shear interaction (hogging) (kN.m) - - - -

Shear buckling: shear force - - - -

Shear buckling: bending / shear interaction - - - -

LTBuckling 0.08 1.00 0.08 No.4

FATIGUE LIMIT STATE Value Limit Ratio CombinationBending stress range in top flange (MPa) 0.02 69.57 0.00 -

Bending stress range in bottom flange (MPa) 0.19 139.13 0.00 -

Page 23 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

Universitatea Tehnica Cluj-Napoca

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User name : Petrut Mirela

E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

CROSS-SECTION CHARACTERISTICS

Beam line No. : 1Section No. : 2Node line No. : 4Type of cross-section : Limit of support regionPosition : 2.25 m Span No. : 1

Effective slab width for internal force and moment calculation (1) : 2.67 m

for stress calculation (2) : 2.49 m

Concrete state Casting Uncracked CrackedLoads Permanent Permanent Live -

Modular ratio - 15.54 15.72 6.16Section modulus of top flange (cm3) (2) -7340. 231512. 239578. 81828. -158305.

Section modulus of bottom fibre (cm3) (2) 7340. 14503. 14485. 15894. 14038.

Section modulus of concrete slab (cm3) (2) -417462. -418864. -302520.

Sect. modulus, top reinforcement layer (cm3) (2) -19327.

Shear area (cm2) 137.10

Plastic moment (M > 0) (kN.m) (2) 5827. 5827. 5827.

Plastic moment (M < 0) (kN.m) (2) 5883.

Plastic neutral axis (M > 0) (mm) (2) 985.41 985.41 985.41

Plastic neutral axis (M < 0) (mm) (2) 700.00

Reduction factor Beta (2) 1.000 1.000 1.000

Elastic neutral axis (mm) (1) 350.00 757.47 755.76 875.89

Bending moment of inertia (cm4) (1) 256887. 1106951. 1103119. 1401531.

Torsional moment of inertia (cm4) (1) 830.94 78042.00 77180.64 195557.40

Cross-sectional area (cm2) (1) 306.38 821.12 815.38 1604.55

Bending moment of inertia (cm4) (2) 256887. 1083067. 1079208. 1380736. 902598.

Elastic neutral axis (mm) (2) 350.00 746.78 745.05 868.74 642.98

Cross-sectional area (cm2) (2) 306.38 786.46 781.10 1517.15 530.22

NB : -Section modulus is positive for fibres below elastic neutral axis. -Section modulus is negative for fibres above elastic neutral axis. -The position of the neutral axis is measured from the bottom fibre of the bottom steel section flange

Page 24 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

Universitatea Tehnica Cluj-Napoca

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User name : Petrut Mirela

E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

INTERNAL FORCES AND MOMENTS IN CROSS-SECTION OF INTEREST

Beam line No. : 1 M : Bending momentSection No. : 2 V : Shear forceNode line No. : 4 d : DeflectionType of cross-section : Limit of support region n : Modular ratioPosition : 2.25 m Span No. : 1

PERMANENT LOADS

left-hand side right-hand side

Load case n M (kN.m) V (kN) M (kN.m) V (kN) d (cm)Self-weight - 246.59 -91.35 246.59 -71.59 -0.67

SDL1 15.54 95.98 -35.93 95.46 -28.26 -0.06

Increased SDL1 15.54 108.48 -40.57 108.09 -31.97 -0.07

Reduced SDL1 15.54 88.74 -33.25 88.15 -26.11 -0.06

SDL2 15.54 20.05 -7.54 19.76 -5.87 -0.01

Simpl. temp. load +DTC 15.72 -203.20 -25.66 -203.19 -25.63 0.07

primary effect -261.06 -261.06

secondary effect 57.86 -25.66 57.87 -25.63

axial force - slab N = 1068.90 kN N = 1068.90 kN

Simpl. temp. load -DTC 15.72 203.20 25.66 203.19 25.63 -0.07

primary effect 261.06 261.06

secondary effect -57.86 25.66 -57.87 25.63

axial force - slab N = -1068.90 kN N = -1068.90 kN

Concrete shrinkage 15.72 442.45 35.32 442.45 35.27 -0.19

primary effect 522.13 522.13

secondary effect -79.68 35.32 -79.68 35.27

axial force - slab N = -2137.79 kN N = -2137.79 kN

LIVE LOADS Modular ratio = 6.16

left-hand side right-hand side

Mmax Mmin Vmax Vmin Vmax Vmin dLoad case (kN.m) (kN.m) (kN) (kN) (kN) (kN) (cm)

Load model 1 UDL 155.72 -23.93 -62.06 11.54 -53.34 12.42 -0.10

Load model 1 TS 460.79 -61.35 -197.25 27.87 -178.47 13.38 -0.26

Load on footways 80.03 -8.01 -32.37 4.59 -27.96 6.37 -0.05

Fatigue LM3 Left-hand slow lane 228.68 -29.16 -101.55 13.75 -87.21 13.83

Page 25 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

Universitatea Tehnica Cluj-Napoca

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User name : Petrut Mirela

E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

CHECKING CROSS-SECTION OF INTEREST

Beam line No. : 1Section No. : 2Node line No. : 4Type of cross-section : Limit of support regionPosition : 2.25 m Span No. : 1

SERVICEABILITY LIMIT STATE Value Limit Ratio CombinationDeflections (m) 0.004 0.030 0.12 UDL + TS

Minimum reinforcement (%) [R] 0.97 3.00 0.32 -

[L] 0.97 3.00 0.32 -

Slab cracking [R] No cracking -

[L] No cracking -

Concrete compressive stress (MPa) [R] -2.57 21.00 0.12 No.9

[L] -2.57 21.00 0.12 No.9

Tensile stress in reinforcement (MPa) [R] 7.91 400.00 0.02 No.4

[L] 7.87 400.00 0.02 No.4

Stress in top fibre of steel section (MPa) [R] -70.47 265.00 0.27 No.16

[L] -70.46 265.00 0.27 No.16

Stress in bottom fibre of steel section (MPa) [R] 89.10 265.00 0.34 No.11

[L] 89.15 265.00 0.34 No.11

Concrete compressive stress (MPa) [R] -0.37 15.75 0.02 No.29

[L] -0.37 15.75 0.02 No.29

Shear stress in steel section (MPa) [R] -27.24 153.00 0.18 No.1

[L] -31.63 153.00 0.21 No.1

Normal stress / shear interaction (MPa) [R] -89.71 265.00 0.34 No.9

[L] -96.45 265.00 0.36 No.9

Shear connection (kN/m) [R] 344.32 564.04 0.61 No.1

[L] 390.33 728.07 0.54 No.1

NB : - The minimum reinforcement for Serviceability Limit States has been checked for the maximum bar diameter :*s = 20 mm.The reinforcement ratio is shown as "Limit" and must be greater than the strength value shown as "Value".

- Tensile stresses are positive; compressive stresses are negative.

Page 26 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

Universitatea Tehnica Cluj-Napoca

Project name : Structuri compuse otel-beton

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User name : Petrut Mirela

E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

Beam line No. : 1Section No. : 2Node line No. : 4Type of cross-section : Limit of support regionPosition : 2.25 m Span No. : 1

ULTIMATE LIMIT STATE Value Limit Ratio CombinationPlastic shear resistance (kN) [R] 479.55 2097.57 0.23 No.1

[L] 560.20 2097.57 0.27 No.1

Sagging, Class 1 or 2 (kN.m) [R] 1834.25 5827.04 0.31 No.7

[L] 1835.17 5827.04 0.31 No.7

Hogging, Class 1 or 2 (kN.m) [R] 0.00 0.00 - -

[L] 0.00 0.00 - -

Bending / shear interaction (sagging) (kN.m) [R] - - - -

[L] - - - -

Bending / shear interaction (hogging) (kN.m) [R] - - - -

[L] - - - -

Shear buckling: shear force [R] - - - -

[L] - - - -

Shear buckling: bending / shear interaction [R] - - - -

[L] - - - -

LTBuckling [R] 0.00 0.00 - -

[L] 0.00 0.00 - -

FATIGUE LIMIT STATE Value Limit Ratio CombinationBending stress range in top flange (MPa) [R] 8.69 69.57 0.12 -

[L] 8.77 69.57 0.13 -

Bending stress range in bottom flange (MPa) [R] 44.74 139.13 0.32 -

[L] 45.16 139.13 0.32 -

Page 27 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

Universitatea Tehnica Cluj-Napoca

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User name : Petrut Mirela

E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

CROSS-SECTION CHARACTERISTICS

Beam line No. : 1Section No. : 3Node line No. : 10Type of cross-section : Mid-spanPosition : 7.50 m Span No. : 1

Effective slab width for internal force and moment calculation (1) : 2.67 m

for stress calculation (2) : 2.67 m

Concrete state Casting Uncracked CrackedLoads Permanent Permanent Live -

Modular ratio - 15.54 15.72 6.16Section modulus of top flange (cm3) (2) -7340. 192613. 197826. 79684. -205832.

Section modulus of bottom fibre (cm3) (2) 7340. 14614. 14596. 16001. 14194.

Section modulus of concrete slab (cm3) (2) -438286. -439782. -315086.

Sect. modulus, top reinforcement layer (cm3) (2) -20421.

Shear area (cm2) 137.10

Plastic moment (M > 0) (kN.m) (2) 5872. 5872. 5872.

Plastic moment (M < 0) (kN.m) (2) 5991.

Plastic neutral axis (M > 0) (mm) (2) 996.49 996.49 996.49

Plastic neutral axis (M < 0) (mm) (2) 700.00

Reduction factor Beta (2) 1.000 1.000 1.000

Elastic neutral axis (mm) (1) 350.00 757.47 755.76 875.89

Bending moment of inertia (cm4) (1) 256887. 1106951. 1103119. 1401531.

Torsional moment of inertia (cm4) (1) 830.94 78042.00 77180.64 195557.40

Cross-sectional area (cm2) (1) 306.38 821.12 815.38 1604.55

Bending moment of inertia (cm4) (2) 256887. 1106951. 1103119. 1401531. 929458.

Elastic neutral axis (mm) (2) 350.00 757.47 755.76 875.89 654.84

Cross-sectional area (cm2) (2) 306.38 821.12 815.38 1604.55 546.38

NB : -Section modulus is positive for fibres below elastic neutral axis. -Section modulus is negative for fibres above elastic neutral axis. -The position of the neutral axis is measured from the bottom fibre of the bottom steel section flange

Page 28 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

Universitatea Tehnica Cluj-Napoca

Project name : Structuri compuse otel-beton

Project reference :

Comment :

User name : Petrut Mirela

E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

INTERNAL FORCES AND MOMENTS IN CROSS-SECTION OF INTEREST

Beam line No. : 1 M : Bending momentSection No. : 3 V : Shear forceNode line No. : 10 d : DeflectionType of cross-section : Mid-span n : Modular ratioPosition : 7.50 m Span No. : 1

PERMANENT LOADS

left-hand side right-hand side

Load case n M (kN.m) V (kN) M (kN.m) V (kN) d (cm)Self-weight - 343.11 34.82 343.11 56.10 -1.19

SDL1 15.54 136.61 11.85 136.76 19.81 -0.11

Increased SDL1 15.54 154.84 13.60 154.96 22.67 -0.13

Reduced SDL1 15.54 126.05 10.83 126.23 18.16 -0.10

SDL2 15.54 28.09 2.28 28.18 3.87 -0.02

Simpl. temp. load +DTC 15.72 -68.80 -25.57 -68.81 -25.57 0.08

primary effect -261.06 -261.06

secondary effect 192.26 -25.57 192.26 -25.57

axial force - slab N = 1068.90 kN N = 1068.90 kN

Simpl. temp. load -DTC 15.72 68.80 25.57 68.81 25.57 -0.08

primary effect 261.06 261.06

secondary effect -192.26 25.57 -192.26 25.57

axial force - slab N = -1068.90 kN N = -1068.90 kN

Concrete shrinkage 15.72 257.81 35.09 257.81 35.06 -0.28

primary effect 522.13 522.13

secondary effect -264.32 35.09 -264.32 35.06

axial force - slab N = -2137.79 kN N = -2137.79 kN

LIVE LOADS Modular ratio = 6.16

left-hand side right-hand side

Mmax Mmin Vmax Vmin Vmax Vmin dLoad case (kN.m) (kN.m) (kN) (kN) (kN) (kN) (cm)

Load model 1 UDL 280.18 -80.24 -16.11 31.70 -11.24 38.50 -0.21

Load model 1 TS 835.54 -202.47 -84.06 112.05 -63.91 134.44 -0.54

Load on footways 133.39 -29.61 -12.92 19.91 -10.69 23.22 -0.10

Fatigue LM3 Left-hand slow lane 334.99 -99.59 -32.76 42.18 -22.70 50.33

Page 29 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

Universitatea Tehnica Cluj-Napoca

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User name : Petrut Mirela

E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

CHECKING CROSS-SECTION OF INTEREST

Beam line No. : 1Section No. : 3Node line No. : 10Type of cross-section : Mid-spanPosition : 7.50 m Span No. : 1

SERVICEABILITY LIMIT STATE Value Limit Ratio CombinationDeflections (m) 0.007 0.030 0.25 UDL + TS

Minimum reinforcement (%) [R] 0.95 3.00 0.32 -

[L] 0.95 3.00 0.32 -

Slab cracking [R] max = 25. mm or emax = 200. mm No.24[L] max = 25. mm or emax = 200. mm No.24

Concrete compressive stress (MPa) [R] -4.42 21.00 0.21 No.1

[L] -4.42 21.00 0.21 No.1

Tensile stress in reinforcement (MPa) [R] 32.38 400.00 0.08 No.12

[L] 32.39 400.00 0.08 No.12

Stress in top fibre of steel section (MPa) [R] -73.95 265.00 0.28 No.16

[L] -73.95 265.00 0.28 No.16

Stress in bottom fibre of steel section (MPa) [R] 139.05 265.00 0.52 No.1

[L] 139.03 265.00 0.52 No.1

Concrete compressive stress (MPa) [R] -0.59 15.75 0.04 No.1

[L] -0.59 15.75 0.04 No.1

Shear stress in steel section (MPa) [R] -23.34 153.00 0.15 No.11

[L] -18.73 153.00 0.12 No.11

Normal stress / shear interaction (MPa) [R] -133.05 265.00 0.50 No.1

[L] -131.66 265.00 0.50 No.1

Shear connection (kN/m) [R] 300.74 856.57 0.35 No.11

[L] 253.04 564.04 0.45 No.11

NB : - The minimum reinforcement for Serviceability Limit States has been checked for the maximum bar diameter :*s = 20 mm.The reinforcement ratio is shown as "Limit" and must be greater than the strength value shown as "Value".

- Tensile stresses are positive; compressive stresses are negative.

Page 30 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

Universitatea Tehnica Cluj-Napoca

Project name : Structuri compuse otel-beton

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User name : Petrut Mirela

E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

Beam line No. : 1Section No. : 3Node line No. : 10Type of cross-section : Mid-spanPosition : 7.50 m Span No. : 1

ULTIMATE LIMIT STATE Value Limit Ratio CombinationPlastic shear resistance (kN) [R] 395.78 2097.57 0.19 No.7

[L] 311.04 2097.57 0.15 No.7

Sagging, Class 1 or 2 (kN.m) [R] 2564.51 5872.03 0.44 No.7

[L] 2564.24 5872.03 0.44 No.7

Hogging, Class 1 or 2 (kN.m) [R] 0.00 0.00 - -

[L] 0.00 0.00 - -

Bending / shear interaction (sagging) (kN.m) [R] - - - -

[L] - - - -

Bending / shear interaction (hogging) (kN.m) [R] - - - -

[L] - - - -

Shear buckling: shear force [R] - - - -

[L] - - - -

Shear buckling: bending / shear interaction [R] - - - -

[L] - - - -

LTBuckling [R] 0.00 0.00 - -

[L] 0.00 0.00 - -

FATIGUE LIMIT STATE Value Limit Ratio CombinationBending stress range in top flange (MPa) [R] 12.73 69.57 0.18 -

[L] 12.73 69.57 0.18 -

Bending stress range in bottom flange (MPa) [R] 63.37 139.13 0.46 -

[L] 63.37 139.13 0.46 -

Page 31 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

Universitatea Tehnica Cluj-Napoca

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User name : Petrut Mirela

E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

CROSS-SECTION CHARACTERISTICS

Beam line No. : 1Section No. : 4Node line No. : 16Type of cross-section : Limit of support regionPosition : 12.75 m Span No. : 1

Effective slab width for internal force and moment calculation (1) : 2.67 m

for stress calculation (2) : 2.45 m

Concrete state Casting Uncracked CrackedLoads Permanent Permanent Live -

Modular ratio - 15.54 15.72 6.16Section modulus of top flange (cm3) (2) -7340. 242159. 251115. 82319. -150783.

Section modulus of bottom fibre (cm3) (2) 7340. 14480. 14462. 15871. 14005.

Section modulus of concrete slab (cm3) (2) -413202. -414585. -299918.

Sect. modulus, top reinforcement layer (cm3) (2) -19106.

Shear area (cm2) 137.10

Plastic moment (M > 0) (kN.m) (2) 5817. 5817. 5817.

Plastic moment (M < 0) (kN.m) (2) 5861.

Plastic neutral axis (M > 0) (mm) (2) 982.98 982.98 982.98

Plastic neutral axis (M < 0) (mm) (2) 700.00

Reduction factor Beta (2) 1.000 1.000 1.000

Elastic neutral axis (mm) (1) [L] 350.00 757.47 755.76 875.89

Elastic neutral axis (mm) (1) [R] 350.00 654.84 654.84 654.84

Bending moment of inertia (cm4) (1) [L] 256887. 1106951. 1103119. 1401531.

Bending moment of inertia (cm4) (1) [R] 256887. 929458.

Torsional moment of inertia (cm4) (1) [L] 830.94 78042.00 77180.64 195557.40

Torsional moment of inertia (cm4) (1) [R] 830.94 830.94

Cross-sectional area (cm2) (1) [L] 306.38 821.12 815.38 1604.55

Cross-sectional area (cm2) (1) [R] 306.38 546.38

Bending moment of inertia (cm4) (2) 256887. 1078035. 1074170. 1376352. 897008.

Elastic neutral axis (mm) (2) 350.00 744.52 742.78 867.20 640.51

Cross-sectional area (cm2) (2) 306.38 779.49 774.21 1499.56 526.97

NB : -Section modulus is positive for fibres below elastic neutral axis. -Section modulus is negative for fibres above elastic neutral axis. -The position of the neutral axis is measured from the bottom fibre of the bottom steel section flange

Page 32 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

Universitatea Tehnica Cluj-Napoca

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User name : Petrut Mirela

E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

INTERNAL FORCES AND MOMENTS IN CROSS-SECTION OF INTEREST

Beam line No. : 1 M : Bending momentSection No. : 4 V : Shear forceNode line No. : 16 d : DeflectionType of cross-section : Limit of support region n : Modular ratioPosition : 12.75 m Span No. : 1

PERMANENT LOADS

left-hand side right-hand side

Load case n M (kN.m) V (kN) M (kN.m) V (kN) d (cm)Self-weight - -230.76 162.52 -230.76 182.28 -0.25

SDL1 15.54 -75.26 62.76 -74.84 71.88 -0.02

Increased SDL1 15.54 -85.83 70.43 -85.51 80.19 -0.03

Reduced SDL1 15.54 -69.14 58.33 -68.66 67.07 -0.02

SDL2 15.54 -14.98 13.58 -14.75 16.00 -0.01

Simpl. temp. load +DTC 15.72 65.38 -25.57 65.38 -25.57 0.01

primary effect -261.06 -261.06

secondary effect 326.45 -25.57 326.44 -25.57

axial force - slab N = 1068.90 kN N = 1068.90 kN

Simpl. temp. load -DTC 15.72 -65.38 25.57 -65.38 25.57 -0.01

primary effect 261.06 261.06

secondary effect -326.45 25.57 -326.44 25.57

axial force - slab N = -1068.90 kN N = -1068.90 kN

Concrete shrinkage 15.72 73.74 35.06 -448.27 35.07 -0.06

primary effect 522.13 0.00

secondary effect -448.39 35.06 -448.27 35.07

axial force - slab N = -2137.79 kN N = 0.00 kN

LIVE LOADS Modular ratio = 6.16

left-hand side right-hand side

Mmax Mmin Vmax Vmin Vmax Vmin dLoad case (kN.m) (kN.m) (kN) (kN) (kN) (kN) (cm)

Load model 1 UDL 49.96 -136.84 -0.25 81.14 -0.05 89.44 -0.08

Load model 1 TS 250.09 -326.39 -0.26 207.43 -0.69 219.82 -0.20

Load on footways 32.57 -71.31 -1.14 48.51 -0.10 57.09 -0.04

Fatigue LM3 Left-hand slow lane 94.55 -175.58 -0.01 111.66 -0.01 127.14

Page 33 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

Universitatea Tehnica Cluj-Napoca

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User name : Petrut Mirela

E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

CHECKING CROSS-SECTION OF INTEREST

Beam line No. : 1Section No. : 4Node line No. : 16Type of cross-section : Limit of support regionPosition : 12.75 m Span No. : 1

SERVICEABILITY LIMIT STATE Value Limit Ratio CombinationDeflections (m) 0.003 0.030 0.10 UDL + TS

Minimum reinforcement (%) [R] 0.98 3.00 0.33 -

[L] 0.98 3.00 0.33 -

Slab cracking [R] max = 25. mm or emax = 200. mm No.23[L] max = 25. mm or emax = 200. mm No.23

Concrete compressive stress (MPa) [R] -1.26 21.00 0.06 No.2

[L] -1.26 21.00 0.06 No.2

Tensile stress in reinforcement (MPa) [R] 72.57 400.00 0.18 No.11

[L] 72.61 400.00 0.18 No.11

Stress in top fibre of steel section (MPa) [R] 47.08 265.00 0.18 No.6

[L] 47.08 265.00 0.18 No.6

Stress in bottom fibre of steel section (MPa) [R] -120.73 265.00 0.46 No.11

[L] -120.78 265.00 0.46 No.11

Concrete compressive stress (MPa) [R] -0.13 15.75 0.01 No.26

[L] -0.13 15.75 0.01 No.26

Shear stress in steel section (MPa) [R] -49.05 153.00 0.32 No.11

[L] -44.83 153.00 0.29 No.11

Normal stress / shear interaction (MPa) [R] -123.58 265.00 0.47 No.11

[L] -122.17 265.00 0.46 No.11

Shear connection (kN/m) [R] 557.13 1019.91 0.55 No.11

[L] 513.94 856.57 0.60 No.11

NB : - The minimum reinforcement for Serviceability Limit States has been checked for the maximum bar diameter :*s = 20 mm.The reinforcement ratio is shown as "Limit" and must be greater than the strength value shown as "Value".

- Tensile stresses are positive; compressive stresses are negative.

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ArcelorMittal Composite Bridge Predesign (v3.14)

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Beam line No. : 1Section No. : 4Node line No. : 16Type of cross-section : Limit of support regionPosition : 12.75 m Span No. : 1

ULTIMATE LIMIT STATE Value Limit Ratio CombinationPlastic shear resistance (kN) [R] 867.05 2097.57 0.41 No.7

[L] 790.18 2097.57 0.38 No.7

Sagging, Class 1 or 2 (kN.m) [R] 2.90 5817.20 0.00 -

[L] 75.69 5817.20 0.01 No.8

Hogging, Class 1 or 2 (kN.m) [R] 1568.66 5861.26 0.27 No.7

[L] 1121.13 5861.26 0.19 No.1

Bending / shear interaction (sagging) (kN.m) [R] - - - -

[L] - - - -

Bending / shear interaction (hogging) (kN.m) [R] - - - -

[L] - - - -

Shear buckling: shear force [R] - - - -

[L] - - - -

Shear buckling: bending / shear interaction [R] - - - -

[L] - - - -

LTBuckling [R] 0.33 1.00 0.33 No.7

[L] 0.24 1.00 0.24 No.1

FATIGUE LIMIT STATE Value Limit Ratio CombinationBending stress range in top flange (MPa) [R] 1.96 69.57 0.03 -

[L] 2.58 69.57 0.04 -

Bending stress range in bottom flange (MPa) [R] 33.85 139.13 0.24 -

[L] 43.53 139.13 0.31 -

Page 35 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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CROSS-SECTION CHARACTERISTICS

Beam line No. : 1Section No. : 5Node line No. : 19Type of cross-section : SupportPosition : 15.00 m Support S1

Effective slab width for internal force and moment calculation (1) : 2.67 m

for stress calculation (2) : 2.13 m

Concrete state Casting Uncracked CrackedLoads Permanent Permanent Live -

Modular ratio - 15.54 15.72 6.16Section modulus of top flange (cm3) (2) -7340. 462101. 500487. 87954. -101566.

Section modulus of bottom fibre (cm3) (2) 7340. 14247. 14229. 15659. 13679.

Section modulus of concrete slab (cm3) (2) -373908. -375127. -275406.

Sect. modulus, top reinforcement layer (cm3) (2) -17114.

Shear area (cm2) 137.10

Plastic moment (M > 0) (kN.m) (2) 5714. 5714. 5714.

Plastic moment (M < 0) (kN.m) (2) 5666.

Plastic neutral axis (M > 0) (mm) (2) 957.59 957.59 957.59

Plastic neutral axis (M < 0) (mm) (2) 700.00

Reduction factor Beta (2) 0.990 0.990 0.990

Elastic neutral axis (mm) (1) 350.00 654.84 654.84 654.84

Bending moment of inertia (cm4) (1) 256887. 929458.

Torsional moment of inertia (cm4) (1) 830.94 830.94

Cross-sectional area (cm2) (1) 306.38 546.38

Bending moment of inertia (cm4) (2) 256887. 1029044. 1025144. 1333507. 843876.

Elastic neutral axis (mm) (2) 350.00 722.27 720.48 851.61 616.91

Cross-sectional area (cm2) (2) 306.38 717.04 712.46 1342.08 497.85

NB : -Section modulus is positive for fibres below elastic neutral axis. -Section modulus is negative for fibres above elastic neutral axis. -The position of the neutral axis is measured from the bottom fibre of the bottom steel section flange

Page 36 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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INTERNAL FORCES AND MOMENTS IN CROSS-SECTION OF INTEREST

Beam line No. : 1 M : Bending momentSection No. : 5 V : Shear forceNode line No. : 19 d : DeflectionType of cross-section : Support n : Modular ratioPosition : 15.00 m Support S1

PERMANENT LOADS

left-hand side right-hand side

Load case n M (kN.m) V (kN) M (kN.m) V (kN) d (cm)Self-weight - -681.95 218.77 -681.96 -218.77 0.00

SDL1 15.54 -254.24 87.72 -254.24 -87.73 0.00

Increased SDL1 15.54 -285.16 97.34 -285.16 -97.34 0.00

Reduced SDL1 15.54 -236.33 82.16 -236.33 -82.16 0.00

SDL2 15.54 -55.13 20.03 -55.13 -20.03 0.00

Simpl. temp. load +DTC 15.72 122.92 -25.57 122.92 25.57 0.00

primary effect -261.06 -261.06

secondary effect 383.98 -25.57 383.98 25.57

axial force - slab N = 1068.90 kN N = 1068.90 kN

Simpl. temp. load -DTC 15.72 -122.92 25.57 -122.92 -25.57 0.00

primary effect 261.06 261.06

secondary effect -383.98 25.57 -383.98 -25.57

axial force - slab N = -1068.90 kN N = -1068.90 kN

Concrete shrinkage 15.72 -527.20 35.09 -527.20 -35.09 0.00

primary effect 0.00 0.00

secondary effect -527.20 35.09 -527.20 -35.09

axial force - slab N = 0.00 kN N = 0.00 kN

LIVE LOADS Modular ratio = 6.16

left-hand side right-hand side

Mmax Mmin Vmax Vmin Vmax Vmin dLoad case (kN.m) (kN.m) (kN) (kN) (kN) (kN) (cm)

Load model 1 UDL 0.00 -304.43 0.00 103.88 -103.88 0.00 0.00

Load model 1 TS 0.00 -363.92 0.00 221.21 -219.77 0.00 0.00

Load on footways 0.00 -182.78 0.00 72.94 -72.94 0.00 0.00

Fatigue LM3 Left-hand slow lane 0.07 -221.35 -0.01 148.86 -149.05 0.02

Page 37 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

CHECKING CROSS-SECTION OF INTEREST

Beam line No. : 1Section No. : 5Node line No. : 19Type of cross-section : SupportPosition : 15.00 m Support S1

SERVICEABILITY LIMIT STATE Value Limit Ratio CombinationDeflections (m) 0.000 0.030 0.00 -

Minimum reinforcement (%) [R] 1.01 3.00 0.34 -

[L] 1.01 3.00 0.34 -

Slab cracking [R] max = 25. mm or emax = 200. mm No.23[L] max = 25. mm or emax = 200. mm No.23

Concrete compressive stress (MPa) [R] -0.05 21.00 0.00 -

[L] -0.05 21.00 0.00 -

Tensile stress in reinforcement (MPa) [R] 117.63 400.00 0.29 No.11

[L] 117.63 400.00 0.29 No.11

Stress in top fibre of steel section (MPa) [R] 111.38 265.00 0.42 No.11

[L] 111.38 265.00 0.42 No.11

Stress in bottom fibre of steel section (MPa) [R] -230.05 265.00 0.87 No.11

[L] -230.05 265.00 0.87 No.11

Concrete compressive stress (MPa) [R] 0.00 15.75 0.00 -

[L] 0.00 15.75 0.00 -

Shear stress in steel section (MPa) [R] -55.00 153.00 0.36 No.11

[L] -55.10 153.00 0.36 No.11

Normal stress / shear interaction (MPa) [R] -225.40 265.00 0.85 No.11

[L] -233.35 265.00 0.88 No.11

Shear connection (kN/m) [R] 604.78 1003.49 0.60 No.11

[L] 606.43 1019.91 0.59 No.11

NB : - The minimum reinforcement for Serviceability Limit States has been checked for the maximum bar diameter :*s = 20 mm.The reinforcement ratio is shown as "Limit" and must be greater than the strength value shown as "Value".

- Tensile stresses are positive; compressive stresses are negative.

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ArcelorMittal Composite Bridge Predesign (v3.14)

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Beam line No. : 1Section No. : 5Node line No. : 19Type of cross-section : SupportPosition : 15.00 m Support S1

ULTIMATE LIMIT STATE Value Limit Ratio CombinationPlastic shear resistance (kN) [R] 975.04 2097.57 0.46 No.7

[L] 976.98 2097.57 0.47 No.7

Sagging, Class 1 or 2 (kN.m) [R] 0.00 0.00 - -

[L] 0.00 0.00 - -

Hogging, Class 1 or 2 (kN.m) [R] 2932.89 5666.32 0.52 No.7

[L] 2932.89 5666.32 0.52 No.7

Bending / shear interaction (sagging) (kN.m) [R] - - - -

[L] - - - -

Bending / shear interaction (hogging) (kN.m) [R] - - - -

[L] - - - -

Shear buckling: shear force [R] - - - -

[L] - - - -

Shear buckling: bending / shear interaction [R] - - - -

[L] - - - -

LTBuckling [R] 0.64 1.00 0.64 No.7

[L] 0.64 1.00 0.64 No.7

FATIGUE LIMIT STATE Value Limit Ratio CombinationBending stress range in top flange (MPa) [R] 3.92 69.57 0.06 -

[L] 3.92 69.57 0.06 -

Bending stress range in bottom flange (MPa) [R] 29.14 139.13 0.21 -

[L] 29.14 139.13 0.21 -

Page 39 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

CROSS-SECTION CHARACTERISTICS

Beam line No. : 1Section No. : 6Node line No. : 22Type of cross-section : Limit of support regionPosition : 17.25 m Span No. : 2

Effective slab width for internal force and moment calculation (1) : 2.67 m

for stress calculation (2) : 2.45 m

Concrete state Casting Uncracked CrackedLoads Permanent Permanent Live -

Modular ratio - 15.54 15.72 6.16Section modulus of top flange (cm3) (2) -7340. 242159. 251115. 82319. -150783.

Section modulus of bottom fibre (cm3) (2) 7340. 14480. 14462. 15871. 14005.

Section modulus of concrete slab (cm3) (2) -413202. -414585. -299918.

Sect. modulus, top reinforcement layer (cm3) (2) -19106.

Shear area (cm2) 137.10

Plastic moment (M > 0) (kN.m) (2) 5817. 5817. 5817.

Plastic moment (M < 0) (kN.m) (2) 5861.

Plastic neutral axis (M > 0) (mm) (2) 982.98 982.98 982.98

Plastic neutral axis (M < 0) (mm) (2) 700.00

Reduction factor Beta (2) 1.000 1.000 1.000

Elastic neutral axis (mm) (1) [L] 350.00 654.84 654.84 654.84

Elastic neutral axis (mm) (1) [R] 350.00 757.47 755.76 875.89

Bending moment of inertia (cm4) (1) [L] 256887. 929458.

Bending moment of inertia (cm4) (1) [R] 256887. 1106951. 1103119. 1401531.

Torsional moment of inertia (cm4) (1) [L] 830.94 830.94

Torsional moment of inertia (cm4) (1) [R] 830.94 78042.00 77180.64 195557.40

Cross-sectional area (cm2) (1) [L] 306.38 546.38

Cross-sectional area (cm2) (1) [R] 306.38 821.12 815.38 1604.55

Bending moment of inertia (cm4) (2) 256887. 1078035. 1074170. 1376352. 897008.

Elastic neutral axis (mm) (2) 350.00 744.52 742.78 867.20 640.51

Cross-sectional area (cm2) (2) 306.38 779.49 774.21 1499.56 526.97

NB : -Section modulus is positive for fibres below elastic neutral axis. -Section modulus is negative for fibres above elastic neutral axis. -The position of the neutral axis is measured from the bottom fibre of the bottom steel section flange

Page 40 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

INTERNAL FORCES AND MOMENTS IN CROSS-SECTION OF INTEREST

Beam line No. : 1 M : Bending momentSection No. : 6 V : Shear forceNode line No. : 22 d : DeflectionType of cross-section : Limit of support region n : Modular ratioPosition : 17.25 m Span No. : 2

PERMANENT LOADS

left-hand side right-hand side

Load case n M (kN.m) V (kN) M (kN.m) V (kN) d (cm)Self-weight - -230.76 -182.28 -230.76 -162.52 -0.25

SDL1 15.54 -74.84 -71.88 -75.26 -62.77 -0.02

Increased SDL1 15.54 -85.51 -80.19 -85.83 -70.43 -0.03

Reduced SDL1 15.54 -68.67 -67.07 -69.14 -58.33 -0.02

SDL2 15.54 -14.75 -16.00 -14.98 -13.58 -0.01

Simpl. temp. load +DTC 15.72 65.38 25.57 65.38 25.57 0.01

primary effect -261.06 -261.06

secondary effect 326.44 25.57 326.44 25.57

axial force - slab N = 1068.90 kN N = 1068.90 kN

Simpl. temp. load -DTC 15.72 -65.38 -25.57 -65.38 -25.57 -0.01

primary effect 261.06 261.06

secondary effect -326.44 -25.57 -326.44 -25.57

axial force - slab N = -1068.90 kN N = -1068.90 kN

Concrete shrinkage 15.72 -448.28 -35.06 73.73 -35.06 -0.06

primary effect 0.00 522.13

secondary effect -448.28 -35.06 -448.39 -35.06

axial force - slab N = 0.00 kN N = -2137.79 kN

LIVE LOADS Modular ratio = 6.16

left-hand side right-hand side

Mmax Mmin Vmax Vmin Vmax Vmin dLoad case (kN.m) (kN.m) (kN) (kN) (kN) (kN) (cm)

Load model 1 UDL 49.95 -136.84 -89.44 0.05 -81.14 0.25 -0.08

Load model 1 TS 257.98 -326.31 -218.05 0.77 -212.07 1.04 -0.20

Load on footways 32.57 -71.31 -57.09 0.10 -48.51 1.14 -0.04

Fatigue LM3 Left-hand slow lane 94.30 -175.58 -127.41 0.02 -111.94 0.02

Page 41 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

CHECKING CROSS-SECTION OF INTEREST

Beam line No. : 1Section No. : 6Node line No. : 22Type of cross-section : Limit of support regionPosition : 17.25 m Span No. : 2

SERVICEABILITY LIMIT STATE Value Limit Ratio CombinationDeflections (m) 0.003 0.030 0.10 UDL + TS

Minimum reinforcement (%) [R] 0.98 3.00 0.33 -

[L] 0.98 3.00 0.33 -

Slab cracking [R] max = 25. mm or emax = 200. mm No.23[L] max = 25. mm or emax = 200. mm No.23

Concrete compressive stress (MPa) [R] -1.28 21.00 0.06 No.2

[L] -1.29 21.00 0.06 No.2

Tensile stress in reinforcement (MPa) [R] 72.60 400.00 0.18 No.11

[L] 72.57 400.00 0.18 No.11

Stress in top fibre of steel section (MPa) [R] 47.15 265.00 0.18 No.6

[L] 47.15 265.00 0.18 No.6

Stress in bottom fibre of steel section (MPa) [R] -120.77 265.00 0.46 No.11

[L] -120.72 265.00 0.46 No.11

Concrete compressive stress (MPa) [R] -0.13 15.75 0.01 No.26

[L] -0.13 15.75 0.01 No.26

Shear stress in steel section (MPa) [R] -45.17 153.00 0.30 No.11

[L] -48.92 153.00 0.32 No.11

Normal stress / shear interaction (MPa) [R] -122.17 265.00 0.46 No.11

[L] -123.58 265.00 0.47 No.11

Shear connection (kN/m) [R] 519.31 856.02 0.61 No.11

[L] 555.08 1003.49 0.55 No.11

NB : - The minimum reinforcement for Serviceability Limit States has been checked for the maximum bar diameter :*s = 20 mm.The reinforcement ratio is shown as "Limit" and must be greater than the strength value shown as "Value".

- Tensile stresses are positive; compressive stresses are negative.

Page 42 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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Beam line No. : 1Section No. : 6Node line No. : 22Type of cross-section : Limit of support regionPosition : 17.25 m Span No. : 2

ULTIMATE LIMIT STATE Value Limit Ratio CombinationPlastic shear resistance (kN) [R] 796.46 2097.57 0.38 No.7

[L] 864.65 2097.57 0.41 No.7

Sagging, Class 1 or 2 (kN.m) [R] 86.33 5817.20 0.01 No.8

[L] 13.55 5817.20 0.00 -

Hogging, Class 1 or 2 (kN.m) [R] 1121.01 5861.26 0.19 No.1

[L] 1568.55 5861.26 0.27 No.7

Bending / shear interaction (sagging) (kN.m) [R] - - - -

[L] - - - -

Bending / shear interaction (hogging) (kN.m) [R] - - - -

[L] - - - -

Shear buckling: shear force [R] - - - -

[L] - - - -

Shear buckling: bending / shear interaction [R] - - - -

[L] - - - -

LTBuckling [R] 0.24 1.00 0.24 No.1

[L] 0.33 1.00 0.33 No.7

FATIGUE LIMIT STATE Value Limit Ratio CombinationBending stress range in top flange (MPa) [R] 2.59 69.57 0.04 -

[L] 1.97 69.57 0.03 -

Bending stress range in bottom flange (MPa) [R] 43.50 139.13 0.31 -

[L] 33.82 139.13 0.24 -

Page 43 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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CROSS-SECTION CHARACTERISTICS

Beam line No. : 1Section No. : 7Node line No. : 28Type of cross-section : Mid-spanPosition : 22.50 m Span No. : 2

Effective slab width for internal force and moment calculation (1) : 2.67 m

for stress calculation (2) : 2.67 m

Concrete state Casting Uncracked CrackedLoads Permanent Permanent Live -

Modular ratio - 15.54 15.72 6.16Section modulus of top flange (cm3) (2) -7340. 192613. 197826. 79684. -205832.

Section modulus of bottom fibre (cm3) (2) 7340. 14614. 14596. 16001. 14194.

Section modulus of concrete slab (cm3) (2) -438286. -439782. -315086.

Sect. modulus, top reinforcement layer (cm3) (2) -20421.

Shear area (cm2) 137.10

Plastic moment (M > 0) (kN.m) (2) 5872. 5872. 5872.

Plastic moment (M < 0) (kN.m) (2) 5991.

Plastic neutral axis (M > 0) (mm) (2) 996.49 996.49 996.49

Plastic neutral axis (M < 0) (mm) (2) 700.00

Reduction factor Beta (2) 1.000 1.000 1.000

Elastic neutral axis (mm) (1) 350.00 757.47 755.76 875.89

Bending moment of inertia (cm4) (1) 256887. 1106951. 1103119. 1401531.

Torsional moment of inertia (cm4) (1) 830.94 78042.00 77180.64 195557.40

Cross-sectional area (cm2) (1) 306.38 821.12 815.38 1604.55

Bending moment of inertia (cm4) (2) 256887. 1106951. 1103119. 1401531. 929458.

Elastic neutral axis (mm) (2) 350.00 757.47 755.76 875.89 654.84

Cross-sectional area (cm2) (2) 306.38 821.12 815.38 1604.55 546.38

NB : -Section modulus is positive for fibres below elastic neutral axis. -Section modulus is negative for fibres above elastic neutral axis. -The position of the neutral axis is measured from the bottom fibre of the bottom steel section flange

Page 44 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

INTERNAL FORCES AND MOMENTS IN CROSS-SECTION OF INTEREST

Beam line No. : 1 M : Bending momentSection No. : 7 V : Shear forceNode line No. : 28 d : DeflectionType of cross-section : Mid-span n : Modular ratioPosition : 22.50 m Span No. : 2

PERMANENT LOADS

left-hand side right-hand side

Load case n M (kN.m) V (kN) M (kN.m) V (kN) d (cm)Self-weight - 343.11 -56.11 343.11 -34.84 -1.19

SDL1 15.54 136.76 -19.81 136.61 -11.84 -0.11

Increased SDL1 15.54 154.95 -22.67 154.84 -13.60 -0.13

Reduced SDL1 15.54 126.22 -18.16 126.05 -10.83 -0.10

SDL2 15.54 28.18 -3.87 28.09 -2.28 -0.02

Simpl. temp. load +DTC 15.72 -68.81 25.57 -68.80 25.57 0.08

primary effect -261.06 -261.06

secondary effect 192.26 25.57 192.27 25.57

axial force - slab N = 1068.90 kN N = 1068.90 kN

Simpl. temp. load -DTC 15.72 68.81 -25.57 68.80 -25.57 -0.08

primary effect 261.06 261.06

secondary effect -192.26 -25.57 -192.27 -25.57

axial force - slab N = -1068.90 kN N = -1068.90 kN

Concrete shrinkage 15.72 257.82 -35.09 257.81 -35.09 -0.28

primary effect 522.13 522.13

secondary effect -264.31 -35.09 -264.32 -35.09

axial force - slab N = -2137.79 kN N = -2137.79 kN

LIVE LOADS Modular ratio = 6.16

left-hand side right-hand side

Mmax Mmin Vmax Vmin Vmax Vmin dLoad case (kN.m) (kN.m) (kN) (kN) (kN) (kN) (cm)

Load model 1 UDL 280.18 -80.24 -38.50 11.24 -31.71 16.10 -0.21

Load model 1 TS 835.03 -202.26 -124.49 61.51 -106.66 81.58 -0.54

Load on footways 133.39 -29.62 -23.22 10.68 -19.90 12.92 -0.10

Fatigue LM3 Left-hand slow lane 334.86 -99.57 -50.44 22.51 -42.31 32.58

Page 45 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

CHECKING CROSS-SECTION OF INTEREST

Beam line No. : 1Section No. : 7Node line No. : 28Type of cross-section : Mid-spanPosition : 22.50 m Span No. : 2

SERVICEABILITY LIMIT STATE Value Limit Ratio CombinationDeflections (m) 0.007 0.030 0.25 UDL + TS

Minimum reinforcement (%) [R] 0.95 3.00 0.32 -

[L] 0.95 3.00 0.32 -

Slab cracking [R] max = 25. mm or emax = 200. mm No.24[L] max = 25. mm or emax = 200. mm No.24

Concrete compressive stress (MPa) [R] -4.42 21.00 0.21 No.1

[L] -4.42 21.00 0.21 No.1

Tensile stress in reinforcement (MPa) [R] 32.38 400.00 0.08 No.12

[L] 32.37 400.00 0.08 No.12

Stress in top fibre of steel section (MPa) [R] -73.96 265.00 0.28 No.16

[L] -73.96 265.00 0.28 No.16

Stress in bottom fibre of steel section (MPa) [R] 139.00 265.00 0.52 No.1

[L] 139.01 265.00 0.52 No.1

Concrete compressive stress (MPa) [R] -0.59 15.75 0.04 No.1

[L] -0.59 15.75 0.04 No.1

Shear stress in steel section (MPa) [R] -18.34 153.00 0.12 No.11

[L] -22.61 153.00 0.15 No.11

Normal stress / shear interaction (MPa) [R] -131.61 265.00 0.50 No.1

[L] -132.91 265.00 0.50 No.1

Shear connection (kN/m) [R] 246.85 574.86 0.43 No.11

[L] 289.32 856.02 0.34 No.11

NB : - The minimum reinforcement for Serviceability Limit States has been checked for the maximum bar diameter :*s = 20 mm.The reinforcement ratio is shown as "Limit" and must be greater than the strength value shown as "Value".

- Tensile stresses are positive; compressive stresses are negative.

Page 46 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

Beam line No. : 1Section No. : 7Node line No. : 28Type of cross-section : Mid-spanPosition : 22.50 m Span No. : 2

ULTIMATE LIMIT STATE Value Limit Ratio CombinationPlastic shear resistance (kN) [R] 303.79 2097.57 0.14 No.7

[L] 382.38 2097.57 0.18 No.7

Sagging, Class 1 or 2 (kN.m) [R] 2563.53 5872.03 0.44 No.7

[L] 2563.82 5872.03 0.44 No.7

Hogging, Class 1 or 2 (kN.m) [R] 0.00 0.00 - -

[L] 0.00 0.00 - -

Bending / shear interaction (sagging) (kN.m) [R] - - - -

[L] - - - -

Bending / shear interaction (hogging) (kN.m) [R] - - - -

[L] - - - -

Shear buckling: shear force [R] - - - -

[L] - - - -

Shear buckling: bending / shear interaction [R] - - - -

[L] - - - -

LTBuckling [R] 0.00 0.00 - -

[L] 0.00 0.00 - -

FATIGUE LIMIT STATE Value Limit Ratio CombinationBending stress range in top flange (MPa) [R] 12.72 69.57 0.18 -

[L] 12.72 69.57 0.18 -

Bending stress range in bottom flange (MPa) [R] 63.35 139.13 0.46 -

[L] 63.35 139.13 0.46 -

Page 47 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

Universitatea Tehnica Cluj-Napoca

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User name : Petrut Mirela

E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

CROSS-SECTION CHARACTERISTICS

Beam line No. : 1Section No. : 8Node line No. : 34Type of cross-section : Limit of support regionPosition : 27.75 m Span No. : 2

Effective slab width for internal force and moment calculation (1) : 2.67 m

for stress calculation (2) : 2.49 m

Concrete state Casting Uncracked CrackedLoads Permanent Permanent Live -

Modular ratio - 15.54 15.72 6.16Section modulus of top flange (cm3) (2) -7340. 231512. 239578. 81828. -158305.

Section modulus of bottom fibre (cm3) (2) 7340. 14503. 14485. 15894. 14038.

Section modulus of concrete slab (cm3) (2) -417462. -418864. -302520.

Sect. modulus, top reinforcement layer (cm3) (2) -19327.

Shear area (cm2) 137.10

Plastic moment (M > 0) (kN.m) (2) 5827. 5827. 5827.

Plastic moment (M < 0) (kN.m) (2) 5883.

Plastic neutral axis (M > 0) (mm) (2) 985.41 985.41 985.41

Plastic neutral axis (M < 0) (mm) (2) 700.00

Reduction factor Beta (2) 1.000 1.000 1.000

Elastic neutral axis (mm) (1) 350.00 757.47 755.76 875.89

Bending moment of inertia (cm4) (1) 256887. 1106951. 1103119. 1401531.

Torsional moment of inertia (cm4) (1) 830.94 78042.00 77180.64 195557.40

Cross-sectional area (cm2) (1) 306.38 821.12 815.38 1604.55

Bending moment of inertia (cm4) (2) 256887. 1083067. 1079208. 1380736. 902598.

Elastic neutral axis (mm) (2) 350.00 746.78 745.05 868.74 642.98

Cross-sectional area (cm2) (2) 306.38 786.46 781.10 1517.15 530.22

NB : -Section modulus is positive for fibres below elastic neutral axis. -Section modulus is negative for fibres above elastic neutral axis. -The position of the neutral axis is measured from the bottom fibre of the bottom steel section flange

Page 48 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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User name : Petrut Mirela

E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

INTERNAL FORCES AND MOMENTS IN CROSS-SECTION OF INTEREST

Beam line No. : 1 M : Bending momentSection No. : 8 V : Shear forceNode line No. : 34 d : DeflectionType of cross-section : Limit of support region n : Modular ratioPosition : 27.75 m Span No. : 2

PERMANENT LOADS

left-hand side right-hand side

Load case n M (kN.m) V (kN) M (kN.m) V (kN) d (cm)Self-weight - 246.59 71.59 246.59 91.35 -0.67

SDL1 15.54 95.46 28.27 95.98 35.94 -0.06

Increased SDL1 15.54 108.08 31.98 108.48 40.57 -0.07

Reduced SDL1 15.54 88.15 26.11 88.74 33.25 -0.06

SDL2 15.54 19.76 5.86 20.05 7.54 -0.01

Simpl. temp. load +DTC 15.72 -203.20 25.65 -203.20 25.67 0.07

primary effect -261.06 -261.06

secondary effect 57.87 25.65 57.86 25.67

axial force - slab N = 1068.90 kN N = 1068.90 kN

Simpl. temp. load -DTC 15.72 203.20 -25.65 203.20 -25.67 -0.07

primary effect 261.06 261.06

secondary effect -57.87 -25.65 -57.86 -25.67

axial force - slab N = -1068.90 kN N = -1068.90 kN

Concrete shrinkage 15.72 442.44 -35.25 442.45 -35.31 -0.19

primary effect 522.13 522.13

secondary effect -79.69 -35.25 -79.68 -35.31

axial force - slab N = -2137.79 kN N = -2137.79 kN

LIVE LOADS Modular ratio = 6.16

left-hand side right-hand side

Mmax Mmin Vmax Vmin Vmax Vmin dLoad case (kN.m) (kN.m) (kN) (kN) (kN) (kN) (cm)

Load model 1 UDL 155.72 -23.93 -12.42 53.33 -11.54 62.07 -0.10

Load model 1 TS 460.34 -61.28 -7.89 187.56 -27.84 202.24 -0.26

Load on footways 80.03 -8.01 -6.37 27.95 -4.59 32.37 -0.05

Fatigue LM3 Left-hand slow lane 229.09 -29.16 -13.82 86.93 -13.75 101.28

Page 49 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

Universitatea Tehnica Cluj-Napoca

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E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

CHECKING CROSS-SECTION OF INTEREST

Beam line No. : 1Section No. : 8Node line No. : 34Type of cross-section : Limit of support regionPosition : 27.75 m Span No. : 2

SERVICEABILITY LIMIT STATE Value Limit Ratio CombinationDeflections (m) 0.004 0.030 0.12 UDL + TS

Minimum reinforcement (%) [R] 0.97 3.00 0.32 -

[L] 0.97 3.00 0.32 -

Slab cracking [R] No cracking -

[L] No cracking -

Concrete compressive stress (MPa) [R] -2.57 21.00 0.12 No.9

[L] -2.56 21.00 0.12 No.9

Tensile stress in reinforcement (MPa) [R] 7.86 400.00 0.02 No.4

[L] 7.91 400.00 0.02 No.4

Stress in top fibre of steel section (MPa) [R] -70.46 265.00 0.27 No.16

[L] -70.47 265.00 0.27 No.16

Stress in bottom fibre of steel section (MPa) [R] 89.12 265.00 0.34 No.11

[L] 89.07 265.00 0.34 No.11

Concrete compressive stress (MPa) [R] -0.37 15.75 0.02 No.29

[L] -0.37 15.75 0.02 No.29

Shear stress in steel section (MPa) [R] -31.99 153.00 0.21 No.1

[L] -27.90 153.00 0.18 No.1

Normal stress / shear interaction (MPa) [R] -96.42 265.00 0.36 No.9

[L] -90.15 265.00 0.34 No.9

Shear connection (kN/m) [R] 396.08 720.24 0.55 No.1

[L] 354.79 574.86 0.62 No.1

NB : - The minimum reinforcement for Serviceability Limit States has been checked for the maximum bar diameter :*s = 20 mm.The reinforcement ratio is shown as "Limit" and must be greater than the strength value shown as "Value".

- Tensile stresses are positive; compressive stresses are negative.

Page 50 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

Beam line No. : 1Section No. : 8Node line No. : 34Type of cross-section : Limit of support regionPosition : 27.75 m Span No. : 2

ULTIMATE LIMIT STATE Value Limit Ratio CombinationPlastic shear resistance (kN) [R] 566.93 2097.57 0.27 No.1

[L] 491.81 2097.57 0.23 No.1

Sagging, Class 1 or 2 (kN.m) [R] 1834.56 5827.04 0.31 No.7

[L] 1833.63 5827.04 0.31 No.7

Hogging, Class 1 or 2 (kN.m) [R] 0.00 0.00 - -

[L] 0.00 0.00 - -

Bending / shear interaction (sagging) (kN.m) [R] - - - -

[L] - - - -

Bending / shear interaction (hogging) (kN.m) [R] - - - -

[L] - - - -

Shear buckling: shear force [R] - - - -

[L] - - - -

Shear buckling: bending / shear interaction [R] - - - -

[L] - - - -

LTBuckling [R] 0.00 0.00 - -

[L] 0.00 0.00 - -

FATIGUE LIMIT STATE Value Limit Ratio CombinationBending stress range in top flange (MPa) [R] 8.79 69.57 0.13 -

[L] 8.70 69.57 0.13 -

Bending stress range in bottom flange (MPa) [R] 45.23 139.13 0.33 -

[L] 44.81 139.13 0.32 -

Page 51 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

CROSS-SECTION CHARACTERISTICS

Beam line No. : 1Section No. : 9Node line No. : 37Type of cross-section : SupportPosition : 30.00 m End abutment

Effective slab width for internal force and moment calculation (1) : 2.67 m

for stress calculation (2) : 2.22 m

Concrete state Casting Uncracked CrackedLoads Permanent Permanent Live -

Modular ratio - 15.54 15.72 6.16Section modulus of top flange (cm3) (2) -7340. 361574. 383828. 86117. -112727.

Section modulus of bottom fibre (cm3) (2) 7340. 14317. 14298. 15720. 13776.

Section modulus of concrete slab (cm3) (2) -385085. -386349. -282477.

Sect. modulus, top reinforcement layer (cm3) (2) -17673.

Shear area (cm2) 137.10

Plastic moment (M > 0) (kN.m) (2) 5746. 5746. 5746.

Plastic moment (M < 0) (kN.m) (2) 5721.

Plastic neutral axis (M > 0) (mm) (2) 965.42 965.42 965.42

Plastic neutral axis (M < 0) (mm) (2) 700.00

Reduction factor Beta (2) 0.994 0.994 0.994

Elastic neutral axis (mm) (1) 350.00 757.47 755.76 875.89

Bending moment of inertia (cm4) (1) 256887. 1106951. 1103119. 1401531.

Torsional moment of inertia (cm4) (1) 830.94 78042.00 77180.64 195557.40

Cross-sectional area (cm2) (1) 306.38 821.12 815.38 1604.55

Bending moment of inertia (cm4) (2) 256887. 1043475. 1039583. 1346175. 859287.

Elastic neutral axis (mm) (2) 350.00 728.86 727.08 856.32 623.77

Cross-sectional area (cm2) (2) 306.38 734.47 729.70 1386.04 505.98

NB : -Section modulus is positive for fibres below elastic neutral axis. -Section modulus is negative for fibres above elastic neutral axis. -The position of the neutral axis is measured from the bottom fibre of the bottom steel section flange

Page 52 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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User name : Petrut Mirela

E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

INTERNAL FORCES AND MOMENTS IN CROSS-SECTION OF INTEREST

Beam line No. : 1 M : Bending momentSection No. : 9 V : Shear forceNode line No. : 37 d : DeflectionType of cross-section : Support n : Modular ratioPosition : 30.00 m End abutment

PERMANENT LOADS

left-hand side right-hand side

Load case n M (kN.m) V (kN) M (kN.m) V (kN) d (cm)Self-weight - -0.01 127.84 0.00

SDL1 15.54 -0.15 50.43 0.00

Increased SDL1 15.54 -0.11 56.61 0.00

Reduced SDL1 15.54 -0.18 46.86 0.00

SDL2 15.54 -0.10 10.92 0.00

Simpl. temp. load +DTC 15.72 -261.01 25.70 0.00

primary effect -261.06

secondary effect 0.06 25.70

axial force - slab N = 1068.90 kN

Simpl. temp. load -DTC 15.72 261.01 -25.70 0.00

primary effect 261.06

secondary effect -0.06 -25.70

axial force - slab N = -1068.90 kN

Concrete shrinkage 15.72 522.01 -35.37 0.00

primary effect 522.13

secondary effect -0.12 -35.37

axial force - slab N = -2137.79 kN

LIVE LOADS Modular ratio = 6.16

left-hand side right-hand side

Mmax Mmin Vmax Vmin Vmax Vmin dLoad case (kN.m) (kN.m) (kN) (kN) (kN) (kN) (cm)

Load model 1 UDL 0.00 0.00 -11.24 77.96 0.00

Load model 1 TS 0.00 0.00 -28.14 208.49 0.00

Load on footways 0.00 0.00 -4.12 45.17 0.00

Fatigue LM3 Left-hand slow lane 0.25 -0.62 -14.00 124.76

Page 53 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

CHECKING CROSS-SECTION OF INTEREST

Beam line No. : 1Section No. : 9Node line No. : 37Type of cross-section : SupportPosition : 30.00 m End abutment

SERVICEABILITY LIMIT STATE Value Limit Ratio CombinationDeflections (m) 0.000 0.030 0.00 -

Minimum reinforcement (%) 1.00 3.00 0.33 -

Slab cracking max = 25. mm or emax = 200. mm No.18Concrete compressive stress (MPa) -0.52 21.00 0.02 No.15

Tensile stress in reinforcement (MPa) 7.76 400.00 0.02 No.2

Stress in top fibre of steel section (MPa) -37.29 265.00 0.14 No.16

Stress in bottom fibre of steel section (MPa) 15.42 265.00 0.06 No.15

Concrete compressive stress (MPa) -0.43 15.75 0.03 No.31

Shear stress in steel section (MPa) -38.25 153.00 0.25 No.1

Normal stress / shear interaction (MPa) -66.24 265.00 0.25 No.1

Shear connection (kN/m) 450.45 720.24 0.63 No.1

NB : - The minimum reinforcement for Serviceability Limit States has been checked for the maximum bar diameter :*s = 20 mm.The reinforcement ratio is shown as "Limit" and must be greater than the strength value shown as "Value".

- Tensile stresses are positive; compressive stresses are negative.

ULTIMATE LIMIT STATE Value Limit Ratio CombinationPlastic shear resistance (kN) 680.94 2097.57 0.32 No.1

Sagging, Class 1 or 2 (kN.m) 913.24 5709.69 0.16 No.11

Hogging, Class 1 or 2 (kN.m) 391.90 5720.73 0.07 No.4

Bending / shear interaction (sagging) (kN.m) - - - -

Bending / shear interaction (hogging) (kN.m) - - - -

Shear buckling: shear force - - - -

Shear buckling: bending / shear interaction - - - -

LTBuckling 0.08 1.00 0.08 No.4

FATIGUE LIMIT STATE Value Limit Ratio CombinationBending stress range in top flange (MPa) 0.02 69.57 0.00 -

Bending stress range in bottom flange (MPa) 0.19 139.13 0.00 -

Page 54 / 167Date : 31.01.2014

ArcelorMittal Composite Bridge Predesign (v3.14)

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E:\FACULTATE\MASTER ECO\ANUL II\ACOBRI\VAR1.APM

CROSS-SECTION CHARACTERISTICS

Beam line No. : 2Section No. : 1Node line No. : 1Type of cross-section : SupportPosition : 0.00 m Origin abutment

Effective slab width for internal force and moment calculation (1) : 2.33 m

for stress calculation (2) : 2.03 m

Concrete state Casting Uncracked CrackedLoads Permanent Permanent Live -

Modular ratio - 15.54 15.72 6.16Section modulus of top flange (cm3) (2) -7340. 669681. 756951. 90130. -91544.

Section modulus of bottom fibre (cm3) (2) 7340. 14172. 14153. 15592. 13574.