STAAD PRO V8i

STAAD.Pro

V8i (SELECTseries 3)

Verification Manual

DAA038960-1/0002

STAAD Verification ProblemsRelease STAAD.Pro 20.07.08.XX

Date last updated: 10 October 2011

Quality Assurance ProgramSTAAD.Pro V8i (SELECTseries 3) is a suite of proprietary computer programs of ResearchEngineers, a Bentley Solutions Center. Although every effort has been made to ensure thecorrectness of these programs, neither REI nor Bentley Systems will accept responsibility for anymistake, error or misrepresentation in or as a result of the usage of these programs.

Verification Manual — iii

Table of ContentsSTAAD Verification Problems

1 Plane Truss: Support Reactions Due to a Joint Load 1

2 Natural Frequency Calculation 5

3 Deflection and Moments for a Plate-Bending Finite Element 9

4 Support Reactions for a Simple Frame 15

5 Deflection and stress for a simple beam 21

6 Plane Frame with no Sidesway 27

7 Plane Truss Joint Deflection 33

8 Unequal Plane frame with Sidesway 39

9 Multiple level plane frame with horizontal loads 45

10 Forces in a Space Frame 51

11 Temperature load in different materials 57

12 Deflection and stress of a truss system 63

13 Steel Design per 1989 AISC Code 69

14 Concrete Design per ACI 318 Code 81

15 Natural Modes of a Simple Beam 87

16 Natural Frequencies of a Circular Plate 95

17 Natural Frequencies of a Rectangular Plate 103

18 Natural Modes of a Framework 111

19 Response of a Simply Supported Beam to a Shock Spectrum 121

20 Thermal Loading on a Simply Supported Rectangular Plate 129

21 Deflection Calculation Through Pushover Analysis 143

22 Fixed – Fixed Beam Excited by Harmonic Distributed Load 153

iv — STAAD.Pro

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Verification Manual — v

http://www.bentley.com/bentleywebsite/files/legal/eula_en.pdf

http://www.bentley.com/bentleywebsite/files/legal/eula_en.pdf

1 Plane Truss: Support Reactions Due to a JointLoad

ObjectiveTo find the support reactions due to a joint load in a plane truss.

ReferenceTimoshenko, S., “Strength of Materials,” Part 1, D. Van Nostrand Co., Inc., 3rd edition, 1956, page346, problem 3.

ProblemDetermine the horizontal reaction at support 4 of the system.

Figure 1-1: Plane truss

Comparison

Result Type TheorySTAAD

Basic SolverSTAAD

Advanced Solver

R4 8.77 8.77 8.77

Table 1-1: Comparison of Support Reaction, in kips, for verification problem no.1

STAAD Output

Verification Manual — 1

***************************************************** ** STAAD.Pro V8i SELECTseries2 ** Version 20.07.07.32 ** Proprietary Program of ** Bentley Systems, Inc. ** Date= MAR 9, 2011 ** Time= 11: 4:26 ** ** USER ID: Bentley Systems, Inc. *****************************************************

1. STAAD TRUSS :A PLANE TRUSSINPUT FILE: ver01.STD

2. * FILE: VER01.STD3. *4. * REFERENCE `STRENGTH OF MATERIALS' PART-1 BY S. TIMOSHENKO5. * PAGE 346 PROBLEM NO. 3. THE ANSWER IS REACTION = 0.877P.6. * THEREFORE IF P=10, REACTION = 8.777. *8. UNITS INCH KIP9. JOINT COORD10. 1 0. 0. ; 2 150. 100. ; 3 150. 50. ; 4 300. 0.11. MEMBER INCI12. 1 1 2 ; 2 1 3 ; 3 2 3 ; 4 2 4 ; 5 3 413. MEMB PROP14. 1 4 PRIS AX 5.0 ; 2 5 PRIS AX 3.0 ; 3 PRIS AX 215. CONSTANT ; E 30000. ALL16. SUPPORT ; 1 4 PINNED17. LOADING 118. JOINT LOAD ; 2 FY -10.19. PERFORM ANALYSIS

**WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MOREMEMBERS/ELEMENTS/SOLIDS. THE DEFAULT VALUE HAS BEEN SET FOR THE SAME.P R O B L E M S T A T I S T I C S-----------------------------------

NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 4/ 5/ 2SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER

ORIGINAL/FINAL BAND-WIDTH= 2/ 2/ 4 DOFTOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 4SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDSREQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB:A PLANE TRUSS -- PAGE NO. 2* FILE: VER01.STD20. PRINT REACTION:A PLANE TRUSS -- PAGE NO. 3* FILE: VER01.STDSUPPORT REACTIONS -UNIT KIP INCH STRUCTURE TYPE = TRUSS-----------------

JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z1 1 8.77 5.00 0.00 0.00 0.00 0.004 1 -8.77 5.00 0.00 0.00 0.00 0.00

************** END OF LATEST ANALYSIS RESULT **************21. FINISH

*********** END OF THE STAAD.Pro RUN *************** DATE= MAR 9,2011 TIME= 11: 4:26 ****

:A PLANE TRUSS -- PAGE NO. 4* FILE: VER01.STD

************************************************************* For questions on STAAD.Pro, please contact ** Bentley Systems or Partner offices ** ** Telephone Web / Email ** USA +1 (714) 974-2500 ** UK +44 (0) 808 101 9246 ** SINGAPORE +65 6225-6158 ** FRANCE +33 (0) 1 55238400 *

2— STAAD.Pro

1 Plane Truss: Support Reactions Due to a Joint Load

* GERMANY +49 0931 40468 ** INDIA +91 (033) 4006-2021 ** JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp ** CHINA +86 21 6288 4040 ** THAILAND +66 (0)2645-1018/19 [email protected]** ** Worldwide http://selectservices.bentley.com/en-US/ ** *************************************************************

:A PLANE TRUSS -- PAGE NO. 5* FILE: VER01.STD

Information about the key files in the current distributionModification Date CRC Size (Bytes) File Name-----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe02/22/2011 0xc181 08667136 SProStaadStl.exe09/19/2003 0x2fc0 00081970 CMesh.dll02/17/2011 0xa7c1 04276294 dbsectioninterface.dll02/22/2011 0x12c0 00294912 EC3Annex.dll02/22/2011 0x2900 00376832 EuroCode3.dll12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll01/24/2001 0x9b40 00073728 LoadGen.dll11/19/2010 0xeb80 00011264 MathExtensions.dll09/25/2003 0x6340 00704512 MeshEngine.dll02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll09/22/2003 0xce00 00069632 QuadPlateEngine.dll12/02/2010 0x5040 00073728 SteelCollection.dll02/22/2011 0xca81 00024064 SteelDesign.dll10/08/2010 0xa940 00072192 SteelSections.dll05/29/2008 0x77c1 00106572 SurfMeshEngine.dll10/08/2010 0x4680 00010752 UnitConversions.dll02/08/2011 0xfc00 00974848 AISCSections.mdb06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb01/05/2005 0xcac1 03651584 aitctimbersections.mdb05/01/2008 0xb001 00552960 aluminumsections.mdb01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb10/02/2008 0x40 00520192 AustralianSections.mdb06/11/2010 0xa101 00585728 BritishSections.mdb09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb06/28/2005 0x8201 00327680 butlercoldformedsections.mdb02/25/2008 0x2e01 00329728 CanadianSections.mdb09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb05/31/2005 0x9e81 00450560 canadiantimbersections.mdb02/10/2010 0x94c1 00483328 ChineseSections.mdb01/05/2005 0xd6c0 00600064 dutchsections.mdb10/07/2010 0xd2c0 03596290 EuropeanSections.mdb01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb01/05/2005 0xd301 00202752 frenchsections.mdb01/05/2005 0x11c1 00233472 germansections.mdb10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb12/08/2009 0xec1 00942080 IndianSections.mdb01/05/2005 0xd540 00180224 iscoldformedsections.mdb02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb03/23/2006 0xa080 00200704 japanesesections.mdb02/04/2011 0x3300 00495616 JindalSections.mdb11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb08/24/2007 0x3ec0 00454656 Koreansections.mdb04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb02/07/2005 0x9a00 00243712 mexicansteeltables.mdb04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb11/20/2009 0xf700 00428034 RussianSections.mdb05/12/2009 0xe001 00237570 SouthAfricanSections.mdb01/06/2005 0x9341 00194560 spanishsections.mdb



11/20/2009 0x5100 00368640 STO_ASChMSections.mdb04/19/2007 0x7480 00223232 uscoldformedsections.mdb10/31/2007 0x3700 00133120 VenezuelanSections.mdb-----------------------------------------------------------------------------------------

4 — STAAD.Pro


2 Natural Frequency CalculationObjectiveTo find the period of free vibration for a beam supported on two springs with a point mass.

ReferenceTimoshenko, S., Young, D., and Weaver, W., “Vibration Problems in Engineering,” John Wiley &Sons, 4th edition, 1974. page 11, problem 1.1-3.

ProblemA simple beam is supported by two spring as shown in the figure. Neglecting the distributed massof the beam, calculate the period of free vibration of the beam subjected to a load of W.

Figure 2-1: Beam supported on springs

GivenEI = 30000.0 ksi

A = 7.0 ft

B = 3.0 ft.

W = 1000 lbfK = 300.0 lb/in.

Comparison


Basic SolverSTAAD

Advanced Solver

Period, sec 0.533 0.533 0.533

Table 2-1: Comparison of period, in sec., for verification problem no. 2

STAAD Output



1. STAAD PLANE :NATURAL FREQUENCY OF A BEAM SUPPORTED ON TWO SPRINGSINPUT FILE: ver02.STD

2. * FILE: VER02.STD3. *4. * REFERENCE: TIMOSHENKO,YOUNG,WEAVER, "VIBRATION PROBLEMS IN5. * ENGINEERING", 4TH EDITION, JOHN WILEY & SONS,6. * NEW YORK, 1974, PAGE 11, PROB 1.1-37. * THE ANSWER IN THE BOOK IS T = 0.533 SEC., VIZ., F = 1.876 CPS8. *9. UNIT POUND FEET10. JOINT COORD ; 1 0. 0. ; 2 7. 0. ; 3 10. 0.11. MEMB INCI ; 1 1 2 212. UNIT INCH13. SUPPORT14. 1 3 FIXED BUT MZ KFY 300.15. MEMB PROP ; 1 2 PRIS AX 1. IZ 1.16. CONSTANT ; E 30E6 ALL17. CUT OFF MODE SHAPE 118. LOADING 1 1000 LB LOAD AT JOINT 219. JOINT LOAD ; 2 FY -1000.20. MODAL CALCULATION21. PERFORM ANALYS


NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 3/ 2/ 2:NATURAL FREQUENCY OF A BEAM SUPPORTED ON TWO SPRINGS -- PAGE NO. 2* FILE: VER02.STD

SOLVER USED IS THE OUT-OF-CORE BASIC SOLVERORIGINAL/FINAL BAND-WIDTH= 1/ 1/ 5 DOFTOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 7SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDSREQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB

NUMBER OF MODES REQUESTED = 1NUMBER OF EXISTING MASSES IN THE MODEL = 1NUMBER OF MODES THAT WILL BE USED = 1

:NATURAL FREQUENCY OF A BEAM SUPPORTED ON TWO SPRINGS -- PAGE NO. 3* FILE: VER02.STD

CALCULATED FREQUENCIES FOR LOAD CASE 1MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY1 1.876 0.53317 2.047E-16

MODAL WEIGHT (MODAL MASS TIMES g) IN POUN GENERALIZEDMODE X Y Z WEIGHT

1 0.000000E+00 9.999999E+02 0.000000E+00 9.999999E+02MASS PARTICIPATION FACTORS IN PERCENT--------------------------------------

MODE X Y Z SUMM-X SUMM-Y SUMM-Z1 0.00100.00 0.00 0.000 100.000 0.000

22. FINISH*********** END OF THE STAAD.Pro RUN *************** DATE= MAR 9,2011 TIME= 11: 4:31 ****


************************************************************

6— STAAD.Pro

2 Natural Frequency Calculation

* For questions on STAAD.Pro, please contact ** Bentley Systems or Partner offices ** ** Telephone Web / Email ** USA +1 (714) 974-2500 ** UK +44 (0) 808 101 9246 ** SINGAPORE +65 6225-6158 ** FRANCE +33 (0) 1 55238400 ** GERMANY +49 0931 40468 ** INDIA +91 (033) 4006-2021 ** JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp ** CHINA +86 21 6288 4040 ** THAILAND +66 (0)2645-1018/19 [email protected]** ** Worldwide http://selectservices.bentley.com/en-US/ ** *************************************************************


Information about the key files in the current distributionModification Date CRC Size (Bytes) File Name-----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe02/22/2011 0xc181 08667136 SProStaadStl.exe09/19/2003 0x2fc0 00081970 CMesh.dll02/17/2011 0xa7c1 04276294 dbsectioninterface.dll02/22/2011 0x12c0 00294912 EC3Annex.dll02/22/2011 0x2900 00376832 EuroCode3.dll12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll01/24/2001 0x9b40 00073728 LoadGen.dll11/19/2010 0xeb80 00011264 MathExtensions.dll09/25/2003 0x6340 00704512 MeshEngine.dll02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll09/22/2003 0xce00 00069632 QuadPlateEngine.dll12/02/2010 0x5040 00073728 SteelCollection.dll02/22/2011 0xca81 00024064 SteelDesign.dll10/08/2010 0xa940 00072192 SteelSections.dll05/29/2008 0x77c1 00106572 SurfMeshEngine.dll10/08/2010 0x4680 00010752 UnitConversions.dll02/08/2011 0xfc00 00974848 AISCSections.mdb06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb01/05/2005 0xcac1 03651584 aitctimbersections.mdb05/01/2008 0xb001 00552960 aluminumsections.mdb01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb10/02/2008 0x40 00520192 AustralianSections.mdb06/11/2010 0xa101 00585728 BritishSections.mdb09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb06/28/2005 0x8201 00327680 butlercoldformedsections.mdb02/25/2008 0x2e01 00329728 CanadianSections.mdb09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb05/31/2005 0x9e81 00450560 canadiantimbersections.mdb02/10/2010 0x94c1 00483328 ChineseSections.mdb01/05/2005 0xd6c0 00600064 dutchsections.mdb10/07/2010 0xd2c0 03596290 EuropeanSections.mdb01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb01/05/2005 0xd301 00202752 frenchsections.mdb01/05/2005 0x11c1 00233472 germansections.mdb10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb12/08/2009 0xec1 00942080 IndianSections.mdb01/05/2005 0xd540 00180224 iscoldformedsections.mdb02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb03/23/2006 0xa080 00200704 japanesesections.mdb02/04/2011 0x3300 00495616 JindalSections.mdb



11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb08/24/2007 0x3ec0 00454656 Koreansections.mdb04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb02/07/2005 0x9a00 00243712 mexicansteeltables.mdb04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb11/20/2009 0xf700 00428034 RussianSections.mdb05/12/2009 0xe001 00237570 SouthAfricanSections.mdb01/06/2005 0x9341 00194560 spanishsections.mdb11/20/2009 0x5100 00368640 STO_ASChMSections.mdb04/19/2007 0x7480 00223232 uscoldformedsections.mdb10/31/2007 0x3700 00133120 VenezuelanSections.mdb-----------------------------------------------------------------------------------------

8— STAAD.Pro


3 Deflection and Moments for a Plate-BendingFinite Element

ObjectiveTo find the deflection and moments for plate-bending finite element due to a pressure load.

ReferenceSimple hand calculation by considering the entire structure as a cantilever beam.

ProblemA simple cantilever plate is divided into 12 4-noded finite elements. A uniform pressure load isapplied and the maximum deflection at the tip of the cantilever and the maximum bending at thesupport are calculated.

Figure 3-1: Finite element mesh of cantilevered plate.

GivenPlate thickness = 25 mm

Uniform pressure= 5 N/mm2

Plate length = 6 spaces at 50 mm = 300 mm

Plate width = 2 space at 50 mm = 100 mm


Hand CalculationMax. deflection = WL3/8EI

Where:

WL3/8EI = [(5 · 300 · 100) · (300)3] / [8 · (210 · 103N/mm2)x(100 · 253/12)] = (405 · 1010)/ (21,875 · 107) = 18.51 mm

Max. moment = WL/2 = (5 · 300 · 100) · 300/2 = 22.5(10)6N·mm = 22.5 KN·m

Comparison

Result TypeHand

Calculation

STAADBasicSolver

STAADAdvancedSolver

δmax (mm) 18.51 18.20 18.20

Mmax (KN·m) 22.50 22.50 22.50

Table 3-1: Comparison of max. defl. and max. moment for verification problemno. 3

STAAD Output

10 — STAAD.Pro

3 Deflection and Moments for a Plate-Bending Finite Element


1. STAAD SPACE FINITE ELEMENT VERIFICATIONINPUT FILE: ver03.STD

2. *3. * FILE : VER03.STD4. *5. * DEFLECTION OF A CANTILEVER PLATE UNDER UNIFORM PRESSURE.6. * COMPARISON WITH ESTABLISHED FORMULA (WL^3/8EI)7. *8. UNIT KNS MMS9. JOINT COORDINATES10. 1 0 0 0 7 300 0 011. REPEAT 2 0 50 012. *13. ELEMENT INCIDENCE14. 1 1 2 9 8 TO 615. REPEAT 1 6 716. *17. ELEMENT PROP18. 1 TO 12 THICK 25.019. *20. CONSTANT21. E 210.0 ALL22. POISSON STEEL ALL23. *24. SUPPORT25. 1 8 15 FIXED26. *27. UNIT NEWTON28. LOAD 1 5N/SQ.MM. UNIFORM LOAD29. ELEMENT LOAD30. 1 TO 12 PRESSURE 5.031. *32. PERFORM ANALYSISFINITE ELEMENT VERIFICATION -- PAGE NO. 2*

P R O B L E M S T A T I S T I C S-----------------------------------


ORIGINAL/FINAL BAND-WIDTH= 8/ 5/ 30 DOFTOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 108SIZE OF STIFFNESS MATRIX = 4 DOUBLE KILO-WORDSREQRD/AVAIL. DISK SPACE = 12.1/ 120711.0 MB33. *34. PRINT DISPLACEMENT LIST 14FINITE ELEMENT VERIFICATION -- PAGE NO. 3*JOINT DISPLACEMENT (CM RADIANS) STRUCTURE TYPE = SPACE------------------

JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN14 1 0.0000 0.0000 1.8159 0.0000 -0.0813 0.0000

************** END OF LATEST ANALYSIS RESULT **************35. *36. UNIT KN METER37. PRINT REACTION



FINITE ELEMENT VERIFICATION -- PAGE NO. 4*SUPPORT REACTIONS -UNIT KN METE STRUCTURE TYPE = SPACE-----------------

JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z1 1 0.00 0.00 -18.91 -1.54 5.47 0.008 1 0.00 0.00 -112.19 0.00 11.56 0.0015 1 0.00 0.00 -18.91 1.54 5.47 0.00

************** END OF LATEST ANALYSIS RESULT **************38. FINISHFINITE ELEMENT VERIFICATION -- PAGE NO. 5*


************************************************************* For questions on STAAD.Pro, please contact ** Bentley Systems or Partner offices ** ** Telephone Web / Email ** USA +1 (714) 974-2500 ** UK +44 (0) 808 101 9246 ** SINGAPORE +65 6225-6158 ** FRANCE +33 (0) 1 55238400 ** GERMANY +49 0931 40468 ** INDIA +91 (033) 4006-2021 ** JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp ** CHINA +86 21 6288 4040 ** THAILAND +66 (0)2645-1018/19 [email protected]** ** Worldwide http://selectservices.bentley.com/en-US/ ** *************************************************************

FINITE ELEMENT VERIFICATION -- PAGE NO. 6*

Information about the key files in the current distributionModification Date CRC Size (Bytes) File Name-----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe02/22/2011 0xc181 08667136 SProStaadStl.exe09/19/2003 0x2fc0 00081970 CMesh.dll02/17/2011 0xa7c1 04276294 dbsectioninterface.dll02/22/2011 0x12c0 00294912 EC3Annex.dll02/22/2011 0x2900 00376832 EuroCode3.dll12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll01/24/2001 0x9b40 00073728 LoadGen.dll11/19/2010 0xeb80 00011264 MathExtensions.dll09/25/2003 0x6340 00704512 MeshEngine.dll02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll09/22/2003 0xce00 00069632 QuadPlateEngine.dll12/02/2010 0x5040 00073728 SteelCollection.dll02/22/2011 0xca81 00024064 SteelDesign.dll10/08/2010 0xa940 00072192 SteelSections.dll05/29/2008 0x77c1 00106572 SurfMeshEngine.dll10/08/2010 0x4680 00010752 UnitConversions.dll02/08/2011 0xfc00 00974848 AISCSections.mdb06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb01/05/2005 0xcac1 03651584 aitctimbersections.mdb05/01/2008 0xb001 00552960 aluminumsections.mdb01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb10/02/2008 0x40 00520192 AustralianSections.mdb06/11/2010 0xa101 00585728 BritishSections.mdb09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb06/28/2005 0x8201 00327680 butlercoldformedsections.mdb02/25/2008 0x2e01 00329728 CanadianSections.mdb

12— STAAD.Pro


09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb05/31/2005 0x9e81 00450560 canadiantimbersections.mdb02/10/2010 0x94c1 00483328 ChineseSections.mdb01/05/2005 0xd6c0 00600064 dutchsections.mdb10/07/2010 0xd2c0 03596290 EuropeanSections.mdb01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb01/05/2005 0xd301 00202752 frenchsections.mdb01/05/2005 0x11c1 00233472 germansections.mdb10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb12/08/2009 0xec1 00942080 IndianSections.mdb01/05/2005 0xd540 00180224 iscoldformedsections.mdb02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb03/23/2006 0xa080 00200704 japanesesections.mdb02/04/2011 0x3300 00495616 JindalSections.mdb11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb08/24/2007 0x3ec0 00454656 Koreansections.mdb04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb02/07/2005 0x9a00 00243712 mexicansteeltables.mdb04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb11/20/2009 0xf700 00428034 RussianSections.mdb05/12/2009 0xe001 00237570 SouthAfricanSections.mdb01/06/2005 0x9341 00194560 spanishsections.mdb11/20/2009 0x5100 00368640 STO_ASChMSections.mdb04/19/2007 0x7480 00223232 uscoldformedsections.mdb10/31/2007 0x3700 00133120 VenezuelanSections.mdb-----------------------------------------------------------------------------------------



14 — STAAD.Pro


NOTES

4 Support Reactions for a Simple FrameObjectiveTo find support reactions due to a load at the free end of a cantilever bent plate with anintermediate support.

ReferenceTimoshenko, S., “Strength of Materials,” Part 1, D. Van Nostrand Co., Inc., 3rd edition, 1956, page346, problem 2.

ProblemDetermine the reaction of the system as shown in the figure.

Figure 4-1: Cantilever model

GivenP = 1 kip

L = 10 in


Comparison


Basic SolverSTAAD

Advanced Solver

Rx 1.5 1.5 1.5

Table 4-1: Comparison of reaction, in kips, for verification problem no. 4

STAAD Output

16— STAAD.Pro

4 Support Reactions for a Simple Frame


1. STAAD PLANE :A CANTILEVER PLANE FRAME WITH AN INTERMEDIATE SUPPORTINPUT FILE: ver04.STD

2. * FILE VER04.STD3. *4. * REFERENCE: 'STRENGTH OF MATERIALS' PART-1 BY S. TIMOSHENKO5. * PAGE 346 PROBLEM NO. 2. THE ANSWER IN THE BOOK AFTER6. * RECALCULATION = 1.57. *8. UNIT INCH KIP9. JOINT COORD10. 1 0. 0. ; 2 0. 10. ; 3 0. 20. ; 4 10. 20.11. SUPPORT12. 1 FIXED ; 2 FIXED BUT FY MZ13. MEMB INCI14. 1 1 2 315. MEMB PROP ; 1 2 3 PRIS AX 10. IZ 100.16. CONSTANT ; E 3000. ALL17. LOADING 118. JOINT LOAD ; 4 FY -1.19. PERFORM ANALYSIS



ORIGINAL/FINAL BAND-WIDTH= 1/ 1/ 6 DOFTOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 8SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDSREQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB:A CANTILEVER PLANE FRAME WITH AN INTERMEDIATE SUPPORT -- PAGE NO. 2* FILE VER04.STD20. PRINT REACTION:A CANTILEVER PLANE FRAME WITH AN INTERMEDIATE SUPPORT -- PAGE NO. 3* FILE VER04.STDSUPPORT REACTIONS -UNIT KIP INCH STRUCTURE TYPE = PLANE-----------------

JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z1 1 1.50 1.00 0.00 0.00 0.00 -5.002 1 -1.50 0.00 0.00 0.00 0.00 0.00



:A CANTILEVER PLANE FRAME WITH AN INTERMEDIATE SUPPORT -- PAGE NO. 4* FILE VER04.STD





:A CANTILEVER PLANE FRAME WITH AN INTERMEDIATE SUPPORT -- PAGE NO. 5* FILE VER04.STD


18— STAAD.Pro





20 — STAAD.Pro


NOTES

5 Deflection and stress for a simple beamObjectiveTo find deflections and stress at the center of a locomotive axle.

ReferenceTimoshenko, S.,“Strength of Materials,” Part- 1, D. Van Nostrand Co., 3rd edition, 1956. page 97,problems 1, 2.

ProblemDetermine the maximum stress in a locomotive axle (as shown in the figure) as well as thedeflection at the middle of the axle.

Figure 5-1: Locomotive axle model

GivenDiameter = 10 in.,

P = 26000 lbf

E = 30E6 psi

L1 = 13.5 in., L2 = 59 in.


Comparison


Basic SolverSTAAD

Advanced Solver

σ 3575.* 3575. 3575.

δ 0.01040 0.01037 0.01037

Table 5-1: Comparison of stress (σ), psi, and Deflection (δ), in. for verificationmodel no. 5

* The value is recalculated.

STAAD Output

22— STAAD.Pro

5 Deflection and stress for a simple beam


1. STAAD PLANE :A LOCOMOTIVE AXLEINPUT FILE: ver05.STD

2. * FILE: VER05.STD3. *4. * REFERENCE 'STRENGTH OF MATERIALS' PART-1 BY S. TIMOSHENKO5. * PAGE 97 PROBLEM NO. 1 AND 2.6. * ANSWERS ARE 3580 FOR MAX. STRESS AND 0.104 INCH FOR MAX. DEFLN.7. *8. UNIT INCH POUND9. JOINT COORD10. 1 0. 0. ; 2 13.5 0. ; 3 43. 0. ; 4 72.5 0. ; 5 86. 0.11. SUPPORT ; 2 4 PINNED12. MEMB INCI ; 1 1 2 413. MEMB PROP ; 1 TO 4 TABLE ST PIPE OD 10. ID 0.14. CONSTANT ; E 30E6 ALL15. LOADING 116. JOINT LOAD ; 1 5 FY -26000.17. PERFORM ANALYSIS



ORIGINAL/FINAL BAND-WIDTH= 1/ 1/ 4 DOFTOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 11SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDSREQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB18. PRINT MEMBER STRESSES:A LOCOMOTIVE AXLE -- PAGE NO. 2* FILE: VER05.STD:A LOCOMOTIVE AXLE -- PAGE NO. 3* FILE: VER05.STD

MEMBER STRESSES---------------ALL UNITS ARE POUN/SQ INCHMEMB LD SECT AXIAL BEND-Y BEND-Z COMBINED SHEAR-Y SHEAR-Z

1 1 .0 0.0 0.0 0.0 0.0 441.4 0.01.00 0.0 0.0 3575.3 3575.3 441.4 0.0

2 1 .0 0.0 0.0 3575.3 3575.3 0.0 0.01.00 0.0 0.0 3575.3 3575.3 0.0 0.0

3 1 .0 0.0 0.0 3575.3 3575.3 0.0 0.01.00 0.0 0.0 3575.3 3575.3 0.0 0.0

4 1 .0 0.0 0.0 3575.3 3575.3 441.4 0.01.00 0.0 0.0 0.0 0.0 441.4 0.0

************** END OF LATEST ANALYSIS RESULT **************19. PRINT DISPLACEMENTS:A LOCOMOTIVE AXLE -- PAGE NO. 4* FILE: VER05.STDJOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = PLANE------------------

JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN1 1 0.00000 -0.01138 0.00000 0.00000 0.00000 0.000862 1 0.00000 0.00000 0.00000 0.00000 0.00000 0.000703 1 0.00000 0.01037 0.00000 0.00000 0.00000 0.00000



4 1 0.00000 0.00000 0.00000 0.00000 0.00000 -0.000705 1 0.00000 -0.01138 0.00000 0.00000 0.00000 -0.00086



:A LOCOMOTIVE AXLE -- PAGE NO. 5* FILE: VER05.STD


:A LOCOMOTIVE AXLE -- PAGE NO. 6* FILE: VER05.STD

Information about the key files in the current distributionModification Date CRC Size (Bytes) File Name-----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe02/22/2011 0xc181 08667136 SProStaadStl.exe09/19/2003 0x2fc0 00081970 CMesh.dll02/17/2011 0xa7c1 04276294 dbsectioninterface.dll02/22/2011 0x12c0 00294912 EC3Annex.dll02/22/2011 0x2900 00376832 EuroCode3.dll12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll01/24/2001 0x9b40 00073728 LoadGen.dll11/19/2010 0xeb80 00011264 MathExtensions.dll09/25/2003 0x6340 00704512 MeshEngine.dll02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll09/22/2003 0xce00 00069632 QuadPlateEngine.dll12/02/2010 0x5040 00073728 SteelCollection.dll02/22/2011 0xca81 00024064 SteelDesign.dll10/08/2010 0xa940 00072192 SteelSections.dll05/29/2008 0x77c1 00106572 SurfMeshEngine.dll10/08/2010 0x4680 00010752 UnitConversions.dll02/08/2011 0xfc00 00974848 AISCSections.mdb06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb01/05/2005 0xcac1 03651584 aitctimbersections.mdb05/01/2008 0xb001 00552960 aluminumsections.mdb01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb10/02/2008 0x40 00520192 AustralianSections.mdb06/11/2010 0xa101 00585728 BritishSections.mdb09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb06/28/2005 0x8201 00327680 butlercoldformedsections.mdb02/25/2008 0x2e01 00329728 CanadianSections.mdb09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb05/31/2005 0x9e81 00450560 canadiantimbersections.mdb02/10/2010 0x94c1 00483328 ChineseSections.mdb01/05/2005 0xd6c0 00600064 dutchsections.mdb10/07/2010 0xd2c0 03596290 EuropeanSections.mdb01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb

24 — STAAD.Pro


01/05/2005 0xd301 00202752 frenchsections.mdb01/05/2005 0x11c1 00233472 germansections.mdb10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb12/08/2009 0xec1 00942080 IndianSections.mdb01/05/2005 0xd540 00180224 iscoldformedsections.mdb02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb03/23/2006 0xa080 00200704 japanesesections.mdb02/04/2011 0x3300 00495616 JindalSections.mdb11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb08/24/2007 0x3ec0 00454656 Koreansections.mdb04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb02/07/2005 0x9a00 00243712 mexicansteeltables.mdb04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb11/20/2009 0xf700 00428034 RussianSections.mdb05/12/2009 0xe001 00237570 SouthAfricanSections.mdb01/06/2005 0x9341 00194560 spanishsections.mdb11/20/2009 0x5100 00368640 STO_ASChMSections.mdb04/19/2007 0x7480 00223232 uscoldformedsections.mdb10/31/2007 0x3700 00133120 VenezuelanSections.mdb-----------------------------------------------------------------------------------------



26— STAAD.Pro


NOTES

6 Plane Frame with no SideswayObjectiveTo find the maximum moment due to a uniform load on the horizontal member in a 1x1 bay planeframe.

ReferenceMcCormack, J. C., “Structural Analysis,” Intext Educational Publishers, 3rd edition, 1975, page 383,example 22 - 5.

ProblemDetermine the maximum moment in the frame.

Figure 6-1: 1x1 bay plane frame

GivenE and I same for all members.


Comparison


Basic SolverSTAAD

Advanced Solver

MMax 44.40 44.44 44.44

Table 6-1: Comparison of moment, in kip-ft, for verification problem no. 6

STAAD Output

28— STAAD.Pro

6 Plane Frame with no Sidesway


1. STAAD PLANE :A 1X1 BAY PLANE FRAMEINPUT FILE: ver06.STD

2. * FILE VER06.STD3. *4. * REFERENCE: 'STRUCTURAL ANALYSIS' BY JACK C. MCCORMACK,5. * PAGE 383 EXAMPLE 22-5, PLANE FRAME WITH NO SIDESWAY6. * ANSWER - MAX BENDING = 44.4 FT-KIP7. *8. UNIT FT KIP9. JOINT COORD10. 1 0. 0. ; 2 0. 20. ; 3 20. 20. ; 4 20. 0.11. MEMB INCI ; 1 1 2 312. MEMB PROP ; 1 2 3 PRIS AX 1. IZ 0.0513. CONSTANT ; E 4132E3 ALL14. SUPPORT ; 1 4 FIXED15. LOADING 1 ; MEMB LOAD ; 2 UNI Y -2.016. PERFORM ANALYSIS



ORIGINAL/FINAL BAND-WIDTH= 1/ 1/ 6 DOFTOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 6SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDSREQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB17. PRINT FORCES:A 1X1 BAY PLANE FRAME -- PAGE NO. 2* FILE VER06.STDMEMBER END FORCES STRUCTURE TYPE = PLANE-----------------ALL UNITS ARE -- KIP FEET (LOCAL )MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z

1 1 1 20.00 -3.33 0.00 0.00 0.00 -22.212 -20.00 3.33 0.00 0.00 0.00 -44.44

2 1 2 3.33 20.00 0.00 0.00 0.00 44.443 -3.33 20.00 0.00 0.00 0.00 -44.44

3 1 3 20.00 3.33 0.00 0.00 0.00 44.444 -20.00 -3.33 0.00 0.00 0.00 22.21



:A 1X1 BAY PLANE FRAME -- PAGE NO. 3* FILE VER06.STD







30 — STAAD.Pro





32— STAAD.Pro


NOTES

7 Plane Truss Joint DeflectionObjectiveTo find the joint deflection due to joint loads in a plane truss.


ProblemDetermine the vertical deflection at point 5 of plane truss structure shown in the figure.

Figure 7-1: Plane truss model

GivenP = 20 kip

Truss width = 4 spaces at 15 ft = 60 ft

Truss height = 15 ft

AX 1-4 = 1 in2, AX 5-6 = 2 in

2, AX 7-8 =1.5 in2,

AX 9-11B = 3 in2P, AX 12-13 = 4 in

2

E = 30E3 ksi


Comparison


Basic SolverSTAAD

Advanced Solver

δ5 (in.) 2.63 2.63 2.63

Table 7-1: Comparison of deflection (δ) for verification problem no. 7

STAAD Output

34 — STAAD.Pro

7 Plane Truss Joint Deflection



2. * FILE VER07.STD3. *4. * REFERENCE 'STRUCTURAL ANALYSIS' BY JACK MCCORMACK, PAGE 271,5. * EXAMPLE 18-2. ANSWER - Y-DISP AT JOINT 5 = 2.63 INCH6. *8. UNIT FT KIP9. JOINT COORD10. 1 0 0 0 5 60 0 011. 6 15. 7.5 ; 7 30. 15. ; 8 45. 7.512. SUPPORT13. 1 PINNED ; 3 FIXED BUT FX MZ14. MEMB INCI15. 1 2 6 ; 2 3 4 ; 3 4 8 ; 4 4 5 ; 5 1 216. 6 2 3 ; 7 3 6 ; 8 3 8 ; 9 3 717. 10 1 6 ; 11 5 8 ; 12 6 7 1318. UNIT INCH19. MEMB PROP20. 1 TO 4 PRI AX 1.021. 5 6 PRIS AX 2.22. 7 8 PRI AX 1.523. 9 10 11 PRI AX 3.24. 12 13 PRI AX 4.25. CONSTANT ; E 30E3 ALL26. LOAD 1 VERTICAL LOAD27. JOINT LOAD28. 2 4 5 FY -20.029. PERFORM ANALYSIS

**WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MOREMEMBERS/ELEMENTS/SOLIDS. THE DEFAULT VALUE HAS BEEN SET FOR THE SAME.

:A PLANE TRUSS -- PAGE NO. 2* FILE VER07.STD



ORIGINAL/FINAL BAND-WIDTH= 5/ 5/ 11 DOFTOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 13SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDSREQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB30. PRINT DISPLACEMENTS LIST 5:A PLANE TRUSS -- PAGE NO. 3* FILE VER07.STDJOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = TRUSS------------------

JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN5 1 -0.72000 -2.63033 0.00000 0.00000 0.00000 0.00000




************************************************************



* For questions on STAAD.Pro, please contact ** Bentley Systems or Partner offices ** ** Telephone Web / Email ** USA +1 (714) 974-2500 ** UK +44 (0) 808 101 9246 ** SINGAPORE +65 6225-6158 ** FRANCE +33 (0) 1 55238400 ** GERMANY +49 0931 40468 ** INDIA +91 (033) 4006-2021 ** JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp ** CHINA +86 21 6288 4040 ** THAILAND +66 (0)2645-1018/19 [email protected]** ** Worldwide http://selectservices.bentley.com/en-US/ ** *************************************************************


Information about the key files in the current distributionModification Date CRC Size (Bytes) File Name-----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe02/22/2011 0xc181 08667136 SProStaadStl.exe09/19/2003 0x2fc0 00081970 CMesh.dll02/17/2011 0xa7c1 04276294 dbsectioninterface.dll02/22/2011 0x12c0 00294912 EC3Annex.dll02/22/2011 0x2900 00376832 EuroCode3.dll12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll01/24/2001 0x9b40 00073728 LoadGen.dll11/19/2010 0xeb80 00011264 MathExtensions.dll09/25/2003 0x6340 00704512 MeshEngine.dll02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll09/22/2003 0xce00 00069632 QuadPlateEngine.dll12/02/2010 0x5040 00073728 SteelCollection.dll02/22/2011 0xca81 00024064 SteelDesign.dll10/08/2010 0xa940 00072192 SteelSections.dll05/29/2008 0x77c1 00106572 SurfMeshEngine.dll10/08/2010 0x4680 00010752 UnitConversions.dll02/08/2011 0xfc00 00974848 AISCSections.mdb06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb01/05/2005 0xcac1 03651584 aitctimbersections.mdb05/01/2008 0xb001 00552960 aluminumsections.mdb01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb10/02/2008 0x40 00520192 AustralianSections.mdb06/11/2010 0xa101 00585728 BritishSections.mdb09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb06/28/2005 0x8201 00327680 butlercoldformedsections.mdb02/25/2008 0x2e01 00329728 CanadianSections.mdb09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb05/31/2005 0x9e81 00450560 canadiantimbersections.mdb02/10/2010 0x94c1 00483328 ChineseSections.mdb01/05/2005 0xd6c0 00600064 dutchsections.mdb10/07/2010 0xd2c0 03596290 EuropeanSections.mdb01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb01/05/2005 0xd301 00202752 frenchsections.mdb01/05/2005 0x11c1 00233472 germansections.mdb10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb12/08/2009 0xec1 00942080 IndianSections.mdb01/05/2005 0xd540 00180224 iscoldformedsections.mdb02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb03/23/2006 0xa080 00200704 japanesesections.mdb02/04/2011 0x3300 00495616 JindalSections.mdb

36— STAAD.Pro


11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb08/24/2007 0x3ec0 00454656 Koreansections.mdb04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb02/07/2005 0x9a00 00243712 mexicansteeltables.mdb04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb11/20/2009 0xf700 00428034 RussianSections.mdb05/12/2009 0xe001 00237570 SouthAfricanSections.mdb01/06/2005 0x9341 00194560 spanishsections.mdb11/20/2009 0x5100 00368640 STO_ASChMSections.mdb04/19/2007 0x7480 00223232 uscoldformedsections.mdb10/31/2007 0x3700 00133120 VenezuelanSections.mdb-----------------------------------------------------------------------------------------



38— STAAD.Pro


NOTES

8 Unequal Plane frame with SideswayObjectiveTo find the maximum moment due to a concentrated load on the horizontal member in a 1x1 bayplane frame.

ReferenceMcCormack, J. C., “Structural Analysis,” Intext Educational Publishers, 3rd edition, 1975, page 385,problem 22 - 6.

ProblemDetermine the maximum moment in the structure.

Figure 8-1: Unequal leg bay model

GivenP = 30 kip

H1 = 20 ft, H3 = 30 ft

L = 30 ft, with P occurring at 10 ft from Leg #1

E and I same for all members


Comparison


Basic SolverSTAAD

Advanced Solver

MMax 69.40 69.44 69.44

Table 8-1: Comparison of max. moment, in kip-ft, for verification model no. 8

STAAD Output

40 — STAAD.Pro

8 Unequal Plane frame with Sidesway

***************************************************** ** STAAD.Pro V8i SELECTseries2 ** Version 20.07.07.32 ** Proprietary Program of ** Bentley Systems, Inc. ** Date= MAR 9, 2011 ** Time= 11: 5: 0 ** ** USER ID: Bentley Systems, Inc. *****************************************************


2. * FILE VER08.STD3. *4. * REFERENCE: 'STRUCTURAL ANALYSIS' BY JACK MCCORMACK,5. * PAGE 385 PROB 22-6.6. * ANSWER - MAX BENDING IN MEMB 1 = 69.4 KIP-FT7. *8. UNIT FT KIP9. JOINT COORD10. 1 0. 10. ; 2 0 30 ; 3 30 30 ; 4 30 011. SUPPORT ; 1 4 FIXED12. MEMB INCI13. 1 1 2 314. MEMB PROP ; 1 2 3 TAB ST W12X2615. CONSTANT ; E 4176E316. LOAD 1 VERTICAL LOAD17. MEMBER LOAD18. 2 CON Y -30. 10.19. PERFORM ANALYSIS



ORIGINAL/FINAL BAND-WIDTH= 1/ 1/ 6 DOFTOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 6SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDSREQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB:A 1X1 BAY PLANE FRAME -- PAGE NO. 2* FILE VER08.STD20. PRINT FORCES:A 1X1 BAY PLANE FRAME -- PAGE NO. 3* FILE VER08.STDMEMBER END FORCES STRUCTURE TYPE = PLANE-----------------ALL UNITS ARE -- KIP FEET (LOCAL )MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z

1 1 1 20.09 -3.74 0.00 0.00 0.00 -5.342 -20.09 3.74 0.00 0.00 0.00 -69.44

2 1 2 3.74 20.09 0.00 0.00 0.00 69.443 -3.74 9.91 0.00 0.00 0.00 -66.66

3 1 3 9.91 3.74 0.00 0.00 0.00 66.664 -9.91 -3.74 0.00 0.00 0.00 45.51


*********** END OF THE STAAD.Pro RUN *************** DATE= MAR 9,2011 TIME= 11: 5: 0 ****


************************************************************* For questions on STAAD.Pro, please contact ** Bentley Systems or Partner offices ** *



* Telephone Web / Email ** USA +1 (714) 974-2500 ** UK +44 (0) 808 101 9246 ** SINGAPORE +65 6225-6158 ** FRANCE +33 (0) 1 55238400 ** GERMANY +49 0931 40468 ** INDIA +91 (033) 4006-2021 ** JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp ** CHINA +86 21 6288 4040 ** THAILAND +66 (0)2645-1018/19 [email protected]** ** Worldwide http://selectservices.bentley.com/en-US/ ** *************************************************************


Information about the key files in the current distributionModification Date CRC Size (Bytes) File Name-----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe02/22/2011 0xc181 08667136 SProStaadStl.exe09/19/2003 0x2fc0 00081970 CMesh.dll02/17/2011 0xa7c1 04276294 dbsectioninterface.dll02/22/2011 0x12c0 00294912 EC3Annex.dll02/22/2011 0x2900 00376832 EuroCode3.dll12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll01/24/2001 0x9b40 00073728 LoadGen.dll11/19/2010 0xeb80 00011264 MathExtensions.dll09/25/2003 0x6340 00704512 MeshEngine.dll02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll09/22/2003 0xce00 00069632 QuadPlateEngine.dll12/02/2010 0x5040 00073728 SteelCollection.dll02/22/2011 0xca81 00024064 SteelDesign.dll10/08/2010 0xa940 00072192 SteelSections.dll05/29/2008 0x77c1 00106572 SurfMeshEngine.dll10/08/2010 0x4680 00010752 UnitConversions.dll02/08/2011 0xfc00 00974848 AISCSections.mdb06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb01/05/2005 0xcac1 03651584 aitctimbersections.mdb05/01/2008 0xb001 00552960 aluminumsections.mdb01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb10/02/2008 0x40 00520192 AustralianSections.mdb06/11/2010 0xa101 00585728 BritishSections.mdb09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb06/28/2005 0x8201 00327680 butlercoldformedsections.mdb02/25/2008 0x2e01 00329728 CanadianSections.mdb09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb05/31/2005 0x9e81 00450560 canadiantimbersections.mdb02/10/2010 0x94c1 00483328 ChineseSections.mdb01/05/2005 0xd6c0 00600064 dutchsections.mdb10/07/2010 0xd2c0 03596290 EuropeanSections.mdb01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb01/05/2005 0xd301 00202752 frenchsections.mdb01/05/2005 0x11c1 00233472 germansections.mdb10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb12/08/2009 0xec1 00942080 IndianSections.mdb01/05/2005 0xd540 00180224 iscoldformedsections.mdb02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb03/23/2006 0xa080 00200704 japanesesections.mdb02/04/2011 0x3300 00495616 JindalSections.mdb11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb08/24/2007 0x3ec0 00454656 Koreansections.mdb04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb

42— STAAD.Pro


02/07/2005 0x9a00 00243712 mexicansteeltables.mdb04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb11/20/2009 0xf700 00428034 RussianSections.mdb05/12/2009 0xe001 00237570 SouthAfricanSections.mdb01/06/2005 0x9341 00194560 spanishsections.mdb11/20/2009 0x5100 00368640 STO_ASChMSections.mdb04/19/2007 0x7480 00223232 uscoldformedsections.mdb10/31/2007 0x3700 00133120 VenezuelanSections.mdb-----------------------------------------------------------------------------------------



44 — STAAD.Pro


NOTES

9 Multiple level plane frame with horizontal loadsObjectiveTo find the maximum moment due to lateral joint loads in a 1x2 bay plane frame.


ProblemDetermine the maximum moment in the frame.

Figure 9-1: Two story frame model

GivenL = 20 ft

H3 = 20 kip, H5 = 10 kip

E and I same for all members.


Comparison


Basic SolverSTAAD

Advanced Solver

MMax 176.40 178.01 178.01

Table 9-1: Comparison of max. moment, in kip-ft, for verification problem no.9

STAAD Output

46— STAAD.Pro

9 Multiple level plane frame with horizontal loads



2. * FILE: VER09.STD3. *4. * REFERENCE: 'STRUCTURAL ANALYSIS' BY JACK MCCORMACK,5. * PAGE 388, PROB 22-7.6. * ANSWER - MAX MOM IN MEMB 1 = 176.4 K-F7. *8. UNIT FT KIP9. JOINT COORD10. 1 0 0 0 5 0 40 0 2 ; 2 20 0 0 6 20 40 0 211. SUPPORT ; 1 2 FIXED12. MEMB INCI13. 1 1 3 2 ; 3 3 5 4 ; 5 3 4 ; 6 5 614. MEMB PROP15. 1 TO 6 PRI AX .2 IZ .116. CONSTANT ; E 4176E317. LOAD 1 HORIZONTAL LOAD18. JOINT LOAD19. 3 FX 20 ; 5 FX 1020. PERFORM ANALYS



ORIGINAL/FINAL BAND-WIDTH= 3/ 3/ 9 DOFTOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 12SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDSREQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB:A 1X2 BAY PLANE FRAME -- PAGE NO. 2* FILE: VER09.STD21. PRINT FORCES:A 1X2 BAY PLANE FRAME -- PAGE NO. 3* FILE: VER09.STDMEMBER END FORCES STRUCTURE TYPE = PLANE-----------------ALL UNITS ARE -- KIP FEET (LOCAL )MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z

1 1 1 -22.26 15.06 0.00 0.00 0.00 178.013 22.26 -15.06 0.00 0.00 0.00 123.16

2 1 2 22.26 14.94 0.00 0.00 0.00 176.734 -22.26 -14.94 0.00 0.00 0.00 122.10

3 1 3 -6.51 4.97 0.00 0.00 0.00 34.495 6.51 -4.97 0.00 0.00 0.00 64.93

4 1 4 6.51 5.03 0.00 0.00 0.00 35.346 -6.51 -5.03 0.00 0.00 0.00 65.24

5 1 3 9.91 -15.75 0.00 0.00 0.00 -157.654 -9.91 15.75 0.00 0.00 0.00 -157.44

6 1 5 5.03 -6.51 0.00 0.00 0.00 -64.936 -5.03 6.51 0.00 0.00 0.00 -65.24


*********** END OF THE STAAD.Pro RUN ***********



**** DATE= MAR 9,2011 TIME= 11: 5: 6 ****:A 1X2 BAY PLANE FRAME -- PAGE NO. 4* FILE: VER09.STD


:A 1X2 BAY PLANE FRAME -- PAGE NO. 5* FILE: VER09.STD

Information about the key files in the current distributionModification Date CRC Size (Bytes) File Name-----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe02/22/2011 0xc181 08667136 SProStaadStl.exe09/19/2003 0x2fc0 00081970 CMesh.dll02/17/2011 0xa7c1 04276294 dbsectioninterface.dll02/22/2011 0x12c0 00294912 EC3Annex.dll02/22/2011 0x2900 00376832 EuroCode3.dll12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll01/24/2001 0x9b40 00073728 LoadGen.dll11/19/2010 0xeb80 00011264 MathExtensions.dll09/25/2003 0x6340 00704512 MeshEngine.dll02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll09/22/2003 0xce00 00069632 QuadPlateEngine.dll12/02/2010 0x5040 00073728 SteelCollection.dll02/22/2011 0xca81 00024064 SteelDesign.dll10/08/2010 0xa940 00072192 SteelSections.dll05/29/2008 0x77c1 00106572 SurfMeshEngine.dll10/08/2010 0x4680 00010752 UnitConversions.dll02/08/2011 0xfc00 00974848 AISCSections.mdb06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb01/05/2005 0xcac1 03651584 aitctimbersections.mdb05/01/2008 0xb001 00552960 aluminumsections.mdb01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb10/02/2008 0x40 00520192 AustralianSections.mdb06/11/2010 0xa101 00585728 BritishSections.mdb09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb06/28/2005 0x8201 00327680 butlercoldformedsections.mdb02/25/2008 0x2e01 00329728 CanadianSections.mdb09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb05/31/2005 0x9e81 00450560 canadiantimbersections.mdb02/10/2010 0x94c1 00483328 ChineseSections.mdb01/05/2005 0xd6c0 00600064 dutchsections.mdb10/07/2010 0xd2c0 03596290 EuropeanSections.mdb01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb01/05/2005 0xd301 00202752 frenchsections.mdb01/05/2005 0x11c1 00233472 germansections.mdb10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb12/08/2009 0xec1 00942080 IndianSections.mdb

48— STAAD.Pro


01/05/2005 0xd540 00180224 iscoldformedsections.mdb02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb03/23/2006 0xa080 00200704 japanesesections.mdb02/04/2011 0x3300 00495616 JindalSections.mdb11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb08/24/2007 0x3ec0 00454656 Koreansections.mdb04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb02/07/2005 0x9a00 00243712 mexicansteeltables.mdb04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb11/20/2009 0xf700 00428034 RussianSections.mdb05/12/2009 0xe001 00237570 SouthAfricanSections.mdb01/06/2005 0x9341 00194560 spanishsections.mdb11/20/2009 0x5100 00368640 STO_ASChMSections.mdb04/19/2007 0x7480 00223232 uscoldformedsections.mdb10/31/2007 0x3700 00133120 VenezuelanSections.mdb-----------------------------------------------------------------------------------------



50 — STAAD.Pro


NOTES

10 Forces in a Space FrameObjectiveTo find the maximum axial force and moment due to load and moment applied at a joint in aSpace frame.

ReferenceWeaver Jr., W., “Computer Programs for Structural Analysis,” page 146, problem 8.

ProblemDetermine the maximum axial force and moment in the space structure.

Figure 10-1: Space frame model

GivenF = 2 kip, P = 1 kip, M = 120 in·kip

L = 120 in.

E = 30E3 ksi,

AX = 11 in2

IX = 83 in4

IY = 56 in4

IZ = 56 in4


Comparison


Basic SolverSTAAD

Advanced Solver

FMax (kips) 1.47 1.47 1.47

MY,Max (in·kip) 84.04 84.04 84.04

MZ,Max (in·kip) 95.319 96.120 96.120

Table 10-1: Comparison of max. Force, F, and max. Moments,M, for verificationproblem no. 10

STAAD Output

52— STAAD.Pro

10 Forces in a Space Frame


1. STAAD SPACE :A SPACE FRAMEINPUT FILE: ver10.STD

2. * FILE VER10.STD3. *4. * REFERENCE 'COMPUTER PROGRAMS FOR STRUCTURAL ANALYSIS'5. * BY WILLIAM WEAVER JR. PAGE 146 STRUCTURE NO. 8.6. * ANSWER - MAX AXIAL FORCE= 1.47 (MEMB 3)7. * MAX BEND-Y= 84.04 (MEMB 3), BEND-Z= 95.32 (MEMB 3)8. *9. * STAAD VERIFICATION PROB NO. 1010. *11. UNIT INCH KIP12. JOINT COORD13. 1 0 120 0 ; 2 240 120 014. 3 0 0 0 ; 4 360 0 12015. SUPPORT16. 3 4 FIXED17. MEMB INCI18. 1 1 2 ; 2 3 1 ; 3 2 419. MEMB PROP20. 1 2 3 PRIS AX 11. IX 83. IY 56. IZ 5621. CONSTANT ; E 30000. ALL22. POISS .25 ALL23. LOAD 1 JOINT LOAD24. JOINT LOAD25. 1 FX 2. ; 2 FY -1. ; 2 MZ -120.26. PERFORM ANALYSIS


NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 4/ 3/ 2:A SPACE FRAME -- PAGE NO. 2* FILE VER10.STD

SOLVER USED IS THE OUT-OF-CORE BASIC SOLVERORIGINAL/FINAL BAND-WIDTH= 2/ 2/ 12 DOFTOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 12SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDSREQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB27. PRINT ANALYSIS RESULT:A SPACE FRAME -- PAGE NO. 3* FILE VER10.STDJOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = SPACE------------------

JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN1 1 0.22267 0.00016 -0.17182 -0.00255 0.00217 -0.002132 1 0.22202 -0.48119 -0.70161 -0.00802 0.00101 -0.004353 1 0.00000 0.00000 0.00000 0.00000 0.00000 0.000004 1 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

:A SPACE FRAME -- PAGE NO. 4* FILE VER10.STDSUPPORT REACTIONS -UNIT KIP INCH STRUCTURE TYPE = SPACE-----------------

JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z3 1 -1.10 -0.43 0.22 48.78 -17.97 96.124 1 -0.90 1.43 -0.22 123.08 47.25 -11.72

:A SPACE FRAME -- PAGE NO. 5



* FILE VER10.STDMEMBER END FORCES STRUCTURE TYPE = SPACE-----------------ALL UNITS ARE -- KIP INCH (LOCAL )MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z

1 1 1 0.90 -0.43 0.22 22.71 -17.97 -36.372 -0.90 0.43 -0.22 -22.71 -34.18 -67.36

2 1 3 -0.43 1.10 0.22 -17.97 -48.78 96.121 0.43 -1.10 -0.22 17.97 22.71 36.37

3 1 2 1.47 -0.71 -0.48 -37.02 15.69 -53.284 -1.47 0.71 0.48 37.02 84.04 -95.32



:A SPACE FRAME -- PAGE NO. 6* FILE VER10.STD


:A SPACE FRAME -- PAGE NO. 7* FILE VER10.STD

Information about the key files in the current distributionModification Date CRC Size (Bytes) File Name-----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe02/22/2011 0xc181 08667136 SProStaadStl.exe09/19/2003 0x2fc0 00081970 CMesh.dll02/17/2011 0xa7c1 04276294 dbsectioninterface.dll02/22/2011 0x12c0 00294912 EC3Annex.dll02/22/2011 0x2900 00376832 EuroCode3.dll12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll01/24/2001 0x9b40 00073728 LoadGen.dll11/19/2010 0xeb80 00011264 MathExtensions.dll09/25/2003 0x6340 00704512 MeshEngine.dll02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll09/22/2003 0xce00 00069632 QuadPlateEngine.dll12/02/2010 0x5040 00073728 SteelCollection.dll02/22/2011 0xca81 00024064 SteelDesign.dll10/08/2010 0xa940 00072192 SteelSections.dll05/29/2008 0x77c1 00106572 SurfMeshEngine.dll10/08/2010 0x4680 00010752 UnitConversions.dll02/08/2011 0xfc00 00974848 AISCSections.mdb06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb01/05/2005 0xcac1 03651584 aitctimbersections.mdb05/01/2008 0xb001 00552960 aluminumsections.mdb01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb10/02/2008 0x40 00520192 AustralianSections.mdb06/11/2010 0xa101 00585728 BritishSections.mdb

54 — STAAD.Pro


09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb06/28/2005 0x8201 00327680 butlercoldformedsections.mdb02/25/2008 0x2e01 00329728 CanadianSections.mdb09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb05/31/2005 0x9e81 00450560 canadiantimbersections.mdb02/10/2010 0x94c1 00483328 ChineseSections.mdb01/05/2005 0xd6c0 00600064 dutchsections.mdb10/07/2010 0xd2c0 03596290 EuropeanSections.mdb01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb01/05/2005 0xd301 00202752 frenchsections.mdb01/05/2005 0x11c1 00233472 germansections.mdb10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb12/08/2009 0xec1 00942080 IndianSections.mdb01/05/2005 0xd540 00180224 iscoldformedsections.mdb02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb03/23/2006 0xa080 00200704 japanesesections.mdb02/04/2011 0x3300 00495616 JindalSections.mdb11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb08/24/2007 0x3ec0 00454656 Koreansections.mdb04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb02/07/2005 0x9a00 00243712 mexicansteeltables.mdb04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb11/20/2009 0xf700 00428034 RussianSections.mdb05/12/2009 0xe001 00237570 SouthAfricanSections.mdb01/06/2005 0x9341 00194560 spanishsections.mdb11/20/2009 0x5100 00368640 STO_ASChMSections.mdb04/19/2007 0x7480 00223232 uscoldformedsections.mdb10/31/2007 0x3700 00133120 VenezuelanSections.mdb-----------------------------------------------------------------------------------------



56— STAAD.Pro


NOTES

11 Temperature load in different materialsObjectiveA rigid bar is suspended by two copper wires and one steel wire. Find the stresses in the wires dueto a rise in temperature.

ReferenceTimoshenko, S., “Strength of Materials,” Part 1, D. Van Nostrand Co., 3rd edition, 1956, page 30,problem 9.

ProblemAssuming the horizontal member to be very rigid, determine the stresses in the copper and steelwires if the temperature rise is 10º F.

Figure 11-1: Model of a rigid wire suspended by wires

GivenEsteel = 30E6 psi, Ecopper = 16E6 psi

αsteel = 70E-7 in/in/°F, αcopper = 92E-7 in/in/°F

AX = 0.1 in2

w = 400 lbf/in.

L = 20 in.

d= 5 in.


Hint:When modeling, assume a large moment of inertia for the horizontal rigid member anddistribute of the concentrated load as uniform.

Comparison


Basic SolverSTAAD

Advanced Solver

σSteel (psi) 19,695 19,698 19,698

σCopper (psi) 10,152 10,151 10,151

Table 11-1: Comparison of stress (σ) for verification model #11

STAAD Output

58— STAAD.Pro

11 Temperature load in different materials


1. STAAD PLANE :A RIGID BAR SUSPENDED BY TWO COPPER WIRES AND A STEEL WIREINPUT FILE: ver11.STD

2. * FILE: VER11.STD3. *4. * REFERENCE: 'STRENGTH OF MATERIALS', TIMOSHENKO (PART 1),5. * PAGE 30, PROB 9.6. * THE ANSWERS ARE 19700 PSI AND 10200 PSI.7. *8. UNIT INCH POUND9. JOINT COORD10. 1 0. 20. ; 2 5. 20. ; 3 10. 20.11. 4 0. 0. ; 5 5. 0. ; 6 10. 0.12. MEMB INCI13. 1 1 4 3 ; 4 4 5 514. MEMB PROP15. 1 2 3 PRI AX 0.1 ; 4 5 PRI AX 1. IZ 100.16. CONSTANT ; E 30E6 MEMB 2 4 517. E 16E6 MEMB 1 318. ALPHA 92E-7 MEMB 1 3 ; ALPHA 70E-7 MEMB 219. MEMB TRUSS ; 1 2 320. SUPPORT ; 1 2 3 PINNED21. LOADING 1 VERT LOAD + TEMP LOAD22. MEMB LOAD ;4 5 UNI Y -400.23. TEMP LOAD ; 1 2 3 TEMP 10.24. PERFORM ANALYSIS

**WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MOREMEMBERS/ELEMENTS/SOLIDS. THE DEFAULT VALUE HAS BEEN SET FOR THE SAME.

:A RIGID BAR SUSPENDED BY TWO COPPER WIRES AND A STEEL W -- PAGE NO. 2* FILE: VER11.STD



ORIGINAL/FINAL BAND-WIDTH= 3/ 3/ 10 DOFTOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 12SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDSREQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MBZERO STIFFNESS IN DIRECTION 6 AT JOINT 1 EQN.NO. 1

LOADS APPLIED OR DISTRIBUTED HERE FROM ELEMENTS WILL BE IGNORED.THIS MAY BE DUE TO ALL MEMBERS AT THIS JOINT BEING RELEASED OREFFECTIVELY RELEASED IN THIS DIRECTION.

ZERO STIFFNESS IN DIRECTION 6 AT JOINT 2 EQN.NO. 2ZERO STIFFNESS IN DIRECTION 6 AT JOINT 3 EQN.NO. 3

***WARNING - INSTABILITY AT JOINT 6 DIRECTION = FXPROBABLE CAUSE SINGULAR-ADDING WEAK SPRINGK-MATRIX DIAG= 6.0000004E+03 L-MATRIX DIAG= 0.0000000E+00 EQN NO 10***NOTE - VERY WEAK SPRING ADDED FOR STABILITY**NOTE** STAAD DETECTS INSTABILITIES AS EXCESSIVE LOSS OF SIGNIFICANT DIGITS

DURING DECOMPOSITION. WHEN A DECOMPOSED DIAGONAL IS LESS THAN THEBUILT-IN REDUCTION FACTOR TIMES THE ORIGINAL STIFFNESS MATRIX DIAGONAL,STAAD PRINTS A SINGULARITY NOTICE. THE BUILT-IN REDUCTION FACTORIS 1.000E-09THE ABOVE CONDITIONS COULD ALSO BE CAUSED BY VERY STIFF OR VERY WEAKELEMENTS AS WELL AS TRUE SINGULARITIES.

25. PRINT STRESSES LIST 1 2 3





1 1 .0 10150.8 T 0.0 0.0 10150.8 0.0 0.01.00 10150.8 T 0.0 0.0 10150.8 0.0 0.0

2 1 .0 19698.3 T 0.0 0.0 19698.3 0.0 0.01.00 19698.3 T 0.0 0.0 19698.3 0.0 0.0

3 1 .0 10150.8 T 0.0 0.0 10150.8 0.0 0.01.00 10150.8 T 0.0 0.0 10150.8 0.0 0.0






Information about the key files in the current distributionModification Date CRC Size (Bytes) File Name-----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe02/22/2011 0xc181 08667136 SProStaadStl.exe09/19/2003 0x2fc0 00081970 CMesh.dll02/17/2011 0xa7c1 04276294 dbsectioninterface.dll02/22/2011 0x12c0 00294912 EC3Annex.dll02/22/2011 0x2900 00376832 EuroCode3.dll12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll01/24/2001 0x9b40 00073728 LoadGen.dll11/19/2010 0xeb80 00011264 MathExtensions.dll09/25/2003 0x6340 00704512 MeshEngine.dll02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll09/22/2003 0xce00 00069632 QuadPlateEngine.dll12/02/2010 0x5040 00073728 SteelCollection.dll02/22/2011 0xca81 00024064 SteelDesign.dll10/08/2010 0xa940 00072192 SteelSections.dll05/29/2008 0x77c1 00106572 SurfMeshEngine.dll10/08/2010 0x4680 00010752 UnitConversions.dll02/08/2011 0xfc00 00974848 AISCSections.mdb06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb01/05/2005 0xcac1 03651584 aitctimbersections.mdb05/01/2008 0xb001 00552960 aluminumsections.mdb01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb10/02/2008 0x40 00520192 AustralianSections.mdb

60 — STAAD.Pro


06/11/2010 0xa101 00585728 BritishSections.mdb09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb06/28/2005 0x8201 00327680 butlercoldformedsections.mdb02/25/2008 0x2e01 00329728 CanadianSections.mdb09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb05/31/2005 0x9e81 00450560 canadiantimbersections.mdb02/10/2010 0x94c1 00483328 ChineseSections.mdb01/05/2005 0xd6c0 00600064 dutchsections.mdb10/07/2010 0xd2c0 03596290 EuropeanSections.mdb01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb01/05/2005 0xd301 00202752 frenchsections.mdb01/05/2005 0x11c1 00233472 germansections.mdb10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb12/08/2009 0xec1 00942080 IndianSections.mdb01/05/2005 0xd540 00180224 iscoldformedsections.mdb02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb03/23/2006 0xa080 00200704 japanesesections.mdb02/04/2011 0x3300 00495616 JindalSections.mdb11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb08/24/2007 0x3ec0 00454656 Koreansections.mdb04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb02/07/2005 0x9a00 00243712 mexicansteeltables.mdb04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb11/20/2009 0xf700 00428034 RussianSections.mdb05/12/2009 0xe001 00237570 SouthAfricanSections.mdb01/06/2005 0x9341 00194560 spanishsections.mdb11/20/2009 0x5100 00368640 STO_ASChMSections.mdb04/19/2007 0x7480 00223232 uscoldformedsections.mdb10/31/2007 0x3700 00133120 VenezuelanSections.mdb-----------------------------------------------------------------------------------------



62— STAAD.Pro


NOTES

12 Deflection and stress of a truss systemObjectiveTo find the joint deflection and member stress due to a joint load in a plane truss.

ReferenceTimoshenko, S., “Strength of Materials,” Part 1, D. Van Nostrand Co., Inc., 3rd edition, 1956, page 10,problem 2.

ProblemDetermine the vertical deflection at point A and the member stresses

Figure 12-1: Model of two member truss

GivenAX = 0.5 in

2

E = 30E6 psi

P = 5000 lbf

L = 180 in.

angle = 30°


Comparison


Basic SolverSTAAD

Advanced Solver

σA (psi) 10,000. 10,000. 10,000.

δA (in) 0.12 0.12 0.12

Table 12-1: Comparison of stress (σ) and Deflection (δ) for verification problem12

STAAD Output

64 — STAAD.Pro

12 Deflection and stress of a truss system



2. * FILE VER12.STD3. *4. * REFERENCE: 'STRENGTH OF MATERIALS', (PART 1) BY TIMOSHENKO,5. * PAGE 10, PROB 2.6. *7. * THE ANSWER IN THE BOOK , DEFLECTION = 0.12 INCH8. * AND STRESS =10000 PSI9. *10. UNIT INCH POUND11. JOINT COORD12. 1 0. 0. ; 2 155.88457 -90. ; 3 311.76914 0.13. SUPPORT ; 1 3 PINNED14. MEMB INCI ; 1 1 2 215. MEMB PROP16. 1 2 PRIS AX 0.517. CONSTANT ; E 30E618. LOAD 1 VERT LOAD19. JOINT LOAD ; 2 FY -5000.20. PERFORM ANALYSIS



ORIGINAL/FINAL BAND-WIDTH= 1/ 1/ 2 DOFTOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 2SIZE OF STIFFNESS MATRIX = 0 DOUBLE KILO-WORDSREQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB:A PLANE TRUSS -- PAGE NO. 2* FILE VER12.STD21. PRINT DISPLACEMENTS LIST 2:A PLANE TRUSS -- PAGE NO. 3* FILE VER12.STDJOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = TRUSS------------------

JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN2 1 0.00000 -0.12000 0.00000 0.00000 0.00000 0.00000

************** END OF LATEST ANALYSIS RESULT **************22. PRINT STRESSES:A PLANE TRUSS -- PAGE NO. 4* FILE VER12.STD


1 1 .0 10000.0 T 0.0 0.0 10000.0 0.0 0.01.00 10000.0 T 0.0 0.0 10000.0 0.0 0.0

2 1 .0 10000.0 T 0.0 0.0 10000.0 0.0 0.01.00 10000.0 T 0.0 0.0 10000.0 0.0 0.0


*********** END OF THE STAAD.Pro RUN ***********



**** DATE= MAR 9,2011 TIME= 11: 5:23 ****:A PLANE TRUSS -- PAGE NO. 5* FILE VER12.STD



Information about the key files in the current distributionModification Date CRC Size (Bytes) File Name-----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe02/22/2011 0xc181 08667136 SProStaadStl.exe09/19/2003 0x2fc0 00081970 CMesh.dll02/17/2011 0xa7c1 04276294 dbsectioninterface.dll02/22/2011 0x12c0 00294912 EC3Annex.dll02/22/2011 0x2900 00376832 EuroCode3.dll12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll01/24/2001 0x9b40 00073728 LoadGen.dll11/19/2010 0xeb80 00011264 MathExtensions.dll09/25/2003 0x6340 00704512 MeshEngine.dll02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll09/22/2003 0xce00 00069632 QuadPlateEngine.dll12/02/2010 0x5040 00073728 SteelCollection.dll02/22/2011 0xca81 00024064 SteelDesign.dll10/08/2010 0xa940 00072192 SteelSections.dll05/29/2008 0x77c1 00106572 SurfMeshEngine.dll10/08/2010 0x4680 00010752 UnitConversions.dll02/08/2011 0xfc00 00974848 AISCSections.mdb06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb01/05/2005 0xcac1 03651584 aitctimbersections.mdb05/01/2008 0xb001 00552960 aluminumsections.mdb01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb10/02/2008 0x40 00520192 AustralianSections.mdb06/11/2010 0xa101 00585728 BritishSections.mdb09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb06/28/2005 0x8201 00327680 butlercoldformedsections.mdb02/25/2008 0x2e01 00329728 CanadianSections.mdb09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb05/31/2005 0x9e81 00450560 canadiantimbersections.mdb02/10/2010 0x94c1 00483328 ChineseSections.mdb01/05/2005 0xd6c0 00600064 dutchsections.mdb10/07/2010 0xd2c0 03596290 EuropeanSections.mdb01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb01/05/2005 0xd301 00202752 frenchsections.mdb01/05/2005 0x11c1 00233472 germansections.mdb10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb12/08/2009 0xec1 00942080 IndianSections.mdb

66— STAAD.Pro


01/05/2005 0xd540 00180224 iscoldformedsections.mdb02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb03/23/2006 0xa080 00200704 japanesesections.mdb02/04/2011 0x3300 00495616 JindalSections.mdb11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb08/24/2007 0x3ec0 00454656 Koreansections.mdb04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb02/07/2005 0x9a00 00243712 mexicansteeltables.mdb04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb11/20/2009 0xf700 00428034 RussianSections.mdb05/12/2009 0xe001 00237570 SouthAfricanSections.mdb01/06/2005 0x9341 00194560 spanishsections.mdb11/20/2009 0x5100 00368640 STO_ASChMSections.mdb04/19/2007 0x7480 00223232 uscoldformedsections.mdb10/31/2007 0x3700 00133120 VenezuelanSections.mdb-----------------------------------------------------------------------------------------



68— STAAD.Pro


NOTES

13 Steel Design per 1989 AISC CodeTypeSteel Design.

ReferenceAttached step by step hand calculation as per 1989 AISC ASD code. Ninth Edition.

ProblemDetermine the allowable stresses (per 1989 AISC code) for the members of the structure as shownin figure. Also, perform a code check for these members based on the results of the analysis.

Figure 13-1: Steel braced frame frame

Members 1, 2 = W12X26, Members 3, 4 = W14X43

Members 5, 6, 7 = W16X36, Memb 8= L40404, Memb 9 = L50506

F = 15 kip (wind load)

w = 2 kip/ft (dead load + liveload)


Comparison

Member No. 1 2 3 4 5 6 7 8 9

Hand Calculation 1.1576 .914 1.117 0.936 .579 1.119 .668 1.024 .823

STAAD Basic Solver 1.157 .916 1.117 0.936 .582 1.120 .668 1.024 .823

STAAD AdvancedSolver

1.157 .916 1.117 0.936 .582 1.120 .668 1.024 .823

Table 13-1: Comparison of governing ratios for the member checks in verificationproblem no. 13

Hand CalculationManual / Code refers to AISC Manual of Steel Construction, Allowable Stress Design, ninthedition.

Member 1

Size W12x26, L = 10 ft., a = 7.65 in2, Sz = 33.39 in3

From clause F1-2, page 5-45 of Manual, Lc = 6.85 ft.

From observation Load case 1 will govern,

Fx = 25.0 kip (compression), Mz = 56.5 ft·kip

Area of compressive flange = 6.49*0.38 = 2.466 in2

Allowable bending stress, per Clause F1-8 (page 5-47 of Manual)

fb = 12. · 1000 · 1.0/[10 · 12 · (12.22/2.466)] = 20.1817 ksi

(kl/r)y = 120/1.5038 = 79.8, so fa = 15.38 ksi

Stresses per Table C-36 (page 3-16 of manual)

fa = 25./7.65 = 3.268

fb = 56.5 · 12/33.39 = 20.31 ksi

(kl/r)z = 120/5.1639 = 23.238, so F'ez = = 276.54 ksi

Equation H1-1, page 5-54 of Manual

3.268/15.38 + 0.85 · 20.31 / [(1-3.268/276.54) · 20.1817] = 1.078

Equation H1-2, page 5-54 of Manual.

3.268/(0.6 · 36) +20.31/20.1817 = 1.1576

Therefore, equation H1-2 governs and ratio = 1.1576

Member 2

Size W12x26, L = 5 ft., a = 7.65 in2, Sz = 33.39 in3

From observation load case 1 will govern,


70 — STAAD.Pro

13 Steel Design per 1989 AISC Code

Since L is less than Lc = 6.85ft, per Clauses F1-1 & F1-2 (page 5-45 of Manual)

fb = 0.66 · 36 = 23.76 ksi

(kl/r)y = 60/1.5038 = 39.90, so fa = 19.19 ksi

Per Table C-36 (page 3-16 of Manual)

fa = 8.71/7.65 = 1.1385, fb = 56.5 · 12/33.39 = 20.31 ksi

Since fa/Fa less than 0.15, apply equation H1-3 (page 5-54 of Manual)

1.1385/19.19 + 20.31/23.76 = .0593 + .8548 = 0.9141

Member 3

Size W14X43, L = 11ft., a = 12.6 in2, Sz = 62.7 in3

From observation load case 3 will govern,


Referring to clause F1-2, page 5-45 of Manual.

Lc = 8.4 ft. Therefore

fb = 0.6 · 36 = 21.6 ksi

(kl/r)y = 132/1.8941 = 69.69,

so fa = 16.46 ksi per Table C-36 (page 3-16 of Manual)

fa = 25.5/12.6 = 2.024

fb = 112.173 · 12/62.66 = 21.48 ksi

since fa/Fa less than 0.15, use equation H1-3, page 5-54 of Manual

2.024/16.46 + 21.48/21.6 = 0.123 + 0.994 = 1.117

Member 4

Size W14x43, L = 4ft, a = 12.6 in2, Sz = 62.7 in3

From observation, load case 3 will govern,

Fx = 8.75 kip (tension), Mz = 112.173 ft·kip

Since L is less than Lc = 8.4 ft

fb = 0.66 · 36 = 23.76 ksi

Clause F1-1 (page 5-45 of Manual)

fa = 8.75/12.6 = 0.694

fb = 112.73x12/62.66 = 21.48 ksi

Combined tension and bending, use equation H2-1, page 5-55 of Manual.

0.694/(0.6 · 36) + 21.48/23.76 = 0.032 + 0.904 = 0.936

Member 5


From observation, load case 3 will govern.



Fx = 14.02 kip (compression), Mz =57.04 ft·kip

Since L is less than Lc = 7.37 (per Clause F1-2, page 5-45 of Manual)

fb = 0.66 · 36 = 23.76 ksi

(kl/r)y = 60./1.52 = 39.47

so fa = 19.23 ksi per Table C-36 (page 3-16 of Manual)

fa = 14.02/10.6 = 1.32

fb = 57.04 · 12/56.5 = 12.12 ksi

Since fa/Fa less than 0.15, use equation H1-3, page 5-54 of Manual

1.32/19.23 + 12.12/23.76 = 0.069 + 0.510 = 0.579

Member 6


From observation, load case 1 will govern. Forces at midspan are


From Chapter F of the AISC ASD 9PthP ed. specs., with Cb = 1.0,

(102,000Cb/Fy)1/2 =53.229

(510,000Cb/Fy)1/2 =119.02

L/rT = 192/1.79 = 107.26

53.229 < 107.26 < 119.02

Therefore Fb (as per F1-6, page 5-47 of Manual)

[(2/3) – 36 · 107.26 · 107.26/(1,530,000)] · 36 = 14.25 ksi

(Kl/r)y = 192/1.5203 = 126.29

so fa = 9.36 per Table C-36 (page 3-16 of Manual)

fa = 5.65/10.6 = 0.533

fb = 71.25x12/56.49 = 15.14 ksi

Since fa/Fa less than 0.15 use formula [H1-3, page 5-54 of Manual]

0.533/9.36 + 15.14/14.25 = 0.057 + 1.062 = 1.119

Member 7

Size W16x36, L =4ft, a = 10.6in2, Sz =56.49in3

Lc = 7.37ft (Clause F1-2 page 5-45 of Manual)

From observation load case 3 will govern, Fx = 24.06 kip (tension), Mz = 62.96 ft·kip

From Clause F1-1, the allowable compressive stress is

fb = 0.66 Fy = 23.76 ksi

Since section is in tension, per Clause F1-5 (page5-45 of Manual)

fb = 0.60 · 36 = 21.60 Ksi

72— STAAD.Pro


Choosing the larger of above 2 values, fb = 23.76 Ksi

fa = 24.06/10.6 = 2.2698

fb = 62.96 · 12/56.49 = 13.37

Since combined tension and bending, use equation H 2-1, page 5-55 of the AISC ASD 9PthP ed.specs.

2.2698/(0.6 · 36) + 13.37(23.76) = 0.105 + 0.5627 = 0.6677

Member 8

Size L4x4x1/4, L = 7.071 ft, a = 1.94 in2

From observation load case 1 will govern, Fx = 23.04 kip (Comp.)

Fa is computed as per page 5-310 of the AISC ASD 9PthP ed.specs.

Qs = 1.34 – 0.00447 · (4/0.25)·(36)1/2 = 0.9108

Qa = 1.0

Q = Qs · Qa = 0.9108

Cc= 92.0·π2·E/(Q·Fy)]

1/2 = [2.0·π2 · 29000/(0.9108 · 36)]1/2 = 132.1241

Kl/r = 7.071 · 12/0.795 = 106.73 < Cc.

Hence, fa = 11.6027 ksi (computed per equation 4-1)

Actual compressive stress

fa = 23.04/1.94 = 11.876 ksi

Therefore, Ratio =

fa/fa = 11.876/11.602 = 1.024

Member 9

Size L5x5x3/8, L = 5.657 ft, a = 3.61 in2

From observation, load case 1 governs, Fx = 48.44 kip (Comp.)

Fa is computed as per page 5-310 of the AISC ASD 9PthP ed.specs.

Qs = 1.34 – 0.00447 · (5/0.375)·(36)1/2 = 0.9824

Qa = 1.0

Q = Qs · Qa = 0.9824

Cc= 92.0·π2·E/(Q·Fy)]

1/2 = [2.0·π2 · 29000/(0.9824 · 36)]1/2 = 127.2238

(Kl/r)min = 5.657 · 12/0.99 = 68.57 < Cc.

Hence, fa = 16.301 ksi (computed per equation 4-1)

Actual compressive stress

fa = 48.44/3.61 = 13.418 ksi

Therefore Ratio =

fa/fa = 13.418/16.301 = 0.823



STAAD Output

74 — STAAD.Pro



1. STAAD PLANE VERIFICATION PROBLEM NO 13INPUT FILE: ver13.STD

2. *3. * THIS DESIGN EXAMPLE IS VERIFIED BY HAND CALCULATION4. * FOLLOWING AISC-89 CODE.5. *6. UNIT FEET KIP7. JOINT COORD8. 1 0 0 ; 2 25 0 ; 3 0 10 ; 4 25 119. 5 0 15 ; 6 25 15 ; 7 5 15 ; 8 21 1510. MEMB INCI11. 1 1 3 ; 2 3 5 ; 3 2 4 ; 4 4 612. 5 5 7 ; 6 7 8 ; 7 8 6 ; 8 3 7 ; 9 4 813. MEMB PROP AMERICAN14. 1 2 TA ST W12X26 ; 3 4 TA ST W14X4315. 5 6 7 TA ST W16X36 ; 8 TA ST L40404 ; 9 TA ST L5050616. MEMB TRUSS ; 8 917. CONSTANT18. E 4176E3 ALL19. POISSON STEEL ALL20. SUPPORT ; 1 2 PINNED21. LOADING 1 DL + LL22. MEMB LOAD ; 5 6 7 UNI Y -2.023. LOADING 2 WIND FROM LEFT24. JOINT LOAD ; 5 FX 15.25. LOAD COMB 3 ; 1 0.75 2 0.7526. PERFORM ANALYSIS


NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 8/ 9/ 2VERIFICATION PROBLEM NO 13 -- PAGE NO. 2*

SOLVER USED IS THE OUT-OF-CORE BASIC SOLVERORIGINAL/FINAL BAND-WIDTH= 4/ 4/ 15 DOFTOTAL PRIMARY LOAD CASES = 2, TOTAL DEGREES OF FREEDOM = 20SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDSREQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MB27. LOAD LIST 1 328. PRINT FORCESVERIFICATION PROBLEM NO 13 -- PAGE NO. 3*MEMBER END FORCES STRUCTURE TYPE = PLANE-----------------ALL UNITS ARE -- KIP FEET (LOCAL )MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z

1 1 1 25.00 -5.65 0.00 0.00 0.00 0.003 -25.00 5.65 0.00 0.00 0.00 -56.50

3 1 12.00 1.05 0.00 0.00 0.00 0.003 -12.00 -1.05 0.00 0.00 0.00 10.52

2 1 3 8.71 10.64 0.00 0.00 0.00 56.505 -8.71 -10.64 0.00 0.00 0.00 -3.29

3 3 15.83 -2.77 0.00 0.00 0.00 -10.525 -15.83 2.77 0.00 0.00 0.00 -3.34

3 1 2 25.00 5.65 0.00 0.00 0.00 0.004 -25.00 -5.65 0.00 0.00 0.00 62.15



3 2 25.50 10.20 0.00 0.00 0.00 0.004 -25.50 -10.20 0.00 0.00 0.00 112.17

4 1 4 6.50 -12.85 0.00 0.00 0.00 -62.156 -6.50 12.85 0.00 0.00 0.00 10.76

3 4 -8.75 -24.06 0.00 0.00 0.00 -112.176 8.75 24.06 0.00 0.00 0.00 15.95

5 1 5 -10.64 8.71 0.00 0.00 0.00 3.297 10.64 1.29 0.00 0.00 0.00 15.25

3 5 14.02 15.83 0.00 0.00 0.00 3.347 -14.02 -8.33 0.00 0.00 0.00 57.04

6 1 7 5.65 15.00 0.00 0.00 0.00 -15.258 -5.65 17.00 0.00 0.00 0.00 -0.75

3 7 10.20 4.50 0.00 0.00 0.00 -57.048 -10.20 19.50 0.00 0.00 0.00 -62.96

7 1 8 -12.85 1.50 0.00 0.00 0.00 0.756 12.85 6.50 0.00 0.00 0.00 -10.76

3 8 -24.06 14.75 0.00 0.00 0.00 62.966 24.06 -8.75 0.00 0.00 0.00 -15.95

8 1 3 23.04 0.00 0.00 0.00 0.00 0.007 -23.04 0.00 0.00 0.00 0.00 0.00

3 3 -5.41 0.00 0.00 0.00 0.00 0.007 5.41 0.00 0.00 0.00 0.00 0.00

9 1 4 26.16 0.00 0.00 0.00 0.00 0.008 -26.16 0.00 0.00 0.00 0.00 0.00

3 4 48.44 0.00 0.00 0.00 0.00 0.008 -48.44 0.00 0.00 0.00 0.00 0.00

VERIFICATION PROBLEM NO 13 -- PAGE NO. 4*************** END OF LATEST ANALYSIS RESULT **************29. PARAMETER30. CODE AISC31. TRACK 1.0 ALL32. CHECK CODE ALLVERIFICATION PROBLEM NO 13 -- PAGE NO. 5*

STAAD.Pro CODE CHECKING - (AISC 9TH EDITION) v1.0***********************

ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE NOTED)MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/

FX MY MZ LOCATION=======================================================================* 1 ST W12X26 (AISC SECTIONS)

FAIL AISC- H1-2 1.157 125.00 C 0.00 56.50 10.00

-----------------------------------------------------------------------| MEM= 1, UNIT KIP-INCH, L= 120.0 AX= 7.65 SZ= 33.4 SY= 5.3|| KL/R-Y= 79.8 CB= 1.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 20.18 || FTZ= 21.60 FCY= 27.00 FTY= 27.00 FC= 15.26 FT= 21.60 FV= 14.40 |-----------------------------------------------------------------------

2 ST W12X26 (AISC SECTIONS)PASS AISC- H1-3 0.916 1

8.71 C 0.00 56.50 0.00-----------------------------------------------------------------------| MEM= 2, UNIT KIP-INCH, L= 60.0 AX= 7.65 SZ= 33.4 SY= 5.3|| KL/R-Y= 39.9 CB= 1.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 23.76 || FTZ= 23.76 FCY= 27.00 FTY= 27.00 FC= 18.61 FT= 21.60 FV= 14.40 |-----------------------------------------------------------------------* 3 ST W14X43 (AISC SECTIONS)

FAIL AISC- H1-3 1.117 325.50 C 0.00 -112.17 11.00


4 ST W14X43 (AISC SECTIONS)

76— STAAD.Pro


PASS AISC- H2-1 0.936 38.75 T 0.00 -112.17 0.00



14.02 C 0.00 -57.04 5.00VERIFICATION PROBLEM NO 13 -- PAGE NO. 6*

ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE NOTED)MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/

FX MY MZ LOCATION=======================================================================-----------------------------------------------------------------------| MEM= 5, UNIT KIP-INCH, L= 60.0 AX= 10.60 SZ= 56.5 SY= 7.0|| KL/R-Y= 39.5 CB= 1.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 23.76 || FTZ= 23.76 FCY= 27.00 FTY= 27.00 FC= 18.39 FT= 21.60 FV= 14.40 |-----------------------------------------------------------------------* 6 ST W16X36 (AISC SECTIONS)

FAIL AISC- H1-3 1.120 15.65 C 0.00 -71.25 8.00



24.06 T 0.00 62.96 0.00-----------------------------------------------------------------------| MEM= 7, UNIT KIP-INCH, L= 48.0 AX= 10.60 SZ= 56.5 SY= 7.0|| KL/R-Y= 31.6 CB= 1.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 23.76 || FTZ= 23.76 FCY= 27.00 FTY= 27.00 FC= 18.87 FT= 21.60 FV= 14.40 |-----------------------------------------------------------------------* 8 ST L40404 (AISC SECTIONS)

FAIL AISC- H1-1 1.024 123.04 C 0.00 0.00 0.00

-----------------------------------------------------------------------| MEM= 8, UNIT KIP-INCH, L= 84.9 AX= 1.94 SZ= 0.8 SY= 1.7|| KL/R- = 106.7 CB= 0.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 0.00 || FTZ= 0.00 FCY= 0.00 FTY= 0.00 FC= 11.60 FT= 21.60 FV= 0.00 |-----------------------------------------------------------------------

9 ST L50506 (AISC SECTIONS)PASS AISC- H1-1 0.823 3

48.44 C 0.00 0.00 0.00-----------------------------------------------------------------------| MEM= 9, UNIT KIP-INCH, L= 67.9 AX= 3.61 SZ= 1.8 SY= 3.9|| KL/R- = 69.0 CB= 0.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 0.00 || FTZ= 0.00 FCY= 0.00 FTY= 0.00 FC= 16.30 FT= 21.60 FV= 0.00 |-----------------------------------------------------------------------VERIFICATION PROBLEM NO 13 -- PAGE NO. 7*33. FINISH


************************************************************* For questions on STAAD.Pro, please contact ** Bentley Systems or Partner offices ** ** Telephone Web / Email ** USA +1 (714) 974-2500 ** UK +44 (0) 808 101 9246 ** SINGAPORE +65 6225-6158 *



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VERIFICATION PROBLEM NO 13 -- PAGE NO. 8*

Information about the key files in the current distributionModification Date CRC Size (Bytes) File Name-----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe02/22/2011 0xc181 08667136 SProStaadStl.exe09/19/2003 0x2fc0 00081970 CMesh.dll02/17/2011 0xa7c1 04276294 dbsectioninterface.dll02/22/2011 0x12c0 00294912 EC3Annex.dll02/22/2011 0x2900 00376832 EuroCode3.dll12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll01/24/2001 0x9b40 00073728 LoadGen.dll11/19/2010 0xeb80 00011264 MathExtensions.dll09/25/2003 0x6340 00704512 MeshEngine.dll02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll09/22/2003 0xce00 00069632 QuadPlateEngine.dll12/02/2010 0x5040 00073728 SteelCollection.dll02/22/2011 0xca81 00024064 SteelDesign.dll10/08/2010 0xa940 00072192 SteelSections.dll05/29/2008 0x77c1 00106572 SurfMeshEngine.dll10/08/2010 0x4680 00010752 UnitConversions.dll02/08/2011 0xfc00 00974848 AISCSections.mdb06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb01/05/2005 0xcac1 03651584 aitctimbersections.mdb05/01/2008 0xb001 00552960 aluminumsections.mdb01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb10/02/2008 0x40 00520192 AustralianSections.mdb06/11/2010 0xa101 00585728 BritishSections.mdb09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb06/28/2005 0x8201 00327680 butlercoldformedsections.mdb02/25/2008 0x2e01 00329728 CanadianSections.mdb09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb05/31/2005 0x9e81 00450560 canadiantimbersections.mdb02/10/2010 0x94c1 00483328 ChineseSections.mdb01/05/2005 0xd6c0 00600064 dutchsections.mdb10/07/2010 0xd2c0 03596290 EuropeanSections.mdb01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb01/05/2005 0xd301 00202752 frenchsections.mdb01/05/2005 0x11c1 00233472 germansections.mdb10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb12/08/2009 0xec1 00942080 IndianSections.mdb01/05/2005 0xd540 00180224 iscoldformedsections.mdb02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb03/23/2006 0xa080 00200704 japanesesections.mdb02/04/2011 0x3300 00495616 JindalSections.mdb11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb08/24/2007 0x3ec0 00454656 Koreansections.mdb04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb02/07/2005 0x9a00 00243712 mexicansteeltables.mdb04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb11/20/2009 0xf700 00428034 RussianSections.mdb05/12/2009 0xe001 00237570 SouthAfricanSections.mdb

78— STAAD.Pro


01/06/2005 0x9341 00194560 spanishsections.mdb11/20/2009 0x5100 00368640 STO_ASChMSections.mdb04/19/2007 0x7480 00223232 uscoldformedsections.mdb10/31/2007 0x3700 00133120 VenezuelanSections.mdb-----------------------------------------------------------------------------------------



80 — STAAD.Pro


NOTES

14 Concrete Design per ACI 318 CodeTypeConcrete design as per ACI code.

ReferenceCRSI Handbook and Notes on ACI-318-99.

ProblemA plane frame is created with such loading as to create 138 Kip-Ft moment on beam and 574 Kip ofaxial load coupled with above moment on column.

Figure 14-1: Concrete moment frame

GivenSize of the beam is 10" x 16"and size of the column 14" x 16".

P = 521.32 kip

w = 5.268 kip/ft

L = 20 ft, H = 15 ft


Comparison

Result TypeTheoryACINotes

TheoryCRSI

Handbook

STAADBasicSolver

STAADAdvancedSolver

Area of Steel inbeam

2.78 in2 X 2.792 in2 2.792 in2

Area of Steel incolumn

X 4.01% 4.09% required

4.23% provided

4.09% required

4.23% provided

Table 14-1: Comparison of concrete designs for verifcation problem no. 14

STAAD Output

82— STAAD.Pro

14 Concrete Design per ACI 318 Code


1. STAAD PLANE VERIFICATION FOR CONCRETE DESIGNINPUT FILE: ver14.STD

2. UNIT KIP FEET3. JOINT COORDINATES4. 1 0. 0. ; 2 0. 15. ; 3 20. 15. ; 4 20. 0.5. MEMBER INCIDENCE6. 1 1 2 ; 2 2 3 ; 3 3 47. UNIT INCH8. MEMBER PROPERTY9. 1 3 PRISMATIC YD 16. ZD 14.10. 2 PRISM YD 16. ZD 10.11. CONSTANTS12. E CONCRETE ALL13. POISSON CONCRETE ALL14. SUPPORT15. 1 4 FIXED16. UNIT FT17. LOADING 1 DEAD + LIVE18. JOINT LOAD19. 2 3 FY -521.3220. MEMBER LOAD21. 2 UNI GY -5.26822. PERFORM ANALYSIS



ORIGINAL/FINAL BAND-WIDTH= 1/ 1/ 6 DOFTOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 6SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDSREQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MBVERIFICATION FOR CONCRETE DESIGN -- PAGE NO. 223. PRINT MEMBER FORCESVERIFICATION FOR CONCRETE DESIGN -- PAGE NO. 3MEMBER END FORCES STRUCTURE TYPE = PLANE-----------------ALL UNITS ARE -- KIP FEET (LOCAL )MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z

1 1 1 574.00 -13.69 0.00 0.00 0.00 -67.442 -574.00 13.69 0.00 0.00 0.00 -137.87

2 1 2 13.69 52.68 0.00 0.00 0.00 137.873 -13.69 52.68 0.00 0.00 0.00 -137.87

3 1 3 574.00 13.69 0.00 0.00 0.00 137.874 -574.00 -13.69 0.00 0.00 0.00 67.44

************** END OF LATEST ANALYSIS RESULT **************24. UNIT INCH25. START CONC DESIGN26. CODE ACI 199927. TRACK 1.0 MEMB 228. FYMAIN 60.0 ALL29. FC 4.0 ALL30. CLB 1.4375 ALL31. DESIGN BEAM 2VERIFICATION FOR CONCRETE DESIGN -- PAGE NO. 4=====================================================================



BEAM NO. 2 DESIGN RESULTS - FLEXURE PER CODE ACI 318-99LEN - 20.00FT. FY - 60000. FC - 4000. SIZE - 10.00 X 16.00 INCHESLEVEL HEIGHT BAR INFO FROM TO ANCHOR

FT. IN. FT. IN. FT. IN. STA END_____________________________________________________________________1 0 + 2-5/8 2-NUM.10 0 + 0-0/0 20 + 0-0/0 YES YES

|----------------------------------------------------------------|| CRITICAL POS MOMENT= 125.53 KIP-FT AT 10.00 FT, LOAD 1|| REQD STEEL= 2.48 IN2, RHO=0.0185, RHOMX=0.0214 RHOMN=0.0033 || MAX/MIN/ACTUAL BAR SPACING= 10.16/ 2.54/ 4.73 INCH || REQD. DEVELOPMENT LENGTH = 48.52 INCH ||----------------------------------------------------------------|Cracked Moment of Inertia Iz at above location = 1837.17 inch^4

*** A SUITABLE BAR ARRANGEMENT COULD NOT BE DETERMINED.REQD. STEEL = 2.792 IN2, MAX. STEEL PERMISSIBLE = 2.873 IN2MAX NEG MOMENT = 137.87 KIP-FT, LOADING 1*** A SUITABLE BAR ARRANGEMENT COULD NOT BE DETERMINED.REQD. STEEL = 2.792 IN2, MAX. STEEL PERMISSIBLE = 2.873 IN2MAX NEG MOMENT = 137.87 KIP-FT, LOADING 1___ 2J____________________ 240.X 10.X 16_____________________ 3J____| || || || || 2#10H 3. 0.TO 240. |||=========================================================================||| ||___________________________________________________________________________|_________ _________ _________ _________ _________ _________| | | | | | | | | | | || | | | | | | | | | | || | | | | | | | | | | || | | | | | | | | | | || 2#10 | | 2#10 | | 2#10 | | 2#10 | | 2#10 | | 2#10 || OO | | OO | | OO | | OO | | OO | | OO || | | | | | | | | | | ||_________| |_________| |_________| |_________| |_________| |_________|********************END OF BEAM DESIGN**************************32. DESIGN COLUMN 1VERIFICATION FOR CONCRETE DESIGN -- PAGE NO. 5====================================================================

COLUMN NO. 1 DESIGN PER ACI 318-99 - AXIAL + BENDINGFY - 60000 FC - 4000 PSI, RECT SIZE - 14.00 X 16.00 INCHES, TIED

AREA OF STEEL REQUIRED = 9.164 SQ. IN.BAR CONFIGURATION REINF PCT. LOAD LOCATION PHI----------------------------------------------------------12 - NUMBER 8 4.232 1 END 0.700(PROVIDE EQUAL NUMBER OF BARS ON EACH FACE)TIE BAR NUMBER 4 SPACING 14.00 IN********************END OF COLUMN DESIGN RESULTS********************33. END CONC DESIGN34. FINISH


VERIFICATION FOR CONCRETE DESIGN -- PAGE NO. 6************************************************************* For questions on STAAD.Pro, please contact ** Bentley Systems or Partner offices ** ** Telephone Web / Email ** USA +1 (714) 974-2500 ** UK +44 (0) 808 101 9246 ** SINGAPORE +65 6225-6158 ** FRANCE +33 (0) 1 55238400 ** GERMANY +49 0931 40468 ** INDIA +91 (033) 4006-2021 *

84 — STAAD.Pro


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VERIFICATION FOR CONCRETE DESIGN -- PAGE NO. 7Information about the key files in the current distributionModification Date CRC Size (Bytes) File Name-----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe02/22/2011 0xc181 08667136 SProStaadStl.exe09/19/2003 0x2fc0 00081970 CMesh.dll02/17/2011 0xa7c1 04276294 dbsectioninterface.dll02/22/2011 0x12c0 00294912 EC3Annex.dll02/22/2011 0x2900 00376832 EuroCode3.dll12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll01/24/2001 0x9b40 00073728 LoadGen.dll11/19/2010 0xeb80 00011264 MathExtensions.dll09/25/2003 0x6340 00704512 MeshEngine.dll02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll09/22/2003 0xce00 00069632 QuadPlateEngine.dll12/02/2010 0x5040 00073728 SteelCollection.dll02/22/2011 0xca81 00024064 SteelDesign.dll10/08/2010 0xa940 00072192 SteelSections.dll05/29/2008 0x77c1 00106572 SurfMeshEngine.dll10/08/2010 0x4680 00010752 UnitConversions.dll02/08/2011 0xfc00 00974848 AISCSections.mdb06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb01/05/2005 0xcac1 03651584 aitctimbersections.mdb05/01/2008 0xb001 00552960 aluminumsections.mdb01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb10/02/2008 0x40 00520192 AustralianSections.mdb06/11/2010 0xa101 00585728 BritishSections.mdb09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb06/28/2005 0x8201 00327680 butlercoldformedsections.mdb02/25/2008 0x2e01 00329728 CanadianSections.mdb09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb05/31/2005 0x9e81 00450560 canadiantimbersections.mdb02/10/2010 0x94c1 00483328 ChineseSections.mdb01/05/2005 0xd6c0 00600064 dutchsections.mdb10/07/2010 0xd2c0 03596290 EuropeanSections.mdb01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb01/05/2005 0xd301 00202752 frenchsections.mdb01/05/2005 0x11c1 00233472 germansections.mdb10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb12/08/2009 0xec1 00942080 IndianSections.mdb01/05/2005 0xd540 00180224 iscoldformedsections.mdb02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb03/23/2006 0xa080 00200704 japanesesections.mdb02/04/2011 0x3300 00495616 JindalSections.mdb11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb08/24/2007 0x3ec0 00454656 Koreansections.mdb04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb02/07/2005 0x9a00 00243712 mexicansteeltables.mdb04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb11/20/2009 0xf700 00428034 RussianSections.mdb05/12/2009 0xe001 00237570 SouthAfricanSections.mdb01/06/2005 0x9341 00194560 spanishsections.mdb11/20/2009 0x5100 00368640 STO_ASChMSections.mdb04/19/2007 0x7480 00223232 uscoldformedsections.mdb10/31/2007 0x3700 00133120 VenezuelanSections.mdb



-----------------------------------------------------------------------------------------

86— STAAD.Pro


15 Natural Modes of a Simple BeamPurposeCompare theoretical answers to the STAAD solution.

ReferenceTimoshenko, S., “Vibration Problems in Engineering”, Third Edition, D. Van Nostrand Company,Inc., 1955, page 322

ProblemThe first five natural frequencies and the associated mode shapes are computed for the flexuralmotion of a simply supported beam.

Figure 15-1: Simple beam diagram

ModelFigure 15-2: Finite element model

The simply supported beam is divided into twenty spanwise beam elements. At nodes 1 and 21, alldegrees of freedom except the rotation about the Z axis are restrained. For the remaining nodes,only the translation along Y and the rotation about Z are permitted. Both shear deformation androtary inertia have been excluded from the model. The mass matrix is a diagonal matrix.


Cross-section Properties

Rectangular Section: 1 inch Width x 2 inch Depth

Area = 2 in2

J = b3a/16 {16/3 - 3.36(b/a)[1 - 1/12(b/a)4]}

where

a = 2

b = 1

J = 0.4578 inch4

I2 = 1x23/12 inch4

I3 = 2x13/12 inch4

Theoretical Results

The natural bending frequencies, for a uniform beam with hinged ends, are given by:

fn = πn2/212(EIg/Aγ)1/2

where

fn = natural frequency for mode n, in cycles per second

l = span of the beam

E = elastic modulus

I = cross-section moment of inertia

g = gravitational constant

A = cross-section area

γ = weight density

The parameters used in the frequency equation are:

l = 20 inches

E = 10x106 psi

I = 0.6667 inches4

g = 386.4 inches per second2

A = 2.0 sq. inches

γ = 0.1 pounds per cubic inch

from which:

fn = n2x 445.685674

The table below shows the natural frequencies computed from the theoretical equation and thesubspace iteration method available within STAAD. Frequencies are in cycles per second.

88— STAAD.Pro

15 Natural Modes of a Simple Beam

Comparison

Mode Number TheoreticalSTAAD

Basic SolverSTAAD

Advanced Solver

1 445.686 445.506 445.506

2 1,782.74 1,782.01 1,782.01

3 4,011.17 4,009.41 4,009.41

4 7,130.97 7,127.25 7,127.25

5 11,142.1 11,134.25 11,134.25

Table 15-1: Comparison of frequency values for verification problem no. 15

Input file

STAAD PLANE STAAD VER. PROB. 15

UNIT POUND INCH

JOINT COORD

1 0 0 0 21 20 0 0

MEMB INCI

1 1 2 20

MEMB PROP

1 TO 20 PRIS AX 2 IZ 0.6667

CONST

E 10E6 ALL

POISSON 0.3 ALL

DENS 0.1 ALL

CUT OFF MODE SHAPE 5

SUPP

1 21 FIXED BUT MZ

2 TO 20 FIXED BUT FY MZ

LOAD 1

SELF X 1.0

SELF Y 1.0

MODAL CALC REQ

PERF ANALY

FINISH



STAAD Output

90 — STAAD.Pro



1. STAAD PLANE STAAD VER. PROB. 15INPUT FILE: ver15.STD

2. * NATURAL MODES OF A SIMPLE BEAM4. UNIT POUND INCH5. JOINT COORD6. 1 0 0 0 21 20 0 07. MEMB INCI8. 1 1 2 209. MEMB PROP10. 1 TO 20 PRIS AX 2 IZ 0.666711. CONST12. E 10E6 ALL13. POISSON 0.3 ALL14. DENS 0.1 ALL15. CUT OFF MODE SHAPE 516. SUPP17. 1 21 FIXED BUT MZ18. 2 TO 20 FIXED BUT FY MZ19. LOAD 120. SELF X 1.021. SELF Y 1.022. MODAL CALC REQ23. PERF ANALY



ORIGINAL/FINAL BAND-WIDTH= 1/ 1/ 4 DOFTOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 40SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDSREQRD/AVAIL. DISK SPACE = 12.0/ 120711.0 MBSTAAD VER. PROB. 15 -- PAGE NO. 2* NATURAL MODES OF A SIMPLE BEAM


STAAD VER. PROB. 15 -- PAGE NO. 3* NATURAL MODES OF A SIMPLE BEAM

CALCULATED FREQUENCIES FOR LOAD CASE 1MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY1 445.506 0.00224 9.509E-162 1782.012 0.00056 1.934E-133 4009.410 0.00025 4.051E-114 7127.250 0.00014 1.334E-095 11134.253 0.00009 1.251E-08

STAAD VER. PROB. 15 -- PAGE NO. 4* NATURAL MODES OF A SIMPLE BEAMThe following Frequencies are estimates that were calculated. These are forinformation only and will not be used. Remaining values are either abovethe cut off mode/freq values or are of low accuracy. To use thesefrequencies, rerun with a higher cutoff mode (or mode + freq) value.

CALCULATED FREQUENCIES FOR LOAD CASE 1MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY6 16027.429 0.00006 2.582E-087 21800.588 0.00005 5.322E-08



8 28441.877 0.00004 4.956E-069 35929.844 0.00003 6.604E-05


1 0.000000E+00 3.228953E+00 0.000000E+00 2.000000E+002 0.000000E+00 3.801267E-26 0.000000E+00 2.000000E+003 0.000000E+00 3.469944E-01 0.000000E+00 2.000000E+004 0.000000E+00 3.572514E-19 0.000000E+00 2.211146E+005 0.000000E+00 1.165685E-01 0.000000E+00 2.000000E+00

MASS PARTICIPATION FACTORS IN PERCENT--------------------------------------

MODE X Y Z SUMM-X SUMM-Y SUMM-Z1 0.00 84.97 0.00 0.000 84.972 0.0002 0.00 0.00 0.00 0.000 84.972 0.0003 0.00 9.13 0.00 0.000 94.104 0.0004 0.00 0.00 0.00 0.000 94.104 0.0005 0.00 3.07 0.00 0.000 97.171 0.000

24. FINISHSTAAD VER. PROB. 15 -- PAGE NO. 5* NATURAL MODES OF A SIMPLE BEAM



STAAD VER. PROB. 15 -- PAGE NO. 6* NATURAL MODES OF A SIMPLE BEAM

Information about the key files in the current distributionModification Date CRC Size (Bytes) File Name-----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe02/22/2011 0xc181 08667136 SProStaadStl.exe09/19/2003 0x2fc0 00081970 CMesh.dll02/17/2011 0xa7c1 04276294 dbsectioninterface.dll02/22/2011 0x12c0 00294912 EC3Annex.dll02/22/2011 0x2900 00376832 EuroCode3.dll12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll01/24/2001 0x9b40 00073728 LoadGen.dll11/19/2010 0xeb80 00011264 MathExtensions.dll09/25/2003 0x6340 00704512 MeshEngine.dll02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll09/22/2003 0xce00 00069632 QuadPlateEngine.dll12/02/2010 0x5040 00073728 SteelCollection.dll02/22/2011 0xca81 00024064 SteelDesign.dll10/08/2010 0xa940 00072192 SteelSections.dll05/29/2008 0x77c1 00106572 SurfMeshEngine.dll10/08/2010 0x4680 00010752 UnitConversions.dll02/08/2011 0xfc00 00974848 AISCSections.mdb06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb

92— STAAD.Pro


01/05/2005 0xcac1 03651584 aitctimbersections.mdb05/01/2008 0xb001 00552960 aluminumsections.mdb01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb10/02/2008 0x40 00520192 AustralianSections.mdb06/11/2010 0xa101 00585728 BritishSections.mdb09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb06/28/2005 0x8201 00327680 butlercoldformedsections.mdb02/25/2008 0x2e01 00329728 CanadianSections.mdb09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb05/31/2005 0x9e81 00450560 canadiantimbersections.mdb02/10/2010 0x94c1 00483328 ChineseSections.mdb01/05/2005 0xd6c0 00600064 dutchsections.mdb10/07/2010 0xd2c0 03596290 EuropeanSections.mdb01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb01/05/2005 0xd301 00202752 frenchsections.mdb01/05/2005 0x11c1 00233472 germansections.mdb10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb12/08/2009 0xec1 00942080 IndianSections.mdb01/05/2005 0xd540 00180224 iscoldformedsections.mdb02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb03/23/2006 0xa080 00200704 japanesesections.mdb02/04/2011 0x3300 00495616 JindalSections.mdb11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb08/24/2007 0x3ec0 00454656 Koreansections.mdb04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb02/07/2005 0x9a00 00243712 mexicansteeltables.mdb04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb11/20/2009 0xf700 00428034 RussianSections.mdb05/12/2009 0xe001 00237570 SouthAfricanSections.mdb01/06/2005 0x9341 00194560 spanishsections.mdb11/20/2009 0x5100 00368640 STO_ASChMSections.mdb04/19/2007 0x7480 00223232 uscoldformedsections.mdb10/31/2007 0x3700 00133120 VenezuelanSections.mdb-----------------------------------------------------------------------------------------



94 — STAAD.Pro


NOTES

16 Natural Frequencies of a Circular PlatePurposeCompare theoretical answers to the STAAD solution.

ReferenceBlevins, Robert D., “Formulas for Natural Frequency and Mode Shape,” Van Nostrand ReinholdCompany, 1979, Page 240.

ProblemA flat circular plate is simply supported around the entire perimeter. The first six modes andtheir associated natural frequencies are to be computed using the subspace iteration methodoffered by STAAD. This problem demonstrates that the natural frequencies of an axi-symmetricstructure can be accurately computed utilizing a 180 degree model with the appropriate boundaryconditions.

Figure 16-1: Diagram of circular plate

ModelThe 180 degree sector was modeled using radial lines at intervals of 15 degrees. Tangential lineswere then located utilizing a relationship such that the aspect ratio of the quad-plate elementswas approximately 1.0. All rotations normal to the plane of the plate were restrained. In-planetranslations for all nodes were restrained because the theoretical solution does not consider in-plane effects. Rotations about the global Y axis for the nodes at X=0.0 were restrained because thisis a symmetry boundary. Z translation of all nodes on the outside radius were restrained toprovide for the simply-supported condition.

95— STAAD.Pro

16 Natural Frequencies of a Circular Plate

Figure 16-2: Finite model for half circular plate

It should be noted that the outside edge of the plate is a series of secant lines instead of a truearc. This will result in a loss of about 1% of the plate’s true mass or about .5% of the mass that iseffective for this problem.

Therefore, it is not unlikely that a few natural frequencies will be lower than the theoretical valuesinstead of higher which is typical for a finite element analysis using plate elements. In addition, atrue simple-support condition for this problem would require restraining the component ofrotation that is radial to the outside edge.

Theoretical Answers

From the reference case 2 in Table 11-1, the first six natural frequencies of the plate are described bythe following equation:

f =ij

λ

π a

Eh

γ ν( )2 12 1 −

ij2

2

3

2

= dimensionless parameter associated with the mode indices i,j

i = number of nodal diameters in this mode shape

j = number of nodal circles in this mode shape not counting the boundary

ν = Poisson’s ratio

E = Elastic Modulus

h = plate thickness

γ = mass of plate per unit area

a = radius of plate

The numerical values used for this example are:



ν = 0.30

E = 10.0x10P6P psi

h = 0.10 inches

γ = (0.10 lbm/in3)(0.10 in)/(386.4 lbm-in/lbf-s

2) = 2.588(10)-5 lbf-s2/in3

a = 10.0 inches

with the numerical values used above

= = 9.467π a

Eh

γ ν π

( )( )

1

2 12 1 −

1

2 (10.0)

10.0 10 (0.10)

12(2.588 10 )[1 − (0.3) ]2

3

2 2

6 3

− 5 2

⋅

⋅ cycles/sec.

cycles/sec

λ2ij is tabulated from the reference as follows:

ModeNumber

λ2ij

Number of NodalDiameters (i)

Number of NodalCircles (j)

1 4.977 0 0

2 13.94 1 0

3 25.65 2 0

4 29.76 0 1

5(l) 3 0

6 48.51 1 1

Table 16-1: Values of λ2ij

(l) not tabulated in the reference

Comparison

ModeNumber

TheoreticalSTAAD Basic

SolverSTAAD Advanced

Solver

1 47.12 46.21 46.21

2 132.0 130.54 130.54

3 242.8 240.15 240.15

4 281.7 283.03 283.03

5 * 373.2 373.2

6 459.3 466.58 466.58

Table 16-2: Comparison of frequency values, Hz, for verification problem no. 16

97— STAAD.Pro


*The reference did not tabulate a value of for the fifth mode of the structure, hence a comparisonwith the theoretical value of this mode cannot be made.

DiscussionAll anti-symmetric mode shapes for the 360 degree circular plate were captured by the 180 degreemodel with a phase angle included in the calculation. Some of the difference between thetheoretical and STAAD frequencies is attributed to the loss of mass due to the piecewise secantrepresentation of the outer radius and, since this mass is about 1 percent lower than for a truecircular plate, it is not surprising that the first few modes are lower than the theoretical solution.

Input file

STAAD SPACE STAAD VER. PROB. 16

* NATURAL FREQUENCIES OF A CIRCULAR PLATE

UNIT POUND INCH

JOINT COORD CYLINDRICAL

1 1 -90 0 13 1 90 0

REP 2 1.244 0 0

REP 1 1.051 0 0

REP 1 1.367 0 0

REP 1 1.779 0 0

REP 1 2.315 0 0

JOINT COORD

1000 0 0 0

ELEM INCI

1 1000 1 2 ; 2 1000 2 3 ; 3 1000 3 4 ; 4 1000 4 5 ; 5 1000 5 6

6 1000 6 7 ; 7 1000 7 8 ; 8 1000 8 9 ; 9 1000 9 10 ; 10 1000 10 11

11 1000 11 12 ; 12 1000 12 13

13 1 14 15 2 TO 24

REP 5 12 13

ELEM PROP

1 TO 84 TH 0.1

CONST

E 10.0E6 ALL

POISS 0.3 ALL

DENS 0.1 ALL

SUPP

* CENTRE OF CIRCLE



1000 FIXED BUT FZ MX

* INTERIOR NODES

2 TO 12 15 TO 25 28 TO 38 41 TO 51 54 TO 64 -

67 TO 77 FIXED BUT FZ MX MY

* NODES ALONG CIRCUMFERENCE

79 TO 91 FIXED BUT MX MY

* NODES ALONG DIAMETER EXCEPT THE TWO AT THE ENDS OF THE DIAMETER.

1 TO 66 BY 13 13 TO 78 BY 13 FIXED BUT FZ MX

LOAD 1

SELF X 1.0

SELF Y 1.0

SELF Z 1.0

MODAL CALC REQ

PERF ANALY

FINI

STAAD Output

99— STAAD.Pro



1. STAAD SPACE STAAD VER. PROB. 16INPUT FILE: ver16.STD

2. * NATURAL FREQUENCIES OF A CIRCULAR PLATE4. UNIT POUND INCH5. JOINT COORD CYLINDRICAL6. 1 1 -90 0 13 1 90 07. REP 2 1.244 0 08. REP 1 1.051 0 09. REP 1 1.367 0 010. REP 1 1.779 0 011. REP 1 2.315 0 013. JOINT COORD14. 1000 0 0 016. ELEM INCI17. 1 1000 1 2 ; 2 1000 2 3 ; 3 1000 3 4 ; 4 1000 4 5 ; 5 1000 5 618. 6 1000 6 7 ; 7 1000 7 8 ; 8 1000 8 9 ; 9 1000 9 10 ; 10 1000 10 1119. 11 1000 11 12 ; 12 1000 12 1321. 13 1 14 15 2 TO 2422. REP 5 12 1324. ELEM PROP25. 1 TO 84 TH 0.127. CONST28. E 10.0E6 ALL29. POISS 0.3 ALL30. DENS 0.1 ALL32. SUPP34. * CENTRE OF CIRCLE35. 1000 FIXED BUT FZ MX37. * INTERIOR NODES38. 2 TO 12 15 TO 25 28 TO 38 41 TO 51 54 TO 64 -39. 67 TO 77 FIXED BUT FZ MX MY41. * NODES ALONG CIRCUMFERENCE42. 79 TO 91 FIXED BUT MX MY44. * NODES ALONG DIAMETER EXCEPT THE TWO AT THE ENDS OF THE DIAMETER.45. 1 TO 66 BY 13 13 TO 78 BY 13 FIXED BUT FZ MX47. LOAD 148. SELF X 1.049. SELF Y 1.050. SELF Z 1.051. MODAL CALC REQ52. PERF ANALYSTAAD VER. PROB. 16 -- PAGE NO. 2* NATURAL FREQUENCIES OF A CIRCULAR PLATE



ORIGINAL/FINAL BAND-WIDTH= 91/ 13/ 40 DOFTOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 250SIZE OF STIFFNESS MATRIX = 10 DOUBLE KILO-WORDSREQRD/AVAIL. DISK SPACE = 12.8/ 120711.0 MB


STAAD VER. PROB. 16 -- PAGE NO. 3



* NATURAL FREQUENCIES OF A CIRCULAR PLATECALCULATED FREQUENCIES FOR LOAD CASE 1

MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY1 46.211 0.02164 5.178E-162 130.541 0.00766 1.038E-153 240.146 0.00416 2.045E-164 283.028 0.00353 8.835E-165 373.198 0.00268 5.081E-166 466.579 0.00214 2.601E-08

STAAD VER. PROB. 16 -- PAGE NO. 4* NATURAL FREQUENCIES OF A CIRCULAR PLATEThe following Frequencies are estimates that were calculated. These are forinformation only and will not be used. Remaining values are either abovethe cut off mode/freq values or are of low accuracy. To use thesefrequencies, rerun with a higher cutoff mode (or mode + freq) value.

CALCULATED FREQUENCIES FOR LOAD CASE 1MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY7 527.844 0.00189 6.230E-138 672.921 0.00149 2.235E-079 701.137 0.00143 6.994E-1010 712.175 0.00140 5.522E-0711 888.597 0.00113 1.377E-0812 903.499 0.00111 5.277E-07


1 0.000000E+00 0.000000E+00 1.053697E+00 4.537235E-012 0.000000E+00 0.000000E+00 2.213951E-10 3.944625E-013 0.000000E+00 0.000000E+00 1.886318E-07 3.935445E-014 0.000000E+00 0.000000E+00 1.275807E-01 1.752588E-015 0.000000E+00 0.000000E+00 1.060158E-08 4.222042E-016 0.000000E+00 0.000000E+00 7.873980E-10 2.165125E-01


MODE X Y Z SUMM-X SUMM-Y SUMM-Z1 0.00 0.00 86.78 0.000 0.000 86.7802 0.00 0.00 0.00 0.000 0.000 86.7803 0.00 0.00 0.00 0.000 0.000 86.7804 0.00 0.00 10.51 0.000 0.000 97.2875 0.00 0.00 0.00 0.000 0.000 97.2876 0.00 0.00 0.00 0.000 0.000 97.287

STAAD VER. PROB. 16 -- PAGE NO. 5* NATURAL FREQUENCIES OF A CIRCULAR PLATE53. FINISTAAD VER. PROB. 16 -- PAGE NO. 6* NATURAL FREQUENCIES OF A CIRCULAR PLATE



STAAD VER. PROB. 16 -- PAGE NO. 7

101 — STAAD.Pro


* NATURAL FREQUENCIES OF A CIRCULAR PLATEInformation about the key files in the current distributionModification Date CRC Size (Bytes) File Name-----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe02/22/2011 0xc181 08667136 SProStaadStl.exe09/19/2003 0x2fc0 00081970 CMesh.dll02/17/2011 0xa7c1 04276294 dbsectioninterface.dll02/22/2011 0x12c0 00294912 EC3Annex.dll02/22/2011 0x2900 00376832 EuroCode3.dll12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll01/24/2001 0x9b40 00073728 LoadGen.dll11/19/2010 0xeb80 00011264 MathExtensions.dll09/25/2003 0x6340 00704512 MeshEngine.dll02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll09/22/2003 0xce00 00069632 QuadPlateEngine.dll12/02/2010 0x5040 00073728 SteelCollection.dll02/22/2011 0xca81 00024064 SteelDesign.dll10/08/2010 0xa940 00072192 SteelSections.dll05/29/2008 0x77c1 00106572 SurfMeshEngine.dll10/08/2010 0x4680 00010752 UnitConversions.dll02/08/2011 0xfc00 00974848 AISCSections.mdb06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb01/05/2005 0xcac1 03651584 aitctimbersections.mdb05/01/2008 0xb001 00552960 aluminumsections.mdb01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb10/02/2008 0x40 00520192 AustralianSections.mdb06/11/2010 0xa101 00585728 BritishSections.mdb09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb06/28/2005 0x8201 00327680 butlercoldformedsections.mdb02/25/2008 0x2e01 00329728 CanadianSections.mdb09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb05/31/2005 0x9e81 00450560 canadiantimbersections.mdb02/10/2010 0x94c1 00483328 ChineseSections.mdb01/05/2005 0xd6c0 00600064 dutchsections.mdb10/07/2010 0xd2c0 03596290 EuropeanSections.mdb01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb01/05/2005 0xd301 00202752 frenchsections.mdb01/05/2005 0x11c1 00233472 germansections.mdb10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb12/08/2009 0xec1 00942080 IndianSections.mdb01/05/2005 0xd540 00180224 iscoldformedsections.mdb02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb03/23/2006 0xa080 00200704 japanesesections.mdb02/04/2011 0x3300 00495616 JindalSections.mdb11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb08/24/2007 0x3ec0 00454656 Koreansections.mdb04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb02/07/2005 0x9a00 00243712 mexicansteeltables.mdb04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb11/20/2009 0xf700 00428034 RussianSections.mdb05/12/2009 0xe001 00237570 SouthAfricanSections.mdb01/06/2005 0x9341 00194560 spanishsections.mdb11/20/2009 0x5100 00368640 STO_ASChMSections.mdb04/19/2007 0x7480 00223232 uscoldformedsections.mdb10/31/2007 0x3700 00133120 VenezuelanSections.mdb-----------------------------------------------------------------------------------------



17 Natural Frequencies of a Rectangular PlatePurposeCompare theoretical answers to the STAAD solution.

ReferenceBlevins, Robert D., ”Formulas for Natural Frequency and Mode Shape,” Van Nostrand ReinholdCompany, 1979, page 258.

ProblemA flat rectangular plate is simply supported on all four sides. The first six modes and theirassociated natural frequencies are to be computed for this structure using the subspace iterationmethod offered by STAAD. This problem also demonstrates that the mesh refinement can bechosen to accurately calculate modes of interest based on the expected mode shapes.

Figure 17-1: Simply supported, rectangular plate

L = 45 in., W = 30 in., t = 0.2 in.

ModelA plate with an aspect ratio of 1.5 was used so that comparison could be made with theoreticalresults tabulated for plates in the reference. An equally spaced mesh was utilized in both the x andthe y dimensions of the plate. The number of elements in each dimension was determined on thebasis of the highest mode of interest. Since the number of half-waves in the sixth mode is 3 inthe length dimension and 2 in the width dimension, a node spacing of 3.75 inches results in eachhalf- wave being represented by four elements which means that no element will be expected to


deform in double curvature. The simply supported edge condition requires that translationnormal to the plane of the plate be restrained for these edge nodes. Rotations normal to the platewere restrained for all nodes.

Figure 17-2: Model: finite element meshed

Theoretical Answers

From the reference case 16 in Table 11-4, the first six natural frequencies of the plate are describedby the following equations:

f =ij

λ

π a

Eh

γ ν( )2 12 1 −

ij2

2

3

2

= dimensionless parameter associated with the mode indices i, j

i = number of half-waves in this mode shape along the horizontal axis

j = number of half-waves in this mode shape along the vertical axis


E = elastic modulus

h = plate thickness

γ = mass of material per unit area

a = length of plate

b = width of plate

104 — STAAD.Pro

17 Natural Frequencies of a Rectangular Plate


ν = 0.30

E =30.0x106 psi

h=0.2 inches

γ = (0.282 lbm/in3)(0.20 in)/(386.4 lbm-in/lbf-s

2) = .1460(10)-4 lbf-s2/in3

a = 45.0 inches

b = 30.0 inches

with the numerical values used above

= = 0.9644π a

Eh

γ ν π

( )( )

1

2 12 1 −

1

2 (10.0)

30.0 10 (0.20)

12(1.460 10 )[1 − (0.3) ]2

3

2 2

6 3

−4 2

⋅

⋅ cycles/sec.

λ2ij is tabulated from the reference as follows:

ModeNumber

λ2ij

Number of Half-Wavesin Length (i)

Number of Half-Wavesin Width (j)

1 32.08 1 1

2 61.69 2 1

3 98.70 1 2

4 111.0 3 1

5 128.3 2 2

6 177.7 3 2

Table 17-1: Values of λ2ij

Comparison

ModeNumber

TheoreticalSTAAD Basic

SolverSTAAD Advanced

Solver

1 30.94 30.6 30.6

2 59.49 58.72 58.72

3 95.18 95.06 95.06

4 107.1 106.28 106.28

5 123.7 122.09 122.09

6 171.3 168.0 168.0

Table 17-2: Comparison of frequency values, Hz, for verificatoin problem no. 17



DiscussionAs was noted earlier, the node spacing was based on the highest mode of interest. It follows thatthe difference between the theoretical and STAAD frequencies generally increases with increasingmode sequence.

Input file

STAAD SPACE STAAD VER. PROB. 17.

* NATURAL FREQUENCIES OF A RECTANGULAR PLATE

UNIT POUND INCH

JOINT COORD

1 0 0 0 13 45 0 0

REP ALL 8 0 3.75 0

ELEM INCI

1 1 2 15 14 TO 12

REP 7 12 13

ELEM PROP

1 TO 96 TH 0.2

CONST

E 30.0E6 ALL

DENS 0.282 ALL

POISSON 0.3 ALL


CUT OFF FREQ 1000

SUPPORT

* CORNER NODES

1 13 105 117 FIXED BUT MX MY

* NODES ALONG Y=0 AND Y=30

2 TO 12 106 TO 116 FIXED BUT MX MY

* NODES ALONG X=0

14 TO 92 BY 13 FIXED BUT MX MY

* NODES ALONG X=45

26 TO 104 BY 13 FIXED BUT MX MY

* INTERIOR NODES

15 TO 25 28 TO 38 41 TO 51 54 TO 64 67 TO 77 80 TO 90 -

93 TO 103 FIXED BUT FZ MX MY

106— STAAD.Pro


LOAD 1

SELF X 1

SELF Y 1

SELF Z 1

MODAL CALC REQ

PERF ANALY

FINI

STAAD Output





2. * NATURAL FREQUENCIES OF A RECTANGULAR PLATE4. UNIT POUND INCH5. JOINT COORD6. 1 0 0 0 13 45 0 07. REP ALL 8 0 3.75 08. ELEM INCI9. 1 1 2 15 14 TO 1210. REP 7 12 1311. ELEM PROP12. 1 TO 96 TH 0.213. CONST14. E 30.0E6 ALL15. DENS 0.282 ALL16. POISSON 0.3 ALL17. CUT OFF MODE SHAPE 618. CUT OFF FREQ 100019. SUPP21. * CORNER NODES22. 1 13 105 117 FIXED BUT MX MY24. * NODES ALONG Y=0 AND Y=3025. 2 TO 12 106 TO 116 FIXED BUT MX MY27. * NODES ALONG X=028. 14 TO 92 BY 13 FIXED BUT MX MY30. * NODES ALONG X=4531. 26 TO 104 BY 13 FIXED BUT MX MY33. * INTERIOR NODES34. 15 TO 25 28 TO 38 41 TO 51 54 TO 64 67 TO 77 80 TO 90 -35. 93 TO 103 FIXED BUT FZ MX MY37. LOAD 138. SELF X 139. SELF Y 140. SELF Z 141. MODAL CALC REQ42. PERF ANALYSTAAD VER. PROB. 17 -- PAGE NO. 2* NATURAL FREQUENCIES OF A RECTANGULAR PLATE





STAAD VER. PROB. 17 -- PAGE NO. 3* NATURAL FREQUENCIES OF A RECTANGULAR PLATE


108— STAAD.Pro


3 95.063 0.01052 9.652E-114 106.277 0.00941 8.480E-105 122.092 0.00819 1.381E-086 168.009 0.00595 9.194E-07

STAAD VER. PROB. 17 -- PAGE NO. 4* NATURAL FREQUENCIES OF A RECTANGULAR PLATEThe following Frequencies are estimates that were calculated. These are forinformation only and will not be used. Remaining values are either abovethe cut off mode/freq values or are of low accuracy. To use thesefrequencies, rerun with a higher cutoff mode (or mode + freq) value.

CALCULATED FREQUENCIES FOR LOAD CASE 1MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY7 173.592 0.00576 3.784E-078 204.044 0.00490 1.762E-069 229.811 0.00435 4.807E-0510 233.369 0.00429 2.127E-0511 261.140 0.00383 4.621E-05


1 0.000000E+00 0.000000E+00 4.833474E+01 1.915442E+012 0.000000E+00 0.000000E+00 4.228619E-20 1.920213E+013 0.000000E+00 0.000000E+00 1.629244E-18 1.925533E+014 0.000000E+00 0.000000E+00 4.837136E+00 1.927464E+015 0.000000E+00 0.000000E+00 1.069665E-13 1.927599E+016 0.000000E+00 0.000000E+00 7.199120E-11 1.936302E+01


MODE X Y Z SUMM-X SUMM-Y SUMM-Z1 0.00 0.00 79.15 0.000 0.000 79.1462 0.00 0.00 0.00 0.000 0.000 79.1463 0.00 0.00 0.00 0.000 0.000 79.1464 0.00 0.00 7.92 0.000 0.000 87.0665 0.00 0.00 0.00 0.000 0.000 87.0666 0.00 0.00 0.00 0.000 0.000 87.066

43. FINISTAAD VER. PROB. 17 -- PAGE NO. 5* NATURAL FREQUENCIES OF A RECTANGULAR PLATESTAAD VER. PROB. 17 -- PAGE NO. 6* NATURAL FREQUENCIES OF A RECTANGULAR PLATE



STAAD VER. PROB. 17 -- PAGE NO. 7* NATURAL FREQUENCIES OF A RECTANGULAR PLATE

Information about the key files in the current distributionModification Date CRC Size (Bytes) File Name-----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe02/22/2011 0xc181 08667136 SProStaadStl.exe



09/19/2003 0x2fc0 00081970 CMesh.dll02/17/2011 0xa7c1 04276294 dbsectioninterface.dll02/22/2011 0x12c0 00294912 EC3Annex.dll02/22/2011 0x2900 00376832 EuroCode3.dll12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll01/24/2001 0x9b40 00073728 LoadGen.dll11/19/2010 0xeb80 00011264 MathExtensions.dll09/25/2003 0x6340 00704512 MeshEngine.dll02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll09/22/2003 0xce00 00069632 QuadPlateEngine.dll12/02/2010 0x5040 00073728 SteelCollection.dll02/22/2011 0xca81 00024064 SteelDesign.dll10/08/2010 0xa940 00072192 SteelSections.dll05/29/2008 0x77c1 00106572 SurfMeshEngine.dll10/08/2010 0x4680 00010752 UnitConversions.dll02/08/2011 0xfc00 00974848 AISCSections.mdb06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb01/05/2005 0xcac1 03651584 aitctimbersections.mdb05/01/2008 0xb001 00552960 aluminumsections.mdb01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb10/02/2008 0x40 00520192 AustralianSections.mdb06/11/2010 0xa101 00585728 BritishSections.mdb09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb06/28/2005 0x8201 00327680 butlercoldformedsections.mdb02/25/2008 0x2e01 00329728 CanadianSections.mdb09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb05/31/2005 0x9e81 00450560 canadiantimbersections.mdb02/10/2010 0x94c1 00483328 ChineseSections.mdb01/05/2005 0xd6c0 00600064 dutchsections.mdb10/07/2010 0xd2c0 03596290 EuropeanSections.mdb01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb01/05/2005 0xd301 00202752 frenchsections.mdb01/05/2005 0x11c1 00233472 germansections.mdb10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb12/08/2009 0xec1 00942080 IndianSections.mdb01/05/2005 0xd540 00180224 iscoldformedsections.mdb02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb03/23/2006 0xa080 00200704 japanesesections.mdb02/04/2011 0x3300 00495616 JindalSections.mdb11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb08/24/2007 0x3ec0 00454656 Koreansections.mdb04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb02/07/2005 0x9a00 00243712 mexicansteeltables.mdb04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb11/20/2009 0xf700 00428034 RussianSections.mdb05/12/2009 0xe001 00237570 SouthAfricanSections.mdb01/06/2005 0x9341 00194560 spanishsections.mdb11/20/2009 0x5100 00368640 STO_ASChMSections.mdb04/19/2007 0x7480 00223232 uscoldformedsections.mdb10/31/2007 0x3700 00133120 VenezuelanSections.mdb-----------------------------------------------------------------------------------------

110 — STAAD.Pro


18 Natural Modes of a FrameworkPurposeCompare the results from STAAD's subspace iteration method with the results from EASE2® andANSYS®.

Reference1. Problem 1, from the ASME 1972 Program Verification and Qualification Library

2. DeSalvo, G.J., and Swanson, J.A., “ANSYS Engineering Analysis System Examples Manual”,Swanson Analysis Systems, Inc., 1979, Example Problem No. 2.

3. Peterson, F.E., “EASE2 Elastic Analysis for Structural Engineering Example ProblemManual”, Engineering Analysis Corporation, 1981, Example 2.03.

ProblemA three dimensional frame is analyzed for its natural frequencies and the associated mode shapesusing the subspace iteration method offered by STAAD.

Figure 18-1: Frame model

All dimensions are in inches.


Model

The only entity present in the model is the general purpose three dimensional beam.

Cross-section Properties

All the beam elements have the same cross section:

Outside radius, Ro = 1.1875 in.

Inside radius, Ri = 1.0335 in.

Area = π(Ro2 - Ri2) = 1.074532 in2

Moment of Inertia, I = π/4(Ro4 - Ri4)

I = 0.665747 in4

Torsion constant = twice the inertia, for closed circular sections = 1.331494 in4

The expression for the shear flexibility factor is derived from the ratio of maximum shear stress tothe average shear stress:

α = AQ/Ib

Where the four items – A, Q, I, and b are properties of the half cross-section about the centerline.For the circular section they are:

A = π/2(Ro2 - Ri2)

Q = 2/3(Ro3 - Ri3)

I = π/8(Ro4 - Ri4)

I = 2(Ro - Ri)

The final expression for the shear flexibility factor, for a circular tube section is:

α = =AQ

Ib

R R

R R R R( )( )4

3

−

− −

o i

o i o i

3 3

2 2

α = 1.993620

Hence the shear area is entered as

AY = Cross Section Area / α = 1.074532 / 1.99362 = 0.538985 in2

ComparisonThe following table compares Twenty-Four Natural Frequencies

ModeNumber

DeSalvo andSwanson2

Peterson3

STAAD BasicSolver


1 111.52 111.53 111.23 111.23

Table 18-1: Comparison of natural frequency values (cycles per second) forverification problem no. 18

112— STAAD.Pro

18 Natural Modes of a Framework

ModeNumber

DeSalvo andSwanson2

Peterson3

STAAD BasicSolver


2 115.95 115.96 115.80 115.80

3 137.60 137.61 137.17 137.17

4 218.02 218.03 215.80 215.80

5 404.23 404.23 404.27 404.27

6 422.70 422.72 422.64 422.64

7 451.72 451.75 451.60 451.60

8 553.99 554.07 549.01 549.01

9 735.70 735.81 733.59 733.59

10 762.32 762.44 758.56 758.56

11 852.57 852.72 851.36 851.36

12 894.08 894.26 892.28 892.28

13 910.21 910.40 893.06 893.06

14 916.98 917.18 910.83 910.83

15 940.02 940.02 932.29 932.29

16 959.98 960.27 956.39 956.39

17 971.15 971.44 964.01 964.01

18 976.92 977.22 967.27 967.27

19 1012.2 1012.5 981.54 981.54

20 1028.4 1028.8 1009.26 1009.26

21 1123.6 1123.9 1070.56 1070.56

22 1134.5 1134.9 1123.16 1123.16

23 1164.1 1164.4 1149.37 1149.37

24 1216.7 1217.2 1199.88 1199.88

In both references by DeSalvo and Swanson2 and Peterson3, the number of dynamic degrees offreedom has been reduced from 42 to 24, by means of the Guyan method. No such reduction isperformed in the STAAD model.



Input File


* NATURAL FREQUENCIES OF A SPACE FRAME

UNIT POUND INCH

JOINT COORD

1 0 0 0 ; 2 27.25 0 0

3 0 10 0 ; 4 27.25 10 0

5 0 18.625 0 ; 6 8.625 18.625 0 ; 7 18.625 18.625 0 ; 8 27.25 18.625 0

9 0 18.625 8.625 ; 10 27.25 18.625 8.625

11 0 0 17.25 ; 12 27.25 0 17.25

13 0 10 17.25 ; 14 27.25 10 17.25

15 0 18.625 17.25 ; 16 8.625 18.625 17.25

17 18.625 18.625 17.25 ; 18 27.25 18.625 17.25

MEMB INCI

1 1 3 ; 2 2 4 ; 3 3 5 ; 4 4 8

5 5 6 7

8 5 9 ; 9 8 10 ; 10 9 15 ; 11 10 18

12 11 13 ; 13 12 14 ; 14 13 15 ; 15 14 18

16 15 16 ; 17 16 17 ; 18 17 18

MEMB PROP

1 TO 18 PRIS AX 1.074532 IZ 0.665747 IY 0.665747 IX 1.331494 -

AY 0.538985 AZ 0.538985

* AY 1.88 AZ 1.88

CONST

E 27.9E6 ALL

POISS 0.3 ALL


114 — STAAD.Pro


1 2 11 12 FIXED

LOAD 1

JOINT LOAD

3 4 13 14 FX 3.4517 FY 3.4517 FZ 3.4517

6 7 16 17 FX 3.4517 FY 3.4517 FZ 3.4517

9 10 FX 3.4517 FY 3.4517 FZ 3.4517

5 8 15 18 FX 9.7973 FY 9.7973 FZ 9.7973

MODAL CALC REQ

PERF ANALY

FINI

STAAD Output





2. * NATURAL MODES OF A SPACE FRAME4. UNIT POUND INCH5. JOINT COORD6. 1 0 0 0 ; 2 27.25 0 07. 3 0 10 0 ; 4 27.25 10 08. 5 0 18.625 0 ; 6 8.625 18.625 0 ; 7 18.625 18.625 0 ; 8 27.25 18.625 010. 9 0 18.625 8.625 ; 10 27.25 18.625 8.62512. 11 0 0 17.25 ; 12 27.25 0 17.2513. 13 0 10 17.25 ; 14 27.25 10 17.2514. 15 0 18.625 17.25 ; 16 8.625 18.625 17.2515. 17 18.625 18.625 17.25 ; 18 27.25 18.625 17.2517. MEMB INCI18. 1 1 3 ; 2 2 4 ; 3 3 5 ; 4 4 819. 5 5 6 721. 8 5 9 ; 9 8 10 ; 10 9 15 ; 11 10 1823. 12 11 13 ; 13 12 14 ; 14 13 15 ; 15 14 1824. 16 15 16 ; 17 16 17 ; 18 17 1826. MEMB PROP27. 1 TO 18 PRIS AX 1.074532 IZ 0.665747 IY 0.665747 IX 1.331494 -28. AY 0.538985 AZ 0.53898529. * AY 1.88 AZ 1.8831. CONST32. E 27.9E6 ALL33. POISS 0.3 ALL34. CUT OFF MODE SHAPE 2436. SUPP37. 1 2 11 12 FIXED39. LOAD 140. JOINT LOAD41. 3 4 13 14 FX 3.4517 FY 3.4517 FZ 3.451742. 6 7 16 17 FX 3.4517 FY 3.4517 FZ 3.451743. 9 10 FX 3.4517 FY 3.4517 FZ 3.451744. 5 8 15 18 FX 9.7973 FY 9.7973 FZ 9.797346. MODAL CALC REQ47. PERF ANALYSTAAD VER. PROB. 18 -- PAGE NO. 2* NATURAL MODES OF A SPACE FRAME





STAAD VER. PROB. 18 -- PAGE NO. 3* NATURAL MODES OF A SPACE FRAME


116— STAAD.Pro


2 115.801 0.00864 4.398E-163 137.169 0.00729 3.134E-164 215.799 0.00463 1.266E-155 404.271 0.00247 4.330E-166 422.642 0.00237 5.283E-167 451.600 0.00221 0.000E+008 549.012 0.00182 1.565E-169 733.589 0.00136 0.000E+0010 758.563 0.00132 3.280E-1611 851.355 0.00117 3.906E-1612 892.281 0.00112 3.556E-1613 893.060 0.00112 0.000E+0014 910.829 0.00110 5.881E-1215 932.286 0.00107 2.171E-1616 956.391 0.00105 2.063E-1617 964.012 0.00104 7.216E-1018 967.267 0.00103 0.000E+0019 981.536 0.00102 0.000E+0020 1009.256 0.00099 3.706E-1621 1070.562 0.00093 1.419E-1022 1123.161 0.00089 4.488E-1623 1149.368 0.00087 9.081E-0924 1199.882 0.00083 3.933E-16

STAAD VER. PROB. 18 -- PAGE NO. 4* NATURAL MODES OF A SPACE FRAMEThe following Frequencies are estimates that were calculated. These are forinformation only and will not be used. Remaining values are either abovethe cut off mode/freq values or are of low accuracy. To use thesefrequencies, rerun with a higher cutoff mode (or mode + freq) value.

CALCULATED FREQUENCIES FOR LOAD CASE 1MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY25 1262.045 0.00079 7.109E-1626 1352.368 0.00074 0.000E+0027 1355.475 0.00074 7.348E-1028 1410.628 0.00071 1.897E-1629 1512.064 0.00066 3.302E-1630 1567.343 0.00064 3.073E-1631 1926.045 0.00052 4.070E-1632 1943.161 0.00051 1.999E-1633 3654.783 0.00027 5.062E-0834 3659.116 0.00027 4.511E-1635 4514.280 0.00022 7.409E-1636 4514.644 0.00022 7.422E-0837 4515.631 0.00022 5.923E-1638 4516.026 0.00022 1.481E-1639 4815.936 0.00021 3.906E-1640 5312.712 0.00019 4.279E-16


1 6.984127E+01 2.148148E-33 2.116575E-28 6.127270E+012 1.278059E-28 4.260871E-33 7.005318E+01 5.765801E+013 1.334786E-26 1.506346E-32 7.258520E-26 7.213568E+014 5.363809E-23 8.246502E-38 9.476748E-28 7.915617E+015 5.181462E-30 4.244586E-03 8.548127E-32 1.532638E+016 1.574093E-27 1.825469E+01 3.599063E-35 1.469096E+017 1.297531E-27 1.703203E-29 5.112395E-03 1.450510E+018 4.947173E-32 1.476836E-32 2.966451E-01 1.825927E+019 6.029626E-28 9.521517E+00 6.548318E-27 1.177227E+0110 9.808873E-04 2.461898E-29 7.138047E-30 1.174657E+0111 1.321193E+00 4.883939E-31 5.697600E-24 1.582130E+0112 4.394276E-25 1.911258E+00 1.705243E-24 1.624941E+0113 1.722238E+00 2.888943E-26 1.809548E-24 3.802992E+0114 2.862893E-26 2.885970E-28 2.865256E-30 2.195000E+0115 2.786326E-28 1.289225E-28 2.363041E-01 1.628835E+0116 1.013788E-24 4.122944E+00 1.025583E-24 1.648078E+0117 2.160889E-24 4.239236E-28 1.355195E-26 1.622822E+01



18 3.256494E-26 1.184829E-28 3.083967E+00 1.640511E+0119 3.491379E-01 1.623903E-30 1.402550E-24 2.835636E+0120 3.469303E-25 1.122183E+01 5.217990E-24 2.560370E+0121 9.923317E-24 1.878264E-27 1.264702E-26 3.464233E+01


22 3.635978E-01 1.612759E-28 2.105646E-25 3.137066E+0123 3.474316E-25 3.040856E-29 1.020214E-23 1.555328E+0124 6.381997E-02 1.963886E-28 1.643944E-29 2.520960E+01



MODE X Y Z SUMM-X SUMM-Y SUMM-Z1 94.76 0.00 0.00 94.756 0.000 0.0002 0.00 0.00 95.04 94.756 0.000 95.0443 0.00 0.00 0.00 94.756 0.000 95.0444 0.00 0.00 0.00 94.756 0.000 95.0445 0.00 0.01 0.00 94.756 0.006 95.0446 0.00 24.77 0.00 94.756 24.773 95.0447 0.00 0.00 0.01 94.756 24.773 95.0518 0.00 0.00 0.40 94.756 24.773 95.4539 0.00 12.92 0.00 94.756 37.691 95.45310 0.00 0.00 0.00 94.758 37.691 95.45311 1.79 0.00 0.00 96.550 37.691 95.45312 0.00 2.59 0.00 96.550 40.284 95.45313 2.34 0.00 0.00 98.887 40.284 95.45314 0.00 0.00 0.00 98.887 40.284 95.45315 0.00 0.00 0.32 98.887 40.284 95.77416 0.00 5.59 0.00 98.887 45.878 95.77417 0.00 0.00 0.00 98.887 45.878 95.77418 0.00 0.00 4.18 98.887 45.878 99.95819 0.47 0.00 0.00 99.360 45.878 99.95820 0.00 15.23 0.00 99.360 61.103 99.95821 0.00 0.00 0.00 99.360 61.103 99.95822 0.49 0.00 0.00 99.854 61.103 99.95823 0.00 0.00 0.00 99.854 61.103 99.95824 0.09 0.00 0.00 99.940 61.103 99.958

48. FINI*********** END OF THE STAAD.Pro RUN *************** DATE= MAR 9,2011 TIME= 11: 5:56 ****




Information about the key files in the current distributionModification Date CRC Size (Bytes) File Name-----------------------------------------------------------------------------------------

118— STAAD.Pro


03/02/2011 0xe4c0 18427904 SProStaad.exe02/22/2011 0xc181 08667136 SProStaadStl.exe09/19/2003 0x2fc0 00081970 CMesh.dll02/17/2011 0xa7c1 04276294 dbsectioninterface.dll02/22/2011 0x12c0 00294912 EC3Annex.dll02/22/2011 0x2900 00376832 EuroCode3.dll12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll01/24/2001 0x9b40 00073728 LoadGen.dll11/19/2010 0xeb80 00011264 MathExtensions.dll09/25/2003 0x6340 00704512 MeshEngine.dll02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll09/22/2003 0xce00 00069632 QuadPlateEngine.dll12/02/2010 0x5040 00073728 SteelCollection.dll02/22/2011 0xca81 00024064 SteelDesign.dll10/08/2010 0xa940 00072192 SteelSections.dll05/29/2008 0x77c1 00106572 SurfMeshEngine.dll10/08/2010 0x4680 00010752 UnitConversions.dll02/08/2011 0xfc00 00974848 AISCSections.mdb06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb01/05/2005 0xcac1 03651584 aitctimbersections.mdb05/01/2008 0xb001 00552960 aluminumsections.mdb01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb10/02/2008 0x40 00520192 AustralianSections.mdb06/11/2010 0xa101 00585728 BritishSections.mdb09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb06/28/2005 0x8201 00327680 butlercoldformedsections.mdb02/25/2008 0x2e01 00329728 CanadianSections.mdb09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb05/31/2005 0x9e81 00450560 canadiantimbersections.mdb02/10/2010 0x94c1 00483328 ChineseSections.mdb01/05/2005 0xd6c0 00600064 dutchsections.mdb10/07/2010 0xd2c0 03596290 EuropeanSections.mdb01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb01/05/2005 0xd301 00202752 frenchsections.mdb01/05/2005 0x11c1 00233472 germansections.mdb10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb12/08/2009 0xec1 00942080 IndianSections.mdb01/05/2005 0xd540 00180224 iscoldformedsections.mdb02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb03/23/2006 0xa080 00200704 japanesesections.mdb02/04/2011 0x3300 00495616 JindalSections.mdb11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb08/24/2007 0x3ec0 00454656 Koreansections.mdb04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb02/07/2005 0x9a00 00243712 mexicansteeltables.mdb04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb11/20/2009 0xf700 00428034 RussianSections.mdb05/12/2009 0xe001 00237570 SouthAfricanSections.mdb01/06/2005 0x9341 00194560 spanishsections.mdb11/20/2009 0x5100 00368640 STO_ASChMSections.mdb04/19/2007 0x7480 00223232 uscoldformedsections.mdb10/31/2007 0x3700 00133120 VenezuelanSections.mdb-----------------------------------------------------------------------------------------



120 — STAAD.Pro


NOTES

19 Response of a Simply Supported Beam to aShock Spectrum

PurposeCompare theoretical answers to the STAAD solution.

Reference1. Biggs, John M., “Introduction to Structural Dynamics,” McGraw Hill, 1964, pp. 256-263

2. Blevins, Robert D.,“ Formulas for Natural Frequency and Mode Shape,” Van Nostrand-Reinhold, 1979.

ProblemThe supports of a simply supported beam are subjected to an acceleration time history. Themaximum bending moment in the beam is computed for the first mode of the structure. Thisproblem demonstrates the capabilities of STAAD to calculate the correct modal response of astructure utilizing response spectrum data.

Figure 19-1: Simple span beam

ModelThe STAAD model consists of 11 nodes and 10 elastic beam elements. Node 1 is completelyrestrained with the exception of having rotational freedom in the Z direction, the remaining nodesare restrained except for X and Y displacements and Z rotations. Node 11 is additionally restrainedagainst displacements in the Y direction to provide for the simple support condition . Only thecontribution of the first mode of the structure is considered.


Figure 19-2: Finite element model

Theoretical SolutionMaterial Properties

L = 240.0 inches

E = 30 x 106 lb/in2

EI = 1.0 x 1010 lb-in2

m = 0.2 lb-sec2 / in2

h = 14.0 in.

From Reference 2, Table 8-1, page 108, the fundamental frequency of the beam is:

f hz= = = 6.098i

λ

π �

EI

m π2

9.869

2 (240)

1.0(10)

0.2i2

2 2

10

The modal participation factor for the fundamental mode is:

=∫

∫

m x d x

m x d x

( )

( )

0

1

0

1 2Γϕ

ϕ

Where the first mode shape, φ(x) = sin(πx/1)

π= = 4 /∫

∫

m d x

m d x

sin

sin

πx

πx

0

1

1

0

1 2

1

Γ

The maximum relative modal displacement is given by:

Amax = Γu0max

Where:

u0max = y''so/ω2(DLF)max

ω - 2π*6.098Hz

y''so = 1.0g

122— STAAD.Pro

19 Response of a Simply Supported Beam to a Shock Spectrum

(DLF)max = 1.648 at 6.098 Hz

therefore:

Amax = 4(1.648)(386.4)/[π(2π)2(6.098)2] = 0.5523 in.

The bending moment

M = -EIδ2u/(δx2)

Where u for the first mode = A sin(πx/l)

δ2u/(δx2) = -π2/l2A·sin(πx/l)

M = AEI·(π2/l2)·sin(πx/l)

Mmax = AmaxEI·(π2/l2)

at x = l/2

Mmax = 1(10)10·(0.5523)·π2/(2402) = 946.351(10)3 lb·in

at x=l/2

Comparison

Solution TheorySTAAD

Basic SolverSTAAD

Advanced Solver

Bending Moment (kip-inch) 946.351 947.09 947.09

Table 19-1: Comparison of max. moment in beam 5 for verification problem no.19

Input File


* RESPONSE OF A SIMPLY SUPPORTED BEAM TO A SHOCK SPECTRUM

UNIT POUND INCH

JOINT COORD

1 0 0 0 11 240 0 0

MEMB INCI

1 1 2 10

MEMB PROP

1 TO 10 PRIS YD 14.0 ZD 1.45777 AX 20.4082 IX 40.0 IY 3.6139 IZ 333.333

CONST

E 30.0E6 ALL

POISS 0.3 ALL

DENS 3.78672 ALL




SUPPORT

1 FIXED BUT MZ

2 TO 10 FIXED BUT FX FY MZ

11 FIXED BUT FX MZ

LOAD 1

SELF X 1.0

SELF Y 1.0

SPECTRUM SRSS Y 1.0 ACC DAMP 0.001 SCALE 386.4

0.15 1.648 ; 0.17 1.648

PERF ANALY

PRINT MEMB FORCE LIST 5

FINI

STAAD Output

124 — STAAD.Pro




2. * RESPONSE OF A SIMPLY SUPPORTED BEAM TO A SHOCK SPECTRUM3. UNIT POUND INCH4. JOINT COORD5. 1 0 0 0 11 240 0 06. MEMB INCI7. 1 1 2 108. MEMB PROP9. 1 TO 10 PRIS YD 14.0 ZD 1.45777 AX 20.4082 IX 40.0 IY 3.6139 IZ 333.33310. CONST11. E 30.0E6 ALL12. POISS 0.3 ALL13. DENS 3.78672 ALL14. CUT OFF MODE SHAPE 115. SUPPORT16. 1 FIXED BUT MZ17. 2 TO 10 FIXED BUT FX FY MZ18. 11 FIXED BUT FX MZ19. LOAD 120. SELF X 1.021. SELF Y 1.022. SPECTRUM SRSS Y 1.0 ACC DAMP 0.001 SCALE 386.423. 0.15 1.648 ; 0.17 1.64824. PERF ANALY


NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 11/ 10/ 11STAAD VER. PROB. 19 -- PAGE NO. 2* RESPONSE OF A SIMPLY SUPPORTED BEAM TO A S

SOLVER USED IS THE OUT-OF-CORE BASIC SOLVERORIGINAL/FINAL BAND-WIDTH= 1/ 1/ 6 DOFTOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 30SIZE OF STIFFNESS MATRIX = 1 DOUBLE KILO-WORDSREQRD/AVAIL. DISK SPACE = 12.0/ 120710.9 MB


STAAD VER. PROB. 19 -- PAGE NO. 3* RESPONSE OF A SIMPLY SUPPORTED BEAM TO A S


STAAD VER. PROB. 19 -- PAGE NO. 4* RESPONSE OF A SIMPLY SUPPORTED BEAM TO A SThe following Frequencies are estimates that were calculated. These are forinformation only and will not be used. Remaining values are either abovethe cut off mode/freq values or are of low accuracy. To use thesefrequencies, rerun with a higher cutoff mode (or mode + freq) value.





1 3.605170E-18 1.478714E+04 0.000000E+00 9.273617E+03RESPONSE LOAD CASE 1SRSS MODAL COMBINATION METHOD USED.DYNAMIC WEIGHT X Y Z 1.761987E+04 1.669251E+04 0.000000E+00 POUNMISSING WEIGHT X Y Z -1.761987E+04 -1.905373E+03 0.000000E+00 POUNMODAL WEIGHT X Y Z 3.605170E-18 1.478714E+04 0.000000E+00 POUN

MODE ACCELERATION-G DAMPING---- -------------- -------

1 1.64933 0.00100MODAL BASE ACTIONS FORCES IN POUN LENGTH IN INCH-----------------------------------------------------------

MOMENTS ARE ABOUT THE ORIGINMODE PERIOD FX FY FZ MX MY MZ

1 0.165 0.00 24388.86 0.00 0.00 0.00 2926662.97STAAD VER. PROB. 19 -- PAGE NO. 5* RESPONSE OF A SIMPLY SUPPORTED BEAM TO A S

MASS PARTICIPATION FACTORS IN PERCENT BASE SHEAR IN POUN-------------------------------------- ------------------

MODE X Y Z SUMM-X SUMM-Y SUMM-Z X Y Z1 0.00 88.59 0.00 0.000 88.585 0.000 0.00 24388.86 0.00

---------------------------TOTAL SRSS SHEAR 0.00 24388.86 0.00TOTAL 10PCT SHEAR 0.00 24388.86 0.00TOTAL ABS SHEAR 0.00 24388.86 0.00

25. PRINT MEMB FORCE LIST 5STAAD VER. PROB. 19 -- PAGE NO. 6* RESPONSE OF A SIMPLY SUPPORTED BEAM TO A SMEMBER END FORCES STRUCTURE TYPE = SPACE-----------------ALL UNITS ARE -- POUN INCH (LOCAL )MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z

5 1 5 0.02 1931.41 0.00 0.00 0.00 900734.256 0.02 1931.41 0.00 0.00 0.00 947088.00

************** END OF LATEST ANALYSIS RESULT **************26. FINI





Information about the key files in the current distributionModification Date CRC Size (Bytes) File Name-----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe02/22/2011 0xc181 08667136 SProStaadStl.exe09/19/2003 0x2fc0 00081970 CMesh.dll02/17/2011 0xa7c1 04276294 dbsectioninterface.dll

126— STAAD.Pro


02/22/2011 0x12c0 00294912 EC3Annex.dll02/22/2011 0x2900 00376832 EuroCode3.dll12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll01/24/2001 0x9b40 00073728 LoadGen.dll11/19/2010 0xeb80 00011264 MathExtensions.dll09/25/2003 0x6340 00704512 MeshEngine.dll02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll09/22/2003 0xce00 00069632 QuadPlateEngine.dll12/02/2010 0x5040 00073728 SteelCollection.dll02/22/2011 0xca81 00024064 SteelDesign.dll10/08/2010 0xa940 00072192 SteelSections.dll05/29/2008 0x77c1 00106572 SurfMeshEngine.dll10/08/2010 0x4680 00010752 UnitConversions.dll02/08/2011 0xfc00 00974848 AISCSections.mdb06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb01/05/2005 0xcac1 03651584 aitctimbersections.mdb05/01/2008 0xb001 00552960 aluminumsections.mdb01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb10/02/2008 0x40 00520192 AustralianSections.mdb06/11/2010 0xa101 00585728 BritishSections.mdb09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb06/28/2005 0x8201 00327680 butlercoldformedsections.mdb02/25/2008 0x2e01 00329728 CanadianSections.mdb09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb05/31/2005 0x9e81 00450560 canadiantimbersections.mdb02/10/2010 0x94c1 00483328 ChineseSections.mdb01/05/2005 0xd6c0 00600064 dutchsections.mdb10/07/2010 0xd2c0 03596290 EuropeanSections.mdb01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb01/05/2005 0xd301 00202752 frenchsections.mdb01/05/2005 0x11c1 00233472 germansections.mdb10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb12/08/2009 0xec1 00942080 IndianSections.mdb01/05/2005 0xd540 00180224 iscoldformedsections.mdb02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb03/23/2006 0xa080 00200704 japanesesections.mdb02/04/2011 0x3300 00495616 JindalSections.mdb11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb08/24/2007 0x3ec0 00454656 Koreansections.mdb04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb02/07/2005 0x9a00 00243712 mexicansteeltables.mdb04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb11/20/2009 0xf700 00428034 RussianSections.mdb05/12/2009 0xe001 00237570 SouthAfricanSections.mdb01/06/2005 0x9341 00194560 spanishsections.mdb11/20/2009 0x5100 00368640 STO_ASChMSections.mdb04/19/2007 0x7480 00223232 uscoldformedsections.mdb10/31/2007 0x3700 00133120 VenezuelanSections.mdb-----------------------------------------------------------------------------------------



128— STAAD.Pro


NOTES

20 Thermal Loading on a Simply SupportedRectangular Plate


ReferenceTimoshenko, S., and Woinowsky-Krieger, S., “Theory of Plates and Shells”, Second Edition,McGraw-Hill, 1959, pages 162 - 165.

ProblemA rectangular plate is simply supported on all four sides. The transverse and longitudinal bendingmoments as well as the deflections at several points on the plate are computed.

Figure 20-1: Rectangular plate model

L = 12 in., W = 16 in.

ModelThe plate is modeled using 1 in. X 1 in. size elements. At the corner nodes, all the degrees offreedom are considered restrained. For the nodes along the four edges, rotation is permitted aboutthat edge.

Theoretical SolutionFrom the Reference, equation (j), the expression for deflection normal to the plate surface is:


w = − ∑ 1 −αt ν �

π h m m α

(1 + )4= 1, 3, 5…

∞sin cosh

cosh

mπx

�

mπy

�

m

2

3 3

where

α = mπb/(2a)

From the Reference, equation (k), the expressions for bending moment per unit width are

M = ∑xDαt ν

πh m m α

4 (1 − )= 1, 3, 5…

∞sin cosh

cosh

mπx

�

mπy

�

m

2

⋅

M = − ∑yαt ν D

h

Dαt ν

πh m m α

(1 − ) 4 (1 − )= 1, 3, 5…

∞sin cosh

cosh

mπx

�

mπy

�

m

2 2

⋅

Where:

α = Coefficient of Thermal Expansion

t = Difference between the temperatures of the upper and lower surfaces of the plate


h = Plate thickness

a = Dimension of the plate along the x1 axis

b = Dimension of the plate along the x2 axis

E = Elastic Modulus

D = Eh3/[12(1 - ν2)


α = 12.0E-06 / °F

t = 450 °F

ν = 0.3

h = 0.3 in.

a = 12 in.

b = 16 in.

E= 10.0E6 psi

130 — STAAD.Pro

20 Thermal Loading on a Simply Supported Rectangular Plate

Comparison

Deflections along X = 6

NodeNumber

X YTheoreticalDeflection

STAAD BasicSolver

Deflection

STAADAdvancedSolver

Deflection

7 6 -8 0.00 0.00 0.00

20 6 -7 0.0897 0.0897 0.0897

33 6 -6 0.1597 0.1597 0.1597

46 6 -5 0.2132 0.2132 0.2132

59 6 -4 0.2531 0.2531 0.2531

72 6 -3 0.2818 0.2818 0.2818

85 6 -2 0.3011 0.3011 0.3011

98 6 -1 0.3122 0.3122 0.3122

111 6 0 0.3158 0.3158 0.3158

124 6 1 0.3122 0.3122 0.3122

Table 20-1: Comparison of deflections along X = 6, in inches, for verificationproblem no. 20



Deflections along Y = 1

NodeNumber

X YTheoreticalDeflection

STAAD BasicSolver

Deflection

STAADAdvancedSolver

Deflection

118 0 1 0 0 0

119 1 1 0.1004 0.1004 0.1004

120 2 1 0.1794 0.1794 0.1794

121 3 1 0.2387 0.2387 0.2387

122 4 1 0.2799 0.2799 0.2799

123 5 1 0.3042 0.3042 0.3042

124 6 1 0.3122 0.3122 0.3122

125 7 1 0.3042 0.3042 0.3042

126 8 1 0.2799 0.2799 0.2799

127 9 1 0.2387 0.2387 0.2387

128 10 1 0.1794 0.1794 0.1794

129 11 1 0.1004 0.1004 0.1004

130 12 1 0 0 0

Table 20-2: Comparison of deflections along Y = 1, in inches, for verificationproblem no. 20

132— STAAD.Pro


Bending Moments along Y = 0.5

ElementNumber

X Y

TheoreticalMoment

(Pound-in/in)

STAAD BASICSOLVERMoment

(Pound-in/in)

STAADADVANCEDSOLVER

Moment (Pound-in/in)

Mx My Mx My Mx My

97 0.5 0.5 16.74 388.26 16.85 388.37 16.85 388.37

98 1.5 0.5 48.93 356.07 49.25 356.37 49.25 356.37

99 2.5 0.5 77.45 327.55 77.92 328.01 77.92 328.01

100 3.5 0.5 100.36 304.64 100.93 305.20 100.93 305.20

101 4.5 0.5 116.31 288.69 116.93 289.32 116.93 289.32

102 5.5 0.5 124.47 280.54 125.11 281.19 125.11 281.19

103 6.5 0.5 124.47 280.54 125.11 281.19 125.11 281.19

104 7.5 0.5 116.31 288.69 116.93 289.32 116.93 289.32

105 8.5 0.5 100.36 304.64 100.93 305.20 100.93 305.20

106 9.5 0.5 77.45 327.55 77.92 328.01 77.92 328.01

107 10.5 0.5 48.93 356.07 49.25 356.37 49.25 356.37

108 11.5 0.5 16.74 388.26 16.85 388.37 16.85 388.37

Table 20-3: Comparison of bending moments along Y = 0.5, in in-lbs/in, forverification problem no. 20



Bending Moments along X = 5.5

ElementNumber

X Y

TheoreticalMoment(Pound-in/in)

STAAD BASICSOLVERMoment

(Pound-in/in)

STAADADVANCEDSOLVER

Moment (Pound-in/in)

Mx My Mx My Mx My

6 5.5 -7.5

373.88 31.12 373.27 32.17 373.27 32.17

18 5.5 -6.5

311.64 93.36 312.19 93.95 312.19 93.95

30 5.5 -5.5

256.83 148.17 257.59 148.94 257.59 148.94

42 5.5 -4.5

211.14 193.87 211.95 194.66 211.95 194.66

54 5.5 -3.5

175.41 229.60 176.20 230.35 176.20 230.35

66 5.5 -2.5

149.47 255.53 150.19 256.25 150.19 256.25

78 5.5 -1.5

132.68 272.32 133.36 273.00 133.36 273.00

90 5.5 -0.5

124.47 280.54 125.11 281.19 125.11 281.19

102 5.5 0.5 124.47 280.54 125.11 281.19 125.11 281.19

114 5.5 1.5 132.68 272.32 133.36 273.00 133.36 273.00

126 5.5 2.5 149.47 255.53 150.19 256.25 150.19 256.25

138 5.5 3.5 175.41 229.59 176.20 230.35 176.20 230.35

150 5.5 4.5 211.14 193.87 211.95 194.66 211.95 194.66

162 5.5 5.5 256.83 148.17 257.59 148.94 257.59 148.94

Table 20-4: Comparison of bending moments along X = 5.5, in in-lbs/in, forverification problem no. 20

Input File


134 — STAAD.Pro


* THERMAL LOADING ON A RECTANGULAR PLATE.

UNIT POUND INCH

JOINT COORD

1 0 -8 0 13 12 -8 0

REP 16 0 1 0

ELEM INCI

1 1 2 15 14 TO 12

REP 15 12 13

ELEM PROP

1 TO 192 TH 0.3

CONST

E 10.0E6 ALL

POISS 0.3 ALL

ALPHA 12.0E-6 ALL

SUPP

1 13 209 221 FIXED

2 TO 12 210 TO 220 FIXED BUT MX

14 TO 196 BY 13 26 TO 208 BY 13 FIXED BUT MY

LOAD 1

TEMP LOAD

1 TO 192 TEMP 0 450

PERF ANALY

PRINT JOINT DISP LIST 119 TO 129 7 TO 215 BY 13

PRINT ELEM FORCE LIST 97 TO 108 6 TO 186 BY 12

FINI

STAAD Output





2. * THERMAL LOADING ON A SIMPLY SUPPORTED RECTANGULAR PLATE.4. UNIT POUND INCH5. JOINT COORD6. 1 0 -8 0 13 12 -8 07. REP 16 0 1 08. ELEM INCI9. 1 1 2 15 14 TO 1210. REP 15 12 1311. ELEM PROP12. 1 TO 192 TH 0.313. CONST14. E 10.0E6 ALL15. POISS 0.3 ALL16. ALPHA 12.0E-6 ALL17. SUPP18. 1 13 209 221 FIXED19. 2 TO 12 210 TO 220 FIXED BUT MX20. 14 TO 196 BY 13 26 TO 208 BY 13 FIXED BUT MY21. LOAD 122. TEMP LOAD23. 1 TO 192 TEMP 0 45024. PERF ANALY



ORIGINAL/FINAL BAND-WIDTH= 14/ 14/ 80 DOFTOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 1042SIZE OF STIFFNESS MATRIX = 84 DOUBLE KILO-WORDSREQRD/AVAIL. DISK SPACE = 13.9/ 120710.4 MBSTAAD VER. PROB. 20 -- PAGE NO. 2* THERMAL LOADING ON A SIMPLY SUPPORTED RECT25. PRINT JOINT DISP LIST 119 TO 129 7 TO 215 BY 13STAAD VER. PROB. 20 -- PAGE NO. 3* THERMAL LOADING ON A SIMPLY SUPPORTED RECTJOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = SPACE------------------

JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN119 1 0.00000 0.00000 0.10040 -0.00193 -0.08944 0.00000120 1 0.00000 0.00000 0.17937 -0.00371 -0.06893 0.00000121 1 0.00000 0.00000 0.23869 -0.00521 -0.05010 0.00000122 1 0.00000 0.00000 0.27991 -0.00635 -0.03262 0.00000123 1 0.00000 0.00000 0.30417 -0.00705 -0.01607 0.00000124 1 0.00000 0.00000 0.31218 -0.00729 0.00000 0.00000125 1 0.00000 0.00000 0.30417 -0.00705 0.01607 0.00000126 1 0.00000 0.00000 0.27991 -0.00635 0.03262 0.00000127 1 0.00000 0.00000 0.23869 -0.00521 0.05010 0.00000128 1 0.00000 0.00000 0.17937 -0.00371 0.06893 0.00000129 1 0.00000 0.00000 0.10040 -0.00193 0.08944 0.000007 1 0.00000 0.00000 0.00000 0.10098 0.00000 0.0000020 1 0.00000 0.00000 0.08974 0.07940 0.00000 0.0000033 1 0.00000 0.00000 0.15969 0.06132 0.00000 0.0000046 1 0.00000 0.00000 0.21318 0.04637 0.00000 0.00000

136— STAAD.Pro


59 1 0.00000 0.00000 0.25310 0.03406 0.00000 0.0000072 1 0.00000 0.00000 0.28181 0.02380 0.00000 0.0000085 1 0.00000 0.00000 0.30109 0.01506 0.00000 0.0000098 1 0.00000 0.00000 0.31218 0.00729 0.00000 0.00000111 1 0.00000 0.00000 0.31579 0.00000 0.00000 0.00000124 1 0.00000 0.00000 0.31218 -0.00729 0.00000 0.00000137 1 0.00000 0.00000 0.30109 -0.01506 0.00000 0.00000150 1 0.00000 0.00000 0.28181 -0.02380 0.00000 0.00000163 1 0.00000 0.00000 0.25310 -0.03406 0.00000 0.00000176 1 0.00000 0.00000 0.21318 -0.04637 0.00000 0.00000189 1 0.00000 0.00000 0.15969 -0.06132 0.00000 0.00000202 1 0.00000 0.00000 0.08974 -0.07940 0.00000 0.00000215 1 0.00000 0.00000 0.00000 -0.10098 0.00000 0.00000************** END OF LATEST ANALYSIS RESULT **************26. PRINT ELEM STRESS LIST 97 TO 108 6 TO 186 BY 12STAAD VER. PROB. 20 -- PAGE NO. 4* THERMAL LOADING ON A SIMPLY SUPPORTED RECTELEMENT STRESSES FORCE,LENGTH UNITS= POUN INCH----------------

STRESS = FORCE/UNIT WIDTH/THICK, MOMENT = FORCE-LENGTH/UNIT WIDTHELEMENT LOAD SQX SQY MX MY MXY

VONT VONB SX SY SXYTRESCAT TRESCAB

97 1 -2.00 -0.08 -16.85 -388.37 16.5325419.74 25419.74 0.00 0.00 0.0025939.96 25939.96

TOP : SMAX= -1074.52 SMIN= -25939.96 TMAX= 12432.72 ANGLE= 2.5BOTT: SMAX= 25939.96 SMIN= 1074.52 TMAX= 12432.72 ANGLE=-87.5

98 1 -1.69 -0.20 -49.25 -356.37 15.2722367.84 22367.84 0.00 0.00 0.0023808.31 23808.31


99 1 -1.23 -0.23 -77.92 -328.01 12.9219844.14 19844.14 0.00 0.00 0.0021911.49 21911.49


100 1 -0.78 -0.21 -100.93 -305.20 9.7617989.87 17989.87 0.00 0.00 0.0020377.92 20377.92


101 1 -0.42 -0.16 -116.93 -289.32 6.0516820.57 16820.57 0.00 0.00 0.0019302.28 19302.28


102 1 -0.13 -0.13 -125.11 -281.19 2.0516269.07 16269.07 0.00 0.00 0.0018747.84 18747.84


103 1 0.13 -0.13 -125.11 -281.19 -2.0516269.07 16269.07 0.00 0.00 0.0018747.84 18747.84

TOP : SMAX= -8338.78 SMIN= -18747.84 TMAX= 5204.53 ANGLE= -0.8BOTT: SMAX= 18747.84 SMIN= 8338.78 TMAX= 5204.53 ANGLE= 89.2

104 1 0.42 -0.16 -116.93 -289.32 -6.0516820.57 16820.57 0.00 0.00 0.0019302.28 19302.28


STAAD VER. PROB. 20 -- PAGE NO. 5* THERMAL LOADING ON A SIMPLY SUPPORTED RECTELEMENT STRESSES FORCE,LENGTH UNITS= POUN INCH



----------------STRESS = FORCE/UNIT WIDTH/THICK, MOMENT = FORCE-LENGTH/UNIT WIDTH

ELEMENT LOAD SQX SQY MX MY MXYVONT VONB SX SY SXYTRESCAT TRESCAB

105 1 0.78 -0.21 -100.93 -305.20 -9.7617989.87 17989.87 0.00 0.00 0.0020377.92 20377.92


106 1 1.23 -0.23 -77.92 -328.01 -12.9219844.14 19844.14 0.00 0.00 0.0021911.49 21911.49


107 1 1.69 -0.20 -49.25 -356.37 -15.2722367.84 22367.84 0.00 0.00 0.0023808.31 23808.31


108 1 2.00 -0.08 -16.85 -388.37 -16.5325419.74 25419.74 0.00 0.00 0.0025939.96 25939.96

TOP : SMAX= -1074.52 SMIN= -25939.96 TMAX= 12432.72 ANGLE= -2.5BOTT: SMAX= 25939.96 SMIN= 1074.52 TMAX= 12432.72 ANGLE= 87.56 1 0.34 -4.36 -373.27 -32.17 -31.51

24160.11 24160.11 0.00 0.00 0.0025076.87 25076.87

TOP : SMAX= -1951.93 SMIN= -25076.87 TMAX= 11562.47 ANGLE=-84.8BOTT: SMAX= 25076.87 SMIN= 1951.93 TMAX= 11562.47 ANGLE= 5.2

18 1 0.74 -2.75 -312.19 -93.95 -29.1918798.88 18798.88 0.00 0.00 0.0021068.45 21068.45


30 1 0.67 -1.03 -257.59 -148.94 -25.1915213.03 15213.03 0.00 0.00 0.0017542.96 17542.96


42 1 0.38 -0.06 -211.95 -194.66 -20.3613792.44 13792.44 0.00 0.00 0.0015028.62 15028.62


STAAD VER. PROB. 20 -- PAGE NO. 6* THERMAL LOADING ON A SIMPLY SUPPORTED RECTELEMENT STRESSES FORCE,LENGTH UNITS= POUN INCH----------------



54 1 0.12 0.39 -176.20 -230.35 -15.4014020.85 14020.85 0.00 0.00 0.0015628.28 15628.28


66 1 -0.02 0.49 -150.19 -256.25 -10.6614918.57 14918.57 0.00 0.00 0.0017154.23 17154.23


78 1 -0.09 0.36 -133.36 -273.00 -6.2315779.24 15779.24 0.00 0.00 0.0018218.24 18218.24

138— STAAD.Pro



90 1 -0.13 0.13 -125.11 -281.19 -2.0516269.07 16269.07 0.00 0.00 0.0018747.84 18747.84


102 1 -0.13 -0.13 -125.11 -281.19 2.0516269.07 16269.07 0.00 0.00 0.0018747.84 18747.84


114 1 -0.09 -0.36 -133.36 -273.00 6.2315779.24 15779.24 0.00 0.00 0.0018218.24 18218.24


126 1 -0.02 -0.49 -150.19 -256.25 10.6614918.57 14918.57 0.00 0.00 0.0017154.23 17154.23


138 1 0.12 -0.39 -176.20 -230.35 15.4014020.85 14020.85 0.00 0.00 0.0015628.28 15628.28


STAAD VER. PROB. 20 -- PAGE NO. 7* THERMAL LOADING ON A SIMPLY SUPPORTED RECTELEMENT STRESSES FORCE,LENGTH UNITS= POUN INCH----------------



150 1 0.38 0.06 -211.95 -194.66 20.3613792.44 13792.44 0.00 0.00 0.0015028.62 15028.62


162 1 0.67 1.03 -257.59 -148.94 25.1915213.03 15213.03 0.00 0.00 0.0017542.96 17542.96


174 1 0.74 2.75 -312.19 -93.95 29.1918798.88 18798.88 0.00 0.00 0.0021068.45 21068.45

TOP : SMAX= -6007.83 SMIN= -21068.45 TMAX= 7530.31 ANGLE= 82.5BOTT: SMAX= 21068.45 SMIN= 6007.83 TMAX= 7530.31 ANGLE= -7.5

186 1 0.34 4.36 -373.27 -32.17 31.5124160.11 24160.11 0.00 0.00 0.0025076.87 25076.87

TOP : SMAX= -1951.93 SMIN= -25076.87 TMAX= 11562.47 ANGLE= 84.8BOTT: SMAX= 25076.87 SMIN= 1951.93 TMAX= 11562.47 ANGLE= -5.2

**** MAXIMUM STRESSES AMONG SELECTED PLATES AND CASES ****MAXIMUM MINIMUM MAXIMUM MAXIMUM MAXIMUMPRINCIPAL PRINCIPAL SHEAR VONMISES TRESCASTRESS STRESS STRESS STRESS STRESS

2.593996E+04 -2.593996E+04 1.243272E+04 2.541974E+04 2.593996E+04PLATE NO. 97 97 97 97 97CASE NO. 1 1 1 1 1********************END OF ELEMENT FORCES********************27. FINISTAAD VER. PROB. 20 -- PAGE NO. 8* THERMAL LOADING ON A SIMPLY SUPPORTED RECT



STAAD VER. PROB. 20 -- PAGE NO. 9* THERMAL LOADING ON A SIMPLY SUPPORTED RECT



STAAD VER. PROB. 20 -- PAGE NO. 10* THERMAL LOADING ON A SIMPLY SUPPORTED RECT

Information about the key files in the current distributionModification Date CRC Size (Bytes) File Name-----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe02/22/2011 0xc181 08667136 SProStaadStl.exe09/19/2003 0x2fc0 00081970 CMesh.dll02/17/2011 0xa7c1 04276294 dbsectioninterface.dll02/22/2011 0x12c0 00294912 EC3Annex.dll02/22/2011 0x2900 00376832 EuroCode3.dll12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll01/24/2001 0x9b40 00073728 LoadGen.dll11/19/2010 0xeb80 00011264 MathExtensions.dll09/25/2003 0x6340 00704512 MeshEngine.dll02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll09/22/2003 0xce00 00069632 QuadPlateEngine.dll12/02/2010 0x5040 00073728 SteelCollection.dll02/22/2011 0xca81 00024064 SteelDesign.dll10/08/2010 0xa940 00072192 SteelSections.dll05/29/2008 0x77c1 00106572 SurfMeshEngine.dll10/08/2010 0x4680 00010752 UnitConversions.dll02/08/2011 0xfc00 00974848 AISCSections.mdb06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb01/05/2005 0xcac1 03651584 aitctimbersections.mdb05/01/2008 0xb001 00552960 aluminumsections.mdb01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb10/02/2008 0x40 00520192 AustralianSections.mdb06/11/2010 0xa101 00585728 BritishSections.mdb09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb06/28/2005 0x8201 00327680 butlercoldformedsections.mdb02/25/2008 0x2e01 00329728 CanadianSections.mdb09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb05/31/2005 0x9e81 00450560 canadiantimbersections.mdb02/10/2010 0x94c1 00483328 ChineseSections.mdb01/05/2005 0xd6c0 00600064 dutchsections.mdb10/07/2010 0xd2c0 03596290 EuropeanSections.mdb01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb01/05/2005 0xd301 00202752 frenchsections.mdb01/05/2005 0x11c1 00233472 germansections.mdb10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb

140 — STAAD.Pro


12/08/2009 0xec1 00942080 IndianSections.mdb01/05/2005 0xd540 00180224 iscoldformedsections.mdb02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb03/23/2006 0xa080 00200704 japanesesections.mdb02/04/2011 0x3300 00495616 JindalSections.mdb11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb08/24/2007 0x3ec0 00454656 Koreansections.mdb04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb02/07/2005 0x9a00 00243712 mexicansteeltables.mdb04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb11/20/2009 0xf700 00428034 RussianSections.mdb05/12/2009 0xe001 00237570 SouthAfricanSections.mdb01/06/2005 0x9341 00194560 spanishsections.mdb11/20/2009 0x5100 00368640 STO_ASChMSections.mdb04/19/2007 0x7480 00223232 uscoldformedsections.mdb10/31/2007 0x3700 00133120 VenezuelanSections.mdb-----------------------------------------------------------------------------------------



142— STAAD.Pro


NOTES

21 Deflection Calculation Through PushoverAnalysis


ReferenceHand calculation.

ProblemFigure 21-1: Cantilever member model

A transverse load P is applied to a cantilever member and increased until the member fails.

Geometry & Loading

Member length = 24 inch

Member Properties

Section = Wide flange W16X77

Material = Steel

Expected yield strength = 36 ksi


Figure 21-2: Plastic Rotation (in radians) vs. Moment (in in-kips) plot for moment hinge

Comparison

Results from STAAD.Pro

The analysis results are saved at an interval of 0.1 inch deflection of the cantilever tip.

Figure 21-3: Capacity curve (Displacement at Control Joint, inches vs. Base Shear, kips) as calculated bySTAAD.Pro

144 — STAAD.Pro

21 Deflection Calculation Through Pushover Analysis

Load Step Displacement in Base Shear kip

1 0 0.153

2 0.001 1.153

3 0.078 57.837

4 0.136 61.953

5 0.237 63.859

6 0.338 65.765

7 0.439 67.671

8 0.54 69.578

9 0.641 71.484

10 0.742 73.39

11 0.843 75.296

12 0.945 77.202

13 1.045 79.096

14 1.057 79.32

15 1.057 21.462

Table 21-1: Tabular form of the different points in Capacitycurve as reported by STAAD.Pro

Results from hand calculation

At Load Step 3

Equation of elastic deflection at cantilever tip

δz = PL3/3EI +PL/GAv

P = 57.837 kip, l = 24 in, E = 29000 ksi, I = 138.0 in4, G = 11154 ksi, Av = 10.4323 in2

Thus elastic deformation

δz elastic = [57.837 x 243 / (3 x 29000 x 138)] + [57.837 x 24 / (11154 x 10.4323)] = 0.066 +

0.012 = 0.078 inch

At Load Step 14

Equation of elastic deflection at cantilever tip

δz = PL3/3EI +PL/GAv

P = 79.32 kip, l = 24 inch, E = 29000 ksi, I = 138.0 inP4, G = 11154 ksi, Av = 10.4323 in2



Thus elastic deformation at cantilever tip

δz elastic= [79.32 x 243 / (3 x 29000 x 138)] + [79.32 x 24 / (11154 x 10.4323)] = 0.091 +

0.016 = 0.107 inch

Plastic rotation = 0.04 radian.

Since STAAD.Pro assumes small displacements (sinθ = θ), plastic deformation at cantilever tip

δz plastic = l x θ = 24 x 0.04 = 0.96 inch

Total deflection = δz elastic + δz plastic = 0.107 + 0.96 = 1.067 inch

Comparison

LoadStep

Force P (freeend) kips

Deflection (free end) inPercentDifferenceSTAAD.Pro

Advanced SolverHand

Calculation

3 57.837 0.078 0.078 0%

14 79.32 1.057 1.067 0.94%

Table 21-2: Comparison of results for verification problem no. 21

Note: The deflection results from STAAD shown in the above table were obtained in the post-processing mode – Pushover-Node Results page.

Pushover analysis can be done through the Advanced Analysis Engine only.

Input File

STAAD SPACE

START JOB INFORMATION

ENGINEER DATE 20-JUL-07

END JOB INFORMATION

INPUT WIDTH 79

UNIT INCHES KIP

JOINT COORDINATES

1 0 0 0; 2 0 24 0;

MEMBER INCIDENCES

1 1 2;

DEFINE MATERIAL START

ISOTROPIC STEEL

E 29000

POISSON 0.3

146— STAAD.Pro


DENSITY 0.000283

ALPHA 6.5E-006

DAMP 0.03

END DEFINE MATERIAL

MEMBER PROPERTY AMERICAN

1 TABLE ST W16X77

CONSTANTS

MATERIAL STEEL ALL

SUPPORTS

1 FIXED

DEFINE PUSHOVER DATA

FRAME 2

FYE 36.000000 ALL

HINGE PROPERTY MOMENT

TYPE 1

A 0 0 B 1 1 C 11.0 1.30 D 11.0 0.32 E 15.0 0.32 YM 1480 YR 0.004

IO 2.0 LS 7.0 CP 10.5

HINGE TYPE 1 MEMBER 1

GNONL 1

DISP Z 2.0 JOINT 2

LOADING PATTERN 1

LDSTEP 1

SPECTRUM PARAMETERS

DAMPING 2.0000

SC 4

SS 1.1

S1 1.6

SAVE LOADSTEP RESULT DISP 0.1

END PUSHOVER DATA

LOAD 1 LOADTYPE GRAVITY

SELFWEIGHT Z 1

LOAD 2 LOADTYPE PUSH

JOINT LOAD

2 FZ 1

PERFORM PUSHOVER ANALYSIS



FINISH

STAAD Output

148— STAAD.Pro


***************************************************** ** STAAD.Pro V8i SELECTseries2 ** Version 20.07.07.32 ** Proprietary Program of ** Bentley Systems, Inc. ** Date= MAR 9, 2011 ** Time= 10:21:38 ** ** USER ID: Bentley Systems, Inc. *****************************************************

1. STAAD SPACEINPUT FILE: ver21.STD

2. START JOB INFORMATION3. ENGINEER DATE 20-JUL-074. END JOB INFORMATION5. INPUT WIDTH 796. UNIT INCHES KIP7. JOINT COORDINATES8. 1 0 0 0; 2 0 24 09. MEMBER INCIDENCES10. 1 1 211. DEFINE MATERIAL START12. ISOTROPIC STEEL13. E 2900014. POISSON 0.315. DENSITY 0.00028316. ALPHA 6.5E-00617. DAMP 0.0318. END DEFINE MATERIAL19. MEMBER PROPERTY AMERICAN20. 1 TABLE ST W16X7721. CONSTANTS22. MATERIAL STEEL ALL23. SUPPORTS24. 1 FIXED25. DEFINE PUSHOVER DATA26. FRAME 227. FYE 36.000000 ALL28. HINGE PROPERTY MOMENT29. TYPE 130. A 0 0 B 1 1 C 11.0 1.30 D 11.0 0.32 E 15.0 0.32 YM 1480 YR 0.00431. IO 2.0 LS 7.0 CP 10.532. HINGE TYPE 1 MEMBER 133. GNONL 134. DISP Z 2.0 JOINT 235. LOADING PATTERN 136. LDSTEP 137. SPECTRUM PARAMETERS38. DAMPING 2.000039. SC 440. SS 1.1STAAD SPACE -- PAGE NO. 241. S1 1.642. SAVE LOADSTEP RESULT DISP 0.143. END PUSHOVER DATA44. LOAD 1 LOADTYPE GRAVITY45. SELFWEIGHT Z 146. LOAD 2 LOADTYPE PUSH47. JOINT LOAD48. 2 FZ 149. PERFORM PUSHOVER ANALYSIS


NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 2/ 1/ 1SOLVER USED IS THE IN-CORE ADVANCED SOLVER



TOTAL PRIMARY LOAD CASES = 2, TOTAL DEGREES OF FREEDOM = 6NUMBER OF MODES REQUESTED = 1NUMBER OF EXISTING MASSES IN THE MODEL = 3NUMBER OF MODES THAT WILL BE USED = 1

STAAD SPACE -- PAGE NO. 3CALCULATED FREQUENCIES FOR LOAD CASE 3

MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC)1 306.356 0.00326

MODAL WEIGHT (MODAL MASS TIMES g) IN KIP GENERALIZEDMODE X Y Z WEIGHT

1 4.391674E-64 2.349593E-61 7.674960E-02 7.674960E-02MASS PARTICIPATION FACTORS IN PERCENT--------------------------------------

MODE X Y Z SUMM-X SUMM-Y SUMM-Z1 0.00 0.00100.00 0.000 0.000 100.000

***WARNING : COLUMN NO. 1 HAS FAILED IN DEFORMATION-CONTROLLED ACTION.*** WARNING : STRUCTURE HAS REACHED AN UNSTABLE STATE WHERE

A VERY SMALL INCREASE IN PUSH LOAD IS CAUSING LARGE DISPLACEMENT.50. FINISHSTAAD SPACE -- PAGE NO. 4

*********** END OF THE STAAD.Pro RUN *************** DATE= MAR 9,2011 TIME= 10:21:44 ****


STAAD SPACE -- PAGE NO. 5Information about the key files in the current distributionModification Date CRC Size (Bytes) File Name-----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe02/22/2011 0xc181 08667136 SProStaadStl.exe09/19/2003 0x2fc0 00081970 CMesh.dll02/17/2011 0xa7c1 04276294 dbsectioninterface.dll02/22/2011 0x12c0 00294912 EC3Annex.dll02/22/2011 0x2900 00376832 EuroCode3.dll12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll01/24/2001 0x9b40 00073728 LoadGen.dll11/19/2010 0xeb80 00011264 MathExtensions.dll09/25/2003 0x6340 00704512 MeshEngine.dll02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll09/22/2003 0xce00 00069632 QuadPlateEngine.dll12/02/2010 0x5040 00073728 SteelCollection.dll02/22/2011 0xca81 00024064 SteelDesign.dll10/08/2010 0xa940 00072192 SteelSections.dll05/29/2008 0x77c1 00106572 SurfMeshEngine.dll10/08/2010 0x4680 00010752 UnitConversions.dll02/08/2011 0xfc00 00974848 AISCSections.mdb06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb01/05/2005 0xcac1 03651584 aitctimbersections.mdb

150 — STAAD.Pro


05/01/2008 0xb001 00552960 aluminumsections.mdb01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb10/02/2008 0x40 00520192 AustralianSections.mdb06/11/2010 0xa101 00585728 BritishSections.mdb09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb06/28/2005 0x8201 00327680 butlercoldformedsections.mdb02/25/2008 0x2e01 00329728 CanadianSections.mdb09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb05/31/2005 0x9e81 00450560 canadiantimbersections.mdb02/10/2010 0x94c1 00483328 ChineseSections.mdb01/05/2005 0xd6c0 00600064 dutchsections.mdb10/07/2010 0xd2c0 03596290 EuropeanSections.mdb01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb01/05/2005 0xd301 00202752 frenchsections.mdb01/05/2005 0x11c1 00233472 germansections.mdb10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb12/08/2009 0xec1 00942080 IndianSections.mdb01/05/2005 0xd540 00180224 iscoldformedsections.mdb02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb03/23/2006 0xa080 00200704 japanesesections.mdb02/04/2011 0x3300 00495616 JindalSections.mdb11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb08/24/2007 0x3ec0 00454656 Koreansections.mdb04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb02/07/2005 0x9a00 00243712 mexicansteeltables.mdb04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb11/20/2009 0xf700 00428034 RussianSections.mdb05/12/2009 0xe001 00237570 SouthAfricanSections.mdb01/06/2005 0x9341 00194560 spanishsections.mdb11/20/2009 0x5100 00368640 STO_ASChMSections.mdb04/19/2007 0x7480 00223232 uscoldformedsections.mdb10/31/2007 0x3700 00133120 VenezuelanSections.mdb-----------------------------------------------------------------------------------------



152— STAAD.Pro


NOTES

22 Fixed – Fixed Beam Excited by HarmonicDistributed Load

ObjectiveTo calculate the deflections at two points along the beam at steady-state condition.

Reference1. Blevins, R. D., “Formulas for natural Frequency and Mode Shape,” Van Nostrand Reinhold,1979, pp 108, 455-486.

2. Warburton, G. B., “The Dynamical Behavior of Structures,” Pergamon Press, 1964, pp. 10-15,85, 86.

ProblemDetermine the steady-state displacements of the quarter and mid-span points of a fixed-fixed beamsubjected to a parabolically varying distributed load operating at a 7.5 Hz frequency.

Figure 22-1: Beam with harmonic distributed load


Figure 22-2: Model: divide span [email protected]”

GivenE = 10.0x106 psi

L = 200 inches

I = 2/3 in4

A = 2 in2

Po = 0.1 lbf/in3

g = 386.4 in/sec2

The DYNRE2 run utilizes all 19 modes calculated by STAAD (Steady State analysis) for which avalue of 1.0(10)-10 times critical damping is assigned. A single forcing frequency equal to 7.5 Hz isspecified for the distributed load. This load is distributed to the nodes by calculating the totalintegrated load for each beam and lumping one-half of this force to the respective i and j nodes.

∫ ∫F F d x xl x d x( )= = = −i j x

x P x

x

x

l

( )

2

1

2

4 2

i

j

i

j2

∫ ∫F F d x xl x d x( )= = = −i j x

x P x

x

x

l

( )

2

1

2

4 2

i

j

i

j2

Theoretical Solution

The theoretical solution for this example is taken from:

1. Blevins, R. D., “Formulas for natural Frequency and Mode Shape,” Van Nostrand Reinhold,1979, pp 108, 455-486.

2. Warburton, G. B., “The Dynamical Behavior of Structures,” Pergamon Press, 1964, pp. 10-15,85, 86.

The natural frequencies of the system are calculated using the equations from reference 1 page 108and reference 2 page 85.

f =i

λ

π �

EI

m2

1

2

2

154 — STAAD.Pro

22 Fixed – Fixed Beam Excited by Harmonic Distributed Load

Where:

m = ρA/g

f =i

λ

π

( )2 (200)

1.0(10) 2 / 3

0.10(2.0 / 386.4)i2

2

6

fi = 4.5156271*10-1λi

2

λisatisfies the characteristic equation:

cosλ coshλ - 1 = 0

i λi

ωi

fi

1 4.730041 63.47865 10.10294

2 7.853205 174.9814 27.84915

3 10.99561 343.0334 54.59546

4 14.13717 567.0517 90.24907

5 17.27876 847.0773 134.8165

6 20.42035 1183.108 188.2975

7 23.56194 1575.144 250.6919

8 26.70354 2023.185 321.9998

Table 22-1: Calculated natural frequency for each mode

The mode shapes are:

σ ( )= cosh − cos − sinh − sini

λ x

�

λ x

�i

λ x

�

λ x

�

i i i iϕ

Where:

σ =iλ λ

λ λ

cosh − cos

sinh − sin

i i

i i

The response of mode i to a harmonic force:

η = −∫

∫i

x P x d x

ω x md x

ω t ψ

( )

( )( ) ( )

( ){ }

sin −

1 − +

l i

i i

i

ω

ωi

cω

k

2 22

2

22

ϕ

ϕ

Where ψi is the response phase lag relative to the applied force and c is the damping.

Since c = 0.0, ψi = 0.0

Upon substitution and rearranging terms:

η ω t= sin∫

∫i

xl x x d x

ω ω x d x( ){ }

−

−

l

P o

li

ρA

g i l i

42

2

2 2 2

ϕ

ϕ



From reference 1, page 466, case c and page 467, case 29:

∫ ∫x x d x x x d x i i σ β l σ β l( ) ( )− = 1 + (− ) − (− ) − 2 −P

l l i

P

l l i

P

β l

i ii i

l P

β li i

4 4 2 8 8(− )o o

i

i

i

2 202

02

ϕ ϕ

Since the load is symmetric, this expression is zero for I = 2, 4, 6 …;

Therefore, i = 1,3,5……, and: (-1)i = -1

And from the reference, βi = λi/l

So:

∫ x P x d x( ) ( ) =l i

P l

λ

16o

i

2ϕ

From Reference 1, page 457 case 5:

∫ x d x{ ( )} = 1l i

2ϕ

Therefore:

ω = 7.5(2π) = 47.1239 radians/sec

η ω t= sin = =i

P

mλ ω ω

ω t

λ ω

ω t

λ ω( ) ( )16

−

16(− 1.0)sin

− 2, 220.661

30, 912 sin

− 2, 220.661

o

i ii i

i i

2 2 2 0.10(2)

386.4

2 22 2

⋅

i λi

ωi

ηi(t) σ

iφ(1/4) φ(1/2)

1 4.730041 63.47865 ω t− 7.63815(10) sin− 1 0.9825022 0.8631319 1.5881463

3 10.99561 343.0334 ω t− 2.21457(10) sin− 3 0.9999664 1.3708047 -1.4059984

5 17.27876 847.0773 ω t− 1.44744(10) sin− 4 0.9999999 -0.5278897

1.4145675

7 23.56194 1575.144 ω t− 2.24623(10) sin− 5 1.0000000 -1.3037973

-1.4141982

Table 22-2: Mode shapes

y x t η t x( ) ( ) ( ), = ∑ i i i= 1, 3, 5, 7 ϕ

i φ(¼)ηi(t) φ(1/2)η

i(t)

1 -0.6592727 -1.2130493

3 -0.0030357 0.0031137

Table 22-3: Steady state displacements for 1/4 and 1/2 points (nodes 6 and 11,respectively)

156— STAAD.Pro


i φ(¼)ηi(t) φ(1/2)η

i(t)

5 0.0000764 -0.0002048

7 0.0000293 -0.0000318

Summation -0.6622028 -1.2101086

Comparison

Location TheorySTAAD

Advanced Solver

Node 6 (X = 50 inches) 0.66220 0.65964

Node 11 (X = 100 inches) 1.21011 1.20545

Table 22-4: Comparison of steady-state displacements of the quarter (Node 6)and mid-span points (Node 11) for verification problem no. 22

Input File

STAAD SPACE

START JOB INFORMATION

ENGINEER DATE 29-MAR-06

END JOB INFORMATION

* FIXED BEAM SUBJECTED TO A HARMONIC LOAD WITH A PARABOLIC DISTRIBUTION X

* NUMBER OF NODES 21 X

* HIGH NODE NUMBER 21 X

* NODES FULLY RESTRAINED 2 X

* NUMBER OF BEAM ELEMENTS 20 X

* NUMBER OF EIGENVECTORS 19

SET SHEAR

UNIT INCHES POUND

JOINT COORDINATES

1 0 0 0; 2 10 0 0; 3 20 0 0; 4 30 0 0; 5 40 0 0; 6 50 0 0; 7 60 0 0;

8 70 0 0; 9 80 0 0; 10 90 0 0; 11 100 0 0; 12 110 0 0; 13 120 0 0;

14 130 0 0; 15 140 0 0; 16 150 0 0; 17 160 0 0; 18 170 0 0; 19 180 0 0;

20 190 0 0; 21 200 0 0;

MEMBER INCIDENCES

1 1 2; 2 2 3; 3 3 4; 4 4 5; 5 5 6; 6 6 7; 7 7 8; 8 8 9; 9 9 10;



10 10 11; 11 11 12; 12 12 13; 13 13 14; 14 14 15; 15 15 16; 16 16 17;

17 17 18; 18 18 19; 19 19 20; 20 20 21;

MEMBER PROPERTY AMERICAN

1 TO 20 PRIS AX 2 AY 0 AZ 0 IX 0.001 IY 0.666667 IZ 0.166667

SUPPORTS

2 TO 20 FIXED BUT FY MZ

1 21 FIXED

DEFINE MATERIAL START

ISOTROPIC MATERIAL1

E 1E+007

POISSON 0.3

DENSITY 0.0999194

END DEFINE MATERIAL

CONSTANTS

BETA 90 ALL

MATERIAL MATERIAL1 MEMB 1 TO 20


CUT OFF FREQUENCY 500

LOAD 1

SELFWEIGHT X 1

SELFWEIGHT Y 1

SELFWEIGHT Z 1

MODAL CALCULATION REQUESTED

PERFORM STEADY STATE ANALYSIS

BEGIN STEADY FORCE

STEADY FORCE FREQ 7.5 DAMP 1E-010

JOINT LOAD

2 FY 1.8666

3 FY 3.5666

4 FY 5.0666

5 FY 6.3666

6 FY 7.4666

7 FY 8.3666

8 FY 9.0666

9 FY 9.5666

158— STAAD.Pro


10 FY 9.8666

11 FY 9.9666

12 FY 9.8666

13 FY 9.5666

14 FY 9.0666

15 FY 8.3666

16 FY 7.4666

17 FY 6.3666

18 FY 5.0666

19 FY 3.5666

20 FY 1.8666

END

PRINT JOINT DISPLACEMENTS LIST 6 11

FINISH

STAAD Output



***************************************************** ** STAAD.Pro V8i SELECTseries2 ** Version 20.07.07.32 ** Proprietary Program of ** Bentley Systems, Inc. ** Date= MAR 9, 2011 ** Time= 10:21:53 ** ** USER ID: Bentley Systems, Inc. *****************************************************

1. STAAD SPACEINPUT FILE: ver22.STD

2. START JOB INFORMATION3. ENGINEER DATE 29-MAR-064. END JOB INFORMATION5. * FIXED BEAM SUBJECTED TO A HARMONIC LOAD WITH A PARABOLIC DISTRIBUTION X6. * NUMBER OF NODES 21 X7. * HIGH NODE NUMBER 21 X8. * NODES FULLY RESTRAINED 2 X9. * NUMBER OF BEAM ELEMENTS 20 X10. * NUMBER OF EIGENVECTORS 1911. SET SHEAR12. UNIT INCHES POUND13. JOINT COORDINATES14. 1 0 0 0; 2 10 0 0; 3 20 0 0; 4 30 0 0; 5 40 0 0; 6 50 0 0; 7 60 0 015. 8 70 0 0; 9 80 0 0; 10 90 0 0; 11 100 0 0; 12 110 0 0; 13 120 0 016. 14 130 0 0; 15 140 0 0; 16 150 0 0; 17 160 0 0; 18 170 0 0; 19 180 0 017. 20 190 0 0; 21 200 0 018. MEMBER INCIDENCES19. 1 1 2; 2 2 3; 3 3 4; 4 4 5; 5 5 6; 6 6 7; 7 7 8; 8 8 9; 9 9 1020. 10 10 11; 11 11 12; 12 12 13; 13 13 14; 14 14 15; 15 15 16; 16 16 1721. 17 17 18; 18 18 19; 19 19 20; 20 20 2122. MEMBER PROPERTY AMERICAN23. 1 TO 20 PRIS AX 2 AY 0 AZ 0 IX 0.001 IY 0.666667 IZ 0.16666724. SUPPORTS25. 2 TO 20 FIXED BUT FY MZ26. 1 21 FIXED27. DEFINE MATERIAL START28. ISOTROPIC MATERIAL129. E 1E+00730. POISSON 0.331. DENSITY 0.099919432. END DEFINE MATERIAL33. CONSTANTS34. BETA 90 ALL35. MATERIAL MATERIAL1 MEMB 1 TO 2036. CUT OFF MODE SHAPE 737. CUT OFF FREQUENCY 50038. LOAD 139. SELFWEIGHT X 140. SELFWEIGHT Y 1STAAD SPACE -- PAGE NO. 241. SELFWEIGHT Z 142. MODAL CALCULATION REQUESTED43. PERFORM STEADY STATE ANALYSIS


NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 21/ 20/ 21SOLVER USED IS THE IN-CORE ADVANCED SOLVER

TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 38NUMBER OF MODES REQUESTED = 7NUMBER OF EXISTING MASSES IN THE MODEL = 19NUMBER OF MODES THAT WILL BE USED = 7

STAAD SPACE -- PAGE NO. 3CALCULATED FREQUENCIES FOR LOAD CASE 1

160 — STAAD.Pro


MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC)1 10.103 0.098982 27.849 0.035913 54.591 0.018324 90.230 0.011085 134.747 0.007426 188.093 0.005327 250.166 0.00400


1 0.000000E+00 2.759074E+01 0.000000E+00 1.584634E+012 0.000000E+00 1.177398E-26 0.000000E+00 1.763389E+013 0.000000E+00 5.287477E+00 0.000000E+00 1.757978E+014 0.000000E+00 2.921260E-28 0.000000E+00 1.788088E+015 0.000000E+00 2.138447E+00 0.000000E+00 1.901368E+016 0.000000E+00 5.413313E-30 0.000000E+00 1.837854E+017 0.000000E+00 1.145139E+00 0.000000E+00 1.756698E+01


MODE X Y Z SUMM-X SUMM-Y SUMM-Z1 0.00 72.67 0.00 0.000 72.666 0.0002 0.00 0.00 0.00 0.000 72.666 0.0003 0.00 13.93 0.00 0.000 86.591 0.0004 0.00 0.00 0.00 0.000 86.591 0.0005 0.00 5.63 0.00 0.000 92.223 0.0006 0.00 0.00 0.00 0.000 92.223 0.0007 0.00 3.02 0.00 0.000 95.239 0.000

44. BEGIN STEADY FORCE45. STEADY FORCE FREQ 7.5 DAMP 1E-01046. JOINT LOADSTAAD SPACE -- PAGE NO. 447. 2 FY 1.866648. 3 FY 3.566649. 4 FY 5.066650. 5 FY 6.366651. 6 FY 7.466652. 7 FY 8.366653. 8 FY 9.066654. 9 FY 9.566655. 10 FY 9.866656. 11 FY 9.966657. 12 FY 9.866658. 13 FY 9.566659. 14 FY 9.066660. 15 FY 8.366661. 16 FY 7.466662. 17 FY 6.366663. 18 FY 5.066664. 19 FY 3.566665. 20 FY 1.866666. ENDSTAAD SPACE -- PAGE NO. 5

7 MODES (EIGENVECTORS) HAVE BEEN SELECTED.MODE NATURAL FREQUENCY GENERALIZED WEIGHT DAMPING DAMPED FREQUENCYNO. (HZ) (RAD/SEC) (WEIGHT) (MASS) COEFFICIENT (HZ)

1 1.010292E+01 6.347852E+01 1.584634E+01 4.104327E-02 1.000000E-10 1.010292E+012 2.784865E+01 1.749782E+02 1.763389E+01 4.567317E-02 1.000000E-10 2.784865E+013 5.459144E+01 3.430081E+02 1.757978E+01 4.553302E-02 1.000000E-10 5.459144E+014 9.022966E+01 5.669297E+02 1.788088E+01 4.631289E-02 1.000000E-10 9.022966E+015 1.347470E+02 8.466406E+02 1.901368E+01 4.924693E-02 1.000000E-10 1.347470E+026 1.880927E+02 1.181821E+03 1.837854E+01 4.760188E-02 1.000000E-10 1.880927E+027 2.501660E+02 1.571840E+03 1.756698E+01 4.549988E-02 1.000000E-10 2.501660E+02

PARTICIPATION FACTORS FOR EACH MODEMODE NO. X Y Z MX MY MZ

1 0.000000E+00 0.218577E+04 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+002 0.000000E+00 0.427319E-10 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00



3 0.000000E+00 0.382113E+03 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+004 0.000000E+00 0.414481E-11 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+005 0.000000E+00 0.148269E+03 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+006 0.000000E+00 0.626353E-12 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+007 0.000000E+00 0.829074E+02 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

67. PRINT JOINT DISPLACEMENTS LIST 6 11STAAD SPACE -- PAGE NO. 6JOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = SPACE------------------

JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN6 1 0.00000 0.65963 0.00000 0.00000 0.00000 0.0183111 1 0.00000 1.20545 0.00000 0.00000 0.00000 0.00000


*********** END OF THE STAAD.Pro RUN *************** DATE= MAR 9,2011 TIME= 10:21:54 ****

STAAD SPACE -- PAGE NO. 7************************************************************* For questions on STAAD.Pro, please contact ** Bentley Systems or Partner offices ** ** Telephone Web / Email ** USA +1 (714) 974-2500 ** UK +44 (0) 808 101 9246 ** SINGAPORE +65 6225-6158 ** FRANCE +33 (0) 1 55238400 ** GERMANY +49 0931 40468 ** INDIA +91 (033) 4006-2021 ** JAPAN +81 (03)5952-6500 http://www.ctc-g.co.jp ** CHINA +86 21 6288 4040 ** THAILAND +66 (0)2645-1018/19 [email protected]** ** Worldwide http://selectservices.bentley.com/en-US/ ** *************************************************************

STAAD SPACE -- PAGE NO. 8Information about the key files in the current distributionModification Date CRC Size (Bytes) File Name-----------------------------------------------------------------------------------------03/02/2011 0xe4c0 18427904 SProStaad.exe02/22/2011 0xc181 08667136 SProStaadStl.exe09/19/2003 0x2fc0 00081970 CMesh.dll02/17/2011 0xa7c1 04276294 dbsectioninterface.dll02/22/2011 0x12c0 00294912 EC3Annex.dll02/22/2011 0x2900 00376832 EuroCode3.dll12/02/2010 0xa6c1 00086016 IS800SteelDesign.dll01/24/2001 0x9b40 00073728 LoadGen.dll11/19/2010 0xeb80 00011264 MathExtensions.dll09/25/2003 0x6340 00704512 MeshEngine.dll02/22/2011 0x2480 00058368 NORSOKSteelDesign.dll09/22/2003 0xce00 00069632 QuadPlateEngine.dll12/02/2010 0x5040 00073728 SteelCollection.dll02/22/2011 0xca81 00024064 SteelDesign.dll10/08/2010 0xa940 00072192 SteelSections.dll05/29/2008 0x77c1 00106572 SurfMeshEngine.dll10/08/2010 0x4680 00010752 UnitConversions.dll02/08/2011 0xfc00 00974848 AISCSections.mdb06/13/2006 0xd4c1 01204224 AISCSectionsRCeco.mdb06/05/2007 0xbc00 00331776 aiscsections_all_editions.mdb01/05/2005 0x4b81 01810432 aiscsteeljoists.mdb01/05/2005 0xcac1 03651584 aitctimbersections.mdb05/01/2008 0xb001 00552960 aluminumsections.mdb01/14/2010 0x40 01019904 AustralianColdFormedSections.mdb10/02/2008 0x40 00520192 AustralianSections.mdb06/11/2010 0xa101 00585728 BritishSections.mdb09/12/2006 0xf4c0 00466944 bscoldformedsections.mdb

162— STAAD.Pro


06/28/2005 0x8201 00327680 butlercoldformedsections.mdb02/25/2008 0x2e01 00329728 CanadianSections.mdb09/26/2006 0x5ec1 00280576 CanadianSections_old.mdb05/31/2005 0x9e81 00450560 canadiantimbersections.mdb02/10/2010 0x94c1 00483328 ChineseSections.mdb01/05/2005 0xd6c0 00600064 dutchsections.mdb10/07/2010 0xd2c0 03596290 EuropeanSections.mdb01/25/2011 0xc901 00692224 EuropeanSectionsLegacy.mdb01/05/2005 0xd301 00202752 frenchsections.mdb01/05/2005 0x11c1 00233472 germansections.mdb10/06/2010 0x1bc1 00393216 GOSTColdFormedSections.mdb12/08/2009 0x6ac0 00569344 IndianLegacySections.mdb12/08/2009 0xec1 00942080 IndianSections.mdb01/05/2005 0xd540 00180224 iscoldformedsections.mdb02/21/2008 0xc380 00327680 JapaneseColdFormedSections.mdb03/23/2006 0xa080 00200704 japanesesections.mdb02/04/2011 0x3300 00495616 JindalSections.mdb11/09/2005 0x9081 00376832 Kingspancoldformedsections.mdb08/24/2007 0x3ec0 00454656 Koreansections.mdb04/24/2007 0x99c0 00114688 lysaghtcoldformedsections.mdb02/07/2005 0x9a00 00243712 mexicansteeltables.mdb04/19/2007 0x9ec1 00421888 RCecoColdFormedSections.mdb11/20/2009 0xf700 00428034 RussianSections.mdb05/12/2009 0xe001 00237570 SouthAfricanSections.mdb01/06/2005 0x9341 00194560 spanishsections.mdb11/20/2009 0x5100 00368640 STO_ASChMSections.mdb04/19/2007 0x7480 00223232 uscoldformedsections.mdb10/31/2007 0x3700 00133120 VenezuelanSections.mdb-----------------------------------------------------------------------------------------



164 — STAAD.Pro


NOTES

List of Tables and FiguresTables

Table 1-1: Comparison of Support Reaction, in kips, for verification problem no. 1 1

Table 2-1: Comparison of period, in sec., for verification problem no. 2 5

Table 3-1: Comparison of max. defl. and max. moment for verification problem no. 3 10

Table 4-1: Comparison of reaction, in kips, for verification problem no. 4 16

Table 5-1: Comparison of stress (σ), psi, and Deflection (δ), in. for verification model no. 5 22

Table 6-1: Comparison of moment, in kip-ft, for verification problem no. 6 28

Table 7-1: Comparison of deflection (δ) for verification problem no. 7 34

Table 8-1: Comparison of max. moment, in kip-ft, for verification model no. 8 40

Table 9-1: Comparison of max. moment, in kip-ft, for verification problem no. 9 46

Table 10-1: Comparison of max. Force, F, and max. Moments,M, for verification problemno. 10

52

Table 11-1: Comparison of stress (σ) for verification model #11 58

Table 12-1: Comparison of stress (σ) and Deflection (δ) for verification problem 12 64

Table 13-1: Comparison of governing ratios for the member checks in verification problemno. 13

70

Table 14-1: Comparison of concrete designs for verifcation problem no. 14 82

Table 15-1: Comparison of frequency values for verification problem no. 15 89

Table 16-1: Values of λ2ij 97

Table 16-2: Comparison of frequency values, Hz, for verification problem no. 16 97

Table 17-1: Values of λ2ij 105

Table 17-2: Comparison of frequency values, Hz, for verificatoin problem no. 17 105

Table 18-1: Comparison of natural frequency values (cycles per second) for verificationproblem no. 18

112

Table 19-1: Comparison of max. moment in beam 5 for verification problem no. 19 123

Table 20-1: Comparison of deflections along X = 6, in inches, for verification problem no.20

131

Table 20-2: Comparison of deflections along Y = 1, in inches, for verification problem no.20

132

Table 20-3: Comparison of bending moments along Y = 0.5, in in-lbs/in, for verificationproblem no. 20

133

Table 20-4: Comparison of bending moments along X = 5.5, in in-lbs/in, for verificationproblem no. 20

134


Table 21-1: Tabular form of the different points in Capacity curve as reported bySTAAD.Pro

145

Table 21-2: Comparison of results for verification problem no. 21 146

Table 22-1: Calculated natural frequency for each mode 155

Table 22-2: Mode shapes 156

Table 22-3: Steady state displacements for 1/4 and 1/2 points (nodes 6 and 11, respectively)156

Table 22-4: Comparison of steady-state displacements of the quarter (Node 6) and mid-span points (Node 11) for verification problem no. 22

157

Figures

Figure 1-1: Plane truss 1

Figure 2-1: Beam supported on springs 5

Figure 3-1: Finite element mesh of cantilevered plate. 9

Figure 4-1: Cantilever model 15

Figure 5-1: Locomotive axle model 21

Figure 6-1: 1x1 bay plane frame 27

Figure 7-1: Plane truss model 33

Figure 8-1: Unequal leg bay model 39

Figure 9-1: Two story frame model 45

Figure 10-1: Space frame model 51

Figure 11-1: Model of a rigid wire suspended by wires 57

Figure 12-1: Model of two member truss 63

Figure 13-1: Steel braced frame frame 69

Figure 14-1: Concrete moment frame 81

Figure 15-1: Simple beam diagram 87

Figure 15-2: Finite element model 87

Figure 16-1: Diagram of circular plate 95

Figure 16-2: Finite model for half circular plate 96

Figure 17-1: Simply supported, rectangular plate 103

Figure 17-2: Model: finite element meshed 104

Figure 18-1: Frame model 111

Figure 19-1: Simple span beam 121

Figure 19-2: Finite element model 122

Figure 20-1: Rectangular plate model 129

Figure 21-1: Cantilever member model 143

166— STAAD.Pro

Figure 21-2: Plastic Rotation (in radians) vs. Moment (in in-kips) plot for moment hinge 144

Figure 21-3: Capacity curve (Displacement at Control Joint, inches vs. Base Shear, kips) ascalculated by STAAD.Pro

144

Figure 22-1: Beam with harmonic distributed load 153

Figure 22-2: Model: divide span [email protected]” 154


168— STAAD.Pro

NOTES

Bentley Systems, Incorporated

685 Stockton Drive, Exton, PA 19341 USA

+1 (800) 236-8539

www.bentley.com

STAAD PRO V8i

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