Effect of Bearing Capacity on Designing Foundations in Iraq Using STAAD Pro-V8i
STAAD PRO V8i
-
Upload
rodolfo-p-mendoza-jr -
Category
Documents
-
view
810 -
download
63
description
Transcript of 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
Copyright InformationTrademark NoticeBentley, the "B" Bentley logo, STAAD.Pro are registered or nonregistered trademarks of BentleySystems, Inc. or Bentley Software, Inc. All other marks are the property of their respective owners.
Copyright Notice© 2011, Bentley Systems, Incorporated. All Rights Reserved.
Including software, file formats, and audiovisual displays; may only be used pursuant to applicablesoftware license agreement; contains confidential and proprietary information of Bentley Systems,Incorporated and/or third parties which is protected by copyright and trade secret law and maynot be provided or otherwise made available without proper authorization.
AcknowledgmentsWindows, Vista, SQL Server, MSDE, .NET, DirectX are registered trademarks of MicrosoftCorporation.
ANSYS is a registered trademark of ANSYS, Inc.
EASE2 is a regesitered trademark of Engineering Analysis Corporation.
Adobe, the Adobe logo, Acrobat, the Acrobat logo are registered trademarks of Adobe SystemsIncorporated.
Restricted Rights LegendsIf this software is acquired for or on behalf of the United States of America, its agencies and/orinstrumentalities ("U.S. Government"), it is provided with restricted rights. This software andaccompanying documentation are "commercial computer software" and "commercial computersoftware documentation," respectively, pursuant to 48 C.F.R. 12.212 and 227.7202, and "restrictedcomputer software" pursuant to 48 C.F.R. 52.227-19(a), as applicable. Use, modification,reproduction, release, performance, display or disclosure of this software and accompanyingdocumentation by the U.S. Government are subject to restrictions as set forth in this Agreementand pursuant to 48 C.F.R. 12.212, 52.227-19, 227.7202, and 1852.227-86, as applicable.Contractor/Manufacturer is Bentley Systems, Incorporated, 685 Stockton Drive, Exton, PA 19341-0678.
Unpublished - rights reserved under the Copyright Laws of the United States and Internationaltreaties.
End User License AgreementTo view the End User License Agreement for this product, review: eula_en.pdf.
Verification Manual — v
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
1 Plane Truss: Support Reactions Due to a Joint Load
Verification Manual — 3
11/20/2009 0x5100 00368640 STO_ASChMSections.mdb04/19/2007 0x7480 00223232 uscoldformedsections.mdb10/31/2007 0x3700 00133120 VenezuelanSections.mdb-----------------------------------------------------------------------------------------
4 — STAAD.Pro
1 Plane Truss: Support Reactions Due to a Joint Load
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
Result Type TheorySTAAD
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
Verification Manual — 5
***************************************************** ** STAAD.Pro V8i SELECTseries2 ** Version 20.07.07.32 ** Proprietary Program of ** Bentley Systems, Inc. ** Date= MAR 9, 2011 ** Time= 11: 4:31 ** ** USER ID: Bentley Systems, Inc. *****************************************************
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
**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 = 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 ****
:NATURAL FREQUENCY OF A BEAM SUPPORTED ON TWO SPRINGS -- PAGE NO. 4* FILE: VER02.STD
************************************************************
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/ ** *************************************************************
:NATURAL FREQUENCY OF A BEAM SUPPORTED ON TWO SPRINGS -- PAGE NO. 5* FILE: VER02.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.mdb
2 Natural Frequency Calculation
Verification Manual — 7
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
2 Natural Frequency Calculation
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
Verification Manual — 9
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
***************************************************** ** STAAD.Pro V8i SELECTseries2 ** Version 20.07.07.32 ** Proprietary Program of ** Bentley Systems, Inc. ** Date= MAR 9, 2011 ** Time= 11: 4:35 ** ** USER ID: Bentley Systems, Inc. *****************************************************
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-----------------------------------
NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 21/ 12/ 3SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER
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
3 Deflection and Moments for a Plate-Bending Finite Element
Verification Manual — 11
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*
*********** END OF THE STAAD.Pro RUN *************** DATE= MAR 9,2011 TIME= 11: 4:36 ****
************************************************************* 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
3 Deflection and Moments for a Plate-Bending Finite Element
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-----------------------------------------------------------------------------------------
3 Deflection and Moments for a Plate-Bending Finite Element
Verification Manual — 13
14 — STAAD.Pro
3 Deflection and Moments for a Plate-Bending Finite Element
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
Verification Manual — 15
Comparison
Result Type TheorySTAAD
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
***************************************************** ** STAAD.Pro V8i SELECTseries2 ** Version 20.07.07.32 ** Proprietary Program of ** Bentley Systems, Inc. ** Date= MAR 9, 2011 ** Time= 11: 4:40 ** ** USER ID: Bentley Systems, Inc. *****************************************************
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
**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/ 3/ 2SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER
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
************** END OF LATEST ANALYSIS RESULT **************21. FINISH
*********** END OF THE STAAD.Pro RUN *************** DATE= MAR 9,2011 TIME= 11: 4:40 ****
:A CANTILEVER PLANE FRAME WITH AN INTERMEDIATE SUPPORT -- PAGE NO. 4* FILE VER04.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 *
4 Support Reactions for a Simple Frame
Verification Manual — 17
* 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 CANTILEVER PLANE FRAME WITH AN INTERMEDIATE SUPPORT -- PAGE NO. 5* FILE VER04.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
18— STAAD.Pro
4 Support Reactions for a Simple Frame
11/20/2009 0x5100 00368640 STO_ASChMSections.mdb04/19/2007 0x7480 00223232 uscoldformedsections.mdb10/31/2007 0x3700 00133120 VenezuelanSections.mdb-----------------------------------------------------------------------------------------
4 Support Reactions for a Simple Frame
Verification Manual — 19
20 — STAAD.Pro
4 Support Reactions for a Simple Frame
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.
Verification Manual — 21
Comparison
Result Type TheorySTAAD
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
***************************************************** ** STAAD.Pro V8i SELECTseries2 ** Version 20.07.07.32 ** Proprietary Program of ** Bentley Systems, Inc. ** Date= MAR 9, 2011 ** Time= 11: 4:46 ** ** USER ID: Bentley Systems, Inc. *****************************************************
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
**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 = 5/ 4/ 2SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER
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
5 Deflection and stress for a simple beam
Verification Manual — 23
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
************** END OF LATEST ANALYSIS RESULT **************20. FINISH
*********** END OF THE STAAD.Pro RUN *************** DATE= MAR 9,2011 TIME= 11: 4:46 ****
:A LOCOMOTIVE AXLE -- PAGE NO. 5* FILE: VER05.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 ** 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 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
5 Deflection and stress for a simple beam
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-----------------------------------------------------------------------------------------
5 Deflection and stress for a simple beam
Verification Manual — 25
26— STAAD.Pro
5 Deflection and stress for a simple beam
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.
Verification Manual — 27
Comparison
Result Type TheorySTAAD
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
***************************************************** ** STAAD.Pro V8i SELECTseries2 ** Version 20.07.07.32 ** Proprietary Program of ** Bentley Systems, Inc. ** Date= MAR 9, 2011 ** Time= 11: 4:50 ** ** USER ID: Bentley Systems, Inc. *****************************************************
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
**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/ 3/ 2SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER
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
************** END OF LATEST ANALYSIS RESULT **************18. FINISH
*********** END OF THE STAAD.Pro RUN *************** DATE= MAR 9,2011 TIME= 11: 4:50 ****
:A 1X1 BAY PLANE FRAME -- PAGE NO. 3* FILE VER06.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 *
6 Plane Frame with no Sidesway
Verification Manual — 29
* 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 1X1 BAY PLANE FRAME -- PAGE NO. 4* FILE VER06.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
30 — STAAD.Pro
6 Plane Frame with no Sidesway
11/20/2009 0x5100 00368640 STO_ASChMSections.mdb04/19/2007 0x7480 00223232 uscoldformedsections.mdb10/31/2007 0x3700 00133120 VenezuelanSections.mdb-----------------------------------------------------------------------------------------
6 Plane Frame with no Sidesway
Verification Manual — 31
32— STAAD.Pro
6 Plane Frame with no Sidesway
NOTES
7 Plane Truss Joint DeflectionObjectiveTo find the joint deflection due to joint loads in a plane truss.
ReferenceMcCormack, J. C., “Structural Analysis,” Intext Educational Publishers, 3rd edition, 1975, page 271,example 18 - 2.
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
Verification Manual — 33
Comparison
Result Type TheorySTAAD
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
***************************************************** ** STAAD.Pro V8i SELECTseries2 ** Version 20.07.07.32 ** Proprietary Program of ** Bentley Systems, Inc. ** Date= MAR 9, 2011 ** Time= 11: 4:55 ** ** USER ID: Bentley Systems, Inc. *****************************************************
1. STAAD TRUSS :A PLANE TRUSSINPUT FILE: ver07.STD
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
P R O B L E M S T A T I S T I C S-----------------------------------
NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 8/ 13/ 2SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER
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
************** END OF LATEST ANALYSIS RESULT **************31. FINISH
*********** END OF THE STAAD.Pro RUN *************** DATE= MAR 9,2011 TIME= 11: 4:55 ****
:A PLANE TRUSS -- PAGE NO. 4* FILE VER07.STD
************************************************************
7 Plane Truss Joint Deflection
Verification Manual — 35
* 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/ ** *************************************************************
:A PLANE TRUSS -- PAGE NO. 5* FILE VER07.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.mdb
36— STAAD.Pro
7 Plane Truss Joint Deflection
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-----------------------------------------------------------------------------------------
7 Plane Truss Joint Deflection
Verification Manual — 37
38— STAAD.Pro
7 Plane Truss Joint Deflection
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
Verification Manual — 39
Comparison
Result Type TheorySTAAD
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. *****************************************************
1. STAAD PLANE :A 1X1 BAY PLANE FRAMEINPUT FILE: ver08.STD
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
**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/ 3/ 2SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER
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 LATEST ANALYSIS RESULT **************21. FINISH
*********** END OF THE STAAD.Pro RUN *************** DATE= MAR 9,2011 TIME= 11: 5: 0 ****
:A 1X1 BAY PLANE FRAME -- PAGE NO. 4* FILE VER08.STD
************************************************************* For questions on STAAD.Pro, please contact ** Bentley Systems or Partner offices ** *
8 Unequal Plane frame with Sidesway
Verification Manual — 41
* 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/ ** *************************************************************
:A 1X1 BAY PLANE FRAME -- PAGE NO. 5* FILE VER08.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.mdb
42— STAAD.Pro
8 Unequal Plane frame with Sidesway
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-----------------------------------------------------------------------------------------
8 Unequal Plane frame with Sidesway
Verification Manual — 43
44 — STAAD.Pro
8 Unequal Plane frame with Sidesway
NOTES
9 Multiple level plane frame with horizontal loadsObjectiveTo find the maximum moment due to lateral joint loads in a 1x2 bay plane frame.
ReferenceMcCormack, J. C., “Structural Analysis,” Intext Educational Publishers, 3rd edition, 1975, page 388,example 22 - 7.
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.
Verification Manual — 45
Comparison
Result Type TheorySTAAD
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
***************************************************** ** STAAD.Pro V8i SELECTseries2 ** Version 20.07.07.32 ** Proprietary Program of ** Bentley Systems, Inc. ** Date= MAR 9, 2011 ** Time= 11: 5: 6 ** ** USER ID: Bentley Systems, Inc. *****************************************************
1. STAAD PLANE :A 1X2 BAY PLANE FRAMEINPUT FILE: ver09.STD
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
**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 = 6/ 6/ 2SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER
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 LATEST ANALYSIS RESULT **************22. FINISH
*********** END OF THE STAAD.Pro RUN ***********
9 Multiple level plane frame with horizontal loads
Verification Manual — 47
**** DATE= MAR 9,2011 TIME= 11: 5: 6 ****:A 1X2 BAY PLANE FRAME -- PAGE NO. 4* FILE: VER09.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 ** 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 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
9 Multiple level plane frame with horizontal loads
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-----------------------------------------------------------------------------------------
9 Multiple level plane frame with horizontal loads
Verification Manual — 49
50 — STAAD.Pro
9 Multiple level plane frame with horizontal loads
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
Verification Manual — 51
Comparison
Result Type TheorySTAAD
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
***************************************************** ** STAAD.Pro V8i SELECTseries2 ** Version 20.07.07.32 ** Proprietary Program of ** Bentley Systems, Inc. ** Date= MAR 9, 2011 ** Time= 11: 5:12 ** ** USER ID: Bentley Systems, Inc. *****************************************************
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
P R O B L E M S T A T I S T I C S-----------------------------------
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
10 Forces in a Space Frame
Verification Manual — 53
* 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
************** END OF LATEST ANALYSIS RESULT **************28. FINISH
*********** END OF THE STAAD.Pro RUN *************** DATE= MAR 9,2011 TIME= 11: 5:12 ****
:A SPACE FRAME -- PAGE NO. 6* FILE VER10.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 ** 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 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
10 Forces in a Space Frame
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-----------------------------------------------------------------------------------------
10 Forces in a Space Frame
Verification Manual — 55
56— STAAD.Pro
10 Forces in a Space Frame
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.
Verification Manual — 57
Hint:When modeling, assume a large moment of inertia for the horizontal rigid member anddistribute of the concentrated load as uniform.
Comparison
Result Type TheorySTAAD
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
***************************************************** ** STAAD.Pro V8i SELECTseries2 ** Version 20.07.07.32 ** Proprietary Program of ** Bentley Systems, Inc. ** Date= MAR 9, 2011 ** Time= 11: 5:17 ** ** USER ID: Bentley Systems, Inc. *****************************************************
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
P R O B L E M S T A T I S T I C S-----------------------------------
NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 6/ 5/ 3SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER
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
11 Temperature load in different materials
Verification Manual — 59
:A RIGID BAR SUSPENDED BY TWO COPPER WIRES AND A STEEL W -- PAGE NO. 3* FILE: VER11.STD
MEMBER STRESSES---------------ALL UNITS ARE POUN/SQ INCHMEMB LD SECT AXIAL BEND-Y BEND-Z COMBINED SHEAR-Y SHEAR-Z
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
************** END OF LATEST ANALYSIS RESULT **************26. FINISH
*********** END OF THE STAAD.Pro RUN *************** DATE= MAR 9,2011 TIME= 11: 5:18 ****
:A RIGID BAR SUSPENDED BY TWO COPPER WIRES AND A STEEL W -- PAGE NO. 4* FILE: VER11.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 ** 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 RIGID BAR SUSPENDED BY TWO COPPER WIRES AND A STEEL W -- PAGE NO. 5* FILE: VER11.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.mdb
60 — STAAD.Pro
11 Temperature load in different materials
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-----------------------------------------------------------------------------------------
11 Temperature load in different materials
Verification Manual — 61
62— STAAD.Pro
11 Temperature load in different materials
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°
Verification Manual — 63
Comparison
Result Type TheorySTAAD
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
***************************************************** ** STAAD.Pro V8i SELECTseries2 ** Version 20.07.07.32 ** Proprietary Program of ** Bentley Systems, Inc. ** Date= MAR 9, 2011 ** Time= 11: 5:23 ** ** USER ID: Bentley Systems, Inc. *****************************************************
1. STAAD TRUSS :A PLANE TRUSSINPUT FILE: ver12.STD
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
**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 = 3/ 2/ 2SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER
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
MEMBER STRESSES---------------ALL UNITS ARE POUN/SQ INCHMEMB LD SECT AXIAL BEND-Y BEND-Z COMBINED SHEAR-Y SHEAR-Z
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 LATEST ANALYSIS RESULT **************23. FINISH
*********** END OF THE STAAD.Pro RUN ***********
12 Deflection and stress of a truss system
Verification Manual — 65
**** DATE= MAR 9,2011 TIME= 11: 5:23 ****:A PLANE TRUSS -- PAGE NO. 5* FILE VER12.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 ** 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. 6* 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
12 Deflection and stress of a truss system
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-----------------------------------------------------------------------------------------
12 Deflection and stress of a truss system
Verification Manual — 67
68— STAAD.Pro
12 Deflection and stress of a truss system
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)
Verification Manual — 69
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,
Fx = 8.71 kip (compression), Mz = 56.50 ft·kip
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,
Fx = 25.5 kip (compression), Mz = 112.173 ft·kip
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
Size W16x36, L = 5ft, a = 10.6 in2, Sz = 56.49 in3
From observation, load case 3 will govern.
13 Steel Design per 1989 AISC Code
Verification Manual — 71
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
Size W16x36, L = 16ft, a = 10.6 in2, Sz = 56.49 in3
From observation, load case 1 will govern. Forces at midspan are
Fx = 5.65 kip (compression), Mz = 71.25 ft·kip
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
13 Steel Design per 1989 AISC Code
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
13 Steel Design per 1989 AISC Code
Verification Manual — 73
STAAD Output
74 — STAAD.Pro
13 Steel Design per 1989 AISC Code
***************************************************** ** STAAD.Pro V8i SELECTseries2 ** Version 20.07.07.32 ** Proprietary Program of ** Bentley Systems, Inc. ** Date= MAR 9, 2011 ** Time= 11: 5:28 ** ** USER ID: Bentley Systems, Inc. *****************************************************
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
P R O B L E M S T A T I S T I C S-----------------------------------
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
13 Steel Design per 1989 AISC Code
Verification Manual — 75
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
-----------------------------------------------------------------------| MEM= 3, UNIT KIP-INCH, L= 132.0 AX= 12.60 SZ= 62.7 SY= 11.3|| KL/R-Y= 69.7 CB= 1.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 21.60 || FTZ= 21.60 FCY= 27.00 FTY= 27.00 FC= 16.46 FT= 21.60 FV= 14.40 |-----------------------------------------------------------------------
4 ST W14X43 (AISC SECTIONS)
76— STAAD.Pro
13 Steel Design per 1989 AISC Code
PASS AISC- H2-1 0.936 38.75 T 0.00 -112.17 0.00
-----------------------------------------------------------------------| MEM= 4, UNIT KIP-INCH, L= 48.0 AX= 12.60 SZ= 62.7 SY= 11.3|| KL/R-Y= 25.3 CB= 1.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 23.76 || FTZ= 23.76 FCY= 27.00 FTY= 27.00 FC= 20.26 FT= 21.60 FV= 14.40 |-----------------------------------------------------------------------
5 ST W16X36 (AISC SECTIONS)PASS AISC- H1-3 0.582 3
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
-----------------------------------------------------------------------| MEM= 6, UNIT KIP-INCH, L= 192.0 AX= 10.60 SZ= 56.5 SY= 7.0|| KL/R-Y= 126.3 CB= 1.00 YLD= 36.00 ALLOWABLE STRESSES: FCZ= 14.24 || FTZ= 21.60 FCY= 27.00 FTY= 27.00 FC= 9.36 FT= 21.60 FV= 14.40 |-----------------------------------------------------------------------
7 ST W16X36 (AISC SECTIONS)PASS AISC- H2-1 0.668 3
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
*********** END OF THE STAAD.Pro RUN *************** DATE= MAR 9,2011 TIME= 11: 5:28 ****
************************************************************* 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 *
13 Steel Design per 1989 AISC Code
Verification Manual — 77
* 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/ ** *************************************************************
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
13 Steel Design per 1989 AISC Code
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-----------------------------------------------------------------------------------------
13 Steel Design per 1989 AISC Code
Verification Manual — 79
80 — STAAD.Pro
13 Steel Design per 1989 AISC Code
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
Verification Manual — 81
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
***************************************************** ** STAAD.Pro V8i SELECTseries2 ** Version 20.07.07.32 ** Proprietary Program of ** Bentley Systems, Inc. ** Date= MAR 9, 2011 ** Time= 11: 5:33 ** ** USER ID: Bentley Systems, Inc. *****************************************************
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
P R O B L E M S T A T I S T I C S-----------------------------------
NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 4/ 3/ 2SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER
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=====================================================================
14 Concrete Design per ACI 318 Code
Verification Manual — 83
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
*********** END OF THE STAAD.Pro RUN *************** DATE= MAR 9,2011 TIME= 11: 5:33 ****
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
14 Concrete Design per ACI 318 Code
* 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/ ** *************************************************************
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
14 Concrete Design per ACI 318 Code
Verification Manual — 85
-----------------------------------------------------------------------------------------
86— STAAD.Pro
14 Concrete Design per ACI 318 Code
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.
Verification Manual — 87
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
15 Natural Modes of a Simple Beam
Verification Manual — 89
STAAD Output
90 — STAAD.Pro
15 Natural Modes of a Simple Beam
***************************************************** ** STAAD.Pro V8i SELECTseries2 ** Version 20.07.07.32 ** Proprietary Program of ** Bentley Systems, Inc. ** Date= MAR 9, 2011 ** Time= 11: 5:38 ** ** USER ID: Bentley Systems, Inc. *****************************************************
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
P R O B L E M S T A T I S T I C S-----------------------------------
NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 21/ 20/ 21SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER
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
NUMBER OF MODES REQUESTED = 5NUMBER OF EXISTING MASSES IN THE MODEL = 19NUMBER OF MODES THAT WILL BE USED = 5
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
15 Natural Modes of a Simple Beam
Verification Manual — 91
8 28441.877 0.00004 4.956E-069 35929.844 0.00003 6.604E-05
MODAL WEIGHT (MODAL MASS TIMES g) IN POUN GENERALIZEDMODE X Y Z WEIGHT
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
*********** END OF THE STAAD.Pro RUN *************** DATE= MAR 9,2011 TIME= 11: 5:38 ****
************************************************************* 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 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
15 Natural Modes of a Simple Beam
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-----------------------------------------------------------------------------------------
15 Natural Modes of a Simple Beam
Verification Manual — 93
94 — STAAD.Pro
15 Natural Modes of a Simple Beam
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:
16 Natural Frequencies of a Circular Plate
Verification Manual — 96
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
16 Natural Frequencies of a Circular Plate
*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
16 Natural Frequencies of a Circular Plate
Verification Manual — 98
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
16 Natural Frequencies of a Circular Plate
***************************************************** ** STAAD.Pro V8i SELECTseries2 ** Version 20.07.07.32 ** Proprietary Program of ** Bentley Systems, Inc. ** Date= MAR 9, 2011 ** Time= 11: 5:45 ** ** USER ID: Bentley Systems, Inc. *****************************************************
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
P R O B L E M S T A T I S T I C S-----------------------------------
NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 92/ 84/ 92SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER
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
NUMBER OF MODES REQUESTED = 6NUMBER OF EXISTING MASSES IN THE MODEL = 79NUMBER OF MODES THAT WILL BE USED = 6
STAAD VER. PROB. 16 -- PAGE NO. 3
16 Natural Frequencies of a Circular Plate
Verification Manual — 100
* 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
MODAL WEIGHT (MODAL MASS TIMES g) IN POUN GENERALIZEDMODE X Y Z WEIGHT
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
MASS PARTICIPATION FACTORS IN PERCENT--------------------------------------
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
*********** END OF THE STAAD.Pro RUN *************** DATE= MAR 9,2011 TIME= 11: 5:46 ****
************************************************************* 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 VER. PROB. 16 -- PAGE NO. 7
101 — STAAD.Pro
16 Natural Frequencies of a Circular Plate
* 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-----------------------------------------------------------------------------------------
16 Natural Frequencies of a Circular Plate
Verification Manual — 102
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
Verification Manual — 103
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
ν = Poisson’s ratio
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
The numerical values used for this example are:
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
17 Natural Frequencies of a Rectangular Plate
Verification Manual — 105
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 MODE SHAPE 6
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
17 Natural Frequencies of a Rectangular Plate
LOAD 1
SELF X 1
SELF Y 1
SELF Z 1
MODAL CALC REQ
PERF ANALY
FINI
STAAD Output
17 Natural Frequencies of a Rectangular Plate
Verification Manual — 107
***************************************************** ** STAAD.Pro V8i SELECTseries2 ** Version 20.07.07.32 ** Proprietary Program of ** Bentley Systems, Inc. ** Date= MAR 9, 2011 ** Time= 11: 5:51 ** ** USER ID: Bentley Systems, Inc. *****************************************************
1. STAAD SPACE STAAD VER. PROB. 17INPUT FILE: ver17.STD
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
P R O B L E M S T A T I S T I C S-----------------------------------
NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 117/ 96/ 117SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER
ORIGINAL/FINAL BAND-WIDTH= 14/ 14/ 43 DOFTOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 311SIZE OF STIFFNESS MATRIX = 14 DOUBLE KILO-WORDSREQRD/AVAIL. DISK SPACE = 12.9/ 120710.9 MB
NUMBER OF MODES REQUESTED = 6NUMBER OF EXISTING MASSES IN THE MODEL = 77NUMBER OF MODES THAT WILL BE USED = 6
STAAD VER. PROB. 17 -- PAGE NO. 3* NATURAL FREQUENCIES OF A RECTANGULAR PLATE
CALCULATED FREQUENCIES FOR LOAD CASE 1MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY1 30.599 0.03268 1.968E-162 58.724 0.01703 4.325E-13
108— STAAD.Pro
17 Natural Frequencies of a Rectangular Plate
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
MODAL WEIGHT (MODAL MASS TIMES g) IN POUN GENERALIZEDMODE X Y Z WEIGHT
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
MASS PARTICIPATION FACTORS IN PERCENT--------------------------------------
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
*********** END OF THE STAAD.Pro RUN *************** DATE= MAR 9,2011 TIME= 11: 5:52 ****
************************************************************* 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 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
17 Natural Frequencies of a Rectangular Plate
Verification Manual — 109
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
17 Natural Frequencies of a Rectangular Plate
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.
Verification Manual — 111
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
STAAD AdvancedSolver
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
STAAD AdvancedSolver
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.
18 Natural Modes of a Framework
Verification Manual — 113
Input File
STAAD SPACE STAAD VER. PROB. 18
* 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
CUT OFF MODE SHAPE 24
114 — STAAD.Pro
18 Natural Modes of a Framework
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
18 Natural Modes of a Framework
Verification Manual — 115
***************************************************** ** STAAD.Pro V8i SELECTseries2 ** Version 20.07.07.32 ** Proprietary Program of ** Bentley Systems, Inc. ** Date= MAR 9, 2011 ** Time= 11: 5:56 ** ** USER ID: Bentley Systems, Inc. *****************************************************
1. STAAD SPACE STAAD VER. PROB. 18INPUT FILE: ver18.STD
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
P R O B L E M S T A T I S T I C S-----------------------------------
NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 18/ 18/ 4SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER
ORIGINAL/FINAL BAND-WIDTH= 8/ 4/ 30 DOFTOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 84SIZE OF STIFFNESS MATRIX = 3 DOUBLE KILO-WORDSREQRD/AVAIL. DISK SPACE = 12.1/ 120710.9 MB
NUMBER OF MODES REQUESTED = 24NUMBER OF EXISTING MASSES IN THE MODEL = 42NUMBER OF MODES THAT WILL BE USED = 24
STAAD VER. PROB. 18 -- PAGE NO. 3* NATURAL MODES OF A SPACE FRAME
CALCULATED FREQUENCIES FOR LOAD CASE 1MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY1 111.236 0.00899 7.150E-16
116— STAAD.Pro
18 Natural Modes of a Framework
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
MODAL WEIGHT (MODAL MASS TIMES g) IN POUN GENERALIZEDMODE X Y Z WEIGHT
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 Natural Modes of a Framework
Verification Manual — 117
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
STAAD VER. PROB. 18 -- PAGE NO. 5* NATURAL MODES OF A SPACE FRAME
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
STAAD VER. PROB. 18 -- PAGE NO. 6* NATURAL MODES OF A SPACE FRAME
MASS PARTICIPATION FACTORS IN PERCENT--------------------------------------
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 ****
STAAD VER. PROB. 18 -- PAGE NO. 7* NATURAL MODES OF A SPACE FRAME
************************************************************* 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 VER. PROB. 18 -- PAGE NO. 8* NATURAL MODES OF A SPACE FRAME
Information about the key files in the current distributionModification Date CRC Size (Bytes) File Name-----------------------------------------------------------------------------------------
118— STAAD.Pro
18 Natural Modes of a Framework
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-----------------------------------------------------------------------------------------
18 Natural Modes of a Framework
Verification Manual — 119
120 — STAAD.Pro
18 Natural Modes of a Framework
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.
Verification Manual — 121
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
STAAD SPACE STAAD VER. PROB. 19
* 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
CUT OFF MODE SHAPE 1
19 Response of a Simply Supported Beam to a Shock Spectrum
Verification Manual — 123
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
19 Response of a Simply Supported Beam to a Shock Spectrum
***************************************************** ** STAAD.Pro V8i SELECTseries2 ** Version 20.07.07.32 ** Proprietary Program of ** Bentley Systems, Inc. ** Date= MAR 9, 2011 ** Time= 11: 6: 1 ** ** USER ID: Bentley Systems, Inc. *****************************************************
1. STAAD SPACE STAAD VER. PROB. 19INPUT FILE: ver19.STD
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
P R O B L E M S T A T I S T I C S-----------------------------------
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
NUMBER OF MODES REQUESTED = 1NUMBER OF EXISTING MASSES IN THE MODEL = 19NUMBER OF MODES THAT WILL BE USED = 1
STAAD VER. PROB. 19 -- PAGE NO. 3* RESPONSE OF A SIMPLY SUPPORTED BEAM TO A S
CALCULATED FREQUENCIES FOR LOAD CASE 1MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY1 6.069 0.16476 2.208E-07
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.
CALCULATED FREQUENCIES FOR LOAD CASE 1MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY2 23.959 0.04174 8.561E-073 52.682 0.01898 1.066E-08
MODAL WEIGHT (MODAL MASS TIMES g) IN POUN GENERALIZEDMODE X Y Z WEIGHT
19 Response of a Simply Supported Beam to a Shock Spectrum
Verification Manual — 125
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
*********** END OF THE STAAD.Pro RUN *************** DATE= MAR 9,2011 TIME= 11: 6: 2 ****
STAAD VER. PROB. 19 -- PAGE NO. 7* RESPONSE OF A SIMPLY SUPPORTED BEAM TO A S
************************************************************* 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 VER. PROB. 19 -- PAGE NO. 8* RESPONSE OF A SIMPLY SUPPORTED BEAM TO A S
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
19 Response of a Simply Supported Beam to a Shock Spectrum
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-----------------------------------------------------------------------------------------
19 Response of a Simply Supported Beam to a Shock Spectrum
Verification Manual — 127
128— STAAD.Pro
19 Response of a Simply Supported Beam to a Shock Spectrum
NOTES
20 Thermal Loading on a Simply SupportedRectangular Plate
PurposeCompare theoretical answers to the STAAD solution.
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:
Verification Manual — 129
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
ν = Poisson’s ratio
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)
The numerical values used for this example are:
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
20 Thermal Loading on a Simply Supported Rectangular Plate
Verification Manual — 131
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
20 Thermal Loading on a Simply Supported Rectangular Plate
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
20 Thermal Loading on a Simply Supported Rectangular Plate
Verification Manual — 133
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
STAAD SPACE STAAD VER. PROB. 20
134 — STAAD.Pro
20 Thermal Loading on a Simply Supported Rectangular Plate
* 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
20 Thermal Loading on a Simply Supported Rectangular Plate
Verification Manual — 135
***************************************************** ** STAAD.Pro V8i SELECTseries2 ** Version 20.07.07.32 ** Proprietary Program of ** Bentley Systems, Inc. ** Date= MAR 9, 2011 ** Time= 11: 6: 7 ** ** USER ID: Bentley Systems, Inc. *****************************************************
1. STAAD SPACE STAAD VER. PROB. 20INPUT FILE: ver20.STD
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
P R O B L E M S T A T I S T I C S-----------------------------------
NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 221/ 192/ 56SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER
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
20 Thermal Loading on a Simply Supported Rectangular Plate
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
TOP : SMAX= -3232.73 SMIN= -23808.31 TMAX= 10287.79 ANGLE= 2.8BOTT: SMAX= 23808.31 SMIN= 3232.73 TMAX= 10287.79 ANGLE=-87.2
99 1 -1.23 -0.23 -77.92 -328.01 12.9219844.14 19844.14 0.00 0.00 0.0021911.49 21911.49
TOP : SMAX= -5150.16 SMIN= -21911.49 TMAX= 8380.67 ANGLE= 3.0BOTT: SMAX= 21911.49 SMIN= 5150.16 TMAX= 8380.67 ANGLE=-87.0
100 1 -0.78 -0.21 -100.93 -305.20 9.7617989.87 17989.87 0.00 0.00 0.0020377.92 20377.92
TOP : SMAX= -6697.43 SMIN= -20377.92 TMAX= 6840.24 ANGLE= 2.7BOTT: SMAX= 20377.92 SMIN= 6697.43 TMAX= 6840.24 ANGLE=-87.3
101 1 -0.42 -0.16 -116.93 -289.32 6.0516820.57 16820.57 0.00 0.00 0.0019302.28 19302.28
TOP : SMAX= -7780.89 SMIN= -19302.28 TMAX= 5760.70 ANGLE= 2.0BOTT: SMAX= 19302.28 SMIN= 7780.89 TMAX= 5760.70 ANGLE=-88.0
102 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
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
TOP : SMAX= -7780.89 SMIN= -19302.28 TMAX= 5760.70 ANGLE= -2.0BOTT: SMAX= 19302.28 SMIN= 7780.89 TMAX= 5760.70 ANGLE= 88.0
STAAD VER. PROB. 20 -- PAGE NO. 5* THERMAL LOADING ON A SIMPLY SUPPORTED RECTELEMENT STRESSES FORCE,LENGTH UNITS= POUN INCH
20 Thermal Loading on a Simply Supported Rectangular Plate
Verification Manual — 137
----------------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
TOP : SMAX= -6697.43 SMIN= -20377.92 TMAX= 6840.24 ANGLE= -2.7BOTT: SMAX= 20377.92 SMIN= 6697.43 TMAX= 6840.24 ANGLE= 87.3
106 1 1.23 -0.23 -77.92 -328.01 -12.9219844.14 19844.14 0.00 0.00 0.0021911.49 21911.49
TOP : SMAX= -5150.16 SMIN= -21911.49 TMAX= 8380.67 ANGLE= -3.0BOTT: SMAX= 21911.49 SMIN= 5150.16 TMAX= 8380.67 ANGLE= 87.0
107 1 1.69 -0.20 -49.25 -356.37 -15.2722367.84 22367.84 0.00 0.00 0.0023808.31 23808.31
TOP : SMAX= -3232.73 SMIN= -23808.31 TMAX= 10287.79 ANGLE= -2.8BOTT: SMAX= 23808.31 SMIN= 3232.73 TMAX= 10287.79 ANGLE= 87.2
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
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
30 1 0.67 -1.03 -257.59 -148.94 -25.1915213.03 15213.03 0.00 0.00 0.0017542.96 17542.96
TOP : SMAX= -9558.82 SMIN= -17542.96 TMAX= 3992.07 ANGLE=-77.6BOTT: SMAX= 17542.96 SMIN= 9558.82 TMAX= 3992.07 ANGLE= 12.4
42 1 0.38 -0.06 -211.95 -194.66 -20.3613792.44 13792.44 0.00 0.00 0.0015028.62 15028.62
TOP : SMAX= -12079.03 SMIN= -15028.62 TMAX= 1474.80 ANGLE=-56.5BOTT: SMAX= 15028.62 SMIN= 12079.03 TMAX= 1474.80 ANGLE= 33.5
STAAD VER. PROB. 20 -- PAGE NO. 6* 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
54 1 0.12 0.39 -176.20 -230.35 -15.4014020.85 14020.85 0.00 0.00 0.0015628.28 15628.28
TOP : SMAX= -11474.99 SMIN= -15628.28 TMAX= 2076.65 ANGLE=-14.8BOTT: SMAX= 15628.28 SMIN= 11474.99 TMAX= 2076.65 ANGLE= 75.2
66 1 -0.02 0.49 -150.19 -256.25 -10.6614918.57 14918.57 0.00 0.00 0.0017154.23 17154.23
TOP : SMAX= -9942.06 SMIN= -17154.23 TMAX= 3606.09 ANGLE= -5.7BOTT: SMAX= 17154.23 SMIN= 9942.06 TMAX= 3606.09 ANGLE= 84.3
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
20 Thermal Loading on a Simply Supported Rectangular Plate
TOP : SMAX= -8871.89 SMIN= -18218.24 TMAX= 4673.17 ANGLE= -2.5BOTT: SMAX= 18218.24 SMIN= 8871.89 TMAX= 4673.17 ANGLE= 87.5
90 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
102 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
114 1 -0.09 -0.36 -133.36 -273.00 6.2315779.24 15779.24 0.00 0.00 0.0018218.24 18218.24
TOP : SMAX= -8871.89 SMIN= -18218.24 TMAX= 4673.17 ANGLE= 2.5BOTT: SMAX= 18218.24 SMIN= 8871.89 TMAX= 4673.17 ANGLE=-87.5
126 1 -0.02 -0.49 -150.19 -256.25 10.6614918.57 14918.57 0.00 0.00 0.0017154.23 17154.23
TOP : SMAX= -9942.06 SMIN= -17154.23 TMAX= 3606.09 ANGLE= 5.7BOTT: SMAX= 17154.23 SMIN= 9942.06 TMAX= 3606.09 ANGLE=-84.3
138 1 0.12 -0.39 -176.20 -230.35 15.4014020.85 14020.85 0.00 0.00 0.0015628.28 15628.28
TOP : SMAX= -11474.99 SMIN= -15628.28 TMAX= 2076.65 ANGLE= 14.8BOTT: SMAX= 15628.28 SMIN= 11474.99 TMAX= 2076.65 ANGLE=-75.2
STAAD VER. PROB. 20 -- PAGE NO. 7* 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
150 1 0.38 0.06 -211.95 -194.66 20.3613792.44 13792.44 0.00 0.00 0.0015028.62 15028.62
TOP : SMAX= -12079.03 SMIN= -15028.62 TMAX= 1474.80 ANGLE= 56.5BOTT: SMAX= 15028.62 SMIN= 12079.03 TMAX= 1474.80 ANGLE=-33.5
162 1 0.67 1.03 -257.59 -148.94 25.1915213.03 15213.03 0.00 0.00 0.0017542.96 17542.96
TOP : SMAX= -9558.82 SMIN= -17542.96 TMAX= 3992.07 ANGLE= 77.6BOTT: SMAX= 17542.96 SMIN= 9558.82 TMAX= 3992.07 ANGLE=-12.4
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
20 Thermal Loading on a Simply Supported Rectangular Plate
Verification Manual — 139
STAAD VER. PROB. 20 -- PAGE NO. 9* THERMAL LOADING ON A SIMPLY SUPPORTED RECT
*********** END OF THE STAAD.Pro RUN *************** DATE= MAR 9,2011 TIME= 11: 6: 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 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
20 Thermal Loading on a Simply Supported Rectangular Plate
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-----------------------------------------------------------------------------------------
20 Thermal Loading on a Simply Supported Rectangular Plate
Verification Manual — 141
142— STAAD.Pro
20 Thermal Loading on a Simply Supported Rectangular Plate
NOTES
21 Deflection Calculation Through PushoverAnalysis
PurposeCompare theoretical answers to the STAAD solution.
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
Verification Manual — 143
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
21 Deflection Calculation Through Pushover Analysis
Verification Manual — 145
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
21 Deflection Calculation Through Pushover Analysis
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
21 Deflection Calculation Through Pushover Analysis
Verification Manual — 147
FINISH
STAAD Output
148— STAAD.Pro
21 Deflection Calculation Through Pushover Analysis
***************************************************** ** 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
P R O B L E M S T A T I S T I C S-----------------------------------
NUMBER OF JOINTS/MEMBER+ELEMENTS/SUPPORTS = 2/ 1/ 1SOLVER USED IS THE IN-CORE ADVANCED SOLVER
21 Deflection Calculation Through Pushover Analysis
Verification Manual — 149
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 ****
************************************************************* 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. 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
21 Deflection Calculation Through Pushover Analysis
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-----------------------------------------------------------------------------------------
21 Deflection Calculation Through Pushover Analysis
Verification Manual — 151
152— STAAD.Pro
21 Deflection Calculation Through Pushover Analysis
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
Verification Manual — 153
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
22 Fixed – Fixed Beam Excited by Harmonic Distributed Load
Verification Manual — 155
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
22 Fixed – Fixed Beam Excited by Harmonic Distributed Load
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;
22 Fixed – Fixed Beam Excited by Harmonic Distributed Load
Verification Manual — 157
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 MODE SHAPE 7
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
22 Fixed – Fixed Beam Excited by Harmonic Distributed Load
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
22 Fixed – Fixed Beam Excited by Harmonic Distributed Load
Verification Manual — 159
***************************************************** ** 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
P R O B L E M S T A T I S T I C S-----------------------------------
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
22 Fixed – Fixed Beam Excited by Harmonic Distributed Load
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
MODAL WEIGHT (MODAL MASS TIMES g) IN POUN GENERALIZEDMODE X Y Z WEIGHT
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
MASS PARTICIPATION FACTORS IN PERCENT--------------------------------------
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
22 Fixed – Fixed Beam Excited by Harmonic Distributed Load
Verification Manual — 161
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 LATEST ANALYSIS RESULT **************68. FINISH
*********** 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
22 Fixed – Fixed Beam Excited by Harmonic Distributed Load
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-----------------------------------------------------------------------------------------
22 Fixed – Fixed Beam Excited by Harmonic Distributed Load
Verification Manual — 163
164 — STAAD.Pro
22 Fixed – Fixed Beam Excited by Harmonic Distributed Load
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
Verification Manual — 165
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
Verification Manual — 167
168— STAAD.Pro
NOTES
Bentley Systems, Incorporated
685 Stockton Drive, Exton, PA 19341 USA
+1 (800) 236-8539
www.bentley.com