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STAAD.Pro
V8i (SELECTseries 5)
Verification Manual
Last Updated: Monday, January 06, 2014
STAAD Verification Problems
Release STAAD.Pro 20.07.10.41
Date last updated: 13 December 2013
Quality Assurance Program
STAAD.Pro V8i (SELECTseries 5) is a suite of proprietary computer programs of Bentley
Systems, Inc.. Although every effort has been made to ensure the correctness of these programs,
Bentley Systems, Inc. will not accept responsibility for any mistake, error, or misrepresentation
in or as a result of the usage of these programs.
Notes on Comparisons
In each verification problem, a table is used to summarize the numerical outputs from
STAAD.Pro with a reference or hand calculations. A difference column presents the percent
deviation from the reference, when a significant difference exists.
The deviation is taken as the reference value minus the value determined by STAAD.Pro, divided
by the reference value to express in percent of the reference.
In this context, "significant" is take as larger than a 1% (one percent) difference. When a
difference between 0.5% and 1% exists, then the difference is simply listed as "<1%". Otherwise,
the difference is listed as "none".
This level of significance is intended to reflect that small differences in rounding or calculation
methods do not present a realistic difference in the calculated result.
Verification Manual — 2
Table of Contents
1 Static Trusses 1
Static Truss 1 1
Static Truss 2 4
Static Truss 3 8
Static Truss 4 12
Static Truss 5 16
Static Truss 6 19
Static Truss 7 31
2 Static Beams 35
Static Beam 1 35
Static Beam 2 39
Static Beam 3 43
Static Beam 4 47
Static Beam 5 53
Static Beam 6 56
Static Beam 7 59
Static Beam 8 62
Static Beam 9 65
Static Beam 11 72
Static Beam 12 75
Static Beam 13 78
Static Beam 15 87
3 Static Frames 91
Static Frame 1 91
Static Frame 2 95
Static Frame 3 99
Static Frame 4 102
Static Frame 5 108
Static Frame 10 123
Static Frame 11 127
Static Frame 12 131
4 Static Plate/Shell Elements 139
Verification Manual — 3
Static Element 1 139
Static Element 2 152
Static Element 3 156
Static Element 4 160
Static Element 5 165
Static Element 6 173
Static Element 7 180
Static Element 8 183
Static Element 9 193
Static Element 10 197
Static Element 11 204
Static Element 12 208
Static Element 13 211
Static Element 14 216
Static Element 15 221
Static Element 16 237
Static Element 17 242
5 Solid Elements 249
Static Solid 1 249
Static Solid 2 253
6 Nonlinear Static Analysis 263
Static Nonlinear 1 263
7 Dynamic Analysis 269
Dynamic Truss 1 269
Dynamic Beam 1 272
Dynamic Beam 2 276
Dynamic Beam 3 278
Dynamic Beam 4 281
Dynamic Beam 7 287
8 Concrete Design - ACI 318 291
Concrete Design per ACI 318 1 291
Concrete Design per ACI 318 3 296
Concrete Design per ACI 318 4 300
Concrete Design per ACI 318 5 303
4 — STAAD.Pro
9 Steel Design - AISC 360-10 307
Steel Design per AISC 360-10 - Example E-2 307
Steel Design per AISC 360-10 - Example G-6 313
Steel Design per AISC 360-10 - Example D-2 319
Steel Design per AISC 360-10 - Example F.2-2 326
Steel Design per AISC 360-10 - Example H.1B 332
Steel Design per AISC 360-10 - Example E.5 339
Steel Design per AISC 360-10 - Example F.1-3B 345
10 Steel Design per AISC ASD 353
Steel Design per AISC ASD 1 353
Steel Design per AISC ASD 2 357
Steel Design per AISC ASD 3 360
Steel Design per AISC ASD 4 363
Steel Design per AISC ASD 5 366
Steel Design per AISC ASD 6 369
Steel Design per AISC ASD 7 372
Steel Design per AISC ASD 8 375
Steel Design per AISC ASD 9 378
Steel Design per AISC ASD 10 381
Steel Design per AISC ASD 11 385
Steel Design per AISC ASD 12 388
Steel Design per AISC ASD 13 391
Steel Design per AISC ASD 14 394
Steel Design per AISC ASD 15 397
Steel Design per AISC ASD 16 401
Steel Design per AISC ASD 17 404
Steel Design per AISC ASD 18 409
11 Steel Design per AISC LRFD 413
Steel Design per AISC LRFD 1 414
Steel Design per AISC LRFD 2 416
Steel Design per AISC LRFD 3 419
Steel Design per AISC LRFD 4 422
Steel Design per AISC LRFD 5 424
Steel Design per AISC LRFD 6 427
Verification Manual — 5
Steel Design per AISC LRFD 7 430
Steel Design per AISC LRFD 8 432
Steel Design per AISC LRFD 9 435
Steel Design per AISC LRFD 10 438
Steel Design per AISC LRFD 11 440
Steel Design per AISC LRFD 12 443
Steel Design per AISC LRFD 13 447
Steel Design per AISC LRFD 14 450
Steel Design per AISC LRFD 15 453
Steel Design per AISC LRFD 16 457
Steel Design per AISC LRFD 17 460
Steel Design per AISC LRFD 18 464
Steel Design per AISC LRFD 19 467
Steel Design per AISC LRFD 20 470
Steel Design per AISC LRFD 21 474
Steel Design per AISC LRFD 22 477
Steel Design per AISC LRFD 23 481
Steel Design per AISC LRFD 24 484
Steel Design per AISC LRFD 25 488
Steel Design per AISC LRFD 26 492
12 Steel Design per AS 4100-1998 497
Steel Design per AS 4100-1998 1 497
Steel Design per AS 4100-1998 2 502
Steel Design per AS 4100-1998 3 507
Steel Design per AS 4100-1998 4 510
13 Steel Design per BS 5950-1:2000 515
Steel Design per BS 5950-1:2000 1 515
Steel Design per BS 5950-1:2000 2 521
Steel Design per BS 5950-1:2000 3 528
Steel Design per BS 5950-1:2000 4 534
Steel Design per BS 5950-1:2000 5 540
Steel Design per BS 5950-1:2000 6 544
Steel Design per BS 5950-1:2000 7 547
6 — STAAD.Pro
Copyright Information
Trademark Notice
Bentley, the "B" Bentley logo, STAAD.Pro are registered or nonregistered trademarks of Bentley
Systems, Inc. or Bentley Software, Inc. All other marks are the property of their respective
owners.
Copyright Notice
© 2013, Bentley Systems, Incorporated. All Rights Reserved.
Including software, file formats, and audiovisual displays; may only be used pursuant to
applicable software 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 may not be provided or otherwise made available without proper authorization.
Acknowledgments
Windows, Vista, SQL Server, MSDE, .NET, DirectX are registered trademarks of Microsoft
Corporation.
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 Systems
Incorporated.
Restricted Rights Legends
If this software is acquired for or on behalf of the United States of America, its agencies and/or
instrumentalities ("U.S. Government"), it is provided with restricted rights. This software and
accompanying documentation are "commercial computer software" and "commercial computer
software documentation," respectively, pursuant to 48 C.F.R. 12.212 and 227.7202, and "restricted
computer 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 accompanying
documentation by the U.S. Government are subject to restrictions as set forth in this Agreement
and 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 International
treaties.
End User License Agreement
To view the End User License Agreement for this product, review: eula_en.pdf.
Verification Manual — 7
8 — STAAD.Pro
Notes
1
Static Trusses
Static Truss 1 1
Static Truss 2 4
Static Truss 3 8
Static Truss 4 12
Static Truss 5 16
Static Truss 6 19
Static Truss 7 31
Static Truss 1
Objective
To find member stress due to a joint load in a space truss using static analysis.
Reference
Beer, F.P., and Johnston, Jr., E.R., Vector Mechanics for Engineers, Statics and Dynamics, McGraw -
Hill, Inc., New York, 1962, p.47, Problem 2.70.
Problem
A 50 lb load is supported by three bars which are pinned to a ceiling as shown. Determine the
stress, σ, in each bar.
Area of each bar = 1 in2, E = 30 (10)6 psi
Verification Manual — 1
Figure 1-1: Space truss
Comparison
Result Type Theory STAAD.Pro Difference
σAD
31.2 31.2 none
σBD
10.4 10.4 none
σCD
22.9 22.9 none
Table 1-1: Comparison of member stress, in psi, for static truss no. 1
STAAD Input
STAAD TRUSS :A SPACE TRUSS
* FILE TRUSS01.STD
*
* REF: "VECTOR MECHANICS FOR ENGINEERS, STATICS &amp; DYNAMICS",
* MCGRAW HILL BOOK CO., INC., NEW YORK, 1962
* PROBLEM 2.70, PAGE 47.
*
UNIT FT POUND
JOINT COORDINATES
1 0. 0. 0.
2 8. 0. 0.
3 0. 6. 0.
4 4. 2. 6.
MEMBER INCIDENCES
1 1 4
2 2 4
3 3 4
UNIT INCH
MEMBER PROPERTIES
1 TO 3 PRIS AX 1.
CONSTANTS
E 30E6 ALL
SUPPORTS
1 TO 3 PINNED
LOAD 1 WEIGHT
JOINT LOAD
4 FZ 50.
PERFORM ANALYSIS
PRINT MEMBER STRESSES
FINISH
2 — STAAD.Pro
1 Static Trusses
Static Truss 1
STAAD Output
PAGE NO. 1
****************************************************
* *
* STAAD.Pro V8i SELECTseries5 *
* Version 20.07.10.41 *
* Proprietary Program of *
* Bentley Systems, Inc. *
* Date= DEC 13, 2013 *
* Time= 12:30: 8 *
* *
* USER ID: Bentley Systems, Inc. *
****************************************************
1. STAAD TRUSS :A SPACE TRUSS
INPUT FILE: TRUSS01.STD
2. * FILE TRUSS01.STD
3. *
4. * REF: "VECTOR MECHANICS FOR ENGINEERS, STATICS &AMP; DYNAMICS",
5. * MCGRAW HILL BOOK CO., INC., NEW YORK, 1962
6. * PROBLEM 2.70, PAGE 47.
7. *
8. UNIT FT POUND
9. JOINT COORDINATES
10. 1 0. 0. 0.
11. 2 8. 0. 0.
12. 3 0. 6. 0.
13. 4 4. 2. 6.
14. MEMBER INCIDENCES
15. 1 1 4
16. 2 2 4
17. 3 3 4
18. UNIT INCH
19. MEMBER PROPERTIES
20. 1 TO 3 PRIS AX 1.
21. CONSTANTS
22. E 30E6 ALL
23. SUPPORTS
24. 1 TO 3 PINNED
25. LOAD 1 WEIGHT
26. JOINT LOAD
27. 4 FZ 50.
28. PERFORM ANALYSIS
**WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE
MEMBERS/ELEMENTS/SOLIDS. THE DEFAULT VALUE HAS BEEN SET FOR THE SAME.
:A SPACE TRUSS -- PAGE NO. 2
* FILE TRUSS01.STD
P R O B L E M S T A T I S T I C S
-----------------------------------
NUMBER OF JOINTS 4 NUMBER OF MEMBERS 3
NUMBER OF PLATES 0 NUMBER OF SOLIDS 0
NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 3
SOLVER USED IS THE IN-CORE ADVANCED SOLVER
TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 3
29. PRINT MEMBER STRESSES
MEMBER STRESSES
:A SPACE TRUSS -- PAGE NO. 3
1 Static Trusses
Verification Manual — 3
* FILE TRUSS01.STD
MEMBER STRESSES
---------------
ALL UNITS ARE POUN/SQ INCH
MEMB LD SECT AXIAL BEND-Y BEND-Z COMBINED SHEAR-Y SHEAR-Z
1 1 .0 10.4 T 0.0 0.0 10.4 0.0 0.0
1.0 10.4 T 0.0 0.0 10.4 0.0 0.0
2 1 .0 31.2 T 0.0 0.0 31.2 0.0 0.0
1.0 31.2 T 0.0 0.0 31.2 0.0 0.0
3 1 .0 22.9 T 0.0 0.0 22.9 0.0 0.0
1.0 22.9 T 0.0 0.0 22.9 0.0 0.0
************** END OF LATEST ANALYSIS RESULT **************
30. FINISH
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= DEC 13,2013 TIME= 12:30:11 ****
:A SPACE TRUSS -- PAGE NO. 4
* FILE TRUSS01.STD
************************************************************
* For technical assistance on STAAD.Pro, please visit *
* http://selectservices.bentley.com/en-US/ *
* *
* Details about additional assistance from *
* Bentley and Partners can be found at program menu *
* Help->Technical Support *
* *
* Copyright © 1997-2013 Bentley Systems, Inc.
* http://www.bentley.com *
************************************************************
Static Truss 2
Objective
To find member force due to a member load in a plane articulate structure.
Reference
Kinney, J. S.,Indeterminate Structural Analysis, Addison - Wesley Publishing Co., 1957, p.275,
Problem 6 - 19.(Original data is in US Customary Units)
Problem
Find the tensile stress in the cable. The cross - sectional area of the cable is 967.74 mm2 with
an E of 137.895 GPa. The timber beam 1-3 is 304.8 mm x 304.8 mm in section, with E = 11.03161
GPa. Each member of the steel cantilever truss has a cross - sectional area of 2,580.64 mm2,
and E of 206.8427 GPa.
4 — STAAD.Pro
1 Static Trusses
Static Truss 2
Figure 1-2: Plane articulate truss
Comparison
Result Type Theory STAAD.Pro Difference
Cable, 3-4 22.7 22.58 0.6% (negligible)
Table 1-2: Comparison of member force, in kN, for static truss no. 2
STAAD Input
STAAD PLANE :A PLANE ARTICULATE STRUCTURE
* FILE TRUSS02.STD
*
* REFERENCE: INDETERMINATE STRURAL ANALYSIS, KINNEY, 1957,
* ADISON-WESLEY PUBLISHING COMPANY, PAGE 275, PROBLEM 6-19.
*
*
UNIT NEWTON METER
JOINT COORDINATES
1 0 0 0
2 3.0480 0 0
3 4.5720 0 0
4 4.5720 2.4384 0
5 6.4008 4.8768 0
6 6.4008 2.4384 0
7 8.2296 4.8768 0
8 8.2296 2.4384 0
9 10.0586 4.8768 0
10 10.0586 2.4384 0
*
MEMBER INCIDENCES
1 1 2 3 1 1
4 4 6
5 6 8
6 8 10
7 4 5
8 6 5
9 6 7
10 8 7
11 8 9
12 5 7
13 7 9
MEMBER PROPERTIES
1 2 PRI YD .3048 ZD .3048
3 PRI AX 9.6774E-4 IZ 41.62314E-8
4 TO 13 PRI AX 25.8064E-4 IZ 41.62314E-8
CONSTANTS
E 11.03161E9 MEMB 1 2
1 Static Trusses
Verification Manual — 5
E 137.89500E9 MEMB 3
E 206.84270E9 MEMB 4 TO 13
MEMBER RELEASES
3 TO 13 START MZ
*
SUPPORT
1 9 10 FIXED
*
LOADING 1
JOINT LOADS
2 FY -44.4822E3
*
PERFORM ANALYSIS
UNITS KNS
PRINT MEMBER FORCES LIST 3
FINISH
STAAD Output
PAGE NO. 1
****************************************************
* *
* STAAD.Pro V8i SELECTseries5 *
* Version 20.07.10.41 *
* Proprietary Program of *
* Bentley Systems, Inc. *
* Date= DEC 13, 2013 *
* Time= 12:30:11 *
* *
* USER ID: Bentley Systems, Inc. *
****************************************************
1. STAAD PLANE :A PLANE ARTICULATE STRUCTURE
INPUT FILE: TRUSS02.STD
2. * FILE TRUSS02.STD
3. *
4. * REFERENCE: INDETERMINATE STRURAL ANALYSIS, KINNEY, 1957,
5. * ADISON-WESLEY PUBLISHING COMPANY, PAGE 275, PROBLEM 6-19.
6. *
7. *
8. UNIT NEWTON METER
9. JOINT COORDINATES
10. 1 0 0 0
11. 2 3.0480 0 0
12. 3 4.5720 0 0
13. 4 4.5720 2.4384 0
14. 5 6.4008 4.8768 0
15. 6 6.4008 2.4384 0
16. 7 8.2296 4.8768 0
17. 8 8.2296 2.4384 0
18. 9 10.0586 4.8768 0
19. 10 10.0586 2.4384 0
20. *
21. MEMBER INCIDENCES
22. 1 1 2 3 1 1
23. 4 4 6
24. 5 6 8
25. 6 8 10
26. 7 4 5
27. 8 6 5
28. 9 6 7
29. 10 8 7
30. 11 8 9
31. 12 5 7
32. 13 7 9
6 — STAAD.Pro
1 Static Trusses
Static Truss 2
33. MEMBER PROPERTIES
34. 1 2 PRI YD .3048 ZD .3048
35. 3 PRI AX 9.6774E-4 IZ 41.62314E-8
36. 4 TO 13 PRI AX 25.8064E-4 IZ 41.62314E-8
37. CONSTANTS
38. E 11.03161E9 MEMB 1 2
:A PLANE ARTICULATE STRUCTURE -- PAGE NO. 2
* FILE TRUSS02.STD
39. E 137.89500E9 MEMB 3
40. E 206.84270E9 MEMB 4 TO 13
41. MEMBER RELEASES
42. 3 TO 13 START MZ
43. *
44. SUPPORT
45. 1 9 10 FIXED
46. *
47. LOADING 1
48. JOINT LOADS
49. 2 FY -44.4822E3
50. *
51. PERFORM ANALYSIS
**WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE
MEMBERS/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 10 NUMBER OF MEMBERS 13
NUMBER OF PLATES 0 NUMBER OF SOLIDS 0
NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 3
SOLVER USED IS THE IN-CORE ADVANCED SOLVER
TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 21
52. UNITS KNS
53. PRINT MEMBER FORCES LIST 3
MEMBER FORCES LIST 3
:A PLANE ARTICULATE STRUCTURE -- PAGE NO. 3
* FILE TRUSS02.STD
MEMBER END FORCES STRUCTURE TYPE = PLANE
-----------------
ALL UNITS ARE -- KNS METE (LOCAL )
MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z
3 1 3 -22.58 0.00 0.00 0.00 0.00 0.00
4 22.58 0.00 0.00 0.00 0.00 0.00
************** END OF LATEST ANALYSIS RESULT **************
54. FINISH
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= DEC 13,2013 TIME= 12:30:14 ****
:A PLANE ARTICULATE STRUCTURE -- PAGE NO. 4
* FILE TRUSS02.STD
************************************************************
* For technical assistance on STAAD.Pro, please visit *
* http://selectservices.bentley.com/en-US/ *
* *
* Details about additional assistance from *
* Bentley and Partners can be found at program menu *
* Help->Technical Support *
* *
* Copyright © 1997-2013 Bentley Systems, Inc.
* http://www.bentley.com *
************************************************************
1 Static Trusses
Verification Manual — 7
Static Truss 3
Objective
To find member forces due to joint loads in a plane truss.
Reference
Norris C.H., Wilbur J. B., Elementary Structural Analysis, 2nd Edition, McGraw – Hill, Inc., Page
159, Problem 4.3. (Original data is in US Customary Units)
Problem
Compute the bar forces in the bars a, b, c, d, e of the truss due to the loads shown.
Figure 1-3: Plane truss
Comparison
Result Type Theory STAAD.Pro Difference
a -202.13 -202.13 none
b -185.76 -190.28 2.4% (negligible)
c -22.42 -23.42 4.5%
d 266.23 269.52 1.2% (negligible)
e 119.61 117.08 2.1% (negligible)
Table 1-3: Comparison of member force, in kN, for static truss no. 3
8 — STAAD.Pro
1 Static Trusses
Static Truss 3
STAAD Input
STAAD PLANE :A PLANE TRUSS
* FILE TRUSS03.STD
*
* REFERENCE: ELEMENTARY STRUCTURAL ANALYSIS, NORIS AND WILBUR,
* 2ND EDITION, MCGRAW-HILL BOOK COMPANY, PAGE 159,
* PROBLEM 4.3 (ORIGINAL DATA IN US CUSTOMAY UNITS)
*
UNIT NEWTON METER
JOINT COORDINATES
1 0 0
2 7.62 0
3 7.62 9.144
4 15.24 0
5 15.24 4.572
6 15.24 9.144
7 22.86 0
8 22.86 12.192
9 30.48 0
10 30.48 4.572
11 30.48 9.144
12 38.10 0
13 38.10 9.144
14 45.72 0
*
MEMBER INCIDENCES
1 1 2; 5 2 4
8 4 7; 11 7 9
14 9 12; 17 12 14
2 1 5; 3 1 3
4 2 3; 6 5 3
7 3 6; 9 7 5
21 4 5; 22 5 6
10 6 8;23 7 8
12 7 10; 13 11 8
24 9 10; 25 10 11
15 10 13; 16 11 13
18 14 10; 19 12 13
20 14 13
MEMBER PROPERTIES
1 TO 25 PRI AX 12.9032E-4
CONSTANT
E 206.84271E9 ALL
MEMBER TRUSS
1 TO 25
*
SUPPORTS
1 PINNED
14 FIXED BUT FX
*
LOADING 1 VERTICAL JOINT LOADS
JOINT LOADS
2 9 FY -4.448222E4
4 7 FY -8.896444E4
12 FY -2.224111E4
*
PERFORM ANALYSIS
UNITS KNS
PRINT MEMBER FORCES LIST 2 5 6 10 12
FINISH
STAAD Output
PAGE NO. 1
1 Static Trusses
Verification Manual — 9
****************************************************
* *
* STAAD.Pro V8i SELECTseries5 *
* Version 20.07.10.41 *
* Proprietary Program of *
* Bentley Systems, Inc. *
* Date= DEC 13, 2013 *
* Time= 12:30:14 *
* *
* USER ID: Bentley Systems, Inc. *
****************************************************
1. STAAD PLANE :A PLANE TRUSS
INPUT FILE: TRUSS03.STD
2. * FILE TRUSS03.STD
3. *
4. * REFERENCE: ELEMENTARY STRUCTURAL ANALYSIS, NORIS AND WILBUR,
5. * 2ND EDITION, MCGRAW-HILL BOOK COMPANY, PAGE 159,
6. * PROBLEM 4.3 (ORIGINAL DATA IN US CUSTOMAY UNITS)
7. *
8. UNIT NEWTON METER
9. JOINT COORDINATES
10. 1 0 0
11. 2 7.62 0
12. 3 7.62 9.144
13. 4 15.24 0
14. 5 15.24 4.572
15. 6 15.24 9.144
16. 7 22.86 0
17. 8 22.86 12.192
18. 9 30.48 0
19. 10 30.48 4.572
20. 11 30.48 9.144
21. 12 38.10 0
22. 13 38.10 9.144
23. 14 45.72 0
24. *
25. MEMBER INCIDENCES
26. 1 1 2; 5 2 4
27. 8 4 7; 11 7 9
28. 14 9 12; 17 12 14
29. 2 1 5; 3 1 3
30. 4 2 3; 6 5 3
31. 7 3 6; 9 7 5
32. 21 4 5; 22 5 6
33. 10 6 8;23 7 8
34. 12 7 10; 13 11 8
35. 24 9 10; 25 10 11
36. 15 10 13; 16 11 13
37. 18 14 10; 19 12 13
38. 20 14 13
:A PLANE TRUSS -- PAGE NO. 2
* FILE TRUSS03.STD
39. MEMBER PROPERTIES
40. 1 TO 25 PRI AX 12.9032E-4
41. CONSTANT
42. E 206.84271E9 ALL
43. MEMBER TRUSS
44. 1 TO 25
45. *
46. SUPPORTS
47. 1 PINNED
48. 14 FIXED BUT FX
49. *
50. LOADING 1 VERTICAL JOINT LOADS
10 — STAAD.Pro
1 Static Trusses
Static Truss 3
51. JOINT LOADS
52. 2 9 FY -4.448222E4
53. 4 7 FY -8.896444E4
54. 12 FY -2.224111E4
55. *
56. PERFORM ANALYSIS
**WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE
MEMBERS/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 14 NUMBER OF MEMBERS 25
NUMBER OF PLATES 0 NUMBER OF SOLIDS 0
NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2
SOLVER USED IS THE IN-CORE ADVANCED SOLVER
TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 38
*WARNING- ZERO 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 OR
EFFECTIVELY RELEASED IN THIS DIRECTION.
*WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 2 EQN.NO. 4
*WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 3 EQN.NO. 7
*WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 4 EQN.NO. 10
*WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 5 EQN.NO. 13
*WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 6 EQN.NO. 16
*WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 7 EQN.NO. 19
*WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 8 EQN.NO. 22
*WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 9 EQN.NO. 25
*WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 10 EQN.NO. 28
*WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 11 EQN.NO. 31
:A PLANE TRUSS -- PAGE NO. 3
* FILE TRUSS03.STD
*WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 12 EQN.NO. 34
**WARNING - THERE WERE MORE THAN 12 DOF WITH ZERO STIFFNESS.
THE FIRST 12 ARE LISTED ABOVE.
TOTAL # TRANSLATIONAL= 0 TOTAL # ROTATIONAL= 13
57. UNITS KNS
58. PRINT MEMBER FORCES LIST 2 5 6 10 12
MEMBER FORCES LIST 2
:A PLANE TRUSS -- PAGE NO. 4
* FILE TRUSS03.STD
MEMBER END FORCES STRUCTURE TYPE = PLANE
-----------------
ALL UNITS ARE -- KNS METE (LOCAL )
MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z
2 1 1 190.28 0.00 0.00 0.00 0.00 0.00
5 -190.28 0.00 0.00 0.00 0.00 0.00
5 1 2 -269.52 0.00 0.00 0.00 0.00 0.00
4 269.52 0.00 0.00 0.00 0.00 0.00
6 1 5 -117.08 0.00 0.00 0.00 0.00 0.00
3 117.08 0.00 0.00 0.00 0.00 0.00
10 1 6 202.12 0.00 0.00 0.00 0.00 0.00
8 -202.12 0.00 0.00 0.00 0.00 0.00
12 1 7 23.42 0.00 0.00 0.00 0.00 0.00
10 -23.42 0.00 0.00 0.00 0.00 0.00
************** END OF LATEST ANALYSIS RESULT **************
59. FINISH
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= DEC 13,2013 TIME= 12:30:17 ****
1 Static Trusses
Verification Manual — 11
:A PLANE TRUSS -- PAGE NO. 5
* FILE TRUSS03.STD
************************************************************
* For technical assistance on STAAD.Pro, please visit *
* http://selectservices.bentley.com/en-US/ *
* *
* Details about additional assistance from *
* Bentley and Partners can be found at program menu *
* Help->Technical Support *
* *
* Copyright © 1997-2013 Bentley Systems, Inc.
* http://www.bentley.com *
************************************************************
Static Truss 4
Objective
To find support reactions and member forces due to a joint load in a space truss.
Reference
Beer F. P., and Johnston, E. R., Vector Mechanics for Engineers - Statics, 4th Edition, McGraw –
Hill, Inc., p.216, Problem 6.20.
Problem
The space truss is supported by the six reactions shown. If a horizontal 2,700 N load is applied
at A, determine the reactions and the force in each member.
12 — STAAD.Pro
1 Static Trusses
Static Truss 4
Figure 1-4: Space truss
Comparison
Result Type Theory STAAD.Pro Difference
Bv
0 0 none
Bz
2,700 2,700 none
Cx
1,800 1,800 none
Cv
3,375 3,375 none
Dx
1,800 1,800 none
Dv
3,375 3,375 none
Table 1-4: Comparison of support reactions, in N, for static truss no. 4
Result Type Theory STAAD.Pro Difference
AB 0 0 none
AC 4,275 4,275 none
Table 1-5: Comparison of member forces, in N, for static truss no. 4
1 Static Trusses
Verification Manual — 13
Result Type Theory STAAD.Pro Difference
AD 4,275 4,275 none
BC 4,270 4,269 negligible
CD 0 0 none
BD 4,270 4,269 negligible
STAAD Input
STAAD SPACE :A SPACE TRUSS
* FILE: TRUSS04.STD
*
* REFERENCE: VECTOR MECHANICS FOR ENGINEERS - STATICS, BEER AND
* JOHNSTON, 4TH EDITION, MCGRAW-HILL BOOK CO.,
* PAGE 216, PROBLEM 6.20.
*
UNITS NEWTON METER
JOINT COORDINATES
1 1.0 0.0 0.6
2 1.0 0.0 -0.6
3 -0.8 0.0 0.0
4 0.0 1.5 0.0
*
MEMBER INCIDENCES
1 1 4
2 2 4
3 3 4
4 1 2 5
6 3 1
MEMBER PROPERTIES
1 TO 6 PRI AX 0.001
CONSTANTS
E 200.0E9 ALL
MEMBER TRUSS
1 TO 6
*
SUPPORTS
1 FIXED BUT FZ
2 FIXED BUT FZ
3 FIXED BUT FX
*
LOADING 1 HORIZONTAL LOAD
JOINT LOAD
4 FZ 2700.0
PERFORM ANALYSIS
PRINT SUPPORT REACTIONS
PRINT MEMBER FORCES
FINISH
STAAD Output
PAGE NO. 1
****************************************************
* *
* STAAD.Pro V8i SELECTseries5 *
* Version 20.07.10.41 *
* Proprietary Program of *
* Bentley Systems, Inc. *
* Date= DEC 13, 2013 *
* Time= 12:30:18 *
14 — STAAD.Pro
1 Static Trusses
Static Truss 4
* *
* USER ID: Bentley Systems, Inc. *
****************************************************
1. STAAD SPACE :A SPACE TRUSS
INPUT FILE: TRUSS04.STD
2. * FILE: TRUSS04.STD
3. *
4. * REFERENCE: VECTOR MECHANICS FOR ENGINEERS - STATICS, BEER AND
5. * JOHNSTON, 4TH EDITION, MCGRAW-HILL BOOK CO.,
6. * PAGE 216, PROBLEM 6.20.
7. *
8. UNITS NEWTON METER
9. JOINT COORDINATES
10. 1 1.0 0.0 0.6
11. 2 1.0 0.0 -0.6
12. 3 -0.8 0.0 0.0
13. 4 0.0 1.5 0.0
14. *
15. MEMBER INCIDENCES
16. 1 1 4
17. 2 2 4
18. 3 3 4
19. 4 1 2 5
20. 6 3 1
21. MEMBER PROPERTIES
22. 1 TO 6 PRI AX 0.001
23. CONSTANTS
24. E 200.0E9 ALL
25. MEMBER TRUSS
26. 1 TO 6
27. *
28. SUPPORTS
29. 1 FIXED BUT FZ
30. 2 FIXED BUT FZ
31. 3 FIXED BUT FX
32. *
33. LOADING 1 HORIZONTAL LOAD
34. JOINT LOAD
35. 4 FZ 2700.0
36. PERFORM ANALYSIS
:A SPACE TRUSS -- PAGE NO. 2
* FILE: TRUSS04.STD
**WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE
MEMBERS/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 4 NUMBER OF MEMBERS 6
NUMBER OF PLATES 0 NUMBER OF SOLIDS 0
NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 3
SOLVER USED IS THE IN-CORE ADVANCED SOLVER
TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 9
*WARNING- ZERO STIFFNESS IN DIRECTION 4 AT JOINT 4 EQN.NO. 7
LOADS APPLIED OR DISTRIBUTED HERE FROM ELEMENTS WILL BE IGNORED.
THIS MAY BE DUE TO ALL MEMBERS AT THIS JOINT BEING RELEASED OR
EFFECTIVELY RELEASED IN THIS DIRECTION.
*WARNING- ZERO STIFFNESS IN DIRECTION 5 AT JOINT 4 EQN.NO. 8
*WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 4 EQN.NO. 9
37. PRINT SUPPORT REACTIONS
SUPPORT REACTION
1 Static Trusses
Verification Manual — 15
:A SPACE TRUSS -- PAGE NO. 3
* FILE: TRUSS04.STD
SUPPORT REACTIONS -UNIT NEWT METE STRUCTURE TYPE = SPACE
-----------------
JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z
1 1 1800.00 3375.00 0.00 0.00 0.00 0.00
2 1 -1800.00 -3375.00 0.00 0.00 0.00 0.00
3 1 0.00 0.00 -2700.00 0.00 0.00 0.00
************** END OF LATEST ANALYSIS RESULT **************
38. PRINT MEMBER FORCES
MEMBER FORCES
:A SPACE TRUSS -- PAGE NO. 4
* FILE: TRUSS04.STD
MEMBER END FORCES STRUCTURE TYPE = SPACE
-----------------
ALL UNITS ARE -- NEWT METE (LOCAL )
MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z
1 1 1 4275.00 0.00 0.00 0.00 0.00 0.00
4 -4275.00 0.00 0.00 0.00 0.00 0.00
2 1 2 -4275.00 0.00 0.00 0.00 0.00 0.00
4 4275.00 0.00 0.00 0.00 0.00 0.00
3 1 3 0.00 0.00 0.00 0.00 0.00 0.00
4 0.00 0.00 0.00 0.00 0.00 0.00
4 1 1 0.00 0.00 0.00 0.00 0.00 0.00
2 0.00 0.00 0.00 0.00 0.00 0.00
5 1 2 4269.07 0.00 0.00 0.00 0.00 0.00
3 -4269.07 0.00 0.00 0.00 0.00 0.00
6 1 3 -4269.07 0.00 0.00 0.00 0.00 0.00
1 4269.07 0.00 0.00 0.00 0.00 0.00
************** END OF LATEST ANALYSIS RESULT **************
39. FINISH
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= DEC 13,2013 TIME= 12:30:21 ****
:A SPACE TRUSS -- PAGE NO. 5
* FILE: TRUSS04.STD
************************************************************
* For technical assistance on STAAD.Pro, please visit *
* http://selectservices.bentley.com/en-US/ *
* *
* Details about additional assistance from *
* Bentley and Partners can be found at program menu *
* Help->Technical Support *
* *
* Copyright © 1997-2013 Bentley Systems, Inc.
* http://www.bentley.com *
************************************************************
Static Truss 5
Objective
To find support reactions due to joint loads in a plane truss.
Reference
McCormack, J.C. Structural Analysis, Intext Educational Publishers, 3rd Edition, 1975.
16 — STAAD.Pro
1 Static Trusses
Static Truss 5
Problem
Find the vertical support reactions of the truss.
E = 30,000.0 ksi
A = 100 in2
Loads as shown.
Figure 1-5: Plane truss
Comparison
Result Type Theory STAAD.Pro Difference
R1
-76.7 -76.67 none
R4
346.7 346.67 none
R9
30 30 none
Table 1-6: Comparison of support reactions, in N, for static truss no. 5
STAAD Input
STAAD TRUSS :A PLANE TRUSS
* FILE: TRUSS05.STD
*
* REFERENCE: MCCORMAC, J.C.,"STRUCTURAL ANALYSIS", INTEXT
* EDUCATIONAL PUBLISHERS, NEW YORK, 3RD EDITION, 1975.
*
INPUT WIDTH 72
UNIT FEET KIP
JOINT COORDINATES
1 0. 0. 0.; 2 30. 0. 0.; 3 60. 0. 0.; 4 90. 0. 0.; 5 120. 0. 0.
6 150. 0. 0.; 7 180. 0. 0.; 8 210. 0. 0.; 9 240. 0. 0.; 10 0. 20. 0.
11 30. 20. 0.; 12 60. 20. 0.; 13 90. 20. 0.; 14 120. 20. 0.
15 150. 20. 0.; 16 180. 20. 0.; 17 210. 20. 0.; 18 240. 20. 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 10 11
10 11 12; 11 12 13; 12 13 14; 13 14 15; 14 16 17; 15 17 18; 16 1 10
17 10 2; 18 2 11; 19 11 3; 20 3 12; 21 12 4; 22 4 13; 23 13 5; 24 5 14
25 14 6; 26 6 15; 27 15 7; 28 7 16; 29 16 8; 30 8 17; 31 17 9; 32 9 18
UNIT INCHES KIP
MEMBER PROPERTY AMERICAN
1 TO 32 PRI AX 100.
* MEMBER TRUSS
* 1 TO 32
CONSTANTS
E 30000. ALL
1 Static Trusses
Verification Manual — 17
SUPPORTS
1 PINNED
4 9 FIXED BUT FX MZ
LOAD 1 POINT LOADS AT SPECIFIC JOINTS
JOINT LOAD
6 TO 8 FY -60.
3 FY -80.
2 FY -40.
PERFORM ANALYSIS
PRINT SUPPORT REACTIONS
FINISH
STAAD Output
PAGE NO. 1
****************************************************
* *
* STAAD.Pro V8i SELECTseries5 *
* Version 20.07.10.41 *
* Proprietary Program of *
* Bentley Systems, Inc. *
* Date= DEC 13, 2013 *
* Time= 12:30:21 *
* *
* USER ID: Bentley Systems, Inc. *
****************************************************
1. STAAD TRUSS :A PLANE TRUSS
INPUT FILE: TRUSS05.STD
2. * FILE: TRUSS05.STD
3. *
4. * REFERENCE: MCCORMAC, J.C.,"STRUCTURAL ANALYSIS", INTEXT
5. * EDUCATIONAL PUBLISHERS, NEW YORK, 3RD EDITION, 1975.
6. *
7. INPUT WIDTH 72
8. UNIT FEET KIP
9. JOINT COORDINATES
10. 1 0. 0. 0.; 2 30. 0. 0.; 3 60. 0. 0.; 4 90. 0. 0.; 5 120. 0. 0.
11. 6 150. 0. 0.; 7 180. 0. 0.; 8 210. 0. 0.; 9 240. 0. 0.; 10 0. 20. 0.
12. 11 30. 20. 0.; 12 60. 20. 0.; 13 90. 20. 0.; 14 120. 20. 0.
13. 15 150. 20. 0.; 16 180. 20. 0.; 17 210. 20. 0.; 18 240. 20. 0.
14. MEMBER INCIDENCES
15. 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 10 11
16. 10 11 12; 11 12 13; 12 13 14; 13 14 15; 14 16 17; 15 17 18; 16 1 10
17. 17 10 2; 18 2 11; 19 11 3; 20 3 12; 21 12 4; 22 4 13; 23 13 5; 24 5 14
18. 25 14 6; 26 6 15; 27 15 7; 28 7 16; 29 16 8; 30 8 17; 31 17 9; 32 9 18
19. UNIT INCHES KIP
20. MEMBER PROPERTY AMERICAN
21. 1 TO 32 PRI AX 100.
22. * MEMBER TRUSS
23. * 1 TO 32
24. CONSTANTS
25. E 30000. ALL
26. SUPPORTS
27. 1 PINNED
28. 4 9 FIXED BUT FX MZ
29. LOAD 1 POINT LOADS AT SPECIFIC JOINTS
30. JOINT LOAD
31. 6 TO 8 FY -60.
32. 3 FY -80.
33. 2 FY -40.
34. PERFORM ANALYSIS
:A PLANE TRUSS -- PAGE NO. 2
* FILE: TRUSS05.STD
18 — STAAD.Pro
1 Static Trusses
Static Truss 5
**WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE
MEMBERS/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 18 NUMBER OF MEMBERS 32
NUMBER OF PLATES 0 NUMBER OF SOLIDS 0
NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 3
SOLVER USED IS THE IN-CORE ADVANCED SOLVER
TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 32
35. PRINT SUPPORT REACTIONS
SUPPORT REACTION
:A PLANE TRUSS -- PAGE NO. 3
* FILE: TRUSS05.STD
SUPPORT REACTIONS -UNIT KIP INCH STRUCTURE TYPE = TRUSS
-----------------
JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z
1 1 0.00 -76.67 0.00 0.00 0.00 0.00
4 1 0.00 346.67 0.00 0.00 0.00 0.00
9 1 0.00 30.00 0.00 0.00 0.00 0.00
************** END OF LATEST ANALYSIS RESULT **************
36. FINISH
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= DEC 13,2013 TIME= 12:30:24 ****
:A PLANE TRUSS -- PAGE NO. 4
* FILE: TRUSS05.STD
************************************************************
* For technical assistance on STAAD.Pro, please visit *
* http://selectservices.bentley.com/en-US/ *
* *
* Details about additional assistance from *
* Bentley and Partners can be found at program menu *
* Help->Technical Support *
* *
* Copyright © 1997-2013 Bentley Systems, Inc.
* http://www.bentley.com *
************************************************************
Static Truss 6
Objective
To find support reactions due to joint loads in a plane truss.
Reference
McCormack, J.C., Structural Analysis, Intext Educational Publishers, 3rd Edition, 1975.
Problem
Find the vertical and horizontal reactions at the supports of the truss.
E = 30,000.0 ksi. A = 100 in2. Loads as shown.
1 Static Trusses
Verification Manual — 19
Figure 1-6: Plane truss
Comparison
Result Type Theory STAAD.Pro Difference
Horizontal, R1
34.3 34.29 none
Vertical, R1
11.5 11.49 none
Horizontal, R2
36.0 36.0 none
Vertical, R2
-31.7 -31.67 none
Table 1-7: Comparison of support reactions, in N, for static truss no. 6
STAAD Input
STAAD TRUSS :A PLANE TRUSS
* FILE TRUSS06.STD
*
* REFERENCE: MCCORMAC, J.C.,"STRUCTURAL ANALYSIS", INTEXT
* EDUCATIONAL PUBLISHERS, NEW YORK, 3RD EDITION, 1975.
*
INPUT WIDTH 72
UNIT FEET KIP
JOINT COORDINATES
1 0. 0. 0.; 2 0. 60. 0.; 3 12.5 60. 0.; 4 0. 15. 0.; 5 0. 30. 0.
6 0. 45. 0.; 7 9.375 45. 0.; 8 6.25 30. 0.; 9 3.125 15. 0.
10 50. 90. 0.; 11 100. 90. 0.; 12 50. 75. 0.; 13 25. 75. 0.
14 66.667 90. 0.; 15 83.333 90. 0.; 16 83.333 85. 0.; 17 66.667 80. 0.
18 31.25 67.5 0.; 19 200. 0. 0.; 20 200. 60. 0.; 21 187.5 60. 0.
22 200. 15. 0.; 23 200. 30. 0.; 24 200. 45. 0.; 25 190.625 45. 0.
26 193.75 30. 0.; 27 196.875 15. 0.; 28 150. 90. 0.; 29 150. 75. 0.
30 175. 75. 0.; 31 133.333 90. 0.; 32 116.667 90. 0.; 33 116.667 85. 0.
34 133.333 80. 0.; 35 168.75 67.5 0.
20 — STAAD.Pro
1 Static Trusses
Static Truss 6
MEMBER INCIDENCES
1 1 4; 2 2 3; 3 3 7; 4 4 5; 5 5 6; 6 6 2; 7 7 8; 8 8 9; 9 9 1; 10 4 9
11 9 5; 12 5 8; 13 8 6; 14 6 7; 15 7 2; 16 2 13; 17 10 14; 18 11 16
19 12 18; 20 13 10; 21 14 15; 22 15 11; 23 16 17; 24 17 12; 25 18 3
26 3 13; 27 13 18; 28 13 12; 29 12 10; 30 10 17; 31 17 14; 32 14 16
33 16 15; 34 19 22; 35 20 21; 36 21 25; 37 22 23; 38 23 24; 39 24 20
40 25 26; 41 26 27; 42 27 19; 43 22 27; 44 27 23; 45 23 26; 46 26 24
47 24 25; 48 25 20; 49 20 30; 50 28 31; 51 11 33; 52 29 35; 53 30 28
54 31 32; 55 32 11; 56 33 34; 57 34 29; 58 35 21; 59 21 30; 60 30 35
61 30 29; 62 29 28; 63 28 34; 64 34 31; 65 31 33; 66 33 32
UNIT INCHES KIP
MEMBER PROPERTY AMERICAN
1 TO 66 PRI AX 100.
CONSTANTS
E 30000. ALL
SUPPORTS
1 19 PINNED
UNIT FEET KIP
LOAD 1 JOINT LOADS AT SPECIFIC NODES
JOINT LOAD
11 14 15 31 32 FY -10.
10 28 FY -5.
4 TO 6 FX 4.
2 FX 2.0
2 10 FX 1.5435
13 FX 3.0870
2 10 FY -2.5725
13 FY -5.145
PERFORM ANALYSIS
PRINT SUPPORT REACTIONS
FINISH
STAAD Output
PAGE NO. 1
****************************************************
* *
* STAAD.Pro V8i SELECTseries5 *
* Version 20.07.10.41 *
* Proprietary Program of *
* Bentley Systems, Inc. *
* Date= DEC 13, 2013 *
* Time= 12:30:24 *
* *
* USER ID: Bentley Systems, Inc. *
****************************************************
1. STAAD TRUSS :A PLANE TRUSS
INPUT FILE: TRUSS06.STD
2. * FILE TRUSS06.STD
3. *
4. * REFERENCE: MCCORMAC, J.C.,"STRUCTURAL ANALYSIS", INTEXT
5. * EDUCATIONAL PUBLISHERS, NEW YORK, 3RD EDITION, 1975.
6. *
7. INPUT WIDTH 72
8. UNIT FEET KIP
9. JOINT COORDINATES
10. 1 0. 0. 0.; 2 0. 60. 0.; 3 12.5 60. 0.; 4 0. 15. 0.; 5 0. 30. 0.
11. 6 0. 45. 0.; 7 9.375 45. 0.; 8 6.25 30. 0.; 9 3.125 15. 0.
12. 10 50. 90. 0.; 11 100. 90. 0.; 12 50. 75. 0.; 13 25. 75. 0.
13. 14 66.667 90. 0.; 15 83.333 90. 0.; 16 83.333 85. 0.; 17 66.667 80. 0.
14. 18 31.25 67.5 0.; 19 200. 0. 0.; 20 200. 60. 0.; 21 187.5 60. 0.
15. 22 200. 15. 0.; 23 200. 30. 0.; 24 200. 45. 0.; 25 190.625 45. 0.
16. 26 193.75 30. 0.; 27 196.875 15. 0.; 28 150. 90. 0.; 29 150. 75. 0.
17. 30 175. 75. 0.; 31 133.333 90. 0.; 32 116.667 90. 0.; 33 116.667 85. 0.
1 Static Trusses
Verification Manual — 21
18. 34 133.333 80. 0.; 35 168.75 67.5 0.
19. MEMBER INCIDENCES
20. 1 1 4; 2 2 3; 3 3 7; 4 4 5; 5 5 6; 6 6 2; 7 7 8; 8 8 9; 9 9 1; 10 4 9
21. 11 9 5; 12 5 8; 13 8 6; 14 6 7; 15 7 2; 16 2 13; 17 10 14; 18 11 16
22. 19 12 18; 20 13 10; 21 14 15; 22 15 11; 23 16 17; 24 17 12; 25 18 3
23. 26 3 13; 27 13 18; 28 13 12; 29 12 10; 30 10 17; 31 17 14; 32 14 16
24. 33 16 15; 34 19 22; 35 20 21; 36 21 25; 37 22 23; 38 23 24; 39 24 20
25. 40 25 26; 41 26 27; 42 27 19; 43 22 27; 44 27 23; 45 23 26; 46 26 24
26. 47 24 25; 48 25 20; 49 20 30; 50 28 31; 51 11 33; 52 29 35; 53 30 28
27. 54 31 32; 55 32 11; 56 33 34; 57 34 29; 58 35 21; 59 21 30; 60 30 35
28. 61 30 29; 62 29 28; 63 28 34; 64 34 31; 65 31 33; 66 33 32
29. UNIT INCHES KIP
30. MEMBER PROPERTY AMERICAN
31. 1 TO 66 PRI AX 100.
32. CONSTANTS
33. E 30000. ALL
34. SUPPORTS
35. 1 19 PINNED
36. UNIT FEET KIP
37. LOAD 1 JOINT LOADS AT SPECIFIC NODES
38. JOINT LOAD
:A PLANE TRUSS -- PAGE NO. 2
* FILE TRUSS06.STD
39. 11 14 15 31 32 FY -10.
40. 10 28 FY -5.
41. 4 TO 6 FX 4.
42. 2 FX 2.0
43. 2 10 FX 1.5435
44. 13 FX 3.0870
45. 2 10 FY -2.5725
46. 13 FY -5.145
47. PERFORM ANALYSIS
**WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE
MEMBERS/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 35 NUMBER OF MEMBERS 66
NUMBER OF PLATES 0 NUMBER OF SOLIDS 0
NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2
SOLVER USED IS THE IN-CORE ADVANCED SOLVER
TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 66
48. PRINT SUPPORT REACTIONS
SUPPORT REACTION
:A PLANE TRUSS -- PAGE NO. 3
* FILE TRUSS06.STD
SUPPORT REACTIONS -UNIT KIP FEET STRUCTURE TYPE = TRUSS
-----------------
JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z
1 1 11.49 34.29 0.00 0.00 0.00 0.00
19 1 -31.67 36.00 0.00 0.00 0.00 0.00
************** END OF LATEST ANALYSIS RESULT **************
49. FINISH
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= DEC 13,2013 TIME= 12:30:27 ****
:A PLANE TRUSS -- PAGE NO. 4
* FILE TRUSS06.STD
************************************************************
* For technical assistance on STAAD.Pro, please visit *
22 — STAAD.Pro
1 Static Trusses
Static Truss 6
* http://selectservices.bentley.com/en-US/ *
* *
* Details about additional assistance from *
* Bentley and Partners can be found at program menu *
* Help->Technical Support *
* *
* Copyright © 1997-2013 Bentley Systems, Inc.
* http://www.bentley.com *
************************************************************
Plane Truss: Support Reactions Due to a Joint Load
Objective
To find the support reactions due to a joint load in a plane truss.
Reference
Timoshenko, S., Strength of Materials, Part 1, D. Van Nostrand Co., Inc., 3rd edition, 1956,  p.346,
problem 3.
Problem
Determine the horizontal reaction at support 4 of the system.
Figure 1-7: Plane truss
Comparison
Result Type Theory
STAAD
Basic Solver
STAAD
Advanced Solver
R4
8.77 8.77 8.77
Table 1-8: Comparison of Support Reaction, in kips, for verification problem
no. 1
1 Static Trusses
Verification Manual — 23
STAAD Input
STAAD TRUSS VERIFICATION PROBLEM NO. 1
*
* REFERENCE `STRENGTH OF MATERIALS' PART-1 BY S. TIMOSHENKO
* PAGE 346 PROBLEM NO. 3. THE ANSWER IS REACTION = 0.877P.
* THEREFORE IF P=10, REACTION = 8.77
*
UNITS INCH KIP
JOINT COORD
1 0. 0. ; 2 150. 100. ; 3 150. 50. ; 4 300. 0.
MEMBER INCI
1 1 2 ; 2 1 3 ; 3 2 3 ; 4 2 4 ; 5 3 4
MEMB PROP
1 4 PRIS AX 5.0 ; 2 5 PRIS AX 3.0 ; 3 PRIS AX 2
CONSTANT
E 30000. ALL
POISSON STEEL ALL
SUPPORT ; 1 4 PINNED
LOADING 1
JOINT LOAD ; 2 FY -10.
PERFORM ANALYSIS
PRINT REACTION
FINISH
STAAD Output
PAGE NO. 1
****************************************************
* *
* STAAD.Pro V8i SELECTseries5 *
* Version 20.07.10.41 *
* Proprietary Program of *
* Bentley Systems, Inc. *
* Date= DEC 13, 2013 *
* Time= 12:30:30 *
* *
* USER ID: Bentley Systems, Inc. *
****************************************************
1. STAAD TRUSS VERIFICATION PROBLEM NO. 1
INPUT FILE: VER01.STD
2. *
3. * REFERENCE `STRENGTH OF MATERIALS' PART-1 BY S. TIMOSHENKO
4. * PAGE 346 PROBLEM NO. 3. THE ANSWER IS REACTION = 0.877P.
5. * THEREFORE IF P=10, REACTION = 8.77
6. *
7. UNITS INCH KIP
8. JOINT COORD
9. 1 0. 0. ; 2 150. 100. ; 3 150. 50. ; 4 300. 0.
10. MEMBER INCI
11. 1 1 2 ; 2 1 3 ; 3 2 3 ; 4 2 4 ; 5 3 4
12. MEMB PROP
13. 1 4 PRIS AX 5.0 ; 2 5 PRIS AX 3.0 ; 3 PRIS AX 2
14. CONSTANT
15. E 30000. ALL
16. POISSON STEEL ALL
17. SUPPORT ; 1 4 PINNED
18. LOADING 1
19. JOINT LOAD ; 2 FY -10.
20. PERFORM ANALYSIS
P R O B L E M S T A T I S T I C S
-----------------------------------
24 — STAAD.Pro
1 Static Trusses
Static Truss 6
NUMBER OF JOINTS 4 NUMBER OF MEMBERS 5
NUMBER OF PLATES 0 NUMBER OF SOLIDS 0
NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2
SOLVER USED IS THE IN-CORE ADVANCED SOLVER
TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 4
VERIFICATION PROBLEM NO. 1 -- PAGE NO. 2
*
21. PRINT REACTION
REACTION
VERIFICATION PROBLEM NO. 1 -- PAGE NO. 3
*
SUPPORT REACTIONS -UNIT KIP INCH STRUCTURE TYPE = TRUSS
-----------------
JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z
1 1 8.77 5.00 0.00 0.00 0.00 0.00
4 1 -8.77 5.00 0.00 0.00 0.00 0.00
************** END OF LATEST ANALYSIS RESULT **************
22. FINISH
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= DEC 13,2013 TIME= 12:30:33 ****
VERIFICATION PROBLEM NO. 1 -- PAGE NO. 4
*
************************************************************
* For technical assistance on STAAD.Pro, please visit *
* http://selectservices.bentley.com/en-US/ *
* *
* Details about additional assistance from *
* Bentley and Partners can be found at program menu *
* Help->Technical Support *
* *
* Copyright © 1997-2013 Bentley Systems, Inc.
* http://www.bentley.com *
************************************************************
Plane Truss Joint Deflection
Objective
To find the joint deflection due to joint loads in a plane truss.
Reference
McCormack, J. C., “Structural Analysis,” Intext Educational Publishers, 3rd edition, 1975, page 271,
example 18 - 2.
Problem
Determine the vertical deflection at point 5 of plane truss structure shown in the figure.
1 Static Trusses
Verification Manual — 25
Figure 1-8: Plane truss model
Given
P = 20 kip
Truss width = 4 spaces at 15 ft = 60 ft
Truss height = 15 ft
AX 1-4
= 1 in2, AX 5-6
= 2 in2, AX 7-8
=1.5 in2, 
AX 9-11B
= 3 in2P, AX 12-13
= 4 in2
E = 30E3 ksi
Comparison
Result Type Theory
STAAD
Basic Solver
STAAD
Advanced Solver
δ5
(in.) 2.63 2.63 2.63
Table 1-9: Comparison of deflection (δ) for verification problem no. 7
STAAD Input
STAAD TRUSS VERIFICATION PROBLEM NO. 7
*
* REFERENCE 'STRUCTURAL ANALYSIS' BY JACK McCORMACK, PAGE
* 271 EXAMPLE 18-2. ANSWER - Y-DISP AT JOINT 5 = 2.63 INCH
*
UNIT FT KIP
JOINT COORD
1 0 0 0 5 60 0 0
6 15. 7.5 ; 7 30. 15. ; 8 45. 7.5
MEMB INCI
1 2 6 ; 2 3 4 ; 3 4 8 ; 4 4 5 ; 5 1 2
6 2 3 ; 7 3 6 ; 8 3 8 ; 9 3 7
10 1 6 ; 11 5 8 ; 12 6 7 13
UNIT INCH
MEMB PROP
1 TO 4 PRI AX 1.0
26 — STAAD.Pro
1 Static Trusses
Static Truss 6
5 6 PRIS AX 2.
7 8 PRI AX 1.5
9 10 11 PRI AX 3.
12 13 PRI AX 4.
CONSTANT
E 30E3 ALL
POISSON STEEL ALL
SUPPORT
1 PINNED ; 3 FIXED BUT FX MZ
LOAD 1 VERTICAL LOAD
JOINT LOAD
2 4 5 FY -20.0
PERFORM ANALYSIS
PRINT DISPLACEMENTS
FINISH
STAAD Output
PAGE NO. 1
****************************************************
* *
* STAAD.Pro V8i SELECTseries5 *
* Version 20.07.10.41 *
* Proprietary Program of *
* Bentley Systems, Inc. *
* Date= DEC 13, 2013 *
* Time= 12:30:48 *
* *
* USER ID: Bentley Systems, Inc. *
****************************************************
1. STAAD TRUSS VERIFICATION PROBLEM NO. 7
INPUT FILE: VER07.STD
2. *
3. * REFERENCE 'STRUCTURAL ANALYSIS' BY JACK MCCORMACK, PAGE
4. * 271 EXAMPLE 18-2. ANSWER - Y-DISP AT JOINT 5 = 2.63 INCH
5. *
6. UNIT FT KIP
7. JOINT COORD
8. 1 0 0 0 5 60 0 0
9. 6 15. 7.5 ; 7 30. 15. ; 8 45. 7.5
10. MEMB INCI
11. 1 2 6 ; 2 3 4 ; 3 4 8 ; 4 4 5 ; 5 1 2
12. 6 2 3 ; 7 3 6 ; 8 3 8 ; 9 3 7
13. 10 1 6 ; 11 5 8 ; 12 6 7 13
14. UNIT INCH
15. MEMB PROP
16. 1 TO 4 PRI AX 1.0
17. 5 6 PRIS AX 2.
18. 7 8 PRI AX 1.5
19. 9 10 11 PRI AX 3.
20. 12 13 PRI AX 4.
21. CONSTANT
22. E 30E3 ALL
23. POISSON STEEL ALL
24. SUPPORT
25. 1 PINNED ; 3 FIXED BUT FX MZ
26. LOAD 1 VERTICAL LOAD
27. JOINT LOAD
28. 2 4 5 FY -20.0
29. PERFORM ANALYSIS
VERIFICATION PROBLEM NO. 7 -- PAGE NO. 2
*
P R O B L E M S T A T I S T I C S
1 Static Trusses
Verification Manual — 27
-----------------------------------
NUMBER OF JOINTS 8 NUMBER OF MEMBERS 13
NUMBER OF PLATES 0 NUMBER OF SOLIDS 0
NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2
SOLVER USED IS THE IN-CORE ADVANCED SOLVER
TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 13
30. PRINT DISPLACEMENTS
DISPLACE
VERIFICATION PROBLEM NO. 7 -- PAGE NO. 3
*
JOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = TRUSS
------------------
JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN
1 1 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
2 1 -0.12000 0.18000 0.00000 0.00000 0.00000 0.00000
3 1 -0.24000 0.00000 0.00000 0.00000 0.00000 0.00000
4 1 -0.48000 -0.89516 0.00000 0.00000 0.00000 0.00000
5 1 -0.72000 -2.63033 0.00000 0.00000 0.00000 0.00000
6 1 -0.00820 0.24000 0.00000 0.00000 0.00000 0.00000
7 1 0.29758 -0.12000 0.00000 0.00000 0.00000 0.00000
8 1 0.06578 -0.83516 0.00000 0.00000 0.00000 0.00000
************** END OF LATEST ANALYSIS RESULT **************
31. FINISH
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= DEC 13,2013 TIME= 12:30:51 ****
VERIFICATION PROBLEM NO. 7 -- PAGE NO. 4
*
************************************************************
* For technical assistance on STAAD.Pro, please visit *
* http://selectservices.bentley.com/en-US/ *
* *
* Details about additional assistance from *
* Bentley and Partners can be found at program menu *
* Help->Technical Support *
* *
* Copyright © 1997-2013 Bentley Systems, Inc.
* http://www.bentley.com *
************************************************************
Deflection and stress of a truss system
Objective
To find the joint deflection and member stress due to a joint load in a plane truss.
Reference
Timoshenko, S., Strength of Materials, Part 1, D. Van Nostrand Co., Inc., 3rd edition, 1956, page 10,
problem 2.
Problem
Determine the vertical deflection at point A and the member stresses
AX
= 0.5 in2
E = 30E6 psi
P = 5000 lbf
28 — STAAD.Pro
1 Static Trusses
Static Truss 6
L = 180 in.
angle = 30°
Figure 1-9: Model of two member truss
Comparison
Result Type Theory
STAAD
Basic Solver
STAAD
Advanced Solver
σA
(psi) 10,000. 10,000. 10,000.
δA
(in) 0.12 0.12 0.12
Table 1-10: Comparison of stress (σ) and Deflection (δ) for verification
problem 12
STAAD Input
STAAD TRUSS VERIFICATION PROBLEM NO 12
*
* THIS EXAMPLE IS TAKEN FROM 'STRENGTH OF MATERIALS'
* (PART 1) BY TIMOSHENKO, PAGE 10 PROB 2.
* THE ANSWER IN THE BOOK , DEFLECTION = 0.12 INCH
* AND STRESS =10000 PSI
*
UNIT INCH POUND
JOINT COORD
1 0. 0. ; 2 155.88457 -90. ; 3 311.76914 0.
MEMB INCI ; 1 1 2 2
MEMB PROP
1 2 PRIS AX 0.5
CONSTANT
E 30E6
POISSON 0.15 ALL
SUPPORT ; 1 3 PINNED
LOAD 1 VERT LOAD
JOINT LOAD ; 2 FY -5000.
PERFORM ANALYSIS
PRINT DISPLACEMENTS
PRINT STRESSES
FINISH
1 Static Trusses
Verification Manual — 29
STAAD Output
PAGE NO. 1
****************************************************
* *
* STAAD.Pro V8i SELECTseries5 *
* Version 20.07.10.41 *
* Proprietary Program of *
* Bentley Systems, Inc. *
* Date= DEC 13, 2013 *
* Time= 12:31: 4 *
* *
* USER ID: Bentley Systems, Inc. *
****************************************************
1. STAAD TRUSS VERIFICATION PROBLEM NO 12
INPUT FILE: VER12.STD
2. *
3. * THIS EXAMPLE IS TAKEN FROM 'STRENGTH OF MATERIALS'
4. * (PART 1) BY TIMOSHENKO, PAGE 10 PROB 2.
5. * THE ANSWER IN THE BOOK , DEFLECTION = 0.12 INCH
6. * AND STRESS =10000 PSI
7. *
8. UNIT INCH POUND
9. JOINT COORD
10. 1 0. 0. ; 2 155.88457 -90. ; 3 311.76914 0.
11. MEMB INCI ; 1 1 2 2
12. MEMB PROP
13. 1 2 PRIS AX 0.5
14. CONSTANT
15. E 30E6
16. POISSON 0.15 ALL
17. SUPPORT ; 1 3 PINNED
18. LOAD 1 VERT LOAD
19. JOINT LOAD ; 2 FY -5000.
20. PERFORM ANALYSIS
P R O B L E M S T A T I S T I C S
-----------------------------------
NUMBER OF JOINTS 3 NUMBER OF MEMBERS 2
NUMBER OF PLATES 0 NUMBER OF SOLIDS 0
NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2
SOLVER USED IS THE IN-CORE ADVANCED SOLVER
TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 2
VERIFICATION PROBLEM NO 12 -- PAGE NO. 2
*
21. PRINT DISPLACEMENTS
DISPLACE
VERIFICATION PROBLEM NO 12 -- PAGE NO. 3
*
JOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = TRUSS
------------------
JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN
1 1 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
2 1 0.00000 -0.12000 0.00000 0.00000 0.00000 0.00000
3 1 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
************** END OF LATEST ANALYSIS RESULT **************
22. PRINT STRESSES
STRESSES
30 — STAAD.Pro
1 Static Trusses
Static Truss 6
VERIFICATION PROBLEM NO 12 -- PAGE NO. 4
*
MEMBER STRESSES
---------------
ALL UNITS ARE POUN/SQ INCH
MEMB 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 0.0
1.0 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 0.0
1.0 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 ***********
**** DATE= DEC 13,2013 TIME= 12:31: 6 ****
VERIFICATION PROBLEM NO 12 -- PAGE NO. 5
*
************************************************************
* For technical assistance on STAAD.Pro, please visit *
* http://selectservices.bentley.com/en-US/ *
* *
* Details about additional assistance from *
* Bentley and Partners can be found at program menu *
* Help->Technical Support *
* *
* Copyright © 1997-2013 Bentley Systems, Inc.
* http://www.bentley.com *
************************************************************
Static Truss 7
Objective
To find member forces due to a thermal load in a plane truss.
Reference
Gere J. M., and Timoshenko, S. P., Mechanics of Materials, 2nd Edition, PWS Engineering, p.21,
Problem 2.6 - 23.
Problem
A symmetric, three-bar truss ABCD undergoes a temperature increase of 20°C in the two outer
bars and 70°C in the middle bar. Calculate the forces F1
and F2
in the bars.
E = 200 GPa
α = 14( 10)-6 / °C
A = 900 mm2
1 Static Trusses
Verification Manual — 31
Figure 1-10: Plane truss subject to differential thermal loading
Comparison
Result Type Theory STAAD.Pro Difference
F1
22,100 22,143 0.2% (negligible)
F2
-31,300 -31,315 0.1% (negligible)
Table 1-11: Comparison of member forces, in N, for static truss no. 7
STAAD Input
STAAD TRUSS :A PLANE TRUSS
* FILE: TRUSS10.STD
* REFERENCE: MECHANICS OF MATERIALS, GERE AND TIMOSHENKO, 2ND EDITION
* PWS ENGINEERING, PAGE 121, PROBLEM 2.6-23
*
UNITS NEWTON METER
JOINT COORDINATES
1 -2.12132 2.12132
2 0.0 2.12132
3 2.12132 2.12132
4 0.0 0.0
*
MEMBER INCIDENCES
1 1 4
2 2 4
3 3 4
UNIT NEWTON MMS
MEMBER PROPERTIES
1 TO 3 PRI AX 900
UNIT NEWTON METER
CONSTANTS
E 200.0E9 ALL
ALPHA 14.0E-6 ALL
32 — STAAD.Pro
1 Static Trusses
Static Truss 7
*
SUPPORTS
1 2 3 PINNED
*
LOADING 1 TEMPERATURE LOAD
TEMPERATURE LOAD
1 3 TEMP 20 800
2 TEMP 70
PERFORM ANALYSIS
PRINT MEMBER FORCES
FINISH
STAAD Output
PAGE NO. 1
****************************************************
* *
* STAAD.Pro V8i SELECTseries5 *
* Version 20.07.10.41 *
* Proprietary Program of *
* Bentley Systems, Inc. *
* Date= DEC 13, 2013 *
* Time= 12:30:27 *
* *
* USER ID: Bentley Systems, Inc. *
****************************************************
1. STAAD TRUSS :A PLANE TRUSS
INPUT FILE: TRUSS07.STD
2. * FILE: TRUSS10.STD
3. * REFERENCE: MECHANICS OF MATERIALS, GERE AND TIMOSHENKO, 2ND EDITION
4. * PWS ENGINEERING, PAGE 121, PROBLEM 2.6-23
5. *
6. UNITS NEWTON METER
7. JOINT COORDINATES
8. 1 -2.12132 2.12132
9. 2 0.0 2.12132
10. 3 2.12132 2.12132
11. 4 0.0 0.0
12. *
13. MEMBER INCIDENCES
14. 1 1 4
15. 2 2 4
16. 3 3 4
17. UNIT NEWTON MMS
18. MEMBER PROPERTIES
19. 1 TO 3 PRI AX 900
20. UNIT NEWTON METER
21. CONSTANTS
22. E 200.0E9 ALL
23. ALPHA 14.0E-6 ALL
24. *
25. SUPPORTS
26. 1 2 3 PINNED
27. *
28. LOADING 1 TEMPERATURE LOAD
29. TEMPERATURE LOAD
30. 1 3 TEMP 20 800
31. 2 TEMP 70
32. PERFORM ANALYSIS
:A PLANE TRUSS -- PAGE NO. 2
* FILE: TRUSS10.STD
**WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE
MEMBERS/ELEMENTS/SOLIDS. THE DEFAULT VALUE HAS BEEN SET FOR THE SAME.
1 Static Trusses
Verification Manual — 33
P R O B L E M S T A T I S T I C S
-----------------------------------
NUMBER OF JOINTS 4 NUMBER OF MEMBERS 3
NUMBER OF PLATES 0 NUMBER OF SOLIDS 0
NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 3
SOLVER USED IS THE IN-CORE ADVANCED SOLVER
TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 2
33. PRINT MEMBER FORCES
MEMBER FORCES
:A PLANE TRUSS -- PAGE NO. 3
* FILE: TRUSS10.STD
MEMBER END FORCES STRUCTURE TYPE = TRUSS
-----------------
ALL UNITS ARE -- NEWT METE (LOCAL )
MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z
1 1 1 -22142.72 0.00 0.00 0.00 0.00 0.00
4 22142.72 0.00 0.00 0.00 0.00 0.00
2 1 2 31314.54 0.00 0.00 0.00 0.00 0.00
4 -31314.54 0.00 0.00 0.00 0.00 0.00
3 1 3 -22142.72 0.00 0.00 0.00 0.00 0.00
4 22142.72 0.00 0.00 0.00 0.00 0.00
************** END OF LATEST ANALYSIS RESULT **************
34. FINISH
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= DEC 13,2013 TIME= 12:30:30 ****
:A PLANE TRUSS -- PAGE NO. 4
* FILE: TRUSS10.STD
************************************************************
* For technical assistance on STAAD.Pro, please visit *
* http://selectservices.bentley.com/en-US/ *
* *
* Details about additional assistance from *
* Bentley and Partners can be found at program menu *
* Help->Technical Support *
* *
* Copyright © 1997-2013 Bentley Systems, Inc.
* http://www.bentley.com *
************************************************************
34 — STAAD.Pro
1 Static Trusses
Static Truss 7
2
Static Beams
Static Beam 1 35
Static Beam 2 39
Static Beam 3 43
Static Beam 4 47
Static Beam 5 53
Static Beam 6 56
Static Beam 7 59
Static Beam 8 62
Static Beam 9 65
Static Beam 11 72
Static Beam 12 75
Static Beam 13 78
Static Beam 15 87
Static Beam 1
Objective
To find the deflection and support reactions due to a trapezoidally varying load applied on part
of the span of a pinned-fixed beam.
Reference
Hand calculation using the following reference:
Roark's Formulas for Stress and Strain, Warren C. Young, 6th edition, McGraw-Hill, Table 3, Case
(2c), p.103
Problem
The beam in the following geometric, load, and section properties: a = 3 m, b =4.5 m, wa
= 4
KN/m, wl
= 7 KN/m, IZ
=5,000 cm4, E = 200 KN/mm2.
Verification Manual — 35
Figure 2-1: Simple supported beam with partial, trapezoidal load
Comparison
Result Type Theory STAAD.Pro Difference
OA
(radians) 0.0020 0.0020 none
RA
(kN) 3.2886 3.2886 none
RB
(kN) 21.461 21.461 none
MB
(kN·m) 25.9605 25.9605 none
Table 2-1: Comparison of results for static beam no. 1
Where
RA
= Vertical reaction at A
OA
= Rotation at A
RB
= Vertical reaction at B
MB
= Moment at B
Note: In the STAAD model, two load cases are used. In case 1, the load is applied using the
"MEMBER LOAD - TRAP" option. In case 2, the load is applied using a combination of
"MEMBER LOAD - UNI" and "MEMBER LOAD - LIN" options. Both cases yield identical results.
Theoretical Solution
( ) ( )
R l a l a l a l a
= ( − ) 3 + + ( − ) 4 +
A
W
l
W W
l
8
3 −
40
3
a l a
3 3
( ) ( )
O l a l a l a l a
= ( − ) + 3 − ( − ) 2 + 3
A
W
EIl
W W
EIl
−
48
3 −
240
3
a l a
( )
R l a R
= − −
B
W W
A
−
2
a l
M R l l a l a
= − ( − ) − ( − )
B A
W W W
2
2 −
6
2
a l a
Where
l = a + b
36 — STAAD.Pro
2 Static Beams
Static Beam 1
STAAD Input
STAAD PLANE REACTIONS AND DISPLACEMENTS OF A PINNED-FIXED BEAM
*
* FILE : BEAM01.STD
*
* REFERENCE : ROARK'S FORMULAS FOR STRESS &amp; STRAIN
* WARREN C. YOUNG, 6TH EDITION, MCGRAW-HILL
*
* TABLE 3, CASE (2C), LOAD ON PARTIAL SPAN
*
UNIT KNS METER
JOINT COORD
1 0 0 0 ; 2 3 0 0 ; 3 7.5 0 0
*
MEMBER INCI
1 1 2 2
*
UNIT CMS
MEMBER PROP
1 2 PRIS AX 50 IZ 5000
*
UNIT METER
CONSTANT
E 200E6 ALL
POISS STEEL ALL
*
SUPPORT
1 PINNED
3 FIXED
*
LOAD 1
MEMBER LOAD
2 TRAP GY -4.0 -7.0
*
LOAD 2
MEMBER LOAD
2 UNI GY -4
2 LIN GY 0 -3
*
PERFORM ANALYSIS
*
PRINT JOINT DISP
*
UNIT NEWTON
PRINT SUPP REAC
FINISH
STAAD Output
PAGE NO. 1
****************************************************
* *
* STAAD.Pro V8i SELECTseries5 *
* Version 20.07.10.41 *
* Proprietary Program of *
* Bentley Systems, Inc. *
* Date= DEC 13, 2013 *
* Time= 12:27:32 *
* *
* USER ID: Bentley Systems, Inc. *
****************************************************
1. STAAD PLANE REACTIONS AND DISPLACEMENTS OF A PINNED-FIXED BEAM
2 Static Beams
Verification Manual — 37
INPUT FILE: BEAM01.STD
2. *
3. * FILE : BEAM01.STD
4. *
5. * REFERENCE : ROARK'S FORMULAS FOR STRESS &AMP; STRAIN
6. * WARREN C. YOUNG, 6TH EDITION, MCGRAW-HILL
7. *
8. * TABLE 3, CASE (2C), LOAD ON PARTIAL SPAN
9. *
10. UNIT KNS METER
11. JOINT COORD
12. 1 0 0 0 ; 2 3 0 0 ; 3 7.5 0 0
13. *
14. MEMBER INCI
15. 1 1 2 2
16. *
17. UNIT CMS
18. MEMBER PROP
19. 1 2 PRIS AX 50 IZ 5000
20. *
21. UNIT METER
22. CONSTANT
23. E 200E6 ALL
24. POISS STEEL ALL
25. *
26. SUPPORT
27. 1 PINNED
28. 3 FIXED
29. *
30. LOAD 1
31. MEMBER LOAD
32. 2 TRAP GY -4.0 -7.0
33. *
34. LOAD 2
35. MEMBER LOAD
36. 2 UNI GY -4
37. 2 LIN GY 0 -3
38. *
REACTIONS AND DISPLACEMENTS OF A PINNED-FIXED BEAM -- PAGE NO. 2
*
39. PERFORM ANALYSIS
P R O B L E M S T A T I S T I C S
-----------------------------------
NUMBER OF JOINTS 3 NUMBER OF MEMBERS 2
NUMBER OF PLATES 0 NUMBER OF SOLIDS 0
NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2
SOLVER USED IS THE IN-CORE ADVANCED SOLVER
TOTAL PRIMARY LOAD CASES = 2, TOTAL DEGREES OF FREEDOM = 4
40. *
41. PRINT JOINT DISP
JOINT DISP
REACTIONS AND DISPLACEMENTS OF A PINNED-FIXED BEAM -- PAGE NO. 3
*
JOINT DISPLACEMENT (CM RADIANS) STRUCTURE TYPE = PLANE
------------------
JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN
1 1 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0020
2 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0020
2 1 0.0000 -0.4626 0.0000 0.0000 0.0000 -0.0006
2 0.0000 -0.4626 0.0000 0.0000 0.0000 -0.0006
38 — STAAD.Pro
2 Static Beams
Static Beam 1
3 1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
************** END OF LATEST ANALYSIS RESULT **************
42. *
43. UNIT NEWTON
44. PRINT SUPP REAC
SUPP REAC
REACTIONS AND DISPLACEMENTS OF A PINNED-FIXED BEAM -- PAGE NO. 4
*
SUPPORT REACTIONS -UNIT NEWT METE STRUCTURE TYPE = PLANE
-----------------
JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z
1 1 0.00 3288.60 0.00 0.00 0.00 0.00
2 0.00 3288.60 0.00 0.00 0.00 0.00
3 1 0.00 21461.40 0.00 0.00 0.00 -25960.50
2 0.00 21461.40 0.00 0.00 0.00 -25960.50
************** END OF LATEST ANALYSIS RESULT **************
45. FINISH
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= DEC 13,2013 TIME= 12:27:35 ****
REACTIONS AND DISPLACEMENTS OF A PINNED-FIXED BEAM -- PAGE NO. 5
*
************************************************************
* For technical assistance on STAAD.Pro, please visit *
* http://selectservices.bentley.com/en-US/ *
* *
* Details about additional assistance from *
* Bentley and Partners can be found at program menu *
* Help->Technical Support *
* *
* Copyright © 1997-2013 Bentley Systems, Inc.
* http://www.bentley.com *
************************************************************
Static Beam 2
Objective
To find the support reactions due to a temperature loads applied on a fixed-fixed beam.
Reference
Hand calculation using the following reference:
Matrix Analysis of Framed Structures, 3rd edition, W.Weaver Jr. & J.M.Gere, Van Nostrand Reinhold,
Table B2, Appendix B, p.500
Problem
The beam in the following geometric, load, and section properties: L = 7.5 m, T = 40° F, T2
, T1
=
50° F, α = 11.7(10)-6/°F, d = 30 cm, IZ
= 5,000 cm4, E =200 KN/mm2.
2 Static Beams
Verification Manual — 39
Figure 2-2: Fixed support beam with temperature load
Comparison
Result Type Theory STAAD.Pro Difference
Horizontal Reaction at Node A (kN) 468 468 none
Moment at Node A (kN·m) 19.5 19.5 none
Table 2-2: Comparison of results for static beam no. 1
Note: In the STAAD model, two load cases are used. In case 1, the uniform expansion is
applied. In case 2, the temperature change between top and bottom flanges is applied.
Theoretical Solution
Horizontal reactions due to case 1 loads:
RA
= - RB
= EAαΔT = [200(10)6]· [50(10)-4]· [11.7(10)-6]· (40) = 468 kN
Moment reactions due to case 2 loads:
⋅






⋅





⋅




( )
M M kN m
= − = = = 19.5
A B
αEI T
d
∆
11.7(10) 200(10) 5, 000(10) 50
0.3
−6 −6 −8
STAAD Input
STAAD PLANE TEMPERATURE LOAD ON A FIXED-FIXED BEAM
*
* FILE : BEAM02.STD
*
* REFERENCE : MATRIX ANALYSIS OF FRAMED STRUCTURES
* GERE &amp; WEAVER, 3RD EDITION, VAN NOSTRAND REINHOLD
*
* TABLE B-2, APPENDIX B, PAGE 500
*
UNIT KNS METER
40 — STAAD.Pro
2 Static Beams
Static Beam 2
JOINT COORD
1 0 0 0 ; 2 3 0 0 ; 3 7.5 0 0
*
MEMBER INCI
1 1 2 2
*
UNIT CMS
MEMBER PROP
1 2 PRIS AX 50 IZ 5000 YD 30
*
UNIT METER
CONSTANT
E 200E6 ALL
POISS STEEL ALL
ALPHA 11.7E-6 ALL
*
SUPPORT
1 FIXED
3 FIXED
*
LOAD 1
TEMPERATURE LOAD
1 2 TEMP 40
*
LOAD 2
TEMPERATURE LOAD
1 2 TEMP 0 50
*
PERFORM ANALYSIS
*
PRINT SUPP REAC
FINISH
STAAD Output
PAGE NO. 1
****************************************************
* *
* STAAD.Pro V8i SELECTseries5 *
* Version 20.07.10.41 *
* Proprietary Program of *
* Bentley Systems, Inc. *
* Date= DEC 13, 2013 *
* Time= 12:27:35 *
* *
* USER ID: Bentley Systems, Inc. *
****************************************************
1. STAAD PLANE TEMPERATURE LOAD ON A FIXED-FIXED BEAM
INPUT FILE: BEAM02.STD
2. *
3. * FILE : BEAM02.STD
4. *
5. * REFERENCE : MATRIX ANALYSIS OF FRAMED STRUCTURES
6. * GERE &AMP; WEAVER, 3RD EDITION, VAN NOSTRAND REINHOLD
7. *
8. * TABLE B-2, APPENDIX B, PAGE 500
9. *
10. UNIT KNS METER
11. JOINT COORD
12. 1 0 0 0 ; 2 3 0 0 ; 3 7.5 0 0
13. *
14. MEMBER INCI
15. 1 1 2 2
16. *
2 Static Beams
Verification Manual — 41
17. UNIT CMS
18. MEMBER PROP
19. 1 2 PRIS AX 50 IZ 5000 YD 30
20. *
21. UNIT METER
22. CONSTANT
23. E 200E6 ALL
24. POISS STEEL ALL
25. ALPHA 11.7E-6 ALL
26. *
27. SUPPORT
28. 1 FIXED
29. 3 FIXED
30. *
31. LOAD 1
32. TEMPERATURE LOAD
33. 1 2 TEMP 40
34. *
35. LOAD 2
36. TEMPERATURE LOAD
37. 1 2 TEMP 0 50
38. *
TEMPERATURE LOAD ON A FIXED-FIXED BEAM -- PAGE NO. 2
*
39. PERFORM ANALYSIS
P R O B L E M S T A T I S T I C S
-----------------------------------
NUMBER OF JOINTS 3 NUMBER OF MEMBERS 2
NUMBER OF PLATES 0 NUMBER OF SOLIDS 0
NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2
SOLVER USED IS THE IN-CORE ADVANCED SOLVER
TOTAL PRIMARY LOAD CASES = 2, TOTAL DEGREES OF FREEDOM = 3
40. *
41. PRINT SUPP REAC
SUPP REAC
TEMPERATURE LOAD ON A FIXED-FIXED BEAM -- PAGE NO. 3
*
SUPPORT REACTIONS -UNIT KNS METE STRUCTURE TYPE = PLANE
-----------------
JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z
1 1 468.00 0.00 0.00 0.00 0.00 0.00
2 0.00 0.00 0.00 0.00 0.00 -19.50
3 1 -468.00 0.00 0.00 0.00 0.00 0.00
2 0.00 0.00 0.00 0.00 0.00 19.50
************** END OF LATEST ANALYSIS RESULT **************
42. FINISH
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= DEC 13,2013 TIME= 12:27:38 ****
TEMPERATURE LOAD ON A FIXED-FIXED BEAM -- PAGE NO. 4
*
************************************************************
* For technical assistance on STAAD.Pro, please visit *
* http://selectservices.bentley.com/en-US/ *
* *
* Details about additional assistance from *
* Bentley and Partners can be found at program menu *
* Help->Technical Support *
* *
* Copyright © 1997-2013 Bentley Systems, Inc.
* http://www.bentley.com *
42 — STAAD.Pro
2 Static Beams
Static Beam 2
************************************************************
Static Beam 3
Objective
To find the twist at the free end of a hollow tapered shaft of uniform thickness.
Reference
Hand calculation using the following reference:
Mechanics of Materials, F.P.Beer & E.R.Johnston, 1981, McGraw-Hill Review Problem 3.120, Page
149.
Problem
The beam in the following figure which has the following geometric, load, and section properties:
L = 2 m, outside diameter at fixed end = 80 mm, outside diameter at free end = 40 mm, uniform
wall thickness of 10 mm, , IZ
= 5,000 cm4, E = 200 KN/mm2, T = 2.0 KNm, and Poisson's ratio =
0.3.
2 Static Beams
Verification Manual — 43
Figure 2-3: Cantilevered member with a tapered, hollow shaft cross section
Comparison
Result Type Theory STAAD.Pro Difference
Twist at free end (radians) 0.0751 0.0751 none
Table 2-3: Comparison of results for static beam no. 1
Theoretical Solution
According to the reference, the twist at the free end is
44 — STAAD.Pro
2 Static Beams
Static Beam 3






( )
Φ =
A
TL
πGt
C C
C C
4
+
A B
A B
2 2
where:
CA
= centerline radius at free end = 40 mm/2 - 10 mm/2 = 15 mm
CB
= center line radius at fixed end = 80 mm/2 - 10 mm/2 = 35 mm
G= = = 76.9
E
ν
kN mm
2(1 + )
200 /
2(1 + 0.3)
2






⋅
( )
Φ = = 0.0751 rad.
A
kN m m
π kN mm mm
mm mm
mm mm
2, 000 ×2, 000
4 × 76.9 / × 10
15 + 35
(15 ) (35 )
2 2 2
STAAD Input File
STAAD SPACE TORSION ON CONICAL SHAFT
*
* FILE : BEAM03.STD
*
* REFERENCE : MECHANICS OF MATERIALS, F.P.BEER &amp; E.R.JOHNSTON
* 1981, MCGRAW-HILL
*
* REVIEW PROBLEM 3.120, PAGE 149. TWIST AT FREE END SHOULD BE
* ABOUT 0.0751 RADIAN
*
UNIT KNS METER
JOINT COORD
1 0 0 0 ; 2 0 2 0
MEMBER INCI
1 1 2
UNIT MMS
MEMBER PROP
1 PRIS ROUND START 80 END 40 THICK 10
CONST
E 200 ALL
POISSON 0.3 ALL
SUPPORT
1 FIXED
UNIT KNS METER
LOAD 1
JOINT LOAD
2 MY 2.0
PERFORM ANALYSIS
PRINT JOINT DISP
FINISH
STAAD Output
PAGE NO. 1
****************************************************
* *
* STAAD.Pro V8i SELECTseries5 *
* Version 20.07.10.41 *
* Proprietary Program of *
* Bentley Systems, Inc. *
* Date= DEC 13, 2013 *
* Time= 12:27:38 *
* *
* USER ID: Bentley Systems, Inc. *
****************************************************
1. STAAD SPACE TORSION ON CONICAL SHAFT
2 Static Beams
Verification Manual — 45
INPUT FILE: BEAM03.STD
2. *
3. * FILE : BEAM03.STD
4. *
5. * REFERENCE : MECHANICS OF MATERIALS, F.P.BEER &AMP; E.R.JOHNSTON
6. * 1981, MCGRAW-HILL
7. *
8. * REVIEW PROBLEM 3.120, PAGE 149. TWIST AT FREE END SHOULD BE
9. * ABOUT 0.0751 RADIAN
10. *
11. UNIT KNS METER
12. JOINT COORD
13. 1 0 0 0 ; 2 0 2 0
14. MEMBER INCI
15. 1 1 2
16. UNIT MMS
17. MEMBER PROP
18. 1 PRIS ROUND START 80 END 40 THICK 10
19. CONST
20. E 200 ALL
21. POISSON 0.3 ALL
22. SUPPORT
23. 1 FIXED
24. UNIT KNS METER
25. LOAD 1
26. JOINT LOAD
27. 2 MY 2.0
28. PERFORM ANALYSIS
TORSION ON CONICAL SHAFT -- PAGE NO. 2
*
P R O B L E M S T A T I S T I C S
-----------------------------------
NUMBER OF JOINTS 2 NUMBER OF MEMBERS 1
NUMBER OF PLATES 0 NUMBER OF SOLIDS 0
NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 1
SOLVER USED IS THE IN-CORE ADVANCED SOLVER
TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 6
29. PRINT JOINT DISP
JOINT DISP
TORSION ON CONICAL SHAFT -- PAGE NO. 3
*
JOINT DISPLACEMENT (CM RADIANS) STRUCTURE TYPE = SPACE
------------------
JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN
1 1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
2 1 0.0000 0.0000 0.0000 0.0000 0.0751 0.0000
************** END OF LATEST ANALYSIS RESULT **************
30. FINISH
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= DEC 13,2013 TIME= 12:27:40 ****
TORSION ON CONICAL SHAFT -- PAGE NO. 4
*
************************************************************
* For technical assistance on STAAD.Pro, please visit *
* http://selectservices.bentley.com/en-US/ *
* *
* Details about additional assistance from *
* Bentley and Partners can be found at program menu *
* Help->Technical Support *
* *
46 — STAAD.Pro
2 Static Beams
Static Beam 3
* Copyright © 1997-2013 Bentley Systems, Inc.
* http://www.bentley.com *
************************************************************
Static Beam 4
Objective
To find the deflection and member forces due to an applied load on a propped cantilever beam
with a compression only support.
Reference
Hand calculation using the following reference:
Manual of Steel Construction, Load and Resistance Factor Design, Second Edition, American
Institute of Steel Construction, 1998, pp. 4-194, 4-197.
Problem
A cantilever beam with an end support capable of resisting only a compressive force is analyzed
for two concentrated loads at 0.6xL 1) +0.5 lb (up) and 2) -0.5 lb (down). E = 10(10)6 psi, width =
0.6 in, depth = 0.3 in. L = 4 ft.
Note: A dummy member is used to represent a compression only support
Figure 2-4: Cantilevered member with a compression only support
Comparison
Result Type Theory STAAD.Pro Difference
Load Case
1
Moment at fixed end (in-lb) -14.4 -14.4 none
Shear at fixed end (lb) 0.50 0.50 none
Deflection at load (.in) 0.295 0.295 none
Table 2-4: Comparison of results for static beam no. 1
2 Static Beams
Verification Manual — 47
Result Type Theory STAAD.Pro Difference
Load Case
2
Moment at fixed end (in-lb) 4.032 4.03 none
Shear at fixed end (lb) 0.284 0.28 1.4%
Deflection at load (.in) -0.040 -.0401 none
Theoretical Solution
Load Case 1: 
General solution equations found on p.2-121 of the reference.
M x b P b x lb x
( < ) = − ( − ) = −0.5 (28.8 − )
At the rigid support, M = 14.4 in-lb.
By inspection, fixed end shear is equal to load value = 0.50 lb.












x b x b
∆ < = 3 −
Px
EI
6
2
















( )( )
in in in
= 3 28.8 . − 28.8 . = 0.295 .
lb in
psi in
0.5 (28.8 .)
6 10, 000, 000 0.00135 .
2
4
Load Case 2:
General solution equations found on p.2-118 of the reference
















( )
R in in lb
= = 19.2 + 2 48 = 0.216 .
Pb a
lb in
in
1
+ 2 ℓ
2 ℓ
0.5 (48 .)
2(48 .)
2
3
2
3
R2
= P - R1
= 0.50lb - 0.216lb = 0.284lb.
Moment at rigid support:
M x b R x P x a
( < ) = (ℓ − ) − (ℓ − − )
1 lb in lb in in
= 0.216 (48 − 0) − 0.5 (48 − 0 − 19.2 ) = −4.032 in lb
Deflection at point of load:












x b x a a x
∆ < = 3ℓ − 3ℓ − 3 ℓ +
Pax
EI
−
12 ℓ
3 2 2 2
2
3
































( )
( )( )
in in in in in in in in
= 3(48 .) − 3(48 .) 28.8 − 3(19.2 .) 48 + (19.2 .) 28.8 = −0.040 .
lb in in
psi in in
−0.5 19.2 (28.8 )
12 10, 000, 000 0.00135 . (48 .)
3 2 2 2
3
4 3
STAAD Input File
STAAD PLANE :A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT
START JOB INFORMATION
ENGINEER DATE 06-Mar-12
END JOB INFORMATION
* FILE: BEAM04.STD
*
* STARDYNE VERIFICATION PROBLEM #16
*********************************************
* THE END SUPPORT IS TO BE DEFINED AS A *
* COMPRESSION ONLY SUPPORT. A DUMMY MEMBER,*
* #7, IS SET AS COMPRESSION ONLY TO MODEL *
* THIS. *
48 — STAAD.Pro
2 Static Beams
Static Beam 4
*********************************************
SET NL 2
***********************************************
* STAAD.Pro Generated Comment *
***********************************************
*1 0. 0. 0. 6 48.0 0. 0.
***********************************************
UNIT INCHES POUND
JOINT COORDINATES
1 0 0 0; 2 9.6 0 0; 3 19.2 0 0; 4 28.8 0 0; 5 38.4 0 0; 6 48 0 0;
7 48 -4 0;
*7 48. -.01 0.
***********************************************
* STAAD.Pro Generated Comment *
***********************************************
*1 1 2 6
************************************************
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 4 5; 5 5 6; 6 6 7;
MEMBER PROPERTY AMERICAN
1 TO 5 PRIS YD 0.3 ZD 0.6
*6 PRISMATIC YD 2.
6 PRIS YD 40
MEMBER COMPRESSION
6
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 1e+007
POISSON 0.33
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 FIXED
7 PINNED
LOAD 1 UPWARD
JOINT LOAD
4 FY 0.5
PERFORM ANALYSIS
PRINT MEMBER FORCES LIST 1 TO 5
PRINT JOINT DISPLACEMENTS LIST 1 TO 6
PRINT SUPPORT REACTION
CHANGE
LOAD 2 DOWNWARD
JOINT LOAD
4 FY -0.5
PERFORM ANALYSIS
PRINT SUPPORT REACTION
PRINT MEMBER FORCES LIST 1 TO 5
PRINT JOINT DISPLACEMENTS LIST 1 TO 6
FINISH
STAAD Output
PAGE NO. 1
****************************************************
* *
* STAAD.Pro V8i SELECTseries5 *
* Version 20.07.10.41 *
* Proprietary Program of *
* Bentley Systems, Inc. *
* Date= DEC 13, 2013 *
* Time= 12:27:41 *
* *
* USER ID: Bentley Systems, Inc. *
2 Static Beams
Verification Manual — 49
****************************************************
1. STAAD PLANE :A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT
INPUT FILE: BEAM04.STD
2. START JOB INFORMATION
3. ENGINEER DATE 06-MAR-12
4. END JOB INFORMATION
5. * FILE: BEAM04.STD
6. *
7. * STARDYNE VERIFICATION PROBLEM #16
8. *********************************************
9. * THE END SUPPORT IS TO BE DEFINED AS A *
10. * COMPRESSION ONLY SUPPORT. A DUMMY MEMBER,*
11. * #7, IS SET AS COMPRESSION ONLY TO MODEL *
12. * THIS. *
13. *********************************************
14. SET NL 2
15. ***********************************************
16. * STAAD.PRO GENERATED COMMENT *
17. ***********************************************
18. *1 0. 0. 0. 6 48.0 0. 0.
19. ***********************************************
20. UNIT INCHES POUND
21. JOINT COORDINATES
22. 1 0 0 0; 2 9.6 0 0; 3 19.2 0 0; 4 28.8 0 0; 5 38.4 0 0; 6 48 0 0
23. 7 48 -4 0
24. *7 48. -.01 0.
25. ***********************************************
26. * STAAD.PRO GENERATED COMMENT *
27. ***********************************************
28. *1 1 2 6
29. ************************************************
30. MEMBER INCIDENCES
31. 1 1 2; 2 2 3; 3 3 4; 4 4 5; 5 5 6; 6 6 7
32. MEMBER PROPERTY AMERICAN
33. 1 TO 5 PRIS YD 0.3 ZD 0.6
34. *6 PRISMATIC YD 2.
35. 6 PRIS YD 40
36. MEMBER COMPRESSION
37. 6
38. DEFINE MATERIAL START
:A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT -- PAGE NO. 2
39. ISOTROPIC MATERIAL1
40. E 1E+007
41. POISSON 0.33
42. END DEFINE MATERIAL
43. CONSTANTS
44. MATERIAL MATERIAL1 ALL
45. SUPPORTS
46. 1 FIXED
47. 7 PINNED
48. LOAD 1 UPWARD
49. JOINT LOAD
50. 4 FY 0.5
51. PERFORM ANALYSIS
P R O B L E M S T A T I S T I C S
-----------------------------------
NUMBER OF JOINTS 7 NUMBER OF MEMBERS 6
NUMBER OF PLATES 0 NUMBER OF SOLIDS 0
NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2
SOLVER USED IS THE IN-CORE ADVANCED SOLVER
TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 16
50 — STAAD.Pro
2 Static Beams
Static Beam 4
*WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 7 EQN.NO. 16
LOADS APPLIED OR DISTRIBUTED HERE FROM ELEMENTS WILL BE IGNORED.
THIS MAY BE DUE TO ALL MEMBERS AT THIS JOINT BEING RELEASED OR
EFFECTIVELY RELEASED IN THIS DIRECTION.
**START ITERATION NO. 2
*WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 7 EQN.NO. 16
LOADS APPLIED OR DISTRIBUTED HERE FROM ELEMENTS WILL BE IGNORED.
THIS MAY BE DUE TO ALL MEMBERS AT THIS JOINT BEING RELEASED OR
EFFECTIVELY RELEASED IN THIS DIRECTION.
**NOTE-Tension/Compression converged after 2 iterations, Case= 1
52. PRINT MEMBER FORCES LIST 1 TO 5
MEMBER FORCES LIST 1
:A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT -- PAGE NO. 3
MEMBER END FORCES STRUCTURE TYPE = PLANE
-----------------
ALL UNITS ARE -- POUN INCH (LOCAL )
MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z
1 1 1 0.00 -0.50 0.00 0.00 0.00 -14.40
2 0.00 0.50 0.00 0.00 0.00 9.60
2 1 2 0.00 -0.50 0.00 0.00 0.00 -9.60
3 0.00 0.50 0.00 0.00 0.00 4.80
3 1 3 0.00 -0.50 0.00 0.00 0.00 -4.80
4 0.00 0.50 0.00 0.00 0.00 0.00
4 1 4 0.00 0.00 0.00 0.00 0.00 0.00
5 0.00 0.00 0.00 0.00 0.00 0.00
5 1 5 0.00 0.00 0.00 0.00 0.00 0.00
6 0.00 0.00 0.00 0.00 0.00 0.00
************** END OF LATEST ANALYSIS RESULT **************
53. PRINT JOINT DISPLACEMENTS LIST 1 TO 6
JOINT DISPLACE LIST 1
:A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT -- PAGE NO. 4
JOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = PLANE
------------------
JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN
1 1 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
2 1 0.00000 0.04370 0.00000 0.00000 0.00000 0.00853
3 1 0.00000 0.15293 0.00000 0.00000 0.00000 0.01365
4 1 0.00000 0.29494 0.00000 0.00000 0.00000 0.01536
5 1 0.00000 0.44239 0.00000 0.00000 0.00000 0.01536
6 1 0.00000 0.58985 0.00000 0.00000 0.00000 0.01536
************** END OF LATEST ANALYSIS RESULT **************
54. PRINT SUPPORT REACTION
SUPPORT REACTION
:A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT -- PAGE NO. 5
SUPPORT REACTIONS -UNIT POUN INCH STRUCTURE TYPE = PLANE
-----------------
JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z
1 1 0.00 -0.50 0.00 0.00 0.00 -14.40
7 1 0.00 0.00 0.00 0.00 0.00 0.00
************** END OF LATEST ANALYSIS RESULT **************
55. CHANGE
56. LOAD 2 DOWNWARD
57. JOINT LOAD
58. 4 FY -0.5
59. PERFORM ANALYSIS
*WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 7 EQN.NO. 16
LOADS APPLIED OR DISTRIBUTED HERE FROM ELEMENTS WILL BE IGNORED.
THIS MAY BE DUE TO ALL MEMBERS AT THIS JOINT BEING RELEASED OR
EFFECTIVELY RELEASED IN THIS DIRECTION.
**NOTE-Tension/Compression converged after 1 iterations, Case= 2
2 Static Beams
Verification Manual — 51
60. PRINT SUPPORT REACTION
SUPPORT REACTION
:A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT -- PAGE NO. 6
SUPPORT REACTIONS -UNIT POUN INCH STRUCTURE TYPE = PLANE
-----------------
JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z
1 2 0.00 0.28 0.00 0.00 0.00 4.03
7 2 0.00 0.22 0.00 0.00 0.00 0.00
************** END OF LATEST ANALYSIS RESULT **************
61. PRINT MEMBER FORCES LIST 1 TO 5
MEMBER FORCES LIST 1
:A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT -- PAGE NO. 7
MEMBER END FORCES STRUCTURE TYPE = PLANE
-----------------
ALL UNITS ARE -- POUN INCH (LOCAL )
MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z
1 2 1 0.00 0.28 0.00 0.00 0.00 4.03
2 0.00 -0.28 0.00 0.00 0.00 -1.31
2 2 2 0.00 0.28 0.00 0.00 0.00 1.31
3 0.00 -0.28 0.00 0.00 0.00 1.42
3 2 3 0.00 0.28 0.00 0.00 0.00 -1.42
4 0.00 -0.28 0.00 0.00 0.00 4.15
4 2 4 0.00 -0.22 0.00 0.00 0.00 -4.15
5 0.00 0.22 0.00 0.00 0.00 2.07
5 2 5 0.00 -0.22 0.00 0.00 0.00 -2.07
6 0.00 0.22 0.00 0.00 0.00 0.00
************** END OF LATEST ANALYSIS RESULT **************
62. PRINT JOINT DISPLACEMENTS LIST 1 TO 6
JOINT DISPLACE LIST 1
:A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT -- PAGE NO. 8
JOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = PLANE
------------------
JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN
1 2 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
2 2 0.00000 -0.01066 0.00000 0.00000 0.00000 -0.00190
3 2 0.00000 -0.03024 0.00000 0.00000 0.00000 -0.00186
4 2 0.00000 -0.04012 0.00000 0.00000 0.00000 0.00012
5 2 0.00000 -0.02714 0.00000 0.00000 0.00000 0.00233
6 2 0.00000 0.00000 0.00000 0.00000 0.00000 0.00307
************** END OF LATEST ANALYSIS RESULT **************
63. FINISH
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= DEC 13,2013 TIME= 12:27:44 ****
:A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT -- PAGE NO. 9
************************************************************
* For technical assistance on STAAD.Pro, please visit *
* http://selectservices.bentley.com/en-US/ *
* *
* Details about additional assistance from *
* Bentley and Partners can be found at program menu *
* Help->Technical Support *
* *
* Copyright © 1997-2013 Bentley Systems, Inc.
* http://www.bentley.com *
************************************************************
52 — STAAD.Pro
2 Static Beams
Static Beam 4
Static Beam 5
Objective
To find end rotation due to torques on a stepped cantilever shaft.
Reference
Hand calculation using the following reference:
Gere J. M., and Timoshenko, S. P., Mechanics of Materials, 2nd Edition, PWS Engineering, Page 171,
Problem 3.3 - 1.
Problem
A stepped shaft is subjected to torques as shown in the figure. The material has shear modulus of
elasticity G = 80 Gpa. Determine the angle of twist θx
in degrees at the free end.
Figure 2-5: Cantilevered member subject to torsional loads
Comparison
Result Theory STAAD.Pro Difference
Angle of twist (rad.) 0.0427 0.0427 none
Table 2-5: Comparison of results for static beam no. 5
Theoretical Solution
Moment of Inertia:
I mm
= = 4.021(10)
p
π mm
1
(80 / 2)
2
6 4
4
I mm
= = 1.272(10)
p
π mm
2
(60 / 2)
2
6 4
4
I mm
= = 0.251(10)
p
π mm
2
(40 / 2)
2
6 4
4
2 Static Beams
Verification Manual — 53
Angle of twist is given by:
θ = ∑i
L T
GI
i i
p
= + +
mm
mm GPa
mm
mm GPa
mm
mm GPa
5, 800N-mm(500 )
4.021(10) 80
2, 800N-mm(500 )
1.272(10) 80
, 800N-mm(500 )
0.251(10) 80
6 4 6 4 6 4
= 0.0090 + 0.0138 + 0.0199 = 0.0427
which is equal to 2.446°.
STAAD Input File
STAAD SPACE :A STEPPED CANTILEVER SHAFT
* FILE: BEAM05.STD
*
* REFERENCE: MECHANICS OF MATERIALS, GERE AND TIMOSHENKO, 2ND EDITION
* PROBLEM 3.3-1 PAGE 171
*
UNIT KN METER
JOINT COORDINATES
1 0.0 0.0
2 0.5 0.0
3 1.0 0.0
4 1.5 0.0
MEMBER INCIDENCES
1 1 2 3
UNIT MMS
MEMBER PROPERTIES
1 TA ST PIPE OD 80 ID 0.0
2 TA ST PIPE OD 60 ID 0.0
3 TA ST PIPE OD 40 ID 0.0
UNIT METER
CONSTANTS
E 200.0E6 ALL
POISSONS .25 ALL
*
SUPPORTS
1 FIXED
UNIT MMS
LOADING 1 TORSIONAL MOMENT
JOINT LOADS
2 MX 3000.0
3 MX 2000.0
4 MX 800.0
PERFORM ANALYSIS
PRINT JOINT DISPLACEMENTS LIST 4
FINISH
STAAD Output
PAGE NO. 1
****************************************************
* *
* STAAD.Pro V8i SELECTseries5 *
* Version 20.07.10.41 *
* Proprietary Program of *
* Bentley Systems, Inc. *
* Date= DEC 13, 2013 *
* Time= 12:27:44 *
* *
* USER ID: Bentley Systems, Inc. *
****************************************************
1. STAAD SPACE :A STEPPED CANTILEVER SHAFT
INPUT FILE: BEAM05.STD
2. * FILE: BEAM05.STD
3. *
54 — STAAD.Pro
2 Static Beams
Static Beam 5
4. * REFERENCE: MECHANICS OF MATERIALS, GERE AND TIMOSHENKO, 2ND EDITION
5. * PROBLEM 3.3-1 PAGE 171
6. *
7. UNIT KN METER
8. JOINT COORDINATES
9. 1 0.0 0.0
10. 2 0.5 0.0
11. 3 1.0 0.0
12. 4 1.5 0.0
13. MEMBER INCIDENCES
14. 1 1 2 3
15. UNIT MMS
16. MEMBER PROPERTIES
17. 1 TA ST PIPE OD 80 ID 0.0
18. 2 TA ST PIPE OD 60 ID 0.0
19. 3 TA ST PIPE OD 40 ID 0.0
20. UNIT METER
21. CONSTANTS
22. E 200.0E6 ALL
23. POISSONS .25 ALL
24. *
25. SUPPORTS
26. 1 FIXED
27. UNIT MMS
28. LOADING 1 TORSIONAL MOMENT
29. JOINT LOADS
30. 2 MX 3000.0
31. 3 MX 2000.0
32. 4 MX 800.0
33. PERFORM ANALYSIS
:A STEPPED CANTILEVER SHAFT -- PAGE NO. 2
* FILE: BEAM05.STD
P R O B L E M S T A T I S T I C S
-----------------------------------
NUMBER OF JOINTS 4 NUMBER OF MEMBERS 3
NUMBER OF PLATES 0 NUMBER OF SOLIDS 0
NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 1
SOLVER USED IS THE IN-CORE ADVANCED SOLVER
TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 18
34. PRINT JOINT DISPLACEMENTS LIST 4
JOINT DISPLACE LIST 4
:A STEPPED CANTILEVER SHAFT -- PAGE NO. 3
* FILE: BEAM05.STD
JOINT DISPLACEMENT (CM RADIANS) STRUCTURE TYPE = SPACE
------------------
JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN
4 1 0.0000 0.0000 0.0000 0.0427 0.0000 0.0000
************** END OF LATEST ANALYSIS RESULT **************
35. FINISH
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= DEC 13,2013 TIME= 12:27:47 ****
:A STEPPED CANTILEVER SHAFT -- PAGE NO. 4
* FILE: BEAM05.STD
************************************************************
* For technical assistance on STAAD.Pro, please visit *
* http://selectservices.bentley.com/en-US/ *
* *
* Details about additional assistance from *
* Bentley and Partners can be found at program menu *
* Help->Technical Support *
2 Static Beams
Verification Manual — 55
* *
* Copyright © 1997-2013 Bentley Systems, Inc.
* http://www.bentley.com *
************************************************************
Static Beam 6
Objective
To find deflections, stress and support reactions due to a uniform load on a beam with one end
fixed and the other end supported by a roller.
Reference
Hand calculation using the following reference:
Roark, R.J., and Young, W.C., Formulas for Stress and Strain, 5th Edition, Page 109, Problem 23.
Problem
A horizontal beam of length 100 in, area 4 in2, height 2 in, and moment of inertia 1.3333 in4 is
simply supported at one end and fixed at the other end. The beam is subjected to a uniform
loading. Determine the deflection δ at x = 42.15 in., the slope θ at end A, the maximum bending
stress σbend
in the beam and the support reactions.
E = 30(10)6 psi
Density = 0.2821 lbs/in3
Figure 2-6: Beam A) problem sketch and B) mathematical model
56 — STAAD.Pro
2 Static Beams
Static Beam 6
Comparison
Result Theory STAAD.Pro Difference
Reaction at Node 1 (lb) 42.31 42.31 none
Reaction at Node 3 (lb) 70.52 70.52 none
Moment at Node 3 (in-lb) 1,410.4 1410.4 none
Bending Stress, σbend
at Node 2 (psi) 585.9 585.9 none
Rotation at Node 1 (rad.) -.000588 -.00059 none
Deflection at Node 2 (in.) -0.01528 -0.01528 none
Table 2-6: Comparison of results for static beam no. 5
STAAD Input File
STAAD PLANE :A FIXED-ROLLER BEAM
* FILE: BEAM06.STD
*
* REFERENCE: ROARK AND YOUNG, PAGE 109, NO. 23.
*
INPUT WIDTH 72
UNIT INCHES POUND
JOINT COORDINATES
1 0. 0. 0.; 2 42.15 0. 0.; 3 100. 0. 0.
MEMBER INCIDENCES
1 1 2; 2 2 3
MEMBER PROPERTY AMERICAN
1 2 PRI AX 4. IZ 1.3333 YD 2.
CONSTANTS
E 30000000. ALL
DENSITY 0.282072 ALL
SUPPORTS
3 FIXED
1 PINNED
LOAD 1 SELF WEIGHT
SELFWEIGHT Y -1.
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
PRINT MEMBER STRESSES ALL
FINISH
STAAD Output
PAGE NO. 1
****************************************************
* *
* STAAD.Pro V8i SELECTseries5 *
* Version 20.07.10.41 *
* Proprietary Program of *
* Bentley Systems, Inc. *
* Date= DEC 13, 2013 *
* Time= 12:27:48 *
* *
* USER ID: Bentley Systems, Inc. *
****************************************************
1. STAAD PLANE :A FIXED-ROLLER BEAM
INPUT FILE: BEAM06.STD
2 Static Beams
Verification Manual — 57
2. * FILE: BEAM06.STD
3. *
4. * REFERENCE: ROARK AND YOUNG, PAGE 109, NO. 23.
5. *
6. INPUT WIDTH 72
7. UNIT INCHES POUND
8. JOINT COORDINATES
9. 1 0. 0. 0.; 2 42.15 0. 0.; 3 100. 0. 0.
10. MEMBER INCIDENCES
11. 1 1 2; 2 2 3
12. MEMBER PROPERTY AMERICAN
13. 1 2 PRI AX 4. IZ 1.3333 YD 2.
14. CONSTANTS
15. E 30000000. ALL
16. DENSITY 0.282072 ALL
17. SUPPORTS
18. 3 FIXED
19. 1 PINNED
20. LOAD 1 SELF WEIGHT
21. SELFWEIGHT Y -1.
22. PERFORM ANALYSIS
**WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE
MEMBERS/ELEMENTS/SOLIDS. THE DEFAULT VALUE HAS BEEN SET FOR THE SAME.
:A FIXED-ROLLER BEAM -- PAGE NO. 2
* FILE: BEAM06.STD
P R O B L E M S T A T I S T I C S
-----------------------------------
NUMBER OF JOINTS 3 NUMBER OF MEMBERS 2
NUMBER OF PLATES 0 NUMBER OF SOLIDS 0
NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2
SOLVER USED IS THE IN-CORE ADVANCED SOLVER
TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 4
23. PRINT ANALYSIS RESULTS
ANALYSIS RESULTS
:A FIXED-ROLLER BEAM -- PAGE NO. 3
* FILE: BEAM06.STD
JOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = PLANE
------------------
JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN
1 1 0.00000 0.00000 0.00000 0.00000 0.00000 -0.00059
2 1 0.00000 -0.01528 0.00000 0.00000 0.00000 0.00000
3 1 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
:A FIXED-ROLLER BEAM -- PAGE NO. 4
* FILE: BEAM06.STD
SUPPORT REACTIONS -UNIT POUN INCH STRUCTURE TYPE = PLANE
-----------------
JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z
3 1 0.00 70.52 0.00 0.00 0.00 -1410.36
1 1 0.00 42.31 0.00 0.00 0.00 0.00
:A FIXED-ROLLER BEAM -- PAGE NO. 5
* FILE: BEAM06.STD
MEMBER END FORCES STRUCTURE TYPE = PLANE
-----------------
ALL UNITS ARE -- POUN INCH (LOCAL )
MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z
58 — STAAD.Pro
2 Static Beams
Static Beam 6
1 1 1 0.00 42.31 0.00 0.00 0.00 0.00
2 0.00 5.25 0.00 0.00 0.00 781.13
2 1 2 0.00 -5.25 0.00 0.00 0.00 -781.13
3 0.00 70.52 0.00 0.00 0.00 -1410.36
************** END OF LATEST ANALYSIS RESULT **************
24. PRINT MEMBER STRESSES ALL
MEMBER STRESSES ALL
:A FIXED-ROLLER BEAM -- PAGE NO. 6
* FILE: BEAM06.STD
MEMBER STRESSES
---------------
ALL UNITS ARE POUN/SQ INCH
MEMB LD SECT AXIAL BEND-Y BEND-Z COMBINED SHEAR-Y SHEAR-Z
1 1 .0 0.0 0.0 0.0 0.0 15.9 0.0
1.0 0.0 C 0.0 585.9 585.9 2.0 0.0
2 1 .0 0.0 0.0 585.9 585.9 2.0 0.0
1.0 0.0 C 0.0 1057.8 1057.8 26.4 0.0
************** END OF LATEST ANALYSIS RESULT **************
25. FINISH
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= DEC 13,2013 TIME= 12:27:50 ****
:A FIXED-ROLLER BEAM -- PAGE NO. 7
* FILE: BEAM06.STD
************************************************************
* For technical assistance on STAAD.Pro, please visit *
* http://selectservices.bentley.com/en-US/ *
* *
* Details about additional assistance from *
* Bentley and Partners can be found at program menu *
* Help->Technical Support *
* *
* Copyright © 1997-2013 Bentley Systems, Inc.
* http://www.bentley.com *
************************************************************
Static Beam 7
Objective
To find support reactions due to an axial load applied at two locations on a column with both
ends pinned.
Reference
Hand calculation using the following reference:
Timoshenko, S., Strength of Materials, Part I, D. Van Nostrand Co., Inc., 3rd Edition, 1956. Page 26,
Problem 10.
Problem
Find the support reactions at the end joints 1 and 4.
E = 30(10)6 psi
2 Static Beams
Verification Manual — 59
Figure 2-7: Column A) problem sketch and B) mathematical model
Comparison
Result Theory STAAD.Pro Difference
Reaction at Node 1 (lb) 600 600 none
Reaction at Node 4 (lb) 900 900 none
Table 2-7: Comparison of results for static beam no. 5
STAAD Input File
STAAD TRUSS :A PINNED-PINNED COLUMN
* FILE: BEAM07.STD
*
* REFERENCE: TIMOSHENKO, STRENGTH OF MATERIALS, PART 1
* PROBLEM 10, PAGE 26
*
INPUT WIDTH 79
UNIT INCHES POUND
JOINT COORDINATES
1 48.000 72.000 0.000
2 48.000 76.000 0.000
3 48.000 79.000 0.000
4 48.000 82.000 0.000
MEMBER INCIDENCES
60 — STAAD.Pro
2 Static Beams
Static Beam 7
1 1 2
2 2 3
3 3 4
MEMBER PROPERTY AMERICAN
1 TO 3 PRISMATIC AX 1.
CONSTANTS
E 30000000. ALL
SUPPORTS
1 4 PINNED
LOAD 1 AXIAL LOAD
JOINT LOAD
3 FY -1000.
2 FY -500.
PERFORM ANALYSIS
PRINT SUPPORT REACTIONS
FINISH
STAAD Output
PAGE NO. 1
****************************************************
* *
* STAAD.Pro V8i SELECTseries5 *
* Version 20.07.10.41 *
* Proprietary Program of *
* Bentley Systems, Inc. *
* Date= DEC 13, 2013 *
* Time= 12:27:51 *
* *
* USER ID: Bentley Systems, Inc. *
****************************************************
1. STAAD TRUSS :A PINNED-PINNED COLUMN
INPUT FILE: BEAM07.STD
2. * FILE: BEAM07.STD
3. *
4. * REFERENCE: TIMOSHENKO, STRENGTH OF MATERIALS, PART 1
5. * PROBLEM 10, PAGE 26
6. *
7. INPUT WIDTH 79
8. UNIT INCHES POUND
9. JOINT COORDINATES
10. 1 48.000 72.000 0.000
11. 2 48.000 76.000 0.000
12. 3 48.000 79.000 0.000
13. 4 48.000 82.000 0.000
14. MEMBER INCIDENCES
15. 1 1 2
16. 2 2 3
17. 3 3 4
18. MEMBER PROPERTY AMERICAN
19. 1 TO 3 PRISMATIC AX 1.
20. CONSTANTS
21. E 30000000. ALL
22. SUPPORTS
23. 1 4 PINNED
24. LOAD 1 AXIAL LOAD
25. JOINT LOAD
26. 3 FY -1000.
27. 2 FY -500.
28. PERFORM ANALYSIS
**WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE
MEMBERS/ELEMENTS/SOLIDS. THE DEFAULT VALUE HAS BEEN SET FOR THE SAME.
2 Static Beams
Verification Manual — 61
:A PINNED-PINNED COLUMN -- PAGE NO. 2
* FILE: BEAM07.STD
P R O B L E M S T A T I S T I C S
-----------------------------------
NUMBER OF JOINTS 4 NUMBER OF MEMBERS 3
NUMBER OF PLATES 0 NUMBER OF SOLIDS 0
NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2
SOLVER USED IS THE IN-CORE ADVANCED SOLVER
TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 4
*WARNING- ZERO STIFFNESS IN DIRECTION 1 AT JOINT 2 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 OR
EFFECTIVELY RELEASED IN THIS DIRECTION.
*WARNING- ZERO STIFFNESS IN DIRECTION 1 AT JOINT 3 EQN.NO. 3
29. PRINT SUPPORT REACTIONS
SUPPORT REACTION
:A PINNED-PINNED COLUMN -- PAGE NO. 3
* FILE: BEAM07.STD
SUPPORT REACTIONS -UNIT POUN INCH STRUCTURE TYPE = TRUSS
-----------------
JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z
1 1 0.00 600.00 0.00 0.00 0.00 0.00
4 1 0.00 900.00 0.00 0.00 0.00 0.00
************** END OF LATEST ANALYSIS RESULT **************
30. FINISH
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= DEC 13,2013 TIME= 12:27:54 ****
:A PINNED-PINNED COLUMN -- PAGE NO. 4
* FILE: BEAM07.STD
************************************************************
* For technical assistance on STAAD.Pro, please visit *
* http://selectservices.bentley.com/en-US/ *
* *
* Details about additional assistance from *
* Bentley and Partners can be found at program menu *
* Help->Technical Support *
* *
* Copyright © 1997-2013 Bentley Systems, Inc.
* http://www.bentley.com *
************************************************************
Static Beam 8
Objective
To find the stress due to an applied moment at the free end of a cantilever beam with inverted
tee section.
Reference
Hand calculation using the following reference:
Crandall, S.H., and Dahl, N.C., An Introduction to the Mechanics of Solids, McGraw-Hill, Inc., 1959,
Page 294, Problem 7.2..
62 — STAAD.Pro
2 Static Beams
Static Beam 8
Problem
Find the maximum bending stress in the beam.
E = 30(10)6 psi
b = 1.5 in., h = 8 in., L = 10 in.
M = 1,000,000 in. - lb.
Figure 2-8: Beam A) problem sketch and B) mathematical model
Comparison
Result Theory STAAD.Pro Difference
Bending stress, σ (psi) 700 700 none
Table 2-8: Comparison of results for static beam no. 5
STAAD Input File
STAAD PLANE :A CANTILEVERED BEAM OF INVERTED TEE SECTION
* FILE: BEAM08.STD
*
* REFERENCE: CRANDALL & DAHL, AN INTRODUCTION TO THE MECHANICS
* OF SOLIDS, PAGE294, EX. 7.2
*
INPUT WIDTH 79
UNIT INCHES POUND
JOINT COORDINATES
1 0.000 0.000 0.000
2 10.000 0.000 0.000
MEMBER INCIDENCES
1 1 2
MEMBER PROPERTY AMERICAN
1 PRISMATIC YD 20. ZD 9. YB 16. ZB 1.5
CONSTANTS
E 30000000. ALL
BETA 180. ALL
SUPPORTS
2 Static Beams
Verification Manual — 63
1 FIXED
LOAD 1 CONSTANT MOMENT
JOINT LOAD
2 MZ 100000.0
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
PRINT MEMBER STRESSES ALL
FINISH
STAAD Output
****************************************************
* *
* STAAD.Pro V8i SELECTseries3 *
* Version 20.07.08.20 *
* Proprietary Program of *
* Bentley Systems, Inc. *
* Date= MAR 6, 2012 *
* Time= 13:37:57 *
* *
* USER ID: Bentley Systems *
****************************************************
1. STAAD PLANE :A CANTILEVERED BEAM OF INVERTED TEE SECTION
INPUT FILE: beam8.STD
2. * FILE: BEAM08.STD
3. *
4. * REFERENCE: CRANDALL & DAHL, AN INTRODUCTION TO THE MECHANICS
5. * OF SOLIDS, PAGE294, EX. 7.2
6. *
7. INPUT WIDTH 79
8. UNIT INCHES POUND
9. JOINT COORDINATES
10. 1 0.000 0.000 0.000
11. 2 10.000 0.000 0.000
12. MEMBER INCIDENCES
13. 1 1 2
14. MEMBER PROPERTY AMERICAN
15. 1 PRISMATIC YD 20. ZD 9. YB 16. ZB 1.5
16. CONSTANTS
17. E 30000000. ALL
18. BETA 180. ALL
19. SUPPORTS
20. 1 FIXED
21. LOAD 1 CONSTANT MOMENT
22. JOINT LOAD
23. 2 MZ 100000.0
24. PERFORM ANALYSIS
**WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE
MEMBERS/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 = 2/ 1/ 1
SOLVER USED IS THE IN-CORE ADVANCED SOLVER
TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 3
25. PRINT MEMBER PROPERTIES ALL
MEMBER PROPERTIES. UNIT - INCH
-----------------
MEMB PROFILE AX/ IZ/ IY/ IX/
AY AZ SZ SY
1 PRISMATIC 60.00 2000.00 247.50 154.89
30.00 36.00 142.86 55.00
64 — STAAD.Pro
2 Static Beams
Static Beam 8
************ END OF DATA FROM INTERNAL STORAGE ************
26. PRINT MEMBER STRESSES ALL
MEMBER STRESSES
---------------
ALL UNITS ARE POUN/SQ INCH
MEMB LD SECT AXIAL BEND-Y BEND-Z COMBINED SHEAR-Y SHEAR-Z
1 1 .0 0.0 0.0 700.0 700.0 0.0 0.0
1.00 0.0 0.0 700.0 700.0 0.0 0.0
************** END OF LATEST ANALYSIS RESULT **************
27. FINISH
Static Beam 9
Objective
To find deflection and stress at the center due to a uniform, static load on a simply supported
beam on elastic foundation.
Reference
Hand calculation using the following reference:
Peterson, F.E., Elastic Analysis for Structural Engineering (EASE2), Example Problem Manual,
Engineering Analysis Corporation, Berkeley, CA, 1981.
Problem
Find the vertical deflection and bending stress at the center of the beam.Spacing between
E = 30(10)6 psi
b = 1.0 in., h = 7.114 in., L = 240 in.
wu
= 43.3 lb/in.
Figure 2-9: One-half beam for mathematical model
Comparison
Result Theory STAAD.Pro Difference
Bending stress, σ (psi) 18,052 18,053.29 none
Vertical deflection (in.) 1.0453 1.04549 none
Table 2-9: Comparison of results for static beam no. 5
2 Static Beams
Verification Manual — 65
STAAD Input File
STAAD SPACE :A SIMPLY SUPPORTED BEAM ON ELASTIC FOUNDATION
* FILE: BEAM09.STD
*
* REFERENCE: PETERSON, EASE2, EXAMPLE PROBLEM MANUAL
*
INPUT WIDTH 72
UNIT INCHES POUND
JOINT COORDINATES
1 0. 0. 0.; 2 0. 7.114 0.; 3 0. 0. 6.; 4 0. 7.114 6.; 5 0. 0. 12.
6 0. 7.114 12.; 7 0. 0. 18.; 8 0. 7.114 18.; 9 0. 0. 24.
10 0. 7.114 24.; 11 0. 0. 30.; 12 0. 7.114 30.; 13 0. 0. 36.
14 0. 7.114 36.; 15 0. 0. 42.; 16 0. 7.114 42.; 17 0. 0. 48.
18 0. 7.114 48.; 19 0. 0. 54.; 20 0. 7.114 54.; 21 0. 0. 60.
22 0. 7.114 60.; 23 0. 0. 66.; 24 0. 7.114 66.; 25 0. 0. 72.
26 0. 7.114 72.; 27 0. 0. 78.; 28 0. 7.114 78.; 29 0. 0. 84.
30 0. 7.114 84.; 31 0. 0. 90.; 32 0. 7.114 90.; 33 0. 0. 96.
34 0. 7.114 96.; 35 0. 0. 102.; 36 0. 7.114 102.; 37 0. 0. 108.
38 0. 7.114 108.; 39 0. 0. 114.; 40 0. 7.114 114.; 41 0. 0. 120.
42 0. 7.114 120.
ELEMENT INCIDENCES
1 1 2 4 3; 2 3 4 6 5; 3 5 6 8 7; 4 7 8 10 9; 5 9 10 12 11; 6 11 12 14 13
7 13 14 16 15; 8 15 16 18 17; 9 17 18 20 19; 10 19 20 22 21
11 21 22 24 23; 12 23 24 26 25; 13 25 26 28 27; 14 27 28 30 29
15 29 30 32 31; 16 31 32 34 33; 17 33 34 36 35; 18 35 36 38 37
19 37 38 40 39; 20 39 40 42 41
ELEMENT PROPERTY
1 TO 20 TH 1.
CONSTANTS
E 30000000. ALL
SUPPORTS
1 FIXED BUT KFY 78.125
41 FIXED BUT FZ MX
2 FIXED BUT FY
3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 -
39 FIXED BUT FZ MX KFY 156.25
LOAD 1 UNIFORM LOAD OF 43.4 LBS/IN
JOINT LOAD
4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 FY 260.4
2 42 FY 130.2
PERFORM ANALYSIS
PRINT JOINT DISPLACEMENTS LIST 1 2
PRINT ELEMENT JOINT STRESSES LIST 1 2
FINISH
STAAD Output
PAGE NO. 1
****************************************************
* *
* STAAD.Pro V8i SELECTseries5 *
* Version 20.07.10.41 *
* Proprietary Program of *
* Bentley Systems, Inc. *
* Date= DEC 13, 2013 *
* Time= 12:27:57 *
* *
* USER ID: Bentley Systems, Inc. *
****************************************************
1. STAAD SPACE :A SIMPLY SUPPORTED BEAM ON ELASTIC FOUNDATION
INPUT FILE: BEAM09.STD
2. * FILE: BEAM09.STD
66 — STAAD.Pro
2 Static Beams
Static Beam 9
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STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf
STAADPro_V8i_Verification_Manual.pdf

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STAADPro_V8i_Verification_Manual.pdf

  • 1. STAAD.Pro V8i (SELECTseries 5) Verification Manual Last Updated: Monday, January 06, 2014
  • 2. STAAD Verification Problems Release STAAD.Pro 20.07.10.41 Date last updated: 13 December 2013 Quality Assurance Program STAAD.Pro V8i (SELECTseries 5) is a suite of proprietary computer programs of Bentley Systems, Inc.. Although every effort has been made to ensure the correctness of these programs, Bentley Systems, Inc. will not accept responsibility for any mistake, error, or misrepresentation in or as a result of the usage of these programs. Notes on Comparisons In each verification problem, a table is used to summarize the numerical outputs from STAAD.Pro with a reference or hand calculations. A difference column presents the percent deviation from the reference, when a significant difference exists. The deviation is taken as the reference value minus the value determined by STAAD.Pro, divided by the reference value to express in percent of the reference. In this context, "significant" is take as larger than a 1% (one percent) difference. When a difference between 0.5% and 1% exists, then the difference is simply listed as "<1%". Otherwise, the difference is listed as "none". This level of significance is intended to reflect that small differences in rounding or calculation methods do not present a realistic difference in the calculated result. Verification Manual — 2
  • 3. Table of Contents 1 Static Trusses 1 Static Truss 1 1 Static Truss 2 4 Static Truss 3 8 Static Truss 4 12 Static Truss 5 16 Static Truss 6 19 Static Truss 7 31 2 Static Beams 35 Static Beam 1 35 Static Beam 2 39 Static Beam 3 43 Static Beam 4 47 Static Beam 5 53 Static Beam 6 56 Static Beam 7 59 Static Beam 8 62 Static Beam 9 65 Static Beam 11 72 Static Beam 12 75 Static Beam 13 78 Static Beam 15 87 3 Static Frames 91 Static Frame 1 91 Static Frame 2 95 Static Frame 3 99 Static Frame 4 102 Static Frame 5 108 Static Frame 10 123 Static Frame 11 127 Static Frame 12 131 4 Static Plate/Shell Elements 139 Verification Manual — 3
  • 4. Static Element 1 139 Static Element 2 152 Static Element 3 156 Static Element 4 160 Static Element 5 165 Static Element 6 173 Static Element 7 180 Static Element 8 183 Static Element 9 193 Static Element 10 197 Static Element 11 204 Static Element 12 208 Static Element 13 211 Static Element 14 216 Static Element 15 221 Static Element 16 237 Static Element 17 242 5 Solid Elements 249 Static Solid 1 249 Static Solid 2 253 6 Nonlinear Static Analysis 263 Static Nonlinear 1 263 7 Dynamic Analysis 269 Dynamic Truss 1 269 Dynamic Beam 1 272 Dynamic Beam 2 276 Dynamic Beam 3 278 Dynamic Beam 4 281 Dynamic Beam 7 287 8 Concrete Design - ACI 318 291 Concrete Design per ACI 318 1 291 Concrete Design per ACI 318 3 296 Concrete Design per ACI 318 4 300 Concrete Design per ACI 318 5 303 4 — STAAD.Pro
  • 5. 9 Steel Design - AISC 360-10 307 Steel Design per AISC 360-10 - Example E-2 307 Steel Design per AISC 360-10 - Example G-6 313 Steel Design per AISC 360-10 - Example D-2 319 Steel Design per AISC 360-10 - Example F.2-2 326 Steel Design per AISC 360-10 - Example H.1B 332 Steel Design per AISC 360-10 - Example E.5 339 Steel Design per AISC 360-10 - Example F.1-3B 345 10 Steel Design per AISC ASD 353 Steel Design per AISC ASD 1 353 Steel Design per AISC ASD 2 357 Steel Design per AISC ASD 3 360 Steel Design per AISC ASD 4 363 Steel Design per AISC ASD 5 366 Steel Design per AISC ASD 6 369 Steel Design per AISC ASD 7 372 Steel Design per AISC ASD 8 375 Steel Design per AISC ASD 9 378 Steel Design per AISC ASD 10 381 Steel Design per AISC ASD 11 385 Steel Design per AISC ASD 12 388 Steel Design per AISC ASD 13 391 Steel Design per AISC ASD 14 394 Steel Design per AISC ASD 15 397 Steel Design per AISC ASD 16 401 Steel Design per AISC ASD 17 404 Steel Design per AISC ASD 18 409 11 Steel Design per AISC LRFD 413 Steel Design per AISC LRFD 1 414 Steel Design per AISC LRFD 2 416 Steel Design per AISC LRFD 3 419 Steel Design per AISC LRFD 4 422 Steel Design per AISC LRFD 5 424 Steel Design per AISC LRFD 6 427 Verification Manual — 5
  • 6. Steel Design per AISC LRFD 7 430 Steel Design per AISC LRFD 8 432 Steel Design per AISC LRFD 9 435 Steel Design per AISC LRFD 10 438 Steel Design per AISC LRFD 11 440 Steel Design per AISC LRFD 12 443 Steel Design per AISC LRFD 13 447 Steel Design per AISC LRFD 14 450 Steel Design per AISC LRFD 15 453 Steel Design per AISC LRFD 16 457 Steel Design per AISC LRFD 17 460 Steel Design per AISC LRFD 18 464 Steel Design per AISC LRFD 19 467 Steel Design per AISC LRFD 20 470 Steel Design per AISC LRFD 21 474 Steel Design per AISC LRFD 22 477 Steel Design per AISC LRFD 23 481 Steel Design per AISC LRFD 24 484 Steel Design per AISC LRFD 25 488 Steel Design per AISC LRFD 26 492 12 Steel Design per AS 4100-1998 497 Steel Design per AS 4100-1998 1 497 Steel Design per AS 4100-1998 2 502 Steel Design per AS 4100-1998 3 507 Steel Design per AS 4100-1998 4 510 13 Steel Design per BS 5950-1:2000 515 Steel Design per BS 5950-1:2000 1 515 Steel Design per BS 5950-1:2000 2 521 Steel Design per BS 5950-1:2000 3 528 Steel Design per BS 5950-1:2000 4 534 Steel Design per BS 5950-1:2000 5 540 Steel Design per BS 5950-1:2000 6 544 Steel Design per BS 5950-1:2000 7 547 6 — STAAD.Pro
  • 7. Copyright Information Trademark Notice Bentley, the "B" Bentley logo, STAAD.Pro are registered or nonregistered trademarks of Bentley Systems, Inc. or Bentley Software, Inc. All other marks are the property of their respective owners. Copyright Notice © 2013, Bentley Systems, Incorporated. All Rights Reserved. Including software, file formats, and audiovisual displays; may only be used pursuant to applicable software 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 may not be provided or otherwise made available without proper authorization. Acknowledgments Windows, Vista, SQL Server, MSDE, .NET, DirectX are registered trademarks of Microsoft Corporation. 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 Systems Incorporated. Restricted Rights Legends If this software is acquired for or on behalf of the United States of America, its agencies and/or instrumentalities ("U.S. Government"), it is provided with restricted rights. This software and accompanying documentation are "commercial computer software" and "commercial computer software documentation," respectively, pursuant to 48 C.F.R. 12.212 and 227.7202, and "restricted computer 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 accompanying documentation by the U.S. Government are subject to restrictions as set forth in this Agreement and 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 International treaties. End User License Agreement To view the End User License Agreement for this product, review: eula_en.pdf. Verification Manual — 7
  • 9. 1 Static Trusses Static Truss 1 1 Static Truss 2 4 Static Truss 3 8 Static Truss 4 12 Static Truss 5 16 Static Truss 6 19 Static Truss 7 31 Static Truss 1 Objective To find member stress due to a joint load in a space truss using static analysis. Reference Beer, F.P., and Johnston, Jr., E.R., Vector Mechanics for Engineers, Statics and Dynamics, McGraw - Hill, Inc., New York, 1962, p.47, Problem 2.70. Problem A 50 lb load is supported by three bars which are pinned to a ceiling as shown. Determine the stress, σ, in each bar. Area of each bar = 1 in2, E = 30 (10)6 psi Verification Manual — 1
  • 10. Figure 1-1: Space truss Comparison Result Type Theory STAAD.Pro Difference σAD 31.2 31.2 none σBD 10.4 10.4 none σCD 22.9 22.9 none Table 1-1: Comparison of member stress, in psi, for static truss no. 1 STAAD Input STAAD TRUSS :A SPACE TRUSS * FILE TRUSS01.STD * * REF: "VECTOR MECHANICS FOR ENGINEERS, STATICS &amp; DYNAMICS", * MCGRAW HILL BOOK CO., INC., NEW YORK, 1962 * PROBLEM 2.70, PAGE 47. * UNIT FT POUND JOINT COORDINATES 1 0. 0. 0. 2 8. 0. 0. 3 0. 6. 0. 4 4. 2. 6. MEMBER INCIDENCES 1 1 4 2 2 4 3 3 4 UNIT INCH MEMBER PROPERTIES 1 TO 3 PRIS AX 1. CONSTANTS E 30E6 ALL SUPPORTS 1 TO 3 PINNED LOAD 1 WEIGHT JOINT LOAD 4 FZ 50. PERFORM ANALYSIS PRINT MEMBER STRESSES FINISH 2 — STAAD.Pro 1 Static Trusses Static Truss 1
  • 11. STAAD Output PAGE NO. 1 **************************************************** * * * STAAD.Pro V8i SELECTseries5 * * Version 20.07.10.41 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= DEC 13, 2013 * * Time= 12:30: 8 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD TRUSS :A SPACE TRUSS INPUT FILE: TRUSS01.STD 2. * FILE TRUSS01.STD 3. * 4. * REF: "VECTOR MECHANICS FOR ENGINEERS, STATICS &AMP; DYNAMICS", 5. * MCGRAW HILL BOOK CO., INC., NEW YORK, 1962 6. * PROBLEM 2.70, PAGE 47. 7. * 8. UNIT FT POUND 9. JOINT COORDINATES 10. 1 0. 0. 0. 11. 2 8. 0. 0. 12. 3 0. 6. 0. 13. 4 4. 2. 6. 14. MEMBER INCIDENCES 15. 1 1 4 16. 2 2 4 17. 3 3 4 18. UNIT INCH 19. MEMBER PROPERTIES 20. 1 TO 3 PRIS AX 1. 21. CONSTANTS 22. E 30E6 ALL 23. SUPPORTS 24. 1 TO 3 PINNED 25. LOAD 1 WEIGHT 26. JOINT LOAD 27. 4 FZ 50. 28. PERFORM ANALYSIS **WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE MEMBERS/ELEMENTS/SOLIDS. THE DEFAULT VALUE HAS BEEN SET FOR THE SAME. :A SPACE TRUSS -- PAGE NO. 2 * FILE TRUSS01.STD P R O B L E M S T A T I S T I C S ----------------------------------- NUMBER OF JOINTS 4 NUMBER OF MEMBERS 3 NUMBER OF PLATES 0 NUMBER OF SOLIDS 0 NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 3 SOLVER USED IS THE IN-CORE ADVANCED SOLVER TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 3 29. PRINT MEMBER STRESSES MEMBER STRESSES :A SPACE TRUSS -- PAGE NO. 3 1 Static Trusses Verification Manual — 3
  • 12. * FILE TRUSS01.STD MEMBER STRESSES --------------- ALL UNITS ARE POUN/SQ INCH MEMB LD SECT AXIAL BEND-Y BEND-Z COMBINED SHEAR-Y SHEAR-Z 1 1 .0 10.4 T 0.0 0.0 10.4 0.0 0.0 1.0 10.4 T 0.0 0.0 10.4 0.0 0.0 2 1 .0 31.2 T 0.0 0.0 31.2 0.0 0.0 1.0 31.2 T 0.0 0.0 31.2 0.0 0.0 3 1 .0 22.9 T 0.0 0.0 22.9 0.0 0.0 1.0 22.9 T 0.0 0.0 22.9 0.0 0.0 ************** END OF LATEST ANALYSIS RESULT ************** 30. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= DEC 13,2013 TIME= 12:30:11 **** :A SPACE TRUSS -- PAGE NO. 4 * FILE TRUSS01.STD ************************************************************ * For technical assistance on STAAD.Pro, please visit * * http://selectservices.bentley.com/en-US/ * * * * Details about additional assistance from * * Bentley and Partners can be found at program menu * * Help->Technical Support * * * * Copyright © 1997-2013 Bentley Systems, Inc. * http://www.bentley.com * ************************************************************ Static Truss 2 Objective To find member force due to a member load in a plane articulate structure. Reference Kinney, J. S.,Indeterminate Structural Analysis, Addison - Wesley Publishing Co., 1957, p.275, Problem 6 - 19.(Original data is in US Customary Units) Problem Find the tensile stress in the cable. The cross - sectional area of the cable is 967.74 mm2 with an E of 137.895 GPa. The timber beam 1-3 is 304.8 mm x 304.8 mm in section, with E = 11.03161 GPa. Each member of the steel cantilever truss has a cross - sectional area of 2,580.64 mm2, and E of 206.8427 GPa. 4 — STAAD.Pro 1 Static Trusses Static Truss 2
  • 13. Figure 1-2: Plane articulate truss Comparison Result Type Theory STAAD.Pro Difference Cable, 3-4 22.7 22.58 0.6% (negligible) Table 1-2: Comparison of member force, in kN, for static truss no. 2 STAAD Input STAAD PLANE :A PLANE ARTICULATE STRUCTURE * FILE TRUSS02.STD * * REFERENCE: INDETERMINATE STRURAL ANALYSIS, KINNEY, 1957, * ADISON-WESLEY PUBLISHING COMPANY, PAGE 275, PROBLEM 6-19. * * UNIT NEWTON METER JOINT COORDINATES 1 0 0 0 2 3.0480 0 0 3 4.5720 0 0 4 4.5720 2.4384 0 5 6.4008 4.8768 0 6 6.4008 2.4384 0 7 8.2296 4.8768 0 8 8.2296 2.4384 0 9 10.0586 4.8768 0 10 10.0586 2.4384 0 * MEMBER INCIDENCES 1 1 2 3 1 1 4 4 6 5 6 8 6 8 10 7 4 5 8 6 5 9 6 7 10 8 7 11 8 9 12 5 7 13 7 9 MEMBER PROPERTIES 1 2 PRI YD .3048 ZD .3048 3 PRI AX 9.6774E-4 IZ 41.62314E-8 4 TO 13 PRI AX 25.8064E-4 IZ 41.62314E-8 CONSTANTS E 11.03161E9 MEMB 1 2 1 Static Trusses Verification Manual — 5
  • 14. E 137.89500E9 MEMB 3 E 206.84270E9 MEMB 4 TO 13 MEMBER RELEASES 3 TO 13 START MZ * SUPPORT 1 9 10 FIXED * LOADING 1 JOINT LOADS 2 FY -44.4822E3 * PERFORM ANALYSIS UNITS KNS PRINT MEMBER FORCES LIST 3 FINISH STAAD Output PAGE NO. 1 **************************************************** * * * STAAD.Pro V8i SELECTseries5 * * Version 20.07.10.41 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= DEC 13, 2013 * * Time= 12:30:11 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD PLANE :A PLANE ARTICULATE STRUCTURE INPUT FILE: TRUSS02.STD 2. * FILE TRUSS02.STD 3. * 4. * REFERENCE: INDETERMINATE STRURAL ANALYSIS, KINNEY, 1957, 5. * ADISON-WESLEY PUBLISHING COMPANY, PAGE 275, PROBLEM 6-19. 6. * 7. * 8. UNIT NEWTON METER 9. JOINT COORDINATES 10. 1 0 0 0 11. 2 3.0480 0 0 12. 3 4.5720 0 0 13. 4 4.5720 2.4384 0 14. 5 6.4008 4.8768 0 15. 6 6.4008 2.4384 0 16. 7 8.2296 4.8768 0 17. 8 8.2296 2.4384 0 18. 9 10.0586 4.8768 0 19. 10 10.0586 2.4384 0 20. * 21. MEMBER INCIDENCES 22. 1 1 2 3 1 1 23. 4 4 6 24. 5 6 8 25. 6 8 10 26. 7 4 5 27. 8 6 5 28. 9 6 7 29. 10 8 7 30. 11 8 9 31. 12 5 7 32. 13 7 9 6 — STAAD.Pro 1 Static Trusses Static Truss 2
  • 15. 33. MEMBER PROPERTIES 34. 1 2 PRI YD .3048 ZD .3048 35. 3 PRI AX 9.6774E-4 IZ 41.62314E-8 36. 4 TO 13 PRI AX 25.8064E-4 IZ 41.62314E-8 37. CONSTANTS 38. E 11.03161E9 MEMB 1 2 :A PLANE ARTICULATE STRUCTURE -- PAGE NO. 2 * FILE TRUSS02.STD 39. E 137.89500E9 MEMB 3 40. E 206.84270E9 MEMB 4 TO 13 41. MEMBER RELEASES 42. 3 TO 13 START MZ 43. * 44. SUPPORT 45. 1 9 10 FIXED 46. * 47. LOADING 1 48. JOINT LOADS 49. 2 FY -44.4822E3 50. * 51. PERFORM ANALYSIS **WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE MEMBERS/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 10 NUMBER OF MEMBERS 13 NUMBER OF PLATES 0 NUMBER OF SOLIDS 0 NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 3 SOLVER USED IS THE IN-CORE ADVANCED SOLVER TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 21 52. UNITS KNS 53. PRINT MEMBER FORCES LIST 3 MEMBER FORCES LIST 3 :A PLANE ARTICULATE STRUCTURE -- PAGE NO. 3 * FILE TRUSS02.STD MEMBER END FORCES STRUCTURE TYPE = PLANE ----------------- ALL UNITS ARE -- KNS METE (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 3 1 3 -22.58 0.00 0.00 0.00 0.00 0.00 4 22.58 0.00 0.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 54. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= DEC 13,2013 TIME= 12:30:14 **** :A PLANE ARTICULATE STRUCTURE -- PAGE NO. 4 * FILE TRUSS02.STD ************************************************************ * For technical assistance on STAAD.Pro, please visit * * http://selectservices.bentley.com/en-US/ * * * * Details about additional assistance from * * Bentley and Partners can be found at program menu * * Help->Technical Support * * * * Copyright © 1997-2013 Bentley Systems, Inc. * http://www.bentley.com * ************************************************************ 1 Static Trusses Verification Manual — 7
  • 16. Static Truss 3 Objective To find member forces due to joint loads in a plane truss. Reference Norris C.H., Wilbur J. B., Elementary Structural Analysis, 2nd Edition, McGraw – Hill, Inc., Page 159, Problem 4.3. (Original data is in US Customary Units) Problem Compute the bar forces in the bars a, b, c, d, e of the truss due to the loads shown. Figure 1-3: Plane truss Comparison Result Type Theory STAAD.Pro Difference a -202.13 -202.13 none b -185.76 -190.28 2.4% (negligible) c -22.42 -23.42 4.5% d 266.23 269.52 1.2% (negligible) e 119.61 117.08 2.1% (negligible) Table 1-3: Comparison of member force, in kN, for static truss no. 3 8 — STAAD.Pro 1 Static Trusses Static Truss 3
  • 17. STAAD Input STAAD PLANE :A PLANE TRUSS * FILE TRUSS03.STD * * REFERENCE: ELEMENTARY STRUCTURAL ANALYSIS, NORIS AND WILBUR, * 2ND EDITION, MCGRAW-HILL BOOK COMPANY, PAGE 159, * PROBLEM 4.3 (ORIGINAL DATA IN US CUSTOMAY UNITS) * UNIT NEWTON METER JOINT COORDINATES 1 0 0 2 7.62 0 3 7.62 9.144 4 15.24 0 5 15.24 4.572 6 15.24 9.144 7 22.86 0 8 22.86 12.192 9 30.48 0 10 30.48 4.572 11 30.48 9.144 12 38.10 0 13 38.10 9.144 14 45.72 0 * MEMBER INCIDENCES 1 1 2; 5 2 4 8 4 7; 11 7 9 14 9 12; 17 12 14 2 1 5; 3 1 3 4 2 3; 6 5 3 7 3 6; 9 7 5 21 4 5; 22 5 6 10 6 8;23 7 8 12 7 10; 13 11 8 24 9 10; 25 10 11 15 10 13; 16 11 13 18 14 10; 19 12 13 20 14 13 MEMBER PROPERTIES 1 TO 25 PRI AX 12.9032E-4 CONSTANT E 206.84271E9 ALL MEMBER TRUSS 1 TO 25 * SUPPORTS 1 PINNED 14 FIXED BUT FX * LOADING 1 VERTICAL JOINT LOADS JOINT LOADS 2 9 FY -4.448222E4 4 7 FY -8.896444E4 12 FY -2.224111E4 * PERFORM ANALYSIS UNITS KNS PRINT MEMBER FORCES LIST 2 5 6 10 12 FINISH STAAD Output PAGE NO. 1 1 Static Trusses Verification Manual — 9
  • 18. **************************************************** * * * STAAD.Pro V8i SELECTseries5 * * Version 20.07.10.41 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= DEC 13, 2013 * * Time= 12:30:14 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD PLANE :A PLANE TRUSS INPUT FILE: TRUSS03.STD 2. * FILE TRUSS03.STD 3. * 4. * REFERENCE: ELEMENTARY STRUCTURAL ANALYSIS, NORIS AND WILBUR, 5. * 2ND EDITION, MCGRAW-HILL BOOK COMPANY, PAGE 159, 6. * PROBLEM 4.3 (ORIGINAL DATA IN US CUSTOMAY UNITS) 7. * 8. UNIT NEWTON METER 9. JOINT COORDINATES 10. 1 0 0 11. 2 7.62 0 12. 3 7.62 9.144 13. 4 15.24 0 14. 5 15.24 4.572 15. 6 15.24 9.144 16. 7 22.86 0 17. 8 22.86 12.192 18. 9 30.48 0 19. 10 30.48 4.572 20. 11 30.48 9.144 21. 12 38.10 0 22. 13 38.10 9.144 23. 14 45.72 0 24. * 25. MEMBER INCIDENCES 26. 1 1 2; 5 2 4 27. 8 4 7; 11 7 9 28. 14 9 12; 17 12 14 29. 2 1 5; 3 1 3 30. 4 2 3; 6 5 3 31. 7 3 6; 9 7 5 32. 21 4 5; 22 5 6 33. 10 6 8;23 7 8 34. 12 7 10; 13 11 8 35. 24 9 10; 25 10 11 36. 15 10 13; 16 11 13 37. 18 14 10; 19 12 13 38. 20 14 13 :A PLANE TRUSS -- PAGE NO. 2 * FILE TRUSS03.STD 39. MEMBER PROPERTIES 40. 1 TO 25 PRI AX 12.9032E-4 41. CONSTANT 42. E 206.84271E9 ALL 43. MEMBER TRUSS 44. 1 TO 25 45. * 46. SUPPORTS 47. 1 PINNED 48. 14 FIXED BUT FX 49. * 50. LOADING 1 VERTICAL JOINT LOADS 10 — STAAD.Pro 1 Static Trusses Static Truss 3
  • 19. 51. JOINT LOADS 52. 2 9 FY -4.448222E4 53. 4 7 FY -8.896444E4 54. 12 FY -2.224111E4 55. * 56. PERFORM ANALYSIS **WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE MEMBERS/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 14 NUMBER OF MEMBERS 25 NUMBER OF PLATES 0 NUMBER OF SOLIDS 0 NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2 SOLVER USED IS THE IN-CORE ADVANCED SOLVER TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 38 *WARNING- ZERO 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 OR EFFECTIVELY RELEASED IN THIS DIRECTION. *WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 2 EQN.NO. 4 *WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 3 EQN.NO. 7 *WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 4 EQN.NO. 10 *WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 5 EQN.NO. 13 *WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 6 EQN.NO. 16 *WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 7 EQN.NO. 19 *WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 8 EQN.NO. 22 *WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 9 EQN.NO. 25 *WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 10 EQN.NO. 28 *WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 11 EQN.NO. 31 :A PLANE TRUSS -- PAGE NO. 3 * FILE TRUSS03.STD *WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 12 EQN.NO. 34 **WARNING - THERE WERE MORE THAN 12 DOF WITH ZERO STIFFNESS. THE FIRST 12 ARE LISTED ABOVE. TOTAL # TRANSLATIONAL= 0 TOTAL # ROTATIONAL= 13 57. UNITS KNS 58. PRINT MEMBER FORCES LIST 2 5 6 10 12 MEMBER FORCES LIST 2 :A PLANE TRUSS -- PAGE NO. 4 * FILE TRUSS03.STD MEMBER END FORCES STRUCTURE TYPE = PLANE ----------------- ALL UNITS ARE -- KNS METE (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 2 1 1 190.28 0.00 0.00 0.00 0.00 0.00 5 -190.28 0.00 0.00 0.00 0.00 0.00 5 1 2 -269.52 0.00 0.00 0.00 0.00 0.00 4 269.52 0.00 0.00 0.00 0.00 0.00 6 1 5 -117.08 0.00 0.00 0.00 0.00 0.00 3 117.08 0.00 0.00 0.00 0.00 0.00 10 1 6 202.12 0.00 0.00 0.00 0.00 0.00 8 -202.12 0.00 0.00 0.00 0.00 0.00 12 1 7 23.42 0.00 0.00 0.00 0.00 0.00 10 -23.42 0.00 0.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 59. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= DEC 13,2013 TIME= 12:30:17 **** 1 Static Trusses Verification Manual — 11
  • 20. :A PLANE TRUSS -- PAGE NO. 5 * FILE TRUSS03.STD ************************************************************ * For technical assistance on STAAD.Pro, please visit * * http://selectservices.bentley.com/en-US/ * * * * Details about additional assistance from * * Bentley and Partners can be found at program menu * * Help->Technical Support * * * * Copyright © 1997-2013 Bentley Systems, Inc. * http://www.bentley.com * ************************************************************ Static Truss 4 Objective To find support reactions and member forces due to a joint load in a space truss. Reference Beer F. P., and Johnston, E. R., Vector Mechanics for Engineers - Statics, 4th Edition, McGraw – Hill, Inc., p.216, Problem 6.20. Problem The space truss is supported by the six reactions shown. If a horizontal 2,700 N load is applied at A, determine the reactions and the force in each member. 12 — STAAD.Pro 1 Static Trusses Static Truss 4
  • 21. Figure 1-4: Space truss Comparison Result Type Theory STAAD.Pro Difference Bv 0 0 none Bz 2,700 2,700 none Cx 1,800 1,800 none Cv 3,375 3,375 none Dx 1,800 1,800 none Dv 3,375 3,375 none Table 1-4: Comparison of support reactions, in N, for static truss no. 4 Result Type Theory STAAD.Pro Difference AB 0 0 none AC 4,275 4,275 none Table 1-5: Comparison of member forces, in N, for static truss no. 4 1 Static Trusses Verification Manual — 13
  • 22. Result Type Theory STAAD.Pro Difference AD 4,275 4,275 none BC 4,270 4,269 negligible CD 0 0 none BD 4,270 4,269 negligible STAAD Input STAAD SPACE :A SPACE TRUSS * FILE: TRUSS04.STD * * REFERENCE: VECTOR MECHANICS FOR ENGINEERS - STATICS, BEER AND * JOHNSTON, 4TH EDITION, MCGRAW-HILL BOOK CO., * PAGE 216, PROBLEM 6.20. * UNITS NEWTON METER JOINT COORDINATES 1 1.0 0.0 0.6 2 1.0 0.0 -0.6 3 -0.8 0.0 0.0 4 0.0 1.5 0.0 * MEMBER INCIDENCES 1 1 4 2 2 4 3 3 4 4 1 2 5 6 3 1 MEMBER PROPERTIES 1 TO 6 PRI AX 0.001 CONSTANTS E 200.0E9 ALL MEMBER TRUSS 1 TO 6 * SUPPORTS 1 FIXED BUT FZ 2 FIXED BUT FZ 3 FIXED BUT FX * LOADING 1 HORIZONTAL LOAD JOINT LOAD 4 FZ 2700.0 PERFORM ANALYSIS PRINT SUPPORT REACTIONS PRINT MEMBER FORCES FINISH STAAD Output PAGE NO. 1 **************************************************** * * * STAAD.Pro V8i SELECTseries5 * * Version 20.07.10.41 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= DEC 13, 2013 * * Time= 12:30:18 * 14 — STAAD.Pro 1 Static Trusses Static Truss 4
  • 23. * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD SPACE :A SPACE TRUSS INPUT FILE: TRUSS04.STD 2. * FILE: TRUSS04.STD 3. * 4. * REFERENCE: VECTOR MECHANICS FOR ENGINEERS - STATICS, BEER AND 5. * JOHNSTON, 4TH EDITION, MCGRAW-HILL BOOK CO., 6. * PAGE 216, PROBLEM 6.20. 7. * 8. UNITS NEWTON METER 9. JOINT COORDINATES 10. 1 1.0 0.0 0.6 11. 2 1.0 0.0 -0.6 12. 3 -0.8 0.0 0.0 13. 4 0.0 1.5 0.0 14. * 15. MEMBER INCIDENCES 16. 1 1 4 17. 2 2 4 18. 3 3 4 19. 4 1 2 5 20. 6 3 1 21. MEMBER PROPERTIES 22. 1 TO 6 PRI AX 0.001 23. CONSTANTS 24. E 200.0E9 ALL 25. MEMBER TRUSS 26. 1 TO 6 27. * 28. SUPPORTS 29. 1 FIXED BUT FZ 30. 2 FIXED BUT FZ 31. 3 FIXED BUT FX 32. * 33. LOADING 1 HORIZONTAL LOAD 34. JOINT LOAD 35. 4 FZ 2700.0 36. PERFORM ANALYSIS :A SPACE TRUSS -- PAGE NO. 2 * FILE: TRUSS04.STD **WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE MEMBERS/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 4 NUMBER OF MEMBERS 6 NUMBER OF PLATES 0 NUMBER OF SOLIDS 0 NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 3 SOLVER USED IS THE IN-CORE ADVANCED SOLVER TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 9 *WARNING- ZERO STIFFNESS IN DIRECTION 4 AT JOINT 4 EQN.NO. 7 LOADS APPLIED OR DISTRIBUTED HERE FROM ELEMENTS WILL BE IGNORED. THIS MAY BE DUE TO ALL MEMBERS AT THIS JOINT BEING RELEASED OR EFFECTIVELY RELEASED IN THIS DIRECTION. *WARNING- ZERO STIFFNESS IN DIRECTION 5 AT JOINT 4 EQN.NO. 8 *WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 4 EQN.NO. 9 37. PRINT SUPPORT REACTIONS SUPPORT REACTION 1 Static Trusses Verification Manual — 15
  • 24. :A SPACE TRUSS -- PAGE NO. 3 * FILE: TRUSS04.STD SUPPORT REACTIONS -UNIT NEWT METE STRUCTURE TYPE = SPACE ----------------- JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 1 1 1800.00 3375.00 0.00 0.00 0.00 0.00 2 1 -1800.00 -3375.00 0.00 0.00 0.00 0.00 3 1 0.00 0.00 -2700.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 38. PRINT MEMBER FORCES MEMBER FORCES :A SPACE TRUSS -- PAGE NO. 4 * FILE: TRUSS04.STD MEMBER END FORCES STRUCTURE TYPE = SPACE ----------------- ALL UNITS ARE -- NEWT METE (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 1 1 1 4275.00 0.00 0.00 0.00 0.00 0.00 4 -4275.00 0.00 0.00 0.00 0.00 0.00 2 1 2 -4275.00 0.00 0.00 0.00 0.00 0.00 4 4275.00 0.00 0.00 0.00 0.00 0.00 3 1 3 0.00 0.00 0.00 0.00 0.00 0.00 4 0.00 0.00 0.00 0.00 0.00 0.00 4 1 1 0.00 0.00 0.00 0.00 0.00 0.00 2 0.00 0.00 0.00 0.00 0.00 0.00 5 1 2 4269.07 0.00 0.00 0.00 0.00 0.00 3 -4269.07 0.00 0.00 0.00 0.00 0.00 6 1 3 -4269.07 0.00 0.00 0.00 0.00 0.00 1 4269.07 0.00 0.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 39. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= DEC 13,2013 TIME= 12:30:21 **** :A SPACE TRUSS -- PAGE NO. 5 * FILE: TRUSS04.STD ************************************************************ * For technical assistance on STAAD.Pro, please visit * * http://selectservices.bentley.com/en-US/ * * * * Details about additional assistance from * * Bentley and Partners can be found at program menu * * Help->Technical Support * * * * Copyright © 1997-2013 Bentley Systems, Inc. * http://www.bentley.com * ************************************************************ Static Truss 5 Objective To find support reactions due to joint loads in a plane truss. Reference McCormack, J.C. Structural Analysis, Intext Educational Publishers, 3rd Edition, 1975. 16 — STAAD.Pro 1 Static Trusses Static Truss 5
  • 25. Problem Find the vertical support reactions of the truss. E = 30,000.0 ksi A = 100 in2 Loads as shown. Figure 1-5: Plane truss Comparison Result Type Theory STAAD.Pro Difference R1 -76.7 -76.67 none R4 346.7 346.67 none R9 30 30 none Table 1-6: Comparison of support reactions, in N, for static truss no. 5 STAAD Input STAAD TRUSS :A PLANE TRUSS * FILE: TRUSS05.STD * * REFERENCE: MCCORMAC, J.C.,"STRUCTURAL ANALYSIS", INTEXT * EDUCATIONAL PUBLISHERS, NEW YORK, 3RD EDITION, 1975. * INPUT WIDTH 72 UNIT FEET KIP JOINT COORDINATES 1 0. 0. 0.; 2 30. 0. 0.; 3 60. 0. 0.; 4 90. 0. 0.; 5 120. 0. 0. 6 150. 0. 0.; 7 180. 0. 0.; 8 210. 0. 0.; 9 240. 0. 0.; 10 0. 20. 0. 11 30. 20. 0.; 12 60. 20. 0.; 13 90. 20. 0.; 14 120. 20. 0. 15 150. 20. 0.; 16 180. 20. 0.; 17 210. 20. 0.; 18 240. 20. 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 10 11 10 11 12; 11 12 13; 12 13 14; 13 14 15; 14 16 17; 15 17 18; 16 1 10 17 10 2; 18 2 11; 19 11 3; 20 3 12; 21 12 4; 22 4 13; 23 13 5; 24 5 14 25 14 6; 26 6 15; 27 15 7; 28 7 16; 29 16 8; 30 8 17; 31 17 9; 32 9 18 UNIT INCHES KIP MEMBER PROPERTY AMERICAN 1 TO 32 PRI AX 100. * MEMBER TRUSS * 1 TO 32 CONSTANTS E 30000. ALL 1 Static Trusses Verification Manual — 17
  • 26. SUPPORTS 1 PINNED 4 9 FIXED BUT FX MZ LOAD 1 POINT LOADS AT SPECIFIC JOINTS JOINT LOAD 6 TO 8 FY -60. 3 FY -80. 2 FY -40. PERFORM ANALYSIS PRINT SUPPORT REACTIONS FINISH STAAD Output PAGE NO. 1 **************************************************** * * * STAAD.Pro V8i SELECTseries5 * * Version 20.07.10.41 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= DEC 13, 2013 * * Time= 12:30:21 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD TRUSS :A PLANE TRUSS INPUT FILE: TRUSS05.STD 2. * FILE: TRUSS05.STD 3. * 4. * REFERENCE: MCCORMAC, J.C.,"STRUCTURAL ANALYSIS", INTEXT 5. * EDUCATIONAL PUBLISHERS, NEW YORK, 3RD EDITION, 1975. 6. * 7. INPUT WIDTH 72 8. UNIT FEET KIP 9. JOINT COORDINATES 10. 1 0. 0. 0.; 2 30. 0. 0.; 3 60. 0. 0.; 4 90. 0. 0.; 5 120. 0. 0. 11. 6 150. 0. 0.; 7 180. 0. 0.; 8 210. 0. 0.; 9 240. 0. 0.; 10 0. 20. 0. 12. 11 30. 20. 0.; 12 60. 20. 0.; 13 90. 20. 0.; 14 120. 20. 0. 13. 15 150. 20. 0.; 16 180. 20. 0.; 17 210. 20. 0.; 18 240. 20. 0. 14. MEMBER INCIDENCES 15. 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 10 11 16. 10 11 12; 11 12 13; 12 13 14; 13 14 15; 14 16 17; 15 17 18; 16 1 10 17. 17 10 2; 18 2 11; 19 11 3; 20 3 12; 21 12 4; 22 4 13; 23 13 5; 24 5 14 18. 25 14 6; 26 6 15; 27 15 7; 28 7 16; 29 16 8; 30 8 17; 31 17 9; 32 9 18 19. UNIT INCHES KIP 20. MEMBER PROPERTY AMERICAN 21. 1 TO 32 PRI AX 100. 22. * MEMBER TRUSS 23. * 1 TO 32 24. CONSTANTS 25. E 30000. ALL 26. SUPPORTS 27. 1 PINNED 28. 4 9 FIXED BUT FX MZ 29. LOAD 1 POINT LOADS AT SPECIFIC JOINTS 30. JOINT LOAD 31. 6 TO 8 FY -60. 32. 3 FY -80. 33. 2 FY -40. 34. PERFORM ANALYSIS :A PLANE TRUSS -- PAGE NO. 2 * FILE: TRUSS05.STD 18 — STAAD.Pro 1 Static Trusses Static Truss 5
  • 27. **WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE MEMBERS/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 18 NUMBER OF MEMBERS 32 NUMBER OF PLATES 0 NUMBER OF SOLIDS 0 NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 3 SOLVER USED IS THE IN-CORE ADVANCED SOLVER TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 32 35. PRINT SUPPORT REACTIONS SUPPORT REACTION :A PLANE TRUSS -- PAGE NO. 3 * FILE: TRUSS05.STD SUPPORT REACTIONS -UNIT KIP INCH STRUCTURE TYPE = TRUSS ----------------- JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 1 1 0.00 -76.67 0.00 0.00 0.00 0.00 4 1 0.00 346.67 0.00 0.00 0.00 0.00 9 1 0.00 30.00 0.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 36. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= DEC 13,2013 TIME= 12:30:24 **** :A PLANE TRUSS -- PAGE NO. 4 * FILE: TRUSS05.STD ************************************************************ * For technical assistance on STAAD.Pro, please visit * * http://selectservices.bentley.com/en-US/ * * * * Details about additional assistance from * * Bentley and Partners can be found at program menu * * Help->Technical Support * * * * Copyright © 1997-2013 Bentley Systems, Inc. * http://www.bentley.com * ************************************************************ Static Truss 6 Objective To find support reactions due to joint loads in a plane truss. Reference McCormack, J.C., Structural Analysis, Intext Educational Publishers, 3rd Edition, 1975. Problem Find the vertical and horizontal reactions at the supports of the truss. E = 30,000.0 ksi. A = 100 in2. Loads as shown. 1 Static Trusses Verification Manual — 19
  • 28. Figure 1-6: Plane truss Comparison Result Type Theory STAAD.Pro Difference Horizontal, R1 34.3 34.29 none Vertical, R1 11.5 11.49 none Horizontal, R2 36.0 36.0 none Vertical, R2 -31.7 -31.67 none Table 1-7: Comparison of support reactions, in N, for static truss no. 6 STAAD Input STAAD TRUSS :A PLANE TRUSS * FILE TRUSS06.STD * * REFERENCE: MCCORMAC, J.C.,"STRUCTURAL ANALYSIS", INTEXT * EDUCATIONAL PUBLISHERS, NEW YORK, 3RD EDITION, 1975. * INPUT WIDTH 72 UNIT FEET KIP JOINT COORDINATES 1 0. 0. 0.; 2 0. 60. 0.; 3 12.5 60. 0.; 4 0. 15. 0.; 5 0. 30. 0. 6 0. 45. 0.; 7 9.375 45. 0.; 8 6.25 30. 0.; 9 3.125 15. 0. 10 50. 90. 0.; 11 100. 90. 0.; 12 50. 75. 0.; 13 25. 75. 0. 14 66.667 90. 0.; 15 83.333 90. 0.; 16 83.333 85. 0.; 17 66.667 80. 0. 18 31.25 67.5 0.; 19 200. 0. 0.; 20 200. 60. 0.; 21 187.5 60. 0. 22 200. 15. 0.; 23 200. 30. 0.; 24 200. 45. 0.; 25 190.625 45. 0. 26 193.75 30. 0.; 27 196.875 15. 0.; 28 150. 90. 0.; 29 150. 75. 0. 30 175. 75. 0.; 31 133.333 90. 0.; 32 116.667 90. 0.; 33 116.667 85. 0. 34 133.333 80. 0.; 35 168.75 67.5 0. 20 — STAAD.Pro 1 Static Trusses Static Truss 6
  • 29. MEMBER INCIDENCES 1 1 4; 2 2 3; 3 3 7; 4 4 5; 5 5 6; 6 6 2; 7 7 8; 8 8 9; 9 9 1; 10 4 9 11 9 5; 12 5 8; 13 8 6; 14 6 7; 15 7 2; 16 2 13; 17 10 14; 18 11 16 19 12 18; 20 13 10; 21 14 15; 22 15 11; 23 16 17; 24 17 12; 25 18 3 26 3 13; 27 13 18; 28 13 12; 29 12 10; 30 10 17; 31 17 14; 32 14 16 33 16 15; 34 19 22; 35 20 21; 36 21 25; 37 22 23; 38 23 24; 39 24 20 40 25 26; 41 26 27; 42 27 19; 43 22 27; 44 27 23; 45 23 26; 46 26 24 47 24 25; 48 25 20; 49 20 30; 50 28 31; 51 11 33; 52 29 35; 53 30 28 54 31 32; 55 32 11; 56 33 34; 57 34 29; 58 35 21; 59 21 30; 60 30 35 61 30 29; 62 29 28; 63 28 34; 64 34 31; 65 31 33; 66 33 32 UNIT INCHES KIP MEMBER PROPERTY AMERICAN 1 TO 66 PRI AX 100. CONSTANTS E 30000. ALL SUPPORTS 1 19 PINNED UNIT FEET KIP LOAD 1 JOINT LOADS AT SPECIFIC NODES JOINT LOAD 11 14 15 31 32 FY -10. 10 28 FY -5. 4 TO 6 FX 4. 2 FX 2.0 2 10 FX 1.5435 13 FX 3.0870 2 10 FY -2.5725 13 FY -5.145 PERFORM ANALYSIS PRINT SUPPORT REACTIONS FINISH STAAD Output PAGE NO. 1 **************************************************** * * * STAAD.Pro V8i SELECTseries5 * * Version 20.07.10.41 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= DEC 13, 2013 * * Time= 12:30:24 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD TRUSS :A PLANE TRUSS INPUT FILE: TRUSS06.STD 2. * FILE TRUSS06.STD 3. * 4. * REFERENCE: MCCORMAC, J.C.,"STRUCTURAL ANALYSIS", INTEXT 5. * EDUCATIONAL PUBLISHERS, NEW YORK, 3RD EDITION, 1975. 6. * 7. INPUT WIDTH 72 8. UNIT FEET KIP 9. JOINT COORDINATES 10. 1 0. 0. 0.; 2 0. 60. 0.; 3 12.5 60. 0.; 4 0. 15. 0.; 5 0. 30. 0. 11. 6 0. 45. 0.; 7 9.375 45. 0.; 8 6.25 30. 0.; 9 3.125 15. 0. 12. 10 50. 90. 0.; 11 100. 90. 0.; 12 50. 75. 0.; 13 25. 75. 0. 13. 14 66.667 90. 0.; 15 83.333 90. 0.; 16 83.333 85. 0.; 17 66.667 80. 0. 14. 18 31.25 67.5 0.; 19 200. 0. 0.; 20 200. 60. 0.; 21 187.5 60. 0. 15. 22 200. 15. 0.; 23 200. 30. 0.; 24 200. 45. 0.; 25 190.625 45. 0. 16. 26 193.75 30. 0.; 27 196.875 15. 0.; 28 150. 90. 0.; 29 150. 75. 0. 17. 30 175. 75. 0.; 31 133.333 90. 0.; 32 116.667 90. 0.; 33 116.667 85. 0. 1 Static Trusses Verification Manual — 21
  • 30. 18. 34 133.333 80. 0.; 35 168.75 67.5 0. 19. MEMBER INCIDENCES 20. 1 1 4; 2 2 3; 3 3 7; 4 4 5; 5 5 6; 6 6 2; 7 7 8; 8 8 9; 9 9 1; 10 4 9 21. 11 9 5; 12 5 8; 13 8 6; 14 6 7; 15 7 2; 16 2 13; 17 10 14; 18 11 16 22. 19 12 18; 20 13 10; 21 14 15; 22 15 11; 23 16 17; 24 17 12; 25 18 3 23. 26 3 13; 27 13 18; 28 13 12; 29 12 10; 30 10 17; 31 17 14; 32 14 16 24. 33 16 15; 34 19 22; 35 20 21; 36 21 25; 37 22 23; 38 23 24; 39 24 20 25. 40 25 26; 41 26 27; 42 27 19; 43 22 27; 44 27 23; 45 23 26; 46 26 24 26. 47 24 25; 48 25 20; 49 20 30; 50 28 31; 51 11 33; 52 29 35; 53 30 28 27. 54 31 32; 55 32 11; 56 33 34; 57 34 29; 58 35 21; 59 21 30; 60 30 35 28. 61 30 29; 62 29 28; 63 28 34; 64 34 31; 65 31 33; 66 33 32 29. UNIT INCHES KIP 30. MEMBER PROPERTY AMERICAN 31. 1 TO 66 PRI AX 100. 32. CONSTANTS 33. E 30000. ALL 34. SUPPORTS 35. 1 19 PINNED 36. UNIT FEET KIP 37. LOAD 1 JOINT LOADS AT SPECIFIC NODES 38. JOINT LOAD :A PLANE TRUSS -- PAGE NO. 2 * FILE TRUSS06.STD 39. 11 14 15 31 32 FY -10. 40. 10 28 FY -5. 41. 4 TO 6 FX 4. 42. 2 FX 2.0 43. 2 10 FX 1.5435 44. 13 FX 3.0870 45. 2 10 FY -2.5725 46. 13 FY -5.145 47. PERFORM ANALYSIS **WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE MEMBERS/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 35 NUMBER OF MEMBERS 66 NUMBER OF PLATES 0 NUMBER OF SOLIDS 0 NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2 SOLVER USED IS THE IN-CORE ADVANCED SOLVER TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 66 48. PRINT SUPPORT REACTIONS SUPPORT REACTION :A PLANE TRUSS -- PAGE NO. 3 * FILE TRUSS06.STD SUPPORT REACTIONS -UNIT KIP FEET STRUCTURE TYPE = TRUSS ----------------- JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 1 1 11.49 34.29 0.00 0.00 0.00 0.00 19 1 -31.67 36.00 0.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 49. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= DEC 13,2013 TIME= 12:30:27 **** :A PLANE TRUSS -- PAGE NO. 4 * FILE TRUSS06.STD ************************************************************ * For technical assistance on STAAD.Pro, please visit * 22 — STAAD.Pro 1 Static Trusses Static Truss 6
  • 31. * http://selectservices.bentley.com/en-US/ * * * * Details about additional assistance from * * Bentley and Partners can be found at program menu * * Help->Technical Support * * * * Copyright © 1997-2013 Bentley Systems, Inc. * http://www.bentley.com * ************************************************************ Plane Truss: Support Reactions Due to a Joint Load Objective To find the support reactions due to a joint load in a plane truss. Reference Timoshenko, S., Strength of Materials, Part 1, D. Van Nostrand Co., Inc., 3rd edition, 1956,  p.346, problem 3. Problem Determine the horizontal reaction at support 4 of the system. Figure 1-7: Plane truss Comparison Result Type Theory STAAD Basic Solver STAAD Advanced Solver R4 8.77 8.77 8.77 Table 1-8: Comparison of Support Reaction, in kips, for verification problem no. 1 1 Static Trusses Verification Manual — 23
  • 32. STAAD Input STAAD TRUSS VERIFICATION PROBLEM NO. 1 * * REFERENCE `STRENGTH OF MATERIALS' PART-1 BY S. TIMOSHENKO * PAGE 346 PROBLEM NO. 3. THE ANSWER IS REACTION = 0.877P. * THEREFORE IF P=10, REACTION = 8.77 * UNITS INCH KIP JOINT COORD 1 0. 0. ; 2 150. 100. ; 3 150. 50. ; 4 300. 0. MEMBER INCI 1 1 2 ; 2 1 3 ; 3 2 3 ; 4 2 4 ; 5 3 4 MEMB PROP 1 4 PRIS AX 5.0 ; 2 5 PRIS AX 3.0 ; 3 PRIS AX 2 CONSTANT E 30000. ALL POISSON STEEL ALL SUPPORT ; 1 4 PINNED LOADING 1 JOINT LOAD ; 2 FY -10. PERFORM ANALYSIS PRINT REACTION FINISH STAAD Output PAGE NO. 1 **************************************************** * * * STAAD.Pro V8i SELECTseries5 * * Version 20.07.10.41 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= DEC 13, 2013 * * Time= 12:30:30 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD TRUSS VERIFICATION PROBLEM NO. 1 INPUT FILE: VER01.STD 2. * 3. * REFERENCE `STRENGTH OF MATERIALS' PART-1 BY S. TIMOSHENKO 4. * PAGE 346 PROBLEM NO. 3. THE ANSWER IS REACTION = 0.877P. 5. * THEREFORE IF P=10, REACTION = 8.77 6. * 7. UNITS INCH KIP 8. JOINT COORD 9. 1 0. 0. ; 2 150. 100. ; 3 150. 50. ; 4 300. 0. 10. MEMBER INCI 11. 1 1 2 ; 2 1 3 ; 3 2 3 ; 4 2 4 ; 5 3 4 12. MEMB PROP 13. 1 4 PRIS AX 5.0 ; 2 5 PRIS AX 3.0 ; 3 PRIS AX 2 14. CONSTANT 15. E 30000. ALL 16. POISSON STEEL ALL 17. SUPPORT ; 1 4 PINNED 18. LOADING 1 19. JOINT LOAD ; 2 FY -10. 20. PERFORM ANALYSIS P R O B L E M S T A T I S T I C S ----------------------------------- 24 — STAAD.Pro 1 Static Trusses Static Truss 6
  • 33. NUMBER OF JOINTS 4 NUMBER OF MEMBERS 5 NUMBER OF PLATES 0 NUMBER OF SOLIDS 0 NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2 SOLVER USED IS THE IN-CORE ADVANCED SOLVER TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 4 VERIFICATION PROBLEM NO. 1 -- PAGE NO. 2 * 21. PRINT REACTION REACTION VERIFICATION PROBLEM NO. 1 -- PAGE NO. 3 * SUPPORT REACTIONS -UNIT KIP INCH STRUCTURE TYPE = TRUSS ----------------- JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 1 1 8.77 5.00 0.00 0.00 0.00 0.00 4 1 -8.77 5.00 0.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 22. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= DEC 13,2013 TIME= 12:30:33 **** VERIFICATION PROBLEM NO. 1 -- PAGE NO. 4 * ************************************************************ * For technical assistance on STAAD.Pro, please visit * * http://selectservices.bentley.com/en-US/ * * * * Details about additional assistance from * * Bentley and Partners can be found at program menu * * Help->Technical Support * * * * Copyright © 1997-2013 Bentley Systems, Inc. * http://www.bentley.com * ************************************************************ Plane Truss Joint Deflection Objective To find the joint deflection due to joint loads in a plane truss. Reference McCormack, J. C., “Structural Analysis,” Intext Educational Publishers, 3rd edition, 1975, page 271, example 18 - 2. Problem Determine the vertical deflection at point 5 of plane truss structure shown in the figure. 1 Static Trusses Verification Manual — 25
  • 34. Figure 1-8: Plane truss model Given P = 20 kip Truss width = 4 spaces at 15 ft = 60 ft Truss height = 15 ft AX 1-4 = 1 in2, AX 5-6 = 2 in2, AX 7-8 =1.5 in2,  AX 9-11B = 3 in2P, AX 12-13 = 4 in2 E = 30E3 ksi Comparison Result Type Theory STAAD Basic Solver STAAD Advanced Solver δ5 (in.) 2.63 2.63 2.63 Table 1-9: Comparison of deflection (δ) for verification problem no. 7 STAAD Input STAAD TRUSS VERIFICATION PROBLEM NO. 7 * * REFERENCE 'STRUCTURAL ANALYSIS' BY JACK McCORMACK, PAGE * 271 EXAMPLE 18-2. ANSWER - Y-DISP AT JOINT 5 = 2.63 INCH * UNIT FT KIP JOINT COORD 1 0 0 0 5 60 0 0 6 15. 7.5 ; 7 30. 15. ; 8 45. 7.5 MEMB INCI 1 2 6 ; 2 3 4 ; 3 4 8 ; 4 4 5 ; 5 1 2 6 2 3 ; 7 3 6 ; 8 3 8 ; 9 3 7 10 1 6 ; 11 5 8 ; 12 6 7 13 UNIT INCH MEMB PROP 1 TO 4 PRI AX 1.0 26 — STAAD.Pro 1 Static Trusses Static Truss 6
  • 35. 5 6 PRIS AX 2. 7 8 PRI AX 1.5 9 10 11 PRI AX 3. 12 13 PRI AX 4. CONSTANT E 30E3 ALL POISSON STEEL ALL SUPPORT 1 PINNED ; 3 FIXED BUT FX MZ LOAD 1 VERTICAL LOAD JOINT LOAD 2 4 5 FY -20.0 PERFORM ANALYSIS PRINT DISPLACEMENTS FINISH STAAD Output PAGE NO. 1 **************************************************** * * * STAAD.Pro V8i SELECTseries5 * * Version 20.07.10.41 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= DEC 13, 2013 * * Time= 12:30:48 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD TRUSS VERIFICATION PROBLEM NO. 7 INPUT FILE: VER07.STD 2. * 3. * REFERENCE 'STRUCTURAL ANALYSIS' BY JACK MCCORMACK, PAGE 4. * 271 EXAMPLE 18-2. ANSWER - Y-DISP AT JOINT 5 = 2.63 INCH 5. * 6. UNIT FT KIP 7. JOINT COORD 8. 1 0 0 0 5 60 0 0 9. 6 15. 7.5 ; 7 30. 15. ; 8 45. 7.5 10. MEMB INCI 11. 1 2 6 ; 2 3 4 ; 3 4 8 ; 4 4 5 ; 5 1 2 12. 6 2 3 ; 7 3 6 ; 8 3 8 ; 9 3 7 13. 10 1 6 ; 11 5 8 ; 12 6 7 13 14. UNIT INCH 15. MEMB PROP 16. 1 TO 4 PRI AX 1.0 17. 5 6 PRIS AX 2. 18. 7 8 PRI AX 1.5 19. 9 10 11 PRI AX 3. 20. 12 13 PRI AX 4. 21. CONSTANT 22. E 30E3 ALL 23. POISSON STEEL ALL 24. SUPPORT 25. 1 PINNED ; 3 FIXED BUT FX MZ 26. LOAD 1 VERTICAL LOAD 27. JOINT LOAD 28. 2 4 5 FY -20.0 29. PERFORM ANALYSIS VERIFICATION PROBLEM NO. 7 -- PAGE NO. 2 * P R O B L E M S T A T I S T I C S 1 Static Trusses Verification Manual — 27
  • 36. ----------------------------------- NUMBER OF JOINTS 8 NUMBER OF MEMBERS 13 NUMBER OF PLATES 0 NUMBER OF SOLIDS 0 NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2 SOLVER USED IS THE IN-CORE ADVANCED SOLVER TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 13 30. PRINT DISPLACEMENTS DISPLACE VERIFICATION PROBLEM NO. 7 -- PAGE NO. 3 * JOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = TRUSS ------------------ JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN 1 1 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 2 1 -0.12000 0.18000 0.00000 0.00000 0.00000 0.00000 3 1 -0.24000 0.00000 0.00000 0.00000 0.00000 0.00000 4 1 -0.48000 -0.89516 0.00000 0.00000 0.00000 0.00000 5 1 -0.72000 -2.63033 0.00000 0.00000 0.00000 0.00000 6 1 -0.00820 0.24000 0.00000 0.00000 0.00000 0.00000 7 1 0.29758 -0.12000 0.00000 0.00000 0.00000 0.00000 8 1 0.06578 -0.83516 0.00000 0.00000 0.00000 0.00000 ************** END OF LATEST ANALYSIS RESULT ************** 31. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= DEC 13,2013 TIME= 12:30:51 **** VERIFICATION PROBLEM NO. 7 -- PAGE NO. 4 * ************************************************************ * For technical assistance on STAAD.Pro, please visit * * http://selectservices.bentley.com/en-US/ * * * * Details about additional assistance from * * Bentley and Partners can be found at program menu * * Help->Technical Support * * * * Copyright © 1997-2013 Bentley Systems, Inc. * http://www.bentley.com * ************************************************************ Deflection and stress of a truss system Objective To find the joint deflection and member stress due to a joint load in a plane truss. Reference Timoshenko, S., Strength of Materials, Part 1, D. Van Nostrand Co., Inc., 3rd edition, 1956, page 10, problem 2. Problem Determine the vertical deflection at point A and the member stresses AX = 0.5 in2 E = 30E6 psi P = 5000 lbf 28 — STAAD.Pro 1 Static Trusses Static Truss 6
  • 37. L = 180 in. angle = 30° Figure 1-9: Model of two member truss Comparison Result Type Theory STAAD Basic Solver STAAD Advanced Solver σA (psi) 10,000. 10,000. 10,000. δA (in) 0.12 0.12 0.12 Table 1-10: Comparison of stress (σ) and Deflection (δ) for verification problem 12 STAAD Input STAAD TRUSS VERIFICATION PROBLEM NO 12 * * THIS EXAMPLE IS TAKEN FROM 'STRENGTH OF MATERIALS' * (PART 1) BY TIMOSHENKO, PAGE 10 PROB 2. * THE ANSWER IN THE BOOK , DEFLECTION = 0.12 INCH * AND STRESS =10000 PSI * UNIT INCH POUND JOINT COORD 1 0. 0. ; 2 155.88457 -90. ; 3 311.76914 0. MEMB INCI ; 1 1 2 2 MEMB PROP 1 2 PRIS AX 0.5 CONSTANT E 30E6 POISSON 0.15 ALL SUPPORT ; 1 3 PINNED LOAD 1 VERT LOAD JOINT LOAD ; 2 FY -5000. PERFORM ANALYSIS PRINT DISPLACEMENTS PRINT STRESSES FINISH 1 Static Trusses Verification Manual — 29
  • 38. STAAD Output PAGE NO. 1 **************************************************** * * * STAAD.Pro V8i SELECTseries5 * * Version 20.07.10.41 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= DEC 13, 2013 * * Time= 12:31: 4 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD TRUSS VERIFICATION PROBLEM NO 12 INPUT FILE: VER12.STD 2. * 3. * THIS EXAMPLE IS TAKEN FROM 'STRENGTH OF MATERIALS' 4. * (PART 1) BY TIMOSHENKO, PAGE 10 PROB 2. 5. * THE ANSWER IN THE BOOK , DEFLECTION = 0.12 INCH 6. * AND STRESS =10000 PSI 7. * 8. UNIT INCH POUND 9. JOINT COORD 10. 1 0. 0. ; 2 155.88457 -90. ; 3 311.76914 0. 11. MEMB INCI ; 1 1 2 2 12. MEMB PROP 13. 1 2 PRIS AX 0.5 14. CONSTANT 15. E 30E6 16. POISSON 0.15 ALL 17. SUPPORT ; 1 3 PINNED 18. LOAD 1 VERT LOAD 19. JOINT LOAD ; 2 FY -5000. 20. PERFORM ANALYSIS P R O B L E M S T A T I S T I C S ----------------------------------- NUMBER OF JOINTS 3 NUMBER OF MEMBERS 2 NUMBER OF PLATES 0 NUMBER OF SOLIDS 0 NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2 SOLVER USED IS THE IN-CORE ADVANCED SOLVER TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 2 VERIFICATION PROBLEM NO 12 -- PAGE NO. 2 * 21. PRINT DISPLACEMENTS DISPLACE VERIFICATION PROBLEM NO 12 -- PAGE NO. 3 * JOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = TRUSS ------------------ JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN 1 1 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 2 1 0.00000 -0.12000 0.00000 0.00000 0.00000 0.00000 3 1 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 ************** END OF LATEST ANALYSIS RESULT ************** 22. PRINT STRESSES STRESSES 30 — STAAD.Pro 1 Static Trusses Static Truss 6
  • 39. VERIFICATION PROBLEM NO 12 -- PAGE NO. 4 * MEMBER STRESSES --------------- ALL UNITS ARE POUN/SQ INCH MEMB 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 0.0 1.0 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 0.0 1.0 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 *********** **** DATE= DEC 13,2013 TIME= 12:31: 6 **** VERIFICATION PROBLEM NO 12 -- PAGE NO. 5 * ************************************************************ * For technical assistance on STAAD.Pro, please visit * * http://selectservices.bentley.com/en-US/ * * * * Details about additional assistance from * * Bentley and Partners can be found at program menu * * Help->Technical Support * * * * Copyright © 1997-2013 Bentley Systems, Inc. * http://www.bentley.com * ************************************************************ Static Truss 7 Objective To find member forces due to a thermal load in a plane truss. Reference Gere J. M., and Timoshenko, S. P., Mechanics of Materials, 2nd Edition, PWS Engineering, p.21, Problem 2.6 - 23. Problem A symmetric, three-bar truss ABCD undergoes a temperature increase of 20°C in the two outer bars and 70°C in the middle bar. Calculate the forces F1 and F2 in the bars. E = 200 GPa α = 14( 10)-6 / °C A = 900 mm2 1 Static Trusses Verification Manual — 31
  • 40. Figure 1-10: Plane truss subject to differential thermal loading Comparison Result Type Theory STAAD.Pro Difference F1 22,100 22,143 0.2% (negligible) F2 -31,300 -31,315 0.1% (negligible) Table 1-11: Comparison of member forces, in N, for static truss no. 7 STAAD Input STAAD TRUSS :A PLANE TRUSS * FILE: TRUSS10.STD * REFERENCE: MECHANICS OF MATERIALS, GERE AND TIMOSHENKO, 2ND EDITION * PWS ENGINEERING, PAGE 121, PROBLEM 2.6-23 * UNITS NEWTON METER JOINT COORDINATES 1 -2.12132 2.12132 2 0.0 2.12132 3 2.12132 2.12132 4 0.0 0.0 * MEMBER INCIDENCES 1 1 4 2 2 4 3 3 4 UNIT NEWTON MMS MEMBER PROPERTIES 1 TO 3 PRI AX 900 UNIT NEWTON METER CONSTANTS E 200.0E9 ALL ALPHA 14.0E-6 ALL 32 — STAAD.Pro 1 Static Trusses Static Truss 7
  • 41. * SUPPORTS 1 2 3 PINNED * LOADING 1 TEMPERATURE LOAD TEMPERATURE LOAD 1 3 TEMP 20 800 2 TEMP 70 PERFORM ANALYSIS PRINT MEMBER FORCES FINISH STAAD Output PAGE NO. 1 **************************************************** * * * STAAD.Pro V8i SELECTseries5 * * Version 20.07.10.41 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= DEC 13, 2013 * * Time= 12:30:27 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD TRUSS :A PLANE TRUSS INPUT FILE: TRUSS07.STD 2. * FILE: TRUSS10.STD 3. * REFERENCE: MECHANICS OF MATERIALS, GERE AND TIMOSHENKO, 2ND EDITION 4. * PWS ENGINEERING, PAGE 121, PROBLEM 2.6-23 5. * 6. UNITS NEWTON METER 7. JOINT COORDINATES 8. 1 -2.12132 2.12132 9. 2 0.0 2.12132 10. 3 2.12132 2.12132 11. 4 0.0 0.0 12. * 13. MEMBER INCIDENCES 14. 1 1 4 15. 2 2 4 16. 3 3 4 17. UNIT NEWTON MMS 18. MEMBER PROPERTIES 19. 1 TO 3 PRI AX 900 20. UNIT NEWTON METER 21. CONSTANTS 22. E 200.0E9 ALL 23. ALPHA 14.0E-6 ALL 24. * 25. SUPPORTS 26. 1 2 3 PINNED 27. * 28. LOADING 1 TEMPERATURE LOAD 29. TEMPERATURE LOAD 30. 1 3 TEMP 20 800 31. 2 TEMP 70 32. PERFORM ANALYSIS :A PLANE TRUSS -- PAGE NO. 2 * FILE: TRUSS10.STD **WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE MEMBERS/ELEMENTS/SOLIDS. THE DEFAULT VALUE HAS BEEN SET FOR THE SAME. 1 Static Trusses Verification Manual — 33
  • 42. P R O B L E M S T A T I S T I C S ----------------------------------- NUMBER OF JOINTS 4 NUMBER OF MEMBERS 3 NUMBER OF PLATES 0 NUMBER OF SOLIDS 0 NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 3 SOLVER USED IS THE IN-CORE ADVANCED SOLVER TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 2 33. PRINT MEMBER FORCES MEMBER FORCES :A PLANE TRUSS -- PAGE NO. 3 * FILE: TRUSS10.STD MEMBER END FORCES STRUCTURE TYPE = TRUSS ----------------- ALL UNITS ARE -- NEWT METE (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 1 1 1 -22142.72 0.00 0.00 0.00 0.00 0.00 4 22142.72 0.00 0.00 0.00 0.00 0.00 2 1 2 31314.54 0.00 0.00 0.00 0.00 0.00 4 -31314.54 0.00 0.00 0.00 0.00 0.00 3 1 3 -22142.72 0.00 0.00 0.00 0.00 0.00 4 22142.72 0.00 0.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 34. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= DEC 13,2013 TIME= 12:30:30 **** :A PLANE TRUSS -- PAGE NO. 4 * FILE: TRUSS10.STD ************************************************************ * For technical assistance on STAAD.Pro, please visit * * http://selectservices.bentley.com/en-US/ * * * * Details about additional assistance from * * Bentley and Partners can be found at program menu * * Help->Technical Support * * * * Copyright © 1997-2013 Bentley Systems, Inc. * http://www.bentley.com * ************************************************************ 34 — STAAD.Pro 1 Static Trusses Static Truss 7
  • 43. 2 Static Beams Static Beam 1 35 Static Beam 2 39 Static Beam 3 43 Static Beam 4 47 Static Beam 5 53 Static Beam 6 56 Static Beam 7 59 Static Beam 8 62 Static Beam 9 65 Static Beam 11 72 Static Beam 12 75 Static Beam 13 78 Static Beam 15 87 Static Beam 1 Objective To find the deflection and support reactions due to a trapezoidally varying load applied on part of the span of a pinned-fixed beam. Reference Hand calculation using the following reference: Roark's Formulas for Stress and Strain, Warren C. Young, 6th edition, McGraw-Hill, Table 3, Case (2c), p.103 Problem The beam in the following geometric, load, and section properties: a = 3 m, b =4.5 m, wa = 4 KN/m, wl = 7 KN/m, IZ =5,000 cm4, E = 200 KN/mm2. Verification Manual — 35
  • 44. Figure 2-1: Simple supported beam with partial, trapezoidal load Comparison Result Type Theory STAAD.Pro Difference OA (radians) 0.0020 0.0020 none RA (kN) 3.2886 3.2886 none RB (kN) 21.461 21.461 none MB (kN·m) 25.9605 25.9605 none Table 2-1: Comparison of results for static beam no. 1 Where RA = Vertical reaction at A OA = Rotation at A RB = Vertical reaction at B MB = Moment at B Note: In the STAAD model, two load cases are used. In case 1, the load is applied using the "MEMBER LOAD - TRAP" option. In case 2, the load is applied using a combination of "MEMBER LOAD - UNI" and "MEMBER LOAD - LIN" options. Both cases yield identical results. Theoretical Solution ( ) ( ) R l a l a l a l a = ( − ) 3 + + ( − ) 4 + A W l W W l 8 3 − 40 3 a l a 3 3 ( ) ( ) O l a l a l a l a = ( − ) + 3 − ( − ) 2 + 3 A W EIl W W EIl − 48 3 − 240 3 a l a ( ) R l a R = − − B W W A − 2 a l M R l l a l a = − ( − ) − ( − ) B A W W W 2 2 − 6 2 a l a Where l = a + b 36 — STAAD.Pro 2 Static Beams Static Beam 1
  • 45. STAAD Input STAAD PLANE REACTIONS AND DISPLACEMENTS OF A PINNED-FIXED BEAM * * FILE : BEAM01.STD * * REFERENCE : ROARK'S FORMULAS FOR STRESS &amp; STRAIN * WARREN C. YOUNG, 6TH EDITION, MCGRAW-HILL * * TABLE 3, CASE (2C), LOAD ON PARTIAL SPAN * UNIT KNS METER JOINT COORD 1 0 0 0 ; 2 3 0 0 ; 3 7.5 0 0 * MEMBER INCI 1 1 2 2 * UNIT CMS MEMBER PROP 1 2 PRIS AX 50 IZ 5000 * UNIT METER CONSTANT E 200E6 ALL POISS STEEL ALL * SUPPORT 1 PINNED 3 FIXED * LOAD 1 MEMBER LOAD 2 TRAP GY -4.0 -7.0 * LOAD 2 MEMBER LOAD 2 UNI GY -4 2 LIN GY 0 -3 * PERFORM ANALYSIS * PRINT JOINT DISP * UNIT NEWTON PRINT SUPP REAC FINISH STAAD Output PAGE NO. 1 **************************************************** * * * STAAD.Pro V8i SELECTseries5 * * Version 20.07.10.41 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= DEC 13, 2013 * * Time= 12:27:32 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD PLANE REACTIONS AND DISPLACEMENTS OF A PINNED-FIXED BEAM 2 Static Beams Verification Manual — 37
  • 46. INPUT FILE: BEAM01.STD 2. * 3. * FILE : BEAM01.STD 4. * 5. * REFERENCE : ROARK'S FORMULAS FOR STRESS &AMP; STRAIN 6. * WARREN C. YOUNG, 6TH EDITION, MCGRAW-HILL 7. * 8. * TABLE 3, CASE (2C), LOAD ON PARTIAL SPAN 9. * 10. UNIT KNS METER 11. JOINT COORD 12. 1 0 0 0 ; 2 3 0 0 ; 3 7.5 0 0 13. * 14. MEMBER INCI 15. 1 1 2 2 16. * 17. UNIT CMS 18. MEMBER PROP 19. 1 2 PRIS AX 50 IZ 5000 20. * 21. UNIT METER 22. CONSTANT 23. E 200E6 ALL 24. POISS STEEL ALL 25. * 26. SUPPORT 27. 1 PINNED 28. 3 FIXED 29. * 30. LOAD 1 31. MEMBER LOAD 32. 2 TRAP GY -4.0 -7.0 33. * 34. LOAD 2 35. MEMBER LOAD 36. 2 UNI GY -4 37. 2 LIN GY 0 -3 38. * REACTIONS AND DISPLACEMENTS OF A PINNED-FIXED BEAM -- PAGE NO. 2 * 39. PERFORM ANALYSIS P R O B L E M S T A T I S T I C S ----------------------------------- NUMBER OF JOINTS 3 NUMBER OF MEMBERS 2 NUMBER OF PLATES 0 NUMBER OF SOLIDS 0 NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2 SOLVER USED IS THE IN-CORE ADVANCED SOLVER TOTAL PRIMARY LOAD CASES = 2, TOTAL DEGREES OF FREEDOM = 4 40. * 41. PRINT JOINT DISP JOINT DISP REACTIONS AND DISPLACEMENTS OF A PINNED-FIXED BEAM -- PAGE NO. 3 * JOINT DISPLACEMENT (CM RADIANS) STRUCTURE TYPE = PLANE ------------------ JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN 1 1 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0020 2 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0020 2 1 0.0000 -0.4626 0.0000 0.0000 0.0000 -0.0006 2 0.0000 -0.4626 0.0000 0.0000 0.0000 -0.0006 38 — STAAD.Pro 2 Static Beams Static Beam 1
  • 47. 3 1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 2 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 ************** END OF LATEST ANALYSIS RESULT ************** 42. * 43. UNIT NEWTON 44. PRINT SUPP REAC SUPP REAC REACTIONS AND DISPLACEMENTS OF A PINNED-FIXED BEAM -- PAGE NO. 4 * SUPPORT REACTIONS -UNIT NEWT METE STRUCTURE TYPE = PLANE ----------------- JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 1 1 0.00 3288.60 0.00 0.00 0.00 0.00 2 0.00 3288.60 0.00 0.00 0.00 0.00 3 1 0.00 21461.40 0.00 0.00 0.00 -25960.50 2 0.00 21461.40 0.00 0.00 0.00 -25960.50 ************** END OF LATEST ANALYSIS RESULT ************** 45. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= DEC 13,2013 TIME= 12:27:35 **** REACTIONS AND DISPLACEMENTS OF A PINNED-FIXED BEAM -- PAGE NO. 5 * ************************************************************ * For technical assistance on STAAD.Pro, please visit * * http://selectservices.bentley.com/en-US/ * * * * Details about additional assistance from * * Bentley and Partners can be found at program menu * * Help->Technical Support * * * * Copyright © 1997-2013 Bentley Systems, Inc. * http://www.bentley.com * ************************************************************ Static Beam 2 Objective To find the support reactions due to a temperature loads applied on a fixed-fixed beam. Reference Hand calculation using the following reference: Matrix Analysis of Framed Structures, 3rd edition, W.Weaver Jr. & J.M.Gere, Van Nostrand Reinhold, Table B2, Appendix B, p.500 Problem The beam in the following geometric, load, and section properties: L = 7.5 m, T = 40° F, T2 , T1 = 50° F, α = 11.7(10)-6/°F, d = 30 cm, IZ = 5,000 cm4, E =200 KN/mm2. 2 Static Beams Verification Manual — 39
  • 48. Figure 2-2: Fixed support beam with temperature load Comparison Result Type Theory STAAD.Pro Difference Horizontal Reaction at Node A (kN) 468 468 none Moment at Node A (kN·m) 19.5 19.5 none Table 2-2: Comparison of results for static beam no. 1 Note: In the STAAD model, two load cases are used. In case 1, the uniform expansion is applied. In case 2, the temperature change between top and bottom flanges is applied. Theoretical Solution Horizontal reactions due to case 1 loads: RA = - RB = EAαΔT = [200(10)6]· [50(10)-4]· [11.7(10)-6]· (40) = 468 kN Moment reactions due to case 2 loads: ⋅       ⋅      ⋅     ( ) M M kN m = − = = = 19.5 A B αEI T d ∆ 11.7(10) 200(10) 5, 000(10) 50 0.3 −6 −6 −8 STAAD Input STAAD PLANE TEMPERATURE LOAD ON A FIXED-FIXED BEAM * * FILE : BEAM02.STD * * REFERENCE : MATRIX ANALYSIS OF FRAMED STRUCTURES * GERE &amp; WEAVER, 3RD EDITION, VAN NOSTRAND REINHOLD * * TABLE B-2, APPENDIX B, PAGE 500 * UNIT KNS METER 40 — STAAD.Pro 2 Static Beams Static Beam 2
  • 49. JOINT COORD 1 0 0 0 ; 2 3 0 0 ; 3 7.5 0 0 * MEMBER INCI 1 1 2 2 * UNIT CMS MEMBER PROP 1 2 PRIS AX 50 IZ 5000 YD 30 * UNIT METER CONSTANT E 200E6 ALL POISS STEEL ALL ALPHA 11.7E-6 ALL * SUPPORT 1 FIXED 3 FIXED * LOAD 1 TEMPERATURE LOAD 1 2 TEMP 40 * LOAD 2 TEMPERATURE LOAD 1 2 TEMP 0 50 * PERFORM ANALYSIS * PRINT SUPP REAC FINISH STAAD Output PAGE NO. 1 **************************************************** * * * STAAD.Pro V8i SELECTseries5 * * Version 20.07.10.41 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= DEC 13, 2013 * * Time= 12:27:35 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD PLANE TEMPERATURE LOAD ON A FIXED-FIXED BEAM INPUT FILE: BEAM02.STD 2. * 3. * FILE : BEAM02.STD 4. * 5. * REFERENCE : MATRIX ANALYSIS OF FRAMED STRUCTURES 6. * GERE &AMP; WEAVER, 3RD EDITION, VAN NOSTRAND REINHOLD 7. * 8. * TABLE B-2, APPENDIX B, PAGE 500 9. * 10. UNIT KNS METER 11. JOINT COORD 12. 1 0 0 0 ; 2 3 0 0 ; 3 7.5 0 0 13. * 14. MEMBER INCI 15. 1 1 2 2 16. * 2 Static Beams Verification Manual — 41
  • 50. 17. UNIT CMS 18. MEMBER PROP 19. 1 2 PRIS AX 50 IZ 5000 YD 30 20. * 21. UNIT METER 22. CONSTANT 23. E 200E6 ALL 24. POISS STEEL ALL 25. ALPHA 11.7E-6 ALL 26. * 27. SUPPORT 28. 1 FIXED 29. 3 FIXED 30. * 31. LOAD 1 32. TEMPERATURE LOAD 33. 1 2 TEMP 40 34. * 35. LOAD 2 36. TEMPERATURE LOAD 37. 1 2 TEMP 0 50 38. * TEMPERATURE LOAD ON A FIXED-FIXED BEAM -- PAGE NO. 2 * 39. PERFORM ANALYSIS P R O B L E M S T A T I S T I C S ----------------------------------- NUMBER OF JOINTS 3 NUMBER OF MEMBERS 2 NUMBER OF PLATES 0 NUMBER OF SOLIDS 0 NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2 SOLVER USED IS THE IN-CORE ADVANCED SOLVER TOTAL PRIMARY LOAD CASES = 2, TOTAL DEGREES OF FREEDOM = 3 40. * 41. PRINT SUPP REAC SUPP REAC TEMPERATURE LOAD ON A FIXED-FIXED BEAM -- PAGE NO. 3 * SUPPORT REACTIONS -UNIT KNS METE STRUCTURE TYPE = PLANE ----------------- JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 1 1 468.00 0.00 0.00 0.00 0.00 0.00 2 0.00 0.00 0.00 0.00 0.00 -19.50 3 1 -468.00 0.00 0.00 0.00 0.00 0.00 2 0.00 0.00 0.00 0.00 0.00 19.50 ************** END OF LATEST ANALYSIS RESULT ************** 42. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= DEC 13,2013 TIME= 12:27:38 **** TEMPERATURE LOAD ON A FIXED-FIXED BEAM -- PAGE NO. 4 * ************************************************************ * For technical assistance on STAAD.Pro, please visit * * http://selectservices.bentley.com/en-US/ * * * * Details about additional assistance from * * Bentley and Partners can be found at program menu * * Help->Technical Support * * * * Copyright © 1997-2013 Bentley Systems, Inc. * http://www.bentley.com * 42 — STAAD.Pro 2 Static Beams Static Beam 2
  • 51. ************************************************************ Static Beam 3 Objective To find the twist at the free end of a hollow tapered shaft of uniform thickness. Reference Hand calculation using the following reference: Mechanics of Materials, F.P.Beer & E.R.Johnston, 1981, McGraw-Hill Review Problem 3.120, Page 149. Problem The beam in the following figure which has the following geometric, load, and section properties: L = 2 m, outside diameter at fixed end = 80 mm, outside diameter at free end = 40 mm, uniform wall thickness of 10 mm, , IZ = 5,000 cm4, E = 200 KN/mm2, T = 2.0 KNm, and Poisson's ratio = 0.3. 2 Static Beams Verification Manual — 43
  • 52. Figure 2-3: Cantilevered member with a tapered, hollow shaft cross section Comparison Result Type Theory STAAD.Pro Difference Twist at free end (radians) 0.0751 0.0751 none Table 2-3: Comparison of results for static beam no. 1 Theoretical Solution According to the reference, the twist at the free end is 44 — STAAD.Pro 2 Static Beams Static Beam 3
  • 53.       ( ) Φ = A TL πGt C C C C 4 + A B A B 2 2 where: CA = centerline radius at free end = 40 mm/2 - 10 mm/2 = 15 mm CB = center line radius at fixed end = 80 mm/2 - 10 mm/2 = 35 mm G= = = 76.9 E ν kN mm 2(1 + ) 200 / 2(1 + 0.3) 2       ⋅ ( ) Φ = = 0.0751 rad. A kN m m π kN mm mm mm mm mm mm 2, 000 ×2, 000 4 × 76.9 / × 10 15 + 35 (15 ) (35 ) 2 2 2 STAAD Input File STAAD SPACE TORSION ON CONICAL SHAFT * * FILE : BEAM03.STD * * REFERENCE : MECHANICS OF MATERIALS, F.P.BEER &amp; E.R.JOHNSTON * 1981, MCGRAW-HILL * * REVIEW PROBLEM 3.120, PAGE 149. TWIST AT FREE END SHOULD BE * ABOUT 0.0751 RADIAN * UNIT KNS METER JOINT COORD 1 0 0 0 ; 2 0 2 0 MEMBER INCI 1 1 2 UNIT MMS MEMBER PROP 1 PRIS ROUND START 80 END 40 THICK 10 CONST E 200 ALL POISSON 0.3 ALL SUPPORT 1 FIXED UNIT KNS METER LOAD 1 JOINT LOAD 2 MY 2.0 PERFORM ANALYSIS PRINT JOINT DISP FINISH STAAD Output PAGE NO. 1 **************************************************** * * * STAAD.Pro V8i SELECTseries5 * * Version 20.07.10.41 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= DEC 13, 2013 * * Time= 12:27:38 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD SPACE TORSION ON CONICAL SHAFT 2 Static Beams Verification Manual — 45
  • 54. INPUT FILE: BEAM03.STD 2. * 3. * FILE : BEAM03.STD 4. * 5. * REFERENCE : MECHANICS OF MATERIALS, F.P.BEER &AMP; E.R.JOHNSTON 6. * 1981, MCGRAW-HILL 7. * 8. * REVIEW PROBLEM 3.120, PAGE 149. TWIST AT FREE END SHOULD BE 9. * ABOUT 0.0751 RADIAN 10. * 11. UNIT KNS METER 12. JOINT COORD 13. 1 0 0 0 ; 2 0 2 0 14. MEMBER INCI 15. 1 1 2 16. UNIT MMS 17. MEMBER PROP 18. 1 PRIS ROUND START 80 END 40 THICK 10 19. CONST 20. E 200 ALL 21. POISSON 0.3 ALL 22. SUPPORT 23. 1 FIXED 24. UNIT KNS METER 25. LOAD 1 26. JOINT LOAD 27. 2 MY 2.0 28. PERFORM ANALYSIS TORSION ON CONICAL SHAFT -- PAGE NO. 2 * P R O B L E M S T A T I S T I C S ----------------------------------- NUMBER OF JOINTS 2 NUMBER OF MEMBERS 1 NUMBER OF PLATES 0 NUMBER OF SOLIDS 0 NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 1 SOLVER USED IS THE IN-CORE ADVANCED SOLVER TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 6 29. PRINT JOINT DISP JOINT DISP TORSION ON CONICAL SHAFT -- PAGE NO. 3 * JOINT DISPLACEMENT (CM RADIANS) STRUCTURE TYPE = SPACE ------------------ JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN 1 1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 2 1 0.0000 0.0000 0.0000 0.0000 0.0751 0.0000 ************** END OF LATEST ANALYSIS RESULT ************** 30. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= DEC 13,2013 TIME= 12:27:40 **** TORSION ON CONICAL SHAFT -- PAGE NO. 4 * ************************************************************ * For technical assistance on STAAD.Pro, please visit * * http://selectservices.bentley.com/en-US/ * * * * Details about additional assistance from * * Bentley and Partners can be found at program menu * * Help->Technical Support * * * 46 — STAAD.Pro 2 Static Beams Static Beam 3
  • 55. * Copyright © 1997-2013 Bentley Systems, Inc. * http://www.bentley.com * ************************************************************ Static Beam 4 Objective To find the deflection and member forces due to an applied load on a propped cantilever beam with a compression only support. Reference Hand calculation using the following reference: Manual of Steel Construction, Load and Resistance Factor Design, Second Edition, American Institute of Steel Construction, 1998, pp. 4-194, 4-197. Problem A cantilever beam with an end support capable of resisting only a compressive force is analyzed for two concentrated loads at 0.6xL 1) +0.5 lb (up) and 2) -0.5 lb (down). E = 10(10)6 psi, width = 0.6 in, depth = 0.3 in. L = 4 ft. Note: A dummy member is used to represent a compression only support Figure 2-4: Cantilevered member with a compression only support Comparison Result Type Theory STAAD.Pro Difference Load Case 1 Moment at fixed end (in-lb) -14.4 -14.4 none Shear at fixed end (lb) 0.50 0.50 none Deflection at load (.in) 0.295 0.295 none Table 2-4: Comparison of results for static beam no. 1 2 Static Beams Verification Manual — 47
  • 56. Result Type Theory STAAD.Pro Difference Load Case 2 Moment at fixed end (in-lb) 4.032 4.03 none Shear at fixed end (lb) 0.284 0.28 1.4% Deflection at load (.in) -0.040 -.0401 none Theoretical Solution Load Case 1:  General solution equations found on p.2-121 of the reference. M x b P b x lb x ( < ) = − ( − ) = −0.5 (28.8 − ) At the rigid support, M = 14.4 in-lb. By inspection, fixed end shear is equal to load value = 0.50 lb.             x b x b ∆ < = 3 − Px EI 6 2                 ( )( ) in in in = 3 28.8 . − 28.8 . = 0.295 . lb in psi in 0.5 (28.8 .) 6 10, 000, 000 0.00135 . 2 4 Load Case 2: General solution equations found on p.2-118 of the reference                 ( ) R in in lb = = 19.2 + 2 48 = 0.216 . Pb a lb in in 1 + 2 ℓ 2 ℓ 0.5 (48 .) 2(48 .) 2 3 2 3 R2 = P - R1 = 0.50lb - 0.216lb = 0.284lb. Moment at rigid support: M x b R x P x a ( < ) = (ℓ − ) − (ℓ − − ) 1 lb in lb in in = 0.216 (48 − 0) − 0.5 (48 − 0 − 19.2 ) = −4.032 in lb Deflection at point of load:             x b x a a x ∆ < = 3ℓ − 3ℓ − 3 ℓ + Pax EI − 12 ℓ 3 2 2 2 2 3                                 ( ) ( )( ) in in in in in in in in = 3(48 .) − 3(48 .) 28.8 − 3(19.2 .) 48 + (19.2 .) 28.8 = −0.040 . lb in in psi in in −0.5 19.2 (28.8 ) 12 10, 000, 000 0.00135 . (48 .) 3 2 2 2 3 4 3 STAAD Input File STAAD PLANE :A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT START JOB INFORMATION ENGINEER DATE 06-Mar-12 END JOB INFORMATION * FILE: BEAM04.STD * * STARDYNE VERIFICATION PROBLEM #16 ********************************************* * THE END SUPPORT IS TO BE DEFINED AS A * * COMPRESSION ONLY SUPPORT. A DUMMY MEMBER,* * #7, IS SET AS COMPRESSION ONLY TO MODEL * * THIS. * 48 — STAAD.Pro 2 Static Beams Static Beam 4
  • 57. ********************************************* SET NL 2 *********************************************** * STAAD.Pro Generated Comment * *********************************************** *1 0. 0. 0. 6 48.0 0. 0. *********************************************** UNIT INCHES POUND JOINT COORDINATES 1 0 0 0; 2 9.6 0 0; 3 19.2 0 0; 4 28.8 0 0; 5 38.4 0 0; 6 48 0 0; 7 48 -4 0; *7 48. -.01 0. *********************************************** * STAAD.Pro Generated Comment * *********************************************** *1 1 2 6 ************************************************ MEMBER INCIDENCES 1 1 2; 2 2 3; 3 3 4; 4 4 5; 5 5 6; 6 6 7; MEMBER PROPERTY AMERICAN 1 TO 5 PRIS YD 0.3 ZD 0.6 *6 PRISMATIC YD 2. 6 PRIS YD 40 MEMBER COMPRESSION 6 DEFINE MATERIAL START ISOTROPIC MATERIAL1 E 1e+007 POISSON 0.33 END DEFINE MATERIAL CONSTANTS MATERIAL MATERIAL1 ALL SUPPORTS 1 FIXED 7 PINNED LOAD 1 UPWARD JOINT LOAD 4 FY 0.5 PERFORM ANALYSIS PRINT MEMBER FORCES LIST 1 TO 5 PRINT JOINT DISPLACEMENTS LIST 1 TO 6 PRINT SUPPORT REACTION CHANGE LOAD 2 DOWNWARD JOINT LOAD 4 FY -0.5 PERFORM ANALYSIS PRINT SUPPORT REACTION PRINT MEMBER FORCES LIST 1 TO 5 PRINT JOINT DISPLACEMENTS LIST 1 TO 6 FINISH STAAD Output PAGE NO. 1 **************************************************** * * * STAAD.Pro V8i SELECTseries5 * * Version 20.07.10.41 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= DEC 13, 2013 * * Time= 12:27:41 * * * * USER ID: Bentley Systems, Inc. * 2 Static Beams Verification Manual — 49
  • 58. **************************************************** 1. STAAD PLANE :A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT INPUT FILE: BEAM04.STD 2. START JOB INFORMATION 3. ENGINEER DATE 06-MAR-12 4. END JOB INFORMATION 5. * FILE: BEAM04.STD 6. * 7. * STARDYNE VERIFICATION PROBLEM #16 8. ********************************************* 9. * THE END SUPPORT IS TO BE DEFINED AS A * 10. * COMPRESSION ONLY SUPPORT. A DUMMY MEMBER,* 11. * #7, IS SET AS COMPRESSION ONLY TO MODEL * 12. * THIS. * 13. ********************************************* 14. SET NL 2 15. *********************************************** 16. * STAAD.PRO GENERATED COMMENT * 17. *********************************************** 18. *1 0. 0. 0. 6 48.0 0. 0. 19. *********************************************** 20. UNIT INCHES POUND 21. JOINT COORDINATES 22. 1 0 0 0; 2 9.6 0 0; 3 19.2 0 0; 4 28.8 0 0; 5 38.4 0 0; 6 48 0 0 23. 7 48 -4 0 24. *7 48. -.01 0. 25. *********************************************** 26. * STAAD.PRO GENERATED COMMENT * 27. *********************************************** 28. *1 1 2 6 29. ************************************************ 30. MEMBER INCIDENCES 31. 1 1 2; 2 2 3; 3 3 4; 4 4 5; 5 5 6; 6 6 7 32. MEMBER PROPERTY AMERICAN 33. 1 TO 5 PRIS YD 0.3 ZD 0.6 34. *6 PRISMATIC YD 2. 35. 6 PRIS YD 40 36. MEMBER COMPRESSION 37. 6 38. DEFINE MATERIAL START :A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT -- PAGE NO. 2 39. ISOTROPIC MATERIAL1 40. E 1E+007 41. POISSON 0.33 42. END DEFINE MATERIAL 43. CONSTANTS 44. MATERIAL MATERIAL1 ALL 45. SUPPORTS 46. 1 FIXED 47. 7 PINNED 48. LOAD 1 UPWARD 49. JOINT LOAD 50. 4 FY 0.5 51. PERFORM ANALYSIS P R O B L E M S T A T I S T I C S ----------------------------------- NUMBER OF JOINTS 7 NUMBER OF MEMBERS 6 NUMBER OF PLATES 0 NUMBER OF SOLIDS 0 NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2 SOLVER USED IS THE IN-CORE ADVANCED SOLVER TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 16 50 — STAAD.Pro 2 Static Beams Static Beam 4
  • 59. *WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 7 EQN.NO. 16 LOADS APPLIED OR DISTRIBUTED HERE FROM ELEMENTS WILL BE IGNORED. THIS MAY BE DUE TO ALL MEMBERS AT THIS JOINT BEING RELEASED OR EFFECTIVELY RELEASED IN THIS DIRECTION. **START ITERATION NO. 2 *WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 7 EQN.NO. 16 LOADS APPLIED OR DISTRIBUTED HERE FROM ELEMENTS WILL BE IGNORED. THIS MAY BE DUE TO ALL MEMBERS AT THIS JOINT BEING RELEASED OR EFFECTIVELY RELEASED IN THIS DIRECTION. **NOTE-Tension/Compression converged after 2 iterations, Case= 1 52. PRINT MEMBER FORCES LIST 1 TO 5 MEMBER FORCES LIST 1 :A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT -- PAGE NO. 3 MEMBER END FORCES STRUCTURE TYPE = PLANE ----------------- ALL UNITS ARE -- POUN INCH (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 1 1 1 0.00 -0.50 0.00 0.00 0.00 -14.40 2 0.00 0.50 0.00 0.00 0.00 9.60 2 1 2 0.00 -0.50 0.00 0.00 0.00 -9.60 3 0.00 0.50 0.00 0.00 0.00 4.80 3 1 3 0.00 -0.50 0.00 0.00 0.00 -4.80 4 0.00 0.50 0.00 0.00 0.00 0.00 4 1 4 0.00 0.00 0.00 0.00 0.00 0.00 5 0.00 0.00 0.00 0.00 0.00 0.00 5 1 5 0.00 0.00 0.00 0.00 0.00 0.00 6 0.00 0.00 0.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 53. PRINT JOINT DISPLACEMENTS LIST 1 TO 6 JOINT DISPLACE LIST 1 :A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT -- PAGE NO. 4 JOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = PLANE ------------------ JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN 1 1 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 2 1 0.00000 0.04370 0.00000 0.00000 0.00000 0.00853 3 1 0.00000 0.15293 0.00000 0.00000 0.00000 0.01365 4 1 0.00000 0.29494 0.00000 0.00000 0.00000 0.01536 5 1 0.00000 0.44239 0.00000 0.00000 0.00000 0.01536 6 1 0.00000 0.58985 0.00000 0.00000 0.00000 0.01536 ************** END OF LATEST ANALYSIS RESULT ************** 54. PRINT SUPPORT REACTION SUPPORT REACTION :A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT -- PAGE NO. 5 SUPPORT REACTIONS -UNIT POUN INCH STRUCTURE TYPE = PLANE ----------------- JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 1 1 0.00 -0.50 0.00 0.00 0.00 -14.40 7 1 0.00 0.00 0.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 55. CHANGE 56. LOAD 2 DOWNWARD 57. JOINT LOAD 58. 4 FY -0.5 59. PERFORM ANALYSIS *WARNING- ZERO STIFFNESS IN DIRECTION 6 AT JOINT 7 EQN.NO. 16 LOADS APPLIED OR DISTRIBUTED HERE FROM ELEMENTS WILL BE IGNORED. THIS MAY BE DUE TO ALL MEMBERS AT THIS JOINT BEING RELEASED OR EFFECTIVELY RELEASED IN THIS DIRECTION. **NOTE-Tension/Compression converged after 1 iterations, Case= 2 2 Static Beams Verification Manual — 51
  • 60. 60. PRINT SUPPORT REACTION SUPPORT REACTION :A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT -- PAGE NO. 6 SUPPORT REACTIONS -UNIT POUN INCH STRUCTURE TYPE = PLANE ----------------- JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 1 2 0.00 0.28 0.00 0.00 0.00 4.03 7 2 0.00 0.22 0.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 61. PRINT MEMBER FORCES LIST 1 TO 5 MEMBER FORCES LIST 1 :A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT -- PAGE NO. 7 MEMBER END FORCES STRUCTURE TYPE = PLANE ----------------- ALL UNITS ARE -- POUN INCH (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 1 2 1 0.00 0.28 0.00 0.00 0.00 4.03 2 0.00 -0.28 0.00 0.00 0.00 -1.31 2 2 2 0.00 0.28 0.00 0.00 0.00 1.31 3 0.00 -0.28 0.00 0.00 0.00 1.42 3 2 3 0.00 0.28 0.00 0.00 0.00 -1.42 4 0.00 -0.28 0.00 0.00 0.00 4.15 4 2 4 0.00 -0.22 0.00 0.00 0.00 -4.15 5 0.00 0.22 0.00 0.00 0.00 2.07 5 2 5 0.00 -0.22 0.00 0.00 0.00 -2.07 6 0.00 0.22 0.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 62. PRINT JOINT DISPLACEMENTS LIST 1 TO 6 JOINT DISPLACE LIST 1 :A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT -- PAGE NO. 8 JOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = PLANE ------------------ JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN 1 2 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 2 2 0.00000 -0.01066 0.00000 0.00000 0.00000 -0.00190 3 2 0.00000 -0.03024 0.00000 0.00000 0.00000 -0.00186 4 2 0.00000 -0.04012 0.00000 0.00000 0.00000 0.00012 5 2 0.00000 -0.02714 0.00000 0.00000 0.00000 0.00233 6 2 0.00000 0.00000 0.00000 0.00000 0.00000 0.00307 ************** END OF LATEST ANALYSIS RESULT ************** 63. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= DEC 13,2013 TIME= 12:27:44 **** :A PROPPED CANTILEVER WITH COMPRESSION ONLY SUPPORT -- PAGE NO. 9 ************************************************************ * For technical assistance on STAAD.Pro, please visit * * http://selectservices.bentley.com/en-US/ * * * * Details about additional assistance from * * Bentley and Partners can be found at program menu * * Help->Technical Support * * * * Copyright © 1997-2013 Bentley Systems, Inc. * http://www.bentley.com * ************************************************************ 52 — STAAD.Pro 2 Static Beams Static Beam 4
  • 61. Static Beam 5 Objective To find end rotation due to torques on a stepped cantilever shaft. Reference Hand calculation using the following reference: Gere J. M., and Timoshenko, S. P., Mechanics of Materials, 2nd Edition, PWS Engineering, Page 171, Problem 3.3 - 1. Problem A stepped shaft is subjected to torques as shown in the figure. The material has shear modulus of elasticity G = 80 Gpa. Determine the angle of twist θx in degrees at the free end. Figure 2-5: Cantilevered member subject to torsional loads Comparison Result Theory STAAD.Pro Difference Angle of twist (rad.) 0.0427 0.0427 none Table 2-5: Comparison of results for static beam no. 5 Theoretical Solution Moment of Inertia: I mm = = 4.021(10) p π mm 1 (80 / 2) 2 6 4 4 I mm = = 1.272(10) p π mm 2 (60 / 2) 2 6 4 4 I mm = = 0.251(10) p π mm 2 (40 / 2) 2 6 4 4 2 Static Beams Verification Manual — 53
  • 62. Angle of twist is given by: θ = ∑i L T GI i i p = + + mm mm GPa mm mm GPa mm mm GPa 5, 800N-mm(500 ) 4.021(10) 80 2, 800N-mm(500 ) 1.272(10) 80 , 800N-mm(500 ) 0.251(10) 80 6 4 6 4 6 4 = 0.0090 + 0.0138 + 0.0199 = 0.0427 which is equal to 2.446°. STAAD Input File STAAD SPACE :A STEPPED CANTILEVER SHAFT * FILE: BEAM05.STD * * REFERENCE: MECHANICS OF MATERIALS, GERE AND TIMOSHENKO, 2ND EDITION * PROBLEM 3.3-1 PAGE 171 * UNIT KN METER JOINT COORDINATES 1 0.0 0.0 2 0.5 0.0 3 1.0 0.0 4 1.5 0.0 MEMBER INCIDENCES 1 1 2 3 UNIT MMS MEMBER PROPERTIES 1 TA ST PIPE OD 80 ID 0.0 2 TA ST PIPE OD 60 ID 0.0 3 TA ST PIPE OD 40 ID 0.0 UNIT METER CONSTANTS E 200.0E6 ALL POISSONS .25 ALL * SUPPORTS 1 FIXED UNIT MMS LOADING 1 TORSIONAL MOMENT JOINT LOADS 2 MX 3000.0 3 MX 2000.0 4 MX 800.0 PERFORM ANALYSIS PRINT JOINT DISPLACEMENTS LIST 4 FINISH STAAD Output PAGE NO. 1 **************************************************** * * * STAAD.Pro V8i SELECTseries5 * * Version 20.07.10.41 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= DEC 13, 2013 * * Time= 12:27:44 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD SPACE :A STEPPED CANTILEVER SHAFT INPUT FILE: BEAM05.STD 2. * FILE: BEAM05.STD 3. * 54 — STAAD.Pro 2 Static Beams Static Beam 5
  • 63. 4. * REFERENCE: MECHANICS OF MATERIALS, GERE AND TIMOSHENKO, 2ND EDITION 5. * PROBLEM 3.3-1 PAGE 171 6. * 7. UNIT KN METER 8. JOINT COORDINATES 9. 1 0.0 0.0 10. 2 0.5 0.0 11. 3 1.0 0.0 12. 4 1.5 0.0 13. MEMBER INCIDENCES 14. 1 1 2 3 15. UNIT MMS 16. MEMBER PROPERTIES 17. 1 TA ST PIPE OD 80 ID 0.0 18. 2 TA ST PIPE OD 60 ID 0.0 19. 3 TA ST PIPE OD 40 ID 0.0 20. UNIT METER 21. CONSTANTS 22. E 200.0E6 ALL 23. POISSONS .25 ALL 24. * 25. SUPPORTS 26. 1 FIXED 27. UNIT MMS 28. LOADING 1 TORSIONAL MOMENT 29. JOINT LOADS 30. 2 MX 3000.0 31. 3 MX 2000.0 32. 4 MX 800.0 33. PERFORM ANALYSIS :A STEPPED CANTILEVER SHAFT -- PAGE NO. 2 * FILE: BEAM05.STD P R O B L E M S T A T I S T I C S ----------------------------------- NUMBER OF JOINTS 4 NUMBER OF MEMBERS 3 NUMBER OF PLATES 0 NUMBER OF SOLIDS 0 NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 1 SOLVER USED IS THE IN-CORE ADVANCED SOLVER TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 18 34. PRINT JOINT DISPLACEMENTS LIST 4 JOINT DISPLACE LIST 4 :A STEPPED CANTILEVER SHAFT -- PAGE NO. 3 * FILE: BEAM05.STD JOINT DISPLACEMENT (CM RADIANS) STRUCTURE TYPE = SPACE ------------------ JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN 4 1 0.0000 0.0000 0.0000 0.0427 0.0000 0.0000 ************** END OF LATEST ANALYSIS RESULT ************** 35. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= DEC 13,2013 TIME= 12:27:47 **** :A STEPPED CANTILEVER SHAFT -- PAGE NO. 4 * FILE: BEAM05.STD ************************************************************ * For technical assistance on STAAD.Pro, please visit * * http://selectservices.bentley.com/en-US/ * * * * Details about additional assistance from * * Bentley and Partners can be found at program menu * * Help->Technical Support * 2 Static Beams Verification Manual — 55
  • 64. * * * Copyright © 1997-2013 Bentley Systems, Inc. * http://www.bentley.com * ************************************************************ Static Beam 6 Objective To find deflections, stress and support reactions due to a uniform load on a beam with one end fixed and the other end supported by a roller. Reference Hand calculation using the following reference: Roark, R.J., and Young, W.C., Formulas for Stress and Strain, 5th Edition, Page 109, Problem 23. Problem A horizontal beam of length 100 in, area 4 in2, height 2 in, and moment of inertia 1.3333 in4 is simply supported at one end and fixed at the other end. The beam is subjected to a uniform loading. Determine the deflection δ at x = 42.15 in., the slope θ at end A, the maximum bending stress σbend in the beam and the support reactions. E = 30(10)6 psi Density = 0.2821 lbs/in3 Figure 2-6: Beam A) problem sketch and B) mathematical model 56 — STAAD.Pro 2 Static Beams Static Beam 6
  • 65. Comparison Result Theory STAAD.Pro Difference Reaction at Node 1 (lb) 42.31 42.31 none Reaction at Node 3 (lb) 70.52 70.52 none Moment at Node 3 (in-lb) 1,410.4 1410.4 none Bending Stress, σbend at Node 2 (psi) 585.9 585.9 none Rotation at Node 1 (rad.) -.000588 -.00059 none Deflection at Node 2 (in.) -0.01528 -0.01528 none Table 2-6: Comparison of results for static beam no. 5 STAAD Input File STAAD PLANE :A FIXED-ROLLER BEAM * FILE: BEAM06.STD * * REFERENCE: ROARK AND YOUNG, PAGE 109, NO. 23. * INPUT WIDTH 72 UNIT INCHES POUND JOINT COORDINATES 1 0. 0. 0.; 2 42.15 0. 0.; 3 100. 0. 0. MEMBER INCIDENCES 1 1 2; 2 2 3 MEMBER PROPERTY AMERICAN 1 2 PRI AX 4. IZ 1.3333 YD 2. CONSTANTS E 30000000. ALL DENSITY 0.282072 ALL SUPPORTS 3 FIXED 1 PINNED LOAD 1 SELF WEIGHT SELFWEIGHT Y -1. PERFORM ANALYSIS PRINT ANALYSIS RESULTS PRINT MEMBER STRESSES ALL FINISH STAAD Output PAGE NO. 1 **************************************************** * * * STAAD.Pro V8i SELECTseries5 * * Version 20.07.10.41 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= DEC 13, 2013 * * Time= 12:27:48 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD PLANE :A FIXED-ROLLER BEAM INPUT FILE: BEAM06.STD 2 Static Beams Verification Manual — 57
  • 66. 2. * FILE: BEAM06.STD 3. * 4. * REFERENCE: ROARK AND YOUNG, PAGE 109, NO. 23. 5. * 6. INPUT WIDTH 72 7. UNIT INCHES POUND 8. JOINT COORDINATES 9. 1 0. 0. 0.; 2 42.15 0. 0.; 3 100. 0. 0. 10. MEMBER INCIDENCES 11. 1 1 2; 2 2 3 12. MEMBER PROPERTY AMERICAN 13. 1 2 PRI AX 4. IZ 1.3333 YD 2. 14. CONSTANTS 15. E 30000000. ALL 16. DENSITY 0.282072 ALL 17. SUPPORTS 18. 3 FIXED 19. 1 PINNED 20. LOAD 1 SELF WEIGHT 21. SELFWEIGHT Y -1. 22. PERFORM ANALYSIS **WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE MEMBERS/ELEMENTS/SOLIDS. THE DEFAULT VALUE HAS BEEN SET FOR THE SAME. :A FIXED-ROLLER BEAM -- PAGE NO. 2 * FILE: BEAM06.STD P R O B L E M S T A T I S T I C S ----------------------------------- NUMBER OF JOINTS 3 NUMBER OF MEMBERS 2 NUMBER OF PLATES 0 NUMBER OF SOLIDS 0 NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2 SOLVER USED IS THE IN-CORE ADVANCED SOLVER TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 4 23. PRINT ANALYSIS RESULTS ANALYSIS RESULTS :A FIXED-ROLLER BEAM -- PAGE NO. 3 * FILE: BEAM06.STD JOINT DISPLACEMENT (INCH RADIANS) STRUCTURE TYPE = PLANE ------------------ JOINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN 1 1 0.00000 0.00000 0.00000 0.00000 0.00000 -0.00059 2 1 0.00000 -0.01528 0.00000 0.00000 0.00000 0.00000 3 1 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 :A FIXED-ROLLER BEAM -- PAGE NO. 4 * FILE: BEAM06.STD SUPPORT REACTIONS -UNIT POUN INCH STRUCTURE TYPE = PLANE ----------------- JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 3 1 0.00 70.52 0.00 0.00 0.00 -1410.36 1 1 0.00 42.31 0.00 0.00 0.00 0.00 :A FIXED-ROLLER BEAM -- PAGE NO. 5 * FILE: BEAM06.STD MEMBER END FORCES STRUCTURE TYPE = PLANE ----------------- ALL UNITS ARE -- POUN INCH (LOCAL ) MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z 58 — STAAD.Pro 2 Static Beams Static Beam 6
  • 67. 1 1 1 0.00 42.31 0.00 0.00 0.00 0.00 2 0.00 5.25 0.00 0.00 0.00 781.13 2 1 2 0.00 -5.25 0.00 0.00 0.00 -781.13 3 0.00 70.52 0.00 0.00 0.00 -1410.36 ************** END OF LATEST ANALYSIS RESULT ************** 24. PRINT MEMBER STRESSES ALL MEMBER STRESSES ALL :A FIXED-ROLLER BEAM -- PAGE NO. 6 * FILE: BEAM06.STD MEMBER STRESSES --------------- ALL UNITS ARE POUN/SQ INCH MEMB LD SECT AXIAL BEND-Y BEND-Z COMBINED SHEAR-Y SHEAR-Z 1 1 .0 0.0 0.0 0.0 0.0 15.9 0.0 1.0 0.0 C 0.0 585.9 585.9 2.0 0.0 2 1 .0 0.0 0.0 585.9 585.9 2.0 0.0 1.0 0.0 C 0.0 1057.8 1057.8 26.4 0.0 ************** END OF LATEST ANALYSIS RESULT ************** 25. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= DEC 13,2013 TIME= 12:27:50 **** :A FIXED-ROLLER BEAM -- PAGE NO. 7 * FILE: BEAM06.STD ************************************************************ * For technical assistance on STAAD.Pro, please visit * * http://selectservices.bentley.com/en-US/ * * * * Details about additional assistance from * * Bentley and Partners can be found at program menu * * Help->Technical Support * * * * Copyright © 1997-2013 Bentley Systems, Inc. * http://www.bentley.com * ************************************************************ Static Beam 7 Objective To find support reactions due to an axial load applied at two locations on a column with both ends pinned. Reference Hand calculation using the following reference: Timoshenko, S., Strength of Materials, Part I, D. Van Nostrand Co., Inc., 3rd Edition, 1956. Page 26, Problem 10. Problem Find the support reactions at the end joints 1 and 4. E = 30(10)6 psi 2 Static Beams Verification Manual — 59
  • 68. Figure 2-7: Column A) problem sketch and B) mathematical model Comparison Result Theory STAAD.Pro Difference Reaction at Node 1 (lb) 600 600 none Reaction at Node 4 (lb) 900 900 none Table 2-7: Comparison of results for static beam no. 5 STAAD Input File STAAD TRUSS :A PINNED-PINNED COLUMN * FILE: BEAM07.STD * * REFERENCE: TIMOSHENKO, STRENGTH OF MATERIALS, PART 1 * PROBLEM 10, PAGE 26 * INPUT WIDTH 79 UNIT INCHES POUND JOINT COORDINATES 1 48.000 72.000 0.000 2 48.000 76.000 0.000 3 48.000 79.000 0.000 4 48.000 82.000 0.000 MEMBER INCIDENCES 60 — STAAD.Pro 2 Static Beams Static Beam 7
  • 69. 1 1 2 2 2 3 3 3 4 MEMBER PROPERTY AMERICAN 1 TO 3 PRISMATIC AX 1. CONSTANTS E 30000000. ALL SUPPORTS 1 4 PINNED LOAD 1 AXIAL LOAD JOINT LOAD 3 FY -1000. 2 FY -500. PERFORM ANALYSIS PRINT SUPPORT REACTIONS FINISH STAAD Output PAGE NO. 1 **************************************************** * * * STAAD.Pro V8i SELECTseries5 * * Version 20.07.10.41 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= DEC 13, 2013 * * Time= 12:27:51 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD TRUSS :A PINNED-PINNED COLUMN INPUT FILE: BEAM07.STD 2. * FILE: BEAM07.STD 3. * 4. * REFERENCE: TIMOSHENKO, STRENGTH OF MATERIALS, PART 1 5. * PROBLEM 10, PAGE 26 6. * 7. INPUT WIDTH 79 8. UNIT INCHES POUND 9. JOINT COORDINATES 10. 1 48.000 72.000 0.000 11. 2 48.000 76.000 0.000 12. 3 48.000 79.000 0.000 13. 4 48.000 82.000 0.000 14. MEMBER INCIDENCES 15. 1 1 2 16. 2 2 3 17. 3 3 4 18. MEMBER PROPERTY AMERICAN 19. 1 TO 3 PRISMATIC AX 1. 20. CONSTANTS 21. E 30000000. ALL 22. SUPPORTS 23. 1 4 PINNED 24. LOAD 1 AXIAL LOAD 25. JOINT LOAD 26. 3 FY -1000. 27. 2 FY -500. 28. PERFORM ANALYSIS **WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE MEMBERS/ELEMENTS/SOLIDS. THE DEFAULT VALUE HAS BEEN SET FOR THE SAME. 2 Static Beams Verification Manual — 61
  • 70. :A PINNED-PINNED COLUMN -- PAGE NO. 2 * FILE: BEAM07.STD P R O B L E M S T A T I S T I C S ----------------------------------- NUMBER OF JOINTS 4 NUMBER OF MEMBERS 3 NUMBER OF PLATES 0 NUMBER OF SOLIDS 0 NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2 SOLVER USED IS THE IN-CORE ADVANCED SOLVER TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 4 *WARNING- ZERO STIFFNESS IN DIRECTION 1 AT JOINT 2 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 OR EFFECTIVELY RELEASED IN THIS DIRECTION. *WARNING- ZERO STIFFNESS IN DIRECTION 1 AT JOINT 3 EQN.NO. 3 29. PRINT SUPPORT REACTIONS SUPPORT REACTION :A PINNED-PINNED COLUMN -- PAGE NO. 3 * FILE: BEAM07.STD SUPPORT REACTIONS -UNIT POUN INCH STRUCTURE TYPE = TRUSS ----------------- JOINT LOAD FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM Z 1 1 0.00 600.00 0.00 0.00 0.00 0.00 4 1 0.00 900.00 0.00 0.00 0.00 0.00 ************** END OF LATEST ANALYSIS RESULT ************** 30. FINISH *********** END OF THE STAAD.Pro RUN *********** **** DATE= DEC 13,2013 TIME= 12:27:54 **** :A PINNED-PINNED COLUMN -- PAGE NO. 4 * FILE: BEAM07.STD ************************************************************ * For technical assistance on STAAD.Pro, please visit * * http://selectservices.bentley.com/en-US/ * * * * Details about additional assistance from * * Bentley and Partners can be found at program menu * * Help->Technical Support * * * * Copyright © 1997-2013 Bentley Systems, Inc. * http://www.bentley.com * ************************************************************ Static Beam 8 Objective To find the stress due to an applied moment at the free end of a cantilever beam with inverted tee section. Reference Hand calculation using the following reference: Crandall, S.H., and Dahl, N.C., An Introduction to the Mechanics of Solids, McGraw-Hill, Inc., 1959, Page 294, Problem 7.2.. 62 — STAAD.Pro 2 Static Beams Static Beam 8
  • 71. Problem Find the maximum bending stress in the beam. E = 30(10)6 psi b = 1.5 in., h = 8 in., L = 10 in. M = 1,000,000 in. - lb. Figure 2-8: Beam A) problem sketch and B) mathematical model Comparison Result Theory STAAD.Pro Difference Bending stress, σ (psi) 700 700 none Table 2-8: Comparison of results for static beam no. 5 STAAD Input File STAAD PLANE :A CANTILEVERED BEAM OF INVERTED TEE SECTION * FILE: BEAM08.STD * * REFERENCE: CRANDALL & DAHL, AN INTRODUCTION TO THE MECHANICS * OF SOLIDS, PAGE294, EX. 7.2 * INPUT WIDTH 79 UNIT INCHES POUND JOINT COORDINATES 1 0.000 0.000 0.000 2 10.000 0.000 0.000 MEMBER INCIDENCES 1 1 2 MEMBER PROPERTY AMERICAN 1 PRISMATIC YD 20. ZD 9. YB 16. ZB 1.5 CONSTANTS E 30000000. ALL BETA 180. ALL SUPPORTS 2 Static Beams Verification Manual — 63
  • 72. 1 FIXED LOAD 1 CONSTANT MOMENT JOINT LOAD 2 MZ 100000.0 PERFORM ANALYSIS PRINT MEMBER PROPERTIES ALL PRINT MEMBER STRESSES ALL FINISH STAAD Output **************************************************** * * * STAAD.Pro V8i SELECTseries3 * * Version 20.07.08.20 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= MAR 6, 2012 * * Time= 13:37:57 * * * * USER ID: Bentley Systems * **************************************************** 1. STAAD PLANE :A CANTILEVERED BEAM OF INVERTED TEE SECTION INPUT FILE: beam8.STD 2. * FILE: BEAM08.STD 3. * 4. * REFERENCE: CRANDALL & DAHL, AN INTRODUCTION TO THE MECHANICS 5. * OF SOLIDS, PAGE294, EX. 7.2 6. * 7. INPUT WIDTH 79 8. UNIT INCHES POUND 9. JOINT COORDINATES 10. 1 0.000 0.000 0.000 11. 2 10.000 0.000 0.000 12. MEMBER INCIDENCES 13. 1 1 2 14. MEMBER PROPERTY AMERICAN 15. 1 PRISMATIC YD 20. ZD 9. YB 16. ZB 1.5 16. CONSTANTS 17. E 30000000. ALL 18. BETA 180. ALL 19. SUPPORTS 20. 1 FIXED 21. LOAD 1 CONSTANT MOMENT 22. JOINT LOAD 23. 2 MZ 100000.0 24. PERFORM ANALYSIS **WARNING** THE POISSON'S RATIO HAS NOT BEEN SPECIFIED FOR ONE OR MORE MEMBERS/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 = 2/ 1/ 1 SOLVER USED IS THE IN-CORE ADVANCED SOLVER TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 3 25. PRINT MEMBER PROPERTIES ALL MEMBER PROPERTIES. UNIT - INCH ----------------- MEMB PROFILE AX/ IZ/ IY/ IX/ AY AZ SZ SY 1 PRISMATIC 60.00 2000.00 247.50 154.89 30.00 36.00 142.86 55.00 64 — STAAD.Pro 2 Static Beams Static Beam 8
  • 73. ************ END OF DATA FROM INTERNAL STORAGE ************ 26. PRINT MEMBER STRESSES ALL MEMBER STRESSES --------------- ALL UNITS ARE POUN/SQ INCH MEMB LD SECT AXIAL BEND-Y BEND-Z COMBINED SHEAR-Y SHEAR-Z 1 1 .0 0.0 0.0 700.0 700.0 0.0 0.0 1.00 0.0 0.0 700.0 700.0 0.0 0.0 ************** END OF LATEST ANALYSIS RESULT ************** 27. FINISH Static Beam 9 Objective To find deflection and stress at the center due to a uniform, static load on a simply supported beam on elastic foundation. Reference Hand calculation using the following reference: Peterson, F.E., Elastic Analysis for Structural Engineering (EASE2), Example Problem Manual, Engineering Analysis Corporation, Berkeley, CA, 1981. Problem Find the vertical deflection and bending stress at the center of the beam.Spacing between E = 30(10)6 psi b = 1.0 in., h = 7.114 in., L = 240 in. wu = 43.3 lb/in. Figure 2-9: One-half beam for mathematical model Comparison Result Theory STAAD.Pro Difference Bending stress, σ (psi) 18,052 18,053.29 none Vertical deflection (in.) 1.0453 1.04549 none Table 2-9: Comparison of results for static beam no. 5 2 Static Beams Verification Manual — 65
  • 74. STAAD Input File STAAD SPACE :A SIMPLY SUPPORTED BEAM ON ELASTIC FOUNDATION * FILE: BEAM09.STD * * REFERENCE: PETERSON, EASE2, EXAMPLE PROBLEM MANUAL * INPUT WIDTH 72 UNIT INCHES POUND JOINT COORDINATES 1 0. 0. 0.; 2 0. 7.114 0.; 3 0. 0. 6.; 4 0. 7.114 6.; 5 0. 0. 12. 6 0. 7.114 12.; 7 0. 0. 18.; 8 0. 7.114 18.; 9 0. 0. 24. 10 0. 7.114 24.; 11 0. 0. 30.; 12 0. 7.114 30.; 13 0. 0. 36. 14 0. 7.114 36.; 15 0. 0. 42.; 16 0. 7.114 42.; 17 0. 0. 48. 18 0. 7.114 48.; 19 0. 0. 54.; 20 0. 7.114 54.; 21 0. 0. 60. 22 0. 7.114 60.; 23 0. 0. 66.; 24 0. 7.114 66.; 25 0. 0. 72. 26 0. 7.114 72.; 27 0. 0. 78.; 28 0. 7.114 78.; 29 0. 0. 84. 30 0. 7.114 84.; 31 0. 0. 90.; 32 0. 7.114 90.; 33 0. 0. 96. 34 0. 7.114 96.; 35 0. 0. 102.; 36 0. 7.114 102.; 37 0. 0. 108. 38 0. 7.114 108.; 39 0. 0. 114.; 40 0. 7.114 114.; 41 0. 0. 120. 42 0. 7.114 120. ELEMENT INCIDENCES 1 1 2 4 3; 2 3 4 6 5; 3 5 6 8 7; 4 7 8 10 9; 5 9 10 12 11; 6 11 12 14 13 7 13 14 16 15; 8 15 16 18 17; 9 17 18 20 19; 10 19 20 22 21 11 21 22 24 23; 12 23 24 26 25; 13 25 26 28 27; 14 27 28 30 29 15 29 30 32 31; 16 31 32 34 33; 17 33 34 36 35; 18 35 36 38 37 19 37 38 40 39; 20 39 40 42 41 ELEMENT PROPERTY 1 TO 20 TH 1. CONSTANTS E 30000000. ALL SUPPORTS 1 FIXED BUT KFY 78.125 41 FIXED BUT FZ MX 2 FIXED BUT FY 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 - 39 FIXED BUT FZ MX KFY 156.25 LOAD 1 UNIFORM LOAD OF 43.4 LBS/IN JOINT LOAD 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 FY 260.4 2 42 FY 130.2 PERFORM ANALYSIS PRINT JOINT DISPLACEMENTS LIST 1 2 PRINT ELEMENT JOINT STRESSES LIST 1 2 FINISH STAAD Output PAGE NO. 1 **************************************************** * * * STAAD.Pro V8i SELECTseries5 * * Version 20.07.10.41 * * Proprietary Program of * * Bentley Systems, Inc. * * Date= DEC 13, 2013 * * Time= 12:27:57 * * * * USER ID: Bentley Systems, Inc. * **************************************************** 1. STAAD SPACE :A SIMPLY SUPPORTED BEAM ON ELASTIC FOUNDATION INPUT FILE: BEAM09.STD 2. * FILE: BEAM09.STD 66 — STAAD.Pro 2 Static Beams Static Beam 9