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1. 1 Torsion and Warping Design based on the AISC Guide 9 Hamid Zand
GT STRUDL Users Group
Jupiter, Florida
June 18-21, 2007
2. 2
3. 3 Steel Design Reference Manuals 1997 Torsional Analysis of Structural Steel Members, Steel Design Gide Series 9
1963 Torsion Analysis of Rolled Steel Sections by Bethlehem Steel
1989 AISC ASD Ninth Edition
2005 AISC Thirteenth Edition
4. 4 Design Codes Considered ASD9 code Based on the 1989 AISC Allowable Stress Design, Ninth Edition
AISC13 code Based on the 2005 AISC Steel Construction Manual, Thirteenth Edition
5. 5 Cross-sections Consideredby ASD9 code I-shapes
Channels
Single Angles
Structural Tubes (Rectangular HSS)
6. 6 Cross-sections Consideredby AISC13 code I-shapes
Channels
Single Angles
Pipes (Round HSS)
Structural Tubes (Rectangular HSS)
7. 7 Cross-section Torsional Categories Open sections - I-shapes, Channels, and
Single Angles
Closed sections - Structural Tubes (HSS)
Pipes (round HSS)
8. 8
9. 9
10. 10 Centroid of a Cross-section Centroid of a cross-section is the center of its cross-sectional area (its mass). The centroid is a location at which the cross-section would be stable, or balance, under the influence of gravity.
11. 11 Shear Center Shear center is the point through which the applied loads must pass to product bending without twisting
Shear center is the location in a cross-section where no torsion occurs when flexural shears act in planes passing through that location. In other words, forces acting through the shear center will cause no torsional stresses to develop.
12. 12 Centroid and Shear Center
13. 13 Selection Sections for Torsion Round HSS and Steel Pipes are the most efficient for resisting torsion
Square and Rectangular HSS (Tubes) also provide good resistance to torsion
Open sections such as W-shapes and Channels are poor choices to resist torsion
14. 14 Stiffen a W-shape to Resist Torsion
15. 15 Torsion Categories Pure Torsion – When the cross-section remains in
plane and the element rotation
occurs during torsion. This is often
called, Saint-Venant’s torsion.
Warping Torsion – The out-of-plane effect which
causes cross-section lateral
displacements
16. 16 Stresses Associated to Torsion Pure Torsion – Shear Stress
Warping Torsion – Shear Stress
Normal Stress
17. 17 Cross-section Torsional Categories Open Sections – Warping stresses are more
significant then the stresses
from pure torsion
Closed Sections – Warping stresses are
generally smaller than the
stresses from pure torsion
and can be neglected
18. 18 Torsion and Warping is defined as when a cross-section goes through twisting and distortion
19. 19 Torsional Angle of Rotation ? = angle of rotation due to torsional moment
?' = first derivative of ? with respect to the local X axis
?'' = second derivative of ? with respect to the local X axis
?''' = third derivative of ? with respect to the local X axis
20. 20 Torsion and Warping Design Shear Stress due to Pure Torsion
Shear Stresses Due to Warping
Normal Stresses Due to Warping
21. 21 Pure Torsional Shear Stress
22. 22 Shear Stresses Due to Warping
23. 23 Normal Stresses Due to Warping
24. 24 Elastic Stresses Due toBending and Shear Normal Stress due to Bending
Shear Stress due to applied Load
25. 25 Normal Stress due to Bending
26. 26 Shear Stress due to applied Load
27. 27 Shear Stress due to applied Load
28. 28 Combining Torsional Stresses with Other Stresses ASD
LRFD
29. 29 Combining Torsional Stresses with Other Stresses for when Second Order Effects Occur but have not been Considered during Analysis ASD
LRFD
30. 30 Combined Torsional Shear Stresses and Transverse Shear tby = shear stress in Y direction
tbz = shear stress in Z direction
tt = pure torsional shear stress
tw = shear stress due to warping
31. 31 Torsional Boundary Condition
32. 32 Torsional Boundary Condition
33. 33 Torsional Boundary Condition
34. 34 Torsional Boundary Condition
35. 35 Torsional and Warping CASEs
36. 36 Torsional and Warping CASEs
37. 37 Torsional and Warping CASEs
38. 38 Cross-sections and Applicable Torsional CASEs
39. 39 Cross-sections and Applicable Torsional CASEs
40. 40 Torsional and Warping Designfor ASD Torsional warping stresses for I-shapes
Torsional warping stresses for Channels
Torsional warping stresses for Single Angles
Torsional warping stresses for Structural Tubes
41. 41 Torsional and Warping Designfor LRFD Torsional warping stresses for I-shapes
Torsional warping stresses for Channels
Torsional warping stresses for Single Angles
Torsional warping stresses for Pipes
Torsional warping stresses for Structural Tubes
42. 42 Torsional and Warping DesignParameters Tor-CASE specify torsion and warping CASE for a load name
Tor-Comp Calculation of torsional moment for a cross-section which has the shear center not in the same location as centroid from a user specified concentrated or uniform force in the local Y direction
WARP-END Parameter to describe the boundary condition of a member respect to warping restraints
43. 43 Torsional and Warping DesignParameters LWARP distance between end restraints as described in the ‘WARP-END’ parameter
CombMeth specify the combined method of the axial, bending, shear, and torsional stresses
SecOrder Indicates that the second order effect occurs but has not been considered in determining the normal stresses
44. 44 Torsional and Warping DesignExample 1 W10x49 spans 15 ft and supports a 10 kips service load at midspan that acts at a 6 in. eccentricity with respect to the shear center
45. 45 Torsional and Warping DesignExample 1 (continued) Check torsional and warping stresses based on the CASE 3
Check torsional and warping stresses based on the CASE 2 with PIN-PIN connections
46. 46 Torsional and Warping Design Example 1 – CASE 3
47. 47 Torsional and Warping DesignExample 1 – CASE 3 (continued) *TITLE 'VMS83 - Torsion and Warping code check for W shape, CASE 3, ASD9'
STRUDL 'VMS83' 'Torsion and Warping code check for W shape, CASE 3, ASD9'
$* ** CASE 3
$* ** Member ends are pinned.
$* ** Torsional moment applied at the center of the member.
$* ** Example 5.1 of "Torsional Analysis of Structural Steel Members" by
$* ** AISC Steel Design Guide Series 9.
$* ** Member defined in the global X directions.
$* ** Local coordinate system for member load is used.
$* ** Fractional option of the member load specified.
UNIT KIP FEET
JOINT COORDINATES
1 0.0 0.0 0.0 SUPPORT
2 15.0 0.0 0.0 SUPPORT
JOINT RELEASES
1 2 MOMENT Z
2 FORCE X
TYPE SPACE FRAME
MEMBER INCIDENCES
1 1 2
48. 48 Torsional and Warping DesignExample 1 – CASE 3 (continued) MATERIAL STEEL
UNITS KIPS INCH
CONSTANTS
G 11200.0 ALL
MEMBER PROPERTIES PRISMATIC
1 TABLE 'WSHAPES9' 'W10x49'
LOADING 1
MEMBER LOADS
1 FORCE Y CONCENTRATED FR P -10.0 L 0.5
1 MOMENT X CONCENTRATED FR M -60.0 L 0.5
STIFFNESS ANALYSIS
49. 49 Torsional and Warping DesignExample 1 – CASE 3 (continued) UNITS INCH KIPS
PARAMETER
CODE ASD9 ALL
Tor-CASE 3 ALL
SUMMARY YES ALL
SECTION FR NS 7 0.0 0.25 0.495 0.5 0.505 0.75 1.0
LIST SECTION FORCES MEM 1
CHECK MEMBER 1
SUMMARIZE CODE CHECK MEMBER 1 ALL POINTS
FINISH $ Output
50. 50 Torsional and Warping DesignExample 1 – CASE 2, PIN-PIN
51. 51 Torsional and Warping DesignExample 1 – CASE 2, PIN-PIN (continued) *TITLE 'VMS83_1 - Torsion and Warping code check for W shape, CASE 2, ASD9'
STRUDL 'VMS83_1' 'Torsion and Warping code check for W shape, CASE 2, ASD9'
$* ** CASE 2 with PIN-PIN end connections
$* ** Member ends are pinned.
$* ** Example 5.1 of "Torsional Analysis of Structural Steel Members" by AISC
$* ** AISC "Steel Design Guide Series 9"
UNIT KIP FEET
JOINT COORDINATES
1 0.0 0.0 0.0 SUPPORT
2 7.5 0.0 0.0
3 15.0 0.0 0.0 SUPPORT
4 7.5 0.0 -0.5
JOINT RELEASES
1 3 MOMENT Z
3 FORCE X
TYPE SPACE FRAME
MEMBER INCIDENCES
1 1 2
2 2 3
3 2 4
52. 52 Torsional and Warping DesignExample 1 – CASE 2, PIN-PIN (continued) MATERIAL STEEL
UNITS KIPS INCH
CONSTANTS
G 11200.0 ALL
MEMBER PROPERTIES PRISMATIC
1 TO 3 TABLE 'WSHAPES9' 'W10x49'
LOADING 1
MEMBER LOADS
3 FORCE Y GLOBAL CONCENTRATED FR P -10.0 L 1.0
STIFFNESS ANALYSIS
53. 53 Torsional and Warping DesignExample 1 – CASE 2, PIN-PIN (continued) UNITS INCH KIPS
PARAMETER
CODE ASD9 ALL
Tor-CASE 2 LOADING 1
WARP-END PIN-FIX MEMBER 1
WARP-END FIX-PIN MEMBER 2
SUMMARY YES ALL
SECTION FR NS 2 0.0 1.0
LIST SECTION FORCES MEMBERS 1 2
CHECK MEMBERS 1 2
SUMMARIZE CODE CHECK MEMBERS 1 2 ALL POINTS
FINISH $ Output
54. 54 Torsional and Warping DesignExample 2 MC18x42.7 channel spans 12 ft and supported a uniformly distributed service load of 2.4 kips/ft acting through the centroid of the channel
55. 55 Torsional and Warping DesignExample 2 (continued)
56. 56 Torsional and Warping DesignExample 2 (continued) *TITLE 'VMS89 - Torsion and Warping code check for Channel, CASE 7, ASD9'
STRUDL 'VMS89' 'Torsion and Warping code check for Channel, CASE 7, ASD9'
$* ** CASE 7
$* ** Member ends are fixed.
$* ** Torsional moment is computed from applied uniformed load which is
$* ** a uniformed torsional moment from the start to the end of the member.
$* ** Example problem #5.5 from "Torsional Analysis of Structural Steel Members"
$* ** by AISC, Steel Design Guide Series 9.
$* ** CASE NUMBER 7 on Page 26
UNIT KIP FEET
JOINT COORDINATES
1 0.0 0.0 0.0 SUPPORT
2 12.0 0.0 0.0 SUPPORT
TYPE SPACE FRAME
MEMBER INCIDENCES
1 2 1
57. 57 Torsional and Warping DesignExample 2 (continued) MATERIAL STEEL
UNITS KIPS INCH
CONSTANTS
G 11200.0 ALL
MEMBER PROPERTIES PRISMATIC
1 TABLE 'CHANNEL9' 'MC18X42.7'
UNIT KIP FEET
LOADING 1
MEMBER LOADS
1 FORCE Y UNIFORM W -2.4
STIFFNESS ANALYSIS
58. 58 Torsional and Warping DesignExample 2 (continued) UNITS INCH KIPS
PARAMETER
CODE ASD9 ALL
Tor-CASE 7 LOAD 1
SUMMARY YES ALL
MXMIN 0.0 ALL
PRINT MEMBER PROPERTIES
SECTION FR NS 4 0.0 0.2 0.5 1.0
LIST SECTION FORCES MEM 1
CHECK MEMBER 1
SUMMARIZE CODE CHECK MEMBER 1 ALL POINTS
PARAMETER
CombMeth ALGEBRAIC ALL
CHECK MEMBER 1
SUMMARIZE CODE CHECK MEMBER 1 ALL POINTS
FINISH $ Output
59. 59 Torsional and Warping DesignExample 3 L3x3x1/2 single angle is cantilevered 2 ft and supports a 1.33 kip service load at midspan that acts as shown with a 1.5 in. eccentricity with respect to the shear center
60. 60 Torsional and Warping DesignExample 3 (continued)
61. 61 Torsional and Warping DesignExample 3 (continued) *TITLE 'VMS92 - Torsion and Warping code check for Single Angle, ASD9'
STRUDL 'VMS92' 'Torsion and Warping code check for Single Angle, ASD9'
$* ** Cantilever Member.
$* ** Concentrated force is applied at the end of the member.
$* ** Example problem #5.6 from "Torsional Analysis of Structural Steel Members"
$* ** by AISC, Steel Design Guide Series 9.
$* ** Page 29
UNIT KIP FEET
JOINT COORDINATES
1 0.0 0.0 0.0 SUPPORT
2 2.0 0.0 0.0
TYPE SPACE FRAME
MEMBER INCIDENCES
1 1 2
62. 62 Torsional and Warping DesignExample 3 (continued) MATERIAL STEEL
UNITS KIPS INCH DEGREE
CONSTANTS
G 11200.0 ALL
BETA -135.0 ALL
MEMBER PROPERTIES PRISMATIC
1 TABLE 'L-EQ-L3' 'L3x3x1/2'
UNIT KIP INCH
LOADING 1
MEMBER LOADS
1 FORCE Y GLOBAL CONCENTRATED FR P -1.33 L 1.0
1 MOMENT X GLOBAL CONCENTRATED FR M 2.0 L 1.0
STIFFNESS ANALYSIS
63. 63 Torsional and Warping DesignExample 3 (continued) UNITS INCH KIPS
PARAMETER
CODE ASD9 ALL
STEELGRD A529-G50 ALL
SUMMARY YES ALL
MXMIN 0.0 ALL
Tor-Comp NO ALL
PRINT MEMBER PROPERTIES
SECTION FR NS 3 0.0 0.5 1.0
LIST SECTION FORCES MEMBER 1
CHECK MEMBER 1
SUMMARIZE CODE CHECK MEMBER 1 ALL POINTS
PARAMETER
CombMeth ALGEBRAIC ALL
CHECK MEMBER 1
SUMMARIZE CODE CHECK MEMBER 1 ALL POINTS
FINISH $ Output
64. 64 Torsional and Warping DesignExample 4
65. 65 Torsional and Warping DesignExample 4 (continued)
66. 66 Torsional and Warping DesignExample 4 (continued) *TITLE 'Example4 - Torsion and Warping code check for W shape, CASEs 3 and 4, ASD9'
STRUDL 'Example4' 'Torsion and Warping code check for W shape, CASEs 3 and 4, ASD9'
$* ** CASEs 3 and 4
$* ** Member ends are pinned.
$* ** Torsional moment applied as a uniformed torsional moment from
$* ** the start to the end of the member.
$* ** Torsional moment applied as a concentrated torsional moment at
$* ** 144.0, 240.0, and 336.0 inches of the member.
$* ** Member defined in the global X directions.
$* ** Local coordinate system for member load is used.
UNIT KIP INCH
JOINT COORDINATES
1 0.0 0.0 0.0 SUPPORT
2 480.0 0.0 0.0 SUPPORT
JOINT RELEASES
1 2 MOMENT Y Z
TYPE SPACE FRAME
MEMBER INCIDENCES
1 1 2
67. 67 Torsional and Warping DesignExample 4 (continued) MATERIAL STEEL
CONSTANTS
G 11200.0 ALL
MEMBER PROPERTIES PRISMATIC
1 TABLE 'WSHAPES9' 'W14x132'
UNITS KIPS INCH
LOADING 1
MEMBER LOADS
1 FORCE Y UNIFORM W -0.05
LOADING 2
MEMBER LOADS
1 FORCE Y CONCENTRATED P -5.0 L 144.0
1 FORCE Y CONCENTRATED P -5.0 L 336.0
1 FORCE Z CONCENTRATED P 5.0 L 240.0
LOADING 3
MEMBER LOADS
1 MOMENT X CONCENTRATED P 50.0 L 144.0
LOADING 4
MEMBER LOADS
1 MOMENT X CONCENTRATED P 50.0 L 240.0
LOADING 5
MEMBER LOADS
1 MOMENT X CONCENTRATED P 50.0 L 336.0
68. 68 Torsional and Warping DesignExample 4 (continued) LOADING 6
MEMBER LOADS
1 MOMENT X UNIFORM W 0.25
LOAD COMBINATIONS 'A' COMBINED 1 1.0 2 1.0 3 1.0 4 1.0 5 1.0 6 1.0
STIFFNESS ANALYSIS
UNITS INCH KIPS
PARAMETER
CODE ASD9 ALL
STEELGRD A992 ALL
Tor-CASE 3 LOADS 3 4 5 $ Pinned-Pinned
Tor-CASE 4 LOAD 6 $ Pinned-Pinned
SUMMARY YES ALL
SECTION FR NS 7 0.0 0.1 0.3 0.5 0.7 0.9 1.0
LIST SECTION FORCES MEMBER 1
LOAD LIST 'A'
CHECK MEMBER 1
SUMMARIZE CODE CHECK MEMBER 1 CRITICAL SECTION ALL VALUES
SUMMARIZE CODE CHECK MEMBER 1 SECTIONS 1 2 3 4 ALL VALUES
FINISH $ Output
69. 69 Torsional and Warping DesignExample 5 LOADING 6
MEMBER LOADS
1 MOMENT X UNIFORM W 0.25
LOAD COMBINATIONS 'A' COMBINED 1 1.0 2 1.0 3 1.0 4 1.0 5 1.0 6 1.0
STIFFNESS ANALYSIS
UNITS INCH KIPS
PARAMETER
CODE ASD9 ALL
STEELGRD A992 ALL
Tor-CASE 6 LOADS 3 4 5 $ Fixed-Fixed
Tor-CASE 7 LOAD 6 $ Fixed-Fixed
SUMMARY YES ALL
SECTION FR NS 7 0.0 0.1 0.3 0.5 0.7 0.9 1.0
LIST SECTION FORCES MEMBER 1
LOAD LIST 'A'
CHECK MEMBER 1
SUMMARIZE CODE CHECK MEMBER 1 CRITICAL SECTION ALL VALUES
SUMMARIZE CODE CHECK MEMBER 1 SECTIONS 1 2 3 4 ALL VALUES
FINISH $ Output
70. 70 Torsion and Warping Design based on the AISC Guide 9
Questions