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Torsion and Warping Design based on the AISC Guide 9

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Torsion and Warping Design based on the AISC Guide 9

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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 Considered by ASD9 code I-shapes Channels Single Angles Structural Tubes (Rectangular HSS)

    6. 6 Cross-sections Considered by 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 to Bending 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 Design for 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 Design for 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 Design Parameters 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 Design Parameters 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 Design Example 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 Design Example 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 Design Example 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 Design Example 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 Design Example 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 Design Example 1 – CASE 2, PIN-PIN

    51. 51 Torsional and Warping Design Example 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 Design Example 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 Design Example 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 Design Example 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 Design Example 2 (continued)

    56. 56 Torsional and Warping Design Example 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 Design Example 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 Design Example 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 Design Example 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 Design Example 3 (continued)

    61. 61 Torsional and Warping Design Example 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 Design Example 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 Design Example 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 Design Example 4

    65. 65 Torsional and Warping Design Example 4 (continued)

    66. 66 Torsional and Warping Design Example 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 Design Example 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 Design Example 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 Design Example 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

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