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V. AISC 360-16 - Torsion

Verify the torsional strength of an angle section using the LRFD method in the AISC 360-16 code. Use the simple method for calculating torsional shears (i.e., no full twist analysis). Perform torsion checks per AISC Design Guide 9.

Reference

  1. Steel Construction Manual, 15th Edition, American Institute of Steel Construction, 2017
  2. Torsional Analysis of Structural Steel Members Deign Guide 9, American Institute of Steel Construction

Details

The angle section is an L 3x3x1/2 angle of ASTM A992 material. The member is a 2 ft long cantilever with a total end torque of 3.0 in·kips.

Validation

Maximum torsional shear stress: τ f = T t f J = 3.0 0.5 0.234 = 6.41 ksi

By observation, direct shear stress is zero (torsion loading only). Therefore, total torsional stress is = τf .

Torsional shear resistance: ϕT×0.6×Fy = 0.9×0.6×50 = 27 ksi

Ratio: 6.41 ksi / 27 ksi = 0.237

Results

Table 1. Comparison of results
Parameter Hand Calculation STAAD.Pro Difference Comments
Torsional shear stress ratio 0.237 0.242 2.1% Negligible difference when considering simplified method used by hand calculations

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\360-2016\Torsion\AISC 360-16 - Torsion.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 23-Feb-18
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 2 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 4.176e+06
POISSON 0.3
DENSITY 0.489024
ALPHA 6.5e-06
DAMP 0.03
TYPE STEEL
STRENGTH FY 5184 FU 8352 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TABLE ST L30308
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
MEMBER LOAD
1 CMOM GX -0.25 2
PERFORM ANALYSIS
PARAMETER 1
CODE AISC UNIFIED 2016
ALH 1 ALL
FU 7200 ALL
FYLD 7200 ALL
METHOD LRFD
SOE 0 ALL
TND 9 ALL
TORSION 1 ALL
TRACK 2 ALL
UNIT KIP INCH
CHECK CODE ALL
FINISH

STAAD Output

                       STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.1)
                     *****************************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted).
 ***NOTE : AISC 360-16 Design Statement for STAAD.Pro.
 *** AXIS CONVENTION ***:
 ========================
 The capacity results and intermediate results in the report follow the notations
 and axes labels as defined in the AISC 360-16 code.
 The analysis results are reported in STAAD.Pro axis convention and the AISC 360:16
 design results are reported in AISC 360-16 code axis convention.
   AISC Spec.      STAAD.Pro      Description
  ------------    -----------     -------------
       X               Z          Axis typically parallel to the sections principal major axis.
       Y               Y          Axis typically parallel to the sections principal minor axis.
       Z               X          Longitudinal axis perpendicular to the cross section.
 SECTION FORCES AXIS MAPPING: -
   AISC Spec.      STAAD.Pro      Description
  ------------    -----------     -------------
       Pz              FX         Axial force.
       Vy              FY         Shear force along minor axis.
       Vx              FZ         Shear force along major axis.
       Tz              MX         Torsional moment.
       My              MY         Bending moment about minor axis.
       Mx              MZ         Bending moment about major axis.
 *** DESIGN MESSAGES ***:
 =======================
    1. Section classification reported is for the cross section and loadcase that
       produced the worst case design ratio for flexure/compression Capacity results.     
    2. Results for any Capacity/Check that is not relevant for a section/loadcase
       based on the code clause in AISC 360-16 will not be shown in the report.     
    3. Bending results are reported as being �about� the relevant axis (X/Y), while 
       the results for shear are reported as being for shear forces �along� the axis.
       E.g : Mx indicates bending about the X axis, while Vx indicates shear along
       the X axis.
 *** ABBREVIATIONS ***:
 ======================
    F-T-B = Flexural-Torsional Buckling
    L-T-B = Lateral-Torsional Buckling
    F-L-B = Flange Local Buckling
    W-L-B = Web Local Buckling
    L-L-B = Leg Local Buckling
    C-F-Y = Compression Flange Yielding
    T-F-Y = Tension Flange Yielding
      STAAD SPACE                                              -- PAGE NO.    4
                       STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.1)
                     *****************************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted).
 - Member :     1 
|-----------------------------------------------------------------------------|
|  Member No:        1       Profile:  ST  L30308              (AISC SECTIONS)|
|  Status:        PASS       Ratio:         0.242       Loadcase:        1    |
|  Location:      0.00       Ref:      DG9:Eq: 4.13                           |
|  Pz:       0.000     T     Vy:        0.000           Vx:      0.000        |
|  Tz:       3.000           My:        0.000           Mx:      0.000        |
|-----------------------------------------------------------------------------|
| SLENDERNESS                                                                 |
| Actual Slenderness Ratio    :     41.379                                    |
| Allowable Slenderness Ratio :    300.000            LOC  :     0.00         |
|-----------------------------------------------------------------------------|
| STRENGTH CHECKS                                                             |
| Critical L/C  :      1             Ratio     :        0.242(PASS)           |
|          Loc  :    0.00            Condition :    DG9:Eq: 4.13              |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES  (LOC:     0.00, PROPERTIES UNIT: IN  )                  |
| Ag  :   2.760E+00     Axx :   1.500E+00     Ayy :   1.500E+00               |
| Ixx :   2.216E+00     Iyy :   2.216E+00     J   :   2.300E-01               |
| Sxx+:   7.071E-01     Sxx-:   1.149E+00     Zxx :   1.273E+00               |
| Syy+:   1.652E+00     Syy-:   1.652E+00     Zyy :   2.974E+00               |
| Cw  :   1.444E-01     x0  :   6.784E-01     y0  :   6.784E-01               |
|-----------------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                         |
| Fyld:          50.000              Fu:          50.000                      |
|-----------------------------------------------------------------------------|
| Actual Member Length:        24.000                                         |
| Design Parameters                                            (Rolled)       |
| Kx:    1.00  Ky:    1.00  NSF:    1.00  SLF:    1.00  CSP:   12.00          |
|-----------------------------------------------------------------------------|
| COMPRESSION CLASSIFICATION (L/C:      1 LOC:    24.00)                      |
|                            λ         λp        λr       CASE                |
| Flange: NonSlender       6.00       N/A      10.84     Table.4.1a.Case3     |
| Web   : NonSlender       6.00       N/A      10.84     Table.4.1a.Case3     |
|                                                                             |
| FLEXURE CLASSIFICATION     (L/C:      1 LOC:    24.00)                      |
|                            λ         λp        λr       CASE                |
| Flange: Compact          6.00      13.00     21.92     Table.4.1b.Case12    |
| Web   : Compact          6.00      13.00     21.92     Table.4.1b.Case12    |
|-----------------------------------------------------------------------------|
      STAAD SPACE                                              -- PAGE NO.    5
                       STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.1)
                     *****************************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted).
                                                       - Member :     1 Contd.
|-----------------------------------------------------------------------------|
|                         CHECKS FOR AXIAL TENSION                            |
|-----------------------------------------------------------------------------|
| TENSILE YIELDING                                                            |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       124.2       0.000     Cl.D2          1      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom. Ten. Yld Cap         : Pn     =  138.00     kip        Eq.D2-1        |
|-----------------------------------------------------------------------------|
| TENSILE RUPTURE                                                             |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       103.5       0.000     Cl.D2          1      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Effective area            : Ae     =  2.7600     in2        Eq.D3-1        |
|  Nom. Ten. Rpt Cap         : Pn     =  138.00     kip        Eq.D2-2        |
|-----------------------------------------------------------------------------|
|                         CHECKS FOR AXIAL COMPRESSION                        |
|-----------------------------------------------------------------------------|
| FLEXURAL BUCKLING X                                                         |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       117.9       0.000     Cl.E3          1      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Effective Slenderness     : Lcx/rx =  26.782                Cl.E2          |
|  Elastic Buckling Stress   : Fex    =  399.04     ksi        Eq.E3-4        |
|  Crit. Buckling Stress     : Fcrx   =  47.445     ksi        Eq.E3-2        |
|  Nom. Flexural Buckling    : Pnx    =  130.95     kip        Eq.E3-1        |
|-----------------------------------------------------------------------------|
| FLEXURAL BUCKLING Y                                                         |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       117.9       0.000     Cl.E3          1      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Effective Slenderness     : Lcy/ry =  26.782                Cl.E2          |
|  Elastic Buckling Stress   : Fey    =  399.04     ksi        Eq.E3-4        |
|  Crit. Buckling Stress     : Fcry   =  47.445     ksi        Eq.E3-2        |
|  Nom. Flexural Buckling    : Pny    =  130.95     kip        Eq.E3-1        |
|-----------------------------------------------------------------------------|
| FLEXURAL BUCKLING U                                                         |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       120.1       0.000     Cl.E3          1      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Effective Slenderness     : Lcu/ru =  21.299                Cl.E2          |
|  Elastic Buckling Stress   : Feu    =  630.92     ksi        Eq.E3-4        |
|  Crit. Buckling Stress     : Fcru   =  48.369     ksi        Eq.E3-2        |
|  Nom. Flexural Buckling    : Pnu    =  133.50     kip        Eq.E3-1        |
|-----------------------------------------------------------------------------|
| FLEXURAL BUCKLING V                                                         |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       109.6       0.000     Cl.E3          1      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Effective Slenderness     : Lcv/rv =  41.379                Cl.E2          |
|  Elastic Buckling Stress   : Fev    =  167.16     ksi        Eq.E3-4        |
|  Crit. Buckling Stress     : Fcrv   =  44.116     ksi        Eq.E3-2        |
|  Nom. Flexural Buckling    : Pnv    =  121.76     kip        Eq.E3-1        |
|-----------------------------------------------------------------------------|
      STAAD SPACE                                              -- PAGE NO.    6
                       STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.1)
                     *****************************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted).
                                                       - Member :     1 Contd.
|-----------------------------------------------------------------------------|
|                         CHECKS FOR SHEAR                                    |
|-----------------------------------------------------------------------------|
| SHEAR ALONG X                                                               |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       40.50       0.000     Cl.G1          1      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Coefficient Cv Along X    : Cv     =  1.0000                Eq.G2-9        |
|  Coefficient Kv Along X    : Kv     =  1.2000                Cl.G3          |
|  Nom. Shear Along X        : Vnx    =  45.000     kip        Eq.G6-1        |
|-----------------------------------------------------------------------------|
| SHEAR ALONG Y                                                               |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       40.50       0.000     Cl.G1          1      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Coefficient Cv Along Y    : Cv     =  1.0000                Eq.G2-9        |
|  Coefficient Kv Along Y    : Kv     =  1.2000                Cl.G3          |
|  Nom. Shear Along Y        : Vny    =  45.000     kip        Eq.G3-1        |
|-----------------------------------------------------------------------------|
      STAAD SPACE                                              -- PAGE NO.    7
                       STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.1)
                     *****************************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted).
                                                       - Member :     1 Contd.
|-----------------------------------------------------------------------------|
|                         CHECKS FOR BENDING                                  |
|-----------------------------------------------------------------------------|
| FLEX YIELDING (X)                                                           |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       72.22       0.000     Cl.F10.1       1      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom Flex Yielding Along X : Mnx    =  80.244     kip-in     Eq.F10-1       |
|-----------------------------------------------------------------------------|
| FLEX. YIELDING (Y)                                                          |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       72.22       0.000     Cl.F10.1       1      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom Flex Yielding Along Y : Mny    =  80.244     kip-in     Eq.F10-1       |
|-----------------------------------------------------------------------------|
| FLEX. YIELDING (U)                                                          |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       111.5       0.000     Cl.F10.1       1      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom Flex Yielding Along U : Mnu    =  123.90     kip-in     Eq.F10-1       |
|-----------------------------------------------------------------------------|
| FLEX. YIELDING (V)                                                          |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       47.73       0.000     Cl.F10.1       1      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom Flex Yielding Along V : Mnv    =  53.034     kip-in     Eq.F10-1       |
|-----------------------------------------------------------------------------|
| LAT TOR BUCK ABOUT X                                                        |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       57.78       0.000     Cl.F10.2       1      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom L-T-B Cap             : Mnx    =  64.196     kip-in     Eq.F10-2       |
|  Mom. Distr. factor        : CbX    =  1.0000                Custom         |
|  Crit. Elastic L-T-B Mom.  : McrX   =  3076.5     kip-in     Eq.F10-5b      |
|-----------------------------------------------------------------------------|
| LAT TOR BUCK ABOUT Y                                                        |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       57.78       0.000     Cl.F10.2       1      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom Flex Yielding About Y : Mny    =  64.196     kip-in     Eq.F10-2       |
|  Mod. factor Cb            : CbY    =  1.0000                Custom         |
|  Crit. Elas. L-T-B Moment  : McrY   =  3076.5     kip-in     Eq.F10-5b      |
|-----------------------------------------------------------------------------|
| LAT TOR BUCK ABOUT U                                                        |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       111.5       0.000     Cl.F10.2       1      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom Flex Yielding About U : Mnu    =  123.90     kip-in     Eq.F10-2       |
|  modification factor Cb    : CbU    =  1.0000                Custom         |
|  Crit. Elast. L-T-B Moment : McrU   =  1088.0     kip-in     Eq.F10-4       |
|-----------------------------------------------------------------------------|
      STAAD SPACE                                              -- PAGE NO.    8
                       STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.1)
                     *****************************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted).
                                                       - Member :     1 Contd.
|-----------------------------------------------------------------------------|
|                         CHECKS FOR AXIAL BEND INTERACTION                   |
|-----------------------------------------------------------------------------|
| CLAUSE H2                                                                   |
|                            RATIO      CRITERIA           L/C      LOC       |
|                            0.000      Eq.H2-1             1        0.00     |
|                                                                             |
| Intermediate Results :                                                      |
|  Allowable Stress          : Fca    =  37.500     ksi        Eq.H2-1        |
|  Allowable Stress          : Fcbz   =  67.500     ksi        Eq.H2-1        |
|  Allowable Stress          : Fcbw   =  41.554     ksi        Eq.H2-1        |
|-----------------------------------------------------------------------------|
      STAAD SPACE                                              -- PAGE NO.    9
                       STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.1)
                     *****************************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted).
                                                       - Member :     1 Contd.
|-----------------------------------------------------------------------------|
|                         CHECKS FOR TORSION                                  |
|-----------------------------------------------------------------------------|
| NORMAL STRESS RATIO                                                         |
|                            RATIO      CRITERIA           L/C      LOC       |
|                            0.000      DG9:Eq: 4.12        1        0.00     |
|                                                                             |
| Intermediate Results :                                                      |
|  Torque                    : Tq     =  3.0000     kip-in     DG9:Eq: 3.1    |
|  Mod. Factor               : Phi    =  1.0000                DG9:Eq: 4.22   |
|-----------------------------------------------------------------------------|
| SHEAR STRESS RATIO                                                          |
|                            RATIO      CRITERIA           L/C      LOC       |
|                            0.242      DG9:Eq: 4.13        1        0.00     |
|-----------------------------------------------------------------------------|
| COMB. BUCK. RATIO                                                           |
|                            RATIO      CRITERIA           L/C      LOC       |
|                            0.000      DG9:Eq: 4.16(b)     1        0.00     |
|-----------------------------------------------------------------------------|