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V. AISC 360-16 I Tension LRFD

To verify the tensile yield strength of an I section using the LRFD method from the AISC 360-16 code.

Reference

  1. Steel Construction Manual, 15th Edition, American Institute of Steel Construction, 2017

Details

Verify the tensile yield and tensile rupture strength of an I section (W8X21) using the LRFD method. The material is A992 (Fy = 50 ksi, Fu = 65 ksi)

The area of the bolt holes is assumed to be zero. A known shear lag factor of 0.908 is directly specified.

The length of the member is 25 ft. It is loaded axial in tension with a dead load of 30 kips and a live load of 90 kips.

Validation

The factored axial load, Pu = 1.2×30 + 1.6×90 = 180 kips

Tensile Yield Strength

The tensile yield strength: ϕtYPnY = ϕtY×Fy×Ag = 0.9×50×6.16 = 277.2 kips

Ratio for yield strength: 0.649

Tensile Rupture Strength

For this example, An is assumed equal to Ag .

Effective area, Ae = An×U = 6.16×0.908 = 5.593 in2

The tensile rupture strength = ϕtRPnR = ϕtR×Fu×Ae = 0.75×65×5.593 = 272.672 kips

Ratio for rupture strength: 0.660

Results

Table 1. Comparison of results
Parameter Hand Calculation STAAD.Pro Difference Comments
Tensile yield strength (kips) 277.2 277.2 none  
Ratio 0.649 0.649 none  
Tensile rupture strength (kips) 272.7 272.7 none
Ratio 0.660 0.660 none

STAAD Input

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

STAAD SPACE
START JOB INFORMATION
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 25 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 7200 FU 9360 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TABLE ST W8X21
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
LOAD 1 LOADTYPE Dead  TITLE LOAD CASE 1
JOINT LOAD
2 FX 30
LOAD 2 LOADTYPE Live  TITLE LOAD CASE 2
JOINT LOAD
2 FX 90
LOAD COMB 3 COMBINATION LOAD CASE 3
1 1.2 2 1.6
LOAD COMB 4 COMBINATION LOAD CASE 4
1 1.0 2 1.0
PERFORM ANALYSIS
LOAD LIST 3
PARAMETER 1
CODE AISC UNIFIED 2016
FU 9360 ALL
FYLD 7200 ALL
KX 1 ALL
KY 1 ALL
KZ 1 ALL
METHOD LRFD
PROFILE W8X ALL
*SGR 28 ALL
SLF 0.908 ALL
STP 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  W8X21               (AISC SECTIONS)|
|  Status:        PASS       Ratio:         0.660       Loadcase:        3    |
|  Location:      0.00       Ref:      Cl.D2                                  |
|  Pz:       180.0     T     Vy:        0.000           Vx:      0.000        |
|  Tz:       0.000           My:        0.000           Mx:      0.000        |
|-----------------------------------------------------------------------------|
| SLENDERNESS                                                                 |
| Actual Slenderness Ratio    :    238.212                                    |
| Allowable Slenderness Ratio :    300.000            LOC  :     0.00         |
|-----------------------------------------------------------------------------|
| STRENGTH CHECKS                                                             |
| Critical L/C  :      3             Ratio     :        0.660(PASS)           |
|          Loc  :    0.00            Condition :    Cl.D2                     |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES  (LOC:     0.00, PROPERTIES UNIT: IN  )                  |
| Ag  :   6.160E+00     Axx :   4.216E+00     Ayy :   2.070E+00               |
| Ixx :   7.530E+01     Iyy :   9.770E+00     J   :   2.820E-01               |
| Sxx+:   1.819E+01     Sxx-:   1.819E+01     Zxx :   2.040E+01               |
| Syy+:   3.708E+00     Syy-:   3.708E+00     Zyy :   5.690E+00               |
| Cw  :   1.515E+02     x0  :   0.000E+00     y0  :   0.000E+00               |
|-----------------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                         |
| Fyld:          50.000              Fu:          65.000                      |
|-----------------------------------------------------------------------------|
| Actual Member Length:       300.000                                         |
| Design Parameters                                            (Rolled)       |
| Kx:    1.00  Ky:    1.00  NSF:    1.00  SLF:    0.91  CSP:   12.00          |
|-----------------------------------------------------------------------------|
| COMPRESSION CLASSIFICATION (L/C:      3 LOC:   300.00)                      |
|                            λ         λp        λr       CASE                |
| Flange: NonSlender       6.59       N/A      13.49     Table.4.1a.Case1     |
| Web   : NonSlender      29.92       N/A      35.88     Table.4.1a.Case5     |
|                                                                             |
| FLEXURE CLASSIFICATION     (L/C:      3 LOC:   300.00)                      |
|                            λ         λp        λr       CASE                |
| Flange: Compact          6.59       9.15     24.08     Table.4.1b.Case10    |
| Web   : Compact         29.92      90.55    137.27     Table.4.1b.Case15    |
|-----------------------------------------------------------------------------|
      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     |
|              180.0       277.2       0.649     Cl.D2          3      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom. Ten. Yld Cap         : Pn     =  308.00     kip        Eq.D2-1        |
|-----------------------------------------------------------------------------|
| TENSILE RUPTURE                                                             |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              180.0       272.7       0.660     Cl.D2          3      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Effective area            : Ae     =  5.5933     in2        Eq.D3-1        |
|  Nom. Ten. Rpt Cap         : Pn     =  363.56     kip        Eq.D2-2        |
|-----------------------------------------------------------------------------|
|                         CHECKS FOR AXIAL COMPRESSION                        |
|-----------------------------------------------------------------------------|
| FLEXURAL BUCKLING X                                                         |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       161.8       0.000     Cl.E3          3      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Effective Slenderness     : Lcx/rx =  85.805                Cl.E2          |
|  Elastic Buckling Stress   : Fex    =  38.875     ksi        Eq.E3-4        |
|  Crit. Buckling Stress     : Fcrx   =  29.186     ksi        Eq.E3-2        |
|  Nom. Flexural Buckling    : Pnx    =  179.79     kip        Eq.E3-1        |
|-----------------------------------------------------------------------------|
| FLEXURAL BUCKLING Y                                                         |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       24.52       0.000     Cl.E3          3      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Effective Slenderness     : Lcy/ry =  238.21                Cl.E2          |
|  Elastic Buckling Stress   : Fey    =  5.0439     ksi        Eq.E3-4        |
|  Crit. Buckling Stress     : Fcry   =  4.4235     ksi        Eq.E3-3        |
|  Nom. Flexural Buckling    : Pny    =  27.249     kip        Eq.E3-1        |
|-----------------------------------------------------------------------------|
| FLEX-TOR-BUCKLING                                                           |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       169.7       0.000     Cl.E4          3      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Elastic F-T-B Stress      : Fe     =  42.637     ksi        Eq.E4-2        |
|  Crit. F-T-B Stress        : Fcr    =  30.606     ksi        Eq.E3-2        |
|  Nom. Flex-tor Buckling    : Pn     =  188.53     kip        Eq.E4-1        |
|-----------------------------------------------------------------------------|
      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       113.8       0.000     Cl.G1          3      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Coefficient Cv Along X    : Cv     =  1.0000                Eq.G2-9        |
|  Coefficient Kv Along X    : Kv     =  1.2000                Cl.G6          |
|  Nom. Shear Along X        : Vnx    =  126.48     kip        Eq.G6-1        |
|-----------------------------------------------------------------------------|
| SHEAR ALONG Y                                                               |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       62.10       0.000     Cl.G1          3      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Coefficient Cv Along Y    : Cv     =  1.0000                -              |
|  Coefficient Kv Along Y    : Kv     =  5.3400                Eq.G2-5        |
|  Nom. Shear Along Y        : Vny    =  62.100     kip        Eq.G2-1        |
|-----------------------------------------------------------------------------|
      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       918.0       0.000     Cl.F2.1        3      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom Flex Yielding Along X : Mnx    =  1020.0     kip-in     Eq.F2-1        |
|-----------------------------------------------------------------------------|
| FLEX. YIELDING (Y)                                                          |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       256.1       0.000     Cl.F6.1        3      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom Flex Yielding Along Y : Mny    =  284.50     kip-in     Eq.F6-1        |
|-----------------------------------------------------------------------------|
| LAT TOR BUCK ABOUT X                                                        |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       302.2       0.000     Cl.F2.2        3      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom L-T-B Cap             : Mnx    =  335.72     kip-in     Eq.F2-3        |
|  Mom. Distr. factor        : CbX    =  1.0000                Custom         |
|  Limiting Unbraced Length  : LpX    =  53.381     in         Eq.F2-5        |
|  coefficient C             : Cx     =  1.0000                Eq.F2-8a       |
|  Effective Rad. of Gyr.    : Rts    =  1.4543     in         Eq.F2-7        |
|  Limiting Unbraced Length  : LrX    =  176.96     in         Eq.F2-6        |
|  Crit. Elas. L-T-B Stress  : FcrX   =  18.458     ksi        Eq.F2-4        |
|-----------------------------------------------------------------------------|
      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 H1                                                                   |
|                            RATIO      CRITERIA           L/C      LOC       |
|                            0.660      Eq.H1-1a            3        0.00     |
|                                                                             |
| Intermediate Results :                                                      |
|  Modification Factor       : Cb     =  2.6064                Eq.H1-2        |
|  Axial Capacity            : Pc     =  272.67     kip        Cl.H1.1        |
|  Moment Capacity           : Mcx    =  787.52     kip-in     Cl.H1.1        |
|  Moment Capacity           : Mcy    =  256.05     kip-in     Cl.H1.1        |