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V.AISC 360-16 L Tension ASD

Verify the tensile yield and tensile rupture strength of an angle section with ASD method for AISC 360-16 code.

Details

The member is an L4x4x1/2 section. Steel grade is ASTM A36. The member is axially loaded with dead load of 20 kips and a live load of 60 kips. The member is connected using bolts in 3/4"⌀ holes. The shear lag factor, U, is calculated as 0.869.

Validation

Service load: P = DL + LL = 80 kips

Tensile Yielding

Nominal tensile yield strength:

PnY = FyAg = 36×3.75 = 135 kip [Eqn. D2-1]

PnYtY = 132 / 1.67 = 80.83 kip

Ratio for tensile yield = 80 / 80.83 = 0.990

Tensile Rupture

Bolt hole area = π(0.75/2)2 = 0.44 in2

Net area, An = Ag - Abolthole = 3.75 - 0.44 = 3.31 in2

Effective net area based on D3: Ae = An×U = 2.875 in2

Nominal tensile rupture strength:

PnR = FuAe = 58×2.875 = 166.7 kip [Eqn. D2-2]

PnRtR = 166.7 / 2.00 = 83.37 kip

Ratio for tensile yield = 80 / 83.4 = 0.960

Results

Table 1. Comparison of results
Result Type Reference STAAD.Pro Difference Comments
Tensile yield strength, PnYtY (kip) 80.83 80.84 negligible  
Ratio 0.990 0.99 none  
Tensile rupture strength, PnRtR (kip) 83.37 83.45 negligible  
Ratio 0.960 0.959 negligible  

STAAD.Pro Input File

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 L Tension ASD.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 15-May-18
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 19.4 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 L40408
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
MEMBER LOAD
1 CON GX 80 9.7
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
PARAMETER 1
CODE AISC UNIFIED 2016
FU 8352 ALL
FYLD 5184 ALL
METHOD ASD
SLF 0.869 ALL
STP 1 ALL
NSF 0.883 ALL
TRACK 2 ALL
UNIT KIP INCH
CHECK CODE ALL
FINISH

STAAD.Pro Output

                       STAAD.PRO CODE CHECKING - AISC 360-16 ASD (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.    7
                       STAAD.PRO CODE CHECKING - AISC 360-16 ASD (V1.1)
                     ****************************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted).
 - Member :     1 
|-----------------------------------------------------------------------------|
|  Member No:        1       Profile:  ST  L40408              (AISC SECTIONS)|
|  Status:        PASS       Ratio:         0.990       Loadcase:        1    |
|  Location:      0.00       Ref:      Cl.D2                                  |
|  Pz:       80.00     T     Vy:        0.000           Vx:      0.000        |
|  Tz:       0.000           My:        0.000           Mx:      0.000        |
|-----------------------------------------------------------------------------|
| SLENDERNESS                                                                 |
| Actual Slenderness Ratio    :    300.000                                    |
| Allowable Slenderness Ratio :    300.000            LOC  :     0.00         |
|-----------------------------------------------------------------------------|
| STRENGTH CHECKS                                                             |
| Critical L/C  :      1             Ratio     :        0.990(PASS)           |
|          Loc  :    0.00            Condition :    Cl.D2                     |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES  (LOC:     0.00, PROPERTIES UNIT: IN  )                  |
| Ag  :   3.750E+00     Axx :   2.000E+00     Ayy :   2.000E+00               |
| Ixx :   5.561E+00     Iyy :   5.561E+00     J   :   3.125E-01               |
| Sxx+:   1.349E+00     Sxx-:   1.955E+00     Zxx :   2.429E+00               |
| Syy+:   3.134E+00     Syy-:   3.134E+00     Zyy :   5.641E+00               |
| Cw  :   3.662E-01     x0  :   9.333E-01     y0  :   9.333E-01               |
|-----------------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                         |
| Fyld:          36.000              Fu:          58.000                      |
|-----------------------------------------------------------------------------|
| Actual Member Length:       232.800                                         |
| Design Parameters                                            (Rolled)       |
| Kx:    1.00  Ky:    1.00  NSF:    0.88  SLF:    0.87  CSP:   12.00          |
|-----------------------------------------------------------------------------|
| COMPRESSION CLASSIFICATION (L/C:      1 LOC:   232.80)                      |
|                            λ         λp        λr       CASE                |
| Flange: NonSlender       8.00       N/A      12.77     Table.4.1a.Case3     |
| Web   : NonSlender       8.00       N/A      12.77     Table.4.1a.Case3     |
|                                                                             |
| FLEXURE CLASSIFICATION     (L/C:      1 LOC:   232.80)                      |
|                            λ         λp        λr       CASE                |
| Flange: Compact          8.00      15.33     25.83     Table.4.1b.Case12    |
| Web   : Compact          8.00      15.33     25.83     Table.4.1b.Case12    |
|-----------------------------------------------------------------------------|
      STAAD SPACE                                              -- PAGE NO.    8
                       STAAD.PRO CODE CHECKING - AISC 360-16 ASD (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     |
|              80.00       80.84       0.990     Cl.D2          1      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Nom. Ten. Yld Cap         : Pn     =  135.00     kip        Eq.D2-1        |
|-----------------------------------------------------------------------------|
| TENSILE RUPTURE                                                             |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              80.00       83.45       0.959     Cl.D2          1      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Effective area            : Ae     =  2.8775     in2        Eq.D3-1        |
|  Nom. Ten. Rpt Cap         : Pn     =  166.89     kip        Eq.D2-2        |
|-----------------------------------------------------------------------------|
|                         CHECKS FOR AXIAL COMPRESSION                        |
|-----------------------------------------------------------------------------|
| FLEXURAL BUCKLING X                                                         |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       15.42       0.000     Cl.E3          1      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Effective Slenderness     : Lcx/rx =  191.16                Cl.E2          |
|  Elastic Buckling Stress   : Fex    =  7.8323     ksi        Eq.E3-4        |
|  Crit. Buckling Stress     : Fcrx   =  6.8689     ksi        Eq.E3-3        |
|  Nom. Flexural Buckling    : Pnx    =  25.758     kip        Eq.E3-1        |
|-----------------------------------------------------------------------------|
| FLEXURAL BUCKLING Y                                                         |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       15.42       0.000     Cl.E3          1      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Effective Slenderness     : Lcy/ry =  191.16                Cl.E2          |
|  Elastic Buckling Stress   : Fey    =  7.8323     ksi        Eq.E3-4        |
|  Crit. Buckling Stress     : Fcry   =  6.8689     ksi        Eq.E3-3        |
|  Nom. Flexural Buckling    : Pny    =  25.758     kip        Eq.E3-1        |
|-----------------------------------------------------------------------------|
| FLEXURAL BUCKLING U                                                         |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       24.59       0.000     Cl.E3          1      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Effective Slenderness     : Lcu/ru =  151.41                Cl.E2          |
|  Elastic Buckling Stress   : Feu    =  12.484     ksi        Eq.E3-4        |
|  Crit. Buckling Stress     : Fcru   =  10.949     ksi        Eq.E3-3        |
|  Nom. Flexural Buckling    : Pnu    =  41.058     kip        Eq.E3-1        |
|-----------------------------------------------------------------------------|
| FLEXURAL BUCKLING V                                                         |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       6.263       0.000     Cl.E3          1      0.00   |
|                                                                             |
| Intermediate Results :                                                      |
|  Effective Slenderness     : Lcv/rv =  300.00                Cl.E2          |
|  Elastic Buckling Stress   : Fev    =  3.1802     ksi        Eq.E3-4        |
|  Crit. Buckling Stress     : Fcrv   =  2.7890     ksi        Eq.E3-3        |
|  Nom. Flexural Buckling    : Pnv    =  10.459     kip        Eq.E3-1        |
|-----------------------------------------------------------------------------|
      STAAD SPACE                                              -- PAGE NO.    9
                       STAAD.PRO CODE CHECKING - AISC 360-16 ASD (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       25.87       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    =  43.200     kip        Eq.G6-1        |
|-----------------------------------------------------------------------------|
| SHEAR ALONG Y                                                               |
|              DEMAND      CAPACITY    RATIO     REFERENCE     L/C    LOC     |
|              0.000       25.87       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    =  43.200     kip        Eq.G3-1        |
|-----------------------------------------------------------------------------|
      STAAD SPACE                                              -- PAGE NO.   10
                       STAAD.PRO CODE CHECKING - AISC 360-16 ASD (V1.1)
                     ****************************************************
 ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted).
                                                       - Member :     1 Contd.
|-----------------------------------------------------------------------------|
|                         CHECKS FOR BENDING                                  |