# V. AISC 360-05 Tension

Verify the tensile yield strength and tensile rupture strength of an I section using both the LRFD and ASD methods per the AISC 360-05 code.

## Reference

1. Design Examples, Version 13.0, American Institute of Steel Construction, 2005, page D-2. Example D.1
2. Steel Construction Manual, Version 13.0, American Institute of Steel Construction, 2005

## Details

Verify the member Tensile Yield strength and Tensile Rupture Strength by both LRFD and ASD with the bolted end connection of a I Section (W8X21) using the LRFD and ASD method

Steel Gr. ASTM A992.

The connection consists of 2 rows of 4- 3/4"Ø bolts in each flange (16 bolts total) in standard holes. The holes are spaced evenly at 3" on center, with a 1-1/4" edge to center at the end of the flange in line with the tensile force.

## Validation

ASTM A992: Fy = 50 ksi, Fu = 65 ksi

Assume a W8X21 section:
• Ag = 6.16 in2
• bf = 5.27 in
• tf = 0.400 in
• d = 8.28 in
• ry = 1.26 in
• y = 0.831 in (for a WT4X10.5)

Calculate the required tensile strength.

LRFD

Pu = 1.2(30 kips) + 1.6(90 kips) = 180 kips

ASD

Pa = 30 kips + 90 kips = 120 kips

Check the tensile yield strength limit state using tabulated values per Table 5-1 in ref. 2:

ϕtPn = 277 kips > 180 kips

Pnt = 184 kips > 120 kips

Check the available tensile rupture strength at the end connection. The tabulated values are for Ae/Ag ≥ 0.75. Verify this assumption is applicable.

Calculate U as the larger of the values from Table D3.1 case 2 or case 7 (ref. 2).

Case 2 - Check as two WT shapes:

 U = 1 - x/l = 1 - 0.831 in / 9.0 in = 0.908

where
 l = length of the bolted connection = 3x 3.0 in = 9.0 in x = distance from the flange face to the plastic neutral axis. This is taken from Table 1-8 of ref. 2.

Case 7

bf = 5.27 in < 2/3d = 2/3(8.28 in) = 5.52 in; U = 0.85

Use U = 0.908

Calculate the net area at the bolted connection:

An = Ag - 4(Øh + 1/16 in)tf = 6.16 in2 - 4×(13/16 in + 1/16 in)(0.400 in) = 4.76 in2

Calculate the effective area:

Ae = AnU = 4.76 in2 × 0.908 = 4.32 in2

Ae/Ag = 4.32 in2/ 6.16 in2 = 0.701 < 0.75

Therefore, the tabulated values for rupture do not apply. Calculate the rupture strength:

Pn = FuAe = 65 ksi (4.32 in2) = 281 kips

LRFD

ϕtPn = 0.75(281 kips) = 211 kips > 180 kips

ASD

Pnt = 281 kips/2.00 = 141 kips > 120 kips

## Results

Table 1. Comparison of results
ϕtPn (kips) [LRFD] Yield 277 277 none
Rupture 211 211 none
Pnt (kips) [ASD] Yield 184 184 none
Rupture 141 141 none

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC 360-05 Tension.STD is typically installed with the program.

``````STAAD PLANE
START JOB INFORMATION
ENGINEER DATE 27-Aug-18
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 0 25 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
ISOTROPIC STEEL_50_KSI
E 4.176e+06
POISSON 0.3
DENSITY 0.489024
ALPHA 6.5e-06
DAMP 0.03
TYPE STEEL
STRENGTH FY 7200 FU 8928 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TABLE ST W8X21
CONSTANTS
MATERIAL STEEL_50_KSI ALL
SUPPORTS
2 PINNED
1 FIXED BUT FY MZ
1 FY -30
1 FY -90
1 1.0 2 1.0
1 1.2 2 1.6
PERFORM ANALYSIS
PARAMETER 1
CODE AISC UNIFIED 2005
METHOD ASD
FYLD 7200 ALL
FU 9360 ALL
NSF 0.773 ALL
SLF 0.908 ALL
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISC UNIFIED 2005
METHOD LRFD
TRACK 2 ALL
NSF 0.773 ALL
SLF 0.908 ALL
FU 9360 ALL
FYLD 7200 ALL
CHECK CODE ALL
FINISH
``````

```                       STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD)   v3.3a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
1 ST   W8X21                    (AISC SECTIONS)
PASS   Eq. H1-1a            0.854         3
120.00 T          0.00           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :    238.212  L/C  :     3                |
| Allowable Slenderness Ratio :    300.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      3    Ratio     :     0.854(PASS)                 |
|          Loc  :    0.00   Condition :   Eq. H1-1a                     |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   1.200E+02(T ) Fy:   0.000E+00     Fz:   0.000E+00               |
| Mx:   0.000E+00     My:   0.000E+00     Mz:   0.000E+00               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   4.216E+00     Ayy:   2.070E+00     Cw:  1.517E+02              |
| Szz:   1.819E+01     Syy:   3.708E+00                                 |
| Izz:   7.530E+01     Iyy:   9.770E+00     Ix:  2.820E-01              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:        7199.999   Fu:        9359.999                           |
|-----------------------------------------------------------------------|
| Actual Member Length:        25.000                                   |
| Design Parameters                                                     |
| Kz:    1.00 Ky:    1.00 NSF:    0.77 SLF:    0.91 CSP:   12.00        |
|-----------------------------------------------------------------------|
| SECTION CLASS  UNSTIFFENED /     λ       λp      λr        CASE       |
|                STIFFENED                                              |
| Compression :  Non-Slender     6.59     N/A     13.49    T.B4.1-3     |
|                Non-Slender    27.52     N/A     35.88    T.B4.1-10    |
| Flexure     :  Compact         6.59     9.15    24.08    T.B4.1-1     |
|                Compact        27.52    90.55   137.27    T.B4.1-9     |
STAAD PLANE                                              -- PAGE NO.    4
STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD)   v3.3a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       1.20E+02   1.84E+02   0.651      Eq. D2-1      3     0.00 |
| Rupture     1.20E+02   1.41E+02   0.854      Eq. D2-2      3     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    0.00E+00   1.08E+02   0.000      Sec. E1       3     0.00 |
| Min Buck    0.00E+00   1.63E+01   0.000      Eq. E3-1      3     0.00 |
| Flexural                                                              |
| Tor Buck    0.00E+00   1.13E+02   0.000      Eq. E4-1      3     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    4.28E-02    85.81   4.20E+03   5.60E+03   1.80E+02        |
| Min Buck    4.28E-02   238.21   6.37E+02   7.26E+02   2.72E+01        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    4.28E-02   4.41E+03   1.89E+02                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   7.57E+01   0.000      Eq. G2-1      3     0.00 |
| Local-Y     0.00E+00   4.14E+01   0.000      Eq. G2-1      3     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     2.93E-02     1.00     1.20     6.59   1.26E+02            |
| Local-Y     1.44E-02     1.00     0.00    27.52   6.21E+01            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   5.09E+01   0.000      Eq. F2-1      3     0.00 |
| Minor       0.00E+00   1.42E+01   0.000      Eq. F6-1      3     0.00 |
| Intermediate   Mn        My                                           |
| Major       8.50E+01   0.00E+00                                       |
| Minor       2.37E+01   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   1.68E+01   0.000      Eq. F2-3      3     0.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       2.80E+01   0.00E+00    1.00     4.45    14.75    25.00    |
STAAD PLANE                                              -- PAGE NO.    5
STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD)   v3.3a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.000      Eq. H1-1b     3     0.00             |
| Flexure Tens          0.854      Eq. H1-1a     3     0.00             |
| Intermediate         Mcx /      Mrx /      Pc /                       |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         1.68E+01   0.00E+00   1.63E+01                   |
|                      1.42E+01   0.00E+00   0.00E+00                   |
| Flexure Tens         1.68E+01   0.00E+00   1.41E+02                   |
|                      1.42E+01   0.00E+00   1.20E+02                   |
|-----------------------------------------------------------------------|
56. PARAMETER 2
57. CODE AISC UNIFIED 2005
58. METHOD LRFD
59. TRACK 2 ALL
60. NSF 0.773 ALL
61. SLF 0.908 ALL
62. FU 9360 ALL
63. FYLD 7200 ALL
64. CHECK CODE ALL
STEEL DESIGN
STAAD PLANE                                              -- PAGE NO.    6
STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD)   v3.3a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
1 ST   W8X21                    (AISC SECTIONS)
PASS   Eq. H1-1a            0.854         4
180.00 T          0.00           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :    238.212  L/C  :     4                |
| Allowable Slenderness Ratio :    300.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      4    Ratio     :     0.854(PASS)                 |
|          Loc  :    0.00   Condition :   Eq. H1-1a                     |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   1.800E+02(T ) Fy:   0.000E+00     Fz:   0.000E+00               |
| Mx:   0.000E+00     My:   0.000E+00     Mz:   0.000E+00               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   4.216E+00     Ayy:   2.070E+00     Cw:  1.517E+02              |
| Szz:   1.819E+01     Syy:   3.708E+00                                 |
| Izz:   7.530E+01     Iyy:   9.770E+00     Ix:  2.820E-01              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:        7199.999   Fu:        9359.999                           |
|-----------------------------------------------------------------------|
| Actual Member Length:        25.000                                   |
| Design Parameters                                                     |
| Kz:    1.00 Ky:    1.00 NSF:    0.77 SLF:    0.91 CSP:   12.00        |
|-----------------------------------------------------------------------|
| SECTION CLASS  UNSTIFFENED /     λ       λp      λr        CASE       |
|                STIFFENED                                              |
| Compression :  Non-Slender     6.59     N/A     13.49    T.B4.1-3     |
|                Non-Slender    27.52     N/A     35.88    T.B4.1-10    |
| Flexure     :  Compact         6.59     9.15    24.08    T.B4.1-1     |
|                Compact        27.52    90.55   137.27    T.B4.1-9     |
STAAD PLANE                                              -- PAGE NO.    7
STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD)   v3.3a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       1.80E+02   2.77E+02   0.649      Eq. D2-1      4     0.00 |
| Rupture     1.80E+02   2.11E+02   0.854      Eq. D2-2      4     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    0.00E+00   1.62E+02   0.000      Sec. E1       4     0.00 |
| Min Buck    0.00E+00   2.45E+01   0.000      Eq. E3-1      4     0.00 |
| Flexural                                                              |
| Tor Buck    0.00E+00   1.70E+02   0.000      Eq. E4-1      4     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    4.28E-02    85.81   4.20E+03   5.60E+03   1.80E+02        |
| Min Buck    4.28E-02   238.21   6.37E+02   7.26E+02   2.72E+01        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    4.28E-02   4.41E+03   1.89E+02                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   1.14E+02   0.000      Eq. G2-1      4     0.00 |
| Local-Y     0.00E+00   6.21E+01   0.000      Eq. G2-1      4     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     2.93E-02     1.00     1.20     6.59   1.26E+02            |
| Local-Y     1.44E-02     1.00     0.00    27.52   6.21E+01            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   7.65E+01   0.000      Eq. F2-1      4     0.00 |
| Minor       0.00E+00   2.13E+01   0.000      Eq. F6-1      4     0.00 |
| Intermediate   Mn        My                                           |
| Major       8.50E+01   0.00E+00                                       |
| Minor       2.37E+01   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   2.52E+01   0.000      Eq. F2-3      4     0.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       2.80E+01   0.00E+00    1.00     4.45    14.75    25.00    |
STAAD PLANE                                              -- PAGE NO.    8
STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD)   v3.3a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.000      Eq. H1-1b     4     0.00             |
| Flexure Tens          0.854      Eq. H1-1a     4     0.00             |
| Intermediate         Mcx /      Mrx /      Pc /                       |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         2.52E+01   0.00E+00   2.45E+01                   |
|                      2.13E+01   0.00E+00   0.00E+00                   |
| Flexure Tens         2.52E+01   0.00E+00   2.11E+02                   |
|                      2.13E+01   0.00E+00   1.80E+02                   |
|-----------------------------------------------------------------------|
```