# V. AISC 360-10 - D-2

## Reference

Design Examples, Version 14.0, American Institute of Steel Construction, 2011, page D-5.

Note: This reference is freely available for download from the AISC website at https://www.aisc.org/globalassets/aisc/university-programs/teaching-aids/first-semester-design-examples.pdf

## Problem

From the reference:

Verify, by both ASD and LRFD, the tensile strength of an L4×4×1/2, ASTM A36 […]. The member carries a dead load of 20 kips and a live load of 60 kips in tension. Calculate at what length this tension member would cease to satisfy the recommended slenderness limit. Assume that connection limit states do not govern.

Refer to the reference for calculations.

## Comparison

Table 1. Comparison of results
Result Type Reference STAAD.Pro Difference
Tensile yielding ϕtPn (kips) [LRFD] 122 122 none
Tensile rupture ϕtPn (kips) [LRFD] 125 125 none
Tensile yielding Pnt (kips) [ASD] 80.8 80.8 none
Tensile rupture Pnt (kips) [ASD] 83.5 83.4 negligible
L at which λ = 300 (ft) 19.4 19.4 none

To calculate the length at which the member would exceed the slenderness limit of 300: (6 in)/(slenderness ratio) × 300

(6 in)/(7.732)×300 = 232.8 in = 19.4 ft

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC 360-10 - D-2.STD is typically installed with the program.

Tip: You can copy and paste this content directly into a .std file to run in STAAD.Pro.
``````STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 25-Oct-12
END JOB INFORMATION
INPUT WIDTH 79
UNIT INCHES KIP
JOINT COORDINATES
1 0 0 0; 2 6 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 29732.7
POISSON 0.3
DENSITY 0.000283
ALPHA 1.2e-05
DAMP 0.03
TYPE STEEL
STRENGTH FY 36.7236 FU 59.1464 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TABLE ST L40408
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
2 FX 20
2 FX 60
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
PARAMETER 1
CODE AISC UNIFIED 2010
METHOD LRFD
NSF 0.88267 ALL
SLF 0.869 ALL
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISC UNIFIED 2010
METHOD ASD
NSF 0.88267 ALL
SLF 0.869 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
``````

```      STAAD SPACE                                              -- PAGE NO.    3
STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
FX            MY             MZ       LOCATION
=======================================================================
1 ST   L40408                   (AISC SECTIONS)
PASS   Eq. H2-1             0.988         3
120.00 T          0.00           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :      7.732  L/C  :     3                |
| Allowable Slenderness Ratio :    300.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      3    Ratio     :     0.988(PASS)                 |
|          Loc  :    0.00   Condition :   Eq. H2-1                      |
|-----------------------------------------------------------------------|
| 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:   2.000E+00     Ayy:   2.000E+00     Cw:  3.662E-01              |
| Szz:   1.371E+00     Syy:   3.121E+00                                 |
| Izz:   2.258E+00     Iyy:   8.865E+00     Ix:  3.125E-01              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:          36.000   Fu:          58.000                           |
|-----------------------------------------------------------------------|
| Actual Member Length:         6.000                                   |
| Design Parameters                                                     |
| Kz:    1.00 Ky:    1.00 NSF:    0.88 SLF:    0.87 CSP:   12.00        |
|-----------------------------------------------------------------------|
| SECTION CLASS  UNSTIFFENED /     λ       λp      λr        CASE       |
|                STIFFENED                                              |
| Compression :  Non-Slender     8.00     N/A     12.93    T.B4.1(a)-3  |
|                  N/A           N/A      N/A      N/A      N/A         |
| Flexure     :  Compact         8.00    15.52    26.15    T.B4.1(b)-12 |
|                  N/A           N/A      N/A      N/A      N/A         |
STAAD SPACE                                              -- PAGE NO.    4
STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       1.20E+02   1.22E+02   0.988      Eq. D2-1      3     0.00 |
| Rupture     1.20E+02   1.25E+02   0.959      Eq. D2-2      3     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Min Buck    0.00E+00   9.85E+01   0.000      Eq. E3-1      3     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Min Buck    3.75E+00    63.94   2.92E+01   7.18E+01   1.09E+02        |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   3.89E+01   0.000      Eq. G2-1      3     0.00 |
| Local-Y     0.00E+00   3.89E+01   0.000      Eq. G2-1      3     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     2.00E+00     1.00     1.20     8.00   4.32E+01            |
| Local-Y     2.00E+00     1.00     1.20     8.00   4.32E+01            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   1.52E+02   0.000      Eq. F10-1     3     0.00 |
| Minor       0.00E+00   6.66E+01   0.000      Eq. F10-1     3     0.00 |
| Intermediate   Mn        My                                           |
| Major       1.69E+02   1.12E+02                                       |
| Minor       7.40E+01   4.94E+01                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   1.52E+02   0.000      Eq. F10-3     3     0.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       1.69E+02   9.12E+03    1.00     0.00     0.00     6.00    |
STAAD SPACE                                              -- PAGE NO.    5
STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR AND NORMAL STRESS INTERACTION                         |
|                                                                       |
|              STRESS     RATIO      CRITERIA     L/C    LOC            |
| Shear       1.94E+01    0.000      Eq. H3-8      3     0.00           |
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.000      Eq. H2-1      3     0.00             |
| Flexure Tens          0.988      Eq. H2-1      3     0.00             |
| Intermediate         frbw /     frbz /     fra /                      |
|                      Fcbw       Fcbz       Fca                        |
| Flexure Comp         0.00E+00   0.00E+00   0.00E+00                   |
|                      4.86E+01   4.86E+01   2.63E+01                   |
| Flexure Tens         0.00E+00   0.00E+00   3.20E+01                   |
|                      4.86E+01   4.86E+01   3.24E+01                   |
GEOMETRIC AXIS DESIGN
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   9.60E+01   0.000      Eq. F10-1     3     0.00 |
| Minor       0.00E+00   9.60E+01   0.000      Eq. F10-1     3     0.00 |
| Intermediate   Mn        My                                           |
| Major       1.07E+02   7.11E+01                                       |
| Minor       1.07E+02   7.11E+01                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   7.68E+01   0.000      Eq. F10-3     3     0.00 |
| Minor       0.00E+00   7.68E+01   0.000      Eq. F10-3     3     0.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       8.53E+01   1.40E+05    1.00     0.00     0.00     6.00    |
| Minor       8.53E+01   1.40E+05    1.00     0.00     0.00     6.00    |
|-----------------------------------------------------------------------|
STAAD SPACE                                              -- PAGE NO.    6
46. LOAD LIST 4
47. PARAMETER 2
48. CODE AISC UNIFIED 2010
49. METHOD ASD
50. NSF 0.88267 ALL
51. SLF 0.869 ALL
52. TRACK 2 ALL
53. CHECK CODE ALL
STEEL DESIGN
STAAD SPACE                                              -- PAGE NO.    7
STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
FX            MY             MZ       LOCATION
=======================================================================
1 ST   L40408                   (AISC SECTIONS)
PASS   Eq. H2-1             0.990         4
80.00 T          0.00           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :      7.732  L/C  :     4                |
| Allowable Slenderness Ratio :    300.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      4    Ratio     :     0.990(PASS)                 |
|          Loc  :    0.00   Condition :   Eq. H2-1                      |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   8.000E+01(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:   2.000E+00     Ayy:   2.000E+00     Cw:  3.662E-01              |
| Szz:   1.371E+00     Syy:   3.121E+00                                 |
| Izz:   2.258E+00     Iyy:   8.865E+00     Ix:  3.125E-01              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:          36.000   Fu:          58.000                           |
|-----------------------------------------------------------------------|
| Actual Member Length:         6.000                                   |
| Design Parameters                                                     |
| Kz:    1.00 Ky:    1.00 NSF:    0.88 SLF:    0.87 CSP:   12.00        |
|-----------------------------------------------------------------------|
| SECTION CLASS  UNSTIFFENED /     λ       λp      λr        CASE       |
|                STIFFENED                                              |
| Compression :  Non-Slender     8.00     N/A     12.93    T.B4.1(a)-3  |
|                  N/A           N/A      N/A      N/A      N/A         |
| Flexure     :  Compact         8.00    15.52    26.15    T.B4.1(b)-12 |
|                  N/A           N/A      N/A      N/A      N/A         |
STAAD SPACE                                              -- PAGE NO.    8
STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       8.00E+01   8.08E+01   0.990      Eq. D2-1      4     0.00 |
| Rupture     8.00E+01   8.34E+01   0.959      Eq. D2-2      4     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Min Buck    0.00E+00   6.55E+01   0.000      Eq. E3-1      4     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Min Buck    3.75E+00    63.94   2.92E+01   7.18E+01   1.09E+02        |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   2.59E+01   0.000      Eq. G2-1      4     0.00 |
| Local-Y     0.00E+00   2.59E+01   0.000      Eq. G2-1      4     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     2.00E+00     1.00     1.20     8.00   4.32E+01            |
| Local-Y     2.00E+00     1.00     1.20     8.00   4.32E+01            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   1.01E+02   0.000      Eq. F10-1     4     0.00 |
| Minor       0.00E+00   4.43E+01   0.000      Eq. F10-1     4     0.00 |
| Intermediate   Mn        My                                           |
| Major       1.69E+02   1.12E+02                                       |
| Minor       7.40E+01   4.94E+01                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   1.01E+02   0.000      Eq. F10-3     4     0.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       1.69E+02   9.12E+03    1.00     0.00     0.00     6.00    |
STAAD SPACE                                              -- PAGE NO.    9
STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR AND NORMAL STRESS INTERACTION                         |
|                                                                       |
|              STRESS     RATIO      CRITERIA     L/C    LOC            |
| Shear       1.29E+01    0.000      Eq. H3-8      4     0.00           |
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.000      Eq. H2-1      4     0.00             |
| Flexure Tens          0.990      Eq. H2-1      4     0.00             |
| Intermediate         frbw /     frbz /     fra /                      |
|                      Fcbw       Fcbz       Fca                        |
| Flexure Comp         0.00E+00   0.00E+00   0.00E+00                   |
|                      3.23E+01   3.23E+01   1.75E+01                   |
| Flexure Tens         0.00E+00   0.00E+00   2.13E+01                   |
|                      3.23E+01   3.23E+01   2.16E+01                   |
GEOMETRIC AXIS DESIGN
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   6.38E+01   0.000      Eq. F10-1     4     0.00 |
| Minor       0.00E+00   6.38E+01   0.000      Eq. F10-1     4     0.00 |
| Intermediate   Mn        My                                           |
| Major       1.07E+02   7.11E+01                                       |
| Minor       1.07E+02   7.11E+01                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   5.11E+01   0.000      Eq. F10-3     4     0.00 |
| Minor       0.00E+00   5.11E+01   0.000      Eq. F10-3     4     0.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       8.53E+01   1.40E+05    1.00     0.00     0.00     6.00    |
| Minor       8.53E+01   1.40E+05    1.00     0.00     0.00     6.00    |
|-----------------------------------------------------------------------|
```