# V. AISC 360-10 HSST Compact Flange F.6

Verify the available flexural strength of a square HSS flexural member with compact flanges per the AISC 360-10 code.

## References

1. American Institute of Steel Construction. 2010 Steel Construction Manual. Fourteenth Edition. AISC: Chicago, IL.
2. American Institute of Steel Construction. 2011. Design Examples, Version 14.0. AISC:Chicago, IL. Example F.6, pp. F30-F31

## Details

From reference (2):

Select a square ASTM A500 Grade B HSS beam to span 7.5 ft. The loads are a uniform dead load of 0.145 kip/ft and a uniform live load of 0.435 kip/ft. Limit the live load deflection to L/240. The beam is continuously braced.

## Validation

Ultimate moment:

Service moment:

Try a HSS 3 1/2×3 1/2×1/8, which has a plastic section modulus, Zx = 1.93 in3.

The yield strength, Fy = 46 ksi

Flange compactness: λ = b/t = 27.2

Determine the compact flange ratio limit from Table B4.1b: $λ p = 1.12 E F y = 1.12 29,000 46 = 28.1 > λ$ (Compact)

The available flexural strength:

LRFD:

ASD:

## Results

ϕbMn (ft·k) [LRFD] 6.66* 6.66 none
Mnb (ft·k) [ASD] 4.43* 4.43 none

* The reference gives ϕbMn = 6.67 ft·k and Mnb = 4.44, respectively. The differences are due to either rounding differences.

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

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 18-Feb-19
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 7.5 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 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TABLE ST HSST3.5X3.5X0.125
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED BUT MZ
2 FIXED BUT FX MZ
1 UNI GY -0.145
1 UNI GY -0.435
1 1.2 2 1.6
1 1.0 2 1.0
PERFORM ANALYSIS
PARAMETER 1
CODE AISC UNIFIED 2010
FU 8352 ALL
FYLD 6624 ALL
FLX 2 ALL
METHOD LRFD
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISC UNIFIED 2010
FU 8352 ALL
FYLD 6624 ALL
FLX 2 ALL
METHOD ASD
TRACK 2 ALL
CHECK CODE ALL
FINISH


                       STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
1 ST   HSST3.5X3.5X0.125        (AISC SECTIONS)
PASS   Eq. H1-1b            0.919         3
0.00            0.00          -6.12        3.75
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     65.585  L/C  :     3                |
| Allowable Slenderness Ratio :    300.000  LOC  :     3.75             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      3    Ratio     :     0.919(PASS)                 |
|          Loc  :    3.75   Condition :   Eq. H1-1b                     |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   0.000E+00(  ) Fy:   0.000E+00     Fz:   0.000E+00               |
| Mx:   0.000E+00     My:   0.000E+00     Mz:  -6.117E+00               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   7.313E-01     Ayy:   7.313E-01     Cw:  0.000E+00              |
| Szz:   1.657E+00     Syy:   1.657E+00                                 |
| Izz:   2.900E+00     Iyy:   2.900E+00     Ix:  4.580E+00              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:        6623.999   Fu:        8351.999                           |
|-----------------------------------------------------------------------|
| Actual Member Length:         7.500                                   |
| Design Parameters                                                     |
| Kz:    1.00 Ky:    1.00 NSF:    1.00 SLF:    1.00 CSP:   12.00        |
|-----------------------------------------------------------------------|
| SECTION CLASS  UNSTIFFENED /     λ       λp      λr        CASE       |
|                STIFFENED                                              |
| Compression :  Non-Slender     0.00     N/A      0.00      N/A        |
|                Non-Slender    27.17     N/A     35.15    T.B4.1(a)-6  |
| Flexure     :  Compact        27.17    28.12    35.15    T.B4.1(b)-17 |
|                Compact        27.17    60.76   143.12    T.B4.1(b)-19 |
STAAD SPACE                                              -- PAGE NO.    4
STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       0.00E+00   6.38E+01   0.000      Eq. D2-1      3     0.00 |
| Rupture     0.00E+00   6.70E+01   0.000      Eq. D2-2      3     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    0.00E+00   4.77E+01   0.000      Eq. E3-1      3     0.00 |
| Min Buck    0.00E+00   4.77E+01   0.000      Eq. E3-1      3     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    1.07E-02    65.58   4.96E+03   9.58E+03   5.30E+01        |
| Min Buck    1.07E-02    65.58   4.96E+03   9.58E+03   5.30E+01        |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   1.82E+01   0.000      Eq. G2-1      3     0.00 |
| Local-Y    -3.26E+00   1.82E+01   0.180      Eq. G2-1      3     7.50 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     5.08E-03     1.00     5.00    27.17   2.02E+01            |
| Local-Y     5.08E-03     1.00     5.00    27.17   2.02E+01            |
|-----------------------------------------------------------------------|
| CHECK FOR TORSION                                                     |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
|             0.00E+00   5.49E+00   0.000      Eq. H3-1      3     0.00 |
| Intermediate Fcr        Tn                                            |
|             3.97E+03   6.10E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       6.12E+00   6.66E+00   0.919      Eq. F7-1      3     3.75 |
| Minor       0.00E+00   6.66E+00   0.000      Eq. F7-1      3     0.00 |
| Intermediate   Mn        My                                           |
| Major       7.40E+00   0.00E+00                                       |
| Minor       7.40E+00   0.00E+00                                       |
STAAD SPACE                                              -- PAGE NO.    5
STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.919      Eq. H1-1b     3     3.75             |
| Flexure Tens          0.919      Eq. H1-1b     3     3.75             |
| Intermediate         Mcx /      Mrx /      Pc /                       |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         6.66E+00   6.12E+00   4.77E+01                   |
|                      6.66E+00   0.00E+00   0.00E+00                   |
| Flexure Tens         6.66E+00   6.12E+00   6.38E+01                   |
|                      6.66E+00   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|
49. PARAMETER 2
50. CODE AISC UNIFIED 2010
51. FU 8352 ALL
52. FYLD 6624 ALL
53. FLX 2 ALL
54. METHOD ASD
55. TRACK 2 ALL
56. CHECK CODE ALL
STEEL DESIGN
WARNING: For member#      1 the profile has been selected from HSS Rect/Round (non A1085)/Pipe
tables of AISC database. Weld type is considered to be Elect-resist-weld.
Thickness is already reduced from the table. Further reductions will not be done.
STAAD SPACE                                              -- PAGE NO.    6
STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
1 ST   HSST3.5X3.5X0.125        (AISC SECTIONS)
PASS   Eq. H1-1b            0.921         4
0.00            0.00          -4.08        3.75
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     65.585  L/C  :     4                |
| Allowable Slenderness Ratio :    300.000  LOC  :     3.75             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      4    Ratio     :     0.921(PASS)                 |
|          Loc  :    3.75   Condition :   Eq. H1-1b                     |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   0.000E+00(  ) Fy:   0.000E+00     Fz:   0.000E+00               |
| Mx:   0.000E+00     My:   0.000E+00     Mz:  -4.078E+00               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   7.313E-01     Ayy:   7.313E-01     Cw:  0.000E+00              |
| Szz:   1.657E+00     Syy:   1.657E+00                                 |
| Izz:   2.900E+00     Iyy:   2.900E+00     Ix:  4.580E+00              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:        6623.999   Fu:        8351.999                           |
|-----------------------------------------------------------------------|
| Actual Member Length:         7.500                                   |
| Design Parameters                                                     |
| Kz:    1.00 Ky:    1.00 NSF:    1.00 SLF:    1.00 CSP:   12.00        |
|-----------------------------------------------------------------------|
| SECTION CLASS  UNSTIFFENED /     λ       λp      λr        CASE       |
|                STIFFENED                                              |
| Compression :  Non-Slender     0.00     N/A      0.00      N/A        |
|                Non-Slender    27.17     N/A     35.15    T.B4.1(a)-6  |
| Flexure     :  Compact        27.17    28.12    35.15    T.B4.1(b)-17 |
|                Compact        27.17    60.76   143.12    T.B4.1(b)-19 |
STAAD SPACE                                              -- PAGE NO.    7
STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       0.00E+00   4.24E+01   0.000      Eq. D2-1      4     0.00 |
| Rupture     0.00E+00   4.47E+01   0.000      Eq. D2-2      4     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    0.00E+00   3.18E+01   0.000      Eq. E3-1      4     0.00 |
| Min Buck    0.00E+00   3.18E+01   0.000      Eq. E3-1      4     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    1.07E-02    65.58   4.96E+03   9.58E+03   5.30E+01        |
| Min Buck    1.07E-02    65.58   4.96E+03   9.58E+03   5.30E+01        |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   1.21E+01   0.000      Eq. G2-1      4     0.00 |
| Local-Y    -2.17E+00   1.21E+01   0.180      Eq. G2-1      4     7.50 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     5.08E-03     1.00     5.00    27.17   2.02E+01            |
| Local-Y     5.08E-03     1.00     5.00    27.17   2.02E+01            |
|-----------------------------------------------------------------------|
| CHECK FOR TORSION                                                     |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
|             0.00E+00   3.65E+00   0.000      Eq. H3-1      4     0.00 |
| Intermediate Fcr        Tn                                            |
|             3.97E+03   6.10E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       4.08E+00   4.43E+00   0.921      Eq. F7-1      4     3.75 |
| Minor       0.00E+00   4.43E+00   0.000      Eq. F7-1      4     0.00 |
| Intermediate   Mn        My                                           |
| Major       7.40E+00   0.00E+00                                       |
| Minor       7.40E+00   0.00E+00                                       |
STAAD SPACE                                              -- PAGE NO.    8
STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
********************************************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.921      Eq. H1-1b     4     3.75             |
| Flexure Tens          0.921      Eq. H1-1b     4     3.75             |
| Intermediate         Mcx /      Mrx /      Pc /                       |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         4.43E+00   4.08E+00   3.18E+01                   |
|                      4.43E+00   0.00E+00   0.00E+00                   |
| Flexure Tens         4.43E+00   4.08E+00   4.24E+01                   |
|                      4.43E+00   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|