V. AISC 360-10 HSST Slender Flange F.8

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

References

American Institute of Steel Construction. 2010 Steel Construction Manual. Fourteenth Edition. AISC: Chicago, IL.
American Institute of Steel Construction. 2011. Design Examples, Version 14.0. AISC:Chicago, IL. Example F.8A and F.8B, pp. F36-F40

Details

From reference (2):

Verify the strength of an ASTM A500 Grade B HSS8×8×x with a span of 21 ft. The loads are a dead load of 0.125 kip/ft and a live load of 0.375 kip/ft. Limit the live load deflection to L/240. The beam is continuously braced.

Validation

Ultimate moment:

w_{u} = 1.2 (0.125 k/ft) + 1.6 (0.375 k/ft) = 0.75 k/ft

M_{u} = \frac{0.75 {(21)}^{2}}{8} = 41.3 ft·k

Service moment:

w_{a} = 0.125 k/ft + 0.375 k/ft = 0.50 k/ft

M_{a} = \frac{0.5 {(21)}^{2}}{8} = 27.6 ft·k

Try a HSS 8×8×3/16, which has a plastic section modulus, Z_x = 15.7 in³ and a section modulus, S_x = 13.6 in³.

The yield strength, F_y = 46 ksi

Flange compactness: λ = b/t = 43.0

Determine the slender flange ratio limit from Table B4.1b: $λ_{r} = 1.40 \sqrt{\frac{E}{F_{y}}} = 1.12 \sqrt{\frac{29,000}{46}} = 35.2 < λ$ (Slender)

Web compactness: λ = h/t = 43.0

λ_{p} = 2.42 \sqrt{\frac{E}{F_{y}}} = 2.42 \sqrt{\frac{29,000}{46}} = 60.8 > λ

Thus, the section has a compact web.

M_{n} = F_{y} \times S_{e}

(F7-3)

where

S_e	=	the effective section modulus determined with the effective compression flange taken as b_e
b_e	=	$1.93 t_{f} \sqrt{\frac{E}{F_{y}}} [1 - \frac{0.38}{b / t_{f}} \sqrt{\frac{E}{F_{y}}}] = 1.93 \times 0.174 \sqrt{\frac{29,000}{46}} [1 - \frac{0.38}{0.43} \sqrt{\frac{29,000}{46}}] = 6.53 in$

The width of the compression flange between the corners (assumed to be 1.5t) is:

b = 8 - 2 × 1.5 × t = 8 - 3(0.174) = 7.48 in > 6.53 in

Thus, the ineffective width of the compression flange is: b - b_e = 7.48 - 6.53 = 0.95 in

Subtract this contribution of this ineffective flange area from the gross moment of inertia to approximate the effective moment of inertia:

I_{eff} \approx 54.4 - 2 [\frac{0.95 {(0.174)}^{3}}{12} + 0.95 (0.174) {(3.91)}^{3}] = 49.3 {in}^{4}

S_{e} = \frac{I_{eff}}{d / 2} = \frac{49.3}{8.0 / 2} = 12.3 {in}^{3}

M_{n} = = 46 \times 12.3 = 566 in-k = 47.2 ft-k

The available flexural strength:

LRFD: $ϕ_{b} M_{n} = 0.90 (47.2) = 42.5 ft·k$

ASD: $M_{n} / Ω_{b} = \frac{47.2}{1.67} = 28.3 ft·k$

Results

Result Type	Reference	STAAD.Pro	Difference	Comments
ϕ_bM_n (ft·k) [LRFD]	42.5	42.5	none
M_n/Ω_b (ft·k) [ASD]	28.3	28.3	none

STAAD.Pro Input

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

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 19-Feb-19
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 21 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 HSST8X8X0.188
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED BUT MZ
2 FIXED BUT FX MZ
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
MEMBER LOAD
1 UNI GY -0.125
LOAD 2 LOADTYPE None  TITLE LOAD CASE 2
MEMBER LOAD
1 UNI GY -0.375
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 2010
FU 8352 ALL
FYLD 6624 ALL
FLX 2 ALL
METHOD LRFD
TRACK 2 ALL
CHECK CODE ALL
LOAD LIST 4
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 Output

                       STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
                       ********************************************
 ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
       1 ST   HSST8X8X0.188            (AISC SECTIONS)
                           PASS   Eq. H1-1b            0.972         3
                        0.00            0.00         -41.34       10.50
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     79.175  L/C  :     3                |
| Allowable Slenderness Ratio :    300.000  LOC  :    10.50             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      3    Ratio     :     0.972(PASS)                 |
|          Loc  :   10.50   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:  -4.134E+01               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   2.602E+00     Ayy:   2.602E+00     Cw:  0.000E+00              |
| Szz:   1.360E+01     Syy:   1.360E+01                                 |
| Izz:   5.440E+01     Iyy:   5.440E+01     Ix:  8.450E+01              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:        6623.999   Fu:        8351.999                           |
|-----------------------------------------------------------------------|
| Actual Member Length:        21.000                                   |
| 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        |
|                Slender        42.98     N/A     35.15    T.B4.1(a)-6  |
| Flexure     :  Slender        42.98    28.12    35.15    T.B4.1(b)-17 |
|                Compact        42.98    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   2.22E+02   0.000      Eq. D2-1      3     0.00 |
| Rupture     0.00E+00   2.34E+02   0.000      Eq. D2-2      3     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    0.00E+00   1.35E+02   0.000      Eq. E7-1      3     0.00 |
| Min Buck    0.00E+00   1.35E+02   0.000      Eq. E7-1      3     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    3.27E-02    79.18   4.01E+03   6.57E+03   1.50E+02        |
| Min Buck    3.27E-02    79.18   4.01E+03   6.57E+03   1.50E+02        |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   6.46E+01   0.000      Eq. G2-1      3     0.00 |
| Local-Y     7.88E+00   6.46E+01   0.122      Eq. G2-1      3     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     1.81E-02     1.00     5.00    42.98   7.18E+01            |
| Local-Y     1.81E-02     1.00     5.00    42.98   7.18E+01            |
|-----------------------------------------------------------------------|
| CHECK FOR TORSION                                                     |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
|             0.00E+00   4.41E+01   0.000      Eq. H3-1      3     0.00 |
| Intermediate Fcr        Tn                                            |
|             3.97E+03   4.90E+01                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       4.13E+01   5.42E+01   0.763      Eq. F7-1      3    10.50 |
| Minor       0.00E+00   5.42E+01   0.000      Eq. F7-1      3     0.00 |
| Intermediate   Mn        My                                           |
| Major       6.02E+01   0.00E+00                                       |
| Minor       6.02E+01   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 BENDING-FLANGE LOCAL BUCKLING                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       4.13E+01   4.25E+01   0.972      Eq. F7-3      3    10.50 |
| Minor       0.00E+00   4.25E+01   0.000      Eq. F7-3      3     0.00 |
| Intermediate   Mn        Fcr                                          |
| Major       4.73E+01   0.00E+00                                       |
| Minor       4.73E+01   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.972      Eq. H1-1b     3    10.50             |
| Flexure Tens          0.972      Eq. H1-1b     3    10.50             |
| Intermediate         Mcx        Mrx        Pc                         |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         4.25E+01   4.13E+01   1.35E+02                   |
|                      4.25E+01   0.00E+00   0.00E+00                   |
| Flexure Tens         4.25E+01   4.13E+01   2.22E+02                   |
|                      4.25E+01   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|
    48. LOAD LIST 4
    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)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
       1 ST   HSST8X8X0.188            (AISC SECTIONS)
                           PASS   Eq. H1-1b            0.974         4
                        0.00            0.00         -27.56       10.50
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     79.175  L/C  :     4                |
| Allowable Slenderness Ratio :    300.000  LOC  :    10.50             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      4    Ratio     :     0.974(PASS)                 |
|          Loc  :   10.50   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:  -2.756E+01               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   2.602E+00     Ayy:   2.602E+00     Cw:  0.000E+00              |
| Szz:   1.360E+01     Syy:   1.360E+01                                 |
| Izz:   5.440E+01     Iyy:   5.440E+01     Ix:  8.450E+01              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:        6623.999   Fu:        8351.999                           |
|-----------------------------------------------------------------------|
| Actual Member Length:        21.000                                   |
| 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        |
|                Slender        42.98     N/A     35.15    T.B4.1(a)-6  |
| Flexure     :  Slender        42.98    28.12    35.15    T.B4.1(b)-17 |
|                Compact        42.98    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   1.48E+02   0.000      Eq. D2-1      4     0.00 |
| Rupture     0.00E+00   1.56E+02   0.000      Eq. D2-2      4     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    0.00E+00   8.96E+01   0.000      Eq. E7-1      4     0.00 |
| Min Buck    0.00E+00   8.96E+01   0.000      Eq. E7-1      4     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    3.27E-02    79.18   4.01E+03   6.57E+03   1.50E+02        |
| Min Buck    3.27E-02    79.18   4.01E+03   6.57E+03   1.50E+02        |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   4.30E+01   0.000      Eq. G2-1      4     0.00 |
| Local-Y     5.25E+00   4.30E+01   0.122      Eq. G2-1      4     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     1.81E-02     1.00     5.00    42.98   7.18E+01            |
| Local-Y     1.81E-02     1.00     5.00    42.98   7.18E+01            |
|-----------------------------------------------------------------------|
| CHECK FOR TORSION                                                     |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
|             0.00E+00   2.93E+01   0.000      Eq. H3-1      4     0.00 |
| Intermediate Fcr        Tn                                            |
|             3.97E+03   4.90E+01                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       2.76E+01   3.60E+01   0.765      Eq. F7-1      4    10.50 |
| Minor       0.00E+00   3.60E+01   0.000      Eq. F7-1      4     0.00 |
| Intermediate   Mn        My                                           |
| Major       6.02E+01   0.00E+00                                       |
| Minor       6.02E+01   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 BENDING-FLANGE LOCAL BUCKLING                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       2.76E+01   2.83E+01   0.974      Eq. F7-3      4    10.50 |
| Minor       0.00E+00   2.83E+01   0.000      Eq. F7-3      4     0.00 |
| Intermediate   Mn        Fcr                                          |
| Major       4.73E+01   0.00E+00                                       |
| Minor       4.73E+01   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.974      Eq. H1-1b     4    10.50             |
| Flexure Tens          0.974      Eq. H1-1b     4    10.50             |
| Intermediate         Mcx        Mrx        Pc                         |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         2.83E+01   2.76E+01   8.96E+01                   |
|                      2.83E+01   0.00E+00   0.00E+00                   |
| Flexure Tens         2.83E+01   2.76E+01   1.48E+02                   |
|                      2.83E+01   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|