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:
Service moment:
Try a HSS 8×8×3/16, which has a plastic section modulus, Zx = 15.7 in3 and a section modulus, Sx = 13.6 in3 .
The yield strength, Fy = 46 ksi
Flange compactness: λ = b/t = 43.0
Determine the slender flange ratio limit from Table B4.1b: (Slender)
Web compactness: λ = h/t = 43.0
Thus, the section has a compact web.
The width of the compression flange between the corners (assumed to be 1.5t) is:
Thus, the ineffective width of the compression flange is: b - be = 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:
The available flexural strength:
LRFD:
ASD:
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
ϕbMn (ft·k) [LRFD] | 42.5 | 42.5 | none | |
Mn/Ωb (ft·k) [ASD] | 28.3 | 28.3 | none |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\09 Steel Design\US\AISC\AISC 360-10 HSST Slender Flange F.8.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 |
|-----------------------------------------------------------------------|