V. AISC 360-10 Rect HSS E.9
Verify the compressive strength of an unbraced column with a rectangular HSS section per the LRFD and ASD methods of 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 E.9, pp. E-47 - E-49
Details
From reference (2):
Select an ASTM A500 Grade B rectangular HSS compression member, with a length of 20 ft, to support a dead load of 85 kips and live load of 255 kips in axial compression. The base is fixed and the top is pinned.
Validation
Ultimate load:
Service load:
Slenderness
The limiting slenderness ratio, λr :
Thus, the section does not contain slender elements.
Per Table C-A-7.1 in Reference 1, K = 0.8 for fixed-pinned columns. Since the unbraced length is the same both directions, by inspection the y-y axis governs.
Nominal Compressive Strength
The available compressive strength:
LRFD:
ASD:
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
ϕcPn (kips) [LRFD] | 518 | 518 | none | |
Pn/Ωc (kips) [ASD] | 344 | 345 | negligible |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\09 Steel Design\US\AISC\AISC 360-10 Rect HSS E.9.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 05-Feb-19
END JOB INFORMATION
INPUT WIDTH 79
UNIT INCHES KIP
JOINT COORDINATES
1 0 0 0; 2 0 240 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 29000
POISSON 0.3
DENSITY 0.000283
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 HSST12X10X0.375
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
2 FIXED BUT FY MX MZ
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
JOINT LOAD
2 FY -85
LOAD 2 LOADTYPE None TITLE LOAD CASE 2
JOINT LOAD
2 FY -255
LOAD COMB 3 LRFD
1 1.2 2 1.6
LOAD COMB 4 ASD
1 1.0 2 1.0
PERFORM ANALYSIS
LOAD LIST 3
PARAMETER 1
CODE AISC UNIFIED 2010
KX 0.8 ALL
KY 0.8 ALL
METHOD LRFD
TRACK 2 ALL
KZ 0.8 ALL
FU 58 ALL
FYLD 46 ALL
CHECK CODE ALL
LOAD LIST 4
PARAMETER 2
CODE AISC UNIFIED 2010
KX 0.8 ALL
KY 0.8 ALL
KZ 0.8 ALL
FU 58 ALL
FYLD 46 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 INCH (UNLESS OTHERWISE Noted)
MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/
FX MY MZ LOCATION
=======================================================================
1 ST HSST12X10X0.375 (AISC SECTIONS)
PASS Eq. H1-1a 0.985 3
510.00 C 0.00 0.00 0.00
|-----------------------------------------------------------------------|
| SLENDERNESS |
| Actual Slenderness Ratio : 47.959 L/C : 3 |
| Allowable Slenderness Ratio : 200.000 LOC : 0.00 |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS |
| Critical L/C : 3 Ratio : 0.985(PASS) |
| Loc : 0.00 Condition : Eq. H1-1a |
|-----------------------------------------------------------------------|
| DESIGN FORCES |
| Fx: 5.100E+02(C ) 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: 6.249E+00 Ayy: 7.645E+00 Cw: 0.000E+00 |
| Szz: 5.167E+01 Syy: 4.680E+01 |
| Izz: 3.100E+02 Iyy: 2.340E+02 Ix: 4.210E+02 |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES |
| Fyld: 46.000 Fu: 58.000 |
|-----------------------------------------------------------------------|
| Actual Member Length: 240.000 |
| Design Parameters |
| Kz: 0.80 Ky: 0.80 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 31.38 N/A 35.15 T.B4.1(a)-6 |
| Flexure : Compact 25.65 28.12 35.15 T.B4.1(b)-17 |
| Compact 31.38 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 INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Yield 0.00E+00 6.04E+02 0.000 Eq. D2-1 3 0.00 |
| Rupture 0.00E+00 6.35E+02 0.000 Eq. D2-2 3 0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Maj Buck 5.10E+02 5.38E+02 0.948 Eq. E3-1 3 0.00 |
| Min Buck 5.10E+02 5.18E+02 0.985 Eq. E3-1 3 0.00 |
| Intermediate |
| Results Eff Area KL/r Fcr Fe Pn |
| Maj Buck 1.46E+01 41.67 4.09E+01 1.65E+02 5.98E+02 |
| Min Buck 1.46E+01 47.96 3.94E+01 1.24E+02 5.75E+02 |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Local-Z -0.00E+00 1.55E+02 0.000 Eq. G2-1 3 0.00 |
| Local-Y 0.00E+00 1.90E+02 0.000 Eq. G2-1 3 0.00 |
| Intermediate |
| Results Aw Cv Kv h/tw Vn |
| Local-Z 6.25E+00 1.00 5.00 25.65 1.72E+02 |
| Local-Y 7.65E+00 1.00 5.00 31.38 2.11E+02 |
|-----------------------------------------------------------------------|
| CHECK FOR TORSION |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| 0.00E+00 1.94E+03 0.000 Eq. H3-1 3 0.00 |
| Intermediate Fcr Tn |
| 2.76E+01 2.16E+03 |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Major -0.00E+00 2.53E+03 0.000 Eq. F7-1 3 0.00 |
| Minor 0.00E+00 2.24E+03 0.000 Eq. F7-1 3 0.00 |
| Intermediate Mn My |
| Major 2.81E+03 0.00E+00 |
| Minor 2.48E+03 0.00E+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 BENDING-FLANGE LOCAL BUCKLING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Minor 0.00E+00 2.10E+03 0.000 Eq. F7-2 3 0.00 |
| Intermediate Mn Fcr |
| Minor 2.33E+03 0.00E+00 |
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION |
| RATIO CRITERIA L/C LOC |
| Flexure Comp 0.985 Eq. H1-1a 3 0.00 |
| Flexure Tens 0.000 Eq. H1-1b 3 0.00 |
| Intermediate Mcx Mrx Pc |
| Mcy Mry Pr |
| Flexure Comp 2.53E+03 -0.00E+00 5.18E+02 |
| 2.10E+03 0.00E+00 5.10E+02 |
| Flexure Tens 2.53E+03 -0.00E+00 6.04E+02 |
| 2.10E+03 0.00E+00 0.00E+00 |
|-----------------------------------------------------------------------|
50. LOAD LIST 4
51. PARAMETER 2
52. CODE AISC UNIFIED 2010
53. KX 0.8 ALL
54. KY 0.8 ALL
55. KZ 0.8 ALL
56. FU 58 ALL
57. FYLD 46 ALL
58. METHOD ASD
59. TRACK 2 ALL
60. 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 INCH (UNLESS OTHERWISE Noted)
MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/
FX MY MZ LOCATION
=======================================================================
1 ST HSST12X10X0.375 (AISC SECTIONS)
PASS Eq. H1-1a 0.987 4
340.00 C 0.00 0.00 0.00
|-----------------------------------------------------------------------|
| SLENDERNESS |
| Actual Slenderness Ratio : 47.959 L/C : 4 |
| Allowable Slenderness Ratio : 200.000 LOC : 0.00 |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS |
| Critical L/C : 4 Ratio : 0.987(PASS) |
| Loc : 0.00 Condition : Eq. H1-1a |
|-----------------------------------------------------------------------|
| DESIGN FORCES |
| Fx: 3.400E+02(C ) 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: 6.249E+00 Ayy: 7.645E+00 Cw: 0.000E+00 |
| Szz: 5.167E+01 Syy: 4.680E+01 |
| Izz: 3.100E+02 Iyy: 2.340E+02 Ix: 4.210E+02 |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES |
| Fyld: 46.000 Fu: 58.000 |
|-----------------------------------------------------------------------|
| Actual Member Length: 240.000 |
| Design Parameters |
| Kz: 0.80 Ky: 0.80 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 31.38 N/A 35.15 T.B4.1(a)-6 |
| Flexure : Compact 25.65 28.12 35.15 T.B4.1(b)-17 |
| Compact 31.38 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 INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Yield 0.00E+00 4.02E+02 0.000 Eq. D2-1 4 0.00 |
| Rupture 0.00E+00 4.23E+02 0.000 Eq. D2-2 4 0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Maj Buck 3.40E+02 3.58E+02 0.950 Eq. E3-1 4 0.00 |
| Min Buck 3.40E+02 3.45E+02 0.987 Eq. E3-1 4 0.00 |
| Intermediate |
| Results Eff Area KL/r Fcr Fe Pn |
| Maj Buck 1.46E+01 41.67 4.09E+01 1.65E+02 5.98E+02 |
| Min Buck 1.46E+01 47.96 3.94E+01 1.24E+02 5.75E+02 |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Local-Z -0.00E+00 1.03E+02 0.000 Eq. G2-1 4 0.00 |
| Local-Y 0.00E+00 1.26E+02 0.000 Eq. G2-1 4 0.00 |
| Intermediate |
| Results Aw Cv Kv h/tw Vn |
| Local-Z 6.25E+00 1.00 5.00 25.65 1.72E+02 |
| Local-Y 7.65E+00 1.00 5.00 31.38 2.11E+02 |
|-----------------------------------------------------------------------|
| CHECK FOR TORSION |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| 0.00E+00 1.29E+03 0.000 Eq. H3-1 4 0.00 |
| Intermediate Fcr Tn |
| 2.76E+01 2.16E+03 |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Major -0.00E+00 1.68E+03 0.000 Eq. F7-1 4 0.00 |
| Minor 0.00E+00 1.49E+03 0.000 Eq. F7-1 4 0.00 |
| Intermediate Mn My |
| Major 2.81E+03 0.00E+00 |
| Minor 2.48E+03 0.00E+00 |
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 BENDING-FLANGE LOCAL BUCKLING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Minor 0.00E+00 1.40E+03 0.000 Eq. F7-2 4 0.00 |
| Intermediate Mn Fcr |
| Minor 2.33E+03 0.00E+00 |
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION |
| RATIO CRITERIA L/C LOC |
| Flexure Comp 0.987 Eq. H1-1a 4 0.00 |
| Flexure Tens 0.000 Eq. H1-1b 4 0.00 |
| Intermediate Mcx Mrx Pc |
| Mcy Mry Pr |
| Flexure Comp 1.68E+03 -0.00E+00 3.45E+02 |
| 1.40E+03 0.00E+00 3.40E+02 |
| Flexure Tens 1.68E+03 -0.00E+00 4.02E+02 |
| 1.40E+03 0.00E+00 0.00E+00 |
|-----------------------------------------------------------------------|