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.
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
Note: The corner radius is taken as 1.5× the design wall thickness per
Section B4.1b of Reference 1.
The limiting slenderness ratio, λr:
| (Table B4.1a, case 3) |
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.
| (Eq. E3-4) |
| (Eq. E3-2) |
Nominal Compressive Strength
| (Eq E7-1) |
The available compressive strength:
LRFD:
ASD:
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 Rect HSS E.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 | |-----------------------------------------------------------------------|