V. AISC 360-05 Compression
Verify the axial compression capacity for a the y-y axis of an I section for both the LRFD and ASD methods per the AISC 360-05 code.
Details
The column is 30 ft long, pinned top and bottom in both axis.
The section is an ASTM A992 (Fy = 50 ksi) W-shape column to carry an axial dead load of 140 kips and live load of 420 kips. The column is 30 feet long
Validation
Calculate the required strength.
LRFD:
Pu = 1.2(140 kips) + 1.6(420 kips) = 840 kips
ASD:
Pa = 140 kips + 420 kips = 560 kips
For a pinned-pinned condition, K = 1.0 (Table C-C2.2 of ref. 2). Because the unbraced length is equal about both x-x and y-y directions, y-y axis buckling governs.
Use Table 4-1 in ref 2 and select a W14x132 (KLy = 30 ft). From this table:
ϕcPn = 892 kips > 840 kips
Pn/Ωc = 594 kips > 560 kips
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC 360-05 Compression.STD is typically installed with the program.
STAAD PLANE
START JOB INFORMATION
ENGINEER DATE 29-Aug-18
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 0 30 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
ISOTROPIC STEEL_50_KSI
E 4.176e+06
POISSON 0.3
DENSITY 0.489024
ALPHA 6.5e-06
DAMP 0.03
TYPE STEEL
STRENGTH FY 7200 FU 8928 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TABLE ST W14X132
CONSTANTS
MATERIAL STEEL_50_KSI ALL
SUPPORTS
1 PINNED
2 FIXED BUT FY MZ
LOAD 1 DEAD LOAD
JOINT LOAD
2 FY -140
LOAD 2 LIVE LOAD
JOINT LOAD
2 FY -420
LOAD COMB 3 SERVICE LOAD
1 1.0 2 1.0
LOAD COMB 4 ULTIMATE LOAD
1 1.2 2 1.6
PERFORM ANALYSIS
UNIT INCHES KIP
LOAD LIST 3
PARAMETER 1
CODE AISC UNIFIED 2005
METHOD ASD
FYLD 50 ALL
TRACK 2 ALL
CHECK CODE ALL
LOAD LIST 4
PARAMETER 2
CODE AISC UNIFIED 2005
METHOD LRFD
FYLD 50 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD Output
STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD) v3.3a ******************************************** ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted) MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION ======================================================================= 1 ST W14X132 (AISC SECTIONS) PASS Eq. H1-1a 0.943 3 560.00 C 0.00 0.00 0.00 |-----------------------------------------------------------------------| | SLENDERNESS | | Actual Slenderness Ratio : 95.792 L/C : 3 | | Allowable Slenderness Ratio : 200.000 LOC : 0.00 | |-----------------------------------------------------------------------| | STRENGTH CHECKS | | Critical L/C : 3 Ratio : 0.943(PASS) | | Loc : 0.00 Condition : Eq. H1-1a | |-----------------------------------------------------------------------| | DESIGN FORCES | | Fx: 5.600E+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: 3.028E+01 Ayy: 9.481E+00 Cw: 2.560E+04 | | Szz: 2.082E+02 Syy: 7.456E+01 | | Izz: 1.530E+03 Iyy: 5.480E+02 Ix: 1.230E+01 | |-----------------------------------------------------------------------| | MATERIAL PROPERTIES | | Fyld: 50.000 Fu: 60.000 | |-----------------------------------------------------------------------| | Actual Member Length: 360.000 | | 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 7.14 N/A 13.49 T.B4.1-3 | | Non-Slender 17.74 N/A 35.88 T.B4.1-10 | | Flexure : Compact 7.14 9.15 24.08 T.B4.1-1 | | Compact 17.74 90.55 137.27 T.B4.1-9 | STAAD PLANE -- PAGE NO. 4 STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD) v3.3a ******************************************** ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted) |-----------------------------------------------------------------------| | CHECK FOR AXIAL TENSION | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Yield 0.00E+00 1.16E+03 0.000 Eq. D2-1 3 0.00 | | Rupture 0.00E+00 1.16E+03 0.000 Eq. D2-2 3 0.00 | |-----------------------------------------------------------------------| | CHECK FOR AXIAL COMPRESSION | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Maj Buck 5.60E+02 9.14E+02 0.613 Sec. E1 3 0.00 | | Min Buck 5.60E+02 5.94E+02 0.943 Eq. E3-1 3 0.00 | | Flexural | | Tor Buck 5.60E+02 9.28E+02 0.603 Eq. E4-1 3 0.00 | | Intermediate | | Results Eff Area KL/r Fcr Fe Pn | | Maj Buck 3.88E+01 57.33 3.93E+01 8.71E+01 1.53E+03 | | Min Buck 3.88E+01 95.79 2.56E+01 3.12E+01 9.92E+02 | | Flexural Ag Fcr Pn | | Tor Buck 3.88E+01 3.99E+01 1.55E+03 | |-----------------------------------------------------------------------| | CHECK FOR SHEAR | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Local-Z 0.00E+00 5.44E+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 3.03E+01 1.00 1.20 7.14 9.08E+02 | | Local-Y 9.48E+00 1.00 0.00 17.74 2.84E+02 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-YIELDING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 0.00E+00 7.01E+03 0.000 Eq. F2-1 3 0.00 | | Minor 0.00E+00 3.38E+03 0.000 Eq. F6-1 3 0.00 | | Intermediate Mn My | | Major 1.17E+04 0.00E+00 | | Minor 5.65E+03 0.00E+00 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 0.00E+00 5.97E+03 0.000 Eq. F2-2 3 0.00 | | Intermediate Mn Me Cb Lp Lr Lb | | Major 9.98E+03 0.00E+00 1.00 159.29 673.75 360.00 | STAAD PLANE -- PAGE NO. 5 STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD) v3.3a ******************************************** ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted) |-----------------------------------------------------------------------| | CHECK FOR FLEXURE TENS/COMP INTERACTION | | RATIO CRITERIA L/C LOC | | Flexure Comp 0.943 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 5.97E+03 0.00E+00 5.94E+02 | | 3.38E+03 0.00E+00 5.60E+02 | | Flexure Tens 5.97E+03 0.00E+00 1.16E+03 | | 3.38E+03 0.00E+00 0.00E+00 | |-----------------------------------------------------------------------| 53. LOAD LIST 4 54. PARAMETER 2 55. CODE AISC UNIFIED 2005 56. METHOD LRFD 57. FYLD 50 ALL 58. TRACK 2 ALL 59. CHECK CODE ALL STEEL DESIGN STAAD PLANE -- PAGE NO. 6 STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD) v3.3a ******************************************** ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted) MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION ======================================================================= 1 ST W14X132 (AISC SECTIONS) PASS Eq. H1-1a 0.941 4 840.00 C 0.00 0.00 0.00 |-----------------------------------------------------------------------| | SLENDERNESS | | Actual Slenderness Ratio : 95.792 L/C : 4 | | Allowable Slenderness Ratio : 200.000 LOC : 0.00 | |-----------------------------------------------------------------------| | STRENGTH CHECKS | | Critical L/C : 4 Ratio : 0.941(PASS) | | Loc : 0.00 Condition : Eq. H1-1a | |-----------------------------------------------------------------------| | DESIGN FORCES | | Fx: 8.400E+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: 3.028E+01 Ayy: 9.481E+00 Cw: 2.560E+04 | | Szz: 2.082E+02 Syy: 7.456E+01 | | Izz: 1.530E+03 Iyy: 5.480E+02 Ix: 1.230E+01 | |-----------------------------------------------------------------------| | MATERIAL PROPERTIES | | Fyld: 50.000 Fu: 60.000 | |-----------------------------------------------------------------------| | Actual Member Length: 360.000 | | 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 7.14 N/A 13.49 T.B4.1-3 | | Non-Slender 17.74 N/A 35.88 T.B4.1-10 | | Flexure : Compact 7.14 9.15 24.08 T.B4.1-1 | | Compact 17.74 90.55 137.27 T.B4.1-9 | STAAD PLANE -- PAGE NO. 7 STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD) v3.3a ******************************************** ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted) |-----------------------------------------------------------------------| | CHECK FOR AXIAL TENSION | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Yield 0.00E+00 1.75E+03 0.000 Eq. D2-1 4 0.00 | | Rupture 0.00E+00 1.75E+03 0.000 Eq. D2-2 4 0.00 | |-----------------------------------------------------------------------| | CHECK FOR AXIAL COMPRESSION | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Maj Buck 8.40E+02 1.37E+03 0.612 Sec. E1 4 0.00 | | Min Buck 8.40E+02 8.93E+02 0.941 Eq. E3-1 4 0.00 | | Flexural | | Tor Buck 8.40E+02 1.39E+03 0.602 Eq. E4-1 4 0.00 | | Intermediate | | Results Eff Area KL/r Fcr Fe Pn | | Maj Buck 3.88E+01 57.33 3.93E+01 8.71E+01 1.53E+03 | | Min Buck 3.88E+01 95.79 2.56E+01 3.12E+01 9.92E+02 | | Flexural Ag Fcr Pn | | Tor Buck 3.88E+01 3.99E+01 1.55E+03 | |-----------------------------------------------------------------------| | CHECK FOR SHEAR | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Local-Z 0.00E+00 8.18E+02 0.000 Eq. G2-1 4 0.00 | | Local-Y 0.00E+00 2.84E+02 0.000 Eq. G2-1 4 0.00 | | Intermediate | | Results Aw Cv Kv h/tw Vn | | Local-Z 3.03E+01 1.00 1.20 7.14 9.08E+02 | | Local-Y 9.48E+00 1.00 0.00 17.74 2.84E+02 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-YIELDING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 0.00E+00 1.05E+04 0.000 Eq. F2-1 4 0.00 | | Minor 0.00E+00 5.08E+03 0.000 Eq. F6-1 4 0.00 | | Intermediate Mn My | | Major 1.17E+04 0.00E+00 | | Minor 5.65E+03 0.00E+00 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 0.00E+00 8.98E+03 0.000 Eq. F2-2 4 0.00 | | Intermediate Mn Me Cb Lp Lr Lb | | Major 9.98E+03 0.00E+00 1.00 159.29 673.75 360.00 | STAAD PLANE -- PAGE NO. 8 STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD) v3.3a ******************************************** ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted) |-----------------------------------------------------------------------| | CHECK FOR FLEXURE TENS/COMP INTERACTION | | RATIO CRITERIA L/C LOC | | Flexure Comp 0.941 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 8.98E+03 0.00E+00 8.93E+02 | | 5.08E+03 0.00E+00 8.40E+02 | | Flexure Tens 8.98E+03 0.00E+00 1.75E+03 | | 5.08E+03 0.00E+00 0.00E+00 | |-----------------------------------------------------------------------|