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.
References
- Design Examples, Version 13.0, American Institute of Steel Construction, 2005, page E-4. Example E.1a
- Steel Construction Manual, Version 13.0, American Institute of Steel Construction, 2005
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:
ASD:
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:
Results
Parameter | Hand Calculation | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
ϕcPn (kips) [LRFD] | 892 | 893 | negligible | |
Pn/Ωc (kips) [ASD] | 594 | 594 | none |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\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 |
|-----------------------------------------------------------------------|