V. AISC 360-10 W E.1D
Verify the compressive strength of a column torsionally braced at the midpoint in the weak axis 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.1D, p E-6, pp.E-9 - E-10
Note: This reference is freely available for download from the AISC website at https://www.aisc.org/globalassets/aisc/university-programs/teaching-aids/first-semester-design-examples.pdf
Details
From the reference example E.1C
Calculate the available strength of a W14×90 with a strong axis unbraced length of 30.0 ft and weak axis and torsional unbraced lengths of 15.0 ft.
From the reference example E.1A:
… 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 ft long and is pinned top and bottom in both axes.
Results
| Result Type | Reference | STAAD.Pro | Difference | Comments |
|---|---|---|---|---|
| ϕcPn (kips) [LRFD] | 927 | 927 | none | |
| Pn/Ωc (kips) [ASD] | 617 | 617 | none | |
| Slenderness ratio | 58.6 | 58.63 | negligible |
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 W E.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 22-Jan-19
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
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TABLE ST W14X90
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FY MX MZ
LOAD 1 LOADTYPE Dead TITLE LOAD CASE 1
JOINT LOAD
2 FY -140
LOAD 2 LOADTYPE Live TITLE LOAD CASE 2
JOINT LOAD
2 FY -420
LOAD COMB 3 LRFD
1 1.2 2 1.6
LOAD COMB 4 ASD
1 1.0 2 1.0
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
LOAD LIST 3
PARAMETER 1
CODE AISC UNIFIED 2010
METHOD LRFD
FYLD 7200 ALL
FU 9360 ALL
KX 0.5 ALL
KY 0.5 ALL
METHOD LRFD
PROFILE W14 ALL
TRACK 2 ALL
CHECK CODE ALL
LOAD LIST 4
PARAMETER 2
CODE AISC UNIFIED 2010
FYLD 7200 ALL
FU 9360 ALL
KX 0.5 ALL
KY 0.5 ALL
METHOD ASD
PROFILE W14 ALL
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 W14X90 (AISC SECTIONS) PASS Eq. H1-1a 0.906 3 840.00 C 0.00 0.00 0.00 |-----------------------------------------------------------------------| | SLENDERNESS | | Actual Slenderness Ratio : 58.633 L/C : 3 | | Allowable Slenderness Ratio : 200.000 LOC : 0.00 | |-----------------------------------------------------------------------| | STRENGTH CHECKS | | Critical L/C : 3 Ratio : 0.906(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: 2.059E+01 Ayy: 6.160E+00 Cw: 1.598E+04 | | Szz: 1.427E+02 Syy: 4.993E+01 | | Izz: 9.990E+02 Iyy: 3.620E+02 Ix: 4.060E+00 | |-----------------------------------------------------------------------| | MATERIAL PROPERTIES | | Fyld: 7199.999 Fu: 9359.999 | |-----------------------------------------------------------------------| | Actual Member Length: 30.000 | | Design Parameters | | Kz: 1.00 Ky: 0.50 NSF: 1.00 SLF: 1.00 CSP: 12.00 | |-----------------------------------------------------------------------| | SECTION CLASS UNSTIFFENED / λ λp λr CASE | | STIFFENED | | Compression : Non-Slender 10.21 N/A 13.49 T.B4.1(a)-1 | | Non-Slender 25.86 N/A 35.88 T.B4.1(a)-5 | | Flexure : Non-Compact 10.21 9.15 24.08 T.B4.1(b)-10 | | Compact 25.86 90.55 137.27 T.B4.1(b)-15 | STAAD SPACE -- PAGE NO. 7 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 1.19E+03 0.000 Eq. D2-1 3 0.00 | | Rupture 0.00E+00 1.29E+03 0.000 Eq. D2-2 3 0.00 | |-----------------------------------------------------------------------| | CHECK FOR AXIAL COMPRESSION | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Maj Buck 8.40E+02 9.27E+02 0.906 Eq. E3-1 3 0.00 | | Min Buck 8.40E+02 1.00E+03 0.838 Eq. E3-1 3 0.00 | | Flexural | | Tor Buck 8.40E+02 1.02E+03 0.821 Eq. E4-1 3 0.00 | | Intermediate | | Results Eff Area KL/r Fcr Fe Pn | | Maj Buck 1.84E-01 58.63 5.60E+03 1.20E+04 1.03E+03 | | Min Buck 1.84E-01 48.70 6.05E+03 1.74E+04 1.11E+03 | | Flexural Ag Fcr Pn | | Tor Buck 1.84E-01 6.18E+03 1.14E+03 | |-----------------------------------------------------------------------| | CHECK FOR SHEAR | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Local-Z 0.00E+00 5.56E+02 0.000 Eq. G2-1 3 0.00 | | Local-Y 0.00E+00 1.85E+02 0.000 Eq. G2-1 3 0.00 | | Intermediate | | Results Aw Cv Kv h/tw Vn | | Local-Z 1.43E-01 1.00 1.20 10.21 6.18E+02 | | Local-Y 4.28E-02 1.00 0.00 25.86 1.85E+02 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-YIELDING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 0.00E+00 5.89E+02 0.000 Eq. F2-1 3 0.00 | | Minor 0.00E+00 2.84E+02 0.000 Eq. F6-1 3 0.00 | | Intermediate Mn My | | Major 6.54E+02 0.00E+00 | | Minor 3.15E+02 0.00E+00 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 0.00E+00 4.66E+02 0.000 Eq. F2-2 3 0.00 | | Intermediate Mn Me Cb Lp Lr Lb | | Major 5.18E+02 0.00E+00 1.00 13.05 42.60 30.00 | STAAD SPACE -- PAGE NO. 8 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 0.00E+00 5.74E+02 0.000 Eq. F3-1 3 0.00 | | Minor 0.00E+00 2.73E+02 0.000 Eq. F6-2 3 0.00 | | Intermediate Mn Fcr | | Major 6.37E+02 0.00E+00 | | Minor 3.03E+02 0.00E+00 | |-----------------------------------------------------------------------| | CHECK FOR FLEXURE TENS/COMP INTERACTION | | RATIO CRITERIA L/C LOC | | Flexure Comp 0.906 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 4.66E+02 0.00E+00 9.27E+02 | | 2.73E+02 0.00E+00 8.40E+02 | | Flexure Tens 4.66E+02 0.00E+00 1.19E+03 | | 2.73E+02 0.00E+00 0.00E+00 | |-----------------------------------------------------------------------| 52. LOAD LIST 4 53. PARAMETER 2 54. CODE AISC UNIFIED 2010 55. FYLD 7200 ALL 56. FU 9360 ALL 57. KX 0.5 ALL 58. KY 0.5 ALL 59. METHOD ASD 60. PROFILE W14 ALL 61. TRACK 2 ALL 62. CHECK CODE ALL STEEL DESIGN STAAD SPACE -- PAGE NO. 9 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 W14X90 (AISC SECTIONS) PASS Eq. H1-1a 0.908 4 560.00 C 0.00 0.00 0.00 |-----------------------------------------------------------------------| | SLENDERNESS | | Actual Slenderness Ratio : 58.633 L/C : 4 | | Allowable Slenderness Ratio : 200.000 LOC : 0.00 | |-----------------------------------------------------------------------| | STRENGTH CHECKS | | Critical L/C : 4 Ratio : 0.908(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: 2.059E+01 Ayy: 6.160E+00 Cw: 1.598E+04 | | Szz: 1.427E+02 Syy: 4.993E+01 | | Izz: 9.990E+02 Iyy: 3.620E+02 Ix: 4.060E+00 | |-----------------------------------------------------------------------| | MATERIAL PROPERTIES | | Fyld: 7199.999 Fu: 9359.999 | |-----------------------------------------------------------------------| | Actual Member Length: 30.000 | | Design Parameters | | Kz: 1.00 Ky: 0.50 NSF: 1.00 SLF: 1.00 CSP: 12.00 | |-----------------------------------------------------------------------| | SECTION CLASS UNSTIFFENED / λ λp λr CASE | | STIFFENED | | Compression : Non-Slender 10.21 N/A 13.49 T.B4.1(a)-1 | | Non-Slender 25.86 N/A 35.88 T.B4.1(a)-5 | | Flexure : Non-Compact 10.21 9.15 24.08 T.B4.1(b)-10 | | Compact 25.86 90.55 137.27 T.B4.1(b)-15 | STAAD SPACE -- PAGE NO. 10 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 7.93E+02 0.000 Eq. D2-1 4 0.00 | | Rupture 0.00E+00 8.61E+02 0.000 Eq. D2-2 4 0.00 | |-----------------------------------------------------------------------| | CHECK FOR AXIAL COMPRESSION | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Maj Buck 5.60E+02 6.17E+02 0.908 Eq. E3-1 4 0.00 | | Min Buck 5.60E+02 6.67E+02 0.839 Eq. E3-1 4 0.00 | | Flexural | | Tor Buck 5.60E+02 6.81E+02 0.822 Eq. E4-1 4 0.00 | | Intermediate | | Results Eff Area KL/r Fcr Fe Pn | | Maj Buck 1.84E-01 58.63 5.60E+03 1.20E+04 1.03E+03 | | Min Buck 1.84E-01 48.70 6.05E+03 1.74E+04 1.11E+03 | | Flexural Ag Fcr Pn | | Tor Buck 1.84E-01 6.18E+03 1.14E+03 | |-----------------------------------------------------------------------| | CHECK FOR SHEAR | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Local-Z 0.00E+00 3.70E+02 0.000 Eq. G2-1 4 0.00 | | Local-Y 0.00E+00 1.23E+02 0.000 Eq. G2-1 4 0.00 | | Intermediate | | Results Aw Cv Kv h/tw Vn | | Local-Z 1.43E-01 1.00 1.20 10.21 6.18E+02 | | Local-Y 4.28E-02 1.00 0.00 25.86 1.85E+02 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-YIELDING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 0.00E+00 3.92E+02 0.000 Eq. F2-1 4 0.00 | | Minor 0.00E+00 1.89E+02 0.000 Eq. F6-1 4 0.00 | | Intermediate Mn My | | Major 6.54E+02 0.00E+00 | | Minor 3.15E+02 0.00E+00 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 0.00E+00 3.10E+02 0.000 Eq. F2-2 4 0.00 | | Intermediate Mn Me Cb Lp Lr Lb | | Major 5.18E+02 0.00E+00 1.00 13.05 42.60 30.00 | STAAD SPACE -- PAGE NO. 11 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 0.00E+00 3.82E+02 0.000 Eq. F3-1 4 0.00 | | Minor 0.00E+00 1.81E+02 0.000 Eq. F6-2 4 0.00 | | Intermediate Mn Fcr | | Major 6.37E+02 0.00E+00 | | Minor 3.03E+02 0.00E+00 | |-----------------------------------------------------------------------| | CHECK FOR FLEXURE TENS/COMP INTERACTION | | RATIO CRITERIA L/C LOC | | Flexure Comp 0.908 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 3.10E+02 0.00E+00 6.17E+02 | | 1.81E+02 0.00E+00 5.60E+02 | | Flexure Tens 3.10E+02 0.00E+00 7.93E+02 | | 1.81E+02 0.00E+00 0.00E+00 | |-----------------------------------------------------------------------|