V. AISC 360-10 Double L E.6
Verify the compressive strength of an unbraced wide-flange section column about the Y-Y 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.6, pp. E-31 - E-36
Details
From the reference example E.1C:
Determine if a 2L5×3×1/4 LLBB (3/4-in. separation) strut, ASTM A36, with a length of 8 ft and pinned ends has sufficient available strength to support a dead load of 10 kips and live load of 30 kips in axial compression. Also, calculate the required number of pretensioned bolted or welded intermediate connectors.
Validation
Ultimate load:
Service load:
Per Table C-A-7.1 in Reference 1, K = 1.0 for pinned-pinned columns. Since the unbraced length is the same both directions, by inspection the y-y axis governs.
Slenderness
The limiting slenderness ratio, λr :
Thus, the outstanding legs are slender.
Check for slender web and then determine the stiffened element (web) reduction factor.
Thus,
Nominal Compressive Strength
The available compressive strength:
LRFD:
ASD:
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
ϕcPn (kips) [LRFD] | 64.3 | 63.8 | negligible | |
Pn/Ωc (kips) [ASD] | 42.8 | 42.4 | 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 Double L E.6.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 5-Dec-12
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 8 0; 2 0 0 0;
MEMBER INCIDENCES
1 1 2;
MEMBER PROPERTY AMERICAN
1 TABLE LD L50304 SP 0.0625
UNIT INCHES KIP
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 29000
POISSON 0.3
ISOTROPIC STEEL
E 29000
POISSON 0.3
DENSITY 0.000283
ALPHA 6e-06
DAMP 0.03
TYPE STEEL
STRENGTH FY 36 FU 58 RY 1.5 RT 1.2
ISOTROPIC STEEL_36_KSI
E 29000
POISSON 0.3
DENSITY 0.000283
ALPHA 6.5e-06
DAMP 0.03
TYPE STEEL
STRENGTH FY 36 FU 58 RY 1.5 RT 1.2
ISOTROPIC STEEL_50_KSI
E 29000
POISSON 0.3
DENSITY 0.000283
ALPHA 6.5e-06
DAMP 0.03
TYPE STEEL
STRENGTH FY 50 FU 62 RY 1.5 RT 1.2
END DEFINE MATERIAL
UNIT FEET KIP
CONSTANTS
MATERIAL STEEL_50_KSI ALL
SUPPORTS
2 PINNED
1 FIXED BUT FY MX MZ
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
JOINT LOAD
1 FY -10
LOAD 2 LOADTYPE None TITLE LOAD CASE 2
JOINT LOAD
1 FY -30
LOAD COMB 3 ULTIMATE LOADS
1 1.2 2 1.6
LOAD COMB 4 SERVICE LOADS
1 1.0 2 1.0
PERFORM ANALYSIS
UNIT INCHES KIP
LOAD LIST 3
PARAMETER 1
CODE AISC UNIFIED 2010
METHOD LRFD
FU 58 ALL
FYLD 36 ALL
CSPACING 32 ALL
TRACK 2 ALL
CHECK CODE ALL
LOAD LIST 4
PARAMETER 2
CODE AISC UNIFIED 2010
METHOD ASD
FU 58 ALL
FYLD 36 ALL
CSPACING 32 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 INCH (UNLESS OTHERWISE Noted)
MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/
FX MY MZ LOCATION
=======================================================================
1 LD L50304 (AISC SECTIONS)
PASS Eq. H2-1 0.941 3
60.00 C 0.00 0.00 0.00
|-----------------------------------------------------------------------|
| SLENDERNESS |
| Actual Slenderness Ratio : 75.420 L/C : 3 |
| Allowable Slenderness Ratio : 200.000 LOC : 0.00 |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS |
| Critical L/C : 3 Ratio : 0.941(PASS) |
| Loc : 0.00 Condition : Eq. H2-1 |
|-----------------------------------------------------------------------|
| DESIGN FORCES |
| Fx: 6.000E+01(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: 1.500E+00 Ayy: 1.250E+00 Cw: 0.000E+00 |
| Szz: 3.055E+00 Syy: 2.075E+00 |
| Izz: 1.022E+01 Iyy: 7.003E+00 Ix: 8.083E-02 |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES |
| Fyld: 36.000 Fu: 58.000 |
|-----------------------------------------------------------------------|
| Actual Member Length: 96.000 |
| Design Parameters |
| Kz: 1.00 Ky: 1.00 NSF: 1.00 SLF: 1.00 CSP: 32.00 |
|-----------------------------------------------------------------------|
| SECTION CLASS UNSTIFFENED / λ λp λr CASE |
| STIFFENED |
| Compression : Slender 20.00 N/A 12.77 T.B4.1(a)-3 |
| N/A N/A N/A N/A N/A |
| Flexure : Non-Compact 20.00 15.33 25.83 T.B4.1(b)-12 |
| N/A N/A N/A N/A N/A |
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 1.26E+02 0.000 Eq. D2-1 3 0.00 |
| Rupture 0.00E+00 1.69E+02 0.000 Eq. D2-2 3 0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Maj Buck 6.00E+01 8.72E+01 0.688 Eq. E7-1 3 0.00 |
| Min Buck 6.00E+01 8.15E+01 0.737 Eq. E7-1 3 0.00 |
| Flexural |
| Tor Buck 6.00E+01 6.38E+01 0.941 Eq. E7-1 3 0.00 |
| Intermediate |
| Results Eff Area KL/r Fcr Fe Pn |
| Maj Buck 3.88E+00 59.15 2.50E+01 8.18E+01 9.69E+01 |
| Min Buck 3.88E+00 71.46 2.33E+01 5.61E+01 9.05E+01 |
| Flexural Ag Fcr Pn |
| Tor Buck 3.88E+00 1.83E+01 7.08E+01 |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Local-Z -0.00E+00 2.92E+01 0.000 Eq. G2-1 3 0.00 |
| Local-Y 0.00E+00 2.43E+01 0.000 Eq. G2-1 3 0.00 |
| Intermediate |
| Results Aw Cv Kv h/tw Vn |
| Local-Z 1.50E+00 1.00 1.20 12.00 3.24E+01 |
| Local-Y 1.25E+00 1.00 1.20 20.00 2.70E+01 |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Major -0.00E+00 1.58E+02 0.000 Eq. F9-1 3 0.00 |
| Minor 0.00E+00 1.08E+02 0.000 Eq. F6-1 3 0.00 |
| Intermediate Mn My |
| Major 1.76E+02 0.00E+00 |
| Minor 1.20E+02 0.00E+00 |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Major -0.00E+00 1.04E+03 0.000 Eq. F9-4 3 0.00 |
| Intermediate Mn Me Cb Lp Lr Lb |
| Major 1.16E+03 0.00E+00 1.00 0.00 0.00 96.00 |
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 FLEXURE TENS/COMP INTERACTION |
| RATIO CRITERIA L/C LOC |
| Flexure Comp 0.941 Eq. H2-1 3 0.00 |
| Flexure Tens 0.000 Eq. H1-1b 3 0.00 |
| Intermediate frbw / frbz / fra / |
| Fcbw Fcbz Fca |
| Flexure Comp 0.00E+00 0.00E+00 1.55E+01 |
| 5.18E+01 5.18E+01 1.64E+01 |
| Intermediate Mcx Mrx Pc |
| Mcy Mry Pr |
| Flexure Tens 1.58E+02 -0.00E+00 1.26E+02 |
| 1.08E+02 0.00E+00 0.00E+00 |
|-----------------------------------------------------------------------|
70. LOAD LIST 4
71. PARAMETER 2
72. CODE AISC UNIFIED 2010
73. METHOD ASD
74. FU 58 ALL
75. FYLD 36 ALL
76. CSPACING 32 ALL
77. TRACK 2 ALL
78. CHECK CODE ALL
STEEL DESIGN
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 LD L50304 (AISC SECTIONS)
PASS Eq. H2-1 0.943 4
40.00 C 0.00 0.00 0.00
|-----------------------------------------------------------------------|
| SLENDERNESS |
| Actual Slenderness Ratio : 75.420 L/C : 4 |
| Allowable Slenderness Ratio : 200.000 LOC : 0.00 |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS |
| Critical L/C : 4 Ratio : 0.943(PASS) |
| Loc : 0.00 Condition : Eq. H2-1 |
|-----------------------------------------------------------------------|
| DESIGN FORCES |
| Fx: 4.000E+01(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: 1.500E+00 Ayy: 1.250E+00 Cw: 0.000E+00 |
| Szz: 3.055E+00 Syy: 2.075E+00 |
| Izz: 1.022E+01 Iyy: 7.003E+00 Ix: 8.083E-02 |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES |
| Fyld: 36.000 Fu: 58.000 |
|-----------------------------------------------------------------------|
| Actual Member Length: 96.000 |
| Design Parameters |
| Kz: 1.00 Ky: 1.00 NSF: 1.00 SLF: 1.00 CSP: 32.00 |
|-----------------------------------------------------------------------|
| SECTION CLASS UNSTIFFENED / λ λp λr CASE |
| STIFFENED |
| Compression : Slender 20.00 N/A 12.77 T.B4.1(a)-3 |
| N/A N/A N/A N/A N/A |
| Flexure : Non-Compact 20.00 15.33 25.83 T.B4.1(b)-12 |
| N/A N/A N/A N/A N/A |
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 8.36E+01 0.000 Eq. D2-1 4 0.00 |
| Rupture 0.00E+00 1.13E+02 0.000 Eq. D2-2 4 0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Maj Buck 4.00E+01 5.80E+01 0.689 Eq. E7-1 4 0.00 |
| Min Buck 4.00E+01 5.42E+01 0.738 Eq. E7-1 4 0.00 |
| Flexural |
| Tor Buck 4.00E+01 4.24E+01 0.943 Eq. E7-1 4 0.00 |
| Intermediate |
| Results Eff Area KL/r Fcr Fe Pn |
| Maj Buck 3.88E+00 59.15 2.50E+01 8.18E+01 9.69E+01 |
| Min Buck 3.88E+00 71.46 2.33E+01 5.61E+01 9.05E+01 |
| Flexural Ag Fcr Pn |
| Tor Buck 3.88E+00 1.83E+01 7.08E+01 |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Local-Z -0.00E+00 1.94E+01 0.000 Eq. G2-1 4 0.00 |
| Local-Y 0.00E+00 1.62E+01 0.000 Eq. G2-1 4 0.00 |
| Intermediate |
| Results Aw Cv Kv h/tw Vn |
| Local-Z 1.50E+00 1.00 1.20 12.00 3.24E+01 |
| Local-Y 1.25E+00 1.00 1.20 20.00 2.70E+01 |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Major -0.00E+00 1.05E+02 0.000 Eq. F9-1 4 0.00 |
| Minor 0.00E+00 7.16E+01 0.000 Eq. F6-1 4 0.00 |
| Intermediate Mn My |
| Major 1.76E+02 0.00E+00 |
| Minor 1.20E+02 0.00E+00 |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Major -0.00E+00 6.93E+02 0.000 Eq. F9-4 4 0.00 |
| Intermediate Mn Me Cb Lp Lr Lb |
| Major 1.16E+03 0.00E+00 1.00 0.00 0.00 96.00 |
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 FLEXURE TENS/COMP INTERACTION |
| RATIO CRITERIA L/C LOC |
| Flexure Comp 0.943 Eq. H2-1 4 0.00 |
| Flexure Tens 0.000 Eq. H1-1b 4 0.00 |
| Intermediate frbw / frbz / fra / |
| Fcbw Fcbz Fca |
| Flexure Comp 0.00E+00 0.00E+00 1.03E+01 |
| 3.45E+01 3.45E+01 1.09E+01 |
| Intermediate Mcx Mrx Pc |
| Mcy Mry Pr |
| Flexure Tens 1.05E+02 -0.00E+00 8.36E+01 |
| 7.16E+01 0.00E+00 0.00E+00 |
|-----------------------------------------------------------------------|