V. AISC 360-10 - D-2
Reference
Design Examples, Version 14.0, American Institute of Steel Construction, 2011, page D-5.
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
Problem
From the reference:
Verify, by both ASD and LRFD, the tensile strength of an L4×4×1/2, ASTM A36 […]. The member carries a dead load of 20 kips and a live load of 60 kips in tension. Calculate at what length this tension member would cease to satisfy the recommended slenderness limit. Assume that connection limit states do not govern.
Refer to the reference for calculations.
Comparison
| Result Type | Reference | STAAD.Pro | Difference |
|---|---|---|---|
| Tensile yielding ϕtPn (kips) [LRFD] | 122 | 122 | none |
| Tensile rupture ϕtPn (kips) [LRFD] | 125 | 125 | none |
| Tensile yielding Pn/Ωt (kips) [ASD] | 80.8 | 80.8 | none |
| Tensile rupture Pn/Ωt (kips) [ASD] | 83.5 | 83.4 | negligible |
| L at which λ = 300 (ft) | 19.4 | 19.4 | none |
To calculate the length at which the member would exceed the slenderness limit of 300: (6 in)/(slenderness ratio) × 300
(6 in)/(7.732)×300 = 232.8 in = 19.4 ft
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC 360-10 - D-2.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 25-Oct-12
END JOB INFORMATION
INPUT WIDTH 79
UNIT INCHES KIP
JOINT COORDINATES
1 0 0 0; 2 6 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 29732.7
POISSON 0.3
DENSITY 0.000283
ALPHA 1.2e-05
DAMP 0.03
TYPE STEEL
STRENGTH FY 36.7236 FU 59.1464 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TABLE ST L40408
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
LOAD 1 LOADTYPE Dead TITLE LOAD CASE 1
JOINT LOAD
2 FX 20
LOAD 2 LOADTYPE Live TITLE LOAD CASE 2
JOINT LOAD
2 FX 60
LOAD COMB 3 COMBINATION LOAD CASE 3
1 1.2 2 1.6
LOAD COMB 4 COMBINATION LOAD CASE 4
1 1.0 2 1.0
PERFORM ANALYSIS
LOAD LIST 3
PARAMETER 1
CODE AISC UNIFIED 2010
METHOD LRFD
NSF 0.88267 ALL
SLF 0.869 ALL
TRACK 2 ALL
CHECK CODE ALL
LOAD LIST 4
PARAMETER 2
CODE AISC UNIFIED 2010
METHOD ASD
NSF 0.88267 ALL
SLF 0.869 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD Output
STAAD SPACE -- PAGE NO. 3 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 L40408 (AISC SECTIONS) PASS Eq. H2-1 0.988 3 120.00 T 0.00 0.00 0.00 |-----------------------------------------------------------------------| | SLENDERNESS | | Actual Slenderness Ratio : 7.732 L/C : 3 | | Allowable Slenderness Ratio : 300.000 LOC : 0.00 | |-----------------------------------------------------------------------| | STRENGTH CHECKS | | Critical L/C : 3 Ratio : 0.988(PASS) | | Loc : 0.00 Condition : Eq. H2-1 | |-----------------------------------------------------------------------| | DESIGN FORCES | | Fx: 1.200E+02(T ) 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: 2.000E+00 Ayy: 2.000E+00 Cw: 3.662E-01 | | Szz: 1.371E+00 Syy: 3.121E+00 | | Izz: 2.258E+00 Iyy: 8.865E+00 Ix: 3.125E-01 | |-----------------------------------------------------------------------| | MATERIAL PROPERTIES | | Fyld: 36.000 Fu: 58.000 | |-----------------------------------------------------------------------| | Actual Member Length: 6.000 | | Design Parameters | | Kz: 1.00 Ky: 1.00 NSF: 0.88 SLF: 0.87 CSP: 12.00 | |-----------------------------------------------------------------------| | SECTION CLASS UNSTIFFENED / λ λp λr CASE | | STIFFENED | | Compression : Non-Slender 8.00 N/A 12.93 T.B4.1(a)-3 | | N/A N/A N/A N/A N/A | | Flexure : Compact 8.00 15.52 26.15 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 1.20E+02 1.22E+02 0.988 Eq. D2-1 3 0.00 | | Rupture 1.20E+02 1.25E+02 0.959 Eq. D2-2 3 0.00 | |-----------------------------------------------------------------------| | CHECK FOR AXIAL COMPRESSION | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Min Buck 0.00E+00 9.85E+01 0.000 Eq. E3-1 3 0.00 | | Intermediate | | Results Eff Area KL/r Fcr Fe Pn | | Min Buck 3.75E+00 63.94 2.92E+01 7.18E+01 1.09E+02 | |-----------------------------------------------------------------------| | CHECK FOR SHEAR | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Local-Z 0.00E+00 3.89E+01 0.000 Eq. G2-1 3 0.00 | | Local-Y 0.00E+00 3.89E+01 0.000 Eq. G2-1 3 0.00 | | Intermediate | | Results Aw Cv Kv h/tw Vn | | Local-Z 2.00E+00 1.00 1.20 8.00 4.32E+01 | | Local-Y 2.00E+00 1.00 1.20 8.00 4.32E+01 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-YIELDING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 0.00E+00 1.52E+02 0.000 Eq. F10-1 3 0.00 | | Minor 0.00E+00 6.66E+01 0.000 Eq. F10-1 3 0.00 | | Intermediate Mn My | | Major 1.69E+02 1.12E+02 | | Minor 7.40E+01 4.94E+01 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 0.00E+00 1.52E+02 0.000 Eq. F10-3 3 0.00 | | Intermediate Mn Me Cb Lp Lr Lb | | Major 1.69E+02 9.12E+03 1.00 0.00 0.00 6.00 | 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 SHEAR AND NORMAL STRESS INTERACTION | | | | STRESS RATIO CRITERIA L/C LOC | | Shear 1.94E+01 0.000 Eq. H3-8 3 0.00 | |-----------------------------------------------------------------------| | CHECK FOR FLEXURE TENS/COMP INTERACTION | | RATIO CRITERIA L/C LOC | | Flexure Comp 0.000 Eq. H2-1 3 0.00 | | Flexure Tens 0.988 Eq. H2-1 3 0.00 | | Intermediate frbw / frbz / fra / | | Fcbw Fcbz Fca | | Flexure Comp 0.00E+00 0.00E+00 0.00E+00 | | 4.86E+01 4.86E+01 2.63E+01 | | Flexure Tens 0.00E+00 0.00E+00 3.20E+01 | | 4.86E+01 4.86E+01 3.24E+01 | GEOMETRIC AXIS DESIGN |-----------------------------------------------------------------------| | CHECK FOR BENDING-YIELDING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 0.00E+00 9.60E+01 0.000 Eq. F10-1 3 0.00 | | Minor 0.00E+00 9.60E+01 0.000 Eq. F10-1 3 0.00 | | Intermediate Mn My | | Major 1.07E+02 7.11E+01 | | Minor 1.07E+02 7.11E+01 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 0.00E+00 7.68E+01 0.000 Eq. F10-3 3 0.00 | | Minor 0.00E+00 7.68E+01 0.000 Eq. F10-3 3 0.00 | | Intermediate Mn Me Cb Lp Lr Lb | | Major 8.53E+01 1.40E+05 1.00 0.00 0.00 6.00 | | Minor 8.53E+01 1.40E+05 1.00 0.00 0.00 6.00 | |-----------------------------------------------------------------------| STAAD SPACE -- PAGE NO. 6 46. LOAD LIST 4 47. PARAMETER 2 48. CODE AISC UNIFIED 2010 49. METHOD ASD 50. NSF 0.88267 ALL 51. SLF 0.869 ALL 52. TRACK 2 ALL 53. CHECK CODE ALL STEEL DESIGN STAAD SPACE -- PAGE NO. 7 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 L40408 (AISC SECTIONS) PASS Eq. H2-1 0.990 4 80.00 T 0.00 0.00 0.00 |-----------------------------------------------------------------------| | SLENDERNESS | | Actual Slenderness Ratio : 7.732 L/C : 4 | | Allowable Slenderness Ratio : 300.000 LOC : 0.00 | |-----------------------------------------------------------------------| | STRENGTH CHECKS | | Critical L/C : 4 Ratio : 0.990(PASS) | | Loc : 0.00 Condition : Eq. H2-1 | |-----------------------------------------------------------------------| | DESIGN FORCES | | Fx: 8.000E+01(T ) 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: 2.000E+00 Ayy: 2.000E+00 Cw: 3.662E-01 | | Szz: 1.371E+00 Syy: 3.121E+00 | | Izz: 2.258E+00 Iyy: 8.865E+00 Ix: 3.125E-01 | |-----------------------------------------------------------------------| | MATERIAL PROPERTIES | | Fyld: 36.000 Fu: 58.000 | |-----------------------------------------------------------------------| | Actual Member Length: 6.000 | | Design Parameters | | Kz: 1.00 Ky: 1.00 NSF: 0.88 SLF: 0.87 CSP: 12.00 | |-----------------------------------------------------------------------| | SECTION CLASS UNSTIFFENED / λ λp λr CASE | | STIFFENED | | Compression : Non-Slender 8.00 N/A 12.93 T.B4.1(a)-3 | | N/A N/A N/A N/A N/A | | Flexure : Compact 8.00 15.52 26.15 T.B4.1(b)-12 | | N/A N/A N/A N/A N/A | 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 AXIAL TENSION | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Yield 8.00E+01 8.08E+01 0.990 Eq. D2-1 4 0.00 | | Rupture 8.00E+01 8.34E+01 0.959 Eq. D2-2 4 0.00 | |-----------------------------------------------------------------------| | CHECK FOR AXIAL COMPRESSION | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Min Buck 0.00E+00 6.55E+01 0.000 Eq. E3-1 4 0.00 | | Intermediate | | Results Eff Area KL/r Fcr Fe Pn | | Min Buck 3.75E+00 63.94 2.92E+01 7.18E+01 1.09E+02 | |-----------------------------------------------------------------------| | CHECK FOR SHEAR | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Local-Z 0.00E+00 2.59E+01 0.000 Eq. G2-1 4 0.00 | | Local-Y 0.00E+00 2.59E+01 0.000 Eq. G2-1 4 0.00 | | Intermediate | | Results Aw Cv Kv h/tw Vn | | Local-Z 2.00E+00 1.00 1.20 8.00 4.32E+01 | | Local-Y 2.00E+00 1.00 1.20 8.00 4.32E+01 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-YIELDING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 0.00E+00 1.01E+02 0.000 Eq. F10-1 4 0.00 | | Minor 0.00E+00 4.43E+01 0.000 Eq. F10-1 4 0.00 | | Intermediate Mn My | | Major 1.69E+02 1.12E+02 | | Minor 7.40E+01 4.94E+01 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 0.00E+00 1.01E+02 0.000 Eq. F10-3 4 0.00 | | Intermediate Mn Me Cb Lp Lr Lb | | Major 1.69E+02 9.12E+03 1.00 0.00 0.00 6.00 | STAAD SPACE -- PAGE NO. 9 STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD) v1.4a ******************************************** ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted) |-----------------------------------------------------------------------| | CHECK FOR SHEAR AND NORMAL STRESS INTERACTION | | | | STRESS RATIO CRITERIA L/C LOC | | Shear 1.29E+01 0.000 Eq. H3-8 4 0.00 | |-----------------------------------------------------------------------| | CHECK FOR FLEXURE TENS/COMP INTERACTION | | RATIO CRITERIA L/C LOC | | Flexure Comp 0.000 Eq. H2-1 4 0.00 | | Flexure Tens 0.990 Eq. H2-1 4 0.00 | | Intermediate frbw / frbz / fra / | | Fcbw Fcbz Fca | | Flexure Comp 0.00E+00 0.00E+00 0.00E+00 | | 3.23E+01 3.23E+01 1.75E+01 | | Flexure Tens 0.00E+00 0.00E+00 2.13E+01 | | 3.23E+01 3.23E+01 2.16E+01 | GEOMETRIC AXIS DESIGN |-----------------------------------------------------------------------| | CHECK FOR BENDING-YIELDING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 0.00E+00 6.38E+01 0.000 Eq. F10-1 4 0.00 | | Minor 0.00E+00 6.38E+01 0.000 Eq. F10-1 4 0.00 | | Intermediate Mn My | | Major 1.07E+02 7.11E+01 | | Minor 1.07E+02 7.11E+01 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 0.00E+00 5.11E+01 0.000 Eq. F10-3 4 0.00 | | Minor 0.00E+00 5.11E+01 0.000 Eq. F10-3 4 0.00 | | Intermediate Mn Me Cb Lp Lr Lb | | Major 8.53E+01 1.40E+05 1.00 0.00 0.00 6.00 | | Minor 8.53E+01 1.40E+05 1.00 0.00 0.00 6.00 | |-----------------------------------------------------------------------|