V. AISC 360-10 Angle F.11A
Verify the available flexural strength of a single angle member per the AISC 360-10 code.
Details
From reference (2):
Select an ASTM A36 single angle with a simple span of 6 ft. The vertical leg of the single angle is up and the toe is in compression. The vertical loads are a uniform dead load of 0.05 kip/ft and a uniform live load of 0.15 kip/ft. There are no horizontal loads. There is no deflection limit for this angle. The angle is braced at the end points only. Assume bending about the geometric x-x axis and that there is no lateral-torsional restraint.
Validation
Ultimate moment:
Service moment:
Try an L4×4×1/4, which has a section modulus, Sx = 1.03 in3.
The yield strength, Fy = 36 ksi
The nominal flexural strength for the flexural yielding limit state:
(F10-1) |
The yield moment for a single angle bent about its geometric axis with no lateral-torsional restraint:
Determine Me:
(F10-6a) |
= |
(F10-3) |
Leg local buckling
Leg slenderness ratio:
Determine the compact and slender leg ratio limits from Table B4.1b:
λp < λ < λr; thus, the leg is non-compact in flexure.
(F10-3) |
= |
The lateral-torsional buckling limit state governs.
The available flexural strength:
LRFD:
ASD:
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\US\AISC\AISC 360-10 Angle F.11A.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 06-Mar-19
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 6 0 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 L40404
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED BUT MZ
2 FIXED BUT FX MZ
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 UNI GZ 0.25
LOAD 2 LOADTYPE None TITLE LOAD CASE 2
MEMBER LOAD
1 UNI GZ 0.2
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
PRINT ANALYSIS RESULTS
LOAD LIST 3
PARAMETER 1
CODE AISC UNIFIED 2010
METHOD LRFD
FU 8352 ALL
FYLD 5184 ALL
CB 1.14 ALL
TRACK 2 ALL
CHECK CODE ALL
LOAD LIST 4
PARAMETER 2
CODE AISC UNIFIED 2010
METHOD ASD
FU 8352 ALL
FYLD 5184 ALL
CB 1.14 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 L40404 (AISC SECTIONS) PASS Sec. F1 0.444 3 0.00 -1.86 -0.00 0.00 |-----------------------------------------------------------------------| | SLENDERNESS | | Actual Slenderness Ratio : 91.954 L/C : 3 | | Allowable Slenderness Ratio : 300.000 LOC : 0.00 | |-----------------------------------------------------------------------| | STRENGTH CHECKS | | Critical L/C : 3 Ratio : 0.444(PASS) | | Loc : 0.00 Condition : Sec. F1 | |-----------------------------------------------------------------------| | DESIGN FORCES | | Fx: 0.000E+00( ) Fy: 0.000E+00 Fz: -1.860E+00 | | Mx: 0.000E+00 My: -1.860E+00 Mz: -0.000E+00 | |-----------------------------------------------------------------------| | SECTION PROPERTIES (UNIT: INCH) | | Azz: 1.000E+00 Ayy: 1.000E+00 Cw: 5.051E-02 | | Szz: 7.837E-01 Syy: 1.719E+00 | | Izz: 1.183E+00 Iyy: 4.895E+00 Ix: 4.021E-02 | |-----------------------------------------------------------------------| | MATERIAL PROPERTIES | | Fyld: 5183.999 Fu: 8351.999 | |-----------------------------------------------------------------------| | Actual Member Length: 6.000 | | 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 : Slender 16.00 N/A 12.77 T.B4.1(a)-3 | | N/A N/A N/A N/A N/A | | Flexure : Non-Compact 16.00 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-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 6.25E+01 0.000 Eq. D2-1 3 0.00 | | Rupture -0.00E+00 8.40E+01 0.000 Eq. D2-2 3 0.00 | |-----------------------------------------------------------------------| | CHECK FOR AXIAL COMPRESSION | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Maj Buck 0.00E+00 5.17E+01 0.000 Eq. E7-1 3 0.00 | | Min Buck 0.00E+00 3.80E+01 0.000 Eq. E7-1 3 0.00 | | Intermediate | | Results Eff Area KL/r Fcr Fe Pn | | Maj Buck 1.34E-02 45.21 4.28E+03 2.02E+04 5.74E+01 | | Min Buck 1.34E-02 91.95 3.15E+03 4.87E+03 4.22E+01 | |-----------------------------------------------------------------------| | CHECK FOR SHEAR | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Local-Z 1.86E+00 1.94E+01 0.096 Eq. G2-1 3 0.00 | | Local-Y 0.00E+00 1.94E+01 0.000 Eq. G2-1 3 0.00 | | Intermediate | | Results Aw Cv Kv h/tw Vn | | Local-Z 6.94E-03 1.00 1.20 16.00 2.16E+01 | | Local-Y 6.94E-03 1.00 1.20 16.00 2.16E+01 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-YIELDING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 1.86E+00 6.96E+00 0.267 Eq. F10-1 3 0.00 | | Minor -0.00E+00 3.17E+00 0.000 Eq. F10-1 3 0.00 | | Intermediate Mn My | | Major 7.74E+00 5.16E+00 | | Minor 3.53E+00 2.35E+00 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 1.86E+00 5.97E+00 0.311 Eq. F10-3 3 0.00 | | Intermediate Mn Me Cb Lp Lr Lb | | Major 6.64E+00 1.76E+01 1.14 0.00 0.00 6.00 | 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-LEG LOCAL BUCKLING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 1.86E+00 6.78E+00 0.274 Eq. F10-7 3 0.00 | | Intermediate Mn Me | | Major 7.53E+00 0.00E+00 | |-----------------------------------------------------------------------| | CHECK FOR SHEAR AND NORMAL STRESS INTERACTION | | | | STRESS RATIO CRITERIA L/C LOC | | Shear 2.80E+03 0.096 Eq. H3-8 3 0.00 | |-----------------------------------------------------------------------| | CHECK FOR FLEXURE TENS/COMP INTERACTION | | RATIO CRITERIA L/C LOC | | Flexure Comp 0.311 Eq. H2-1 3 0.00 | | Flexure Tens 0.311 Eq. H2-1 3 0.00 | | Intermediate frbw / frbz / fra / | | Fcbw Fcbz Fca | | Flexure Comp 1.87E+03 0.00E+00 0.00E+00 | | 6.00E+03 7.00E+03 2.83E+03 | | Flexure Tens 1.87E+03 0.00E+00 -0.00E+00 | | 6.00E+03 7.00E+03 4.67E+03 | GEOMETRIC AXIS DESIGN |-----------------------------------------------------------------------| | CHECK FOR BENDING-YIELDING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 1.32E+00 4.24E+00 0.310 Eq. F10-1 3 0.00 | | Minor 1.32E+00 4.24E+00 0.310 Eq. F10-1 3 0.00 | | Intermediate Mn My | | Major 4.71E+00 3.14E+00 | | Minor 4.71E+00 3.14E+00 | STAAD SPACE -- PAGE NO. 9 STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD) v1.4a ******************************************** ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted) |-----------------------------------------------------------------------| | CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 1.32E+00 2.96E+00 0.444 Eq. F10-3 3 0.00 | | Minor 1.32E+00 3.39E+00 0.388 Eq. F10-3 3 0.00 | | Intermediate Mn Me Cb Lp Lr Lb | | Major 3.29E+00 9.20E+00 1.14 0.00 0.00 6.00 | | Minor 3.77E+00 5.41E+01 1.14 0.00 0.00 6.00 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-LEG LOCAL BUCKLING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 1.32E+00 3.30E+00 0.398 Eq. F10-7 3 0.00 | | Minor -6.58E-01 3.30E+00 0.199 Eq. F10-7 3 3.00 | | Intermediate Mn Me | | Major 3.67E+00 0.00E+00 | | Minor 3.67E+00 0.00E+00 | |-----------------------------------------------------------------------| 49. LOAD LIST 4 50. PARAMETER 2 51. CODE AISC UNIFIED 2010 52. METHOD ASD 53. FU 8352 ALL 54. FYLD 5184 ALL 55. CB 1.14 ALL 56. TRACK 2 ALL 57. CHECK CODE ALL STEEL DESIGN STAAD SPACE -- PAGE NO. 10 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 L40404 (AISC SECTIONS) PASS Sec. F1 0.485 4 0.00 -1.35 -0.00 0.00 |-----------------------------------------------------------------------| | SLENDERNESS | | Actual Slenderness Ratio : 91.954 L/C : 4 | | Allowable Slenderness Ratio : 300.000 LOC : 0.00 | |-----------------------------------------------------------------------| | STRENGTH CHECKS | | Critical L/C : 4 Ratio : 0.485(PASS) | | Loc : 0.00 Condition : Sec. F1 | |-----------------------------------------------------------------------| | DESIGN FORCES | | Fx: 0.000E+00( ) Fy: 0.000E+00 Fz: -1.350E+00 | | Mx: 0.000E+00 My: -1.350E+00 Mz: -0.000E+00 | |-----------------------------------------------------------------------| | SECTION PROPERTIES (UNIT: INCH) | | Azz: 1.000E+00 Ayy: 1.000E+00 Cw: 5.051E-02 | | Szz: 7.837E-01 Syy: 1.719E+00 | | Izz: 1.183E+00 Iyy: 4.895E+00 Ix: 4.021E-02 | |-----------------------------------------------------------------------| | MATERIAL PROPERTIES | | Fyld: 5183.999 Fu: 8351.999 | |-----------------------------------------------------------------------| | Actual Member Length: 6.000 | | 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 : Slender 16.00 N/A 12.77 T.B4.1(a)-3 | | N/A N/A N/A N/A N/A | | Flexure : Non-Compact 16.00 15.33 25.83 T.B4.1(b)-12 | | N/A N/A N/A N/A N/A | 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 AXIAL TENSION | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Yield -0.00E+00 4.16E+01 0.000 Eq. D2-1 4 0.00 | | Rupture -0.00E+00 5.60E+01 0.000 Eq. D2-2 4 0.00 | |-----------------------------------------------------------------------| | CHECK FOR AXIAL COMPRESSION | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Maj Buck 0.00E+00 3.44E+01 0.000 Eq. E7-1 4 0.00 | | Min Buck 0.00E+00 2.53E+01 0.000 Eq. E7-1 4 0.00 | | Intermediate | | Results Eff Area KL/r Fcr Fe Pn | | Maj Buck 1.34E-02 45.21 4.28E+03 2.02E+04 5.74E+01 | | Min Buck 1.34E-02 91.95 3.15E+03 4.87E+03 4.22E+01 | |-----------------------------------------------------------------------| | CHECK FOR SHEAR | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Local-Z 1.35E+00 1.29E+01 0.104 Eq. G2-1 4 0.00 | | Local-Y 0.00E+00 1.29E+01 0.000 Eq. G2-1 4 0.00 | | Intermediate | | Results Aw Cv Kv h/tw Vn | | Local-Z 6.94E-03 1.00 1.20 16.00 2.16E+01 | | Local-Y 6.94E-03 1.00 1.20 16.00 2.16E+01 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-YIELDING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 1.35E+00 4.63E+00 0.291 Eq. F10-1 4 0.00 | | Minor -0.00E+00 2.11E+00 0.000 Eq. F10-1 4 0.00 | | Intermediate Mn My | | Major 7.74E+00 5.16E+00 | | Minor 3.53E+00 2.35E+00 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 1.35E+00 3.97E+00 0.340 Eq. F10-3 4 0.00 | | Intermediate Mn Me Cb Lp Lr Lb | | Major 6.64E+00 1.76E+01 1.14 0.00 0.00 6.00 | STAAD SPACE -- PAGE NO. 12 STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD) v1.4a ******************************************** ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted) |-----------------------------------------------------------------------| | CHECK FOR BENDING-LEG LOCAL BUCKLING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 1.35E+00 4.51E+00 0.299 Eq. F10-7 4 0.00 | | Intermediate Mn Me | | Major 7.53E+00 0.00E+00 | |-----------------------------------------------------------------------| | CHECK FOR SHEAR AND NORMAL STRESS INTERACTION | | | | STRESS RATIO CRITERIA L/C LOC | | Shear 1.86E+03 0.104 Eq. H3-8 4 0.00 | |-----------------------------------------------------------------------| | CHECK FOR FLEXURE TENS/COMP INTERACTION | | RATIO CRITERIA L/C LOC | | Flexure Comp 0.340 Eq. H2-1 4 0.00 | | Flexure Tens 0.340 Eq. H2-1 4 0.00 | | Intermediate frbw / frbz / fra / | | Fcbw Fcbz Fca | | Flexure Comp 1.36E+03 0.00E+00 0.00E+00 | | 3.99E+03 4.66E+03 1.89E+03 | | Flexure Tens 1.36E+03 0.00E+00 -0.00E+00 | | 3.99E+03 4.66E+03 3.10E+03 | GEOMETRIC AXIS DESIGN |-----------------------------------------------------------------------| | CHECK FOR BENDING-YIELDING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 9.55E-01 2.82E+00 0.338 Eq. F10-1 4 0.00 | | Minor 9.55E-01 2.82E+00 0.338 Eq. F10-1 4 0.00 | | Intermediate Mn My | | Major 4.71E+00 3.14E+00 | | Minor 4.71E+00 3.14E+00 | STAAD SPACE -- PAGE NO. 13 STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD) v1.4a ******************************************** ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted) |-----------------------------------------------------------------------| | CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 9.55E-01 1.97E+00 0.485 Eq. F10-3 4 0.00 | | Minor 9.55E-01 2.26E+00 0.423 Eq. F10-3 4 0.00 | | Intermediate Mn Me Cb Lp Lr Lb | | Major 3.29E+00 9.20E+00 1.14 0.00 0.00 6.00 | | Minor 3.77E+00 5.41E+01 1.14 0.00 0.00 6.00 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-LEG LOCAL BUCKLING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 9.55E-01 2.20E+00 0.434 Eq. F10-7 4 0.00 | | Minor -4.77E-01 2.20E+00 0.217 Eq. F10-7 4 3.00 | | Intermediate Mn Me | | Major 3.67E+00 0.00E+00 | | Minor 3.67E+00 0.00E+00 | |-----------------------------------------------------------------------| 58. FINISH