V. AISC 360-10 Angle F.11A
Verify the available flexural strength of a single angle member per 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 Example F.11A, pp. F47-F49
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:
The yield moment for a single angle bent about its geometric axis with no lateral-torsional restraint:
Determine Me:
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.
The lateral-torsional buckling limit state governs.
The available flexural strength:
LRFD:
ASD:
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
LTB ϕbMn (ft·k) [LRFD] | 2.93 | 2.96 | negligible | |
LTB Mn/Ωb (ft·k) [ASD] | 1.95 | 1.97 | 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 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