V. AISC 360-10 C LTB Test F.2-2
Verify the lateral flexural strength of a compact channel section braced at the fifth points per the LRFD and ASD methods of the AISC 360-10 code.
Reference
- 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 F.2-2A and F.2-2B, pp F-19 - F21
Problem
Check a C15x33.9 channel of ASTM A36 steel which serves as a roof edge beam. The simple span is 25 ft. The nominal loads on the member are a dead load 0.23 kip/ft and a uniform live load of 0.69 kip/ft. The beam is braced at fifth points and at ends.
Validation
Ultimate moment:
Service moment:
Try a C15×33.9, which has a plastic section modulus, Zx = 50.8 in3 .
All ASTM A36 grade C-shapes are compact. The member is continuously braced, so therefore the yielding limit state governs.
The available flexural strength:
LRFD:
ASD:
The unbraced length, >Lb = 5 ft.
Try a C15×33.9, which has a plastic section modulus, Zx = 50.8 in3 .
The lateral-torsional buckling modification factor, Cb = 1.0 for the center span of this bracing & loading condition.
All ASTM A36 grade C-shapes are compact.
The nominal flexural strength for the flexural yielding limit state is:
The nominal flexural strength for the lateral-torsional buckling limit state is:
The available flexural strength:
LRFD:
ASD:
Comparison
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
ϕbMn (kips) [LRFD] | 131 | 130 | negligible | |
Mn/Ωb (kips) [ASD] | 86.8 | 86.7 | negligible |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\09 Steel Design\US\AISC\AISC 360-10 F.2-2.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 02-Nov-12
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 5 0; 2 25 5 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 4.176e+06
POISSON 0.3
DENSITY 0.489024
ALPHA 6e-06
DAMP 0.03
TYPE STEEL
STRENGTH FY 5184 FU 8352 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TABLE ST C15X33
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FX MZ
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 UNI GY -0.23
LOAD 2 LOADTYPE None TITLE LOAD CASE 2
MEMBER LOAD
1 UNI GY -0.69
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
UNT 5 ALL
TRACK 2 ALL
CHECK CODE ALL
LOAD LIST 4
PARAMETER 1
CODE AISC UNIFIED 2010
METHOD ASD
UNT 5 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD Output
ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted)
MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/
FX MY MZ LOCATION
=======================================================================
* 1 ST C15X33 (AISC SECTIONS)
FAIL SLENDERNESS 1.113 3
0.00 0.00 0.00 0.00
|-----------------------------------------------------------------------|
| SLENDERNESS |
| Actual Slenderness Ratio : 333.952 L/C : 3 |
| Allowable Slenderness Ratio : 300.000 LOC : 0.00 |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS |
| Critical L/C : 3 Ratio : 1.113(FAIL) |
| Loc : 0.00 Condition : SLENDERNESS |
|-----------------------------------------------------------------------|
| DESIGN FORCES |
| Fx: 0.000E+00( ) Fy: 1.725E+01 Fz: 0.000E+00 |
| Mx: 0.000E+00 My: 0.000E+00 Mz: 0.000E+00 |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES (UNIT: INCH) |
| Azz: 4.420E+00 Ayy: 6.000E+00 Cw: 3.555E+02 |
| Szz: 4.200E+01 Syy: 3.178E+00 |
| Izz: 3.150E+02 Iyy: 8.070E+00 Ix: 1.010E+00 |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES |
| Fyld: 5183.999 Fu: 8351.999 |
|-----------------------------------------------------------------------|
| Actual Member Length: 25.000 |
| 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 : Non-Slender 5.23 N/A 15.89 T.B4.1(a)-1 |
| Non-Slender 34.25 N/A 42.29 T.B4.1(a)-5 |
| Flexure : Compact 5.23 10.79 28.38 T.B4.1(b)-10 |
| Compact 34.25 106.72 161.78 T.B4.1(b)-15 |
STAAD SPACE -- PAGE NO. 4
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 3.24E+02 0.000 Eq. D2-1 3 0.00 |
| Rupture -0.00E+00 4.35E+02 0.000 Eq. D2-2 3 0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Maj Buck 0.00E+00 2.79E+02 0.000 Eq. E3-1 3 0.00 |
| Min Buck 0.00E+00 2.03E+01 0.000 Eq. E3-1 3 0.00 |
| Flexural |
| Tor Buck 0.00E+00 2.07E+02 0.000 Eq. E4-1 3 0.00 |
| Intermediate |
| Results Eff Area KL/r Fcr Fe Pn |
| Maj Buck 6.94E-02 53.45 4.46E+03 1.44E+04 3.10E+02 |
| Min Buck 6.94E-02 333.95 3.24E+02 3.70E+02 2.25E+01 |
| Flexural Ag Fcr Pn |
| Tor Buck 6.94E-02 3.31E+03 2.30E+02 |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Local-Z -0.00E+00 8.59E+01 0.000 Eq. G2-1 3 0.00 |
| Local-Y 1.72E+01 1.17E+02 0.148 Eq. G2-1 3 0.00 |
| Intermediate |
| Results Aw Cv Kv h/tw Vn |
| Local-Z 3.07E-02 1.00 1.20 5.23 9.55E+01 |
| Local-Y 4.17E-02 1.00 5.00 34.25 1.30E+02 |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Major 1.08E+02 1.37E+02 0.786 Eq. F2-1 3 12.50 |
| Minor 0.00E+00 1.37E+01 0.000 Eq. F6-1 3 0.00 |
| Intermediate Mn My |
| Major 1.52E+02 0.00E+00 |
| Minor 1.53E+01 0.00E+00 |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Major 1.08E+02 1.30E+02 0.827 Eq. F2-2 3 12.50 |
| Intermediate Mn Me Cb Lp Lr Lb |
| Major 1.45E+02 0.00E+00 1.00 3.74 14.49 5.00 |
STAAD SPACE -- PAGE NO. 5
STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD) v1.4a
********************************************
ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION |
| RATIO CRITERIA L/C LOC |
| Flexure Comp 0.827 Eq. H1-1b 3 12.50 |
| Flexure Tens 0.827 Eq. H1-1b 3 12.50 |
| Intermediate Mcx Mrx Pc |
| Mcy Mry Pr |
| Flexure Comp 1.30E+02 1.08E+02 2.03E+01 |
| 1.37E+01 0.00E+00 0.00E+00 |
| Flexure Tens 1.30E+02 1.08E+02 3.24E+02 |
| 1.37E+01 0.00E+00 -0.00E+00 |
|-----------------------------------------------------------------------|
46. LOAD LIST 4
47. PARAMETER 1
48. CODE AISC UNIFIED 2010
49. METHOD ASD
50. UNT 5 ALL
51. TRACK 2 ALL
52. CHECK CODE ALL
STEEL DESIGN
STAAD SPACE -- PAGE NO. 6
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 C15X33 (AISC SECTIONS)
FAIL SLENDERNESS 1.113 4
0.00 0.00 0.00 0.00
|-----------------------------------------------------------------------|
| SLENDERNESS |
| Actual Slenderness Ratio : 333.952 L/C : 4 |
| Allowable Slenderness Ratio : 300.000 LOC : 0.00 |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS |
| Critical L/C : 4 Ratio : 1.113(FAIL) |
| Loc : 0.00 Condition : SLENDERNESS |
|-----------------------------------------------------------------------|
| DESIGN FORCES |
| Fx: 0.000E+00( ) Fy: 1.150E+01 Fz: 0.000E+00 |
| Mx: 0.000E+00 My: 0.000E+00 Mz: 0.000E+00 |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES (UNIT: INCH) |
| Azz: 4.420E+00 Ayy: 6.000E+00 Cw: 3.555E+02 |
| Szz: 4.200E+01 Syy: 3.178E+00 |
| Izz: 3.150E+02 Iyy: 8.070E+00 Ix: 1.010E+00 |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES |
| Fyld: 5183.999 Fu: 8351.999 |
|-----------------------------------------------------------------------|
| Actual Member Length: 25.000 |
| 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 : Non-Slender 5.23 N/A 15.89 T.B4.1(a)-1 |
| Non-Slender 34.25 N/A 42.29 T.B4.1(a)-5 |
| Flexure : Compact 5.23 10.79 28.38 T.B4.1(b)-10 |
| Compact 34.25 106.72 161.78 T.B4.1(b)-15 |
STAAD SPACE -- PAGE NO. 7
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 2.16E+02 0.000 Eq. D2-1 4 0.00 |
| Rupture -0.00E+00 2.90E+02 0.000 Eq. D2-2 4 0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Maj Buck 0.00E+00 1.85E+02 0.000 Eq. E3-1 4 0.00 |
| Min Buck 0.00E+00 1.35E+01 0.000 Eq. E3-1 4 0.00 |
| Flexural |
| Tor Buck 0.00E+00 1.38E+02 0.000 Eq. E4-1 4 0.00 |
| Intermediate |
| Results Eff Area KL/r Fcr Fe Pn |
| Maj Buck 6.94E-02 53.45 4.46E+03 1.44E+04 3.10E+02 |
| Min Buck 6.94E-02 333.95 3.24E+02 3.70E+02 2.25E+01 |
| Flexural Ag Fcr Pn |
| Tor Buck 6.94E-02 3.31E+03 2.30E+02 |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Local-Z -0.00E+00 5.72E+01 0.000 Eq. G2-1 4 0.00 |
| Local-Y 1.15E+01 7.76E+01 0.148 Eq. G2-1 4 0.00 |
| Intermediate |
| Results Aw Cv Kv h/tw Vn |
| Local-Z 3.07E-02 1.00 1.20 5.23 9.55E+01 |
| Local-Y 4.17E-02 1.00 5.00 34.25 1.30E+02 |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Major 7.19E+01 9.13E+01 0.788 Eq. F2-1 4 12.50 |
| Minor 0.00E+00 9.14E+00 0.000 Eq. F6-1 4 0.00 |
| Intermediate Mn My |
| Major 1.52E+02 0.00E+00 |
| Minor 1.53E+01 0.00E+00 |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Major 7.19E+01 8.67E+01 0.829 Eq. F2-2 4 12.50 |
| Intermediate Mn Me Cb Lp Lr Lb |
| Major 1.45E+02 0.00E+00 1.00 3.74 14.49 5.00 |
STAAD SPACE -- PAGE NO. 8
STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD) v1.4a
********************************************
ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION |
| RATIO CRITERIA L/C LOC |
| Flexure Comp 0.829 Eq. H1-1b 4 12.50 |
| Flexure Tens 0.829 Eq. H1-1b 4 12.50 |
| Intermediate Mcx Mrx Pc |
| Mcy Mry Pr |
| Flexure Comp 8.67E+01 7.19E+01 1.35E+01 |
| 9.14E+00 0.00E+00 0.00E+00 |
| Flexure Tens 8.67E+01 7.19E+01 2.16E+02 |
| 9.14E+00 0.00E+00 -0.00E+00 |
|-----------------------------------------------------------------------|
53. FINISH
*********** END OF THE STAAD.Pro RUN ***********
**** DATE= JUL 4,2024 TIME= 12:38:57 ****
STAAD SPACE -- PAGE NO. 9
************************************************************
* For technical assistance on STAAD.Pro, please visit *