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.
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:
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.
(F2-5) |
(F2-6) |
Lp < Lb ≤ Lr
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:
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\360-2010\AISC 360-10 - F.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
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 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: 0.000E+00 Syy: 0.000E+00 | | Izz: 3.150E+02 Iyy: 8.070E+00 Ix: 9.595E-01 | |-----------------------------------------------------------------------| | 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 2.03E+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 3.24E+03 2.25E+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 0.828 Eq. F2-2 3 12.50 | | Intermediate Mn Me Cb Lp Lr Lb | | Major 1.45E+02 0.00E+00 1.00 3.74 14.26 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 0.828 Eq. H1-1b 3 12.50 | | Flexure Tens 0.828 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 **WARNING-DUPLICATE PARAMETER BLOCK NUMBER. PLEASE PROVIDE VALID PARAMETER BLOCK NUMBER. 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: 0.000E+00 Syy: 0.000E+00 | | Izz: 3.150E+02 Iyy: 8.070E+00 Ix: 9.595E-01 | |-----------------------------------------------------------------------| | 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 1.35E+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 3.24E+03 2.25E+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 14.26 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 | |-----------------------------------------------------------------------|