V. AISC 360-05 Bending
To verify the flexural member strength in strong-axis bending of an I section for both LRFD and ASD methods per the AISC 360-05 code.
Details
Verify the Flexural Member Strength in Strong- Axis Bending by both LRFD and ASD method with ASTM A992 W18X50 beam with a simple span of 35 feet. The nominal loads are a uniform dead load of 0.45 kip/ft and a uniform live load of 0.75 kip/ft. Assuming the beam is continuously braced.
Validation
ASTM A992: Fy = 50 ksi, Fu = 65 ksi
Calculate the required flexural strength:
LRFD
wu = 1.2(0.450 kip/ft) + 1.6(0.750 kip/ft) = 1.74 kip/ft
ASD
wa = 0.450 kip/ft + 0.750 kip/ft = 1.20 kip/ft
Per the User Note in section F-2 of ref 2 (p.16.1-47), the W18X50 section is compact. Since the beam is continuously braced and compact, only the yielding limit state applies.
Tip: Per Table 3-2
of ref. 2 (p.3-17), the W18X50 is not the most efficient shape for
this individual beam. This example follows that given in ref 1.
STAAD.Pro will select a lighter beam if the
member selection command is used.
LRFD
ϕbMn = ϕbMpx = 0.9× (101 in3 × 50 ksi)(1 ft /12 in) = 379 ft·kip > 266 ft·kip
ASD
Mn/Ωb = Mpx/Ωb = (101 in3 × 50 ksi)(1 ft /12 in) / 1.67 = 252 ft·kip > 180 ft·kip
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC 360-05 Bending.STD is typically installed with the program.
STAAD PLANE
START JOB INFORMATION
ENGINEER DATE 27-Aug-18
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 35 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
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TABLE ST W18X50
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FX MZ
LOAD 1 DEAD LOAD
MEMBER LOAD
1 UNI Y -0.45
LOAD 2 LIVE LOAD
MEMBER LOAD
1 UNI Y -0.75
LOAD COMB 3 SERVICE LOAD
1 1.0 2 1.0
LOAD COMB 4 ULTIMATE LOAD
1 1.2 2 1.6
PERFORM ANALYSIS
LOAD LIST 3
PARAMETER 1
CODE AISC UNIFIED 2005
METHOD ASD
FYLD 7200 ALL
FU 9360 ALL
TRACK 2 ALL
CHECK CODE ALL
LOAD LIST 4
PARAMETER 2
CODE AISC UNIFIED 2005
METHOD LRFD
FYLD 7200 ALL
FU 9360 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD Output
STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD) v3.3a ******************************************** ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted) MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION ======================================================================= * 1 ST W18X50 (AISC SECTIONS) FAIL Eq. H1-1b 3.331 3 0.00 0.00 -183.75 17.50 |-----------------------------------------------------------------------| | SLENDERNESS | | Actual Slenderness Ratio : 254.294 L/C : 3 | | Allowable Slenderness Ratio : 300.000 LOC : 17.50 | |-----------------------------------------------------------------------| | STRENGTH CHECKS | | Critical L/C : 3 Ratio : 3.331(FAIL) | | Loc : 17.50 Condition : Eq. H1-1b | |-----------------------------------------------------------------------| | DESIGN FORCES | | Fx: 0.000E+00( ) Fy: 0.000E+00 Fz: 0.000E+00 | | Mx: 0.000E+00 My: 0.000E+00 Mz: -1.838E+02 | |-----------------------------------------------------------------------| | SECTION PROPERTIES (UNIT: INCH) | | Azz: 8.550E+00 Ayy: 6.390E+00 Cw: 3.046E+03 | | Szz: 8.889E+01 Syy: 1.069E+01 | | Izz: 8.000E+02 Iyy: 4.010E+01 Ix: 1.240E+00 | |-----------------------------------------------------------------------| | MATERIAL PROPERTIES | | Fyld: 7199.999 Fu: 9359.999 | |-----------------------------------------------------------------------| | Actual Member Length: 35.000 | | 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 6.58 N/A 13.49 T.B4.1-3 | | Slender 45.23 N/A 35.88 T.B4.1-10 | | Flexure : Compact 6.58 9.15 24.08 T.B4.1-1 | | Compact 45.23 90.55 137.27 T.B4.1-9 | STAAD PLANE -- PAGE NO. 4 STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD) v3.3a ******************************************** ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted) |-----------------------------------------------------------------------| | CHECK FOR AXIAL TENSION | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Yield 0.00E+00 4.40E+02 0.000 Eq. D2-1 3 0.00 | | Rupture 0.00E+00 4.78E+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 3.39E+02 0.000 Sec. E1 3 0.00 | | Min Buck 0.00E+00 3.42E+01 0.000 Eq. E7-1 3 0.00 | | Flexural | | Tor Buck 0.00E+00 1.73E+02 0.000 Eq. E7-1 3 0.00 | | Intermediate | | Results Eff Area KL/r Fcr Fe Pn | | Maj Buck 9.88E-02 56.93 5.54E+03 1.27E+04 5.65E+02 | | Min Buck 1.02E-01 254.29 5.59E+02 6.37E+02 5.71E+01 | | Flexural Ag Fcr Pn | | Tor Buck 1.02E-01 2.82E+03 2.88E+02 | |-----------------------------------------------------------------------| | CHECK FOR SHEAR | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Local-Z 0.00E+00 1.54E+02 0.000 Eq. G2-1 3 0.00 | | Local-Y 2.10E+01 1.28E+02 0.164 Eq. G2-1 3 0.00 | | Intermediate | | Results Aw Cv Kv h/tw Vn | | Local-Z 5.94E-02 1.00 1.20 6.58 2.56E+02 | | Local-Y 4.44E-02 1.00 0.00 45.23 1.92E+02 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-YIELDING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 1.84E+02 2.52E+02 0.729 Eq. F2-1 3 17.50 | | Minor 0.00E+00 4.14E+01 0.000 Eq. F6-1 3 0.00 | | Intermediate Mn My | | Major 4.21E+02 0.00E+00 | | Minor 6.92E+01 0.00E+00 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 1.84E+02 5.52E+01 3.331 Eq. F2-3 3 17.50 | | Intermediate Mn Me Cb Lp Lr Lb | | Major 9.21E+01 0.00E+00 1.00 5.83 16.97 35.00 | STAAD PLANE -- PAGE NO. 5 STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD) v3.3a ******************************************** ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted) |-----------------------------------------------------------------------| | CHECK FOR FLEXURE TENS/COMP INTERACTION | | RATIO CRITERIA L/C LOC | | Flexure Comp 3.331 Eq. H1-1b 3 17.50 | | Flexure Tens 3.331 Eq. H1-1b 3 17.50 | | Intermediate Mcx Mrx Pc | | Mcy Mry Pr | | Flexure Comp 5.52E+01 1.84E+02 3.42E+01 | | 4.14E+01 0.00E+00 0.00E+00 | | Flexure Tens 5.52E+01 1.84E+02 4.40E+02 | | 4.14E+01 0.00E+00 0.00E+00 | |-----------------------------------------------------------------------| 45. LOAD LIST 4 46. PARAMETER 2 47. CODE AISC UNIFIED 2005 48. METHOD LRFD 49. FYLD 7200 ALL 50. FU 9360 ALL 51. TRACK 2 ALL 52. CHECK CODE ALL STEEL DESIGN STAAD PLANE -- PAGE NO. 6 STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD) v3.3a ******************************************** ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted) MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION ======================================================================= * 1 ST W18X50 (AISC SECTIONS) FAIL Eq. H1-1b 3.213 4 0.00 0.00 -266.44 17.50 |-----------------------------------------------------------------------| | SLENDERNESS | | Actual Slenderness Ratio : 254.294 L/C : 4 | | Allowable Slenderness Ratio : 300.000 LOC : 17.50 | |-----------------------------------------------------------------------| | STRENGTH CHECKS | | Critical L/C : 4 Ratio : 3.213(FAIL) | | Loc : 17.50 Condition : Eq. H1-1b | |-----------------------------------------------------------------------| | DESIGN FORCES | | Fx: 0.000E+00( ) Fy: 0.000E+00 Fz: 0.000E+00 | | Mx: 0.000E+00 My: 0.000E+00 Mz: -2.664E+02 | |-----------------------------------------------------------------------| | SECTION PROPERTIES (UNIT: INCH) | | Azz: 8.550E+00 Ayy: 6.390E+00 Cw: 3.046E+03 | | Szz: 8.889E+01 Syy: 1.069E+01 | | Izz: 8.000E+02 Iyy: 4.010E+01 Ix: 1.240E+00 | |-----------------------------------------------------------------------| | MATERIAL PROPERTIES | | Fyld: 7199.999 Fu: 9359.999 | |-----------------------------------------------------------------------| | Actual Member Length: 35.000 | | 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 6.58 N/A 13.49 T.B4.1-3 | | Slender 45.23 N/A 35.88 T.B4.1-10 | | Flexure : Compact 6.58 9.15 24.08 T.B4.1-1 | | Compact 45.23 90.55 137.27 T.B4.1-9 | STAAD PLANE -- PAGE NO. 7 STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD) v3.3a ******************************************** ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted) |-----------------------------------------------------------------------| | CHECK FOR AXIAL TENSION | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Yield 0.00E+00 6.61E+02 0.000 Eq. D2-1 4 0.00 | | Rupture 0.00E+00 7.17E+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 5.09E+02 0.000 Sec. E1 4 0.00 | | Min Buck 0.00E+00 5.14E+01 0.000 Eq. E7-1 4 0.00 | | Flexural | | Tor Buck 0.00E+00 2.59E+02 0.000 Eq. E7-1 4 0.00 | | Intermediate | | Results Eff Area KL/r Fcr Fe Pn | | Maj Buck 9.88E-02 56.93 5.54E+03 1.27E+04 5.65E+02 | | Min Buck 1.02E-01 254.29 5.59E+02 6.37E+02 5.71E+01 | | Flexural Ag Fcr Pn | | Tor Buck 1.02E-01 2.82E+03 2.88E+02 | |-----------------------------------------------------------------------| | CHECK FOR SHEAR | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Local-Z 0.00E+00 2.31E+02 0.000 Eq. G2-1 4 0.00 | | Local-Y 3.05E+01 1.92E+02 0.159 Eq. G2-1 4 0.00 | | Intermediate | | Results Aw Cv Kv h/tw Vn | | Local-Z 5.94E-02 1.00 1.20 6.58 2.56E+02 | | Local-Y 4.44E-02 1.00 0.00 45.23 1.92E+02 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-YIELDING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 2.66E+02 3.79E+02 0.703 Eq. F2-1 4 17.50 | | Minor 0.00E+00 6.23E+01 0.000 Eq. F6-1 4 0.00 | | Intermediate Mn My | | Major 4.21E+02 0.00E+00 | | Minor 6.92E+01 0.00E+00 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major 2.66E+02 8.29E+01 3.213 Eq. F2-3 4 17.50 | | Intermediate Mn Me Cb Lp Lr Lb | | Major 9.21E+01 0.00E+00 1.00 5.83 16.97 35.00 | STAAD PLANE -- PAGE NO. 8 STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD) v3.3a ******************************************** ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted) |-----------------------------------------------------------------------| | CHECK FOR FLEXURE TENS/COMP INTERACTION | | RATIO CRITERIA L/C LOC | | Flexure Comp 3.213 Eq. H1-1b 4 17.50 | | Flexure Tens 3.213 Eq. H1-1b 4 17.50 | | Intermediate Mcx Mrx Pc | | Mcy Mry Pr | | Flexure Comp 8.29E+01 2.66E+02 5.14E+01 | | 6.23E+01 0.00E+00 0.00E+00 | | Flexure Tens 8.29E+01 2.66E+02 6.61E+02 | | 6.23E+01 0.00E+00 0.00E+00 | |-----------------------------------------------------------------------|