V. AISC 360-16 W Flexural Check LRFD
Verify the flexural yielding strength and lateral torsional buckling of an I section using the LRFD method per AISC 360-16.
Details
Verify the flexural yielding strength and lateral torsional buckling of an I section (W12X90) gr. ASTM A992 material, with a member length of 41'-8", and a concentrated moment of 35,000 in-kip applied at midspan. The member is unbraced along its length.
Validation
Flexural yielding about X axis
As the section is compact, nominal flexural yielding strength
about X axis is:
| Mnx = fy × Zxx = 65 ksi × 311 in3 = 20,215 in·kip | (F2-1, ref. 1) |
Mx = ϕc×Mnx = 0.9(20,215 in·kip) = 18,193.5 in·kip
Flexural yielding about Y axis
As this is the minor axis, nominal flexural yielding strength
about Y axis is:
| Mny = fy × Zyy = 65 ksi × 143 in3 = 9,295 in·kip | (F6-1, ref. 1) |
My = ϕc×Mny = 0.9(9,295 in·kip) = 8,365.5 in·kip
Lateral torsional buckling about X axis
limiting laterally unbraced length for the yielding limit
state:
| (F2-5, ref. 1) |
| (F2-7, ref. 1) |
For an I section, C = 1 (per F2-28a in ref. 1). The limiting
unbraced length for the inelastic lateral-torsional buckling limit state is:
h0 = d - tf = 12.66 in
Lp < Lb = 500 in < Lr
| (F1-1, ref. 1) |
Mp = fy × Zxx = 65 ksi × 311 in3 = 20,215 in·kip
Nominal LTB strength:
Mn = 20,611.4 in·kip > Mp
ϕcMnx = 0.9(20,215 in·kip) = 18,193.5 in·kip
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC 360-16 W Flexural Check LRFD.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 05-Feb-18
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 41.67 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 FY 5184 FU 8352 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TABLE ST W12X190
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT MY
UNIT INCHES KIP
LOAD 2 LOADTYPE Dead TITLE LOAD CASE 1
MEMBER LOAD
1 CMOM GZ 35000 250
UNIT FEET KIP
PERFORM ANALYSIS
PARAMETER 1
CODE AISC UNIFIED 2016
LY 41.6667 ALL
LZ 41.6667 ALL
CB 0 ALL
FU 9360 ALL
FYLD 9360 ALL
METHOD LRFD
PROFILE W12 ALL
STP 1 ALL
TRACK 2 ALL
UNIT KIP INCHES
CHECK CODE ALL
FINISH
STAAD Output
STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2) ***************************************************** ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted). ***NOTE : AISC 360-16 Design Statement for STAAD.Pro. *** AXIS CONVENTION ***: ======================== The capacity results and intermediate results in the report follow the notations and axes labels as defined in the AISC 360-16 code. The analysis results are reported in STAAD.Pro axis convention and the AISC 360:16 design results are reported in AISC 360-16 code axis convention. AISC Spec. STAAD.Pro Description ------------ ----------- ------------- X Z Axis typically parallel to the sections principal major axis. Y Y Axis typically parallel to the sections principal minor axis. Z X Longitudinal axis perpendicular to the cross section. SECTION FORCES AXIS MAPPING: - AISC Spec. STAAD.Pro Description ------------ ----------- ------------- Pz FX Axial force. Vy FY Shear force along minor axis. Vx FZ Shear force along major axis. Tz MX Torsional moment. My MY Bending moment about minor axis. Mx MZ Bending moment about major axis. *** DESIGN MESSAGES ***: ======================= 1. Section classification reported is for the cross section and loadcase that produced the worst case design ratio for flexure/compression Capacity results. 2. Results for any Capacity/Check that is not relevant for a section/loadcase based on the code clause in AISC 360-16 will not be shown in the report. 3. Bending results are reported as being �about� the relevant axis (X/Y), while the results for shear are reported as being for shear forces �along� the axis. E.g : Mx indicates bending about the X axis, while Vx indicates shear along the X axis. *** ABBREVIATIONS ***: ====================== F-T-B = Flexural-Torsional Buckling L-T-B = Lateral-Torsional Buckling F-L-B = Flange Local Buckling W-L-B = Web Local Buckling L-L-B = Leg Local Buckling C-F-Y = Compression Flange Yielding T-F-Y = Tension Flange Yielding STAAD SPACE -- PAGE NO. 4 STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2) ***************************************************** ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted). - Member : 1 |-----------------------------------------------------------------------------| | Member No: 1 Profile: ST W12X190 (AISC SECTIONS)| | Status: PASS Ratio: 0.903 Loadcase: 2 | | Location: 208.35 Ref: Cl.F2.1 | | Pz: 0.000 T Vy: 78.85 Vx: 0.000 | | Tz: 0.000 My: 0.000 Mx: -.1643E+05 | |-----------------------------------------------------------------------------| | TENSION SLENDERNESS | | Actual Slenderness Ratio : 154.185 | | Allowable Slenderness Ratio : 300.000 LOC : 0.00 | |-----------------------------------------------------------------------------| | STRENGTH CHECKS | | Critical L/C : 2 Ratio : 0.903(PASS) | | Loc : 208.35 Condition : Cl.F2.1 | |-----------------------------------------------------------------------------| | SECTION PROPERTIES (LOC: 208.35, PROPERTIES UNIT: IN ) | | Ag : 5.600E+01 Axx : 4.420E+01 Ayy : 1.526E+01 | | Ixx : 1.890E+03 Iyy : 5.890E+02 J : 4.880E+01 | | Sxx+: 2.625E+02 Sxx-: 2.625E+02 Zxx : 3.110E+02 | | Syy+: 9.276E+01 Syy-: 9.276E+01 Zyy : 1.430E+02 | | Cw : 2.380E+04 x0 : 0.000E+00 y0 : 8.882E-16 | |-----------------------------------------------------------------------------| | MATERIAL PROPERTIES | | Fyld: 65.000 Fu: 65.000 | |-----------------------------------------------------------------------------| | Actual Member Length: 500.040 | | Design Parameters (Rolled) | | Kx: 1.00 Ky: 1.00 NSF: 1.00 SLF: 1.00 CSP: 12.00 | |-----------------------------------------------------------------------------| | COMPRESSION CLASSIFICATION (L/C: 2 LOC: 500.04) | | λ λp λr CASE | | Flange: NonSlender 3.65 N/A 11.83 Table.B4.1a.Case1 | | Web : NonSlender 9.19 N/A 31.47 Table.B4.1a.Case5 | | | | FLEXURE CLASSIFICATION (L/C: 1 LOC: 500.04) | | λ λp λr CASE | | Flange: Compact 3.65 8.03 21.12 Table.B4.1b.Case10 | | Web : Compact 9.19 79.42 120.40 Table.B4.1b.Case15 | |-----------------------------------------------------------------------------| STAAD SPACE -- PAGE NO. 5 STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2) ***************************************************** ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted). - Member : 1 Contd. |-----------------------------------------------------------------------------| | CHECKS FOR AXIAL TENSION | |-----------------------------------------------------------------------------| | TENSILE YIELDING | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 3276. 0.000 Cl.D2 2 0.00 | | | | Intermediate Results : | | Nom. Ten. Yld Cap : Pn = 3640.0 kip Eq.D2-1 | |-----------------------------------------------------------------------------| | TENSILE RUPTURE | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 2730. 0.000 Cl.D2 2 0.00 | | | | Intermediate Results : | | Effective area : Ae = 56.000 in2 Eq.D3-1 | | Nom. Ten. Rpt Cap : Pn = 3640.0 kip Eq.D2-2 | |-----------------------------------------------------------------------------| | CHECKS FOR AXIAL COMPRESSION | |-----------------------------------------------------------------------------| | FLEXURAL BUCKLING X | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 1620. 0.000 Cl.E3 2 0.00 | | | | Intermediate Results : | | Effective Slenderness : Lcx/rx = 86.066 Cl.E2 | | Elastic Buckling Stress : Fex = 38.639 ksi Eq.E3-4 | | Crit. Buckling Stress : Fcrx = 32.146 ksi Eq.E3-2 | | Nom. Flexural Buckling : Pnx = 1800.2 kip Eq.E3-1 | |-----------------------------------------------------------------------------| | FLEXURAL BUCKLING Y | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 532.2 0.000 Cl.E3 2 0.00 | | | | Intermediate Results : | | Effective Slenderness : Lcy/ry = 154.17 Cl.E2 | | Elastic Buckling Stress : Fey = 12.042 ksi Eq.E3-4 | | Crit. Buckling Stress : Fcry = 10.560 ksi Eq.E3-3 | | Nom. Flexural Buckling : Pny = 591.39 kip Eq.E3-1 | |-----------------------------------------------------------------------------| | FLEXURAL-TORSIONAL-BUCKLING | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 2911. 0.000 Cl.E4 2 0.00 | | | | Intermediate Results : | | Elastic F-T-B Stress : Fe = 230.56 ksi Eq.E4-2 | | Crit. F-T-B Stress : Fcr = 57.765 ksi Eq.E3-2 | | Nom. Flex-tor Buckling : Pn = 3234.9 kip Eq.E4-1 | |-----------------------------------------------------------------------------| STAAD SPACE -- PAGE NO. 6 STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2) ***************************************************** ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted). - Member : 1 Contd. |-----------------------------------------------------------------------------| | CHECKS FOR SHEAR | |-----------------------------------------------------------------------------| | SHEAR ALONG X | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 1551. 0.000 Cl.G1 2 0.00 | | | | Intermediate Results : | | Coefficient Cv Along X : Cv = 1.0000 Eq.G2-9 | | Coefficient Kv Along X : Kv = 1.2000 Cl.G6 | | Nom. Shear Along X : Vnx = 1723.6 kip Eq.G6-1 | |-----------------------------------------------------------------------------| | SHEAR ALONG Y | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 78.85 595.3 0.132 Cl.G1 2 0.00 | | | | Intermediate Results : | | Coefficient Cv Along Y : Cv = 1.0000 - | | Coefficient Kv Along Y : Kv = 5.3400 Eq.G2-5 | | Nom. Shear Along Y : Vny = 595.30 kip Eq.G2-1 | |-----------------------------------------------------------------------------| STAAD SPACE -- PAGE NO. 7 STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2) ***************************************************** ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted). - Member : 1 Contd. |-----------------------------------------------------------------------------| | CHECKS FOR BENDING | |-----------------------------------------------------------------------------| | FLEXURAL YIELDING (X) | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | -.1643E+05 0.1819E+05 0.903 Cl.F2.1 2 208.35 | | | | Intermediate Results : | | Nom Flex Yielding Along X : Mnx = 20215. kip-in Eq.F2-1 | |-----------------------------------------------------------------------------| | FLEXURAL YIELDING (Y) | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 8366. 0.000 Cl.F6.1 2 0.00 | | | | Intermediate Results : | | Nom Flex Yielding Along Y : Mny = 9295.0 kip-in Eq.F6-1 | |-----------------------------------------------------------------------------| | LAT TOR BUCK ABOUT X | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | -.1643E+05 0.1819E+05 0.903 Cl.F2.2 2 208.35 | | | | Intermediate Results : | | Nom L-T-B Cap : Mnx = 20215. kip-in Eq.F2-2 | | Mom. Distr. factor : CbX = 1.3868 Eq.F1-1 | | Limiting Unbraced Length : LpX = 120.56 in Eq.F2-5 | | coefficient C : Cx = 1.0000 Eq.F2-8a | | Effective Rad. of Gyr. : Rts = 3.7768 in Eq.F2-7 | | Limiting Unbraced Length : LrX = 812.00 in Eq.F2-6 | |-----------------------------------------------------------------------------| STAAD SPACE -- PAGE NO. 8 STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2) ***************************************************** ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted). - Member : 1 Contd. |-----------------------------------------------------------------------------| | CHECKS FOR AXIAL BEND INTERACTION | |-----------------------------------------------------------------------------| | COMBINED FORCES CLAUSE H1 | | RATIO CRITERIA L/C LOC | | 0.903 Eq.H1-1b 2 208.35 | | | | Intermediate Results : | | Modification Fact. for Cb : Cbf = 1.0000 Eq.H1-2 | | Axial Capacity : Pc = 2730.0 kip Cl.H1.1 | | Moment Capacity : Mcx = 18194. kip-in Cl.H1.1 | | Moment Capacity : Mcy = 8365.5 kip-in Cl.H1.1 | |-----------------------------------------------------------------------------|