V. AISC 360-16 I Tension LRFD
To verify the tensile yield strength of an I section using the LRFD method from the AISC 360-16 code.
Details
Verify the tensile yield and tensile rupture strength of an I section (W8X21) using the LRFD method. The material is A992 (Fy = 50 ksi, Fu = 65 ksi)
The area of the bolt holes is assumed to be zero. A known shear lag factor of 0.908 is directly specified.
The length of the member is 25 ft. It is loaded axial in tension with a dead load of 30 kips and a live load of 90 kips.
Validation
The factored axial load, Pu = 1.2×30 + 1.6×90 = 180 kips
Tensile Yield Strength
The tensile yield strength: ϕtYPnY = ϕtY×Fy×Ag = 0.9×50×6.16 = 277.2 kips
Ratio for yield strength: 0.649
Tensile Rupture Strength
For this example, An is assumed equal to Ag .
Effective area, Ae = An×U = 6.16×0.908 = 5.593 in2
The tensile rupture strength = ϕtRPnR = ϕtR×Fu×Ae = 0.75×65×5.593 = 272.672 kips
Ratio for rupture strength: 0.660
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC 360-16 I Tension LRFD.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 25 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 7200 FU 9360 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TABLE ST W8X21
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
LOAD 1 LOADTYPE Dead TITLE LOAD CASE 1
JOINT LOAD
2 FX 30
LOAD 2 LOADTYPE Live TITLE LOAD CASE 2
JOINT LOAD
2 FX 90
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 2016
FU 9360 ALL
FYLD 7200 ALL
KX 1 ALL
KY 1 ALL
KZ 1 ALL
METHOD LRFD
PROFILE W8X ALL
*SGR 28 ALL
SLF 0.908 ALL
STP 1 ALL
TRACK 2 ALL
UNIT KIP INCH
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 W8X21 (AISC SECTIONS)| | Status: PASS Ratio: 0.660 Loadcase: 3 | | Location: 0.00 Ref: Cl.D2 | | Pz: 180.0 T Vy: 0.000 Vx: 0.000 | | Tz: 0.000 My: 0.000 Mx: 0.000 | |-----------------------------------------------------------------------------| | TENSION SLENDERNESS | | Actual Slenderness Ratio : 238.212 | | Allowable Slenderness Ratio : 300.000 LOC : 0.00 | |-----------------------------------------------------------------------------| | STRENGTH CHECKS | | Critical L/C : 3 Ratio : 0.660(PASS) | | Loc : 0.00 Condition : Cl.D2 | |-----------------------------------------------------------------------------| | SECTION PROPERTIES (LOC: 0.00, PROPERTIES UNIT: IN ) | | Ag : 6.160E+00 Axx : 4.216E+00 Ayy : 2.070E+00 | | Ixx : 7.530E+01 Iyy : 9.770E+00 J : 2.820E-01 | | Sxx+: 1.819E+01 Sxx-: 1.819E+01 Zxx : 2.040E+01 | | Syy+: 3.708E+00 Syy-: 3.708E+00 Zyy : 5.690E+00 | | Cw : 1.515E+02 x0 : 0.000E+00 y0 : 0.000E+00 | |-----------------------------------------------------------------------------| | MATERIAL PROPERTIES | | Fyld: 50.000 Fu: 65.000 | |-----------------------------------------------------------------------------| | Actual Member Length: 300.000 | | Design Parameters (Rolled) | | Kx: 1.00 Ky: 1.00 NSF: 1.00 SLF: 0.91 CSP: 12.00 | |-----------------------------------------------------------------------------| | COMPRESSION CLASSIFICATION (L/C: 3 LOC: 300.00) | | λ λp λr CASE | | Flange: NonSlender 6.59 N/A 13.49 Table.B4.1a.Case1 | | Web : NonSlender 27.52 N/A 35.88 Table.B4.1a.Case5 | | | | FLEXURE CLASSIFICATION (L/C: 3 LOC: 300.00) | | λ λp λr CASE | | Flange: Compact 6.59 9.15 24.08 Table.B4.1b.Case10 | | Web : Compact 27.52 90.55 137.27 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 | | 180.0 277.2 0.649 Cl.D2 3 0.00 | | | | Intermediate Results : | | Nom. Ten. Yld Cap : Pn = 308.00 kip Eq.D2-1 | |-----------------------------------------------------------------------------| | TENSILE RUPTURE | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 180.0 272.7 0.660 Cl.D2 3 0.00 | | | | Intermediate Results : | | Effective area : Ae = 5.5933 in2 Eq.D3-1 | | Nom. Ten. Rpt Cap : Pn = 363.56 kip Eq.D2-2 | |-----------------------------------------------------------------------------| | CHECKS FOR AXIAL COMPRESSION | |-----------------------------------------------------------------------------| | FLEXURAL BUCKLING X | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 161.8 0.000 Cl.E3 3 0.00 | | | | Intermediate Results : | | Effective Slenderness : Lcx/rx = 85.805 Cl.E2 | | Elastic Buckling Stress : Fex = 38.875 ksi Eq.E3-4 | | Crit. Buckling Stress : Fcrx = 29.186 ksi Eq.E3-2 | | Nom. Flexural Buckling : Pnx = 179.79 kip Eq.E3-1 | |-----------------------------------------------------------------------------| | FLEXURAL BUCKLING Y | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 24.52 0.000 Cl.E3 3 0.00 | | | | Intermediate Results : | | Effective Slenderness : Lcy/ry = 238.21 Cl.E2 | | Elastic Buckling Stress : Fey = 5.0439 ksi Eq.E3-4 | | Crit. Buckling Stress : Fcry = 4.4235 ksi Eq.E3-3 | | Nom. Flexural Buckling : Pny = 27.249 kip Eq.E3-1 | |-----------------------------------------------------------------------------| | FLEXURAL-TORSIONAL-BUCKLING | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 169.7 0.000 Cl.E4 3 0.00 | | | | Intermediate Results : | | Elastic F-T-B Stress : Fe = 42.637 ksi Eq.E4-2 | | Crit. F-T-B Stress : Fcr = 30.606 ksi Eq.E3-2 | | Nom. Flex-tor Buckling : Pn = 188.53 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 | | 0.000 113.8 0.000 Cl.G1 3 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 = 126.48 kip Eq.G6-1 | |-----------------------------------------------------------------------------| | SHEAR ALONG Y | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 62.10 0.000 Cl.G1 3 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 = 62.100 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 | | 0.000 918.0 0.000 Cl.F2.1 3 0.00 | | | | Intermediate Results : | | Nom Flex Yielding Along X : Mnx = 1020.0 kip-in Eq.F2-1 | |-----------------------------------------------------------------------------| | FLEXURAL YIELDING (Y) | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 256.1 0.000 Cl.F6.1 3 0.00 | | | | Intermediate Results : | | Nom Flex Yielding Along Y : Mny = 284.50 kip-in Eq.F6-1 | |-----------------------------------------------------------------------------| | LAT TOR BUCK ABOUT X | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 302.2 0.000 Cl.F2.2 3 0.00 | | | | Intermediate Results : | | Nom L-T-B Cap : Mnx = 335.72 kip-in Eq.F2-3 | | Mom. Distr. factor : CbX = 1.0000 Custom | | Limiting Unbraced Length : LpX = 53.381 in Eq.F2-5 | | coefficient C : Cx = 1.0000 Eq.F2-8a | | Effective Rad. of Gyr. : Rts = 1.4543 in Eq.F2-7 | | Limiting Unbraced Length : LrX = 176.96 in Eq.F2-6 | | Crit. Elas. L-T-B Stress : FcrX = 18.458 ksi Eq.F2-4 | |-----------------------------------------------------------------------------| 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 | | 0.660 Eq.H1-1a 3 0.00 | | | | Intermediate Results : | | Modification Fact. for Cb : Cbf = 2.6064 Eq.H1-2 | | Axial Capacity : Pc = 272.67 kip Cl.H1.1 | | Moment Capacity : Mcx = 787.52 kip-in Cl.H1.1 | | Moment Capacity : Mcy = 256.05 kip-in Cl.H1.1 | |-----------------------------------------------------------------------------| 53. FINISH