V.AISC 360-16 L Tension LRFD
Verify the tensile yield and tensile rupture strength of an angle section with LRFD method for AISC 360-16 code.
Details
The member is an L4x4x1/2 section. Steel grade is ASTM A36. The member is axially loaded with dead load of 20 kips and a live load of 60 kips. The member is connected using bolts in 3/4"⌀ holes. The shear lag factor, U, is calculated as 0.869.
Validation
Ultimate load: Pu = 1.2×DL + 1.6×LL = 120 kips
Tensile Yielding
Nominal tensile yield strength:
| PnY = FyAg = 36×3.75 = 135 kip | [Eqn. D2-1] |
| ϕtYPnY = 0.9×135 = 121.5 kip |
Ratio for tensile yield = 120 / 121.5 = 0.988
Tensile Rupture
Bolt hole area = π(0.75/2)2 = 0.44 in2
Net area, An = Ag - Abolthole = 3.75 - 0.44 = 3.31 in2
Effective net area based on D3: Ae = An×U = 2.875 in2
Nominal tensile rupture strength:
| PnR = FuAe = 58×2.875 = 166.7 kip | [Eqn. D2-2] |
| ϕtRPnR = 0.75×166.7 = 125.1 kip |
Ratio for tensile yield = 80 / 83.4 = 0.960
Results
| Result Type | Reference | STAAD.Pro | Difference | Comments |
|---|---|---|---|---|
| Tensile yield strength, ϕtYPnY (kip) | 121.5 | 121.5 | none | |
| Ratio | 0.988 | 0.988 | none | |
| Tensile rupture strength, ϕtRPnR (kip) | 125.1 | 125.2 | negligible | |
| Ratio | 0.960 | 0.959 | negligible |
STAAD.Pro Input File
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC 360-16 L Tension LRFD.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 15-May-18
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 19.4 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 L40408
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 CON GX 20
LOAD 2 LOADTYPE None TITLE LOAD CASE 2
MEMBER LOAD
1 CON GX 60
LOAD COMB 3 COMBINATION LOAD CASE 3
1 1.2 2 1.6
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
PARAMETER 1
CODE AISC UNIFIED 2016
FU 8352 ALL
FYLD 5184 ALL
METHOD LRFD
SLF 0.869 ALL
STP 1 ALL
NSF 0.883 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD.Pro Output
STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2) ***************************************************** ALL UNITS ARE - KIP FEET (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 ------------ ----------- ------------- U Z Axis typically parallel to the sections principal major axis. V 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. 7 STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2) ***************************************************** ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted). - Member : 1 |-----------------------------------------------------------------------------| | Member No: 1 Profile: ST L40408 (AISC SECTIONS)| | Status: PASS Ratio: 0.988 Loadcase: 3 | | Location: 0.00 Ref: Eq.H2-1 | | Pz: 120.0 T Vy: 0.000 Vx: 0.000 | | Tz: 0.000 My: 0.000 Mx: 0.000 | |-----------------------------------------------------------------------------| | TENSION SLENDERNESS | | Actual Slenderness Ratio : 300.000 | | Allowable Slenderness Ratio : 300.000 LOC : 0.00 | |-----------------------------------------------------------------------------| | STRENGTH CHECKS | | Critical L/C : 3 Ratio : 0.988(PASS) | | Loc : 0.00 Condition : Eq.H2-1 | |-----------------------------------------------------------------------------| | SECTION PROPERTIES (LOC: 0.00, PROPERTIES UNIT: IN ) | | Ag : 3.750E+00 Axx : 2.000E+00 Ayy : 2.000E+00 | | Ixx : 5.561E+00 Iyy : 5.561E+00 J : 3.125E-01 | | Sxx+: 1.349E+00 Sxx-: 1.955E+00 Zxx : 2.429E+00 | | Syy+: 3.134E+00 Syy-: 3.134E+00 Zyy : 5.641E+00 | | Cw : 3.662E-01 x0 : 9.333E-01 y0 : 9.333E-01 | |-----------------------------------------------------------------------------| | MATERIAL PROPERTIES | | Fyld: 5184.000 Fu: 8351.999 | |-----------------------------------------------------------------------------| | Actual Member Length: 19.400 | | Design Parameters (Rolled) | | Kx: 1.00 Ky: 1.00 NSF: 0.88 SLF: 0.87 CSP: 1.00 | |-----------------------------------------------------------------------------| | COMPRESSION CLASSIFICATION (L/C: 1 LOC: 232.80) | | λ λp λr CASE | | Flange: NonSlender 8.00 N/A 12.77 Table.B4.1a.Case3 | | Web : NonSlender 8.00 N/A 12.77 Table.B4.1a.Case3 | | | | FLEXURE CLASSIFICATION (L/C: 1 LOC: 232.80) | | λ λp λr CASE | | Flange: Compact 8.00 15.33 25.83 Table.B4.1b.Case12 | | Web : Compact 8.00 15.33 25.83 Table.B4.1b.Case12 | |-----------------------------------------------------------------------------| STAAD SPACE -- PAGE NO. 8 STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2) ***************************************************** ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted). - Member : 1 Contd. |-----------------------------------------------------------------------------| | CHECKS FOR AXIAL TENSION | |-----------------------------------------------------------------------------| | TENSILE YIELDING | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 120.0 121.5 0.988 Cl.D2 3 0.00 | | | | Intermediate Results : | | Nom. Ten. Yld Cap : Pn = 135.00 kip Eq.D2-1 | |-----------------------------------------------------------------------------| | TENSILE RUPTURE | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 120.0 125.2 0.959 Cl.D2 3 0.00 | | | | Intermediate Results : | | Effective area : Ae = 0.19982E-01 ft2 Eq.D3-1 | | Nom. Ten. Rpt Cap : Pn = 166.89 kip Eq.D2-2 | |-----------------------------------------------------------------------------| | CHECKS FOR AXIAL COMPRESSION | |-----------------------------------------------------------------------------| | FLEXURAL BUCKLING X | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 23.18 0.000 Cl.E3 1 0.00 | | | | Intermediate Results : | | Effective Slenderness : Lcx/rx = 191.16 Cl.E2 | | Elastic Buckling Stress : Fex = 1127.9 kip/ft2 Eq.E3-4 | | Crit. Buckling Stress : Fcrx = 989.13 kip/ft2 Eq.E3-3 | | Nom. Flexural Buckling : Pnx = 25.758 kip Eq.E3-1 | |-----------------------------------------------------------------------------| | FLEXURAL BUCKLING Y | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 23.18 0.000 Cl.E3 1 0.00 | | | | Intermediate Results : | | Effective Slenderness : Lcy/ry = 191.16 Cl.E2 | | Elastic Buckling Stress : Fey = 1127.9 kip/ft2 Eq.E3-4 | | Crit. Buckling Stress : Fcry = 989.13 kip/ft2 Eq.E3-3 | | Nom. Flexural Buckling : Pny = 25.758 kip Eq.E3-1 | |-----------------------------------------------------------------------------| | FLEXURAL BUCKLING U | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 36.95 0.000 Cl.E3 1 0.00 | | | | Intermediate Results : | | Effective Slenderness : Lcu/ru = 151.41 Cl.E2 | | Elastic Buckling Stress : Feu = 1797.8 kip/ft2 Eq.E3-4 | | Crit. Buckling Stress : Fcru = 1576.6 kip/ft2 Eq.E3-3 | | Nom. Flexural Buckling : Pnu = 41.058 kip Eq.E3-1 | |-----------------------------------------------------------------------------| | FLEXURAL BUCKLING V | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 9.413 0.000 Cl.E3 1 0.00 | | | | Intermediate Results : | | Effective Slenderness : Lcv/rv = 300.00 Cl.E2 | | Elastic Buckling Stress : Fev = 457.95 kip/ft2 Eq.E3-4 | | Crit. Buckling Stress : Fcrv = 401.62 kip/ft2 Eq.E3-3 | | Nom. Flexural Buckling : Pnv = 10.459 kip Eq.E3-1 | |-----------------------------------------------------------------------------| STAAD SPACE -- PAGE NO. 9 STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2) ***************************************************** ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted). - Member : 1 Contd. |-----------------------------------------------------------------------------| | CHECKS FOR SHEAR | |-----------------------------------------------------------------------------| | SHEAR ALONG X | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 38.88 0.000 Cl.G1 1 0.00 | | | | Intermediate Results : | | Coefficient Cv Along X : Cv = 1.0000 Eq.G2-9 | | Coefficient Kv Along X : Kv = 1.2000 Cl.G3 | | Nom. Shear Along X : Vnx = 43.200 kip Eq.G6-1 | |-----------------------------------------------------------------------------| | SHEAR ALONG Y | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 38.88 0.000 Cl.G1 1 0.00 | | | | Intermediate Results : | | Coefficient Cv Along Y : Cv = 1.0000 Eq.G2-9 | | Coefficient Kv Along Y : Kv = 1.2000 Cl.G3 | | Nom. Shear Along Y : Vny = 43.200 kip Eq.G3-1 | |-----------------------------------------------------------------------------| STAAD SPACE -- PAGE NO. 10 STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2) ***************************************************** ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted). - Member : 1 Contd. |-----------------------------------------------------------------------------| | CHECKS FOR BENDING | |-----------------------------------------------------------------------------| | FLEXURAL YIELDING (X) | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 7.997 0.000 Cl.F10.1 1 0.00 | | | | Intermediate Results : | | Nom Flex Yielding Along X : Mnx = 8.8852 kip-ft Eq.F10-1 | |-----------------------------------------------------------------------------| | FLEXURAL YIELDING (Y) | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 7.997 0.000 Cl.F10.1 1 0.00 | | | | Intermediate Results : | | Nom Flex Yielding Along Y : Mny = 8.8852 kip-ft Eq.F10-1 | |-----------------------------------------------------------------------------| | FLEXURAL YIELDING (U) | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 12.69 0.000 Cl.F10.1 1 0.00 | | | | Intermediate Results : | | Nom Flex Yielding Along U : Mnu = 14.104 kip-ft Eq.F10-1 | |-----------------------------------------------------------------------------| | FLEXURAL YIELDING (V) | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 5.465 0.000 Cl.F10.1 1 0.00 | | | | Intermediate Results : | | Nom Flex Yielding Along V : Mnv = 6.0722 kip-ft Eq.F10-1 | |-----------------------------------------------------------------------------| | LAT TOR BUCK ABOUT X | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 6.064 0.000 Cl.F10.2 1 0.00 | | | | Intermediate Results : | | Nom L-T-B Cap : Mnx = 6.7380 kip-ft Eq.F10-2 | | Mom. Distr. factor : CbX = 1.0000 Custom | | Crit. Elastic L-T-B Mom. : McrX = 26.144 kip-ft Eq.F10-5b | |-----------------------------------------------------------------------------| | LAT TOR BUCK ABOUT Y | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 6.064 0.000 Cl.F10.2 1 0.00 | | | | Intermediate Results : | | Nom Flex Yielding About Y : Mny = 6.7380 kip-ft Eq.F10-2 | | Mod. factor Cb : CbY = 1.0000 Custom | | Crit. Elas. L-T-B Moment : McrY = 26.144 kip-ft Eq.F10-5b | |-----------------------------------------------------------------------------| | LAT TOR BUCK ABOUT U | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 8.883 0.000 Cl.F10.2 1 0.00 | | | | Intermediate Results : | | Nom Flex Yielding About U : Mnu = 9.8695 kip-ft Eq.F10-2 | | modification factor Cb : CbU = 1.0000 Custom | | Crit. Elast. L-T-B Moment : McrU = 16.992 kip-ft Eq.F10-4 | |-----------------------------------------------------------------------------| STAAD SPACE -- PAGE NO. 11 STAAD.PRO CODE CHECKING - AISC 360-16 LRFD (V1.2) ***************************************************** ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted). - Member : 1 Contd. |-----------------------------------------------------------------------------| | CHECKS FOR AXIAL BEND INTERACTION | |-----------------------------------------------------------------------------| | COMBINED FORCES CLAUSE H2 | | RATIO CRITERIA L/C LOC | | 0.988 Eq.H2-1 3 0.00 | | | | Intermediate Results : | | Applied Stress : fra = 4608.0 kip/ft2 Eq.H2-1 | | Allowable Stress : Fca = 4665.6 kip/ft2 Eq.H2-1 | | Allowable Stress : Fcbz = 4897.4 kip/ft2 Eq.H2-1 | | Allowable Stress : Fcbw = 4829.9 kip/ft2 Eq.H2-1 | |-----------------------------------------------------------------------------| 47. FINISH *********** END OF THE STAAD.Pro RUN ***********