V. AISC 360-16 - Torsion
Verify the torsional strength of an angle section using the LRFD method in the AISC 360-16 code. Use the simple method for calculating torsional shears (i.e., no full twist analysis). Perform torsion checks per AISC Design Guide 9.
Details
The angle section is an L 3x3x1/2 angle of ASTM A992 material. The member is a 2 ft long cantilever with a total end torque of 3.0 in·kips.
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC 360-16 - Torsion.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 23-Feb-18
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 2 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 L30308
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 CMOM GX -0.25 2
PERFORM ANALYSIS
PARAMETER 1
CODE AISC UNIFIED 2016
ALH 1 ALL
FU 7200 ALL
FYLD 7200 ALL
METHOD LRFD
SOE 0 ALL
TND 9 ALL
TORSION 1 ALL
TRACK 2 ALL
UNIT KIP INCH
CHECK CODE ALL
FINISH
STAAD Output
PARAMETER 1 STAAD SPACE -- PAGE NO. 3 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 ------------ ----------- ------------- 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. 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 L30308 (AISC SECTIONS)| | Status: PASS Ratio: 0.242 Loadcase: 1 | | Location: 0.00 Ref: DG9:Eq: 4.13 | | Pz: 0.000 T Vy: 0.000 Vx: 0.000 | | Tz: 3.000 My: 0.000 Mx: 0.000 | |-----------------------------------------------------------------------------| | TENSION SLENDERNESS | | Actual Slenderness Ratio : 41.379 | | Allowable Slenderness Ratio : 300.000 LOC : 0.00 | |-----------------------------------------------------------------------------| | STRENGTH CHECKS | | Critical L/C : 1 Ratio : 0.242(PASS) | | Loc : 0.00 Condition : DG9:Eq: 4.13 | |-----------------------------------------------------------------------------| | SECTION PROPERTIES (LOC: 0.00, PROPERTIES UNIT: IN ) | | Ag : 2.760E+00 Axx : 1.500E+00 Ayy : 1.500E+00 | | Ixx : 2.216E+00 Iyy : 2.216E+00 J : 2.300E-01 | | Sxx+: 7.071E-01 Sxx-: 1.149E+00 Zxx : 1.273E+00 | | Syy+: 1.652E+00 Syy-: 1.652E+00 Zyy : 2.974E+00 | | Cw : 1.444E-01 x0 : 6.784E-01 y0 : 6.784E-01 | |-----------------------------------------------------------------------------| | MATERIAL PROPERTIES | | Fyld: 50.000 Fu: 50.000 | |-----------------------------------------------------------------------------| | Actual Member Length: 24.000 | | Design Parameters (Rolled) | | Kx: 1.00 Ky: 1.00 NSF: 1.00 SLF: 1.00 CSP: 12.00 | |-----------------------------------------------------------------------------| | COMPRESSION CLASSIFICATION (L/C: 1 LOC: 24.00) | | λ λp λr CASE | | Flange: NonSlender 6.00 N/A 10.84 Table.B4.1a.Case3 | | Web : NonSlender 6.00 N/A 10.84 Table.B4.1a.Case3 | | | | FLEXURE CLASSIFICATION (L/C: 1 LOC: 24.00) | | λ λp λr CASE | | Flange: Compact 6.00 13.00 21.92 Table.B4.1b.Case12 | | Web : Compact 6.00 13.00 21.92 Table.B4.1b.Case12 | |-----------------------------------------------------------------------------| 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 | | 0.000 124.2 0.000 Cl.D2 1 0.00 | | | | Intermediate Results : | | Nom. Ten. Yld Cap : Pn = 138.00 kip Eq.D2-1 | |-----------------------------------------------------------------------------| | TENSILE RUPTURE | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 103.5 0.000 Cl.D2 1 0.00 | | | | Intermediate Results : | | Effective area : Ae = 2.7600 in2 Eq.D3-1 | | Nom. Ten. Rpt Cap : Pn = 138.00 kip Eq.D2-2 | |-----------------------------------------------------------------------------| | CHECKS FOR AXIAL COMPRESSION | |-----------------------------------------------------------------------------| | FLEXURAL BUCKLING X | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 117.9 0.000 Cl.E3 1 0.00 | | | | Intermediate Results : | | Effective Slenderness : Lcx/rx = 26.782 Cl.E2 | | Elastic Buckling Stress : Fex = 399.04 ksi Eq.E3-4 | | Crit. Buckling Stress : Fcrx = 47.445 ksi Eq.E3-2 | | Nom. Flexural Buckling : Pnx = 130.95 kip Eq.E3-1 | |-----------------------------------------------------------------------------| | FLEXURAL BUCKLING Y | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 117.9 0.000 Cl.E3 1 0.00 | | | | Intermediate Results : | | Effective Slenderness : Lcy/ry = 26.782 Cl.E2 | | Elastic Buckling Stress : Fey = 399.04 ksi Eq.E3-4 | | Crit. Buckling Stress : Fcry = 47.445 ksi Eq.E3-2 | | Nom. Flexural Buckling : Pny = 130.95 kip Eq.E3-1 | |-----------------------------------------------------------------------------| | FLEXURAL BUCKLING U | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 120.1 0.000 Cl.E3 1 0.00 | | | | Intermediate Results : | | Effective Slenderness : Lcu/ru = 21.299 Cl.E2 | | Elastic Buckling Stress : Feu = 630.92 ksi Eq.E3-4 | | Crit. Buckling Stress : Fcru = 48.369 ksi Eq.E3-2 | | Nom. Flexural Buckling : Pnu = 133.50 kip Eq.E3-1 | |-----------------------------------------------------------------------------| | FLEXURAL BUCKLING V | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 109.6 0.000 Cl.E3 1 0.00 | | | | Intermediate Results : | | Effective Slenderness : Lcv/rv = 41.379 Cl.E2 | | Elastic Buckling Stress : Fev = 167.16 ksi Eq.E3-4 | | Crit. Buckling Stress : Fcrv = 44.116 ksi Eq.E3-2 | | Nom. Flexural Buckling : Pnv = 121.76 kip Eq.E3-1 | |-----------------------------------------------------------------------------| 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 40.50 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 = 45.000 kip Eq.G6-1 | |-----------------------------------------------------------------------------| | SHEAR ALONG Y | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 40.50 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 = 45.000 kip Eq.G3-1 | |-----------------------------------------------------------------------------| 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 72.22 0.000 Cl.F10.1 1 0.00 | | | | Intermediate Results : | | Nom Flex Yielding Along X : Mnx = 80.244 kip-in Eq.F10-1 | |-----------------------------------------------------------------------------| | FLEXURAL YIELDING (Y) | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 72.22 0.000 Cl.F10.1 1 0.00 | | | | Intermediate Results : | | Nom Flex Yielding Along Y : Mny = 80.244 kip-in Eq.F10-1 | |-----------------------------------------------------------------------------| | FLEXURAL YIELDING (U) | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 111.5 0.000 Cl.F10.1 1 0.00 | | | | Intermediate Results : | | Nom Flex Yielding Along U : Mnu = 123.90 kip-in Eq.F10-1 | |-----------------------------------------------------------------------------| | FLEXURAL YIELDING (V) | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 47.73 0.000 Cl.F10.1 1 0.00 | | | | Intermediate Results : | | Nom Flex Yielding Along V : Mnv = 53.034 kip-in Eq.F10-1 | |-----------------------------------------------------------------------------| | LAT TOR BUCK ABOUT X | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 57.78 0.000 Cl.F10.2 1 0.00 | | | | Intermediate Results : | | Nom L-T-B Cap : Mnx = 64.196 kip-in Eq.F10-2 | | Mom. Distr. factor : CbX = 1.0000 Custom | | Crit. Elastic L-T-B Mom. : McrX = 3076.5 kip-in Eq.F10-5b | |-----------------------------------------------------------------------------| | LAT TOR BUCK ABOUT Y | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 57.78 0.000 Cl.F10.2 1 0.00 | | | | Intermediate Results : | | Nom Flex Yielding About Y : Mny = 64.196 kip-in Eq.F10-2 | | Mod. factor Cb : CbY = 1.0000 Custom | | Crit. Elas. L-T-B Moment : McrY = 3076.5 kip-in Eq.F10-5b | |-----------------------------------------------------------------------------| | LAT TOR BUCK ABOUT U | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 111.5 0.000 Cl.F10.2 1 0.00 | | | | Intermediate Results : | | Nom Flex Yielding About U : Mnu = 123.90 kip-in Eq.F10-2 | | modification factor Cb : CbU = 1.0000 Custom | | Crit. Elast. L-T-B Moment : McrU = 1088.0 kip-in Eq.F10-4 | |-----------------------------------------------------------------------------| 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 TORSION | |-----------------------------------------------------------------------------| | TORSION - NORMAL STRESS RATIO | | RATIO CRITERIA L/C LOC | | 0.000 DG9:Eq: 4.12 1 0.00 | | | | Intermediate Results : | | Torque : Tq = 3.0000 kip-in DG9:Eq: 3.1 | | Mod. Factor : Phi = 1.0000 DG9:Eq: 4.22 | |-----------------------------------------------------------------------------| | TORSION - SHEAR STRESS RATIO | | RATIO CRITERIA L/C LOC | | 0.242 DG9:Eq: 4.13 1 0.00 | |-----------------------------------------------------------------------------| | TORSION - COMB. BUCK. RATIO | | RATIO CRITERIA L/C LOC | | 0.000 DG9:Eq: 4.16(b) 1 0.00 | |-----------------------------------------------------------------------------|