V. AISC 360-16 I Compression LRFD
Verify the flexural buckling capacity of an I section under compressive load using the LRFD method per the ASIC 360-16 code.
Details
Verify the Flexural Buckling strength of an I Section (W14x90) using the LRFD method
Steel Gr. ASTM A992, about X and Y axis with a member length of 30 ft with dead load 140 kips and Live Load 420 kips.
Validation
Strong axis unbraced length, Lx = 360 in
Torsional axis unbraced length Ly = 180 in
Ultimate load, Pu = 1.2(180 kips) + 1.6(420 kips) = 840 kips
Calculation for major axis (X axis)
From Table C-A-7.1 of ref. 1, K = 1.0 for a pinned-pinned condition.
, thus the flange is non-slender.
Slenderness ratio about X axis
Calculate the elastic critical buckling stress:
Calculate the flexural buckling stress:
Compressive strength for flexural buckling along X:
Ratio for flexural buckling strength = 0.906
Calculation for minor axis (Y axis)
h = d - 2·tf = 12.58 in
, thus the flange is non-slender.
Slenderness ratio about Y axis
Calculate the elastic critical buckling stress:
Calculate the flexural buckling stress:
Compressive strength for flexural buckling along Y:
Ratio for flexural buckling strength = 0.838
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 Compression LRFD.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 12-Jan-18
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 0 30 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 W14X90
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FY MX MZ
LOAD 1 LOADTYPE Dead TITLE LOAD CASE 1
JOINT LOAD
2 FY -140
LOAD 2 LOADTYPE Live REDUCIBLE TITLE LOAD CASE 2
JOINT LOAD
2 FY -420
LOAD COMB 3 COMBINATION LOAD CASE 3
1 1.2 2 1.6
PERFORM ANALYSIS
LOAD LIST 3
*CODE AISC UNIFIED 2016
PARAMETER 1
CODE AISC UNIFIED 2016
FU 9360 ALL
FYLD 7200 ALL
KX 1 ALL
KY 1 ALL
KZ 1 ALL
LX 30 ALL
LY 15 ALL
LZ 30 ALL
METHOD LRFD
PROFILE W14 ALL
STP 1 ALL
*SGR 28 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD 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 ------------ ----------- ------------- 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 FEET (UNLESS OTHERWISE Noted). - Member : 1 |-----------------------------------------------------------------------------| | Member No: 1 Profile: ST W14X90 (AISC SECTIONS)| | Status: FAIL Ratio: 1.004 Loadcase: 3 | | Location: 0.00 Ref: Cl.E4 | | Pz: 840.0 C Vy: 0.000 Vx: 0.000 | | Tz: 0.000 My: 0.000 Mx: 0.000 | |-----------------------------------------------------------------------------| | COMPRESSION SLENDERNESS | | Actual Slenderness Ratio : 58.633 | | Allowable Slenderness Ratio : 200.000 LOC : 0.00 | |-----------------------------------------------------------------------------| | STRENGTH CHECKS | | Critical L/C : 3 Ratio : 1.004(FAIL) | | Loc : 0.00 Condition : Cl.E4 | |-----------------------------------------------------------------------------| | SECTION PROPERTIES (LOC: 0.00, PROPERTIES UNIT: IN ) | | Ag : 2.650E+01 Axx : 2.059E+01 Ayy : 6.160E+00 | | Ixx : 9.990E+02 Iyy : 3.620E+02 J : 4.060E+00 | | Sxx+: 1.427E+02 Sxx-: 1.427E+02 Zxx : 1.570E+02 | | Syy+: 4.993E+01 Syy-: 4.993E+01 Zyy : 7.560E+01 | | Cw : 1.593E+04 x0 : 0.000E+00 y0 : 0.000E+00 | |-----------------------------------------------------------------------------| | MATERIAL PROPERTIES | | Fyld: 7200.000 Fu: 9359.999 | |-----------------------------------------------------------------------------| | Actual Member Length: 30.000 | | Design Parameters (Rolled) | | Kx: 1.00 Ky: 1.00 NSF: 1.00 SLF: 1.00 CSP: 1.00 | |-----------------------------------------------------------------------------| | COMPRESSION CLASSIFICATION (L/C: 3 LOC: 360.00) | | λ λp λr CASE | | Flange: NonSlender 10.21 N/A 13.49 Table.B4.1a.Case1 | | Web : NonSlender 25.86 N/A 35.88 Table.B4.1a.Case5 | | | | FLEXURE CLASSIFICATION (L/C: 3 LOC: 360.00) | | λ λp λr CASE | | Flange: NonCompact 10.21 9.15 24.08 Table.B4.1b.Case10 | | Web : Compact 25.86 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 FEET (UNLESS OTHERWISE Noted). - Member : 1 Contd. |-----------------------------------------------------------------------------| | CHECKS FOR AXIAL TENSION | |-----------------------------------------------------------------------------| | TENSILE YIELDING | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 1192. 0.000 Cl.D2 3 0.00 | | | | Intermediate Results : | | Nom. Ten. Yld Cap : Pn = 1325.0 kip Eq.D2-1 | |-----------------------------------------------------------------------------| | TENSILE RUPTURE | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 1292. 0.000 Cl.D2 3 0.00 | | | | Intermediate Results : | | Effective area : Ae = 0.18403 ft2 Eq.D3-1 | | Nom. Ten. Rpt Cap : Pn = 1722.5 kip Eq.D2-2 | |-----------------------------------------------------------------------------| | CHECKS FOR AXIAL COMPRESSION | |-----------------------------------------------------------------------------| | FLEXURAL BUCKLING X | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 840.0 927.5 0.906 Cl.E3 3 0.00 | | | | Intermediate Results : | | Effective Slenderness : Lcx/rx = 58.633 Cl.E2 | | Elastic Buckling Stress : Fex = 11989. kip/ft2 Eq.E3-4 | | Crit. Buckling Stress : Fcrx = 5599.7 kip/ft2 Eq.E3-2 | | Nom. Flexural Buckling : Pnx = 1030.5 kip Eq.E3-1 | |-----------------------------------------------------------------------------| | FLEXURAL BUCKLING Y | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 840.0 1003. 0.838 Cl.E3 3 0.00 | | | | Intermediate Results : | | Effective Slenderness : Lcy/ry = 48.701 Cl.E2 | | Elastic Buckling Stress : Fey = 17377. kip/ft2 Eq.E3-4 | | Crit. Buckling Stress : Fcry = 6053.6 kip/ft2 Eq.E3-2 | | Nom. Flexural Buckling : Pny = 1114.0 kip Eq.E3-1 | |-----------------------------------------------------------------------------| | FLEXURAL-TORSIONAL-BUCKLING | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 840.0 837.0 1.004 Cl.E4 3 0.00 | | | | Intermediate Results : | | Elastic F-T-B Stress : Fe = 8513.5 kip/ft2 Eq.E4-2 | | Crit. F-T-B Stress : Fcr = 5053.6 kip/ft2 Eq.E3-2 | | Nom. Flex-tor Buckling : Pn = 930.01 kip Eq.E4-1 | |-----------------------------------------------------------------------------| STAAD SPACE -- PAGE NO. 6 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 | | 0.000 555.9 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 = 617.70 kip Eq.G6-1 | |-----------------------------------------------------------------------------| | SHEAR ALONG Y | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 184.8 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 = 184.80 kip Eq.G2-1 | |-----------------------------------------------------------------------------| 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 Contd. |-----------------------------------------------------------------------------| | CHECKS FOR BENDING | |-----------------------------------------------------------------------------| | FLEXURAL YIELDING (Y) | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 283.5 0.000 Cl.F6.1 3 0.00 | | | | Intermediate Results : | | Nom Flex Yielding Along Y : Mny = 315.00 kip-ft Eq.F6-1 | |-----------------------------------------------------------------------------| | LAT TOR BUCK ABOUT X | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 465.8 0.000 Cl.F2.2 3 0.00 | | | | Intermediate Results : | | Nom L-T-B Cap : Mnx = 517.55 kip-ft Eq.F2-2 | | Mom. Distr. factor : CbX = 1.0000 Custom | | Limiting Unbraced Length : LpX = 13.055 ft Eq.F2-5 | | coefficient C : Cx = 1.0000 Eq.F2-8a | | Effective Rad. of Gyr. : Rts = 0.34183 ft Eq.F2-7 | | Limiting Unbraced Length : LrX = 42.564 ft Eq.F2-6 | |-----------------------------------------------------------------------------| | FLANGE LOCAL BUCK(X) | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 573.6 0.000 Cl.F3.1 3 0.00 | | | | Intermediate Results : | | Nom F-L-B Cap : Mnx = 637.28 kip-ft Eq.F3-1 | |-----------------------------------------------------------------------------| | FLANGE LOCAL BUCK(Y) | | DEMAND CAPACITY RATIO REFERENCE L/C LOC | | 0.000 272.7 0.000 Cl.F6.2 3 0.00 | | | | Intermediate Results : | | Nom F-L-B Cap : Mny = 302.98 kip-ft Eq.F6-2 | |-----------------------------------------------------------------------------| 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 BEND INTERACTION | |-----------------------------------------------------------------------------| | COMBINED FORCES CLAUSE H1 | | RATIO CRITERIA L/C LOC | | 1.004 Eq.H1-1a 3 0.00 | | | | Intermediate Results : | | Axial Capacity : Pc = 837.01 kip Cl.H1.1 | | Moment Capacity : Mcx = 465.79 kip-ft Cl.H1.1 | | Moment Capacity : Mcy = 272.68 kip-ft Cl.H1.1 | |-----------------------------------------------------------------------------| 55. FINISH