V. AISC LRFD - Wide Flange Compression Capacity 4
To determine the design bending strength of a non-compact American wide flange section bent about its strong axis.
Validation
The inelastic limiting unbraced length is given by:
(F1-6) |
= | ||
= | ||
= |
Lb > Lr, thus the section is subject to elastic lateral-torsional buckling.
(F1-3) |
Since the moment diagram is symmetric about the mid-span point of the beam, the maximum moment is the same as the mid-span moment and the quarter-point moments are equal.
The quarter-point moments of a uniformly loaded beam are likewise equal:
The terms factor out and the constants simply as follows:
The critical buckling moment is given by:
(F1-13) |
The lateral-torsional buckling limit state capacity:
ϕbMn = 0.9×(935.0) = 841.5 in·k
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Modification factor, Cb | 1.14 | 1.14 | none | |
Design flexural strength, ϕbMn (in·kips) | 841.5 | 834.4 | <1% |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\US\AISC\AISC LRFD - Wide Flange Compression Capacity 4.STD is typically installed with the program.
STAAD SPACE BENDING CAPACITY PER AISC LRFD 3RD ED
START JOB INFORMATION
ENGINEER DATE 23-Sep-18
END JOB INFORMATION
*
* EXAMPLE PROBLEM 5.2, CASE (C), PAGE 5-16, AISC LRFD 3RD ED.
* CAPACITY (MNZ) SHOULD BE ABOUT 70.2 KIP-FT
*
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 40 0 0;
*
MEMBER INCIDENCES
1 1 2;
*
MEMBER PROPERTY AMERICAN
1 TABLE ST W21X48
*
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 4.176e+06
POISSON 0.3
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
*
SUPPORTS
1 PINNED
2 FIXED BUT MZ
*
LOAD 1
MEMBER LOAD
1 CON GY -10 13.333
1 CON GY -10 26.667
*
PERFORM ANALYSIS
*
PARAMETER 1
CODE LRFD
MAIN 1 ALL
FYLD 7200 ALL
CB 0 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD.Pro Output
STAAD.PRO CODE CHECKING - (LRFD 3RD EDITION) v1.0 ******************************************** |--------------------------------------------------------------------------| | Y PROPERTIES | |************* | IN INCH UNIT | | * |=============================| ===|=== ------------ | |MEMBER 1 * | AISC SECTIONS | | AX=0.1410E+2 | | * | ST W21X48 | | --Z AY=0.7210E+1 | |DESIGN CODE * | | | AZ=0.4667E+1 | | LRFD 2001 * =============================== ===|=== PY=0.1490E+2 | | * PZ=0.1070E+3 | | * |<---LENGTH (FT)= 40.00 --->| RY=0.1657E+1 | |************* RZ=0.8247E+1 | | | | 133.3 (KIP-FEET) | |PARAMETER | L1 L1 L1 CAPACITIES | |IN KIP INCH | IN KIP INCH | |--------------- + L1 L1 -------------| | KL/R-Y= 289.73 | PNC=0.3584E+2| | KL/R-Z= 58.20 + L1 L1 pnc=0.0000E+0| | UNL = 480.00 | PNT=0.6345E+3| | CB = 1.14 + pnt=0.0000E+0| | PHIC = 0.85 | L1 L1 MNZ=0.8344E+3| | PHIB = 0.90 + mnz=0.1600E+4| | FYLD = 50.00 |L0 L0 MNY=0.6367E+3| | NSF = 1.00 +---+---+---+---+---+---+---+---+---+---| mny=0.0000E+0| | DFF = 0.00 -7.4 VN =0.1947E+3| | dff = 0.00 ABSOLUTE MZ ENVELOPE vn =0.1000E+2| | (WITH LOAD NO.) | | | | MAX FORCE/ MOMENT SUMMARY (KIP-FEET) | | ------------------------- | | | | AXIAL SHEAR-Y SHEAR-Z MOMENT-Y MOMENT-Z | | | | VALUE 0.0 10.0 0.0 0.0 133.3 | | LOCATION 0.0 0.0 0.0 0.0 13.3 | | LOADING 0 1 0 0 1 | | | |**************************************************************************| |* *| |* DESIGN SUMMARY (KIP-FEET) *| |* -------------- *| |* *| |* RESULT/ CRITICAL COND/ RATIO/ LOADING/ *| | FX MY MZ LOCATION | | ====================================================== | | FAIL LRFD-H1-1B-C 1.917 1 | | 0.00 C 0.00 -133.33 13.33 | |* *| |**************************************************************************| | | |--------------------------------------------------------------------------|