V. AISC LRFD - Wide Flange Flexural Strength 3
To determine the design flexural strength of an ASTM A992 W18X40 bent about its strong axis on a 35-ft span with a uniformly distributed load.
Reference
Hand calculation using the following reference:
AISC Load Factor Resistance Design, 3rd Edition, Example 5.1, Case (c), page 5-12.
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×(675.6) = 608.1 in·k
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Modification factor, Cb | 1.14 | 1.14 | none | |
Design flexural strength, ϕbMn (in·kips) | 608.1 |
607.2 |
negligible |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\US\AISC\AISC LRFD - Wide Flange Flexural Strength 3.STD is typically installed with the program.
The input parameter CB 0 directs the program to calculate the value of the modification factor.
STAAD SPACE BENDING CAPACITY PER AISC LRFD 3RD ED
START JOB INFORMATION
ENGINEER DATE 23-Sep-18
END JOB INFORMATION
*
* EXAMPLE PROBLEM 5.1, CASE (C), PAGE 5-12, AISC LRFD 3RD ED.
* CAPACITY (MNZ) SHOULD BE ABOUT 50.8 KIP-FT
*
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 35 0 0;
MEMBER INCIDENCES
1 1 2;
MEMBER PROPERTY AMERICAN
1 TABLE ST W18X40
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 UNI GY -0.3
PERFORM ANALYSIS
PARAMETER 1
CODE LRFD
MAIN 1 ALL
CB 0 ALL
FYLD 7200 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD Output
STAAD.PRO CODE CHECKING - (LRFD 3RD EDITION) v1.0 ******************************************** |--------------------------------------------------------------------------| | Y PROPERTIES | |************* | IN INCH UNIT | | * |=============================| ===|=== ------------ | |MEMBER 1 * | AISC SECTIONS | | AX=0.1180E+2 | | * | ST W18X40 | | --Z AY=0.5638E+1 | |DESIGN CODE * | | | AZ=0.4214E+1 | | LRFD 2001 * =============================== ===|=== PY=0.1000E+2 | | * PZ=0.7840E+2 | | * |<---LENGTH (FT)= 35.00 --->| RY=0.1272E+1 | |************* RZ=0.7202E+1 | | | | 45.9 (KIP-FEET) | |PARAMETER | L1 L1 L1 CAPACITIES | |IN KIP INCH | IN KIP INCH | |--------------- + L1 L1 -------------| | KL/R-Y= 330.12 | PNC=0.2310E+2| | KL/R-Z= 58.32 + L1 L1 pnc=0.0000E+0| | UNL = 420.00 | PNT=0.5310E+3| | CB = 1.14 + L1 L1 pnt=0.0000E+0| | PHIC = 0.85 | MNZ=0.6072E+3| | PHIB = 0.90 + mnz=0.5512E+3| | FYLD = 50.00 |L0 L0 MNY=0.4283E+3| | NSF = 1.00 +---+---+---+---+---+---+---+---+---+---| mny=0.0000E+0| | DFF = 0.00 -2.6 VN =0.1522E+3| | dff = 0.00 ABSOLUTE MZ ENVELOPE vn =0.0000E+0| | (WITH LOAD NO.) | | | | MAX FORCE/ MOMENT SUMMARY (KIP-FEET) | | ------------------------- | | | | AXIAL SHEAR-Y SHEAR-Z MOMENT-Y MOMENT-Z | | | | VALUE 0.0 5.2 0.0 0.0 45.9 | | LOCATION 0.0 0.0 0.0 0.0 17.5 | | LOADING 0 1 0 0 1 | | | |**************************************************************************| |* *| |* DESIGN SUMMARY (KIP-FEET) *| |* -------------- *| |* *| |* RESULT/ CRITICAL COND/ RATIO/ LOADING/ *| | FX MY MZ LOCATION | | ====================================================== | | PASS LRFD-H1-1B-C 0.908 1 | | 0.00 C 0.00 -45.94 17.50 | |* *| |**************************************************************************| | | |--------------------------------------------------------------------------|