V. AISC LRFD - Wide Flange Flexural Strength 2
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 (b), page 5-12.
Details
The beam is braced at the ends and at third points such that Lb = 140 in.
Fy = 50 ksi |
Length = 35 ft |
Validation
The plastic limiting unbraced length is given by:
The inelastic limiting unbraced length is given by:
(F1-6) |
= | ||
= | ||
= |
Mr = FLSx = 40 × 68.4 = 2,736 in·k | (F1-7) |
Lp = 53.8 in.
Lr = 144.9 in.
Lp < Lb < Lr; thus, the section is inelastic.
The nominal flexural strength is:
(F1-2) |
Mp = FyZx = 50 × 78.4 = 3,920 in·k
Conservatively assume Cb = 1.0.
The lateral-torsional buckling limit state capacity:
ϕbMn = 0.9×(2,800) = 2,520 in·k
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Design flexural strength, ϕbMn (in·kips) | 2,520 | 2,514 | 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 2.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 5.1, CASE (B), PAGE 5-12, AISC LRFD 3RD ED.
* CAPACITY (MNZ) SHOULD BE ABOUT 211 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 -1.3
PERFORM ANALYSIS
PARAMETER 1
CODE LRFD
MAIN 1 ALL
CB 1 ALL
FYLD 7200 ALL
UNT 11.7 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 | | | | 199.1 (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 = 140.40 | PNT=0.5310E+3| | CB = 1.00 + L1 L1 pnt=0.0000E+0| | PHIC = 0.85 | MNZ=0.2514E+4| | PHIB = 0.90 + mnz=0.2389E+4| | FYLD = 50.00 |L0 L0 MNY=0.4283E+3| | NSF = 1.00 +---+---+---+---+---+---+---+---+---+---| mny=0.0000E+0| | DFF = 0.00 -11.1 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 22.7 0.0 0.0 199.1 | | 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 0.950 1 | | 0.00 C 0.00 -199.06 17.50 | |* *| |**************************************************************************| | | |--------------------------------------------------------------------------|