V. AISC LRFD - Non Compact Wide Flange 2
To determine the design bending strength of a non-compact American wide flange section bent about its strong axis. The deflection at mid-span due to two 10 kip concentrated loads acting at the third points along the beam is also to be calculated.
Validation
Evaluate section for lateral-torsional buckling:
The plastic limiting unbraced length is given by:
Lb < Lp; thus, the member is plastic.
Check flange slenderness:
FL = 50 ksi - 10 ksi = 40 ksi
Mr = FLSx = 40 × 93.0 = 3,720 in·k | (F1-7) |
Flanges are non-compact. The nominal moment capacity for the limit state of flange local buckling is:
(A-F1-3) |
Mp = FyZx = 50 × 107 = 5,350 in·k |
The flange local buckling limit state capacity:
ϕbMn = 0.9×(5,311) = 4,780 in·k
The ultimate moment is:
The capacity ratio is: 1,600 / 4,780 = 0.335
The deflection at mid-span for a beam loaded at third points:
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Design flexural strength, ϕbMn (in·kips) | 4,780 |
4,780.24 |
negligible | |
Capacity ratio | 0.335 | 0.335 | none | |
Deflection (in) | 1.42 | 1.4114 | negligible |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\US\AISC\AISC LRFD - Non Compact Wide Flange 2.STD is typically installed with the program.
The UNT 5 parameter specifies an unbraced length of 5'.
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 (A), PAGE 5-16, AISC LRFD 3RD ED.
* CAPACITY (MNZ) SHOULD BE ABOUT 398 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
*
SECTION 0.5 ALL
PRINT SECTION DISPL
*
PARAMETER 1
CODE LRFD
MAIN 1 ALL
FYLD 7200 ALL
UNT 5 ALL
TRACK 1 ALL
CHECK CODE ALL
FINISH
STAAD Output
MEMBER SECTION DISPLACEMENTS ---------------------------- UNITS ARE - INCH MEMB LOAD GLOBAL X,Y,Z DISPL FROM START TO END JOINTS AT 1/12TH PTS 1 1 0.0000 0.0000 0.0000 0.0000 -0.3644 0.0000 0.0000 -0.7057 0.0000 0.0000 -1.0010 0.0000 0.0000 -1.2273 0.0000 0.0000 -1.3654 0.0000 0.0000 -1.4114 0.0000 0.0000 -1.3654 0.0000 0.0000 -1.2273 0.0000 0.0000 -1.0010 0.0000 0.0000 -0.7057 0.0000 0.0000 -0.3644 0.0000 0.0000 0.0000 0.0000 MAX LOCAL DISP = 1.41141 AT 240.00 LOAD 1 L/DISP= 340 ************ END OF SECT DISPL RESULTS *********** 40. * 41. PARAMETER 1 42. CODE LRFD 43. MAIN 1 ALL 44. FYLD 7200 ALL 45. UNT 5 ALL 46. TRACK 1 ALL 47. CHECK CODE ALL STEEL DESIGN BENDING CAPACITY PER AISC LRFD 3RD ED -- PAGE NO. 4 STAAD.Pro CODE CHECKING - (LRFD 3RD EDITION) v1.0 *********************** ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted) MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION ======================================================================= 1 ST W21X48 (AISC SECTIONS) PASS LRFD-H1-1B-C 0.335 1 0.00 C 0.00 -133.33 13.33 +---------------------------------------------------------------------+ | DESIGN STRENGTHS FOR MEMBER 1 UNITS - KIP IN | | PNC= 35.84 PNT= 634.50 MNZ= 4780.24 MNY= 636.75 VN= 194.67 | +---------------------------------------------------------------------+