V. AISC LRFD - Load Capacity of 3 Wide Flange Beams
To find the design flexural strength capacity of 3 beams of different spans using the data in Table 5-4 of AISC LRFD 3rd edition.
Details
W21x62 section.
Fy = 50 ksi |
40 ft, 30 ft, and 8 ft spans are investigated. All beams are fully braced.
Validation
Bending Capacity
The beam is fully braced so it can reach full plastic capacity:
The total load capacity on the beam is then calculated by setting the ultimate capacity equal to the load, and then solving for the total load:
Shear Capacity
Check for web slenderness:
The nominal shear capacity of a W21x62 section:
The total load capacity on the beam is then calculated by setting the ultimate capacity equal to the load, and then solving for the total load:
This governs the total load capacity for the short span (8') case.
Using the total weight values from the reference, the following distributed loads are calculated:
Results
There is no direct comparison of the results from STAAD.Pro with the Reference, as the program does not directly compute the total member load. However, when the total member load is applied as a distributed load (see previous table), the Utilization ratio will then nominally be unity (1.0) for a beam loaded at its capacity.
Result Type | Reference | STAAD.Pro | Difference | Comments | |
---|---|---|---|---|---|
Beam #1: 30 ft span | Bending capacity, ϕMn (in·k) | 6,480 | 6,480 | none | |
Utilization ratio | 1.0 | 1.0 | none | ||
Beam #2: 20 ft span | Bending capacity, ϕMn (in·k) | 6,480 | 6,480 | none | |
Utilization ratio | 1.0 | 1.0 | none | ||
Beam #3: 8 ft span | Shear capacity, ϕVn (kips) | 226.8 | 226.8 | none | |
Utilization ratio | 1.0 | 1.001 | negligible |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\US\AISC\AISC LRFD - Load Capacity of 3 Wide Flange Beams.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
*
* OBJECTIVE : TO DETERMINE THE MAXIMUM UNIFORMLY
* DISTRIBUTED LOAD CARRYING CAPACITY OF 3 BEAMS.
*
* EXAMPLE PROBLEM 5.5 PAGE 5-21, AISC LRFD 3RD ED.
*
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 40 0 0; 3 0 10 0; 4 30 10 0; 5 0 20 0; 6 8 20 0;
MEMBER INCIDENCES
1 1 2; 2 3 4; 3 5 6;
MEMBER PROPERTY AMERICAN
1 TO 3 TABLE ST W21X62
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 4.176e+06
POISSON 0.3
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 3 5 PINNED
2 4 6 FIXED BUT MZ
*
LOAD 1
MEMBER LOAD
* ON MEMBER 1, W=108/40=2.7
1 UNI GY -2.7
* ON MEMBER 2, W=144/30
2 UNI GY -4.8
* ON MEMBER 3, W=454/8
3 UNI GY -56.75
*
PERFORM ANALYSIS
PARAMETER 1
CODE LRFD
MAIN 1 ALL
FYLD 7200 ALL
* FULLY BRACED CONDITION CAN BE ACHIEVED BY SETTING UNT TO 1.0 INCH
UNT 0.1 ALL
TRACK 1 ALL
CHECK CODE ALL
FINISH
STAAD Output
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 W21X62 (AISC SECTIONS) FAIL LRFD-H1-1B-C 1.000 1 0.00 C 0.00 -540.00 20.00 +---------------------------------------------------------------------+ | DESIGN STRENGTHS FOR MEMBER 1 UNITS - KIP IN | | PNC= 53.25 PNT= 823.50 MNZ= 6480.00 MNY= 942.05 VN= 226.80 | +---------------------------------------------------------------------+ 2 ST W21X62 (AISC SECTIONS) PASS LRFD-H1-1B-C 1.000 1 0.00 C 0.00 -540.00 15.00 +---------------------------------------------------------------------+ | DESIGN STRENGTHS FOR MEMBER 2 UNITS - KIP IN | | PNC= 94.66 PNT= 823.50 MNZ= 6480.00 MNY= 942.05 VN= 226.80 | +---------------------------------------------------------------------+ * 3 ST W21X62 (AISC SECTIONS) FAIL SHEAR-Y 1.001 1 0.00 C 0.00 0.00 0.00 +---------------------------------------------------------------------+ | DESIGN STRENGTHS FOR MEMBER 3 UNITS - KIP IN | | PNC= 608.18 PNT= 823.50 MNZ= 6161.00 MNY= 942.05 VN= 226.80 | +---------------------------------------------------------------------+ ************** END OF TABULATED RESULT OF DESIGN **************