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.

Reference

AISC Load Factor Resistance Design, 3rd Edition, Example 5.5, page 5-21.

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, $ϕ M n = M u = W × l / 8$ and then solving for the total load:

Shear Capacity

Check for web slenderness:

$h t w = 46.9 < 2.45 E / F yw = 2.45 29,000 / 50 = 59.0$

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, $ϕ V n = V u = W / 2$ 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:

Member W (kips) l (ft) w (kips/ft)
1 108 40 2.7
2 144 30 4.8
3 454 8 56.75

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.

Table 1. Comparison of results
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

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC LRFD - Load Capacity of 3 Wide Flange Beams.STD is typically installed with the program.

Note: The UNT parameter is set to 1.0 in. in order to approximate a fully-braced condition.
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
*
* 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.Pro CODE CHECKING - (LRFD 3RD EDITION)   v1.0
***********************
ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
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 **************