Page 291 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch06.qxd 9/29/05 5:15 PM Page 6.13

DESIGN OF BUILDING MEMBERS

DESIGN OF BUILDING MEMBERS 6.13

TABLE 6.2 Properties of Selected W Shapes for LRFD
Property W18 × 35 Grade 50 W18 × 40 Grade 50 W21 × 50 Grade 50 W21 × 62 Grade 50
ϕM p , kip⋅ft 249 294 416 540
L p , ft 4.31 4.49 4.59 6.25
L r , ft 11.5 12.0 12.5 16.7
ϕM r , kip⋅ft 173 205 285 381
S x , in 3 57.6 68.4 94.5 127
l y , in 4 15.3 19.1 24.9 57.5
h o , in 17.28 17.38 20.28 20.39
r y , in 1.22 1.27 1.30 1.77
J, in 4 0.506 0.81 1.14 57.5
1140 1440 2560 5970
C w

The next step is to find a section that if its L r is less than 20 ft, its M r exceeds 277.5 kip⋅ft.
The manual table indicates that a W21 × 50 has the required properties (Table 6.2). With the aid of
Table 6.2, the nominal flexural design strength M n can be computed from

M n = F cr S x
The buckling stress is defined as follows:

C π 2 E Jc  L  2
F = buckling stress = b 1 + 0 078  b  (6.22)
.
cr
( Lr / ) 2 Sh  r 
ts
x o
b ts
The effective radius of gyration r tx (in) is
IC
r = yw
2
ts
S x
where h o = distance between the flange centroids, in
J = torsional constant, in 4
C w = warping constant
c = 1.0 for doubly symmetric I-shape
Therefore,
/
 24 9 . × 2560  12
r =   = 1 635 in
.
tx
 94 5 . 
Also,
.
,
F = 1 0 . × π 2 × 29 000 1 + 0 078 114 ×10 .  20 ×12  2 = 18 77 ksi
.
.
cr 2 
.
.
[( 20 ×12 1 635] 94 5 . × 20 28  1 635
)/ .
Thus, the nominal flexural strength is
M n = 18.77 × 94.5 = 1774 kip⋅in = 147.9 kip⋅ft < 277.5 kip⋅ft
The W21 × 50 does not have adequate flexural strength. Therefore, trials to find the lowest-weight
larger size must be continued. This trial-and-error process can be eliminated by using beam-selector
charts in the AISC manual. These charts give the beam design moment corresponding to unbraced
Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)
Copyright © 2004 The McGraw-Hill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.