Page 162 - Handbook of Civil Engineering Calculations, Second Edition

STRUCTURAL STEEL DESIGN 1.145

– p
M nx M px – (M px – M rx )

r – p
The properties S x and Z x of the cross section in Fig. 40 must now be calculated.
I x d 58 in.
S x , where c 29 in. (73.7 cm)
C 2 2
The contributions of the two flanges and the web to the moment of inertia I x are

BT 3
Elements + AD 2
12
18 in. × (1 in.) 3 2
4
2 Flanges + (18 in. 1 in.)(28.5 in.) 2 29,244 in
12
4
(1,217,227 cm )
0.44 in. × (56 in.) 3
Web + 0 6,403 in (266,513 cm )
4
4
12
35,647 in. 4
S x 1230 in. (20,156 cm )
3
3
I x
29 in.
To determine Z x , we calculate AD, where A is the cross-sectional area of each element
and D represents its distance from the centroidal x axis.
In calculating Z x , the upper and lower halves of the web are taken separately.
Elements AD
Flanges [(18 in. 1 in.) 28.5 in.]2 1026 in. (16,813 cm )
3
3
1
3
2 /2 Webs [(28 in. 0.44 in.) 14 in.]2 343 in. (5,620 cm )
3
3
1369 in. (22,433 cm )
3
Z x
Z x 1369 in. (22,433 cm )
3
3

FIGURE 40