Page 165 - Handbook of Civil Engineering Calculations, Second Edition

1.148 STRUCTURAL STEEL ENGINEERING AND DESIGN

3
0.90 × 27.2 in. × 36 ksi
b M nx b M p b Z x F y 73.4 kip-ft (99.5 kNm)
12 in./ft
which is also the tabulated value for b M p for a W8 28 in the Beam Selection Table in
Part 3 of the AISC LRFD Manual.
Since
P u 100 kips
0.37 > 0.2
t P n 267 kips
the first of two interaction formulas applies.

P u 8 M ux M uy
+ 1.0
t P n 9
b M nx b M ny

8 50 kip-ft
0.37 + + 0 0.37 + 0.61 0.98 < 1.0 o.k.
9
73.4 kip-ft
2. Analyze the second orientation being considered
For orientation (b) in Fig. 41
P u 100 kips (444.8 kN), M ux 0, M uy 50 kip-ft (67.8 kNm)

Again, try a W8 28. For all L b . the design flexural strength for y-axis bending

b M ny b M p b Z y F y
3
0.90 × 10.1 in. × 36 ksi
27.2 kip-ft (36.9 kNm)
12 in./ft
Because M uy 50 kip-ft > b M ny 27.2 kip-ft, a W8 28 is inadequate. Try a W8 48:
3
2
3
A g 14.1 sq.in. (90.0 cm ), Z y 22.9 in. (375.3 cm )
3
0.90 × 22.9 in. × 36 ksi
b M ny 61.8 kip-ft (83.8 kNm)
12 in./ft
kips
t P n t F y A g 0.90 36 14.1 sq.in. 457 kips (2032.7 kN)
sq.in.
Because (P u / t P n ) (100 kips/457 kips) 0.22 > 0.2, interaction formula (H1-1a) again
applies.
P u 8 M ux M uy
+ + 1.0
t P n 9
b M nx b M ny
8 50 kip-ft
0.22 +
0 + 0.22 + 0.72 0.94 < 1.0 o.k.
9 61.8 kip-ft
3. Find the section for a load eccentric with respect to both
principal axes
For orientation (c) in Fig. 41, assume that the load is eccentric with respect to both princi-
pal axes. Referring to Fig. 41c