Handbook of Civil Engineering Calculations

ex = e cos 45° = 6 in x 0.707 = 4.2 in (10.7 cm)

ey = e sin 45° = 6 in x 0.707 = 4.2 in (10.7 cm)

M

-=*-• =

1001

S

8

^

4

"

2 in

=

35

4 kip

ft (48

**">

"„->,-

i

^g^

£

= 35.4 kip-ft (48 IcNm)

Again, try a W8 x 48. As above

<£,M^n>, - 61.8 ^- kip-ft (83.8 kNm)

Although the W8 x 48 is not listed in the Beam Selection Table in the AISC LRFD Man-
ual, Lp and 0^Mn* can be calculated. From Eq. (Fl-4) (Chap. 5):

_ 30Or, _ 30Or, _

Lp=

VJp V36

=5

°^

= 50 x 2.08 in = 104 in - 8.7 ft (2.65 m)

Since (Lb = 6.0 ft) < (Lp = 8.7 ft)

<M4, - Wp = 4 AFy

0.90 x 49.0 in^3 x 36 ksi A/1-7001 XT A

= —- = 132 kip-ft (178.9 kNm)

12 in/ft

In Interaction Formula (Hl-Ia)

8 /35.4 kip-ft 35.4 kip-ft \

0.22 + — I — + — < 1.0

9 \ 132kip-ft 61.8kip-ft/

0.22 + %(0.27 + 0.57)

0.22 + 0.75 = 0.97 < 1.0 o.k.

The most efficient configuration is orientation (a) 9 strong axis bending, which requires a
W8 x 28 as opposed to a W8 x 48 for the other two cases.

Related Calculations. This procedure is the work of Abraham J. Rokach, MSCE,
Associate Director of Education, American Institute of Steel Construction. SI values were
prepared by the handbook editor.

COMBINED FLEXURE AND COMPRESSION

IN BEAM-COLUMNS IN A BRACED FRAME

Select, in A36 steel, a W14 section for a beam-column in a braced frame with the follow-
ing combination of factored loads: Pu = 800 kips (3558 kN); first-order moments