Page 314 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch06.qxd 9/29/05 5:15 PM Page 6.36

DESIGN OF BUILDING MEMBERS

6.36 CHAPTER SIX

The interaction result, which may be considered a section efficiency ratio, is P u /φP n = 1513/4830 =
0.313 > 0.2,

.
R = 0 312 + 8  253 5 . + 111.  1
9  3259 1628 
8
.
.
= 0 312 + ( 0 0778 + 0 682. ) = 0 443 1 0. < .
9
Interaction Equation for Full Gravity Loading. For use in the interaction equation based on fac-
tored loads and moments due to 1.2 times the dead load plus 1.6 times the live load,
+
+
×
=
.
.
(
P = 1 2 750 325 0 426 ×13) +1 6 250 1697 kips
.
u
Determined in the same way as for the dead load, the magnification factors are
B = 10 . = .
1 007
−
x 1
,
/
1 1697 247 000
B = 10 . = .
1 065
−
y 1
/,
1 1697 27 700
Application of the magnification factors to the factored moments yields
⋅
×
+
.
M = 1 007 1 2 ×180 1 6 75) = 338 4 kip ft
(
.
.
.
ux
×
×
⋅
+
.
.
.
M = 1 065 1 2 75 1 6 40) = 164 0 kip ft
(
.
uy
With P u /φP n = 1697/4830 = 0.351 > 0.2, substitution of the preceding values in the interaction equa-
tion (Eq. 5.102) yields
.
R = 0 351 + 8  338 4 . + 164 0 .  
9  3259 1628
8
<
.
.
= 0 351 + ( . + 0 1008) = 0 533 1
.
0 1038
9
Interaction Equation with Wind Load. For use in the interaction equation based on factored loads
and moments due to 1.2 times the dead load plus 0.5 times the live load plus 1.3 times the wind load
of 600 kips, including the P–∆ effect,
P = 1.2(750 + 325 + 0.426 × 13) + 0.5 × 250 + 1.3 × 600 = 2202 kips
Under wind action, double curvature may occur for strong-axis bending. For this condition, with
M 1 = M 2 ,
C mx = 0.6 − 0.4 × 1 = 0.2
In this case, the magnification factor for strong-axis bending is
B = 02 . = . <
0 202 1
x 1 −
1 2202 247 000
,
/
Use B 1x = 1.0. The magnification factor for minor-axis bending is, with C m = 1 for single-curvature
bending,
B = 10 . = .
1 0864
y 1
−
1 2202 27 700
/,
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