Page 302 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch06.qxd 9/30/05 4:27 PM Page 6.24

DESIGN OF BUILDING MEMBERS

6.24 CHAPTER SIX

90/13.6 = 6.62"
3.25" X = 4.05"

2" E.N.A.

W14 × 22
13.7" A = 6.49 in 2
I = 199 in 4

FIGURE 6.7 Transformed section of a composite beam.

4
inertia I s = 199 in . The location of the elastic neutral axis is determined by taking moments of the
transformed concrete area and the steel area about the top of the concrete slab:
.
× 325 2 / )
.
+ .
. (
X = 2152 ( . + 649 05 . ×137 525) = 405 in
.
21 52 + 6 49
.
.
The elastic transformed moment of inertia for full composite action is

.
.
I = 90 × 3 25 3 + 21 52 405 − 325  2 + 649  13 7 . + 525 405  2 +199
.
.
.
.
− .
tr
13 6 . ×12  2   2 
= 765 0 . in 4
Since partial composite construction is used, the effective moment of inertia is determined from
∑ Q
I
I eff = I + ( I − ) n (6.30)
s
s
tr
C f
where C f = concrete compression force based on full composite action
.
−
I eff = 199 + 765 199) 119 1 = 541 8. in 4
(
.
324 5
I eff is used to calculate the immediate deflection under service loads (without long-term effects).
For long-term effect on deflections due to creep of the concrete, the moment of inertia is reduced
to correspond to a 50% reduction in E c . Accordingly, the transformed moment of inertia with full
4
composite action and 50% reduction in E c is I tr = 652.6 in and is based on a modular ratio 2n = 27.2.
2
The corresponding transformed concrete area is A 1 = 10.76 in .
The reduced effective moment of inertia for partial composite construction with long-term effect
is determined from Eq. (6.30):
.
119 1
(
I eff = 199 + 652 6 −199) = 473 8. in 4
.
.
324 5
Since unshored construction is specified, the deflection under the weight of concrete when placed
and the steel weight is compensated for by the camber specified. Long-term effect due to these
weights need not be considered because the concrete is not stressed by them.
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