Page 305 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch06.qxd 9/29/05 5:15 PM Page 6.27

DESIGN OF BUILDING MEMBERS

DESIGN OF BUILDING MEMBERS 6.27

where C j = 2.0 for joists and beams in most areas
= 1.0 for joists and beams parallel to an interior edge
D s = transformed slab moment of inertia per unit width
4
3
= d e /(12n), in /ft
d s = effective depth of the concrete slab, usually taken as the depth of the concrete above
the form deck plus one-half the depth of the form deck
n = dynamic modular ratio, see Eq. (6.34)
D j = beam or joist transformed moment of inertia per unit width
4
= I t /S, in /ft
L j = joist or beam span above the form deck plus one-half the depth of the form deck,
.
D = 12 × 4 25 3 = 763 in 4 /ft
.
s
.
12 ×10 06
D = 843 2 . ×12 = 84 32 in /ft
4
.
j
120
For this beam, C j = 2.0.
/
B =×  843 2 . 120 ×12   14 × 30 = 32 91 ft < 2 3 × floor width
.
2

j
Since 0.7 × girder spacing = 21 ft, less than the beam span, an increase of 50% of the effective
weight must be applied due to continuous action.
.
W = 15 . × 0 559 ×12 × 32 91 30. × = 88 76. kips
j
120
Interior Girder Vibration Investigation. The girder vibration calculations will be based on full
composite action and the shear deformations will not be included. The concrete flange width is the
smaller of b = 10 × 12 = 120 in or b = 0.4 × 30 × 12 = 144 in. The transformed moment of inertia
4
I t = 4315 in for the W24 × 55 beam considering the 1-in effective concrete in the deck.
The total load is
×
.
30 × 0 5593 12 + 0 055 1 853 kips/ft
=
.
.
120
and the girder deflection is calculated as
×
.
∆ = 5 × 0 5993 30 4 ×12 3 = 0 269 in
.
g
×
,
384 × 29 000 4315
386
f comb = 018 = 6 808 Hz
.
.
0 246
.
The effective width of a girder is
/
 D  14 2
B = C g s  L < × floor length (6.36)
g
 D  g 3
g
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