Page 304 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch06.qxd 9/29/05 5:15 PM Page 6.26

DESIGN OF BUILDING MEMBERS

6.26 CHAPTER SIX

The effective supported weight of joist, beam, or girder is
W = wBL (6.33)

where w = supported weight per unit area
B = effective width
L = member span
For the vibration analysis, additional parameters pertaining to the entire floor system must be
established first for the best estimation of peak accelerations due to a heel-drop forcing function.
The entire floor dimensions are 180 ft × 90 ft. The girders on all four sides are W24 × 55 Grade 50. The
interior girders are also W24 × 55 Grade 50 sections spaced at 30 ft in the longitudinal and latitudi-
nal directions.
The loading must be adjusted to estimate the least loading scenario which is most critical to
2
extreme vibrations. A dead load of 46.7 lb/ft is estimated by considering 3.5 in of concrete, 1-in
2
2
effective concrete thickness of deck, 2 lb/ft metal deck, and 4 lb/ft for ceiling, mechanical, and min-
2
imal partition loads. The live load is reduced to a magnitude of 11 lb/ft .
For transformed composite moment of inertia calculations, there are two modifications that dif-
fer from traditional composite calculations. First, a dynamic modulus of elasticity is considered
because the stiffness of concrete is greater under a dynamic load as compared to a static load. The
dynamic modular ratio is defined as
n = E s (6.34)
.
135 × E s
For this example,
,
n = 29 000 = 10 06
.
1 35 × 2136
.
The effective width of the slab is the minimum of the member spacing or 0.4 × (member span)
for an interior member and 0.20 × (member span) for an exterior member. The concrete flange width
is the smaller of b = 10 × 12 = 120 in or b = 0.4 × 30 × 12 = 144 in.
Interior Beam Vibration Investigation. The beam vibration calculations will be based on full com-
posite action, and the shear deformations will not be included.
The concrete flange width is the smaller of b = 120 in or b = 144 in. The transformed moment of
4
inertia I t = 843.2 in for the W14 × 22 beam, not considering the 1-in effective concrete in the deck.
The total load is
(46.7 + 11.0) × 10 + 22 = 0.6 kip/ft
and the beam deflection is calculated as

× 6 30
∆ = 50. × 4 ×12 3 = 0 447 in
.
j
×
,
384 × 29 000 843 2 .
386
.
.
f = 018 = 529 Hz
n
0 447
.
The effective width of a joist or beam is
/
 D  14 2
B = C j s  L < × floor width (6.35)
 D  j 3
j
j
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