Page 303 - Structural Steel Designers Handbook AISC, AASHTO, AISI, ASTM, and ASCE-07 Design Standards

Brockenbrough_Ch06.qxd 9/29/05 5:15 PM Page 6.25

DESIGN OF BUILDING MEMBERS

DESIGN OF BUILDING MEMBERS 6.25

Deflection due to long-term superimposed dead load is
5 0 25 30 × 12 3
×
4
× .
D = = .
0 331in
×
×
1
,
384 29 000 473 8 .
Deflection due to short-term (reduced) live load is
×
5 0 44 30 × 12 3
4
× .
D = = .
0 510 in
2
×
×
,
384 29 000 541 8 .
Total deflection is
D = D + D = 0 331 0 510 = 0 842 in = L OK
+
.
.
.
1
2
428
Vibration Investigation. The vibration study of composite beams is based on the following report:
T. M. Murray et al., “Floor Vibrations due to Human Activity,” AISC Steel Design Guide, No. 11, 1997.
Utilization of lightweight concrete and longer girder spans has resulted in lower natural frequencies in
similar structural floor systems. A more detailed analysis for a floor-vibration design criterion is rec-
ommended due to a walking excitation or impact “heel drop” force to determine the peak acceler-
ation a p . The peak acceleration, presented as the percentage of the acceleration of gravity, (a p /g) ×
100%, will be the governing acceleration limit to satisfy, as calculated in the following formula:
a P exp ( −035 f )
.
= o n (6.31)
p
g β W
where P o = a constant force representing the excitation
f n = fundamental natural frequency of a beam or joist, girder, or combination, Hz
β= modal damping ratio
W = effective weight supported by the beam or joist, girder, or combination
The suggested limiting values for the constant force, damping ratio, and acceleration limit are
shown in Table 6.4. A damping ratio of 0.02 can be used for floors with few nonstructural compo-
nents (ceilings, ducts, partitions, etc.), as can occur in open work areas and churches. For floors with
nonstructural components and furnishings but with only small demountable partitions, typical of
many modular office areas, a damping ratio of 0.03 is recommended. For floors with full-story-
height partitions, a damping ratio of 0.05 is suggested.
The fundamental frequency of a uniformly loaded simply supported joist, beam, or girder is
g
.
f = 018 (6.32)
n
∆
where g = acceleration due to gravity, 386 in/s 2
∆= midspan deflection relative to the supports due to the weight supported
TABLE 6.4 Recommended Values of Parameters
Constant force Damping ratio Acceleration limit
Type of occupancy P o (lb) β (a o /g) × 100%
Offices, residences, churches 65 0.02–0.05 0.5%
Shopping malls 65 0.02 1.5%
Footbridges—indoor 92 0.01 1.5%
Footbridges—outdoor 92 0.01 5.0%
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