Page 342 - Civil Engineering Formulas

BRIDGE AND SUSPENSION-CABLE FORMULAS 273

where n integer, 1 for fundamental mode of vibration, 2 for second mode, . . .
l span of cable, ft (m)
w load on cable, kip/ft (kN/m)
g acceleration due to gravity 32.2 ft/s 2
T cable tension, kip (N)
The spreaders of a cable truss impose the condition that under a given load
the change in sag of the cables must be equal. Nevertheless, the changes in ten-
sion of the two cables may not be equal. If the ratio of sag to span f/l is small
(less than about 0.1), for a parabolic cable, the change in tension is given
approximately by
16 AEf
H f (10.100)
3 l 2
where f change in sag
A cross-sectional area of cable
E modulus of elasticity of cable steel

RAINWATER ACCUMULATION
AND DRAINAGE ON BRIDGES

Rainwater accumulation and drainage are important considerations in highway
bridge design. The runoff rate of rainwater from a bridge during a rainstorm is
given by:*
Q kCiA (10.101)
3
where Q peak runoff rate (ft /s)
C runoff coefficient
i average rainfall intensity (in/h)
A drainage area (acres)
k 1.00083
The runoff coefficient, C, ranges from 0.70 to 0.95 for pavements made of
asphalt, concrete, or brick. Specific values are available in Tonias—Bridge Engi-
neering, McGraw-Hill.
Most bridge designers base the rainfall intensity on a once-in-10-year storm
lasting for 5 min. Historic rainfall intensities can be determined from local munic-
ipal records available from the city or state in which a bridge will be located.
To drain the water from a highway bridge the sheet flow of the rainwater
must be studied. Determine the deck width for handling the rainwater runoff to
the drain scuppers by using:*
1
W Shoulder Width (Traffic Lane) (10.102)
3
where W width of deck used in analysis

*Tonias—Bridge Engineering, McGraw-Hill.