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4.5.1 Design of Cables
Each cable carries a triangular slice of load.
The maximum tension in the cable is equal to the resultant reaction at the
supports. This reaction can be calculated by considering the equilibrium of
one cable, such as cable AB in
Fig. 4.6. Considering the moment equilibrium of AB about the point B
(compression ring), we find the value of tension To at the lowest point A (tension ring).
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(4.7)
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where L is the span length, s is the sag of cable, and W is the total load carried by a
pair of cables. Quantity To
is the minimum tension on the cable. The horizontal component of tension at
any point on the cable is equal to To.
Noting that the vertical component of reaction at B is W/2, the
magnitude of reaction at B, equal
to the maximum tension in the cable, becomes
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(4.8)
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It should
be noted that in this approximate analysis the weight of cables has been
neglected. Thus, the required cross-sectional area of cable is
where Ft is the allowable
tensile stress in steel cables.
Cables used in
suspension roofs are made by twisting thin wires, and their cross-sectional
area is approximately equal to 2/3(3.14/4)d2 (Cowan and Wilson, 1981), where d is the diameter of the cable. The
load W carried by a pair of
cables depends on the spacing of cables around the circumference. Thus, for
a given sag, the area of steel required depends in the spacing of cables
around the circumference.
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