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Date: 16-3-2021
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Date: 25-7-2016
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Date: 30-8-2016
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Suspension Bridge
A flexible massless cable in a suspension bridge is subject to uniform loading along the x-axis. The weight of the load per unit length of the cable is ω, and the tension in the cable at the center of the bridge (at x = 0) is T0 (see Figure 1.1).
Figure 1.1
a) Find the shape of the cable at equilibrium.
b) What is the tension T(x) in the cable at position x at equilibrium?
SOLUTION
a) We use an elementary method to solve this problem. The conditions for a static equilibrium are
(1)
(2)
(see Figure 1.2). (1) and (2) can be rewritten in the form
(3)
(4)
Figure 1.2
Integrating (3) and (4), we obtain
(5)
(6)
At x = 0, θ = 0, so C0 = 0, C1 = T0 and dividing (5) by (6), we have
(7)
From (7) we find the shape of the suspension bridge, which is parabolic
(8)
b) To find the tension T(x) at x ≠ 0 ( θ ≠ 0) multiply (5) by (6).
(9)
(10)
So
(11)
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