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BVP Example - Sagging of a Cable Boundary Value Problem Dr...

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Sagging of a Cable: Boundary Value Problem Dr. S.V. Sreenivasan ME 218 Spring 2006
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The Problem Power transmission lines, generally, have cables that have significant weight of their own. This causes the cable to sag. Some amount of sag is also necessary to account for the thermal expansion and contraction during seasonal changes. The sag can be controlled by adjusting the tension in the cable by applying a force (T) at the two ends. T T w(x) x Load distribution
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The Governing Equation The sag ( w ) of a flexible cable is governed by the equation: Where k is the distributed vertical load, T is the tension in the cable (assumed constant) and R is the flexural stiffness R l x kx R Tw dx w d 2 ) ( 2 2 - + =
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Boundary Value Problem This is a Boundary Value Problem since it is known that the cable is fixed at the ends w (0) = 0 w ( l ) = 0 Data: l = 100”, T = 1000 lb, k = 100 lb/in, and R = 50 x 10 6 lb-in 2
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Finite Difference Formulation This BVP can be solved using the finite difference formulation For a linear 2 nd
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