Slimjimi
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Homework Statement
Hang a weight (F) from the middle of a horizontal wire of length L, attached on both sides. The wire has an effective modulus (E) and effective area (A). Find an equation for the new length of the wire LF. (NOTE: Do not try to solve for a form LF =, this is too hard).
Homework Equations
To see the equations I thought were relevant, see my attempt at the solution.
The Attempt at a Solution
Force Balance Equation: T = \frac{Fcosθ}{2}
Compatibility Equation: ∂ = ∂1 + ∂2. ∂1 = ∂2.
Force-Displacement Equation: ∂1 = \frac{TL}{2EA} = \frac{FLcosθ}{4EA}.
This gives: ∂=2∂1 = \frac{FLcosθ}{2EA}
Which gives a final answer of: LF=L+∂ = L + \frac{FLcosθ}{2EA}.
But I'm not confident in my work, because professor said it would be too difficult to solve for the solution in this form.