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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 L

_{F}. (NOTE: Do not try to solve for a form L

_{F}=, 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 = [itex]\frac{Fcosθ}{2}[/itex]

Compatibility Equation: ∂ = ∂

_{1}+ ∂

_{2}. ∂

_{1}= ∂

_{2}.

Force-Displacement Equation: ∂

_{1}= [itex]\frac{TL}{2EA}[/itex] = [itex]\frac{FLcosθ}{4EA}[/itex].

This gives: ∂=2∂

_{1}= [itex]\frac{FLcosθ}{2EA}[/itex]

Which gives a final answer of: L

_{F}=L+∂ = L + [itex]\frac{FLcosθ}{2EA}[/itex].

But I'm not confident in my work, because professor said it would be too difficult to solve for the solution in this form.