The uniaxial bar shown below can be modeled as a onedimensional bar. The bar has the following properties: \(L=1 \mathrm{~m}, A=10^{-4} \mathrm{~m}^{2}, E=100 \mathrm{GPa}\), and \(\alpha=2 \times 10^{-6} /{ }^{\circ} \mathrm{C}\). From the stressfree initial state, a force of 5,000 \(\mathrm{N}\) is applied at node 2, and the temperature is lowered by \(50^{\circ} \mathrm{C}\) below the reference temperature.

a. Calculate the global matrix equation after applying boundary conditions.

b. Solve for the displacement \(u_{2}\).

c. What is the element force \(P\) in the bar?

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2 5,000 N A, E, L