Solve the nodal displacements and element forces of the plane truss problem in figure 1.23. Use the following numerical values: \(A E=10^{7} \mathrm{~N}, L=1 \mathrm{~m}, \alpha=10^{-5} /{ }^{\circ} \mathrm{C}, \Delta T=100^{\circ} \mathrm{C}\).

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(a) (b) AEAT 2 AT (3) AT 2 L 3 30 30 X 4 AEAT (c) + AEAT Figure 1.23 A threeelement truss: (a) The middle element is subjected to a temperature rise. This is the given problem. (b) A pair of compressive forces is applied to element 2 to prevent it from expanding. This is called problem I. (c) The forces in problem I are reversed. No thermal stresses are involved in this problem. This is called problem II.