The truss shown in the figure supports the force \(F=1,000 \mathrm{~N}\). Both elements have the same axial rigidity of \(A E=10^{7} \mathrm{~N}\), thermal expansion coefficient of \(\alpha=2 \times 10^{-6} /{ }^{\circ} \mathrm{C}\), and length \(L\) \(=1 \mathrm{~m}\). While the temperature at element 1 remains constant, that of element 2 is dropped by \(50^{\circ} \mathrm{C}\).

a. Write the \(4 \times 4\) element stiffness matrices [k] and the \(4 \times 1\) thermal force vectors \(\left\{\mathbf{f}_{\mathrm{T}}ight\}\) for elements 1 and 2 . Show the row addresses clearly.

b. Assemble two elements and apply the boundary conditions to obtain the global matrix equation in the form of \([\mathbf{K}]\{\mathbf{Q}\}=\{\mathbf{F}\}+\left\{\mathbf{F}_{T}ight\}\).

c. Solve for the nodal displacements.

Transcribed Image Text:

1 y 1 2 2 F X 3