31. The truss shown in the figure supports the force F = 2,000 N. Both elements have the same axial rigidity of AE = 107 N, thermal expansion coefficient of a = 10~6/OC, and length L = 1 ra.

While the temperature at Element 1 remains constant, that of Element 2 is dropped by 100oC.

(a) Write the 4 x 4 element stiffness matrices [k] and the 4 x 1 thermal force vectors {fTj 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 [K]{Q}= {F}+{F7-}.

(c) Solve for the nodal displacements.

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