A nonprismatic bar ABC made up of segments AB (length L1, cross-sectional area A1) and BC (length L2, cross-sectional area A2) is fixed at end A and free at end C (see figure). The modulus of elasticity of the bar is E. A small gap of dimension s exists between the end of the bar and an elastic spring of length L3 and spring constant k3. If bar ABC only (not the spring) is subjected to temperature increase ΔT determine the following.
(a) Write an expression for reaction forces RA and RD if the elongation of ABC exceeds gap length s.
(b) Find expressions for the displacements of points B and C if the elongation of ABC exceeds gap length s.

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RA DI RD