A plastic bar ACB having two different solid circular cross sections is held between rigid supports as shown in the figure. The diameters in the left- and right-hand parts are 50 mm and 75 mm, respectively. The corresponding lengths are 225 mm and 300 mm. Also, the modulus of elasticity E is 6.0 GPa, and the coefficient of thermal expansion α is 100 × 106 / °C. The bar is subjected to a uniform temperature increase of 30°C.
(a) Calculate the following quantities: (1) the compressive force N in the bar; (2) the maximum compressive stress σc; and (3) the displacement σC of point C.
(b) Repeat (a) if the rigid support at A is replaced by an elastic support having spring constant k = 50 MN/m (see figure part b; assume that only the bar ACB is subject to the temperature increase).

A 150 mm C 175 mm 225mm300 mm- k A 150 mm C75R -225 mm300 mm