Two bars, one of steel and the other of copper having areas of cross-sections A_{s} and A_{c}, coefficient of expansion αs and αc and Young's Modulii E_{s} and E_{s} are rigidly connected together at the ends and subjected to temperature change of t°. If the length of the bars initially is L, the final extension δ of the two bars at t° temperature is given by

There are two hinged semicircular arches A, B and C of radii 5 m, 7.5 m and 10 m respectively and each carries a concentrated load W at their crowns. The horizontal thrust at their supports will be in the ratio of

A spring of mean radius 40 mm contains 8 action coils of steel (N = 80000 N/mm^{2}), 4 mm in diameter. The clearance between the coils being 1 mm when unloaded, the minimum compressive load to remove the clearance, is