Question

A steel bar of 20 mm diameter and 400 mm long is placed concentrically inside a gunmetal tube (Fig. 2.9). The tube has inside diameter 22 mm and thickness 4 mm. The length of the tube exceeds the length of the steel bar by 0.12 mm. Rigid plates are placed on the compound assembly. Find: 

(a) the load which will just make tube and bar of same length and 

(b) the stresses in the steel and gunmetal when a load of 50 kN is applied. E for steel = 213 GN/m² , E for gunmetal = 100 GN/m² .

Answer 1

(a) For tube to compress 0.12 mm:

(b) Load available to compress bar and tube as a compound bar is given by, let σ₂ be the additional stress produced in the gunmetal tube due to this load and σ_s be the corresponding stress in the steel bar, then