Question

A steel bar and a brass bar are each secured to a rigid support and fastened together at their ends by a 20-mm diameter pin as shown in Fig. 2.15. The area of cross-section of the steel rod is 600 mm² and that of the brass bar is 800mm². Determine the maximum normal stress induced in the brass bar by 40°C drop in temperature. E_S = 2E_b = 200 GPa, α_S = 11.2 × 10⁻⁶ /°C, α_B = 18.6 × 10⁻⁶/°C. What is the shear stress developed in the pin?

Answer 1

Decrease in temperature = 40°C 

Free contraction in length = L × 40 × 11.2 × 10⁻⁶ + L × 40 × 18.6 × 10⁻⁶ 

= L(448 + 744) × 10⁻⁶ 

= 1.192 × 10⁻³L mm