Question

Figure 2.11 shows a composite bar of steel and copper. The temperature of the bar is raised by 80°C. Determine the compressive force developed in the bars after the rise in temperature and the change in length of the copper bar. The area of the copper bar is 600 mm² and that of the steel bar is 1,000mm². 

E_cu = 1,05,000N/mm², E_s = 2,10,000N/mm² . 

α_s = 11 × 10⁻⁶/°C, α_cu = 18 × 10⁻⁶/°C, clearance between support and composite bar is 0.5 mm.

Answer 1

Free expansion in bars due to temperature change 

= 18 × 10⁻⁶ × 80 × 500 + 11 × 10⁻⁶ × 80 × 500 

= 1.16 mm Temperature rise = 80°C 

Clearance = 0.5 mm. 

Contraction in length of the bars = 1.16 − 0.5 = 0.66 mm 

Say, the compressive force developed is P Newton. Then