Question

Two similar bars of Steel and Aluminium are heated to a same temperature. Forces are applied at the ends of the bars to maintain their lengths unaltered. If the ratio of Young's modulii of Steel and Aluminium is 3, and the ratio of the coefficients of thermal expansion of Steel to that of Aluminium is 0.5, what is the stress on the Aluminium bar if the stress on the Steel bar is 100 MPa?

• A. 16.7 MPa
• B. 66.7 MPa
• C. 136.7 MPa
• D. 1500 MPa

Answer 1

The correct option is B 66.7 MPa

$\frac{E_S}{E_{Al}}=3;\frac{{\alpha }_s}{{\alpha }_{Al}}=0.5$

$\frac{{\sigma }_{steel}}{{\sigma }_{Al}}=\frac{(E\alpha \Delta T{)}_{steel}}{(E\alpha \Delta T{)}_{Al}}$

${\sigma }_{Al}=\frac{2}{3}\times 100=66.67MPa$