(Solved): The diagram opposite shows a bar acted upon by two point loads. The bar is \( 30 \mathrm{~mm} \) sq ...

The diagram opposite shows a bar acted upon by two point loads. The bar is \( 30 \mathrm{~mm} \) square between \( a \) and c and is \( 20 \mathrm{~mm} \) square between \( c \) and \( e \). Use the principles of equilibrium and compatibility to calculate the stress distribution in the bar if it is made from aluminium with an elastic constant of \( 80 \mathrm{GPa} \). All dimensions on the diagram are in \( \mathrm{mm} \). \( V=360 \Delta_{b}^{2}+320 \Delta_{c}^{2}+160 \Delta_{d}^{2}-480 \Delta_{b} \Delta_{c}-160 \Delta_{c} \Delta_{d}-20 \Delta_{b}+30 \Delta_{d} \) \( \Delta_{b}=0.02315 \mathrm{~mm} \) \( \Delta_{c}=-0.006944 \mathrm{~mm} \) \( \Delta_{d}=-0.09722 \mathrm{~mm} \) \( F_{a b}=5.556 \mathrm{kN} \) \( F_{b c}=14.44 \mathrm{kN} \) \( F_{c d}=14.44 \mathrm{kN} \) \( F_{d e}=-15.556 \mathrm{kN} \)