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The diagram opposite shows a bar acted upon by two point loads. The bar is $30$ mm square between a and $c$ and is $20$ 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 $80$ GPa $.$ All dimensions on the diagram are in mm$.$

Answers:

Freedoms Used

$V=360{}_b^2+320{}_c^2+160{}_d^2-480{}_b{}_c-160{}_c{}_d-20{}_b+30{}_d$

${}_b=0\mathrm{.}02315mm$

${}_c=-0\mathrm{.}006944mm$

${}_d=-0\mathrm{.}09722mm$

$F_{ab}=5\mathrm{.}556kN$

$F_{bc}=14\mathrm{.}44kN$

$F_{cd}=14\mathrm{.}44kN$

$F_{de}=-15\mathrm{.}556kN$