A rigid beam $AB$ is supported by circular columns $AC$ and $BD$ as shown in Figure $Q1.$

Column $AC$ is made of steel and has a diameter of $20mm$ and column $BD$ is made of aluminium and has a diameter of $40mm.$

The elastic modulus of steel, $E_{st}=200$GPa and that of the aluminium $E_{al}=70$GPa.

A vertical load of $90kN$ is applied at a point $F$ on the beam $AB.$

a$.)$ Calculate the axial support reactions and stresses on columns $AC$ and $BD(12$ marks$)$

b$.)$ Calculate the shortening of compressive columns $AC$ and $BD$

$(7$ marks$)$

c$.)$ Calculate the displacement of point $F$ of the rigid beam $AB$ due to the shortenings of columns $AC$ and $BD.$

$(6$ marks$)$