Problem $2)$

An anti$-$roll bar in a car suspension is mounted in bearings in which allow rotation about

the z $-$axis at points B and C but prevent any bending of section BC $.$ It is attached to

opposite wheels at points A and D $.$ The required effective roll rate at the wheels is

$280,000Nm\frac{m}{d}eg$ and the roll rate loss due to rubber $=30\%.$ What vertical force on the

bar would be generated at point A when the wheel attached to point A raises by $1$ mm

and point D falls by $1$ mm $.$ The bar is made of steel, with $E=200$GPa and $v=0\mathrm{.}3.$

b$)$ Determine the bending stress due to the force generated in point $A.$

$30$ pts