QUESTION $1$

A compressive load $P$ is transmitted through a rigid plate to three magnesium$-$alloy bars that

are identical except that initially the middle bar is slighly shorter than the other bars $($See

Figure Q$1).$ The dimensions and properties of the assembly are as follows:

Length $L=1m,$ cross$-$sectional area of each bar $A=3000m^2,$ modulus of alasticity

$E=45$GPa, and the gap $s=1mm.$

Questions:

Calculate the load P$1$ required to close the gap.

Calculate the downward displacement d of the rigid plate when $P=400kN.$

Calculate the total strain energy $U$ of the three bars when $P=400kN.$