a$)$ In the expression above, $u(x)$ provides the vertical deflection of a beam due to a

constant downward$-$pointing distributed load $w$ as shown in the diagram, and can

be derived from integrating the shear and moment that you know how to solve for.

What will be the deflection at the middle of the horizontal beam $(x=5m)?L$ is

the length of the beam, $E$ is the Young's modulus, and I is the second moment of

area. $($You don't have to do any force or moment balances to solve this problem$).$

b$)$ The two supporting columns will fail through buckling if the force applied to

them is greater than $P_{cr}.$ Find the effective load on the top beam and solve for

the reaction forces due to the pin and roller. Those reaction forces will be the

forces on the two columns. How tall $(H)$ can the columns be before that reaction

force causes the columns to buckle?