Consider the two$-$member frame shown in $($Figure $1).$ Suppose that w$1$

$=2\mathrm{.}6$ kN$/$m

$,$ w$2$

$=1\mathrm{.}3$ kN$/$m

$.$ Follow the sign convention.

Figure$1$ of $1$

The figure shows a frame $\text{'}$A$\text{'}$ B C that is composed of two members pin connected at point B$.$ An L shaped member $\text{'}$A$\text{'}$ B extends upward from a pin supported end at A to the elbow and then bends and extends to the right from the elbow to point B$.$ Point D is marked in the middle of the horizontal segment of $\text{'}$A$\text{'}$ B$,1\mathrm{.}5$ meters from its ends. A member B C extends downward from B to a pin supported end at C$,$ which lies on the same horizontal line with A$.$ Point E is marked in the middle of B C$,1\mathrm{.}5$ meters from its ends. The vertical segment of $\text{'}$A$\text{'}$ B bears a distributed loading acting to the right that decreases linearly from w subscript $1$ at $\text{'}$A$\text{'}$ to $0$ at the elbow. The member B C bears a uniform distributed loading w subscript $2$ acting to the left.

Part A

Determine the normal force at point E

$.$