$($Due: November $01,2024)$

Question $1$: $10$ points. The three$-$pin parabolic arch shown in Figure $1$ has a profile shape,

$y(x)=[\frac{4f}{l^2}]x(l-x).$

where $f=4m$ and $l=16m.$

Figure $1$: Elevation view of a parabolic three$-$pin arch.

Questions:

$[1$a$]$ Calculate the horizontal and vertical components of reaction force at A and B$.$

$[1$b$]$ Calculate the internal forces $($i$.$e$.,$ shear, moment and axial forces$)$ at point E$.$

$[1$c$]$ Draw the bending moment diagram.