The figure $($not drawn to scale$)$ shows a overhanging metallic bar $($supported at A and $C),$ of flexural modulus $EI.$ It is subjected to a point load of amplitude $P$ at $B,$ and UDL load $w$ between points $C$ and $D.$

All distances are multiple of a unit distance $L.$

You are given

the distance between A and $B$ as $2L,$

the distance between $B$ and $C$ as $3L,$

and the distance between $C$ and $D$ as $3L.$

$($The length of the beam is thus $8L.)$

All answers can be expressed in term of fractions timed by functions of $P,w,L$ and $EI.$

a$)$ Calculate the reaction forces at points A and $C,R_A$ and $R_C.$

The answers are to be entered as fractions in the appropriate boxes below.

b$)$ Calculate the bending moment at point $C{M}_C.$

The answers are to be entered as fractions in the appropriate boxes below. Respect the sign conventions!

$M_C=$

$|PL+,w{L}^2(2$ marks $)||$

c$)$ Calculate the slope at point $A{}_A.$

The answers are to be entered as fractions in the appropriate boxes below. Respect the sign conventions!

${}_A=$

$\frac{P{L}^2}{EI}+$

$\frac{w{L}^3}{EI}(2$ marks$)$

d$)$ Calculate the deflections at point $D{}_D.$

The answers are to be entered as fractions in the appropriate boxes below. Respect the sign conventions!

${}_D=$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{P{L}^3}{EI}+$

$|\frac{w{L}^4}{EI}(2$ marks$)||$