Handwritten please

Problem $2$

A frame consisting of a simple span $BD,$ an overhang $AB,$ and a bracket CEF, is supported by a

pin at $B$ and a roller at $D($see Figure $2).$ The beam ABCD has a uniform cross section with a

moment of inertia $I=0\mathrm{.}00025f{t}^4.$ The frame is subjected to a concentrated load $P$ at point $F$ as

shown in the figure. Take $E=32,000$ksi,$L=12ft,a=6ft,$ and $P=900lb.$

a$)$ Draw the shear force and bending moment diagrams of the horizontal section ABCD using

the graphical method. $($Hint: use the method of sections to study CEF first$)$

b$)$ Using the method of superposition, find an expression for the elastic curve $v(x)$ of the

segment $BC.x$ is a horizontal coordinate measured from point of $A.($Hint: select

appropriate cases from the table shown below and use superposition to find $v(x^{\text{'}})$ for $0$

$x^{\text{'}}\frac{L}{3},$ then translate the origin of the coordinate system to point A to get the final expression

in terms of $x).$

c$)$ Using the method of integration, find expressions for the elastic curve $v(x)$ of the segments

$AB$ and $CD.x$ is a horizontal coordinate measure from point of $A.$

d$)$ Plot the elastic curve for the horizontal section ABCD using appropriate computer software.