For the simply$-$supported beam shown below:

$($a$)$ Write the reactions in terms of the variables $P,a,L.$

$($b$)$ Sketch the shear and moment diagrams and the deflected shape.

$($c$)$ Derive expressions for the shear $V(x)$ using equilibrium of a section of the beam. You will need one expression for $M(x)P,a,La.$ Algebraically simplify $an\frac{d}{o}r$ factor your answer.

$(e)$ Calculate the maximum values $of$ shear and moment $in$ terms $of$ the variables $P,a,L.$

$(f)If$ necessary revise your sketches from part $(b),$ based $on$ the results derived $in$ parts $(d)$ and $(e)\mathrm{.}0,$ and another for $a.$ Algebraically simplify $an\frac{d}{o}r$ factor your answer.

$(e)$ Calculate the maximum values $of$ shear and moment $in$ terms $of$ the variables $P,a,L.$

$(f)If$ necessary revise your sketches from part $(b),$ based $on$ the results derived $in$ parts $(d)$ and $(e).a.$ Algebraically simplify $an\frac{d}{o}r$ factor your answer.

$(d)$ Derive expressions for the moment $M(x)$ using equilibrium $of$ a section $of$ the beam. You will need one expression for $0,$ and another for $a.$ Algebraically simplify $an\frac{d}{o}r$ factor your answer.

$(e)$ Calculate the maximum values $of$ shear and moment $in$ terms $of$ the variables $P,a,L.$

$(f)If$ necessary revise your sketches from part $(b),$ based $on$ the results derived $in$ parts $(d)$ and $(e)\mathrm{.}0,$ and another for $a.$ Algebraically simplify $an\frac{d}{o}r$ factor your answer.

$(d)$ Derive expressions for the moment $M(x)$ using equilibrium $of$ a section $of$ the beam. You will need one expression for $0,$ and another for $a.$ Algebraically simplify $an\frac{d}{o}r$ factor your answer.

$(e)$ Calculate the maximum values $of$ shear and moment $in$ terms $of$ the variables $P,a,L.$

$(f)If$ necessary revise your sketches from part $(b),$ based $on$ the results derived $in$ parts $(d)$ and $(e).$