Problem $1$

For the beam shown,

$(1)$ derive equations for the shear force $V$ and the bending moment $M$ for any location in the beam. $($Place the origin at point $A.)$

$(2)$ use the derived functions to plot the shear$-$force and bending$-$moment diagrams for the beam. Specify the values for key points on the diagrams.

Let $a=7\mathrm{.}0ft,b=8\mathrm{.}7ft,w_a=13$kip$\frac{s}{f}t,$ and $w_b=7$kip$\frac{s}{f}t.$

Derive the equations and construct the shear$-$force and bending$-$moment diagrams on paper and use the results to answer questions $1-5.$

E$.$q$31.$PNG

What is the shear force $($in kips rounded to the nearest whole number$)$ at $x=6\mathrm{.}0ft?-$