Use the graphical method to construct the shear$-$force and bending$-$moment diagrams for the beam shown. Let $a=5\mathrm{.}0m,b=3\mathrm{.}0$ Determine the shear force acting at each of the following locations:

$($a$)x=0+m($i$.$e$.,$ just to the right of point A$)$

$($b$)x=5\mathrm{.}0m$

$($c$)x=8\mathrm{.}0-m($i$.$e$.,$ just to the left of $C)$

$($d$)x=8\mathrm{.}0+m($i$.$e$.,$ just to the right of $C)$

When entering your answers, use the shear force sign convention.

Answers:

$($a$)V=$

i

$kN.$

$($b$)V=$

i

$kN.$

$($c$)V=$

$kN.$

$($d$)V=$

$kN.$ The shear$-$force diagram crosses the $V=0$ axis between points A and $B.$ Determine the location $x_c($measured from $A)$ where $V=0$

$kN.$

Answer: $x_C=$

i

$m.$

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Attempts: unlimited

Part $4_{?}$

Determine the bending moment acting at each of the following locations:

$($a$)x=0+m($i$.$e$.,$ just to the right of $A)$

$($b$)x=x_c($the value calculated in part $3)$

$($c$)x=5\mathrm{.}0m$

$($d$)x=8\mathrm{.}0m$

When entering your answers, use the bending moment sign convention.

Answers:

$($a$)M=$

$kN-m.$

$($b$)M=$

$kN-m.$

$($c$)M=$

$=$

$kN-m.$

$($d$)M=$

$kN-m.$

$m,c=2\mathrm{.}5m,w_{AB}=80k\frac{N}{m},w_{CD}=40k\frac{N}{m},$ and $M_A=165kN-m.$ Construct the shear$-$force and bending$-$moment diagrams on

paper and use the results to answer the questions in the subsequent parts of this GO exercise.

Calculate the reaction forces $A_y$ and $C_y$ acting on the beam. Positive values for the reactions are indicated by the directions of the

red arrows shown on the free$-$body diagram below. $($Note: Since $A_x=0,$ it has been omitted from the free$-$body diagram.$)$