Consider the beam shown in $($Figure $1).$ Suppose that $\backslash ($ P$=7\mathrm{.}5\backslash$mathrm$\{$kN$\}\backslash ).$ EI is constant. Solve this problem using the conjugate$-$beam method. Follow the sign convention.

Part A

Select the correct theorems of the conjugate$-$beam method.

Check all that apply.

The displacement $\backslash ($ v $\backslash )$ of a point in the real beam is numerically equal to the shear $\backslash ($ V $\backslash )$ at the corresponding point in the conjugate beam.

The displacement $\backslash ($ v $\backslash )$ of a point in the real beam is numerically equal to the moment $\backslash ($ M $\backslash )$ at the corresponding point in the conjugate beam.

The slope $\backslash (\backslash$theta $\backslash )$ at a point in the real beam is numerically equal to the moment $\backslash ($ M $\backslash )$ at the corresponding point in the conjugate beam.

The slope $\backslash (\backslash$theta $\backslash )$ at a point in the real beam is numerically equal to the shear $\backslash ($ V $\backslash )$ at the corresponding point in the conjugate beam.

Previous Answers

Correct

Part B

Determine the slope at $\backslash ($ A $\backslash ).$

Express your answer using three significant figures.

Part C

Determine the displacement at $\backslash ($ C $\backslash ).$

Express your answer using three significant figures.

$\backslash (\backslash$Delta$\_\{$C$\}=\backslash )$

$\backslash [$

$\backslash$times $\backslash$frac$\{1\backslash$mathrm$\{$kN$\}\backslash$cdot $\backslash$mathrm$\{$~m$\}^\{3\}\}\{$E I$\}$

$\backslash ]$

Figure