Consider the beam shown in $($Figure $1).$ Use the conjugate$-$beam method. Take $\backslash ($ E$=200\backslash$mathrm$\{$GPa$\},$ I$=550\backslash$left$(10^\{6\}\backslash$right$)\backslash$mathrm$\{$mm$\}^\{4\}\backslash ).$ Suppose that $\backslash ($ P$=30\backslash$mathrm$\{$kN$\}\backslash ).$

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 shear $\backslash ($ V $\backslash )$ 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.

Previous Answers

Correct

Part B

Determine the slope at $\backslash ($ B $\backslash )$ measured counterclockwise from the positive $\backslash ($ x $\backslash )$ axis.

Express your answer using three significant figures.

$\backslash [$

$\backslash$theta$\_\{$B$\}$

$\backslash ]$

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Part C

Determine the maximum displacement of the beam measured upward.

Express your answer to three significant figures and include the appropriate units. Enter positive value if the displacement is upward and negative value if the displacement is downward.

Figure