Learning Goal:

In a coplanar structure, the internal loading at a point is composed of a normal force $N,$ a shear force $V,$ and a bending moment $M.$ These internal loads can be determined by analyzing internal sign conventions and applying equilibrium conditions using the following process:

Determine the support reactions for the entire structure.

Keep all loadings exactly as they are specified and pass an imaginary section through the member at the point where the internal loading is to be determined.

Draw a free$-$body diagram of the segment with the least number of loads. At the section, indicate the unknown forces $N$ and $V.$ and moment $M,$ acting in their positive directions $($described below$).$

Use the equations of equilibrium for the segment to solve for unknowns.

For the left$-$hand segment, the sign convention for internal loadings is as follows: the normal force $N$ acts to the right, the shear force $V$ acts downward, and the moment $M$ acts counterclockwise. $($Figure $1)$

igure

$1$ of $4$

Part A $-$ Internal moment

The simply supported bearn shown $($Figure$\mathrm{.}2)$ is subject to loads. $P_1=12kN$ ar Introduction.

Express your answer with appropriate units to three significant figures.

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Part B $-$ Internal shear

The simply supported beam $($Figure $3)$ is subject to loads $P_1=23kN,P_2=8$ convention provided in the Introduction.

Express your answer with appropriate units to three significant figures.

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$V=$

Part C $-$ Internal normal force