Review

Express your answer with appropriate units to three significant figures.

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Learning Goal:

In a coplanar structure, the intemal 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 equitibrium conditions using the following process:

Determine the support reactions for the entire structure.

Keep all loadings exactly as they are speclfed 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.

Figure

$3$ of $4$

Previous Answers

Correct

By using the centroid of the section as the point for summing the moments, the normal force and shear force do not appear in the equation. Once you know the support reactions, you can calculate the moment. Because the result is positive, it means the top of the beam is in compression and the bottom of the beam is in tension.

Part B $-$ Internal shear

The simply supported beam $($Figure $3)$ is subject to loads $P_1=20kN,P_2=12kN,$ and $w=1\mathrm{.}4k\frac{N}{m}$ as shown. What is the internal shear force at point $C?$ Use the standard sign convention provided in the Introduction.

Express your answer with appropriate units to three significant figures.

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$V=$