irning Goal: $$

calculate internal forces in structural members under different loading and port conditions.

design a structural member, it is necessary to know the resultant forces and nents within the member to ensure the material will be able to support the ling. The method of sections is used to determine internal loadings isider the cantilever beam shown in the image below. $($Figure $1)$

e internal loadings acting on the beam at $B$ are to be determined, we make maginary cut at section $a-$a perpendicular to the axis of the beam and arate the beam into two segments. The internal loadings at $B$ then become ernal on the free$-$body diagram of each segment, as shown in the image w: $($Figure $2)$

force component $N_B$ acting perpendicular to the cut, or parallel to the axis ne beam, is called the normal force; the force component $V_B$ acting jentially to the cut, or perpendicular to the axis of the beam, is called the ar force; the couple moment $M_B$ is called the bending moment. The forces moments acting on the two segments act in opposite directions, as uired by Newton's third law, and can be determined by applying the ilibrium equations to the free$-$body diagram of either segment. Provided the ctural member is homogeneous and is not irreversibly deformed, these fings can be considered to act at the centroid of the member's crossion. The customary sign conventions are to say the normal force is positive creates tension, the shear force is positive if it causes the beam segment to te clockwise, and a bending moment is positive if it causes the beam to d concave upward. Oppositely$-$acting loadings are considered negative.

Part A $-$ Internal Loading Due to a Variable, Distributed Load

Consider the cantilever beam and loading shown in the image below where $d=11\mathrm{.}0ft,w_B=790l\frac{b}{f}t,$ and $w_A=350l\frac{b}{f}t.($Figure $3)$

Determine the magnitudes of the internal loadings on the beam at point $C.$

Express your answers, separated by commas, to three significant figures.

View Available Hint$($s$)$

$N_C=V_C=M_C=$

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Part B $-$ Internal Loading on a Semicircular Member

Consider the semicircular member and loading shown in the image where $d=0\mathrm{.}510m$ and $F=45\mathrm{.}0N.($Figure $4)$

Determine the magnitudes of the internal loadings on the beam at point $B.$

Express your answers, separated by commas, to three significant figures.

View Available Hint$($s$)$

$N_B=V_B=M_B=,N,N,N*m$

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