The beam shown $($Figure $1)$ is supported by a pin at $\backslash ($ A $\backslash )$ and a cable at $\backslash ($ B $\backslash ).$ Two loads $\backslash ($ P$=15\backslash$mathrm$\{$kN$\}\backslash )$ are applied straight down from the centerline of the bottom face. Determine the state of stress at the point shown $($ Figure $2)$ in a section $2$ m from the wall. The dimensions are $\backslash ($ w$=4\backslash$mathrm$\{$~cm$\},$ h$=10\mathrm{.}5\backslash$mathrm$\{$~cm$\},$ L$=0\mathrm{.}8\backslash$mathrm$\{$~m$\},$ a$=1\mathrm{.}5\backslash$mathrm$\{$~cm$\}\backslash ),$ and $\backslash ($ b$=4\backslash$mathrm$\{$~cm$\}\backslash ).$

Learning Goal:

To calculate the normal and shear stresses at a point in a beam subjected to a combined loading.

The state of stress at a point is a description of the normal and shear stresses at that point When a structural element is subjected to multiple kinds of loads, the effects of each can be combined using the principle of superposition, as long as the deflections remain small, the response is elastic, and the material is homogenous.

Figure

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Part B $-$ Normal stress due to bending

The section $2$ m from the wall also has a bending moment, which causes a normal stress at points that are not on the neutral axis. What is the normal stress at the point due to the bending moment? Let a compressive stress be negative.

Express your answer with appropriate units to three significant figures.

$-$ View Available Hint$($s$)$ Part C $-$ Shear stress

The shear force in the beam is also not zero $2$ m from the wall. What is the magnitude of the shear stress in the $\backslash ($ x y $\backslash )-$plane at the given point? Express your answer with appropriate units to three significant figures.

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$\backslash (\backslash$tau$=\backslash )$

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