Problem $5$:

a$.$ A $5-$m$-$long simply supported timber beam carries two concentrated loads as shown in the figure at top right. The cross$-$sectional dimensions of the beam are shown in the figure below, at right. $($Note: for each part below, draw the stress element in the appropriate plane. Include coordinate axes and label the stresses, showing proper direction and magnitude. Label the location on the diagrams at top$-$right $($or on your own sketches$).)$

b$.$ At section $\backslash ($ a$-$a $\backslash ),$ determine the magnitude of the shear stress in the beam at point $\backslash ($ H $\backslash ).$ If the magnitude of the bending stress at point $\backslash ($ H $\backslash )$ is $1\mathrm{.}3$ MPa $,$ draw a stress element, showing both of these stresses on the same stress element.

c$.$ At section $\backslash ($ a$-$a $\backslash ),$ determine the magnitude of the shear stress in the beam at point $\backslash ($ K $\backslash ).$ If the magnitude of the bending stress at point $\backslash ($ K $\backslash )$ is $2\mathrm{.}2$ MPa $,$ draw a stress element, showing both of these stresses on the same stress element.

d$.$ Determine the location of the maximum shear stress that occurs in the beam at any location within the $\backslash (5-\backslash$mathrm$\{$m$\}\backslash )$ span length. Compute all stresses that occur at that point and draw them on a single stress element.

e$.$ Determine the location of the maximum compression bending stress that occurs in the beam at any location within the $\backslash (5-\backslash$mathrm$\{$m$\}\backslash )$ span length. Compute all stresses that occur at that point and draw them on a single stress element.