Problem $3$

The shown beam has the given channel section that has its centroid at a distance of $\backslash (\backslash$mathbf$\{59.09$ ~ m m$\}\backslash )$ from the top surface and its centroidal second moment of area $\backslash ($ I$\_\{$z$\}=\backslash$mathbf$\{42.26\}*10^\{6\}\backslash$mathrm$\{$~mm$\}^\{4\}\backslash ).$ You are required to:

i$-\backslash (\backslash$quad $\backslash )$ Determine the shearing stress in the $8$ mm diameter pin at point C $.$

ii$-$ Determine the bearing stress at the pin at C $.$

iii$-$ Plot the internal reaction diagrams.

iv$-$ Determine the maximum tensile and compressive stresses due to bending and show their locations.

v$-$ Determine the maximum transverse shear stress and its location