Problem $1(30$ points$)$

The state of internal load at a specific cross section of a member is shown in the figure.

Find the following cross$-$sectional properties using the dimension given above:

a$)$ the area of the cross$-$section.

b$)$ the location of the neutral axis, N$.$A$.($clearly show it on the pictures above$)$

c$)$ the area moment of inertia of the cross section about the N$.$A$.$

Answer the following questions for the internal loads seen in the $3$D view:

Force $\backslash (\backslash$mathbf$\{$N$\}=10\backslash$mathrm$\{$kN$\}\backslash )$

d$)$ What type of stress does this force create on the cross section $($normal stress vs shear stress$)?$

e$)$ What is the formula for calculating this stress $($clearly define each term represented in the formula$)?$

f$)$ Calculate this stress using the dimensions given above.

Moment M$=15$ kN$.$m

a$)$ What type of stress does this moment create on the cross section $($normal stress vs shear stress$)?$

b$)$ What is the formula for calculating this stress $($clearly define each term represented in the formula$)?$

c$)$ Does the magnitude of this stress change over the cross section? If yes, what lines on the cross section have the maximum and minimum stress $($clearly show these lines on the $3$D view$)?$

d$)$ Calculate the maximum stress using the dimensions given above and your answers to parts b and c$.$

Force $\backslash (\backslash$boldsymbol$\{$V$\}\backslash )$

g$)$ What type of stress does this force create on the cross section $($normal stress vs shear stress$)?$

h$)$ What is the formula for calculating this stress $($clearly define each term represented in the formula$)?$

i$)$ Does the magnitude of this stress change over the cross section? If yes, what points on the cross section have the maximum and minimum stress $($clearly show these lines on the $3$D view$)?$

Note: no need to calculate the magnitude of the maximum stress.