Problem #$2$: $(15$ points$)$ An unsymmetric single$-$celled stringer$-$web cross section is shown in

Figure $2.$ Each stringer has a cross sectional area A$.$

The y $-$ z coordinate system $($not shown in the figure$)$:

has its origin at the centroid C of the cross section $($location to be determined$)$;

in which the y$-$axis is horizontal $($and positive to the right$)$; and

in which the z$-$axis is vertical $($and positive upward$).$

Note: please do the following calculations very carefully because you will need the results in

Problems #$3$ and #$4.$

a$)$ Determine the horizontal and vertical locations of the centroid of the cross section. Express

your answers as horizontal and vertical distances from the lower left stringer #$3.$ Express

your results in terms of h$.$

b$)$ Calculate the moments of inertia I$\_($yy$),$I$\_($zz$),$ and I$\_($yz$)$ of the cross section. Express the results in

terms of A and h$.$

The cross section in Figure $2$ is subjected to a non$-$zero bending moment

M$\_($y$)=10$kN$-$m $($not shown in the figure$)$ with bending moment M$\_($z$)=0.$ The y$-$z coordinate system

is as described in Problem #$2.$ Each stringer has an area A$=\mathrm{.}002$m$^(2),$ and the length h$=1\mathrm{.}2$m$.$

a$)$ Use the results of Problem #$1$ to calculate the numerical values of the moments of inertia I$\_($yy$),$

I$\_($zz$),$ and I$\_($yz$)$ of the cross section.

b$)$ Calculate the bending stresses sigma$\_($xx$)$ at stringers #$3$ and #$4.$ Briefly explain why they are not

equal.

c$)$ Find the neutral axis of the cross section, and draw it clearly in the y$-$z coordinate system.

please show all details