An closed stringer$-$web cross$-$section is shown in Figure $2.$ The area of stringer #$1,$

#$2,$ and #$3$ is $10$cm $2.$

The cross$-$section shown in the figure is subjected to a vertical shear force Vz $=5000$N in the

positive z$-$ direction as shown. Let Vy $=0.$ The overall dimensions of the cross$-$section are given

in the figure. The shear modulus is G $=27$GPa. Assume that the thin sheets are ineffective in

bending.

a$)$ Determine the location of the centroid C of the cross$-$section. Specify the location of C as

horizontal and vertical distances from stringer #$2.$

b$)$ Determine the moments of inertia $($ Iyy and Izz $)$ of the cross$-$ section $($in which the y$-$z

coordinate system has its origin at the centroid C of the cross section.$)$

c$)$ Find the shear flows q$12,$ q$23,$ and q$31$ on the closed cross section.

d$)$ Find the angle of twist$/$length

e$)$ Find the location of the shear center of the closed section. Figure $2$