Consider a multi$-$celled wing cross$-$section with aerodynamic Lift and Moment acting at the quarter chord. The wing has nonstructural leading edge and trailing edge $($i$.$e$.,$ hashed area is nonstructural$).$ The box$-$beam is composed of $6$ stringers and connecting webs. The web sections all have a constant equivalent thickness.

a$)$ Find the Centroid relative to the primed reference frame shown on the airfoil $[5$ points$].$

b$)$ Find the Area moments of Inertia of the airfoil $[5$ points$].$

c$)$ Write down the equations and process needed to find the shear center location relative to the primed reference frame shown on the airfoil $[10$ points$].$

d$)$ Write down the equations and process needed to find the torsional stiffness of the wing $[10$ points$].$

e$)$ Write down the equations and process needed to find the shear flow in each of the web sections as a function of the lift and moment $[10$ points$].$