A highway sign structure of dimensions 12 ft (L = Length) x 4 ft (H = Height) x 1 ft (D = Thickness) is supported at an elevation of 60 ft (mid-height of the sign). The longer dimension of the sign is parallel to the ground. It is located in an open terrain (zo = 0.23 ft) where the design mean hourly wind speed at the mid-height of the sign can be taken as 60 mph. The generalized mass, frequency and critical damping ratio of the sign structure are 2 slugs. 2 Hz and 0.2%, respectively, calculated with respect to the generalized coordinates at the mid-height of the sign in the directions normal to the sign or along the plane of the sign (along its length). The vertical support of the sign is a single hollow circular section of 6 in. diameter and 0.2 in. thickness. Calculate the following: (a) Steady amplitude of vibration of the sign due to vortex shedding and assess the wind speeds at which it will occur. (b) The peak dynamic response of the sign and hence its peak response (mean plus peak dynamic) due to buffeting for a wind direction normal to the sign at the design wind speed with 92% confidence. (c) The maximum (peak) bending moment and the peak stress at the base of the support structure in both cases (Parts a and b). The axial stress () due to bending of a beam section on its outer surface is given by M.c/I, where M is bending moment on that section about a principal axis, c is the distance of the outer surface normal to this axis. i.e. outer radius of the hollow section of the support, and I is its moment of inertia, I = (4-r)/4 for a hollow section with outer radius ro and inner radius ri. Plot the stress cycles (qualitatively) that the support will see at its base for both VIV (Part A) and buffeting (Part B). The Aerodynamic Admittance Function for drag of a flat plate of area A is given as x(K) == 1 OA where K is the reduced frequency, A = projected 4/3 U K 1+ area of the plate normal to the wind.