Consider a reinforced concrete circular plate characterized by a 4 in thickness and a 16 ft radius. The plate is fixed at the boundary and subjected to its own weight and a superim- posed dead load of 20 psf. Assume a concrete compressive strength fr modulus E = 4,000 ksi, and a Poisson's ratio v = = 0.18. 1. Derive the governing equations for this problem. = 4 ksi, an elastic 2. Integrate the governing equations with appropriate boundary conditions. 3. For a factored load, compute analytically, and plot as function of the radial position, the following quantities: deflection, rotation, bending moments, and shear force. 4. Perform the analysis of the plate by using any finite element software; compare the analytical maximum deflection with the finite element solution for different mesh re- finements. 5. Find the location and magnitude of the maximum positive and negative bending mo- ments. 6. Design a square-grid steel reinforcement for positive and negative moments using grade 60 rebar.