The lower ends of the members of a 4-bar pined-joint truss shown in the figure below are fixed in the x-y plane and a load is applied at the upper joint. The (x,y,z) coordinates of the base points A, B, C, D and the load point O are (8,0,0), (0,10,0), (-8,0,0), (0,-5,0), and (0,-20,20) respectively. P 0 12 A 2 B P The relative cross sectional areas of the members are A = 1/2, A2 = 1, A3 = A4 = 14. The bars have an axial stiffness k =AE. The load P applied at point O causes a displacement at O, d=(0,v,w). (i) Write the equilibrium equations for the truss in terms of the displacements v and w. (ii) Determine the loads in the truss members in terms of the load P and the modulus E.