Consider the following homogeneous beam with triangular cross-section. The beam is of length L. and is made of a material of stiffness E, density p and Poisson's ratio v. It is subjected to the effect of gravity (use g for the acceleration of gravity acting in the negative z-direction) and a varying tangential loading applied on its top surface (Figure 1) q(x) = qo (1) where 4 is given is Pa. The torsional and linear springs have a stiffness of K and k, respectively. q(x) Coco cross-section gring Figure 1 a) Write down the BVP describing the axial displacement u(x), and the transverse deflections v(x) and w(x) for this problem. Write only the relevant equations (i.e., the equations for the non-zero displacements) and explain why the other displacements are zero. You do not need to compute the geometrical quantities such as moments of inertia (unless they are obviously zero), but you need to explain how you would compute them. b) Solve the equation for the axial displacement u and put your solution in a non-dimensional form. c) Explain what to expect for the axial displacement of the end of the beam when the stiffness k of the linear spring (at x-I) goes to infinity. Then show that your solution found in b) matches your expectation.