The 4 meters long street lamp shown in the figure, changes shape under the influence of gravity and under the change of ambient temperature. (Given: The ambient temperature rises from 20 C to 30 C, thermal expansion coefficient is a = 2x10* 1/"C, young Modulus E = 4x10" Pa, cross sectional area A = 0.01 m, the mass of the lamp miamp = 5 kg, gravitational acceleration g = 10 m/s, density p = 8000 kg /m) |(a) (5P) Model the street bar with a single finite element. (b) (10P) Obtain the global stiffness matrix K. (c) (10P) Define the load vector F, and the boundary condition(s). (d) (15P) Find the displacement value at the midpoint of the lamp using the same finite element model (single finite element). (e) (10P) Find the stress in the element. () (10P) Find the reaction force at the support. mjamp L = 4m