• 

Q. 2 Consider the beam shown below F = Q(x) L The differential equation for transverse deflection w of the beam is valid for the given problem. d dw ( dx dx-9(x) = 0 a) Write the required nodal variables of element (u). b) Assume the interpolation function such that w = C + x + C3x + Cx Find the nodal variable by using the above interpolation function. c) Write the equations obtained in part (b) in matrix form such that {U} = [A] {C} d) Calculate [A]- using Matlab symbolic programming. (1 mark) (2 marks) (2 marks) (2 marks) e) Calculate the shape functions by {N} = {X} [A]- f) Plot the value of shape functions for 0 x 1. Take L = 1 for plotting g) Calculate the local stiffness matrix [K]e -Le [K]e = [] dx h) Calculate the local force vector {F}e Le = ["" N S 0 {F}e = []dx N F dx