Question

(b) State the importance of deflection analysis in structural design. Determine the vertical deflection at A for the beam (shown in Fig. 1b) using the Method of Superposition. El is constant for the beam. The support at B is a roller while the support at C is a pin. (8 Marks) 20 KN 20kN/m 40 kNm Fig. 1b

Show solution for this assignment question

Answer 1

In simple words method of super position is which we consider each individual type of load and its action at one of a time and combined action is considered at last. Here 2 types of loads are active 1 Udo 2 Moment 3 Point load Let�s divide into 3 parts and \.\n null Reaction be R_e & R_e at B & C sigma M_c = 0 R_B times 10 - 20 times 15^2/2 + 20 times 5^2/2 = 0 R_B = 200 kN R_C = 200 KN BM at centre M = R_B times 5 - 20 times 10^2/2 = 0 = zero So no deflection occurs at centre & centre = 0 M_A = 0 So no deflection at A & A = 0 \.\n null B M_B = 20 times 5 times 5/2 = 250 KN - m Apply conjugate been method delta_a = M_A = 2/3 times 250/EI times 5 times (5 times 5/8)