Question

Problem 5: Determine the equations of the elastic curve, v(x), for the beam using the xi and x2 coordinates Specify the beam's maximum deflection. El is constant. x1 2 2a

Answer 1

(P) (a) = (RB) (3) (P)/3 = RB 2P/3 = RA v(x) = 2P/s rightarrow from A to c v(n) = P/3 rightarrow from B to C Elastic curve equation M = 2P/3(x) +/- (p)(x - a) EI . d^2 /dn^2 = 2P/3 (x)/- P(x - a) EI dy/dx = 2P/3 times n^2/2P + c_1/- -P(x - a)^2/2 EI . dy/dx = Px^2/3 + c_1/- P(x - a)^2/2 EI. y = Px^3/9 + c_1 x + c_2/- P(x - a)^3/6 Elastic curve equation at x = 0, y = 0 c_2 = 0, x = 3a, y = 0 0 = P(3a)^3/9 + c_1 (3a) - P(3a - a)^3/6 c_1 (3a) = P(2a)^3/6 - P(3a)^3/9 == 8 pa^3/6 - 27 Pa^3/9] = Pa^3 [8/6 - 27/9] c_1 (3a) = -6 Pa^3/3 c_1 = -5 pa^2/9 Elastic curve equation E I. y = Px^3/P - 5 Pa^2/9 n/- P(x - a)^3/6 MAX deflection;- Max deflection occur b/w C to b, So slope = 0,