P Problem #1 The cantilever beam in Fig. la has a constant moment of inertia I and a constant Modulus of Elasticity E. T

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P Problem 1 The Cantilever Beam In Fig La Has A Constant Moment Of Inertia I And A Constant Modulus Of Elasticity E T 1 (77.68 KiB) Viewed 35 times

P Problem #1 The cantilever beam in Fig. la has a constant moment of inertia I and a constant Modulus of Elasticity E. The beam is fixed at one end and supported by an elastic spring having a constant K at its second end. The beam is loaded by a moment M at its free end x = L. Assume that the deflection is given by the following relation w(x) = ax?, where a is a constant. Use the Rayleigh- Ritz method to evaluate the end deflection (at x = L). Also find the expression for the bending moment along the length of the beam. (b) The same cantilever beam is now subjected to a downward uniformly distributed load p, as shown in Fig. 1b. Assume that the deflection w(x) is given by a similar relation w(x) = bx?, where b is a constant. Use the Rayleigh-Ritz method to evaluate the end deflection (at x = L) and also find the expression for the bending moment along the length of the beam. (c) Assume K = 0. Compare the expression for the bending moment diagrams of both cases (a and b) to the exact ones. Comment on the results. a P. ML E1 E1 L Fig. 1a Fig. 1b Problem #2