Show transcribed image text Problem 2. A beam of rectangular cross section has sudden changes in sid

Show transcribed image text Problem 2. A beam of rectangular cross section has sudden changes in side dimension from 2d to d and in Young modulus from E1 to E2 at position B as shown in Fig. 1. It is fixed at one end (position A) and loaded by a bending moment M at the other end (position C). The length between A and B is L1 and between B and C is L2. The deformation in the beam is linearly elastic. i) Find the deflections of VB and VC at positions B and C, respectively, in terms of M, d, L1, L2, E1, and E2. ii) If the ratio L1/L2 = 2, what should the ratio E1/E2 be for the segments AB and BC to have the same deflection, i.e. vc = 2 VB? iii) Plot the normal stress distribution along the vertical direction on two cross sections, one in segment AB and the other in segment BC. iv) For the E1/E2 that satisfies the condition in ii), compare the maximum normal stresses on the two cross sections in iii).

 

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