Prof.Kodali Srinivas

Problem no: 1 Find the Slope at the supports and deflection at the center of the beam shown in fig.  The conjugate beam is also simply supported beam with M/EI diagram as a Loading diagram. There fore the Reactions at supports,  Ra and Rb = 1/EI xTotal load on conjugate beam/2  Ra = Rb = (2x4 + 2x2/2)/ 2EI = 5/EI  The Shear Force at Supports = Ra and Rb  There fore the Slope at the supports = 5 /EI   The B.M. at the Mid point in the conjugate beam = Deflection at mid point.  EI x Mc = 5x2.5 - 1/2x2x1x(2+1/3) - 2x2x1 = 6.167 yc = 6.167/EI  Problem no: 2 Determine the Slope and Deflection at free end of the cantilever beam as shown fig. S olution: The conjugate beam of the actual beam is shown in Figure 4.8(b).  A linearly varying distributed upward  elastic load  with intensity equal to zero at  A, and equal to  PL/EI  at  B.  The free-body diagram for the conjugate beam is shown in Figure.  The reactions at  A  of the conjugate beam are given by

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