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 conj...
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