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...
Lecture Notes