Answer :
To determine the slopes and deflections at points A, B, and C using the conjugate beam method,
follow these steps:
1. Identify the supports and loads: Determine the supports and applied loads on the beam. In this case, it seems the beam is simply supported at points A and C, with a concentrated load of magnitude P acting at point B.
2. Determine the reaction forces: Use the equilibrium equations to calculate the reactions at points A and C. Since the beam is simply supported, the reaction at A and C will be half of the applied load.
3. Draw the conjugate beam: Sketch a new beam, called the conjugate beam, with the same dimensions as the original beam. However, replace the applied loads with moments and the supports with springs.
4. Apply the principle of virtual work: Apply the principle of virtual work to determine the slopes and deflections at points A, B, and C of the conjugate beam. This involves considering virtual rotations and virtual displacements.
5. Calculate the slope and deflection: Using the principle of virtual work, equate the virtual work done by the real loads on the original beam to the virtual work done by the equivalent moments on the conjugate beam.
6. Solve for the slopes and deflections: Apply the appropriate equations derived from the conjugate beam method to calculate the slopes and deflections at points A, B, and C of the original beam.
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