slope of the beam

The slope or deflection at any point on the beam is equal to the resultant of the slopes or deflections at that point caused by each of the load acting separately.
 

Another method of determining the slopes and deflections in beams is the area-moment method, which involves the area of the moment diagram.
 

Problem 617
Replace the load P in Prob. 616 by a clockwise couple M applied at the right end and determine the slope and deflection at the right end.
 

Problem 616
For the beam loaded as shown in Fig. P-616, determine (a) the deflection and slope under the load P and (b) the maximum deflection between the supports.