(It is to be noted that the
. The negative sign is because of the slope being in the clockwise direction. As per sign convention a positive slope is in the anti-clockwise direction)
The deflection at the centre of the beam can be obtained with the help of the second moment area theorem between points A and C i.e.
(downward direction)
Example 4.2 Using the moment area method, determine the slope at B and C and deflection at C of the cantilever beam as shown in Figure 4.3(a). The beam is subjected to uniformly distributed load over entire length and point load at the free end.
Solution: The moment curves produced by the concentrated load, W and the uniformly distributed load,w are plotted separately and divided by EI (refer Figures 4.3(b) and (c)). This results in the simple geometric shapes in which the area and locations of their centroids are known.
Since the end A is fixed, therefore,
. Applying the first moment-area theorem between points A and C
(negative sign is due to hogging moment)
(clockwise direction)
The slope at B can be obtained by applying the first moment area theorem between points B and C i.e.
. The negative sign is because of the slope being in the clockwise direction. As per sign convention a positive slope is in the anti-clockwise direction) 
(downward direction)
. Applying the first moment-area theorem between points A and C 
(negative sign is due to hogging moment) 
(clockwise direction)
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