How to draw a shear force diagram - 02

In the previous lecture, A simple example of SFD for a point load was explained. Today we will learn how to draw shear force diagram for uniformly distributed load (UDL) for a simple beam. Figure 1 shows a simple beam with a P lb/ft uniformly distributed load. The reactions are calculated and place at A and C point. 

Figure 01

It is mentioned in the previous lecture that drawing of SFD should be started from the left side and it is seen that at A point, a upward load (reaction) is present. Hence the figure 2 is drawn at A point. Note that the upward load is considered as positive shear.

Figure 02

Now, it is seen that between A and B, there is a uniform load available. The point is how to draw SFD for Uniformly distributed load? Uniformly distributed load is nothing but a load acting per unit length. Consider figure 03, starting form the left, at the beginning point there is a 1 unit shear. When, 2nd line is considered, the total shear is 2 unit. The point is the more distance the more shear (UDL*distance). So the shear would be downward and UDL will be multiplied by distance.

Figure 03

Using the above mentioned techniques, the SFD between A and C can be drawn. We have a shear load of PL/2 at A point. So the shear at C point would be PL/2-P*L=-PL/2 [See figure 4]. If any point load is placed at B point or other, than the shear should have been drawn between the starting point and that particular point . 

Figure 04

Finally at point C, it is seen a upward load (PL/2) is available. Hence the calculation of shear of that point will be,  -PL/2 + PL/2 = 0 (figure5). 

Figure 05

 

For getting the lecture of drawing SFD for a point load please follow the link.