Question

the area of the Shear Force diagram is equal to

Answer 1

Step 1:

After you calculate the reactions at supports at A and B, start the Shear Force Diagram at the first value of the force acting on the beam. In this case it is a +10kN due to the reaction at point A:


Step 2:

Keep moving across the beam, stopping at every load that acts on the beam. When you get to a load, add to the Shear Force Diagram by the amount of the force. In this case we have come to a negative 20kN force, so we will minus 20kN from the existing 10kN. i.e. 10kN - 20kN = -10kN.


Step 2 (Repeated):

Moving across the beam again, we come to another force; a positive 10kN reaction at support B. Again, add this +10kN to the shear force diagram (which is currently at -10kN) which will bring us to a shear force of 0. Since we are at the end of the beam, we will go no further and we have our final Shear Force Diagram (SFD)

Things to keep in mind:

The area under the SFD above the x axis should equal the area between the x-axis and the SFD below the x axis. i.e the area should sum to zero. Check this is true in our above example.

Any points where the SFD cross the x-axis, will be a max or min Bending Moment

The SFD should always equal zero at both ends

Answer 2

Is equal to bending moment at any point along the beam