We were discussing meaning and importance of Shear force and bending moment and sign conventions for shear force and bending moment in our recent posts. We have also discussed the basics of shear force and bending moment diagrams during our previous posts.
Today we will see here the concept to draw shear force and bending moment diagrams for a cantilever beam with a point load or force acting at free end with the help of this post.
Let us consider one beam AB of length L as displayed in following figure. As we can see here that one end of the beam AB is fixed at one end i.e. at A and other end is free i.e. at end B. Therefore, we can say that we have one cantilever beam here and we will have to find the method to draw shear force and bending moment diagram.
Let us consider that a point load W is acting at free end of the cantilever beam as displayed in following figure.
Let us consider one section XX at a distance x from free end i.e. from end B. Now we will have two portion of the beam AB i.e. left portion and right portion. Let us deal with the right portion here; you can also go with left portion of the beam in order to draw shear force and bending moment diagram.
Shear force diagram
Let us assume that FX is shear force and MX is the bending moment at section XX. Shear force at section XX will be equal to the resultant force acting to the right portion of the section. We will recall here the sign conventions for shear force and bending moment and we can conclude here that resultant force acting to the right portion of the section will be W and it will be positive.
Therefore, shear force at section XX will be as mentioned here
FX = W
As we have seen in our post “Basics of shear force and bending moment diagrams” that if there will not be any load between two points then shear force will be constant. Following figure shows here shear force diagram.
Bending moment diagram
Bending moment at section XX will be written as
MX = - W. x
Above equation indicates that bending moment will follow here the linear equation.
Again if we will recall sign conventions for shear force and bending moment, we will conclude here that bending moment at section XX will be negative.
Bending moment will be directionally proportional with the distance x and we can secure here the value of bending moment at point A and at point B as mentioned here.
Bending moment at free end i.e. at B, value of distance x = 0
Bending moment at fixed end i.e. at A, value of distance x = L
MB= - W.L
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Strength of material, By R. K. Bansal
Image Courtesy: Google
We will see another important topic i.e. concept to draw shear force and bending moment diagrams for a cantilever beam with a uniformly distributed load in the category of strength of material.