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 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 F

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.

_{X}is shear force and M_{X}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

F

_{X}= 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

M

_{X}= - 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

M

_{B}= 0
Bending moment at fixed end i.e. at A, value of
distance x = L

M

_{B}= - W.L
Do you have any suggestions? Please write in comment
box

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**Reference:**

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.