We were discussing meaning and importance of shear force and bending moment and also some basic concepts of strength of materials
in our recent posts. We have already seen the various types of beams and different types of loads on beam during our previous posts.

Today we will see here the sign conventions for
shear force and bending moment diagram in subject of strength of materials with
the help of this post.

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**Sign
conventions for shear force**

Let us consider that we have one beam AB and we have assumed one section XX as displayed in following figure. Now we will understand here that what sign conventions will be used here for shear force.

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*Shear force at a section will be positive *

*Shear force at a section will be positive*

Shear force at a section will be considered as
positive if resultant of the forces to the left of the section is in upward
direction.

Shear force at a section will be considered as
positive if resultant of the forces to the right of the section is in downward direction.

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*Shear
force at a section will be negative *

*Shear force at a section will be negative*

Shear force at a section will be considered as negative
if resultant of the forces to the left of the section is in downward direction.

Shear force at a section will be considered as negative
if resultant of the forces to the right of the section is in upward direction.

###
**Sign
conventions for bending**

Let us consider that we have one beam AB and we have
assumed one section XX as displayed in following figure. Now we will understand
here that what sign conventions will be used here for bending moment.

###
*Bending
moment at a section will be positive *

*Bending moment at a section will be positive*

Bending moment at a section will be considered as
positive if bending moment to the left of the section is in clockwise direction
and bending moment to the right of the section is in anti-clockwise direction.

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Such type of bending moment will also termed as hogging
bending moment.

Such type of bending moment will also termed as
sagging bending moment.

In other words, we can also say that bending moment at
a section will be considered as positive if the bending moment at that section
will tend to bend the beam in a curvature having concavity at the top.

###
*Bending
moment at a section will be negative *

*Bending moment at a section will be negative*

Bending moment at a section will be considered as negative
if bending moment to the left of the section is in anti-clockwise direction and
bending moment to the right of the section is in clockwise direction.

Similarly, we can also say that bending moment at a
section will be considered as negative if the bending moment at that section
will tend to bend the beam in a curvature having convexity at the top.

Above figure indicates the condition of positive
bending moment and negative bending moment. We can easily see that in case of
positive bending moment, beam will be bent in a curvature with concavity at the
top.

We can also see that that in case of negative
bending moment beam will be bent in a curvature with convexity at the top.

Do you have any suggestions? Please write in comment
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**Reference:**

Strength of material, By R. K. Bansal

Image Courtesy: Google

We will see another important topic i.e. basics of shear force and bending moment diagrams in the
category of strength of material.