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.Â

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.

### 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.Â

#### 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.

#### 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 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.
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 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.

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

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.Â

We will see another important topic i.e.Â in the category of strength of material.Â

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### Reference:

Strength of material, By R. K. BansalÂ