Sign Conventions Of Shear Force And Bending Moment

Most of the people that deal with the mechanics of materials are generally confused with the directions and sign conventions of shear forces and bending moments. 

In calculations, it is very important to assign the direction of forces and bending moments to obtain correct results. We will show you the sign conventions of bending moments and shear forces here. 

Strength of Materials, Third Edition

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Sign Convention Of Shear Forces 

Shear forces are a very important aspect of most engineering mechanics problems. To show the sign convention of shear forces, consider that a beam is loaded with vertical shear forces. 

Illustration of the sign of shear forces on a beam(Image Source: D. K. Singh – Strength of Materials-Springer-2020).

If the right side of the shear force application on the beam is tending to move upwards, the shear force is considered positive. Otherwise, it is considered negative. So, the situation on the left side above, is the positive shear and the right side is the negative shear. 

Sign Convention Of Bending Moments

We will also consider a piece of beam that undergoes bending moment. We will define the sign of bending moment according to the behavior of the beam under this moment. 

Sign conventions of the bending moment on a beam(Image Source: D. K. Singh – Strength of Materials-Springer-2020).

As you see above, there are two situations of bending on beams. At the left side, the beam is bent fromconcave to upward. In this situation, the bending moment is positive. Otherwise which is like the left, bending moment is considered as negative. 


As you see, defining the signs of bending moments and shear forces is very easy. 

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