Shear Forces and Bending Moment Diagrams

Beams play an important role in the life of humans. Different types of beams can be seen everywhere daily. Different types of beams are used for different purposes. Some beams are used to support weight, some beams are used to connect two objects. In mechanical engineering, beams play an important role because beams can be used in different types of machinery. The concept of shear force and bending moment are applied on beams. Following is a detailed description of shear force and bending moment. 

Definition of Shear force and bending moment

Shear forces can be explained by stating that it is the algebraic sum of all vertical forces. It can be applied on the right or the left side of the respective section. 

The bending moment can be explained by stating that it is the algebraic sum of all the moments of every force that are present on the left or right side of the section. 

What is the sign convention of shear force and bending moment?

Sign convention of shear force:

One easy sign convention must be remembered, that is, the section present on the right side where the external force acts in the direction moving upward is considered to be negative. Therefore, the right side of a convention is always negative. Similarly, it is obvious that when a downward force acts on the right side of the same section, it is considered to be positive. However, the same thing goes in reverse when the left side of the section is taken into consideration. 

(A Shear force that rotates a beam in an anti-clockwise direction is considered to be positive and vice versa)

Sign convention of the bending moment:

The moment that is internal resistive at a section, will make the beam sag or sink or droop down. It is considered to be positive. One dropped beam will form a structure that is called concave curvature on the top side. Hence, a convex curvature will form at the lower part. Opposite to this, an internal resistive moment that will result in hogging up the beam will be considered as negative. Opposite to the positive structure, a hogged beam will depict a concave curvature at the bottom and a convex curvature at the top. 

Definition of Shear force diagram and bend moment diagram

After the aforementioned discussion it can be understood that at a specific section taken on a beam that is loaded, a couple of internal forces could be imagined, namely, the bending moment and the shear force. It can also prevail that the amount of bending moment and shear force are different depending on the cross-sections over the beam. When a diagram is made which signifies variation of shear force and bending moment on a beam it is known as shear force diagram and bending moment diagram. Such a diagram helps to graphically visualize and determine the location of the maximum bending force and the maximum shearing force. This diagram also helps in calculating the highest shear stress and the highest bending stress that has been put on a beam at a given point in time. The graphic representation also assists in estimating the qualitative shape of the axis of a beam that is deflected.

Conclusion

As beams are an important part of mechanics, a proper understanding of how beams work and how much force can be applied on a beam would help an engineer in making an appropriate beam for a given situation. The shear force diagram and bending moment diagram helps in ascertaining the exact location of the section where the maximum amount of shear force and bending moment is being applied on a given beam. Therefore, a student who aspires to become a mechanical engineer must have a proper understanding of beams. A student must learn how to study the graphical representation of shear force and bending moment. To crack competitive examinations, a proper understanding of shear force and bending moment diagram is also required.