EngineeringManufacturing

Drawing Shear Force Diagrams Effectively

Shear forces are a very common aspect in mechanical engineering to calculate different engineering and physical conditions, especially for beams. When you are making calculations for beams, you will probably need to draw shear force diagrams. 

Here, we explain how to draw shear force diagrams effectively. 

How To Draw Shear Force Diagrams?

Shear force diagrams are generally a prerequisite of bending moment diagrams. But first of all, you need to understand the sign conventions of the shear forces and bending moments. 

Force Equilibrium

On simply supported beams or cantilevered beams, shear forces generally occur radially(perpendicularly) to beam orientation. First of all, you need to build the force equilibrium in the application direction of shear forces. This will give you the reaction forces are the supports or cantilevers. 

After finding all reaction forces on all supports, you can start the draw shear force diagram on that beam.

Drawing Shear Force Diagram

In general, application, drawing shear force diagrams starts from left to right. 

The shear force diagram starts with the reaction of the left-most side of the beam, which can be simply supported or cantilevered. Take a look at the very basic simply supported example below.

Cantilevered beam with a single shear force(Image Source:D. K. Singh – Strength of Materials-Springer, 2020, pg.149)

As you see in the example above, there is a simple shear force application at the right edge of a cantilevered beam. And there must be a positive reaction at the cantilevered side which is the reaction of the left side.
The shear force diagram is drawn with this reaction for up to the shear force application place on the right side. This is the general rule of the shear force diagram drawing. You need to start with the left-most force or reaction to draw the shear force diagram.

Image Source:D. K. Singh – Strength of Materials-Springer, 2020, pg.162

In the example above, if you calculate the reaction force at the left-side simple support. The shear force diagram is started with this reaction. 

What you need to do is when you face a force or reaction like above, you need to add this reaction into the diagram, and you need to go on with the new value of the shear force diagram. 

Check the example above to see that diagram turned to the opposite side, after the shear force application point. This is another important rule. 

If There Is A Evenly Distributed Load?

If your system has an evenly distributed load, the effect of this evenly distributed load is; 

  • If it has the same direction as the shear force diagram, it has a constant increasing effect on the diagram, which will be the inclined shape. 
  • If it has an opposite direction with the shear force, it has a constantly decreasing effect as inclined. 
Image Source:D. K. Singh – Strength of Materials-Springer, 2020, pg.152

You can understand the general rule of it. The reaction force is calculated for the left cantilevered side, and the evenly distributed load has a decreasing effect on the shear force diagram. 

If There Is A Uniformly Varying Load?

The actual effect of this kind of load is the same as the evenly distributed load. But the increment and decrement will have a second-order curve form. Check the example below. 

Image Source:D. K. Singh – Strength of Materials-Springer, 2020, pg.157

You can see the second-order decrement on the shear force diagram. 

Conclusion

In general, all the problems related to the drawing of shear force diagrams depend on these rules. 

Do not forget to leave your comments and questions below about the drawing of shear force diagrams.

Your precious feedbacks are very important to us.

Related Articles

Leave a Reply

Your email address will not be published. Required fields are marked *

Back to top button