How to Calculate and Draw Shear and Bending Moment Diagrams

These instructions will help you to calculate and draw shear and bending moment diagram, as well as draw the resulting deflection. Knowing how to calculate and draw these diagrams are important for any engineer that deals with any type of structure because it is critical to know where large amounts of loads and bending are taking place on a beam so that you can make sure your structure can hold the load. There are a few different ways to find your diagrams, but this one is the easiest to lay out, explain, and understand. When you first start the diagrams they can take awhile to calculate and draw, but as you get better the time will be significantly reduced. With the help of these instructions and some practice you will be able to calculate and draw these types of problems quickly and with ease.

Step 1: Materials

To complete a shear force and bending moment diagram neatly you will need the following materials.
     - Ruler or straight edge
     - Pencil
     - Eraser
     - Calculator

Step 2: Step 1: Knowing Forces Effect on Beams

- Knowing how different forces effect beams is important to be able to calculate the shear and bending moments.
- A point force will cause a rectangular shear and a triangular bending moment.
- A rectangular distributed load will cause a triangular shear and a quadratic bending moment.

Step 3: Step 2: Find Reactions Using Moment Equations

- Take a moment about some point that will allow you to find one of the resultant forces.
- You may need to use two equations to find two different forces.

Step 4: Step 3: Find Reactions Using Sum of Forces

- Find your remaining resultant forces using the sum of the forces in the x and y directions.

Step 5: Step 4: Analyze Structure to See How Forces Affect Shear

- Only forces perpendicular to the beam cause a shear.
- Point forces create rectangular shear.
- Rectangular distributed forces create triangular shear.

Step 6: Step 5: Draw Shear Diagram

- Using the calculated forces and analysis draw your shear diagram.

Step 7: Step 6: Determine How Shear Diagram Will Effect the Bending Diagram

- Rectangular shear areas will cause a triangular bending.
- Triangular shear areas will cause a quadratic bending.

Step 8: Step 7: Calculate the Area Under Shear Curves

- For rectangular areas multiply the height by the length.
- For triangular areas multiply the height by the length and divide by 2 (equation for the area of a triangle).

Step 9: Step 8: Draw the Bending Moment Diagram

- Knowing the area under curve and your analysis, draw the bending moment diagram.

Step 10: Step 9: Indicate Curvature on the Bending Moment Diagram

- Consider the physical reaction of forces.
- The beam will bend in the direction of the shear.

Step 11: Step 10: Draw Deflection

- Knowing your curvature, draw a rough deflection diagram.
- Angles between beams must be conserved.

Step 12: Video

- Here is a video on how to carry out an example shear and bending moment diagrams along with displacement. 

Step 13: Conclusion

Congratulations! You have finished calculating and drawing shear and bending moment diagrams as well as an approximate deflection diagram. This will help you become better at calculating all typed of these problems, and you will certainly be ahead of the curve the next time you need to know how to do this.