Guide to Drawing Shear Force Diagram from Bending Moment Diagram

Understanding how to draw a shear force diagram (SFD) from a given bending moment diagram (BMD) is crucial in structural analysis. This guide will walk you through a step-by-step process to accurately plot the SFD. Whether you're an undergraduate student, a practicing engineer, or a hobbyist interested in structural engineering, this will provide the necessary tools to make your calculations more precise.

Steps to Draw Shear Force Diagram from Bending Moment Diagram

To draw a shear force diagram from a given bending moment diagram, follow these detailed steps:

1. Identify Sections

The first step is to divide the structure into sections based on where the loads and supports are applied. This division will help you analyze the shear force in each segment of the beam. Remember, the choice of sections will directly impact your understanding of the shear forces.

2. Determine the Bending Moment Values

The second step involves noting the bending moment values at key points along the beam from the BMD. Key points typically include the supports, points of load application, and other critical points where the bending moment changes.

3. Calculate Shear Force Changes

To calculate the shear force changes, recognize that the shear force changes are related to the slope of the bending moment diagram. The relationship can be expressed as:

V dM/dx

where V is the shear force and M is the bending moment. This means that:

If the BMD is linear, the shear force will change uniformly. If the BMD has a curve, the shear force will change non-linearly.

4. Apply the Relationships

At Points of Zero Moment

At points where the bending moment is zero (or changes from positive to negative or vice versa), the shear force will typically be at its maximum or minimum values. This is a critical point to mark on your SFD.

At Points of Applied Loads

At points where a load is applied, the shear force will change by the magnitude of the load. For upward loads, the shear force increases, and for downward loads, it decreases. This relationship is essential for capturing the dynamic changes in shear force across the structure.

5. Construct the Shear Force Diagram

Start from One End of the Beam

Begin your SFD by plotting the shear force values at the key points identified in the previous steps. Use the following method:

Start from one end of the beam. Plot the shear force values at the key points. Connect the points with straight lines if the changes are uniform or curves if they are non-linear.

6. Check the Diagram

Ensure Correct Values at End Points

Make sure that the SFD starts and ends at the correct values. For example, in a simply supported beam, the shear force is usually zero at the free ends.

Verify Changes Correspond to Loads and Moments

Confirm that the changes in shear force accurately reflect the applied loads and moments. This step helps in verifying the integrity of your calculations.

Example

Consider a simple example to illustrate the process. Suppose you have a beam with the following BMD values at points A, B, C, and D:

A: 0 kNm B: 10 kNm C: 5 kNm D: 0 kNm

Calculate Shear Forces

Between A and B: If the moment increases, the shear must be positive.

At B (point of load): Subtract the load value from the shear force.

Between B and C: The shear force will change due to the change in BMD.

At C (point of load): Again, subtract the load value from the shear force.

Plot Points and Connect

Start from A and note the shear force at B, C, and D. Connect the points with straight lines or curves as appropriate.

Final Check

Ensure that the diagram correctly reflects the applied loads and moments. This step is crucial in confirming the accuracy of your calculations.

Conclusion

By following these steps, you should be able to construct a shear force diagram based on a bending moment diagram effectively. Accurate structural analysis relies on these diagrams, and understanding the relationship between them is key to making informed decisions in structural design.