How to Draw Shear and Bending Moment Diagrams

Shear and bending moment diagrams are essential tools used in structural analysis to determine the internal forces and moments within a beam or structure. These diagrams help engineers and designers understand the behavior of the structure under different loading conditions. In this article, we will provide a step--step guide on how to draw shear and bending moment diagrams.

Step 1: Determine the Support Reactions
The first step in drawing shear and bending moment diagrams is to determine the support reactions. This can be done applying the principles of equilibrium. By summing the forces and moments at each support, you can calculate the reaction forces and moments.

Step 2: Determine the Shear Diagram
To draw the shear diagram, start at one end of the beam and move along the beam length. At each point, calculate the shear force considering the applied loads and support reactions. Plot these values on the diagram, taking into account the sign convention for positive and negative forces.

Step 3: Determine the Bending Moment Diagram
Once the shear diagram is complete, you can move on to drawing the bending moment diagram. Start at one end of the beam and move along the beam length. At each point, calculate the bending moment considering the applied loads, support reactions, and shear forces. Plot these values on the diagram, again following the sign convention for positive and negative moments.

Step 4: Identify Key Points and Regions
After completing the shear and bending moment diagrams, it is important to identify the key points and regions of interest. These include points of zero shear or bending moment, points of maximum shear or bending moment, and regions where the shear or bending moment changes sign. Mark these points and regions on the diagrams for easy reference.

Now that we have covered the basic steps for drawing shear and bending moment diagrams, let’s address some common questions related to this topic:

Q1: What are shear and bending moment diagrams used for?
Shear and bending moment diagrams are used to analyze and understand the internal forces and moments within a beam or structure. They provide valuable information for designing and optimizing the structural elements.

Q2: What is the sign convention for shear and bending moment?
The sign convention for shear and bending moment is generally positive when the forces or moments cause clockwise rotation or upward shear.

Q3: Can the shear force or bending moment be negative?
Yes, the shear force or bending moment can be negative. This occurs when the forces or moments cause counterclockwise rotation or downward shear.

Q4: How do concentrated loads affect the shear and bending moment diagrams?
Concentrated loads create abrupt changes in the shear and bending moment diagrams. The values of shear and bending moment will change at the location of the concentrated load.

Q5: How do distributed loads affect the shear and bending moment diagrams?
Distributed loads cause gradual changes in the shear and bending moment diagrams. The values of shear and bending moment will vary linearly along the span of the distributed load.

Q6: What are the key points to look for in a shear diagram?
Key points in a shear diagram include points of zero shear, where the shear force changes sign, and points of maximum or minimum shear.

Q7: What are the key points to look for in a bending moment diagram?
Key points in a bending moment diagram include points of zero bending moment, where the bending moment changes sign, and points of maximum or minimum bending moment.

Q8: How do support reactions affect the shear and bending moment diagrams?
Support reactions contribute to the shear and bending moment diagrams. They are typically present at the ends of the beam and can significantly affect the values of shear and bending moment.

Q9: Can shear and bending moment diagrams be drawn for non-uniformly distributed loads?
Yes, shear and bending moment diagrams can be drawn for non-uniformly distributed loads. The values of shear and bending moment will vary along the span of the load.