Bending Topic: Step-by-Step Guide to Drawing Shear and Bending-Moment Diagrams for a Beam

How can you create shear and bending-moment diagrams for a beam with a specific loading?

Step-by-Step Guide to Drawing Shear and Bending-Moment Diagrams:

To draw the shear and bending-moment diagrams for a beam, follow these steps: 1. Draw the Free Body Diagram (FBD) for Each Segment: First, draw the FBD of the beam and divide it into segments based on the changes in the loading. Identify the reaction forces at the supports, such as points A and B in this case. Consider each segment of the beam and draw the FBD for that segment. 2. Calculate Shear Force at Each Section: Calculate the shear force at each section of the beam by considering the applied loads and reaction forces. Shear force is the sum of the forces acting in the vertical direction at a specific section. 3. Calculate Bending Moment at Each Section: Calculate the bending moment at each section by considering the moments caused by the applied loads and reaction forces. Bending moment is the sum of the moments acting on the beam at a specific section. 4. Plot Shear and Bending-Moment Values: Plot the shear force values on the shear diagram and the bending moment values on the bending-moment diagram along the length of the beam.

Calculating Reaction Forces and FBD:

To calculate the reaction forces at supports A and B, sum the forces and moments around each point. For example, for support A: RA - 10 - 20 - 30 = 0 RA = 60 kN For support B: RB * 6 - 10 * 2 - 20 * 4 - 30 * 6 = 0 RB = 50 kN

Calculating Shear Force and Bending Moment:

Shear force can be calculated by summing vertical forces at each section along the beam. Bending moment can be calculated by summing moments caused by loads and reaction forces.

Plotting Diagrams:

Shear diagram will show downward steps at each section based on shear force values. Bending-moment diagram will show changes in bending moments along the beam's length. By following these steps, you can accurately draw shear and bending-moment diagrams for beams with specific loadings. Understanding the distribution of forces and moments along the beam is crucial for structural analysis and design.

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