Part 3 Problem no. 6 on SFD and BMD - Shear Force and Bending Moment - Strength of Materials

TL;DR

The content explains how to construct shear force and bending moment diagrams for a given beam and calculates the location of the point of contraflexure.

Transcript

now sf at point a was 21 kilo newton positive except at point b we were having two values the first is one kilo newton positive and the second one is minus 14 kilo newton a negative value now the values which i have plotted above the line they are positive the values which are below the line they are negative so here i have drawn the sfd shear forc... Read More

Key Insights

• 😁 The content explains the process of constructing shear force and bending moment diagrams for a beam, providing a visual representation of the internal forces.
• 0️⃣ The bending moment at hinge supports is always zero, while the bending moment at overhanging sections can be calculated using the given loads and distances.
• 🔄 The sign convention of clockwise and counterclockwise moments determines the positive and negative values on the bending moment diagram.
• 🔺 The point of contraflexure is a significant location in the bending moment diagram, indicating a change in the sign of the bending moment and can be determined using the principle of similarity of triangles.
• 😥 The location of the point of contraflexure affects the shape and behavior of the bending moment diagram.
• 😁 The content emphasizes the importance of correctly determining the sign convention and understanding the concepts of shear force and bending moment in beam analysis.
• 😥 The calculations for bending moment at critical points require considering the forces and distances involved.

Questions & Answers

Q: What determines if a value on the shear force diagram is positive or negative?

In the given content, values plotted above the line on the shear force diagram are positive, while values below the line are negative, following a specific sign convention.

Q: How is the bending moment at point B calculated?

The bending moment at point B is calculated by taking the moment of the upward reacting force (RA) and the intensity of the uniformly distributed load (UDL) about point B, following the clockwise moment as positive convention.

Q: What is the significance of the point of contraflexure in the bending moment diagram?

The point of contraflexure is where the bending moment changes sign from positive to negative or vice versa, resulting in a zero bending moment. It indicates a shift in bending moment behavior along the beam.

Q: How is the location of the point of contraflexure determined?

The location of the point of contraflexure can be determined using the principle of similarity of triangles. By setting up and solving a similarity equation between the larger and smaller triangles formed in the beam, the position can be calculated.

Summary & Key Takeaways

• The content discusses the process of creating a shear force diagram (SFD) for a given beam, with positive values above the line and negative values below the line.

• Bending moment calculations are then performed for critical points, including calculating moments at hinge supports and overhanging sections of the beam.

• The bending moment diagram (BMD) is then plotted based on the calculated values, showing parabolic curves and inclined lines.