Part A Draw the shear diagram for the beam. Follow the sign convention. Part B Draw the moment diagram for the beam. Follow the sign convention.
The Correct Answer and Explanation is :
o analyze the shear and moment diagrams for a simply supported beam subjected to a central point load, we can follow these steps:
Part A: Shear Force Diagram (SFD)
- Determine Reactions at Supports: – or a simply supported beam with a central point load ( P ) applied at the midpoint, the reactions at both supports are equal and can be calculated as: [ R_A = R_B = \frac{P}{2} ] his is because the load is symmetrically placed, and the beam is in static equilibrium.
- Construct the Shear Force Diagram: – he shear force is constant between the supports and equal to the reaction forces. – t the left support (A), the shear force is ( +\frac{P}{2} ). – t the right support (B), the shear force is ( -\frac{P}{2} ). – he shear force diagram is a horizontal line at ( +\frac{P}{2} ) from A to the midpoint, and then a drop to ( -\frac{P}{2} ) from the midpoint to B.
Part B: Bending Moment Diagram (BMD) - Calculate Bending Moments at Key Points: – t the supports (A and B), the bending moment is zero because there is no moment arm. – t the midpoint (C), the bending moment is maximum and can be calculated as: [ M_C = R_A \times \frac{L}{2} = \frac{P}{2} \times \frac{L}{2} = \frac{P \times L}{4} ] here ( L ) is the length of the beam.
- Construct the Bending Moment Diagram: – he bending moment increases linearly from A to C, reaching a maximum of ( \frac{P \times L}{4} ) at C. – t then decreases linearly from C to B, returning to zero at B. – he BMD is a triangle with a peak at the midpoint.
Sign Conventions:
- Shear Force:* Positive when the left side of the section is pushed upward.- Bending Moment:* Positive when the moment causes compression at the top of the beam.
or a visual demonstration of constructing shear and moment diagrams for a simply supported beam with a central point load, you can refer to the following video:
videoSIMPLY SUPPORTED BEAM WITH POINT LOAD AT CENTRE SHEAR FORCE AND BENDING MOMENT DIAGRAMturn0search0