Shear Force Diagram

The shear force diagram is a graphical representation of the variation of shear force along the length of a beam. It shows the magnitude and direction of the internal forces that act within the beam. The shear force diagram is obtained by plotting the shear force values at different sections of the beam.

Parabolic Curve in Shear Force Diagram

When the shear force diagram is a parabolic curve between two points, it indicates that there is a uniformly varying load between those two points. This means that the load acting on the beam is increasing or decreasing uniformly along the length between the two points.

Explanation

To understand why a parabolic curve in the shear force diagram indicates a uniformly varying load, let's consider the equilibrium conditions of a beam.

- The shear force at any section of a beam is equal to the algebraic sum of all the external forces acting to the left or right of that section.
- If the external loads acting on the beam are constant, the shear force remains constant along the length of the beam.
- However, if the external load is varying uniformly, the shear force will also vary uniformly along the length of the beam.

When a uniformly varying load is applied to a beam, the resulting shear force diagram will be a parabolic curve. The magnitude of the shear force increases or decreases uniformly from one end of the beam to the other.

Example

Let's consider a simply supported beam with a uniformly varying load applied to it. The load intensity at one end is 10 kN/m, and at the other end, it is 30 kN/m. The length of the beam is 5 meters.

- The shear force at the left support is zero since there are no external loads acting to the left of that section.
- As we move towards the right, the shear force starts increasing linearly due to the increasing load intensity.
- At the midpoint of the beam, the shear force will be the average of the shear forces at the two supports, which is (0 + (10 + 30)/2) = 25 kN.
- As we move further towards the right, the shear force continues to increase linearly until it reaches 60 kN at the right support.

Plotting these shear force values on a graph will result in a parabolic curve, indicating a uniformly varying load.

Therefore, when the shear force diagram is a parabolic curve between two points, it indicates that there is a uniformly varying load between those two points. The correct answer to the given question is option 'D'.