The slope of the shear force in the shear-force diagram of a loaded beam is the distributed load
(A) minus (the distributed load)
(B) the bending moment
(C) minus (the bending moment)
The correct answer and explanation is:
The correct answer is A) the distributed load.
Explanation:
In the shear force diagram (SFD) of a loaded beam, the slope of the shear force curve represents the distributed load applied to the beam at any given point. To explain this in more detail, it is important to understand the relationship between shear force, bending moment, and distributed loads.
- Shear Force (V): The shear force at a given point on the beam is the internal force that resists the external load applied to the beam. It varies along the length of the beam depending on the type and magnitude of the loads.
- Distributed Load (w): A distributed load is a load that is applied continuously over a section of the beam. It is usually represented as a force per unit length, measured in units like Newtons per meter (N/m).
- Slope of Shear Force: The relationship between the shear force and distributed load can be described by a fundamental equation of equilibrium: dVdx=w(x)\frac{dV}{dx} = w(x) Here, dVdx\frac{dV}{dx} represents the slope of the shear force at a point, and w(x)w(x) is the distributed load at that point. This equation states that the slope of the shear force diagram is equal to the magnitude of the distributed load applied at that point.
- Why the Slope is Equal to the Distributed Load: The shear force is a result of the balance of internal forces within the beam. The distributed load, when integrated along the length of the beam, determines the change in shear force between two points. If the load is uniform, the shear force will change at a constant rate, creating a straight line in the shear force diagram. If the load varies, the slope of the shear force diagram will change correspondingly.
In contrast, bending moments are related to the integral of shear forces, and their slope is not directly related to the distributed load but to the shear force itself.
Therefore, the slope of the shear force diagram corresponds directly to the value of the distributed load, making A) the correct answer.