What is the relationship between the bending moment and shear force in a beam?

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Question: What is the relationship between the bending moment and shear force in a beam?

Options:

Correct Answer: V = dM/dx

Solution:

The relationship is given by V = dM/dx, meaning the shear force is the derivative of the bending moment with respect to the position along the beam.

What is the relationship between the bending moment and shear force in a beam?

What is the relationship between the bending moment and shear force in a beam?

Step 1: Understand what a beam is. A beam is a long, horizontal structure that supports loads.
Step 2: Know what shear force (V) is. Shear force is the internal force that acts along the beam, trying to slide one part of the beam past another.
Step 3: Understand what bending moment (M) is. Bending moment is the internal moment that causes the beam to bend due to applied loads.
Step 4: Learn about the relationship between shear force and bending moment. The shear force at any point in the beam is related to how the bending moment changes along the length of the beam.
Step 5: The relationship is expressed mathematically as V = dM/dx. This means that the shear force (V) is the rate of change of the bending moment (M) with respect to the position (x) along the beam.
Step 6: If the bending moment increases as you move along the beam, the shear force is positive. If the bending moment decreases, the shear force is negative.

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