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

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

Options:

Correct Answer: V = dM/dx

Solution:

The relationship between shear force V and bending moment M in a beam is given by V = dM/dx, where x is the distance along the beam.

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

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

Step 1: Understand that a beam is a structural element that can carry loads.
Step 2: Recognize that when a load is applied to a beam, it creates internal forces.
Step 3: Identify that shear force (V) is the internal force that acts along the beam to resist sliding.
Step 4: Understand that bending moment (M) is the internal moment that causes the beam to bend.
Step 5: Learn that the relationship between shear force and bending moment is expressed mathematically.
Step 6: The formula V = dM/dx means that the shear force at a point in the beam is equal to the rate of change of the bending moment at that point.
Step 7: This means if you know how the bending moment changes along the beam, you can find the shear force.

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