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

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

Options:

  1. M = V*L
  2. M = ∫V dx
  3. M = V*E
  4. M = V*I

Correct Answer: M = ∫V dx

Solution: 

The relationship between bending moment (M) and shear force (V) in a beam is given by M = ∫V dx, where the integral is taken along the length of the beam.

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

Practice Questions

Q1
What is the relationship between bending moment and shear force in a beam?
  1. M = V*L
  2. M = ∫V dx
  3. M = V*E
  4. M = V*I

Questions & Step-by-Step Solutions

What is the relationship between bending moment and shear force in a beam?
  • Step 1: Understand what a beam is. A beam is a structural element that supports loads and can bend.
  • Step 2: Learn about shear force (V). Shear force is the internal force that acts along the beam's length, trying to slide one part of the beam past another.
  • Step 3: Learn about bending moment (M). Bending moment is the internal moment that causes the beam to bend. It depends on the shear force and the distance from a point on the beam.
  • Step 4: Recognize the relationship between shear force and bending moment. The bending moment at any point in the beam is related to the shear force acting on the beam.
  • Step 5: Understand the formula M = ∫V dx. This means that to find the bending moment (M) at a point, you need to add up (integrate) the shear force (V) along the length of the beam (dx).
  • Step 6: Realize that this relationship helps engineers design beams to ensure they can safely carry loads without failing.
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