In a simply supported beam, what is the relationship between the bending moment

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Question: In a simply supported beam, what is the relationship between the bending moment and shear force?

Options:

Correct Answer: M = ∫V dx

Solution:

The relationship is given by M = ∫V dx, where M is the bending moment and V is the shear force.

In a simply supported beam, what is the relationship between the bending moment and shear force?

In a simply supported beam, what is the relationship between the bending moment and shear force?

Step 1: Understand that a simply supported beam is a structure that can support loads and has supports at both ends.
Step 2: Recognize that the shear force (V) is the internal force that acts along the beam to resist vertical loads.
Step 3: Know that the bending moment (M) is the internal moment that causes the beam to bend due to the applied loads.
Step 4: The relationship between bending moment and shear force is expressed mathematically as M = ∫V dx.
Step 5: This equation means that to find the bending moment at a certain point along the beam, you need to integrate (sum up) the shear force over the length of the beam.

Bending Moment and Shear Force Relationship – The bending moment at a section of a beam is the integral of the shear force over the length of the beam.