What is the relationship between bending moment and shear force in a beam?
Practice Questions
1 question
Q1
What is the relationship between bending moment and shear force in a beam?
M = V*L
M = ∫V dx
M = V*E
M = V*I
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.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the relationship between bending moment and shear force in a beam?
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.
Steps: 6
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.
