In a beam subjected to bending, what is the relationship between the bending moment and the curvature?
Practice Questions
1 question
Q1
In a beam subjected to bending, what is the relationship between the bending moment and the curvature?
M = EI * ρ
M = ρ / EI
M = E * I * ρ
M = ρ / E
The relationship between the bending moment (M) and the curvature (ρ) in a beam is given by M = EI * ρ, where E is the modulus of elasticity and I is the moment of inertia.
Questions & Step-by-step Solutions
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Q
Q: In a beam subjected to bending, what is the relationship between the bending moment and the curvature?
Solution: The relationship between the bending moment (M) and the curvature (ρ) in a beam is given by M = EI * ρ, where E is the modulus of elasticity and I is the moment of inertia.
Steps: 7
Step 1: Understand that a beam can bend when a force is applied to it.
Step 2: Know that the bending moment (M) is a measure of the internal forces that cause the beam to bend.
Step 3: Recognize that curvature (ρ) is a measure of how much the beam bends.
Step 4: Learn that the relationship between bending moment and curvature is expressed in the formula M = EI * ρ.
Step 5: Identify that E is the modulus of elasticity, which measures the stiffness of the material of the beam.
Step 6: Understand that I is the moment of inertia, which depends on the shape of the beam's cross-section.
Step 7: Conclude that as the bending moment increases, the curvature of the beam also increases, assuming E and I are constant.
