Bending strain occurs in a material subjected to bending moments, causing deformation along its length. It is a fundamental concept in the design and analysis of beams, plates, and other structural members.
Bending strain (εb) is the strain experienced by fibers in a material at a given distance from the neutral axis when the material is bent. It is calculated using the formula:
εb = y / R
Where:
The bending strain is positive for fibers in tension (above the neutral axis) and negative for fibres in compression (below the neutral axis).
Bending strain is related to bending stress (σb) through Young’s modulus (E):
σb = E * εb
Where:
This relationship is valid in the elastic region of the material, where the stress-strain relationship remains linear.
Bending strain is measured using a flexural test. The procedure involves:
The stress-strain data obtained from such tests are used to assess material properties like flexural strength and modulus.
Worked Example 1:
A rectangular beam with a height of 200 mm is bent such that the radius of curvature of the neutral axis is 5 m. Calculate the bending strain at the outermost fiber.
Solution:
εb = y / R = 0.1 / 5 = 0.02
Bending strain = 0.02 (dimensionless).
Worked Example 2:
A steel beam with Young’s modulus of 200 GPa experiences a bending strain of 0.001 at its outermost fiber. Calculate the bending stress in the beam.
Solution:
σb = 200 × 109 * 0.001 = 200 × 106 Pa = 200 MPa
Bending stress = 200 MPa.
Bending strain quantifies the deformation of a material under bending loads. It transitions to a measure of stress when multiplied by the material’s Young’s modulus. Engineers use bending strain to ensure that structural members can withstand bending moments without exceeding their elastic limit or ultimate strength.
Understanding bending strain is crucial in the design of beams, bridges, and structural components, where resistance to bending is a key performance criterion.
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