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Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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Strain has __________ unit
Pascal
Newton
N c m 2
no
no
Quick Summary: Strain is defined as the ratio of the change in dimension to the original dimension of a body. Because it is a ratio of two similar physical quantities with the same SI units, the units cancel out, making strain a dimensionless quantity.
Strain is defined as the ratio of the change in dimension to the original dimension of a body. Because it is a ratio of two similar physical quantities with the same SI units, the units cancel out, making strain a dimensionless quantity.
ϵ=LΔL — Linear strain defined as change in length divided by original length
γ=tan(θ) — Shear strain defined as the tangent of the angular deformation
When an external force (stress) is applied to an elastic material, it undergoes deformation. The change in length (ΔL) compared to the original length (L) provides a measure of this deformation. Mathematically, ϵ=LΔL, where both numerator and denominator share the unit of length (meters), leading to a unitless result.
Strain represents the degree of deformation or distortion in a material.
Being a dimensionless quantity, it remains consistent across all systems of units (SI, CGS, etc.).
It is closely related to Young's Modulus (E=ϵσ), where σ is stress.
Simplifies calculations in structural analysis by eliminating unit conversion complexities.
Provides a standardized metric to compare materials of different sizes under load.
Does not inherently indicate the magnitude of force causing the deformation without the material's elastic modulus.
Structural health monitoring using strain gauges.
Mechanical testing of materials (e.g., tensile testing).
While strain is dimensionless, it is often expressed in microstrain (μϵ) or as a percentage to represent very small values.
Option A (Pascal) is the unit of stress or pressure (N/m²).
Option B (Newton) is the unit of force.
Option C (N/cm2) is another unit of pressure or stress.
D is correct — Strain is a dimensionless quantity because it is the ratio of two quantities having the same physical unit.
Always verify if a physical quantity is a ratio of identical units; if it is, the quantity will always be dimensionless, like strain, relative permittivity, or refractive index.