If curvature κ is zero, the local strain ε(z) reduces to which quantity?

If curvature κ is zero, the local strain ε(z) reduces to which quantity?

• A. ε0
• B. 0
• C. ε0 z
• D. κ z

Answer: (A)

In bending theory, the strain at a point a distance z from the mid-surface consists of a uniform in-plane part ε0 plus a bending part that varies linearly with z, typically written as ε(z) = ε0 ± κ z depending on convention. The key idea is that curvature introduces a linear variation through the thickness. If the curvature κ is zero, the bending term disappears, so every fiber across the thickness experiences the same strain, equal to the mid-plane strain ε0. Therefore, the local strain reduces to ε0.

In bending theory, the strain at a point a distance z from the mid-surface consists of a uniform in-plane part ε0 plus a bending part that varies linearly with z, typically written as ε(z) = ε0 ± κ z depending on convention. The key idea is that curvature introduces a linear variation through the thickness. If the curvature κ is zero, the bending term disappears, so every fiber across the thickness experiences the same strain, equal to the mid-plane strain ε0. Therefore, the local strain reduces to ε0.