What is the expression for the local strain ε(z) at a distance z from the midplane in a typical laminated panel?

• A. ε0 + zκ
• B. ε0 − zκ
• C. ε0κ + z
• D. ε0

Answer: (A)

In a laminated panel under bending, the strain varies linearly through the thickness because plane sections stay plane. The strain at a distance z from the midplane is written as ε(z) = ε0 + z κ, where ε0 is the in-plane strain at the midplane and κ is the curvature (how quickly the slope changes along the length). This means the midplane experiences ε0, and as you move away from the midplane by a distance z, the strain changes by z times the curvature. That linear relationship is why the expression uses ε0 plus z times κ. The other forms lose the linear dependence, mix units, or assume no bending, which isn’t consistent with bending behavior in laminates.