Which formula describes laminate bending stiffness D?

Which formula describes laminate bending stiffness D?

• A. D = sum Qbar_i h_i
• B. D = sum Q_i (z_i^2 − z_{i−1}^2)
• C. D = (1/3) Σ_i Qbar_i (z_i^2 − z_{i−1}^2)
• D. D = (1/2) Σ_i Qbar_i h_i^2

Answer: (C)

Bending stiffness D represents how the laminate resists bending by accounting for how stiffness is distributed through its thickness and how far each layer sits from the mid-plane. For each ply you use its transformed stiffness Q̄ and weight it by the z-distance squared over that ply, which comes from integrating z^2 through the ply thickness. Evaluating that integral across all plies leads to a sum that includes a factor of 1/3 and depends on the boundary positions z_i and z_{i−1}. When you add up all plies, you obtain D = (1/3) Σ Q̄_i (z_i^2 − z_{i−1}^2). This captures the idea that stiffer layers farther from the mid-plane contribute more to bending resistance, with the 1/3 coming from the z^2 integration. The other forms either don’t weight by the correct distance from the mid-plane or mix in the wrong thickness dependence, so they don’t reflect how bending stiffness builds up through the laminate.

Bending stiffness D represents how the laminate resists bending by accounting for how stiffness is distributed through its thickness and how far each layer sits from the mid-plane. For each ply you use its transformed stiffness Q̄ and weight it by the z-distance squared over that ply, which comes from integrating z^2 through the ply thickness. Evaluating that integral across all plies leads to a sum that includes a factor of 1/3 and depends on the boundary positions z_i and z_{i−1}. When you add up all plies, you obtain D = (1/3) Σ Q̄i (z_i^2 − z{i−1}^2). This captures the idea that stiffer layers farther from the mid-plane contribute more to bending resistance, with the 1/3 coming from the z^2 integration. The other forms either don’t weight by the correct distance from the mid-plane or mix in the wrong thickness dependence, so they don’t reflect how bending stiffness builds up through the laminate.