How do you compute laminate extensional stiffness A given Qbar_i and ply thickness t_i?

How do you compute laminate extensional stiffness A given Qbar_i and ply thickness t_i?

• A. A = product_i (Qbar_i × t_i)
• B. A = sum_i (Qbar_i × t_i)
• C. A = sum_i (Qbar_i / t_i)
• D. A = sum_i (t_i / Qbar_i)

Answer: (B)

In laminate theory, the extensional stiffness that links in-plane forces to mid-plane strains is found by accumulating each ply’s stiffness contribution through the thickness. Since the transformed stiffness Q̄ varies only from ply to ply and is constant within a ply, the integral across the whole thickness becomes a simple sum: A = sum over all plies of (Q̄_i × t_i). This is the correct form because you’re adding up how much each layer resists in-plane deformation per unit width, weighted by how thick that layer is. The other forms mix or invert these factors and don’t represent the cumulative in-plane resistance of the stack.

In laminate theory, the extensional stiffness that links in-plane forces to mid-plane strains is found by accumulating each ply’s stiffness contribution through the thickness. Since the transformed stiffness Q̄ varies only from ply to ply and is constant within a ply, the integral across the whole thickness becomes a simple sum: A = sum over all plies of (Q̄_i × t_i). This is the correct form because you’re adding up how much each layer resists in-plane deformation per unit width, weighted by how thick that layer is. The other forms mix or invert these factors and don’t represent the cumulative in-plane resistance of the stack.