Laminate Strength Calculator

Analyze stacked plies under membrane and bending loads. Review stiffness, coupling, and failure margins instantly. Export neat reports for design checks and classroom review.

Calculator inputs

Enter laminate loads, strength allowables, and ply properties. Results appear above this form after submission.

Membrane loads use N/mm. Bending resultants use N.

Ply stacking sequence

One row per ply. Keep the layup order from bottom surface to top surface.

Ply 1
Ply 2
Ply 3
Ply 4
Tip: Use symmetric layups to reduce coupling. A near-zero B matrix signals weak extension-bending coupling.

Example data table

Sample carbon/epoxy style layup for testing the calculator interface and exports.

Ply Angle (°) Thickness (mm) E1 (MPa) E2 (MPa) G12 (MPa) ν12
100.1251350001000050000.30
2450.1251350001000050000.30
3-450.1251350001000050000.30
4900.1251350001000050000.30
Example load case: Nx = 500 N/mm, Ny = 120 N/mm, Nxy = 75 N/mm, Mx = 0, My = 0, Mxy = 0, Xt = 1500 MPa, Xc = 1200 MPa, Yt = 40 MPa, Yc = 200 MPa, S = 80 MPa.

Formula used

The calculator applies classical laminate plate relations for orthotropic plies under plane stress. Each ply first uses the reduced stiffness matrix Q:

Q11 = E1 / (1 - ν12ν21)
Q22 = E2 / (1 - ν12ν21)
Q12 = ν12E2 / (1 - ν12ν21)
Q66 = G12

The transformed stiffness matrix Q̅ is built from ply angle θ. Then the laminate stiffness terms are assembled through thickness coordinates z:

A = Σ(Q̅k · (zk - zk-1))
B = 1/2 · Σ(Q̅k · (zk² - zk-1²))
D = 1/3 · Σ(Q̅k · (zk³ - zk-1³))

Mid-plane strains and curvatures come from the ABD system:

{N, M} = [ A  B ; B  D ] · {ε0, κ}

Ply stresses are evaluated in material axes. Failure review includes Maximum Stress, Tsai-Hill, and Tsai-Wu style indices. A governing failure index above 1.0 indicates the submitted load state exceeds the chosen limits.

How to use this calculator

  1. Enter laminate force resultants Nx, Ny, and Nxy. Add bending resultants when curvature effects matter.
  2. Provide strength allowables Xt, Xc, Yt, Yc, and S in consistent stress units.
  3. List plies from bottom to top. Set each angle, thickness, E1, E2, G12, and ν12.
  4. Submit the form. The calculator solves the laminate ABD matrix and shows results above the form.
  5. Review equivalent laminate constants, per-ply stresses, failure indices, and the critical ply chart.
  6. Use the CSV button for spreadsheet review and the PDF button for a printable report.

FAQs

1) What does the laminate status mean?

It compares the largest calculated failure index against 1. A value at or below 1 passes this load case. A value above 1 suggests the selected strength limits are exceeded for at least one ply.

2) Why is the B matrix important?

The B matrix measures extension-bending coupling. When it is near zero, membrane loading causes much less unwanted curvature. Unsymmetric layups often produce larger B values and stronger coupling effects.

3) Should plies be entered bottom to top?

Yes. Stacking order changes the z positions, B matrix, D matrix, and ply stresses. Two laminates with identical angles but different order can show different curvatures and strength margins.

4) Can I use mixed materials in one laminate?

Yes. Each row accepts its own orthotropic constants, so hybrid laminates can be modeled. Keep units consistent across every ply and strength input to avoid misleading results.

5) What units should I use?

Use one consistent unit system. This page is arranged for MPa and millimeters, with membrane loads in N/mm and bending resultants in N. Consistency matters more than the specific system.

6) Why are Ex and Ey called equivalent values?

They are laminate-level engineering constants derived from the in-plane compliance of the full stack. They summarize the whole laminate response rather than the behavior of any single ply.

7) What does the reserve ratio show?

Reserve ratio is shown as 1 divided by the governing failure index. Values above 1 indicate spare capacity for this simplified comparison. Values below 1 indicate overload relative to the chosen criterion.

8) Does this replace detailed composite certification analysis?

No. It is a design-screening and study tool. Real projects may also need knockdown factors, environmental effects, progressive damage, manufacturing defects, test data, and certification-specific methods.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.