What it does
A fibre-reinforced laminate is a stack of thin plies, each much stiffer and stronger along its fibres than across them. Turning the plies to different angles gives a laminate with the stiffness you need in each direction. This page does the standard hand calculation, classical lamination theory (CLT), in three steps:
- Ply properties. From the fibre and matrix moduli, Poisson’s ratios and the fibre volume fraction Vf, the rule of mixtures gives E₁ = Vf Ef + (1 − Vf) Em and ν₁₂. Across the fibres you choose the inverse rule of mixtures (Reuss, a lower bound) or Halpin-Tsai (ξ = 2 for E₂, ξ = 1 for G₁₂), which is usually much closer to tests. Or type measured ply properties.
- Stacking. For a sequence such as [0/±45/90]s it builds the ply stiffness Q, the turned stiffness Q-bar for each angle, and the A, B and D matrices: A links in-plane forces to stretching, D links moments to bending, and B couples the two (B = 0 for a symmetric stack). It then gives the effective laminate moduli Ex, Ey, Gxy, νxy and the bending moduli, from the inverse of the full ABD matrix.
- Loads and failure. For in-plane forces N and moments M per unit width it solves for the mid-plane strains and curvatures, and gives the strains and stresses at the bottom and top face of every ply, in laminate axes and in ply axes. Each point gets a strength ratio R: the factor on all the loads at which that point fails by maximum stress (with the failure mode) and by Tsai-Wu. The smallest R is first-ply failure.
How to use it
- Type fibre and matrix properties, or switch to “Type ply properties”.
- Type the ply angles and the ply thickness. Write angles with / or commas; ±45 adds +45 and −45; 0_2 repeats a ply; ]2 repeats the bracketed group; a final s mirrors the stack. Ply 1 sits at z = −h/2.
- Type the loads and the five ply strengths (compressive strengths as positive numbers). Read the strength ratios, the through-thickness plot and the ply table, and download the table as CSV or everything as an image, PDF or Word file.
Worked example
Made-up glass-like fibres (Ef = 75 GPa, νf = 0.2) in a resin (Em = 3.5 GPa, νm = 0.35) at Vf = 0.6 give E₁ = 46.40 GPa, ν₁₂ = 0.2600, and with Halpin-Tsai E₂ = 15.02 GPa and G₁₂ = 4.493 GPa (the Reuss bound gives only 8.178 and 3.051 GPa).
Eight plies of 0.125 mm in [0/±45/90]s make a 1 mm quasi-isotropic laminate: Ex = Ey = 24.03 GPa, Gxy = 9.098 GPa and νxy = 0.3209, with A₁₁ = 26,793 N/mm. It is symmetric and balanced, so B = 0 and there is no stretch-shear coupling.
Under Nx = 40 N/mm the laminate stretches by 1664 microstrain. The 90° plies carry σ₂ = 23.43 MPa across their fibres, against a made-up transverse strength of 30 MPa. Tsai-Wu gives R = 1.249, so the first ply (the 90° plies in the middle) fails at Nx = 49.94 N/mm; maximum stress gives R = 1.281, in transverse tension. The 0° plies are far from failing (R = 12.84).
Tips
- First-ply failure is usually matrix cracking in the plies across the load. The laminate can often carry more after that; a progressive (last-ply) analysis needs reduced ply stiffnesses and is beyond this page.
- Thermal and moisture residual stresses from curing are not included here, and in 90° plies they can be a large part of the transverse stress.
- For an unsymmetric stack, in-plane loads also bend and twist the laminate (look at the curvatures).
FAQ
Why do maximum stress and Tsai-Wu differ? Maximum stress checks each stress on its own; Tsai-Wu is one quadratic surface that lets the stresses interact, so a ply under both σ₂ and τ₁₂ fails earlier with Tsai-Wu.
Which Q-bar sign convention? θ is measured from the x axis towards y, and Q-bar₁₆ changes sign with θ, as in Jones and in Daniel and Ishai.
Is my input stored? No, all the sums happen on this page.
Where the numbers come from
- Rule of mixtures, Halpin-Tsai (Halpin and Kardos, 1976) and classical lamination theory with the maximum stress and Tsai-Wu (1971) criteria, in the textbook forms of Jones, Mechanics of Composite Materials, and Daniel and Ishai, Engineering Mechanics of Composite Materials. fibub's code is checked in the tests against an independent NumPy implementation.
- The example fibre, matrix and strength values are made-up round numbers, not data for any real material.
- Nothing you type is sent or stored.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.