Snap-Fit Design — Cheat Sheet
Strain-based equations for cantilever, annular and torsional snap joints, plus angles and limits.
The governing idea
| Design to | STRAIN, not stress |
| Why | The deflection is brief and plastics are non-linear |
| Modulus for forces | SECANT modulus at that strain, not Young’s |
| Consequence | Young’s modulus overpredicts stress AND force by the same ratio |
Permissible strain
| Semi-crystalline | ≈ yield strain (PP, PE, POM, PA, PBT) |
| Amorphous | 70% of yield strain (PC, ABS, PS, PMMA, PVC) |
| Glass filled | 50% of elongation at break |
| Repeated assembly | × 0.6 on any of the above |
| Rough magnitudes | unfilled ≈ 6%, filled ≈ 1.5% |
Cantilever, rectangular
| Strain | ε = 3·y·h / (2·L²·K) |
| Deflection | y = 2·ε·L²·K / (3·h) |
| Thickness | h = 2·ε·L²·K / (3·y) |
| Length | L = √(3·y·h / (2·ε·K)) |
| Deflection force | P = (b·h²/6)·(Es·ε/L) |
| General form | P = Es·ε·Z / L |
Reference beams
| 6% strain | h = 0.2L and y = 0.2L (5:1 L/h) |
| 1.5% strain | h = 0.1L and y = 0.1L (10:1 L/h) |
| Scaling | ε ∝ 1/L², ε ∝ h, width does not appear |
Taper (K factor)
| hL/h₀ = 1.00 | K = 1.000 — parallel |
| hL/h₀ = 0.75 | K = 1.235 |
| hL/h₀ = 0.50 | K = 1.636 — 64% more deflection |
| hL/h₀ = 0.33 | K = 2.137 |
| Cost | None — same tooling, less material |
Circular sections
| Half circle | y = 0.578·ε·L²/r |
| One-third circle | y = 0.580·ε·L²/r |
| Quarter circle | y = 0.555·ε·L²/r |
Angles & forces
| Mating / separation | W = P·(µ + tan α)/(1 − µ·tan α) |
| Lead angle | 15–30° |
| Return angle (separable) | 30–45° |
| Self-locking at | tan α = 1/µ (73° at µ = 0.3) |
| Beyond it | Cannot be pulled apart — it can only break |
Annular (cylindrical)
| Permissible interference | y = ε·d (diametral) |
| Both parts flexible | Interference may be 2× larger |
| Thick-wall factor | [(d₀/d)²+1]/[(d₀/d)²−1] + ν |
| Deflection force | P = y·d·Es·X |
| Caveat | Mating force is an estimate, not a prediction |
Torsional
| Permissible shear strain | γ ≈ (1+ν)·ε ≈ 1.35·ε |
| Twist angle | θ = γ·L/r (radians) |
| Shear modulus | G = Es / [2(1+ν)] |
| Polar moment | Ip = πr⁴/2 (solid bar) |
| Torque | T = G·Ip·γ/r (×2 for two bars) |
Failure modes & details
| Roll-off | Force off the neutral axis rolls the foot off the ledge — a 90° face does NOT prevent it |
| The fix | Snap loop / sleeve retainer puts the force through the neutral axis |
| Root fillet | ≈ half the beam thickness, never below 0.5 mm |
| Creep | Never leave a snap assembled under strain |
| Weld line | Loops and sleeves have one — thicken or move the gate |
Formula reference — verify against the governing standard. Not a substitute for engineering judgment.