Root strain
-Safety factor on strain
-Max permissible deflection
-Insertion force
-All results
| Deflection force P (at hook) | - |
| Root bending stress (elastic, E x strain) | - |
| Stiffness of beam P/y | - |
| Minimum length for this deflection and strain limit | - |
Method and formulas
Straight cantilever of constant rectangular section, small deflection, linear elastic.
| Quantity | Formula |
|---|---|
| Root strain | ε = 1.5 h y / L2 |
| Permissible deflection | ymax = εallow L2 / (1.5 h) |
| Deflection force | P = E b h3 y / (4 L3) |
| Insertion force | W = P (μ + tan α) / (1 − μ tan α) |
| Minimum length | Lmin = √(1.5 h y / εallow) |
Worked example: 15 mm ABS hook, 1.0 mm deflection
L = 15 mm, h = 1.5 mm, b = 5 mm, y = 1.0 mm, E = 2300 MPa, allowable strain 2 %, μ = 0.3, α = 30°. Strain = 1.5 x 1.5 x 1.0 / 152 = 1.00 %, a safety factor of 2.0 on strain. Permissible deflection is 2.00 mm. P = 2300 x 5 x 1.53 x 1.0 / (4 x 153) = 2.88 N, and the insertion force is 3.05 N.
Questions
How do you calculate snap-fit strain?
For a straight cantilever beam of constant rectangular section, the maximum strain at the root is e = 1.5 h y / L^2, where h is the thickness, y the deflection at the hook and L the beam length. Compare it with the allowable strain of the plastic, not with a stress limit.
What is a safe allowable strain for plastic snap fits?
Typical short-term guide values are roughly 1.5 to 2 % for glass-filled or brittle grades, about 2 to 4 % for unfilled engineering plastics such as ABS and PC, and higher for PP and nylon at the right moisture content. Values depend on grade, temperature, and whether the joint is assembled once or many times. Use your supplier's data and test parts; the presets here are typical guides only.
How is the insertion force calculated?
The deflection force is P = E b h^3 y / (4 L^3). The force needed to push the hook over its lead-in ramp is W = P (mu + tan a) / (1 - mu tan a), with mu the friction coefficient and a the ramp angle measured from the direction of insertion.
How can I reduce strain without a longer beam?
Taper the thickness so it reduces toward the tip (thickness at the tip about half the root), add a generous root fillet radius (at least 0.5 h), or use a thinner section. A tapered beam can allow roughly 50 to 100 % more deflection for the same root strain; this calculator uses a constant section, which is conservative.
Does this cover creep, fatigue and temperature?
No. Permanently loaded snap fits creep and relax, and repeated assembly lowers the allowable strain. Modulus and strain limits change with temperature and moisture. It also ignores stress concentration at the root and the stiffness of the mating part.
What does this calculator not cover?
Annular and torsional snap fits, tapered beams, retention force and part tolerances. It is an engineering aid for early sizing: verify critical designs by test.
Engineering aid for guidance. Constant-section beam, short-term elastic loading only. Plastic properties vary with grade, moisture and temperature: verify critical designs by test.