Inputs
The same spring-body data as the existing EN 13906-3 torsion-spring calculator (wire diameter, coil diameter, number of coils, two working angles φ1/φ2, coiling direction), plus the free leg lengths L1 and L2.
Springs · Leg deflection
Torsion spring: leg deflection and stress
Calculate the additional rotation and bending stress of a torsion spring's legs between two working points φ1 and φ2, plus the resulting total angle. The moments and body stress come unchanged from the validated EN 13906-3 spring-body core.
This is a generic bending model for the legs (superposition of body twist and classical beam-theory leg bending), not a DIN EN 13906-3 leg dataset: the standard covers only the spring body.
φLeg
02
Leg deflection and stress
Set the inputs and calculate.
Inputs and method
Torsion spring: leg deflection and stress
Calculate leg bending stress, additional leg rotation and total angle of a torsion spring at two working points, building on the validated EN 13906-3 spring-body core.
Calculation
Moments M1, M2 at φ1, φ2 and the corrected body stress are taken from the spring-body core. The legs are treated as straight bending beams under the transverse force introduced at the load point: leg stress σ_leg=32M/(πd³) at the coil junction (no curvature factor) and additional rotation θ_leg=M(L1+L2)/(3·EI) with I=πd⁴/64. The total angle is the working angle plus this leg rotation.
Example
At d=3 mm, D=24 mm, n=10, φ2=90° and L1+L2=35 mm, the additional leg rotation is about 1.39°, raising the total angle at φ2 to about 91.4°.
Sources and limits: Spring body taken unchanged from EN 13906-3; leg bending stress and rotation follow classical beam theory (Castigliano, superposition principle) -- no DIN EN 13906-3 leg dataset, since the standard covers only the spring body.
Torsion spring: leg deflection and stress in detail
Calculate leg bending stress, additional leg rotation and total angle of a torsion spring at two working points, building on the validated EN 13906-3 spring-body core.
What are leg deflection and leg stress?
Leg deflection describes the additional angular change, beyond the body twist, that arises because the straight legs of a torsion spring themselves bend under the applied load. Leg stress is the corresponding bending stress in the straight, uncurved wire section.
Formula and variables
theta_leg = M(L1+L2)/(3*EI), sigma_leg = 32M/(pi*d^3)
I = pi*d^4/64Total angle = working angle + theta_leg
| Symbol / input | Meaning |
|---|---|
| L1, L2 | Free leg lengths between the end of the coil and the load or support point. |
| theta_leg | Additional angular change from bending of the straight legs under the moment M. |
| sigma_leg | Bending stress in the straight leg, without a curvature factor, since the leg is not coiled. |
Choose the inputs correctly
The same spring-body data as the existing EN 13906-3 torsion-spring calculator (wire diameter, coil diameter, number of coils, two working angles φ1/φ2, coiling direction), plus the free leg lengths L1 and L2.
How to use the calculator
Enter the same spring-body data as the existing torsion-spring calculator (wire diameter, coil diameter, number of coils, the two working angles φ1/φ2, coiling direction). Add the free leg lengths L1 and L2.
Worked example
At d=3 mm, D=24 mm, n=10, φ2=90° and L1+L2=35 mm, the additional leg rotation is about 1.39°, raising the total angle at φ2 to about 91.4°.
How should the total angle and governing location be interpreted?
A total angle larger than the entered working angle shows how much leg compliance affects the actual motion at the load point. The governing location (body or leg) with the higher stress sets the design limit.
Lengths in mm, angles in degrees; results in MPa (stress) and degrees (angle).
Typical applications
Estimating whether the legs of a torsion spring already sized to EN 13906-3 experience higher or lower stress than the spring body at the intended working angles φ1/φ2, and how much the total angle increases due to leg compliance.
Assumptions, limits and common mistakes
Spring body taken unchanged from EN 13906-3; leg bending stress and rotation follow classical beam theory (Castigliano, superposition principle) -- no DIN EN 13906-3 leg dataset, since the standard covers only the spring body.
Common mistake: Don't confuse leg length with coil diameter -- L1/L2 are the free, straight sections between the end of the coil and the load or support point, independent of D. For very short legs, leg stress can exceed body stress even though the body is usually the critical location.
Frequently asked questions
Why doesn't the existing torsion-spring calculator include the legs?
Because DIN EN 13906-3 explicitly covers only the spring body and excludes leg bending, supports, friction and hysteresis. This calculator adds the legs using a classical, standards-neutral bending model.
Is this a DIN EN 13906-3 verification for the legs?
No. It is a generic straight-leg bending model from classical beam theory, not a normatively documented leg stress formula.
Where does the factor 3 in theta = M*L/(3*EI) come from?
The leg is not loaded by a pure end moment -- the load is a transverse force at the load-introduction point, so the bending moment rises linearly from zero at the load point to M at the coil junction. Castigliano's theorem then gives theta = M*L/(3*EI) per leg rather than M*L/(EI). Shigley's equivalent active coils N_e=(L1+L2)/(3*pi*D), fed through the spring-body characteristic, give the same answer.
Why does the total angle exceed the entered working angle?
Because the entered working angle only describes the spring body's twist; the legs themselves bend further under the moment, producing an additional angle increase at the load point.
What does it mean if the leg is reported as the governing location?
The leg stress exceeds the corrected body stress at φ2 -- typically for very short, thick legs or coils with a high spring index where the body's curvature factor is small.