Calculate rate, forces, spring work, and body shear stresses for a cold-formed cylindrical extension spring including initial tension.
Set the inputs and run the calculation.
Calculate force-deflection behavior and body stress of a cylindrical extension spring.
Wire d, mean diameter D, active coils, initial tension and working deflections describe the body; hook geometry is separate.
Initial tension must be overcome before the spring carries external load. It is strongly affected by hooks and manufacturing; a correct body calculation does not verify the hook.
Extension force equals initial tension plus body spring force from deflection. Index and shear stress are evaluated as for a compression spring.
Higher initial tension shifts the force curve upward without changing body rate.
Sources and limits: EN 13906-2; verify hooks, fatigue and manufacturing tolerances separately.
Calculate force-deflection behavior and body stress of a cylindrical extension spring.
Wire diameter d, mean coil diameter D and active coil count n determine the rate of the close-wound spring body. Initial tension F0 is the force required to open the touching coils. Only above F0 does the idealized characteristic follow F = F0 + R·s. Loops, hooks and other attachments are outside the body model and require separate assessment.
Extension force equals initial tension plus body spring force from deflection. Index and shear stress are evaluated as for a compression spring.
| Symbol / input | Meaning |
|---|---|
| d, D | Wire diameter and mean coil diameter of the spring body; D is measured from wire centre to wire centre. |
| n | Number of active body coils; attachment coils and loops must be distinguished from it. |
| F0 | Initial tension that must be overcome before the touching coils open. |
| s1, s2 | Working deflections of the opened body, paired with total forces F1 and F2. |
| R | Spring rate in N/mm: force increase per millimetre after F0 has been overcome. |
Wire d, mean diameter D, active coils, initial tension and working deflections describe the body; hook geometry is separate. Initial tension must be overcome before the spring carries external load. It is strongly affected by hooks and manufacturing; a correct body calculation does not verify the hook.
Enter wire diameter, mean coil diameter, active coils and the extension spring's initial tension. Also provide two working deflections to find the resulting tensile force within the used range.
Higher initial tension shifts the force curve upward without changing body rate.
F1 and F2 are total spring forces at deflections s1 and s2 — F0 is already included and must not be added again. Rate R describes only the slope after the coils open. Corrected body stress assesses the coiled wire; it says nothing about local bending and torsional stresses in the hook. EN 13906-2 also notes that initial tension can decrease over time through relaxation.
Diameter in millimetres, force in N, deflection in millimetres, stress in MPa.
Designing an extension spring for a known force-deflection range, for example in return springs, tensioning mechanisms or door closers.
EN 13906-2; verify hooks, fatigue and manufacturing tolerances separately.
Common mistake: Don't forget initial tension – unlike a compression spring, an extension spring only starts to stretch once this preload is exceeded; a pure rate calculation without initial tension underestimates the force needed early in the travel. Hook or loop geometry is not covered by this body calculation and is often the actual failure-critical location.
It arises during coiling of the extension spring because the coils already touch in the unloaded state; only an external force above this tension opens the coils and produces deflection.
Hook or loop geometry creates local stress concentrations not captured by the pure EN 13906-2 body-stress calculation, and these often govern actual fatigue life.
Barely, without remaking the spring – it is set during the coiling process and cannot be practically adjusted on the finished part.
Yes. For working deflection s the model uses F = F0 + R·s, so F0 must not be added a second time to result F1 or F2.
Not necessarily. EN 13906-2 notes that spring forces can decrease when initial tension relaxes over time; temperature and material condition matter.
Wire diameter, mean coil diameter, active coils, initial tension, and two working deflections define the linear body characteristic. Typical uses include return springs for flaps or actuation mechanisms.
Spring hooks are often more critical than the spring body and are not verified here. Dynamic loading also requires hook transitions, stress range, material diagrams, and manufacturing effects to be assessed.