Calculate the bending stress σA at point A and the torsional stress τB at point B of an extension spring's hook between two working points s1 and s2, plus their stress amplitude and fatigue utilization against a permissible amplitude you supply. The spring forces come unchanged from the validated EN 13906-2 spring-body core.
This is a generic model using classical hook stress equations (Shigley), not a DIN EN 13906-2 fatigue diagram: the standard explicitly excludes hook stresses and the fatigue diagram from its scope.
Set the inputs and calculate.
Calculate bending and torsional stress at the hook (points A and B) of an extension spring at two working points, plus their stress amplitude and fatigue utilization, building on the validated EN 13906-2 spring-body core.
The same spring geometry and material data as the existing EN 13906-2 extension-spring calculator (wire diameter, coil diameter, number of coils, initial tension, two deflections, tensile strength), plus the bend radii r1 and r2 at the hook transition and two permissible stress amplitudes (bending at A, shear at B) from your own source.
Forces F1, F2 at the working points are taken from the spring-body core. Classical hook stress equations (Shigley) with curvature factors K_A=(4C1²−C1−1)/(4C1(C1−1)) and K_B=(4C2−1)/(4C2−4), C1=2r1/d, C2=2r2/d, give σA and τB. From these follow the stress amplitude and fatigue utilization at both locations; the governing location has the higher utilization.
At d=3 mm, D=18 mm, r1=9 mm (C1=6) and r2=6 mm (C2=4), K_A≈1.142 and K_B≈1.250; with F1≈161.5 N and F2≈303.0 N this gives σA1≈649 MPa, σA2≈1,217 MPa, τB1≈343 MPa, τB2≈643 MPa. The amplitudes are 284 MPa (A) and 150 MPa (B), i.e. 47% and 50% utilization -- point B governs, and the peak stress stays below Rm=1,800 MPa.
Sources and limits: Classical hook stress equations after Shigley (corroborated by EngineersEdge/Tokai Bane); DIN EN 13906-2 explicitly excludes hook stresses and the fatigue diagram from its scope -- the permissible stress amplitudes must come from your own documented source.
Calculate bending and torsional stress at the hook (points A and B) of an extension spring at two working points, plus their stress amplitude and fatigue utilization, building on the validated EN 13906-2 spring-body core.
Hook stress analysis assesses the two geometry-driven stress concentrations in the curved transition region of an extension spring's end loop: bending stress with a direct-stress term at point A, and torsional stress at point B. Both are computed with classical, empirically corroborated curvature factors that capture the stress concentration at the inner fiber of the curve.
Utilization_A = σA,amplitude / σA,perm; Utilization_B = τB,amplitude / τB,perm
K_A=(4C1²−C1−1)/(4C1(C1−1))K_B=(4C2−1)/(4C2−4)C1=2r1/d, C2=2r2/d| Symbol / input | Meaning |
|---|---|
| r1, r2 | Bend radii at the hook transition at points A and B respectively; determine the curvature factors K_A and K_B. |
| σA, τB | Bending stress at point A and torsional stress at point B of the hook, evaluated at working points s1 and s2. |
| σA,perm, τB,perm | Permissible stress amplitudes at A and B, from your own source, since DIN EN 13906-2 does not cover the hook. |
The same spring geometry and material data as the existing EN 13906-2 extension-spring calculator (wire diameter, coil diameter, number of coils, initial tension, two deflections, tensile strength), plus the bend radii r1 and r2 at the hook transition and two permissible stress amplitudes (bending at A, shear at B) from your own source.
Enter the same spring geometry and material data as the existing extension-spring calculator (wire diameter, coil diameter, number of coils, initial tension, the two deflections s1/s2, tensile strength). Add the bend radii r1 (point A) and r2 (point B) at the hook transition and two permissible stress amplitudes from your own documented source.
At d=3 mm, D=18 mm, r1=9 mm (C1=6) and r2=6 mm (C2=4), K_A≈1.142 and K_B≈1.250; with F1≈161.5 N and F2≈303.0 N this gives σA1≈649 MPa, σA2≈1,217 MPa, τB1≈343 MPa, τB2≈643 MPa. The amplitudes are 284 MPa (A) and 150 MPa (B), i.e. 47% and 50% utilization -- point B governs, and the peak stress stays below Rm=1,800 MPa.
A utilization below 100% at both points means the calculated stress amplitude stays under the permissible amplitude entered for that point. The location reported as critical (A or B) has the higher utilization and should be addressed first in any design change.
Lengths and radii in mm, forces in N, tensile strength and permissible stress amplitudes in MPa; results in MPa and percent.
Estimating whether the hook of an extension spring already sized to EN 13906-2 stays within known permissible stress amplitudes at the critical hook points A and B under dynamic loading between two working points (s1, s2), without re-implementing the existing spring calculator's force/rate formulas.
Classical hook stress equations after Shigley (corroborated by EngineersEdge/Tokai Bane); DIN EN 13906-2 explicitly excludes hook stresses and the fatigue diagram from its scope -- the permissible stress amplitudes must come from your own documented source.
Common mistake: Don't confuse the bend radii r1/r2 with the coil radius D/2 -- for a classical half-loop hook, r1≈r2≈D/2 is a common approximation, but the actual hook shape can differ. C1=2r1/d and C2=2r2/d must exceed 1, otherwise the curvature formula becomes singular and the calculator rejects the input.
Because DIN EN 13906-2 explicitly excludes hook stresses and the associated fatigue diagram from its scope. This calculator instead uses classical, standards-neutral hook stress equations after Shigley with a permissible stress amplitude you supply yourself.
From your own documented material or design source for spring-wire fatigue strength at curved cross-sections, e.g. manufacturer data or the FKM guideline -- not from DIN EN 13906-2, since that standard does not cover the hook.
The existing calculator computes rate, forces and the body stress, but explicitly excludes hook stresses and the fatigue diagram. This calculator adds exactly those missing hook stresses and their fatigue assessment.
That depends on geometry and material -- the calculator compares the normalized utilizations at both points and reports the higher one as the critical location.
No -- the utilization compares stress amplitudes only, i.e. the fatigue part. The peak stress at s2 can still exceed the material strength, in which case the hook fails statically before fatigue ever matters. The calculator explicitly flags it when the bending stress at point A reaches the entered tensile strength Rm.