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The influence of the dimensions can be illustrated best by using the single side fixed beam model <xr id="fig:One side fixed contact bending spring"/> (Fig. 6.20). For small deflections the following equation is valid:
:<math>$F = \frac{3 \cdot E \cdot J}{L^3} </math>$
where J is the momentum of inertia of the rectangular cross section of the beam
:<math>$J = \frac{B \cdot D^3}{12}</math>$
For springs with a circular cross-sectional area the momentum of inertia is
:<math>$J=\pi D^4/64</math>$:<math>$D= Durchmesser</math>$
To avoid plastic deformation of the spring the max bending force σ<sub>max</sub> cannot be exceeded
:<math>$\sigma_{max} = \frac{3 \cdot E \cdot D}{2L^2}\cdot_{max}</math>$
The stress limit is defined through the fatigue limit and the 0.2% elongation limit resp.
:<math>$\times_{max} = \frac{2 \cdot L^2}{3 \cdot D \cdot E}R_{p0,2}</math>$
<br />and/or<br />
:<math>$F_{max} = \frac{B \cdot D^2}{6L}R_{p0,2}</math>$
Deflection
:<math> $ \times = \frac{F}{2 \cdot E \cdot J}L^3</math> $
:<math>$= \frac{6 \cdot F}{E \cdot B}\cdot \frac{L^3}{D^3}</math>$
Max. bending force
:<math>$\sigma_{max}= \frac{18 \cdot F \cdot L}{B \cdot D^2}</math> $
<li>'''Trapezoidal spring'''</li>
Deflection
:<math> $ \times = \frac{F}{(2 + B_{min} /B_{max})}\times \frac{L^3}{E \cdot J}</math>$
:<math>$\times= \frac{12 \cdot F}{(2 + B_{min} /B_{max})}\cdot \frac{L^3}{E \cdot B \cdot D^3}</math>$
Max. bending force
:<math>$\sigma_{max}= \frac{18 \cdot F \cdot L}{(2 + B_{min} /B_{max}) \cdot B_{max} \cdot D^2 }</math>$
</ul>
==References==
[[Application Tables and Guideline Data for Use of Electrical Contact Design#References|References]]
