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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 x E x J}{L^3} x</math>
where J is the momentum of inertia of the rectangular cross section of the beam
:<math>J = \frac {B x D^3}{12}</math>
For springs with a circular cross-sectional area the momentum of inertia is
To avoid plastic deformation of the spring the max bending force σ<sub>max</sub> cannot be exceeded
:<math>\sigma _sigma_{max} = \frac {3 x E x D}{2L^2}x_{max}</math>
The stress limit is defined through the fatigue limit and the 0.2% elongation limit resp.
:<math>x _x_{max} = \frac {2 x L^2}{3 x D x E}R_{p0,2}</math>
<br />and/or<br />
:<math>F _F_{max} = \frac {B x D^2}{6L}R_{p0,2}</math>
Deflection
:<math>x = \frac {F}{2 x E x J}L^3</math>
:<math>= \frac {6 x F}{E x B}x \frac{L^3}{D^3}</math>
Max. bending force
:<math>\sigma _sigma_{max}= \frac {18 x F x L}{B x D^2}</math>
<li>'''Trapezoidal spring'''</li>
Deflection
:<math>x= \frac {F}{(2 + B_{min} /B_{max})}\times \frac{L^3}{E x J}</math>
:<math>x= \frac {12 x F}{(2 + B_{min} /B_{max})}\times \frac{L^3}{E \times B \times D^3}</math>
Max. bending force
:<math>\sigma _sigma_{max}= \frac {18 x F x L}{(2 + B_{min} /B_{max}) x B_{max} x D^2 }</math>
</ul>
==References==
[[Application Tables and Guideline Data for Use of Electrical Contact Design#References|References]]
