EQUIVALENT STIFFNESS

Construction fundamentals

INTRODUCTION

In many applications it is relevant to know the total connection stiffness of an object in relation to a given reference. In many cases there are several stiffness paths which introduces the need to calculate the ‘equivalent’ stiffness. This is a single stiffness representing the sum of all individual stiffness’ in the appropriate way, taking into account the series/parallel configuration and possible movement amplifications/reductions. Below a number of cases is listed.

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Equivalent Stiffness 01

C_{eq}=\frac {F}{s}=\frac{C_1 \bullet C_2}{C_1+C_2}

Equivalent Stiffness 06

C_{eq}=\frac {F}{s}=\frac{a^2 \bullet C_1 \bullet C_2}{(a-b)^2 \bullet C_1+b^2 \bullet C_2}

Equivalent Stiffness 02

C_{eq}=\frac {F}{s}=C_1+C_2

Equivalent Stiffness 07

C_{eq}=\frac {F}{s}=\frac{b^2 \bullet C_1 \bullet C_2}{(a-b)^2 \bullet C_1+a^2 \bullet C_2}

Equivalent Stiffness 03
Equivalent Stiffness 04
Equivalent Stiffness 05

C_{eq}=\frac {F}{s} =(\frac {a}{b})^2 \bullet C_1 =i^2 \bullet C_1

Equivalent Stiffness 08

C_{eq}=\frac {F}{s} =\cos ^2\alpha \bullet C_1

Equivalent Stiffness 09

C_{eq}=\frac {F}{s} =\sin ^2\alpha \bullet C_1

Equivalent Stiffness 10

C_{eq}=\frac {F}{s} =\frac{K_{rot}}{a^2}

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