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I am trying to understand the concept of equivalent stiffness of a beam. As I see it, the equivalent stiffness is the stiffness of a linear spring that would deflect the same amount under the same load. For a cantilever beam with a load P and a deflection [itex]\delta[/itex] at the free end, if we just look at the deflection of the free end, and somehow lump the stiffness and elastic properties of the beam into the term [itex]k_{eq}[/itex], it's motion will be the same as a linear spring with stiffness [itex]k_{eq}[/itex] when the same load P is applied to the spring.

My vibrations textbook mentions the [itex]k_{eq}[/itex] for a cantilever with a moment applied to the free end as [itex]\frac{EI}{L}[/itex]. Assuming that the spring being considered is a linear torsional spring, how do we interpret this? I am thinking it goes something like - 'The equivalent stiffness of a cantilever beam with a moment at the free end is the stiffness of a linear torsional spring that would coil by an angle say [itex]\theta[/itex] when the same moment is applied to it.' Now, is [itex]\theta[/itex] the same as the tip deflection [itex]\delta[/itex] or is it the local slope at the free end ie [itex]\theta \approx \tan(\theta) = \frac{dy}{dx}[/itex]

Thanks a lot for the help!

PS - Any suggestions for books that explain the equivalent stiffness concept well?

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# Equivalent stiffness of a beam

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