How to find beam spring stiffness coefficient?

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SUMMARY

The discussion focuses on calculating the beam spring stiffness coefficient using the formula Ktotal = F/Δtotal, where Δtotal is defined as ½(Δ1 + Δ2). It emphasizes that if K1 equals K2, then Ktotal equals K1 + K2, indicating no flexibility in the beam. The conversation also highlights the distinction between parallel and series springs, asserting that a unique formula must be derived for cases where springs displace differently to maintain equilibrium.

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  • Knowledge of equilibrium principles in mechanical systems
  • Basic grasp of series and parallel spring configurations
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cognosco123
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The problem is attached.
2015-09-13 22.58.08.jpg
 
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I think you can solve it generally using the relationships:
Ktotal =F/Δtotal
Δtotal = ½(Δ1 + Δ2)

assuming the mass is located at mid-span.
 
Last edited:
The statement "If K1 = K2, Ktotal = K1 + K2" implies that there is no flexibility in the beam. The post title suggest that you want the stiffness to reflect the stiffness of the beam as well. Which is it?
 
Daniel Sadlier said:
The equivalent spring constant Ktot = k1 + k2 no matter the values of k1 or k2.
I'll disagree on this. The parallel springs formula assumes that both springs displace the same. Here, however, the springs will displace differently to maintain equilibrium. Therefore, a unique formula needs to be derived.
 

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