How to find beam spring stiffness coefficient?

AI Thread Summary
To find the beam spring stiffness coefficient, the total stiffness can be calculated using Ktotal = F/Δtotal, with Δtotal defined as ½(Δ1 + Δ2) for a mass at mid-span. The assumption that K1 equals K2 leads to Ktotal being the sum of K1 and K2, indicating no flexibility in the beam. However, the discussion highlights that the parallel springs formula may not apply since the springs displace differently to maintain equilibrium. A unique formula may be necessary to accurately reflect this behavior. The conversation emphasizes the need for careful consideration of spring displacement in beam stiffness calculations.
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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