How to find beam spring stiffness coefficient?

In summary, the conversation discusses the problem of finding the equivalent spring constant for a beam with two springs attached. The relationships Ktotal = F/Δtotal and Δtotal = ½(Δ1 + Δ2) are suggested as possible solutions. The statement "If K1 = K2, Ktotal = K1 + K2" implies that there is no flexibility in the beam, but the post title suggests that the stiffness should reflect the beam's stiffness. The conversation also mentions the concept of parallel and series springs, with the conclusion that the equivalent spring constant Ktot = k1 + k2 regardless of the values of k1 and k2. However, one person argues that a unique formula is needed because the springs
  • #1
cognosco123
1
0
The problem is attached.
2015-09-13 22.58.08.jpg
 
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  • #2
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.
 
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  • #3
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?
 
  • #5
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.
 

FAQ: How to find beam spring stiffness coefficient?

1. How do I calculate the beam spring stiffness coefficient?

The beam spring stiffness coefficient can be calculated by dividing the load (force applied to the beam) by the deflection (amount the beam bends). This calculation can be represented by the equation k = F/d, where k is the stiffness coefficient, F is the applied load, and d is the deflection.

2. What factors affect the beam spring stiffness coefficient?

The beam spring stiffness coefficient is affected by the material properties of the beam, such as its Young's modulus and cross-sectional area. The geometry of the beam, including its length and thickness, also plays a role in determining the stiffness coefficient. Additionally, the type of loading and support conditions can impact the stiffness coefficient.

3. Can I use the same formula for calculating stiffness coefficient for all types of beams?

No, the formula for calculating stiffness coefficient may vary depending on the type of beam and its loading and support conditions. For example, a cantilever beam will have a different formula for calculating stiffness compared to a simply supported beam.

4. How can I measure the deflection of a beam?

The deflection of a beam can be measured using a variety of methods, including strain gauges, displacement sensors, and deflection gauges. These tools can be attached to the beam and used to measure the amount of bending or displacement under a given load.

5. Can I change the beam spring stiffness coefficient?

Yes, the beam spring stiffness coefficient can be changed by altering the material properties, geometry, or support conditions of the beam. For example, increasing the cross-sectional area of the beam or using a stiffer material can result in a higher stiffness coefficient.

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