Calculating stiffness from load and defletion

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Discussion Overview

The discussion revolves around calculating the stiffness of a composite laminate beam subjected to a load and resulting deflection. Participants explore theoretical and experimental approaches to determine stiffness, including the use of specific equations and definitions.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant describes a composite laminate beam loaded with 415N, resulting in a deflection of 0.05m, and seeks assistance in calculating stiffness.
  • Another participant questions the definition of stiffness being used, suggesting that if it is force per unit displacement, the experimental data provides the answer directly.
  • A third participant clarifies that the equation provided for deflection is for a simply supported beam and emphasizes the distinction between deflection and stiffness, suggesting the use of Hooke's law to find the equivalent stiffness.
  • A later reply indicates that the original poster found the solution using Hooke's law, expressing appreciation for the assistance received.

Areas of Agreement / Disagreement

Participants generally agree on the need to clarify the definition of stiffness and the relationship between load, deflection, and stiffness. However, there are multiple approaches discussed, and the conversation reflects differing perspectives on how to derive or calculate stiffness.

Contextual Notes

Participants note potential uncertainties regarding the material properties (E and I) of the composite laminate, which may affect theoretical calculations. The discussion also highlights the importance of definitions in the context of stiffness.

Who May Find This Useful

Individuals interested in material mechanics, composite materials, or structural analysis may find this discussion relevant, particularly those looking to understand the relationship between load, deflection, and stiffness in beam theory.

Jackcheasley
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ok i loaded a composite laminate beam across the centre of a 1.44meter span with 415N load. This deflected the beam to a distance of 0.05m (5cm).
Im having trouble calculating the stiffness from this.
The composite laminate is 5mm of wood in a glass fiber sandwich with both the top and bottom layer measuring 1mm thick making a total depth of 7mm. The beam has a base of 27cm.


some of the equations i have are:
s=415*1.44^3/48EI
or
D=Eskin/12*(0.07^3-0.05^3)+Ec*0.05^3/12



If anyone had any idea even if its different equations as I am unsure on these, any help is great

Thanks
 
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What definition of stiffness would you be wanting to use? If it is force per unit displacement, then the experiment gives it you. If you want to compare that with a theoretical value, then maybe you should derive the formula for D from 1st principles, rather than trust it?
 
Jackcheasley said:
some of the equations i have are:
s=415*1.44^3/48EI
This equation is the theortical deflection of the beam at mid point if the beam is simply supported at each end. Since you may not know E or I for the composite material, your experiment gives you the deflection, as Pongo38 as noted. The stiffness of the beam under this loading and end condition is not the same as the deflection. The deflection has length units, and the stiffness has force/length units. Try using Hooke's law to calculate the equivalent stiffness of the beam loaded in this manner. you have the load and the deflection, what is the stiffness under this definition?
 
Awesome
Cheers guys Got it from hooks.
thanks
 

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