Force-Deformation Equations Application

In summary, the conversation discusses the use of equations for solving problems involving deflection and axial loading. The first equation, δ=FL/AE, is used for axial members that are loaded only at the ends. The second equation, σ=δL/E, is also used for axial loading and comes from Hookes Law. The conversation also mentions that statically indeterminate problems require additional equations to solve and can involve more supports and members.
  • #1
depressivemoron86
1
0
Just found this forum--hope there isn't a max post limit haha.

I have been a bit stumped on this, but when doing problems about deflection and axial loadings, I am confused when to use which equation.

I think I know that axial member need to be 2 force members, loaded only at the ends, and this means you can use δ=FL/AE. However, I had a problem with two axial bars connected at two ends and it was made clear that I could not use the above equation, but had to use σ=δL/E.

I guess my main question is where do I use which, what exactly is axial loading, and what is statically indeterminate mean does this make it unusable??

Thanks!
 
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  • #2
Your 2nd formula is incorrect , perhaps you copied it down incorrectly, for axial loading it should be [itex] \delta = \sigma L/E[/itex], and since axial stress is F/A, this equation is identical to your first equation. It comes from Hookes Law, where stress is proportional to strain, and the proportionality constant is E, the Elasticity of the material, or that is [itex] \sigma = \epsilon E[/itex], where the strain [itex] \epsilon [/itex] is axial deformation/L. I'm not sure why you have to use the 2nd equation (as I have corrected) rather than the first , which gives the same result, unless the givens make it easier to use, perhaps you can post the problem. Deformations for bending loads are a bit more complex.

Statically indeterminate problems mean that you have to use more than the equilibrium equations to solve them, like calculating deflections and such, but they certainly are valid beams or trusses with more supports and members.
 

1. What are force-deformation equations?

Force-deformation equations are mathematical representations of the relationship between applied force and resulting deformation in a physical system. They are often used in engineering and physics to predict the behavior of materials under different loading conditions.

2. How are force-deformation equations applied in real-world situations?

Force-deformation equations are applied by using known values for force and deformation to solve for other unknown variables, such as material stiffness or stress. These equations can then be used to design structures or predict the behavior of materials under different loading conditions.

3. What types of materials can be analyzed using force-deformation equations?

Force-deformation equations can be used to analyze the behavior of both elastic and plastic materials. Elastic materials, such as rubber or metal springs, return to their original shape after being deformed. Plastic materials, such as metals or plastics, undergo permanent deformation when subjected to force.

4. Are force-deformation equations accurate in all situations?

While force-deformation equations are useful tools for predicting the behavior of materials, they are not always accurate in every situation. This is because real-world materials can behave differently than idealized mathematical models. It is important to consider other factors, such as material properties and external forces, when using force-deformation equations.

5. How can force-deformation equations be used to improve product design?

By using force-deformation equations, engineers and designers can predict how different materials will behave under different loading conditions. This information can then be used to make more informed decisions about material selection and design choices, ultimately leading to safer and more efficient products.

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