How accurate is Mohr's circle?

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In summary, Mohr's circle is a graphical method for representing the stress state at a point in a material. It is based on the assumptions of homogeneity, isotropy, and linear elasticity, and it can only be used for two-dimensional stress states. While it is relatively accurate, it may introduce some error due to its simplifications. It can be used to determine principal stresses by finding the intersections on the horizontal axis, with the difference between these points representing the difference between the two principal stresses.
  • #1
Fusiontron
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I'm getting approximations within 5% of the actual values. Does that sound about right?
 
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  • #2
Depends on the values, really.

5% of 10Pa is 10 +/- .5 Pa, that's pretty close.

5% of 10MPa is 10MPa plus or minus 500000 Pa. That's a pretty big swing in precision.

I don't see that 5% is too horribly bad though, for estimation purposes.
 
  • #3
What do you mean by "actual values"?

Mohr's circle is mathematically "perfectly accurate". Whether your real life situation exactly matches the mathematical assumptions, or whether your phyiscal measurements are accurate to within 5%, are different questions.
 

Related to How accurate is Mohr's circle?

1. How is Mohr's circle used to represent stress states?

Mohr's circle is a graphical method used to represent the stress state at a point in a material. It is a plot of the normal stress (σ) on the horizontal axis and the shear stress (τ) on the vertical axis.

2. What assumptions are made in using Mohr's circle?

Mohr's circle assumes that the material being analyzed is homogeneous, isotropic, and linearly elastic. It also assumes that the stress state is at a point and not varying over an area.

3. How accurate is Mohr's circle in representing stress states?

Mohr's circle is a relatively accurate graphical method for representing stress states. However, it is not exact and may introduce some error due to the assumptions made and the approximation of the stress state as a point.

4. What are the limitations of using Mohr's circle?

One major limitation of Mohr's circle is that it can only be used for two-dimensional stress states. It also does not account for factors such as material nonlinearity, plastic deformation, or stress concentrations.

5. How can Mohr's circle be used to determine principal stresses?

Mohr's circle can be used to determine the principal stresses at a point by finding the points where the circle intersects with the horizontal axis. The corresponding values on the vertical axis represent the maximum and minimum shear stresses, and the distance between these points represents the difference between the two principal stresses.

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