Radius of curvature usng: M/I= σ/Y = E/R

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SUMMARY

The formula M/I = σ/Y = E/R is essential for calculating the radius of curvature (R) in structural engineering. To isolate R, rearrange the equation to R = E/(M/I). This allows for the determination of the radius of curvature when the modulus of elasticity (E), bending moment (M), and second moment of area (I) are known. Understanding this relationship is crucial for engineers working with materials under stress.

PREREQUISITES
  • Understanding of bending moment (M) in structural analysis
  • Familiarity with the second moment of area (I) in beam theory
  • Knowledge of stress (σ) and its relation to material deformation
  • Concept of modulus of elasticity (E) in material science
NEXT STEPS
  • Study the derivation of the bending moment equation in beam theory
  • Learn how to calculate the second moment of area for different cross-sections
  • Explore the relationship between stress and strain in materials
  • Investigate practical applications of the radius of curvature in engineering design
USEFUL FOR

Structural engineers, mechanical engineers, and students studying material mechanics will benefit from this discussion, particularly those focused on analyzing material behavior under bending loads.

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Question:

How do I use this formula to find the Radius of curvature?

Formula:

M/I= σ/Y = E/R (M = bending moment, I = second moment of aria, σ = stress, y = distance from nutral axia, E = modulus of elasticity & R = radius of curvature)

Attempt:

In this question, I have all of the values except the radius of curvature, but I don't understand how to use this formula. If someone could rearrange the formula for me and post it, it would be much apriciated.

Thanx
 
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They are all equal to one another. But if you have to use them to solve anything, you need to use any pair of the equations. For example, I could use

M/I = σ/y OR M/I=E/R
 

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