Roark's Equations for Discontinuity Stresses Syntax

In summary, R_A refers to the radius of common circumference, which is the intersection of the midsurfaces of two different shells. It is measured vertically from an axis bisecting the shell horizontally and can be a function of the radius of one of the shells. R_A is not to be confused with delta R_A, as seen in the table provided.
  • #1
josep233
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I am looking for clarification of some terms found in Roark's Formulas for Stress and Strain 9E. Table 13.4 pg 543 as well as preceding tables frequently reference R_A as the radius of common circumference. I take this to mean that this value could include any radius that both cylinders share through their thicknesses, but do not know for sure. To further confuse this, some tables say R_A = R_1. Does anyone with more exposure to this understand what R_A means?
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  • #2
R_A =radius of common circumference, i.e. it is defined as the intersection of the midsurfaces of the two different shells (not just any shared radius). It is generally defined as a vertical distance from an axis bisecting the shell horizontally. So if the left-most section isn't curved, then R_a should equal R_1.
1686676572241.png


If the left section is e.g. more circular, then the R_a is a function of R_1*sin() -> since R_a is measured vertically in the fashion the diagrams are usually portrayed, not radially.
1686676452828.png

It's maybe worth saying that R_A is not delta R_A, which is all I see in the table you shared.
 
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Related to Roark's Equations for Discontinuity Stresses Syntax

What are Roark's Equations for Discontinuity Stresses?

Roark's Equations for Discontinuity Stresses are a set of mathematical formulas and principles used to calculate the stress concentrations and discontinuities in various structural elements. These equations are essential in mechanical and structural engineering to predict areas where stress might be significantly higher due to abrupt changes in geometry or material properties.

Why are discontinuity stresses important in engineering?

Discontinuity stresses are crucial in engineering because they can lead to failure points in structures. Areas with high stress concentrations are more prone to cracking, yielding, or other forms of material failure. By understanding and calculating these stresses, engineers can design safer and more efficient structures by reinforcing or modifying areas susceptible to high stress.

How do Roark's Equations help in predicting failure in structures?

Roark's Equations help predict failure in structures by providing a mathematical framework to identify and quantify stress concentrations. By applying these equations, engineers can determine the maximum stress levels at discontinuities and compare them to the material's strength limits. This allows for the identification of potential failure points and the implementation of design changes to mitigate these risks.

What types of structures can benefit from Roark's Equations for Discontinuity Stresses?

Roark's Equations for Discontinuity Stresses can be applied to a wide range of structures, including beams, plates, shells, and pressure vessels. These equations are used in various fields such as aerospace, civil, mechanical, and structural engineering to ensure the integrity and safety of different types of constructions and components.

Where can I find detailed information and examples of Roark's Equations for Discontinuity Stresses?

Detailed information and examples of Roark's Equations for Discontinuity Stresses can be found in the reference book "Roark's Formulas for Stress and Strain." This book is a comprehensive resource that provides detailed explanations, mathematical derivations, and practical examples for a wide range of stress and strain calculations, including those related to discontinuities.

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