Cross-sectional area for stress calculations

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SUMMARY

The discussion focuses on calculating cross-sectional areas for normal and shear stress problems, particularly when dealing with diagonal sections. The user expresses difficulty in determining the appropriate angles and trigonometric functions for these calculations. They seek guidance on treating the cross-sectional area as the hypotenuse of a triangle, utilizing known angles and horizontal leg measurements. The conversation emphasizes the importance of understanding geometry and trigonometry in engineering stress analysis.

PREREQUISITES
  • Understanding of normal and shear stress concepts
  • Basic knowledge of geometry and trigonometry
  • Familiarity with Free Body Diagrams (FBDs)
  • Ability to interpret angles and lengths in engineering contexts
NEXT STEPS
  • Study trigonometric functions and their applications in engineering
  • Learn how to construct and analyze Free Body Diagrams (FBDs)
  • Explore the calculation of cross-sectional areas in complex shapes
  • Review examples of stress analysis in mechanical engineering problems
USEFUL FOR

Engineering students, mechanical engineers, and professionals involved in structural analysis who need to calculate cross-sectional areas for stress evaluations.

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I am having a lot of difficulty calculating the cross-sectional areas necessary for normal/shear stress problems. If the cross-section is a square or circle, I'm fine, but when the problem makes a diagonal section through the object I get really confused on which angle/trig function to use to calculate the cross-sectional area.

Below are a few FBDs of problems I'm working on just to give a better idea of what I'm talking about.

http://i53.tinypic.com/69fjvc.png
http://i51.tinypic.com/2lji5ol.png
http://i56.tinypic.com/2gv4fet.png
http://i52.tinypic.com/2rrw094.png
http://i56.tinypic.com/2e6a1qt.png

Can someone please walk me through how to calculate cross-sectional area for these kind of problems (what angle/trig functions to use, etc)
 
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Treat the cross sectional area needed as the hypotenuse of a triangle. You know the angle theta. You know the leg A, which is the horizontal area of the figure.

angle.jpg
 
Thanks for the response. I think I am starting to get the hang of it.
 

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