Cross-sectional area for stress calculations

AI Thread Summary
Calculating cross-sectional areas for stress problems can be challenging, especially with diagonal sections. The key is to identify the correct angle and use trigonometric functions to determine the area. For diagonal cuts, treat the cross-sectional area as the hypotenuse of a triangle, using the known angle theta and the horizontal leg A to find the necessary dimensions. Visual aids like free body diagrams can help clarify the relationships between angles and areas. Understanding these concepts can significantly improve the ability to solve such stress calculation problems.
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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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