Cross-sectional area for stress calculations

In summary, the speaker is struggling with calculating cross-sectional areas for normal/shear stress problems, particularly when the cross-section is a diagonal section through the object. They are asking for guidance on how to approach these types of problems, specifically what angle/trig functions to use. They also provide some example problems to illustrate their difficulty. The speaker is advised to treat the cross-sectional area as the hypotenuse of a triangle and use the known angle and horizontal area to calculate the area needed. They express gratitude for the response and believe they are beginning to understand the concept.
  • #1
PNGeng
17
0
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)
 
Physics news on Phys.org
  • #2
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
 
  • #3
Thanks for the response. I think I am starting to get the hang of it.
 

Related to Cross-sectional area for stress calculations

1. What is cross-sectional area?

Cross-sectional area refers to the area of a two-dimensional shape when it is cut perpendicular to its longitudinal axis. In other words, it is the area of the shape when viewed from the side.

2. Why is cross-sectional area important for stress calculations?

Cross-sectional area is important for stress calculations because it is used to determine the amount of force that can be applied to a material before it reaches its breaking point. The larger the cross-sectional area, the more force the material can withstand without failing.

3. How is cross-sectional area calculated?

Cross-sectional area is calculated by multiplying the width of the object by its height or diameter, depending on the shape. For example, the cross-sectional area of a rectangular object would be calculated by multiplying its length by its width.

4. Does the material of an object affect its cross-sectional area?

Yes, the material of an object does affect its cross-sectional area. Different materials have different strengths and densities, which can impact the amount of force they can withstand. For example, a steel rod and a wooden rod of the same size will have different cross-sectional areas due to their different material properties.

5. How does cross-sectional area relate to stress and strain?

Cross-sectional area is directly related to stress and strain. When an object is subjected to stress, the force applied to it is spread out over its cross-sectional area. This results in strain, or deformation, of the object. A larger cross-sectional area can distribute the force more evenly and result in less strain, while a smaller cross-sectional area may experience higher levels of strain.

Similar threads

Engineering Analyzing Shear & Bending on Idealized Cross Section
    • Engineering and Comp Sci Homework Help
Replies
4
Views
1K
Engineering Transverse shear stress calculation in non-slender built up members
    • Engineering and Comp Sci Homework Help
Replies
6
Views
1K
How Do You Calculate the Area of an Airfoil Cross-Section?
    • Engineering and Comp Sci Homework Help
Replies
2
Views
6K
Find beam stress in a beam with varying cross section
    • Engineering and Comp Sci Homework Help
Replies
4
Views
2K
How do I estimate stress in a non-prismatic shape?
    • Engineering and Comp Sci Homework Help
Replies
3
Views
2K
Calculate the maximum vertical point force P that this beam can sustain
    • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
Maximum shear stress in an assymetric cross-section
    • Mechanical Engineering
Replies
4
Views
1K
Mechanics of Materials: Cross Sectional Area Problem
    • Engineering and Comp Sci Homework Help
Replies
1
Views
2K
Cross Sectional Area, Stress and Strain confusion
    • Engineering and Comp Sci Homework Help
Replies
5
Views
15K
Izod Impact test Cross Sectional Area
    • Engineering and Comp Sci Homework Help
Replies
1
Views
4K

Hot Threads

Recent Insights

Back
Top