Is A_θ equal to A_0/cos θ in stress on an oblique plane?

In summary, the conversation discusses the relationship between A_θ and A_0/cos θ in regards to the geometry of a bar. The speaker is having trouble understanding this relationship but eventually comes to the conclusion that A_θ is equal to A_0/cos θ. They also discuss the dimensions of A_0 and how it relates to the cutting plane. Eventually, the speaker is able to understand and thanks the other person for their help.
  • #1
member 392791
Hello,

I am looking at my lecture notes PDF, and I am having trouble seeing the geometry how A_θ is A_0/cos θ. I can understand how the force acting on that cross section is Pcosθ, just not the part about the area for which F is acting. I think F is normal to the plane, so the cross section area is not just A_0??
 

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  • #2
I think you must assume that A0 is the cross sectional area of the bar when the cutting plane is normal to the longitudinal axis of the bar.

It's easy to calculate Aθ, assuming A0 has dimensions height 'h' and width 'w' and the cutting plane makes angle θ with the vertical. Try it, and compare Aθ with A0.
 
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  • #3
Okay, I have convinced myself that A_θ is A_0 / cos θ. I think I have convinced myself of the slide now, Thanks SteamKing
 

1. What is the equation for Aθ in stress on an oblique plane?

The equation for Aθ is equal to A0/cos θ, where A0 is the stress on the perpendicular plane and θ is the angle between the oblique plane and the perpendicular plane.

2. How is Aθ related to A0 and the angle of the oblique plane?

Aθ is inversely proportional to the cosine of the angle θ between the oblique plane and the perpendicular plane. This means that as the angle increases, Aθ decreases and vice versa.

3. What is the significance of Aθ in stress analysis?

Aθ is important in determining the stress on an oblique plane, which is necessary for analyzing the structural integrity of a material or object. It helps determine the maximum stress that the material can withstand before failure.

4. Can Aθ ever be greater than A0?

No, Aθ can never be greater than A0. This is because the cosine of any angle is always less than or equal to 1, making Aθ always less than or equal to A0.

5. How is Aθ affected by changes in the angle of the oblique plane?

Aθ is directly affected by changes in the angle of the oblique plane. As the angle increases, Aθ decreases and as the angle decreases, Aθ increases. This relationship is represented by the inverse proportionality between Aθ and cos θ.

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