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

[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??

 

[SteamKing]

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.

 

[member 392791]

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