How Do You Calculate Stress on a Point in 3D Mechanics of Materials?

[Bluestribute]

So I'm studying for an upcoming Mechanics of Materials exam. Gotta ace it! Anyways, I'm having trouble with these types of problems. Finding state of stress on a point in 3D. This picture comes from: http://www.academia.edu/6204133/Chapter_09

Which has worn shown, but not explanations. I have two questions to start, but hopefully more will surface and get answered . . .

1) I always have trouble finding Q and I don't know why. Does anyone have a solid equation or "explanation for dummies"? It's just the centroid-to-center-of-area distance, right?

2) Which equation to use and what it corresponds to. I think what would really help is just, what does each equation mean in terms of stress. For example, I know Normal Stress is σ = F/A, and I know it acts parallel to the plane it's on (so σ_x points in the X direction).

I think using this problem as an example could work. Also, feel free to move this if it's in the wrong place.

 

[wilsont23274]

1) To calculate the centroid-to-center-of-area distance, you will need to use the equation: Q = √A/2π. Where A is the area of the plane. 2) The equations you need to use for this problem are as follows: Normal Stress: σ = F/A Shear Stress: τ = F/A Torsion Stress: τ = T/J The normal stress corresponds to the force acting in the direction normal to the plane. This means that if a force is applied in the x-direction, then the normal stress in the x-direction would be σx = F/A. The shear stress corresponds to the force acting in the direction parallel to the plane. This means that if a force is applied in the y-direction, then the shear stress in the y-direction would be τy = F/A. The torsion stress corresponds to the torque, or twisting force, acting on a body. This means that if a torque is applied in the z-direction, then the torsion stress in the z-direction would be τz = T/J. Where J is the polar moment of inertia.