Compressive stress on piece of rock

[vtmike]

Hi,
I have a configuration in which a piece of rock is under hydrostatic pressure (see attached figure) and I'm trying to figure out what the stress on this rock will be.
The boundary conditions on the Steel end plates are such that the right and left plates are restricted to move in the -ve X and +ve X directions respectively.

According to my calculations:From FBD, -(6000 X 41.3) + (6500 X 31.6) = -42,400 lbf
Stress = 42400/41.3 = 1027 psi Compressive in axial direction

But I'm not sure about my approach here. I did not account for the force due to 5,850 psi in the rock because it cancels out but I am not sure if it should cancel out or taken into account as an additional compressive load on the rock?

Thanks,
Mike

 

[Studiot]

Hello VTmike.

I would start by considering the fact that your rock would be proceeding leftwards rather rapidly if the pressures were indeed what you have written.

Forces driving the rock rightwards = 6500*31.6 = 205400 lbs

Forces driving the rock leftwards = 6000*41.3 = 247800 lbs

So there is a net force driving leftwards of 42400 lbs.

For this to be true there must be other forces acting, eg shear or friction at the horizontal surfaces.

 

[Unrest]

Is it really supposed to by under hydrostatic compression? ie the same pressure over all the surface. From your diagram it looks like biaxial compression, which could lead to shear failure.

And, yes, as StudioT said, the forces don't balance. Another example is the unbalanced force on the right-hand end plate. That means the plate is accelerating.