force calc for pipe on rollers

huangyhg

force calc for pipe on rollers?
i have a pipe sitting on five rollers around the circumference of the pipe. the bottom/center roller is directly below the cg of the pipe. the other four rollers are at a 30 degree angle from each other about the center of the pipe.
i am trying to find the weight distribution on each roller. the force on two outside rollers at 60 degrees should equal each other and the force on the next two rollers should equal each other. i have found analysis for all five rollers to be indeterminate. when i go down to three, i.e. the center and the inner two using sum of forces and sum of moments i get a cancelling out.
can anyone recommend another method, or a rule of thumb that might apply in this situation?
thanks in advance for any advice.

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the problem is indeed indeterminate.
as two rollers are sufficient for the equilibrium, you are indeterminate even with three. to solve, you must assume the exact position of each roller, its stiffness, then calculate with an equation (or fem) accounting for the bending behavior of the pipe. with five rollers is the same, only more complex when solved by formulae.
prex
unless there is a horizontal force on the pipe, and neglecting deformation of the pipe and rollers, all the gravity loading from the pipe will be taken by the central roller.