Support Reactions of Columns placed on Hydraulic bed (same pressure) with Unequal Loading

Question

Suppose columns are supported on a deck with hydraulic cylinders which are coupled together with the same pressure. These columns are loaded with unequal loads F1 and F2 (F1 > F2). Will the reaction at column support (R1 and R2) will be the same since its supported by hydraulic cylinders with equal pressure? Refer the Figure.

I can understand that there would be some movements of the support and it cannot be considered as a simply supported static problem. What should be the approach to find the loads transferred through each column?

Answer 1

Can the bed tilt?

I assume the upward force from all the supports adds up to $R_1 + R_2$

You need $R_1 > R_2$, but for that to happen the upward force from the left two supports would have to be larger than on the right. That means the pressure would have to be larger.

If you have pistons in small closed cylinders, the left supports could sink, compressing the gas inside and raising the pressure. The bed would tilt and become stable.

For a hydraulic system at constant pressure, the bed would tilt until it hit an obstruction or the load fell over.

If the supports prevent the bed from tilting, there would be sideways forces on them the create a torque keeping the bed level. This would be stable. See Toppling of a cylinder on a block for more.