What is the Load Distribution on a Wobbly 4-Legs Table?

[chungaaabb]

Homework Statement

Hi everyone. I need to do project on a 4-legs square table of dimensions 0.5m*0.5m*0.5m with weight X Newtons. At each corner, there is a column supporting the table. A downward force of 150 Newtons will act on the table at the place where one of the column is. Before handing in the project, I need to calculate the force acting on each column. However, I can only give 3 equations with 4 unknowns.

Homework Equations

The Attempt at a Solution

I tried using similar triangle that formed by the deflections of the four legs to solve the problem but I failed since no unknowns could eliminate from the equations.

Thanks in advance for any efforts to show me how to do this

P.S. I am a Hong Kong student studying materials engineering so my English isn't very good. If there is any grammatical mistake, please ignore it.

 

[mfb]

With 4 legs, load distribution can vary, and will depend on details of the legs (as they will not have exactly the same length and so on). You could consider the worst case for each leg, for example.

 

[pongo38]

Suppose the table were wobbly. What would the distribution of loads on the legs be just due to self-weight? When you have figured that out, you can add the effect of the 120 N.