Maths / Physics question. Any clever people out there?

Question

I am needing to calculate the distribution of a mass at 6 different points.

There is a body which is 1100mm long(X), 500 Width(Y), 650 High (Z) (rectangular in shape, i.e. a box)

The box weighs 1687 Kg

The centre of gravity is in the centre of the body, i.e. X=550mm, Y=250mm & Z=325

The body is mounted in 6 positions. All at the bottom of the box. One in each of the bottom corners & the other 2 mounts in the middle of the bottom section, one on either side. (I.e. the box is sitting on 6 equally spaced mounts on a floor)

For example, mount positions as follows:

Mount 1 X=0, Y=0

Mount 2 X=0, Y=500

Mount 3 X=550, Y=0

Mount 4 X=550, Y=500

Mount 5 X=1100, Y=0

Mount 6 X=1100, Y=500

I am fully aware that this arrangment makes all the mountings points bear the same load (i.e. equally loaded), but I require the calculation method to determine the load at each mount. (For example if the mounting points were different and not equally loaded).

I look forward to your reply.

Thanks

Answer 1

I'm taking a day off from being clever!

Answer 2

This is fairly straight forward.  You have 6 unknown variables... therefore you will need 6 equations.   The first equation is a force balance in the Z-direction.  The next 5 equations will need to be moment equations about the lines made by mounts (1 & 5), (2 & 6), (1 & 2), (5 & 6), and (3 & 4).

All 5 moment equations will be set equal to zero because there is no rotation about any axis.

The force balance will be set equal to the weight of the body.

You can either try and solve this by hand, use a matrix, or an equation solver.  I recommend the latter two.