Am I in the correct forum?

Don't get too bogged down with the rail/hanger modelling, The problem boils down to the two simple equations:

Ft = SUM(Fh) : Total Force = sum of the individual hanger forces

Mt = SUM(Fh x Ph) : Total Moment = sum of the cross product of the forces and the hanger positions.

I Know Ft, Mt and all the values of Ph. I want to find sensible values for Fh.

This gives a single point solution for 2 hangers, a line of solutions for 3 hangers, a plane for 4 hangers...

What I want is to find the point within these solution spaces that minimises the maximum value of Fh.

Perhaps I should have posted this question in the inequalities and graphing forum?

Mark.

Consider the 3 hanger problem...

For three hangers I was thinking along the lines of:

Assume the force on hanger 1 is zero, this reduces the problem to a 2 hanger problem, that can be solved (simultaneous equn.).

Then assume the force on hanger 2 is zero, solve for the hangers 1 and 3.

This gives two points on the line of possible solutions to:

**F**t=**F**1+**F**2+**F**3

**M**t=**F**1x**H**1+**F**2x**H**2+**F**3x**H**3

Find the perpendicular to this line that passes through the point **F**1=0, **F**2=0, **F**3=0.

I'm looking for a method for solving this for any values of **F**t, **M**t, **H**1, **H**2 and **H**3 (**H**1,**H**2,**H**3 are all different).

If I can get that working I would like to extend to any number of hangers.

Am I barking up the wrong tree? Am I in the correct forest? :)

Mark.