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?
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:
Find the perpendicular to this line that passes through the point F1=0, F2=0, F3=0.
I'm looking for a method for solving this for any values of Ft, Mt, H1, H2 and H3 (H1,H2,H3 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? :)