Minimizing the maximum bending moment

[hamdal]

Homework Statement

The question is asking us to minimize the maximum bending moment by changing l3.
l1=3(m)
l2=6.5(m)
l4=12(m)
P1=1200(KN)
P2=2300(KN)
P3=410(KN)
and we know that obviously, 6.5<l3<12

Homework Equations

The Attempt at a Solution

We made relevant cuts and acquired the equations for our bending moments in different sections of the beam.In the end,we have too many unknowns and not enough equations.We even tried plotting 3D graphs on MATLAB to find the optimum point,however we failed since we still had too many unknowns.We tried trial and error to give different values and we optimized it at l3=6.5(m),but we can't really get the value using maths.Something doesn't feel right about our method.

 

[Chestermiller]

It's very hard to help you without seeing your shear and bending moment equations. Maybe you could write these out for us?

Chet

 

[hamdal]

It's very hard to help you without seeing your shear and bending moment equations. Maybe you could write these out for us?

Chet

After a long day,we were able to solve the problem and I blame myself for the delay.
So in general,the minimum happens when the positive moments are equal to the negative moments (since we're talking about the magnitude of the moment).I came up with the idea when I read the question but I made a huge mathematical mistake which kept us from getting the answer.
So we solved the relevant equations and we even plotted bending moment vs l3 graph.

 

[Chestermiller]

After a long day,we were able to solve the problem and I blame myself for the delay.
So in general,the minimum happens when the positive moments are equal to the negative moments (since we're talking about the magnitude of the moment).I came up with the idea when I read the question but I made a huge mathematical mistake which kept us from getting the answer.
So we solved the relevant equations and we even plotted bending moment vs l3 graph.

Congrats. Sometimes the "arithmetic" can get pretty hairy.

Chet