Optimising Support Location - Bending moments

[schmiggy]

Homework Statement

Firstly, I know posting images and asking for help is generally frowned upon, however in this case given the number of diagrams and equations involved I'm hoping it's warranted.

So we're given a diagram as at the top of the attached image and we're asked, given most of the unknowns, to find at what value of 'L3' reaction force no. 2 should be located such that the maximum bending moment is minimised.

Homework Equations

sum of forces = 0
sum of moments = 0

The Attempt at a Solution

see attached image - I have written it out in terms of parameters, however I am at a loss of how to find R1, R2, and L3.. there seems to be too many unknown variables. Any hints would be appreciated.

 

[SteamKing]

First, take your equations of static equilibrium and substitute the known values of the quantities given. You will have one unknown value, namely L4, which you will use in optimizing the maximum bending moment. You should be able to express R1 and R2 in terms of L4. This will simplify you problem greatly.

 

[SteamKing]

Substitute L3 for L4 in the post above.