How would you calculate tension/compression in a truss bridge (diagram shown)?

You convert the load in the centre into an equivalent load at the joints. In this case, you have 10kN downwards, in a perfectly centred location. This is indistinguishable from 5kN downwards at the joints at each end of the central member. To check this, consider force equilibrium and moments (from the loads only) about the centre of the member.

To start (10kN central):

Vertical force: 10kN downwards

Horizontal force: 0kN

Central moment: 10kN*0mm = 0kNmm

Equivalent load (5kN at joints):

Vertical Force: 5kN + 5kN = 10kN downwards

Horizontal force: 0kN

Central moment: 5kN *100mm - 5kN*100mm = 0kNmm

And so are identical. You can work out equivalent loads for any load at any position on the member by considering the loads that would create an identical effect if placed at the joints.

I wasn't sure if you wanted the solution as well. I can go back and calculate it if you wish.

Truss Bridge Diagram

Force diagram starts from one point, and follow the members by directing the compression forces up wards and tension members say down wards, by completing all members the lines must meet to close the diagram, if I does not , then there is some thing wrong with members forces