# Bridge mechanics [closed]

The emergency bridge shown in picture above is constructed in the form of a framework with 11 bars. On one bank, the bridge is anchored by the bivalent fixed bearing A and on the opposite bank by the monovalent sliding bearing B. It is assumed that a truck with the weight FG is at a standstill on the bridge and this is statically loaded. The wheels of the truck touch the bridge exactly at junctions III and IV. The center of gravity of the truck is at distances k and l to these junctions. Use the torque balance in node III. Is this node subject to compressive or tensile forces? Where does the center of gravity of the vehicle have to be in order to maximize F6? To do this, specify the values for k and l as a function of a?

How can I calculate that if I know that all forces are coming through III expect $$F_g$$ and $$F_6$$?

In my case Torque Equilibrium would like something like this:

$$(k+a)F_Gh$$=$$F_6h$$

Which isn't correct, where am I making the mistake?

• Did you transcribe the problem correctly? Should "rod" be "node"? – Bob D Oct 26 '19 at 13:23
• @BobD Hello, I am not sure since I am translating it from another language. – Majica Oct 26 '19 at 13:24
• If its a rod, then i would have to say which one (I-II, I-III, III-IV, ...). – Bob D Oct 26 '19 at 13:33
• @BobD If "something" is subject to compressive or tensile forces, the "something" must be a rod, not a node. But we don't know what "this rod" refers to. I guess a sentence is missing from the question. – alephzero Oct 26 '19 at 13:37
• @alephzero Agree, but which rod? Seems unlikely to omit an entire sentence. And what is $F_6$? The force in the 6 unit rod? Maybe that's the rod? – Bob D Oct 26 '19 at 13:56