The key is to balance the (vertical) forces and torques. You have the downward force of the weight on the beam, of 800 N. This must be balanced by the upward forces the springs exert on the beam, and , so that we have . Now, consider the torques about the center of the beam. The load acts 0.5 m from the beam center, and so exerts a torque of (800 N)(0.5 m)=400 N•m counterclockwise (in our diagram). Spring B, in turn, exerts a torque in the same direction of . Lastly, spring A exerts a torque in the opposite direction of , thus

And so you have a system of two equations for your two unknown forces; solving for these forces, you use the fact that the force exerted by each spring will be the stiffness k=5 kN/m times the compression of the spring; you can then find how much each spring is compressed. The difference in these is the difference in the heights of the ends of the beams, which is 3 m (the length of the beam) times the sine of the angle you want to find.

--Kevin C.