Problem: Before any load is applied, a gap of 20 mm exists between the W410 x 60 rolled-steel beam and the support at C.  Given that E = 200 GPa, determine the reaction at each support caused by a uniformly distributed load of 24 kN/m.

Solution: If I start out with a free body diagram and apply Newton's Laws I get two equations and three unknowns; i.e., the problem is statically indeterminate.

Using the method of superposition, I draw two separate diagrams, the sum of which equals the single original free body:

The condition that the problem imposes is that the deflection at C must be -20 mm:

That is, I am superposing the deflections from each separate loading to get the actual deflection. From Appendix D, I get the following formulas for the maximum deflections (note the sign change for case 4):

Using Appendix C to get the moment of inertia for a W410 x 60 (216 x 10⁶ mm⁴)...

From an overall free body, now that the indeterminacy has been removed,

From the sum of the forces, we see that R_B has the same value.

¹ This is problem 8.138 in Beer & Johnston's Mechanics of Materials, 2nd Edition.