Problem 2: An 8 m long cantilever steel W130 x 523.8 beam carries a 3 kN/m load and is simply supported at end B. Determine the reactions.

Solution: From Appendix C, a W130 x 23.8 shape has a moment of inertia of 8.80 x 10⁶ mm⁴. The free body diagram is

Newton's Laws result in two independent equations, which contain three unknowns:

For this reason, at least one more equation must be found. Using the method from an earlier chapter...

And now, using the flexural rigidity equation,

At x = 0, y' = 0, so C₁ = 0. Integrating again,

At x = 0, y = 0, so C₂ = 0. At x = 8 m, y = 0, so

Solving this simultaneously with the equations from Newton's Laws, I get A_y = 15.0 kN, B_y = 9.0 kN, and M_A = -24 kN-m (the direction initially assumed for M_A was wrong).