A cantilever of length 2 m is subjected to a uniform distributed load of 5 kN/m. What is the fixed-end moment at the wall?

• A. 5 kN·m
• B. 10 kN·m
• C. 15 kN·m
• D. 20 kN·m

Answer: (B)

For a cantilever carrying a uniform distributed load along its length, the fixed-end moment is the moment needed at the wall to resist the bending caused by the load. The resulting force from a uniform load is wL, and its line of action is at a distance L/2 from the wall, so the moment that must be resisted is wL times L/2, which simplifies to wL^2/2. This shows that the fixed-end moment scales with both the load intensity and the square of the span. The value you obtain from this formula is the magnitude the wall must resist to keep the beam in equilibrium.