Engineering Practice Test 2026 – All-in-One Exam Prep

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What is the deflection at the free end of a cantilever beam of length L subjected to a concentrated load P at the free end?

δ = P L^4 /(4 E I)

δ = P L^3 /(3 E I)

When a cantilever is loaded with a point load at the tip, the bending moment along the beam varies linearly: M(x) = P(L − x). The beam curvature follows y″ = M/(EI), so y″ = P(L − x)/(EI). Integrating twice and applying the fixed-end conditions y(0) = 0 and y′(0) = 0 gives the deflected shape. Evaluating the deflection at the free end x = L yields δ = P L^3 / (3 E I). This shows the end deflection grows with the load and with the cube of the length, and is reduced by higher stiffness EI.

δ = P L /(E I)

δ = P L^2 /(2 E I)