The Euler–Bernoulli equation describing the deflection of a beam is a vital tool in structural and
mechanical engineering. However, its derivation usually entails a number of intermediate steps that
may confuse engineering or science students at the beginnig of their undergraduate studies. We
explain how this equation may be deduced, beginning with an approximate expression for the energy,
from which the forces and finally the equation itself may be obtained. The description is begun at
the level of small ‘particles’, and the continuum level is taken later on. However, when a
computational solution is sought, the description turns back to the discrete level again. We first
consider the easier case of a string under tension, and then focus on the beam. Numerical solutions
for several loads are obtained.