= Self-weight deflection of a square cantilever
{title2=$y(l)=3\rho g l^4/(2Ea^2)$}
A uniform square section has <second moment of area> $a^4/12$ and gravitational load per length $\rho g a^2$. Euler-Bernoulli bending therefore gives $y''''=12\rho g/(Ea^2)$, with zero displacement and slope at the clamp and zero moment and shear at the free end. Integrating gives the displayed tip deflection and $y(x)=\rho g x^2(x^2-4lx+6l^2)/(2Ea^2)$. Small slope and <strain> are required.
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