Luego Para: \(v=0\ \ \ \ \ x=L\)

\(v\left(x=L\right)=C_1\sin\sqrt{\frac{p}{EI}}L=0\)\(v\left(x=L\right)=C_1\sin\sqrt{\frac{p}{EI}}L=0\)

\(\sin\left(\sqrt{\frac{p}{EI}}L\right)=0\)

\(\sqrt{\frac{p}{EI}}=L=n\pi\)

Se despeja P

\(\frac{p}{EI}L^2=n^2\pi^2\)

\(p=\frac{n^2\pi^2EI}{L^2}\)

Para calcular la critica

n=1

\(P_{cr}=\frac{\pi^2EI}{L^2}\)