Understanding the formula $\psi =
\int \kappa ds$
Consider a beam which is a perfect arc of a circle
Calculate $\int \kappa ds$ along this section. Can you relate
$\phi$ to $\psi$?
Finding $v$ in terms of $\kappa$
Consider a very small section of the beam, curved length $\delta s$
and vertical deflection $- \delta v$. Can you express $\delta v$ in
terms of the other quantities?