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1.5: Euler-Bernoulli Hypothesis
https://eng.libretexts.org/Bookshelves/Mechanical_Engineering/Structural_Mechanics_(Wierzbicki)/01%3A_The_Concept_of_Strain/1.05%3A_Euler-Bernoulli_Hypothesis
The second Euler-Bernoulli hypothesis is satisfied if the rotation of the deformed crosssection $\theta$ is equal to the local slope of the bent middle axis $\frac{ d w}{ d x}$ \[\begin{align} \ep...The second Euler-Bernoulli hypothesis is satisfied if the rotation of the deformed crosssection $\theta$ is equal to the local slope of the bent middle axis $\frac{ d w}{ d x}$ $\begin{align} \epsilon_{zx} & = \frac{1}{2} \left(\frac{ d u_{z}}{ d x} + \frac{ d u_x}{ d z} \right) = \frac{1}{2} \left(\frac{ d w}{ d x} + \frac{ d u}{ d z} \right) \\ & = \frac{1}{2} \left(\frac{ d w}{ d x} - \frac{ d w}{ d x} \right) = 0 \nonumber \end{align}$

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