[![enter image description here](https://i.stack.imgur.com/lNtsG.png)](https://i.stack.imgur.com/lNtsG.png)

If we look at a cross section at any point, stress will be the same $\sigma=F/A$ and the hooke law says that $\sigma=E\*\epsilon$ 

It means that the deformation will be constant throughout the beam, which obviously can't be correct. So what am I missinterpreting here?