I read from Timoshenko's book Theory of Elasticity that for prismatical beam bending (uniaxial), the assumption is

[tex]\sigma_x>>\sigma_z,\sigma_y=0[/tex]

where [tex]\sigma_x [/tex]is stress in the direction parallel to the deflection curve.

And for uniaxial plate bending the assumption is

[tex]$\sigma_x,\sigma_y>>\sigma_z=0$[/tex]

and

[tex]\epsilon_y=0[/tex]

where x is the direction parrallel to the deflection curve.

I don't understand the assumption for uniaxial plate bending. Why should it be different to the assumption for uniaxial beam bending? Why is [tex]\epsilon_y=0 [/tex]for plate bending?

What is the difference between uniaxial plate bending and uniaxial beam bending apart from the fact that the thickness of the plate compared to its width is much smaller than for a beam?

Thanks in advanced.