# In displacement-based plate theories, which assumption of Classical Plate Theory is relaxed in Shear Deformation Theory?

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In displacement-based plate theories, which assumption of Classical Plate Theory is relaxed in Shear Deformation Theory?

(a) A straight-line perpendicular to the plane of the plate is inextensible

(b) A straight line perpendicular to the plane of the plate remains straight

(c) A straight line perpendicular to the plane of the plate rotates such that it remains perpendicular to the tangent to the deformed surface

(d) A straight line perpendicular to the plane of the plate rotates

I got this question in an online quiz.

This intriguing question originated from Shear Deformable Plate Model in section Bending of Elastic Plates of Finite Element Method

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Correct answer is (c) A straight line perpendicular to the plane of the plate rotates such that it remains perpendicular to the tangent to the deformed surface

To explain I would say: In the SDT, we relax the normality assumption of CPT, i.e., transverse normal may   rotate without remaining perpendicular to the mid-plane. The Classical Plate Theory is based on the assumption that a straight line perpendicular to the plane of the plate is (1) inextensible, (2) remains straight, and (3) rotates such that it remains perpendicular to the tangent to the deformed surface.

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