Question

Solid Mechanics question.

in the first photo, the beam seems to be a perfect square from the side, but then deformed to a different shape. the length of the shape based on the y axis seems to elongate along the positive and shrink on the negative.
So the question is, is the deformed shape is because poisson's ratio? I asked my proff. and he says squares deforms to squares and that deformed liked shape is because the original is shaped liked that..
so confused.. if there is a method to approximate the deformation shape I would be very glad to know thankyou

BENDING DEFORMATION OF A STRAIGHT MEMBER Assumptions: 1. Plane section remains plane 2. Length of longitudinal axis remains unchanged 8. Paptusincaioa-ismains perpendicular to the longitudinal axis In-plane distortion of section is negligible 4. Axis of symmetry y Neutral surface Horizontal lines become curved Longitudinal Vertical tines remain straight, yet cotats axis Befora deformation After deformation Fig.6-18 Fig.6-19 ENDING DEFORMATION OF A STRAIGHTv EMBER 군 Normal strain distribution Fig 6 23 Fig. 6-22 incep then by division

Answer 1

Since in the figure anticlockwise moment is acting,hence on the bottom layer tensile stress will act and on the upper layer there will be compressive stress.

Now since poisson ratio is =-(lateral strain/longitudinal strain)

Since on the bottom layer ,the length will increase(tensile stress) and the lateral section will shrink,by poisson's ratio relation

Similarly as in above layer compressive stress is induced hence longitudinal length will decrease and lateral length will increase on upper layer.

Hence you will get a trapezoidal shape on lateral section.