Bending: stress and deformation

Tensile bending stress is at a maximum in the outer layers of the beam. The smaller the moment of inertia I_xx, the larger the maximum bending stress. Shear stress is equal to zero at the outer layers. It is at a maximum on the neutral axis of the beam. Tensile bending stress is equal to zero at the neutral axis.

The deflection is proportional to force and length³. This means that a doubled length increase deflection by 8 times.

For a distributed load the order for length is higher.

Deflection and rotation in the center can affect deflection of the right end of the cantilever beam.

Heating of the upper flange of the cantilever beam causes thermal expansion of upper layers and changes the beam shape.

The shape of the flexible beam depends on the external moments at the beam ends M_i = F_i h_i.