# Bending - Quasistatic Bending of Beams

Quasistatic Bending of Beams

A beam deforms and stresses develop inside it when a transverse load is applied on it. In the quasistatic case, the amount of bending deflection and the stresses that develop are assumed not to change over time. In a horizontal beam supported at the ends and loaded downwards in the middle, the material at the over-side of the beam is compressed while the material at the underside is stretched. There are two forms of internal stresses caused by lateral loads:

• Shear stress parallel to the lateral loading plus complementary shear stress on planes perpendicular to the load direction;
• Direct compressive stress in the upper region of the beam, and direct tensile stress in the lower region of the beam.

These last two forces form a couple or moment as they are equal in magnitude and opposite in direction. This bending moment resists the sagging deformation characteristic of a beam experiencing bending. The stress distribution in a beam can be predicted quite accurately even when some simplifying assumptions are used.

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Quasistatic Bending of Beams - Timoshenko Bending Theory
... In 1921, Timoshenko improved upon the Euler-Bernoulli theory of beams by adding the effect of shear into the beam equation ... of the Timoshenko theory are normals to the axis of the beam remain straight after deformation there is no change in beam thickness after deformation However, normals to the axis ... The equation for the quasistatic bending of a linear elastic, isotropic, homogeneous beam of constant cross-section beam under these assumptions is where is the area moment of ...

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