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The beam is initially straight with a cross section that is constant throughout the beam length. The beam has an axis of symmetry in the plane of bending. The proportions of the beam are such that it would fail by bending rather than by crushing, wrinkling or sideways buckling. Cross-sections of the beam remain plane during bending.
Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) [1] is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams. It covers the case corresponding to small deflections of a beam that is subjected to lateral ...
in these formulas the following parameters are used: = Stress in outer fibers at midpoint, = load at a given point on the load deflection curve, = Support span, (mm) = Width of test beam, (mm) = Depth or thickness of tested beam, (mm)
The flexural strength is stress at failure in bending. It is equal to or slightly larger than the failure stress in tension. Flexural strength, also known as modulus of rupture, or bend strength, or transverse rupture strength is a material property, defined as the stress in a material just before it yields in a flexure test. [1]
Stress resultants are simplified representations of the stress state in structural elements such as beams, plates, or shells. [1] The geometry of typical structural elements allows the internal stress state to be simplified because of the existence of a "thickness'" direction in which the size of the element is much smaller than in other directions.
In mechanics, the flexural modulus or bending modulus [1] is an intensive property that is computed as the ratio of stress to strain in flexural deformation, or the tendency for a material to resist bending. It is determined from the slope of a stress-strain curve produced by a flexural test (such as the ASTM D790), and uses units of force per ...
Clamped beams: The displacement and the rotation ... is the axial stress and the thickness of the beam has been assumed to be . The combined beam equation with axial ...
The Euler–Bernoulli beam equation defines the behaviour of a beam element (see below). It is based on five assumptions: Continuum mechanics is valid for a bending beam. The stress at a cross section varies linearly in the direction of bending, and is zero at the centroid of every cross section.