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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.
The deflection of beam elements is usually calculated on the basis of the Euler–Bernoulli beam equation while that of a plate or shell element is calculated using plate or shell theory. An example of the use of deflection in this context is in building construction. Architects and engineers select materials for various applications.
If the beam is bent side to side, it functions as an 'H', where it is less efficient. The most efficient shape for both directions in 2D is a box (a square shell); the most efficient shape for bending in any direction, however, is a cylindrical shell or tube. For unidirectional bending, the Ɪ-beam or wide flange beam is superior. [5]
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. Deflection of a beam deflected symmetrically and principle of superposition. Compressive and tensile forces develop in the direction of the beam axis under bending loads.
Cellular beams are usually made of structural steel, but can also be made of other materials. [5] The cellular beam is a structural element that mainly withstands structural load laterally applied to the axis of the beam, and influences the overall performance of steel framed buildings. [6] The type of deflection is mainly done by bending.
Bending torque and resulting stress in case of bi-axial bending of a symmetric beam. The complex bending is the superposition of two simple bendings around the y and z axes (small deformation, linear behaviour). The largest stresses (𝜎 xx) in a beam under bending are in the locations farthest from the neutral axis.
The bending stiffness (EI/L) of a member is represented as the flexural rigidity of the member (product of the modulus of elasticity (E) and the second moment of area (I)) divided by the length (L) of the member. What is needed in the moment distribution method is not the specific values but the ratios of bending stiffnesses between all members.
The secant stiffness of the connection is compared to the rotational stiffness of the connected member as follows, in which L and EI are the length and bending rigidity, respectively, of the beam. If K s L/EI ≥ 20, it is acceptable to consider the connection to be fully restrained (in other words, able to maintain the angles between members).