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is the density of the beam material (but not the linear density). is the cross section area. is the elastic modulus. is the shear modulus. is the second moment of area., called the Timoshenko shear coefficient, depends on the geometry
Mechanics of Materials, with J. M. Gere, 1st edition, D. Van Nostrand Company, 1972 Erinnerungen , Translation from the Russian original edition (Translator: Albert Duda), Berlin: Wiley , 2006, ISBN 3-433-01816-2 (in German)
In the mechanics of materials, the strength of a material is its ability to withstand an applied load without failure or plastic deformation.The field of strength of materials deals with forces and deformations that result from their acting on a material.
The three-point bending test is a classical experiment in mechanics. It represents the case of a beam resting on two roller supports and subjected to a concentrated load applied in the middle of the beam. The shear is constant in absolute value: it is half the central load, P / 2.
Solid mechanics (also known as mechanics of solids) is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and other external or internal agents.
The material is isotropic (or orthotropic) and homogeneous. The material obeys Hooke's law (it is linearly elastic and will not deform plastically). 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.
Deflection (f) in engineering. In structural engineering, deflection is the degree to which a part of a long structural element (such as beam) is deformed laterally (in the direction transverse to its longitudinal axis) under a load.
Most methods in micromechanics of materials are based on continuum mechanics rather than on atomistic approaches such as nanomechanics or molecular dynamics. In addition to the mechanical responses of inhomogeneous materials, their thermal conduction behavior and related problems can be studied with analytical and numerical continuum methods ...