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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)
The strength of materials is determined using various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as its yield strength, ultimate strength, Young's modulus ...
Material failure theory is an interdisciplinary field of materials science and solid mechanics which attempts to predict the conditions under which solid materials fail under the action of external loads. The failure of a material is usually classified into brittle failure or ductile failure .
The J-integral represents a way to calculate the strain energy release rate, or work per unit fracture surface area, in a material. [1] The theoretical concept of J-integral was developed in 1967 by G. P. Cherepanov [2] and independently in 1968 by James R. Rice, [3] who showed that an energetic contour path integral (called J) was independent of the path around a crack.
In continuum mechanics, the maximum distortion energy criterion (also von Mises yield criterion [1]) states that yielding of a ductile material begins when the second invariant of deviatoric stress reaches a critical value. [2] It is a part of plasticity theory that mostly applies to ductile materials, such as some metals.
A solid is a material that can support a substantial amount of shearing force over a given time scale during a natural or industrial process or action. This is what distinguishes solids from fluids, because fluids also support normal forces which are those forces that are directed perpendicular to the material plane across from which they act and normal stress is the normal force per unit area ...
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.