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For rectangular plates, Navier in 1820 introduced a simple method for finding the displacement and stress when a plate is simply supported. The idea was to express the applied load in terms of Fourier components, find the solution for a sinusoidal load (a single Fourier component), and then superimpose the Fourier components to get the solution ...
Torsion of a square section bar Example of torsion mechanics. In the field of solid mechanics, torsion is the twisting of an object due to an applied torque [1] [2].Torsion could be defined as strain [3] [4] or angular deformation [5], and is measured by the angle a chosen section is rotated from its equilibrium position [6].
In continuum mechanics, plate theories are mathematical descriptions of the mechanics of flat plates that draw on the theory of beams. Plates are defined as plane structural elements with a small thickness compared to the planar dimensions. [1] The typical thickness to width ratio of a plate structure is less than 0.1.
The maximum compressive stress is found at the uppermost edge of the beam while the maximum tensile stress is located at the lower edge of the beam. Since the stresses between these two opposing maxima vary linearly , there therefore exists a point on the linear path between them where there is no bending stress.
The torsion constant or torsion coefficient is a geometrical property of a bar's cross-section. It is involved in the relationship between angle of twist and applied torque along the axis of the bar, for a homogeneous linear elastic bar. The torsion constant, together with material properties and length, describes a bar's torsional stiffness.
• The behavior of bodies under stress • Analytical, numerical, and experimental methods • Tension, compression, shear, and combined stress • Beams and curved beams • Torsion, flat plates, and columns • Shells of revolution, pressure vessels, and pipes • Bodies under direct pressure and shear stress • Elastic stability
The polar second moment of area appears in the formulae that describe torsional stress and angular displacement. Torsional stresses: τ = T r J z {\displaystyle \tau ={\frac {T\,r}{J_{z}}}} where τ {\displaystyle \tau } is the torsional shear stress, T {\displaystyle T} is the applied torque, r {\displaystyle r} is the distance from the ...
This type of stress may be called (simple) normal stress or uniaxial stress; specifically, (uniaxial, simple, etc.) tensile stress. [13] If the load is compression on the bar, rather than stretching it, the analysis is the same except that the force F and the stress σ {\displaystyle \sigma } change sign, and the stress is called compressive ...