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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. As a consequence the three traction components that vary from point to point in a cross-section can be replaced with a set of resultant forces and resultant moments. These are the stress resultants (also called membrane forces, shear forces, and bending moment) that may be used to determine the detailed stress state in the structural element. A three-dimensional problem can then be reduced to a one-dimensional problem (for beams) or a two-dimensional problem (for plates and shells).
Stress resultants are defined as integrals of stress over the thickness of a structural element. The integrals are weighted by integer powers the thickness coordinate z (or x3). Stress resultants are so defined to represent the effect of stress as a membrane force N (zero power in z), bending moment M (power 1) on a beam or shell (structure). Stress resultants are necessary to eliminate the z dependency of the stress from the equations of the theory of plates and shells.
^Barbero, Ever J. (2010). Introduction to composite materials design. Boca Raton, FL: CRC Press. ISBN 978-1-4200-7915-9.
Stressresultants are simplified representations of the stress state in structural elements such as beams, plates, or shells. The geometry of typical structural...
the stressresultants in a cross-section of the structural element. For example, in a beam in the figure, the bending moment vector due to stresses in...
^{0}+\kappa \cdot z} Furthermore, a three-dimensional stress field is replaced by six stressresultants; three membrane forces (forces per unit length) and...
}&=0\\M_{\alpha \beta ,\alpha \beta }&=0\end{aligned}}} where the stressresultants and stress moment resultants are defined as N α β := ∫ − h h σ α β d x 3 ; ...
stress tensor (symbol σ {\displaystyle {\boldsymbol {\sigma }}} , named after Augustin-Louis Cauchy), also called true stress tensor or simply stress...
membrane stress system it may be a desirable solution to the design problem, i.e., thin, light and stiff. Theory of plates and shells Stressresultants in plates...
symmetry of the Cauchy stress tensor. For the resultants of the stresses do not exert a torque on the volume element, the resultant force must lead through...
be used to deduce the bending equation for the sandwich beam. The stressresultants and the corresponding deformations of the beam and of the cross section...
Linear elasticity Mindlin–Reissner plate theory Plate theory Stress (mechanics) Stressresultants Structural acoustics Vibration of plates Reddy, J. N., 2007...
quantity integral equation formulation for evaluation of boundary stressresultants in shear deformable plate bending problems, Eng. Analysis with Boundary...
theoretical line that through the structure represents the path of the resultants of the compressive forces, [3]. For a structure to be stable, the line...
plate is 2 h {\displaystyle 2h} and that the resultants are defined as weighted averages of the in-plane stresses σ α β {\displaystyle \sigma _{\alpha \beta...
terror and dread. Resulting panic attacks can include hyperventilation and stress. These negative and agitating symptoms can be produced by both the thought...
is applied, and the resultant shear force measured using a load cell. Displacement is measured using an LVDT. Thus the basic stress–strain parameters are...
the amount of stress applied and/or the significance of the resultant hemolysis may vary.[citation needed] When multiple levels of stress are applied to...
Rankine's theory (maximum-normal stress theory), developed in 1857 by William John Macquorn Rankine, is a stress field solution that predicts active and...
some referred to it as Meares-Irlen syndrome, Irlen syndrome, and visual stress.[citation needed] Early studies investigating Irlen syndrome as a treatable...
an agent in a nuclear medicine scan, during one type of nuclear cardiac stress test. Soluble thallium salts (many of which are nearly tasteless) are highly...
unfolded protein response (UPR) is a cellular stress response related to the endoplasmic reticulum (ER) stress. It has been found to be conserved between...
land, and dependence on the Nile all continue to overtax resources and stress the economy.[citation needed] For further information on the types of business...
previous material unaffected), and resultant final stops will fricativize (r becomes sh). Aside from losing stress, any vowels preceding these shifted...
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