Force per unit area circled

 

The journey is the way is the destination

clear from the presentation the most frequently quoted constant the last word out of the mouth of every seeker of the way which can be named as the way orthogonal to the other way over there in the other quadrant...+++----++ as pointed out by Wittgenstein the point is the

pointer the circle is the point the pointer the pointed to too the proud mother of all ideas circling the drain now never taken apart in the least

common calculated calculus demonstrating that broken circles make arcs are like all dead horse droppings βarcs than can be pushed into

road apples where μμμ...theories of this might account for that in the other end of the food processor all the while ignoring the three separate systems creating the thingζαζα which is the blinΓ Given the orthogonal angle at the tip of the C/(())^{}{}=24

186 the diameter of the circus drawn by the pale blue dot around the golden ring in 365 flings factors into 31 χ 6 aka 62 χ 3 ακα 124 χ 1.5

8000 the diameter of the curcus circling us at the rate of circles aka three the idee of 24000 multiples of 5280 the feet full of inches sized

at twice the day rate of 186 making the other end of the f(ultiplication) another num er num beer σιμιλαρ το 11 χ 24 χ 10 χ 2 a couple of afternoons in the warm winter afternoon sun coupled with a few nights in the Casbah at Ricks famous piano parlour f(()) Casablanca

every big theory theorizing the this was the that before the that became the thus is using the rhyme of a clean 3/8 at the end of the

186 aka 31 day sets f(((}{))) 3 by 2 balls of burning salt strung out along lines of fire in the sky at a 24 degree semaphorΣ(γοθΓ) μ(())νευ

the most appropi ate 240,000 smiles of cheese eating moon miles from the us of us on a slightly slower bus thus appearing to run at the

reverse sum of the total sin that we are in here in the sphere of at most there the big old ball of (((1))) frozen in the sky like a perfectly

tasted pizza pasted to the light of the night until ΖυΣυ ψομεΣ οθτ and the moon to a loon is eaten like trout

never more quoth the raven when living for eva was more than a proposal to daddy living beyond the becoming became the way to

put the foot in front of the pen ending at the beginning when the description describes what the feather flip find in the fasture of the

pastuer where milk is made more water like than the NaCl in the swill whence ink will well do too to uβerζεθgt man es davon? page

7ε 11. Foundations of Mathematics LidvviG VVitgenstein For how do we Learn to infer? Or don't we learn it?

Certainly not from the writers of feather scale lore one grain of sand cemented too gather ideas of large blocks moved by ants of

people more than one grain at a bag sized pile a time...the weighing of the live against the falling of a feather find fine feather friend

fall in G with a minor Σ where the eyeless can Ψ the damage done by thee treading the tree to keep warm

And so onc upon a rhyme a ball calculating spin doctor took the 24000 groups of 5280 feat slimming at the 24 hour/day rate to the

angle of 24 fate and wala the time of your life is shackled to the ball of now for ever to be nailed to a dead tree signifying noon in vegas

The most fudged kluge factor in the history if itself as perfectly elicudated here it can and it does as it has proven itself to do over itself

mean absolutely anything that is needed to fuge the fudge back into the road apple hole whence it by the other orthogonal friction of

shivering slucitude sent a few pieces of (()) back to the moo for a mother day

Stress (mechanics)

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This article is about stresses in classical (continuum) mechanics. For stresses in material science, see Strength of materials.

For other uses, see Stress.

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Stress
Residual stresses inside a plastic protractor are revealed by the polarized light.
Common symbols	σ
SI unit	pascal
Other units	lbf per square inch ( lbf/in2 ) psi, bar
In SI base units	Pa = kg⋅m−1⋅s−2
Dimension	${\displaystyle {\mathsf {L}}^{-1}{\mathsf {M}}{\mathsf {T}}^{-2}}$

Part of a series on
Continuum mechanics
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In continuum mechanics, stress is a physical quantity. It is a quantity that describes the magnitude of forces that cause deformation. Stress is defined as force per unit area. When an object is pulled apart by a force it will cause elongation which is also known as deformation, like the stretching of an elastic band, it is called tensile stress. But, when the forces result in the compression of an object, it is called compressive stress^[1][2]. It results when forces like tension or compression act on a body. The greater this force and the smaller the cross-sectional area of the body on which it acts, the greater the stress. Therefore, stress is measured in newton per square meter (N/m²) or pascal (Pa).

Stress expresses the internal forces that neighbouring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material^[3]. For example, when a solid vertical bar is supporting an overhead weight, each particle in the bar pushes on the particles immediately below it. When a liquid is in a closed container under pressure, each particle gets pushed against by all the surrounding particles. The container walls and the pressure-inducing surface (such as a piston) push against them in (Newtonian) reaction. These macroscopic forces are actually the net result of a very large number of intermolecular forces and collisions between the particles in those molecules. Stress is frequently represented by a lowercase Greek letter sigma (σ).

Strain inside a material may arise by various mechanisms, such as stress as applied by external forces to the bulk material (like gravity) or to its surface (like contact forces, external pressure, or friction). Any strain (deformation) of a solid material generates an internal elastic stress, analogous to the reaction force of a spring, that tends to restore the material to its original non-deformed state. In liquids and gases, only deformations that change the volume generate persistent elastic stress. However, if the deformation changes gradually with time, even in fluids there will usually be some viscous stress, opposing that change. Elastic and viscous stresses are usually combined under the name mechanical stress.

Mechanical stress

Significant stress may exist even when deformation is negligible or non-existent (a common assumption when modeling the flow of water). Stress may exist in the absence of external forces; such built-in stress is important, for example, in prestressed concrete and tempered glass. Stress may also be imposed on a material without the application of net forces, for example by changes in temperature or chemical composition, or by external electromagnetic fields (as in piezoelectric and magnetostrictive materials).

The relation between mechanical stress, deformation, and the rate of change of deformation can be quite complicated, although a linear approximation may be adequate in practice if the quantities are sufficiently small. Stress that exceeds certain strength limits of the material will result in permanent deformation (such as plastic flow, fracture, cavitation) or even change its crystal structure and chemical composition.

In some branches of engineering, the term stress is occasionally used in a looser sense as a synonym of "internal force". For example, in the analysis of trusses, it may refer to the total traction or compression force acting on a beam, rather than the force divided by the area of its cross-section.

Figure 1. Mohr's circles for a three-dimensional state of stress

Mohr's circle is a two-dimensional graphical representation of the transformation law for the Cauchy stress tensor.

Mohr's circle is often used in calculations relating to mechanical engineering for materials' strength, geotechnical engineering for strength of soils, and structural engineering for strength of built structures. It is also used for calculating stresses in many planes by reducing them to vertical and horizontal components. These are called principal planes in which principal stresses are calculated; Mohr's circle can also be used to find the principal planes and the principal stresses in a graphical representation, and is one of the easiest ways to do so.^[1]

After performing a stress analysis on a material body assumed as a continuum, the components of the Cauchy stress tensor at a particular material point are known with respect to a coordinate system. The Mohr circle is then used to determine graphically the stress components acting on a rotated coordinate system, i.e., acting on a differently oriented plane passing through that point.

The abscissa and ordinate (${\displaystyle \sigma _{\mathrm {n} }}$,${\displaystyle \tau _{\mathrm {n} }}$) of each point on the circle are the magnitudes of the normal stress and shear stress components, respectively, acting on the rotated coordinate system. In other words, the circle is the locus of points that represent the state of stress on individual planes at all their orientations, where the axes represent the principal axes of the stress element.

19th-century German engineer Karl Culmann was the first to conceive a graphical representation for stresses while considering longitudinal and vertical stresses in horizontal beams during bending. His work inspired fellow German engineer Christian Otto Mohr (the circle's namesake), who extended it to both two- and three-dimensional stresses and developed a failure criterion based on the stress circle.^[2]