|
|
| Line 1: |
Line 1: |
| {{See|Shear force}}
| | 53 yrs old Endocrinologist Toney Leonette from St. Albert, spends time with passions including basketball, ganhando dinheiro na internet and vehicle racing. Last month just traveled to Archaeological Site of Olympia.<br><br>Here is my blog post; [http://ganhedinheiro.comoganhardinheiro101.com/ como ganhar dinheiro] |
| {{Refimprove|date=July 2008}}
| |
| {{Infobox Physical quantity
| |
| | bgcolour =
| |
| | name = Shear stress
| |
| | image =
| |
| | caption =
| |
| | unit = [[Pascal (unit)|pascal]]
| |
| | symbols = [[tau|τ]]
| |
| | derivations = τ = ''[[Force|F]]'' / ''[[Area|A]]''
| |
| }}
| |
| [[File:Shear stress simple.svg|thumb|A shearing force is applied to the top of the rectangle while the bottom is held in place. The resulting shear stress, <math>\tau\,</math>, deforms the rectangle into a [[parallelogram]]. The area involved would be the top of the parallelogram.]]
| |
| | |
| A '''shear stress''', denoted <math>\tau\,</math> ([[Greek alphabet|Greek]]: [[tau]]), is defined as the component of [[stress (physics)|stress]] coplanar with a material cross section. Shear stress arises from the [[force vector]] component [[parallel (geometry)|parallel]] to the cross section. [[Normal stress]], on the other hand, arises from the force vector component [[perpendicular]] to the material cross section on which it acts.
| |
| | |
| ==General shear stress==
| |
| The formula to calculate average shear stress is:<ref>{{cite book|last=Hibbeler|first=R.C.|title=Mechanics of Materials|year=2004|publisher=Pearson Education|location=New Jersey USA|isbn=0-13-191345-X|pages=32}}</ref>
| |
| | |
| :<math> \tau = {F \over A},</math>
| |
| | |
| where:
| |
| | |
| :<math>\tau</math> = the shear stress;
| |
| :<math>F</math> = the force applied;
| |
| :<math>A</math> = the cross-sectional area of material with area parallel to the applied force vector.
| |
| | |
| ==Other forms of shear stress==
| |
| | |
| ===Pure shear===
| |
| [[Pure shear]] stress is related to pure [[shear strain]], denoted <math>\gamma</math>, by the following equation:<ref>{{cite web|url=http://www.eformulae.com/engineering/strength_materials.php#pureshear|title=Strength of Materials|work=Eformulae.com|accessdate=24 December 2011}}</ref>
| |
| | |
| :<math>\tau = \gamma G\,</math>
| |
| | |
| where <math>G</math> is the [[shear modulus]] of the material, given by
| |
| | |
| :<math> G = \frac{E}{2(1+\nu)}. </math>
| |
| | |
| Here <math>E</math> is [[Young's modulus]] and <math>\nu</math> is [[Poisson's ratio]].
| |
| | |
| ===Beam shear===
| |
| Beam shear is defined as the internal shear stress of a beam caused by the shear force applied to the beam.
| |
| :<math> \tau = {VQ \over It},</math>
| |
| | |
| where
| |
| | |
| :''V'' = total shear force at the location in question;
| |
| :''Q'' = [[first moment of area#Statical moment of area|statical moment of area]];
| |
| :''t'' = thickness in the material perpendicular to the shear;
| |
| :''I'' = [[Second moment of area|Moment of Inertia]] of the entire cross sectional area.
| |
| The beam shear formula is also knowns as Zhuravskii Shear Stress formula after [[Dmitrii Ivanovich Zhuravskii]] who derived it in 1855.<ref>{{cite web|title=ЛЕКЦИЯ ФОРМУЛА ЖУРАВСКОГО|url=http://sopromato.ru/pryamoy-izgib/formula-zhuravskogo.html|work=СОПРОМАТ ЛЕКЦИИ}}</ref><ref>{{cite web|title=Flexure of Beams|url=http://www.eng.mcmaster.ca/civil/mechanicslecture/4flexurebeams1.pdf|work=Mechanical Engineering Lectures|publisher=[[McMaster University]]}}</ref>
| |
| | |
| ===Semi-monocoque shear===
| |
| | |
| Shear stresses within a [[semi-monocoque]] structure may be calculated by idealizing the cross-section of the structure into a set of stringers (carrying only axial loads) and webs (carrying only [[shear flow]]s). Dividing the shear flow by the thickness of a given portion of the semi-monocoque structure yields the shear stress. Thus, the maximum shear stress will occur either in the web of maximum shear flow or minimum thickness.
| |
| | |
| Also constructions in soil can fail due to shear; [[wiktionary:e.g.|e.g.]], the weight of an earth-filled [[dam]] or [[dyke (construction)|dike]] may cause the subsoil to collapse, like a small [[landslide]].
| |
| | |
| ===Impact shear===
| |
| The maximum shear stress created in a solid round bar subject to impact is given as the equation:<br />
| |
| :<math>\tau=2\left({UG \over V}\right)^{1 \over 2},</math>
| |
| | |
| where
| |
| | |
| :''U'' = change in kinetic energy;
| |
| :''G'' = [[shear modulus]];
| |
| :''V'' = volume of rod;
| |
| | |
| and
| |
| | |
| :<math> U = U_{rotating}+U_{applied} \,;</math>
| |
| :<math> U_{rotating} = {1 \over 2}I\omega^2 \,;</math>
| |
| :<math> U_{applied} = T \theta_{displaced} \,;</math>
| |
| :<math>I \,</math> = mass moment of inertia;
| |
| :<math>\omega \,</math> = angular speed.
| |
| | |
| ===Shear stress in fluids===<!-- [[Shear (fluid)]] and [[Wind stress]] redirect here -->
| |
| {{see also|Viscosity|Couette flow|Hagen-Poiseuille equation|Depth-slope product|Simple shear}}
| |
| | |
| Any real [[fluids]] ([[liquid]]s and [[gas]]es included) moving along solid boundary will incur a shear stress on that boundary. The [[no-slip condition]]<ref>{{Citation | last = Day | first = Michael A. | title = The no-slip condition of fluid dynamics | publisher = Springer Netherlands | pages = 285–296 | year = 2004 | url = http://www.springerlink.com/content/k1m4t1p02m778u88/ | issn = 0165-0106}}.</ref> dictates that the speed of the fluid at the boundary (relative to the boundary) is zero, but at some height from the boundary the flow speed must equal that of the fluid. The region between these two points is aptly named the [[boundary layer]]. For all [[Newtonian fluid]]s in [[laminar flow]] the shear stress is proportional to the [[strain rate]] in the fluid where the viscosity is the constant of proportionality. However for [[Non Newtonian fluids]], this is no longer the case as for these fluids the [[viscosity]] is not constant. The shear stress is imparted onto the boundary as a result of this loss of velocity. The shear stress, for a Newtonian fluid, at a surface element parallel to a flat plate, at the point y, is given by:
| |
| | |
| :<math>\tau (y) = \mu \frac{\partial u}{\partial y}</math>
| |
| | |
| where
| |
| :<math>\mu</math> is the [[dynamic viscosity]] of the fluid;
| |
| :<math>u</math> is the velocity of the fluid along the boundary;
| |
| :<math>y</math> is the height above the boundary.
| |
| | |
| Specifically, the wall shear stress is defined as:
| |
| | |
| :<math>\tau_\mathrm{w} \equiv \tau(y=0)= \mu \left.\frac{\partial u}{\partial y}\right|_{y = 0}~~.</math>
| |
| | |
| In case of [[wind]], the shear stress at the boundary is called [[wind stress]].
| |
| | |
| == Measurement by shear stress sensors ==
| |
| | |
| ===Diverging fringe shear stress sensor===
| |
| | |
| This relationship can be exploited to measure the wall shear stress. If a sensor could directly measure the gradient of the velocity profile at the wall, then multiplying by the dynamic viscosity would yield the shear stress. Such a sensor was demonstrated by A. A. Naqwi and W. C. Reynolds.<ref>{{citation | last1 = Naqwi |first1 = A. A. | last2 = Reynolds |first2 = W. C. | title = Dual cylindrical wave laser-Doppler method for measurement of skin friction in fluid flow | journal = NASA STI/Recon Technical Report N |date=jan 1987 | volume = 87}}</ref> The interference pattern generated by sending a beam of light through two parallel slits forms a network of linearly diverging fringes that seem to originate from the plane of the two slits (see [[double-slit experiment]]). As a particle in a fluid passes through the fringes, a receiver detects the reflection of the fringe pattern. The signal can be processed, and knowing the fringe angle, the height and velocity of the particle can be extrapolated. The measured value of wall velocity gradient is independent of the fluid properties and as a result does not require calibration.
| |
| Recent advancements in the micro-optic fabrication technologies have made it possible to use integrated diffractive optical element to fabricate diverging fringe shear stress sensors usable both in air and liquid.
| |
| | |
| ===Micro-pillar shear-stress sensor===
| |
| A further technique is that of slender wall-mounted micro-pillars made of the flexible polymer PDMS, which bend in reaction to the applying drag forces in the vicinity of the wall. The sensor thereby belongs to the indirect measurement principles relying on the relationship between near-wall velocity gradients and the local wall-shear stress.<ref>{{citation | last1 = Große |first1 = S. | last2 = Schröder |first2 = W. | title = Two-Dimensional Visualization of Turbulent Wall Shear Stress Using Micropillars | journal = AIAA Journal | year = 2009 | doi = 10.2514/1.36892 | volume = 47 | issue=2 | pages = 314–321 |bibcode = 2009AIAAJ..47..314G }}</ref><ref>{{citation | last1 = Große |first1 = S. | last2 = Schröder |first2 = W. | title = Dynamic Wall-Shear Stress Measurements in Turbulent Pipe Flow using the Micro-Pillar Sensor MPS³ | journal = International Journal of Heat and Fluid Flow | year = 2008 | doi = 10.1016/j.ijheatfluidflow.2008.01.008 | volume = 29 | issue=3 | pages = 830–840 }}</ref>
| |
| | |
| ==See also==
| |
| * [[Direct shear test]]
| |
| * [[Shear rate]]
| |
| * [[Shear strain]]
| |
| * [[Shear strength]]
| |
| * [[Shear and moment diagrams]]
| |
| * [[Tensile stress]]
| |
| * [[Triaxial shear test]]
| |
| * [[Critical resolved shear stress]]
| |
| * [[Critical resolved shear and normal stress]]
| |
| *[[Difference between shear strain and shear stress]]
| |
| | |
| ==References==
| |
| {{reflist}}
| |
| | |
| ==External links==
| |
| *[http://measurementsci.com/papers/microS_description.pdf The second page of this brochure] explains the concept of the diverging fringe shear stress sensor mentioned above.
| |
| | |
| {{DEFAULTSORT:Shear Stress}}
| |
| [[Category:Continuum mechanics]]
| |
| [[Category:Concepts in physics]]
| |
53 yrs old Endocrinologist Toney Leonette from St. Albert, spends time with passions including basketball, ganhando dinheiro na internet and vehicle racing. Last month just traveled to Archaeological Site of Olympia.
Here is my blog post; como ganhar dinheiro