Shear stress is a stress state where the stress is parallel or tangential to a face of the material, as opposed to normal stress when the stress is perpendicular to the face. Stress is a measure of the average amount of Force exerted per unit Area. Stress is a measure of the average amount of Force exerted per unit Area. For the tangent function see Trigonometric functions. For other uses see Tangent (disambiguation. Stress is a measure of the average amount of Force exerted per unit Area. In Geometry, two lines or planes (or a line and a plane are considered perpendicular (or orthogonal) to each other if they form congruent The variable used to denote shear stress is $\tau\,$ (tau). Tau (uppercase Τ, lowercase τ; Ταυ) is the 19th letter of the Greek alphabet.

Physical quantities of shear stress are measured in force divided by area. In SI, the unit is the pascal (Pa) or newtons per square meter. In United States customary units, shear stress is also commonly measured in pounds-force per square inch (psi) or kilopounds-force per square inch (ksi). US customary units, also known in the United States as English units or Imperial units (in reference to the British Empire) (but see English The area is always the area resisting the shear, and not the area that the force is acting on. These two areas are always at right angles.

There are two forms of shear stress: direct shear and beam shear.

## Direct shear

The formula for shear stress in a direct shear is:

$\tau = {V \over A}$,

where

V = shear force at that location, measured in newtons
A = area of section parallel with the shear force, measured in square metres
Figure of a bolt in shear. Top figure illustrates single shear, bottom figure illustrates a bolt in double shear.

Structural members that are often considered to be in pure shear stress are riveted and bolted joints. A rivet is a mechanical Fastener. Before it is installed it consists of a smooth cylindrical shaft with a head on one end Theory The clamp load also called preload of a cap screw is created when a torque is applied and is generally a percentage of the cap screw's proof strength For bolts and rivets the two plates must be touching, and locked together for the pure shear case to apply. Welds may also be subjected to pure shear stress depending on the location and loading. Cantilever beams, consoles and column heads are subject to composite loading, consisting of shear, tensile and compressive stress. A cantilever is a beam supported on only one end The beam carries the load to the support where it is resisted by moment and Shear stress. In Architecture a corbel (or console) is a piece of stone jutting out of a wall to carry any superincumbent weight A column in Structural engineering is a vertical structural element that transmits through compression, the weight of the structure above to other structural

## Beam shear

The formula for shear stress in a beam is:

$\tau = {VQ \over It}$,

where

V = shear force at that location
Q = statical moment of area
t = thickness in the material perpendicular to the shear
I = second moment of area of the cross section. The first moment of area, sometimes misnamed as the first moment of inertia, is based in the mathematical construct moments in metric spaces, stating that the moment The second moment of area, also known as the area moment of inertia or second moment of inertia, is a property of a shape that is used to predict its resistance to .

This formula is also known as the Jourawski formula.

## 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 flows). Monocoque, from the French for single ( mono) and shell ( coque) is a construction technique that supports structural load by using an object's external Shear flow is- in a solid body the gradient of a Shear stress force through the body in a Fluid, it is the flow induced by such a 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.

A road destroyed by shear. A road is an identifiable route, way or path between two or more places.

Also constructions in soil can fail due to shear; e. g. , the weight of an earth-filled dam or dike may cause the subsoil to collapse, like a small landslide. A dam is a barrier that divides waters. Dams generally serve the primary purpose of retaining water while other structures such as Floodgates, Levees LeveeEmbankmentDitch A dike (or dyke) levee, levée, embankment, floodbank or stopbank is a natural or artificial A landslide is a geological phenomenon which includes a wide range of ground movement such as rock falls deep failure of slopes and shallow debris flows which can occur

Shear stress is relevant to the motion of fluids upon surfaces, which result in the generation of shear stress. Particularly, the laminar fluid flow over the surface has a zero velocity and shear stress occurs between the zero-velocity surface and the higher-velocity flow away from the surface

## Impact Shear

The maximum shear stress created in a solid round bar subject to impact is given. Laminar flow, sometimes known as streamline flow occurs when a fluid flows in parallel layers with no disruption between the layers

The equation is

$\tau=2\left({UG \over V}\right)^{1 \over 2},$

where

U = Change in Kinetic Energy
G = Shear Modulus
V = Volume of Rod

and

$U = U_{rotating}+U_{applied} \,$
$U_{rotating} = {1 \over 2}I\omega^2$
$U_{applied} = T \theta_{displaced} \,$
$I \,$ = Mass Moment of Inertia
$\omega \,$ = Angular Speed

## Shear stress in fluids

A viscous, Newtonian fluid (including air and water) moving along a solid boundary will incur a shear stress on that boundary. The no-slip condition dictates that the speed of the fluid at the boundary (relative to the boundary) is 0, but at some height from the boundary the flow speed must equal that of the fluid. In Fluid dynamics, the no-slip condition for viscous fluid states that at a solid boundary the fluid will have zero velocity relative to the boundary The region between these two points is aptly named the boundary layer. In Physics and Fluid mechanics, a boundary layer is that layer of Fluid in the immediate vicinity of a bounding surface The shear stress is imparted onto the boundary as a result of this loss of velocity and can be expressed as

$\tau_\mathrm{w} = \mu \left.\frac{\partial u}{\partial y}\right|_{y = 0}$

where

μ is the dynamic viscosity of the fluid,
u is the velocity of the fluid along the boundary, and
y is the height of the boundary. Viscosity is a measure of the resistance of a Fluid which is being deformed by either Shear stress or Extensional stress.

### 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. Viscosity is a measure of the resistance of a Fluid which is being deformed by either Shear stress or Extensional stress. Such a sensor was demonstrated by A. A. Naqwi and W. C. Reynolds[1]. 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.

## References

1. ^ Naqwi, A. A. & Reynolds, W. C. (1987), “Dual cylindrical wave laser-Doppler method for measurement of skin friction in fluid flow”, NASA STI/Recon Technical Report N 87