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Concept
Shear stress
Summary
Shear stress (often denoted by τ (Greek: tau)) is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. Normal stress, on the other hand, arises from the force vector component perpendicular to the material cross section on which it acts.
The formula to calculate average shear stress is force per unit area.:
where:
τ = the shear stress;
F = the force applied;
A = the cross-sectional area of material with area parallel to the applied force vector.
Wall shear stress expresses the retarding force (per unit area) from a wall in the layers of a fluid flowing next to the wall. It is defined as:
Where is the dynamic viscosity, the flow velocity and the distance from the wall.
It is used, for example, in the description of arterial blood flow in which case which there is evidence that it affects the atherogenic process.
Pure shear stress is related to pure shear strain, denoted γ, by the following equation:
where G is the shear modulus of the isotropic material, given by
Here E is Young's modulus and ν is Poisson's ratio.
Beam shear is defined as the internal shear stress of a beam caused by the shear force applied to the beam.
where
f = total shear force at the location in question;
Q = statical moment of area;
b = thickness (width) in the material perpendicular to the shear;
I = moment of inertia of the entire cross-sectional area.
The beam shear formula is also known as Zhuravskii shear stress formula after Dmitrii Ivanovich Zhuravskii who derived it in 1855.
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). 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
Constructions in soil can also fail due to shear; e.
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