Shear stress

Overview

**shear stress**, denoted (Greek

Greek alphabet

The Greek alphabet is the script that has been used to write the Greek language since at least 730 BC . The alphabet in its classical and modern form consists of 24 letters ordered in sequence from alpha to omega...

: tau

Tau

Tau is the 19th letter of the Greek alphabet. In the system of Greek numerals it has a value of 300.The name in English is pronounced , but in modern Greek it is...

), is defined as the component of stress

Stress (physics)

In continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are a reaction to external forces applied on the body...

coplanar with a material cross section. Shear stress arises from the force vector component parallel

Parallel

-Mathematics and science:* Parallel , an imaginary east-west line circling a globe* Parallel circuits, as opposed to series* Parallel * Parallel evolution* Parallel transport* Parallel of declination, used in astronomy-Computing:...

to the cross section. Normal stress, on the other hand, arises from the force vector component perpendicular

Perpendicular

In geometry, two lines or planes are considered perpendicular to each other if they form congruent adjacent angles . The term may be used as a noun or adjective...

or antiparallel

Antiparallel (mathematics)

-Definitions:Given two lines m_1 \, and m_2 \,, lines l_1 \, and l_2 \, are anti-parallel with respect to m_1 \, and m_2 \, if \angle 1 = \angle 2 \,....

to the material cross section on which it acts.

The formula to calculate average shear stress is:

where

= the shear stress; = the force applied; = the cross-sectional area of material with area parallel to the applied force vector.

Beam shear is defined as the internal shear stress of a beam caused by the shear force applied to the beam.

where

*V*= total shear force at the location in question;*Q*= statical moment of area;*t*= thickness in the material perpendicular to the shear;*I*= Moment of InertiaSecond moment of areaThe second moment of area, also known as the area moment of inertia, moment of inertia of plane area, or second moment of inertia is a property of a cross section that can be used to predict the resistance of beams to bending and deflection, around an axis that lies in the cross-sectional plane...

of the entire cross sectional area.

This formula is also known as the Jourawski formula.

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

Shear flow

The term shear flow is used in solid mechanics as well as in fluid dynamics. Loosely speaking, shear flow is defined as:* the gradient of a shear stress force through the body ;...

s).