Shear Stress

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Shear stress, abbreviated as $$\tau$$ (Greek symbol tau), tends to deform the material by breaking rather than stretching without changing the volume by restraining the object.  Shear stress is the amount of force per unit area perpendicular to the axle of the object.

Shear stress formula

 $$\large{ \tau = \frac{F}{A_c} }$$

Where:

 Units English SI $$\large{ \tau }$$  (Greek symbol tau) = shear stress $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$ $$\large{ F }$$ = applied force $$\large{ lbf }$$ $$\large{N}$$ $$\large{ A_c }$$ = area cross-section of material perpendicular to the applied force $$\large{ in^2 }$$ $$\large{ mm^2 }$$

Related Shear Stress formulas

 $$\large{ \tau = \frac{ 8 \; K \; D }{ \pi \; d^3 } \; F_s }$$ (Spring) (occures on the inside surface of the coils) $$\large{ \tau = \frac{ V \; Q }{ I \; t } }$$ (beam)

Where:

$$\large{ \tau }$$ (Greek symbol tau) = shear stress

$$\large{ Q }$$ = first moment of area

$$\large{ t }$$ = material thickness perpendicular to shear

$$\large{ D }$$ = mean coil diameter

$$\large{ I }$$ = moment of inertia of entire area cross-section

$$\large{ \pi }$$ = Pi

$$\large{ F_s }$$ = spring force

$$\large{ V }$$ = total shear force at the point of location

$$\large{ K }$$ = Wahl correction factor

$$\large{ d }$$ = wire diameter