# Shear Force

on . Posted in Classical Mechanics

Shear force, abbreviated as V, is the force that acts perpendicular to the longitudinal axis of a beam or structure and causes it to deform in a transverse direction.  The shear force at any point along a beam is equal to the rate of change of the bending moment at that point.  The bending moment is the moment of force that causes a beam to bend, and it varies along the length of the beam due to the distribution of external loads and internal stresses.  This is used in mechanics and the design of structures, such as bridges, buildings, and aircraft.  It is also used in the analysis of materials and the development of new materials and manufacturing processes.

In engineering and structural analysis, shear forces is used for designing and analyzing structures like beams and bridges.  Engineers calculate shear forces to ensure that a structure can withstand the lateral loads and forces it may experience during its lifetime.  Mathematically, shear force is represented as a function of position along the length of an object or structure.  The shear force diagram typically shows how the magnitude and direction of shear force change along the object's length, helping engineers and designers make informed decisions about the materials and dimensions needed for a particular application.

### Shear Force formula

$$V = M\;/\;x$$     (Shear Force)

$$M = V \; x$$

$$x = M\;/\;V$$

### Solve for V

 bending moment, M reaction distance on beam, x

### Solve for M

 shear force, V reaction distance on beam, x

### Solve for x

 bending moment, M shear force, V

Symbol English Metric
$$V$$ = shear force $$lbf - ft$$ $$N-m$$
$$M$$ = bending moment $$lbf\;/\;sec$$ $$kg-m\;/\;s$$
$$x$$ = horizontal distance from reaction to point on beam $$in$$ $$mm$$
$$dM\;/\;dx$$ = rate of change of the bending moment with respect to distance -