Shear Force and Bending Moment:

Shear Force : General

The static equilibrium of a space might be ensured if the algebraic sum of all of the forces working on the particle in the directions x, y, z are separately zero

Mathematically specking, ∑F_x = 0, ∑F_y = 0, and ∑F_z = 0.

where, ∑F_x = algebraic sum of all of the forces working on the particle in the x direction

                                = F_x1 - F_{x 2} ,

∑F_y = algebraic sum of all the forces working on the particle

             in the y direction = F_y1 - F_y2

, and

∑F_z = algebraic sum of all of the forces working on the particle in the Shear Forces and z direction =

                   =

         Figure: Equilibrium of a Particle under a System of Forces

These forces are general forces & their positive or negative sign shall depend on, whether the forces are directed away from the origin or towards the origin. Let us assume a section A-A parallel to y-z plane in the body

       Figure: Equilibrium of a Body under System of Forces