Forces and Stresses in Beams:

The right hand location is eliminated and the forces exposed on section A-A in the left hand portion of the body are illustrated in Figure (c). The three resultant forces in the x, y, z directions, mention as F_x, F_y and F_z do not build the same type of stresses on the section. Since the area of the section A-A is normal to x axis, F_x shall produce axial stresses or normal stress τ_x on the section. Though, the remaining two forces F_y & F_z act tangential or along the plane and produce shear stresses τ_xy and τ_xz. By using the common nomenclature of beams & bending, these forces F_y and F_z are called as shear forces, while F_x is simply an axial force.

F_x = resultant of all the forces working on the left portion of the body in the x direction.

F_y = resultant of all the forces working on the left portion of the body in the y direction.

F_z = resultant of all of the forces working on the left portion of the body in the z direction.

Figure: Development of Shear Force at Section C

Now let us assume a beam (for instance, cantilever beam) subjected to point load P. let a section at C. At this section there is a possibility of failure by shear as illustrated in Figure. If such a failure take place at section C, the cantilever is liable to be sheared off into two parts. For the symmetry of the cantilever, the fixed support at A shall provide a vertical reaction vertically upwards, of magnitude R_A = P. It is apparent that the force acting normal to the centre line of the member on each part equals S = P. The force working on the right part on the section C is downward. The resultant force working on the left part is upward. The resultant force working on anyone on the parts normal to the axis of the member is known shear force at the section C.