BENDING MOMENT AND SHEAR FORCE

Bending Moment

The bending moment (B.M.) at any point along a loaded beam is the algebraic sum of the moments of all the vertical forces acting to one side of the point abcut the point. Consider a simply supported beam AB carrying concentrated loads as shown in Fig. 3.1 Lé R and RB be the

vertical reactions at supports A and B respectively. Consider a section x—x at a distance x from end A. The clockwise moment at this sectioh due to all the loads acting on the beam to the left of the section is:

If we consider the forces to the right of the section x—x, then anticloc4wise moment is:

For equilibrium of the beam, the B.M. given by equations (1) and (2) are equal. The SI units of B.M. are N.m or kN.n.

ShearForce

The shear force (S F) at any point along a loaded beam is the algebraic sum of all the vertical forces acting to one side of the point. Thus, for the beam AB shown in Fig. 3.1, the shear force at cross-section x—x as measured from the left hand side is:    

The shear force as measured from the right hand side is:

Since the beam is in equilibrium, the S.F. given by equations (1) and (2) are equal.