Shear Force and Bending Moment
Shear Force
Shear force at any cross section of the beam is the algebraic sum of vertical forces on the beam acting on the right or left side of the section.
Bending Moment
Bending moment at any section of a beam is the algebraic sum of the moments of all forces acting on the right or left side of the section.
Relation between Rate of Loading, Shear Force, and Bending Moment
a) Relation between rate of loading and shear force:
dF/dx = W
The rate of change of shear force with respect to the distance is equal to the intensity of loading.
b) Relation between shear force and bending moment:
dm/dx = F
The rate of change of bending moment at any section is equal to the shear force at that section with respect to the distance.
Point of Contraflexure
The point of contraflexure is the point at which the bending moment diagram changes sign from positive to negative or vice versa, or the point at which the bending moment is zero.
Location of point of contraflexure:
- At the point of contraflexure, the bending moment is zero.
- Take the bending moment at the point of contraflexure and equate it to zero.
- The distance (location) of the point of contraflexure can be found from either end of the beam.
Point D, B.M. = 0, Point D is the Point of Contraflexure.
