Shearing Forces and Bending Moments

The bending moment at a section in a beam is the algebraic sum of the moments about that section of all the forces to the right or to the left of that section.

Bending moments which cause a beam to sag are taken as positive .
Bending moments which cause a beam to hog are taken as negative .

Bending moment diagrams showing the variation of bending moment along a beam are plotted on the tensile side of the beam.

Bending moment diagrams resulting from the action of concentrated point loads consist of straight lines with changes of direction at the point of application of the loads .

Bending moment diagrams resulting from the action of uniformly distributed loads consist of parabolic curves.


Shearing force at a point in a beam is the algebraic sum of all the vertical forces to the right or to the left of that point.

Shearing force diagrams resulting from the action of concentrated point loads on horizontal beams consist of horizontal straight lines with vertical jumps at load positions.

Shearing force diagrams resulting from the action of  uniformly distributed loads on horizontal beams consist of sloping straight lines .

The maximum bending moment occurs at a point where the shearing force is zero.

The bending moment at a pin is zero.