Sign convention which is used for solving problems of beam:
Although different sign conventions can be used, most of the engineers use following sign conventions for shear forces and bending moment.
(i) Shear force which tends to move left portion upward relative to right portion shall be called as positive shear force.
(ii) The bending moment which is trying to sag (Concave upward) beam shall be taken as positive bending moment. If the left portion is considered positive bending moment comes out as clockwise moment.
To decide sign of moment because of a force about section, assume that the beam is held tightly at that section and observe deflected shape. Then looking at shape sign can be assigned.
Shear force and bending moment vary along the length of the beam and this variation is represented graphically. The plots are called as shear force and bending moment diagrams. In this type of diagrams, the abscissa indicates position of section along the beam, and ordinate represents the value of Shear Force and BM respectively. These plots assist to determine maximum value of each of these quantities.