Shear Force at a section of beam - Definition, equation, calculation and diagram

Shearing force and bending moment are very important factors to be considered while designing any structural component.

Shearing force at a section of beam is defined as the algebraic sum of all the vertical forces acting on one side of the section. For example consider the following figure which shows the free body diagram of a simply supported beam.

Sign convention for shearing force

The force trying to push the left hand part of the beam upward will be taken as positive, whereas the force trying to push the left hand part of the beam downward will be taken as negative.

See the following figure;

Similarly the force trying to push the right hand part of the beam downward will be taken as positive and the force trying to push the right hand part of the beam upward is taken as negative.

In the beam given above, the shearing force at section x-x (by considering the forces on the left hand side) can be written as

  F_x = R_A – F₁ – F₂

Alternatively by considering the forces on the right hands side the shear force at section x-x can be written as

  F_x = F₃ + F₄ - R_B

 The graphical representation of variation of shearing force along the span of the beam is known as shearing force diagram (SFD)

• Shearing force diagram between two point loads is horizontal with a vertical rise or fall at the position of the loads

• Shearing force variation in the region of a uniformly distributed load (UDL) is linear with a slope equal to the intensity of the UDL

• Shearing force variation in the region of a uniformly varying load (UVL) is parabolic