What is Shear Force?
• Shear force is a force that acts on a substance
in a direction which is perpendicular to the
extension of that substance
• Force instance the pressure of air down the
border of an airplane wing. Shear forces
frequently result in shear strain.
Definition of SFD
• If the variation of V (Shear) is written as
functions of position, x, and plotted, the
resulting graphs are called the shear force
• Shear Force Diagrams are analytical tools
which help to perform structural design.
• These diagrams can be used to easily
determine the type , size and material of
member in a structure.
• Deflection of a beam can be determined with
the help of these diagrams.
• Bending moment diagram can be drawn from
SFD as well.
Convention to draw SFD
• Engineers have adopted a standard
convention to draw SFD & use them in design
practice. The convention is—
• Shear that produces clockwise moment is
positive & anti-clockwise is negative
• The are 2 methods for drawing shear force
• 1) the basic method
• 2) the integration method
• The basic method is used when a beam may
be subjected to a loading that is a fairly
• In other case, many problems require only the
maximum values of shear and moment, and
the location at which this values occur. The
graphical method is most useful for these
Steps for Basic Method
• 1) Determine the support reactions for the beam.
• 2) Specify an origin for a co-ordinate x along the length
of the beam.
• 3) Section the beam with an imaginary cut at a distance
x, and draw the free-body diagram.
• 4) Determine shear and bending moment as a function
of x using equilibrium equations.
• 5) Repeat steps 3 and 4 for all regions between any two
discontinuities of loading.
• 6) Draw, to scale, the functions on a sketch of the
• an overhanging beam is subjected to a
• uniform load of q = 1 kN/m on AB
• and a couple M0 = 12 kN-m on midpoint
• of BC, construct the shear for
• the beam
Soln- RB = 5.25 kN RC = 1.25 kN
• shear force diagram
• V = - q x on AB
• V = constant on BC
• A constant load of ωo per unit length is
applied on a simply supported beam as shown
below. Draw the shear force and bending