Shear Force Diagram is a graphical representation of shear force (V) along the length of a beam subjected to external loads. It is an analytical tool used in structural design to determine member type, size, and material. There are two methods for constructing SFDs - basic and integration. The basic method involves determining support reactions, sectioning the beam, drawing free body diagrams, and calculating shear and moment as a function of position along the beam. SFDs can be used to find maximum shear values, bending moment diagrams, and deflection of beams under different loading conditions such as concentrated, uniform, and variable loads as demonstrated in the examples.

1. Shear Force Diagram
• By
• Monija Ahmed

2. 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.

3. 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
diagram

4. Implementations
• 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.

5. • Deflection of a beam can be determined with
the help of these diagrams.
• Bending moment diagram can be drawn from
SFD as well.

6. 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

8. Method
• The are 2 methods for drawing shear force
diagram:
• 1) the basic method
• 2) the integration method

9. • The basic method is used when a beam may
be subjected to a loading that is a fairly
complicated function.
• 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
situations

10. 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
beam.

11. Example-1

12. • concentrated loads
• consider a simply support beam AB
• with a concentrated load P
•
•
•
•
•
•
RA = P b / L RB = P a / L
for 0 < x < a
V = RA = P b / L
for a < x < L
V = RA - P = - P a / L

14. Example-2

15. • 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

16. Example-3
• A constant load of ωo per unit length is
applied on a simply supported beam as shown
below. Draw the shear force and bending
moment diagram

18. Σ Fx=0=> RAx=0
By symmetry,RAy=RBy= ωoL/2

19. Σ Fx=0=> V= ωoL/2-ωox

20. Example-4
A beam with a hinge is loaded as
above

21. •
•
•
•
•
Σ Fx=0=> RAx=0
MB=0 => RAy X2=0=> RAy=0
Σ MD=0=> 10 X 5 X 5 X 4 X 2= RCy X 4
RCy= 22.5 kN
RDy= 10+5X4-22.5=7.5 kN

23. •Thank you