4th Year 2nd Semester
Dept. Of Civil Engineering
Ahsanullah University Of Science and Technology
•What is “SHEAR FORCE”?
is the algebraic sum of the vertical
forces acting to the left or right of a cut section
along the span of the beam.
•What is „SHEAR FORCE DIAGRAM‟?
Shear force diagram(SFD):
The graphical representation of shear force in which ordinates
represents shear force and the abscissa represents the position of the section is called
“shear force diagram” or it can be defined as “ A shear force diagram is the one which
shows the variation shear force along the length of a beam section.”
What is the importance of SFD in case of
Shear force diagrams are analytical tools used in
conjunction with structural analysis to help perform
structural design by determining the value of shear force at
a given point of a structural element such as a beam. These
type, size, and material of a member in a structure so that a
given set of loads can be supported without structural
Sign convention for SFD drawing?
The normal convention used in most engineering applications
is to label a positive shear force one that spins an element
clockwise (up on the left, and down on the right).
Also for simplification in solving many structural
problems the shear force at a section will be
considered positive when the resultant of the forces to
the left section is upwards, or to the right of the
section is downward.
IMPORTANT POINTS FOR DRAWING SHEAR FORCE DIAGRAM
Consider the left or right portion of the section,
Add the forces ( including reactions ) normal to the beam on one
of the portion. [ If right portion of the section is chosen, a force on
the right portion acting downwards is positive while a force acting
upward is negative, if left section is chosen then sign convention
will be vice versa. ]
The positive values of shear force are plotted above base line, and
negative values below base line.
The shear force diagram will increase or decrease suddenly by a vertical
straight line at a section where there is a vertical point load.
The shear force between any two vertical loads will be constant and
hence the shear force diagram between any two vertical loads will be
WHAT IS THE USE OF SFD?
To determine the internal shear forces at any given point on a
PRACTICAL APPLICATION OF SHEAR FORCE DIAGRAM
The figure below is referring the practical application of
shear force diagram in case of designing shear
reinforcement of a beam.
Some Examples of SFD
Simply Supported beam with UDL
Simply Supported beam carrying double point load and UDL
A detail example of drawing SHEAR FORCE DIAGRAM
A simply supported beam overhanging on one side is subjected to a U.D.L. of 1 kN/m. Sketch
the shear force diagram.
Solution: Consider a section (X – X’) at a distance x from end C of the beam.
To draw the Shear Force Diagram, RA and RB has to be defined,
By taking moment of all the forces about point A
RB × 3 – w/2 × (4)2 = 0
RB = 1 × (4)2 / 2 × 3 = 8/3 kN
For static equilibrium;
∑Fy = 0
RA + RB – 1 × 4 = 0
RA = 4 – 8/3 = 4/3 kN
Now, To draw SFD we need S.F. at all salient points:
Taking a section between C and B, SF at a distance x from end C. we have,
Fx = + w.x kN
At x = 0;
FC = 0
x = 1 m;
FB just right = 1 × 1 = + 1 kN
Now, again taking section between B and A, at a distance x from end C, the SF is:
Fx = x – 8/3
When, x = 1 m; FB = 1 – 8/3 = –5/3 kN = –1.67 kN
At x = 4 m;
FA = 4 – 8/3 = + 4/3 kN = + 1.33 kN
When The S.F. becomes zero;
Fx = x – 8/3 = 0
⇒ x = 2.67 m
(The sign is taken positive taken when the resultant
force is in downward direction on the RHS of the
Now the Final Shear Force Diagram
The SFD can be drawn by joining the ordinates at salient point by straight line, as
defined by governing equations.
NECESSITY OF SFD IN CASE OF PRESTRESSED CONCRETE