Axial Force
Definition: Force which is parallel to the longitudinal
axis of the member.
Shearing force
Definition: Force which is perpendicular to the
longitudinal axis of the member.
Shearing force
Shearing force


The shearing forces at the end of the beam is equal
to the vertical reaction at the support.
The shearing force F(x) at any other section “x” on
the beam can be found by using the following
equation.
Shearing force
L
q kN/m
V= F(x)
x
R1
Bending Moment
Definition: Turning effect of a force can be called as
bending moment.
M
L
Axial Force, Shear Force and Bending Moment
Diagram

To determine the change in internal forces along the
length of the beam or frame

To determine the location of maximum stress caused by
these internal forces

To ensure that this stress must remain with in elastic
limit
Axial Force, Shear Force and Bending Moment
Diagram
How to draw internal force, shear force and bending
moment diagram



Take an imaginary cut at any point along the length of beam and
frame
Draw the free body diagram
Calculate the magnitude of these forces using equations of
equilibrium
Axial Force, Shear Force and Bending Moment
Diagram
Methods: To draw internal force, shear force and
1.
2.
bending moment diagram
Basic Method
Integration or graphical method
Fundamental Principle:
1.
2.
The basic function representing shearing force or bending moment
is developed
This function is plotted along the length of the member
Axial Force, Shear Force and Bending Moment
Diagram
Sign Convention:
+ Positive
1.
2.
- Negative
Shearing force that tends to rotate the free body in clock wise
direction is positive
Shearing force that tends to rotate the free body in anti-clock wise
direction is negative
Axial Force, Shear Force and Bending Moment
Diagram
Sign Convention:
+ Positive
1.
2.
- Negative
Bending Moment that tends to produce sag in the beam is positive
Bending Moment that tends to produce hog in the beam is positive
Axial Force, Shear Force and Bending Moment
Diagram
Procedure of Basic Method:
1.
2.
3.
4.
Calculate the reactions at supports of the beam
Take an origin for a co-ordinate x along the length of
the beam.
Cut the beam with an imaginary cut at a distance x,
and draw the free-body diagram.
Calculate the shear force and bending moment as a
function of x using equilibrium equations.
Shearing force diagram


Shear force diagram is plots of the shearing force
(on the vertical-axis) versus
The position of various sections along the length of
the beam (on the Horizontal-axis).
Bending Moment Diagram


Bending moment diagram is plots of the bending
moment (on the vertical-axis) versus
The position of various sections along the length of
the beam (on the Horizontal-axis).
Bending Moment and shearing
force Diagram
Class Notes
Axial Force, Shear Force and Bending Moment
relation ship
Class notes