
Whenever a beam is loaded with transverse loads, the bending moments
are developed which cause the axis of beam to deflect from the
original undisturbed position as seen in the following figure.
In the above figure the undisturbed axis of cantilever beam is AB
and the deflected shape is AB'. The deflected shape of the beam is
also known as elastic curve. The deviation of point B to B' is
shown as deflection δ_{B} and the
change in slope of tangent at B is shown as slope θ_{B} .
The differential equation of elastic
curve was first given by Euler and written as
where E = Modulus of
elasticity of the beam material
I =
moment of inertia of the beam xsection
v = deflection along yaxis
x = distance from the origin to the point of deflection
M =
bending moment at section
Deflection calculations are required for buildings,
bridges and machines
to satisfy some design criteria and to control vibration.

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There are different methods available to determine slope and
deflection of beam. Some of them are given below;

Integration method:
 Areamoment method
 Conjugatebeam method
 Strainenergy method (Castigliano's
theorems)

Virtual work method (Unit Load
method)
 Method of superposition (used
to find the slope and deflection for different loading cases by
taking the resultant of the values for individual cases)
Use our
Deflection Calculator
Easy to use
calculator for different loads on beams
Moment Distribution Calculator^{New}
Solving Indeterminate Beams with different loads
RC Beam
Calculator^{New}
Calculate the strength of reinforced concrete beams
See more about
bending moment
and shearing force
Quiz on Structural Analysis
Quiz on Structural Design
Visit
Problem Solver for solved examples on deflection 
