
Unit load method also referred to as
method of virtual work was developed by John Bernoulli in 1717. It
is used to determine the slope and
deflection at a specified point
of a beam, frame, or truss.
In this method a virtual unit load is
applied at the point of deflection (δ) and in the direction of
deflection, whereas a unit virtual moment is applied at the point of
desired slope.
By applying the principle of work and energy we get
external virtual work = internal
virtual work
External virtual work =1kN.δ
Therefore, δ = Internal virtual work
Based on internal virtual work for
different types of loading the deflection formula is given as
follows;
Flexural members
In case of flexural members (beam,
frame) the total internal virtual work is obtained by integration.
Where δ = deflection
at point C
M_{x} =
bending moment at x due to actual loading
m_{x} =
bending moment at x due to virtual unit load applied at point of
deflection, C.
L = beam span
E = Modulus of
elasticity of beam material
I = moment of
inertia of beam section.
Note: In case of calculation of
slope at a point we should apply a unit moment at the
specified point of slope and write the equation for
m_{x}
See our solved
Problem 73 for deflection of beam by unit load method 
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Pinjointed
Truss
In case of truss the total internal
virtual work is obtained by taking the algebraic sum
Where,
δ_{C}
= deflection of joint C
N=axial force in a
member due to real loading
n = axial force in
the member due to virtual unit load applied at the joint C
L= length of member
A= area of
crosssection of the member
E = modulus of
elasticity of the member
Note: compressive
forces are taken as negative whereas tensile forces are taken as
positive.
See our solved
Problem 75 for deflection of Truss by unit load method
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