The Conjugate Beam Method in Structural Analysis
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THE CONJUGATE BEAM
METHOD
The Conjugate Beam Method
The conjugate beam is derived from the fact that
similar relationships can be observed b/n the
moment-area theorems and statical procedures
The Conjugate Beam Method
Reformulating, we see that if the beam was loaded
with the equivalent load magnitude of M/EI instead
of
w
,
the moment produced at any point due to this
loading is equal to the deflection at that point in the
beam due to the actual loading
The Conjugate Beam Method
the shear produced at any point due to the M/EI
loading is equal to the rotation at that point in the
beam due to the actual loading
The Conjugate Beam Method
The Conjugate Beam Method
The beam to which the M/EI diagram is applied to
is called
the conjugate beam.
As a consequence of the two theorems from
moment-area,
supports and joints
corresponding to
the real beam shall have their appropriate
counterparts in the conjugate beam equivalent,
such
that V(rotation) and M(deflection) values obtained
in the conjugate beam reflect those present in the
actual beam.
The Conjugate Beam Method
The Conjugate Beam Method
The Conjugate Beam Method
Examples
The Conjugate Beam Method
Procedure:-
1. Develop the bending moment diagram of the
beam from static analysis.
2. Draw the M/EI diagram for the beam, using
respective values at different parts of the
beam.
3.
Draw the Conjugate beam and load it with
the real beam’s M/EI diagram.
The loading
always
acts away
from the beam.
(upward if
M/EI is positive and downward if negative)
ANY QUESTIONS ??
The Conjugate Beam Method is a powerful technique in structural engineering, derived from moment-area theorems and statical procedures. By applying an equivalent load magnitude to the beam, the method allows for the analysis of deflections and rotations in a more straightforward manner. This article explores the theory behind the method, its application in determining shear and moment values, and provides a step-by-step procedure for using the Conjugate Beam Method in practical scenarios.
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Presentation Transcript
THE CONJUGATE BEAM METHOD
The Conjugate Beam Method The conjugate beam is derived from the fact that similar relationships can be observed b/n the moment-area theorems and statical procedures
The Conjugate Beam Method Reformulating, we see that if the beam was loaded with the equivalent load magnitude of M/EI instead of w, the moment produced at any point due to this loading is equal to the deflection at that point in the beam due to the actual loading
The Conjugate Beam Method the shear produced at any point due to the M/EI loading is equal to the rotation at that point in the beam due to the actual loading
The Conjugate Beam Method The beam to which the M/EI diagram is applied to is called the conjugate beam. As a consequence of the two theorems from moment-area, supports and joints corresponding to the real beam shall have their appropriate counterparts in the conjugate beam equivalent, such that V(rotation) and M(deflection) values obtained in the conjugate beam reflect those present in the actual beam.
The Conjugate Beam Method Examples
The Conjugate Beam Method Procedure:- 1. Develop the bending moment diagram of the beam from static analysis. 2. Draw the M/EI diagram for the beam, using respective values at different parts of the beam. 3. Draw the Conjugate beam and load it with the real beam s M/EI diagram. The loading always acts away from the beam. (upward if M/EI is positive and downward if negative)
