What is conjugate beam Theorem?
What is conjugate beam Theorem?
A conjugate beam is defined as an imaginary beam with the same dimensions (length) as that of the original beam but load at any point on the conjugate beam is equal to the bending moment at that point divided by EI.
How the conjugate beam method is used to find the deflection?
If the convention stated for positive curvature diagrams is followed, then a positive shear force in the conjugate beam equals the positive slope in the real beam, and a positive moment in the conjugate beam equals a positive deflection (upward movement) of the real beam.
How do you draw a conjugate beam?
How to draw conjugate beam:
- Step 1: Draw the bending moment diagram for the real beam.
- Step 2: Divide the magnitudes of bending moments by flexural rigidity and draw the M/EI diagram.
- Step 3: Draw the conjugate beam having the same length as a real beam.
- Step 4: Plot the loading same as the M/EI diagram in step-2.
How do you solve beam deflection?
Beam Deflection Equations Generally, deflection can be calculated by taking the double integral of the Bending Moment Equation, M(x) divided by EI (Young’s Modulus x Moment of Inertia).
Why conjugate beam method is used?
The conjugate beam method is the method used to determine the slope and deflection of the beam in which the imaginary conjugate beam is constructed from the real beam and the shear forces and bending moments of the conjugate beam are equal to the slope and deflection of the real beam.
Is conjugate beam method and moment-area method same?
Conjugate beam method is the modified moment–area method. This method is based on the construction of a conjugate beam, defined as an imaginary beam of length equal to that of the original beam and loaded with an elastic weight M/EI, where M is the BM of the actual beam.
What are the characteristics of conjugate beam?
Properties of conjugate beam method: The length of a conjugate beam is always equal to the length of the actual beam. The load on the conjugate beam is the M/EI diagram of the loads on the actual beam. Simple support for the real beam remains simple support for the conjugate beam.