The document reports on the conjugate beam method, which uses an imaginary beam with the same length as the original beam but with loads equal to the bending moment at each point divided by EI. The method can be used to derive the slope and displacement of a beam and was developed by H.Müller-Breslau in 1865. It requires similar computations as moment-area theorems but relies only on statics principles. Key principles are that the conjugate beam has the same length and its load is the M/EI diagram of the actual beam, and that the points of zero shear/maximum moment correspond to zero slope/maximum deflection on the actual beam.

1. REPORT WORK 1
(CONJUGATE BEAM METHOD)
SUBMITTED BY:
PRECIOUS ONG SORMILLO
SUBMITTED TO:
ENGR. FELIPE FAJANEL

2. Conjugate beam isdefinedasthe imaginarybeamwiththe same dimensions(length) asthatof the
original beambutloadat any pointonthe conjugate beamisequal tothe bendingmomentatthatpoint
dividedbyEI.The conjugate-beammethodisan engineeringmethodtoderive the slope and
displacementof abeam.The conjugate-beammethodwasdevelopedbyH.Müller-Breslauin1865.
Essentially,itrequiresthe same amountof computationasthe moment-areatheoremstodetermine a
beam'sslope ordeflection;however,thismethodreliesonlyonthe principlesof statics,soits
applicationwillbe more familiar.
PRINCIPLES OF CONJUGATE BEAM METHOD
1. The length of a conjugate beam is always equal to the length of the actual beam.
2. The load on the conjugate beam is the M/EI diagram of the loads on the actual beam.
3. A simple support for the real beam remains simple support for the conjugate beam.
4. A fixed end for the real beam becomes free end for the conjugate beam.
5. The point of zero shear for the conjugate beam corresponds to a point of zero slope for
the real beam.
6. The point of maximum moment for the conjugate beam corresponds to a point of
maximum deflection for the real beam.
Supports of Conjugate Beam

3. THEOREMS OF CONJUGATE BEAM
1st theorem
Slope of actual beam = Shear force of conjugate beam
2nd theorem
Deflection of actual beam = Moment of conjugate beam

4. Ex.1 )
Ex. 2)

5. Ex. 3)