Who is Muller Breslau?
The real and full name of Muller Breslau is “Heinrich Franz Bernhard Muller” and he was born in a city name Breslau. He was a German civil engineer and also a high school teacher. He was known as “Muller Breslau” (it means Muller from Breslau) to distinguish himself from other people with similar name. He provided significant contribution to the theory of beam and frame in structural analysis.
Muller Breslau Principle:
It states that, if an internal stress component or reaction is considered to act through some small distance and there by to deflect or displaced the structure. The curve of the deflected structure will be to some scale of influence line for the stress or reaction component.
Or we can say that, “the ordinate of influence line diagram for a reaction is given by the ordinate of elastic curve if a unit deflection is applied in the direction of reaction”.
Let us consider a two-span continuous beam ABC, simply supported at A & C and continuous over support B.
Let unit load act at point X at a distance of x from support A.
If support B is removed, the beam will deflect as shown in fig-b.
Apply the unit load at B, beam will deflect as shown in fig-c.
δBx = deflection at B due to unit load at x
δxB = deflection at x due to unit load at B.
δBB = deflection at B due to unit load at B.
By consistent deformation,
RB* δBB = δBx
By Maxwell’s reciprocal theorem,
δBx = δxB
؞ RB* δBB = δxB
؞ RB = δxB / δBB
When δBB = 1, RB = δxB
Thus, we can say that the reaction at B due to unit load at any point X is proportional to the deflection at the point X due to unit load acting at B.
The deflection curve shown in fig-c represents the influence line to some scale for RB.
