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The Müller-Breslau principle is a method to determine influence lines. The principle states that the influence lines of an action (force or moment) assumes the scaled form of the deflection displacement. OR, This principle states that "ordinate of ILD for a reactive force is given by ordinate of elastic curve if a unit deflection is applied in ...
The Müller-Breslau Principle can only produce qualitative influence lines. [2] [5] This means that engineers can use it to determine where to place a load to incur the maximum of a function, but the magnitude of that maximum cannot be calculated from the influence line. Instead, the engineer must use statics to solve for the functions value in ...
Heinrich Mueller-Breslau. Heinrich Franz Bernhard Müller (May 13, 1851 in Breslau – April 24, 1925 in Grunewald, Berlin, known as Müller-Breslau from around 1875 to distinguish him from other people with similar names) was a German civil engineer and high school teacher.
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The conjugate-beam method was developed by Heinrich Müller-Breslau in 1865. Essentially, it requires the same amount of computation as the moment-area theorems to determine a beam's slope or deflection; however, this method relies only on the principles of statics, so its application will be more familiar. [2]
After further review, I don't believe it is a good idea. There are ways to define the influence line of a structure which don't rely on Müller-Breslau's principle, and Müller-Breslau's principle refers to a very specific application of an important theorem which provides a convenient way to define influence lines.
Littlewood's three principles are quoted in several real analysis texts, for example Royden, [2] Bressoud, [3] and Stein & Shakarchi. [4] Royden [5] gives the bounded convergence theorem as an application of the third principle. The theorem states that if a uniformly bounded sequence of functions converges pointwise, then their integrals on a ...
While in Breslau, Dirichlet continued his number-theoretic research, publishing important contributions to the biquadratic reciprocity law which at the time was a focal point of Gauss's research. Alexander von Humboldt took advantage of these new results, which had also drawn enthusiastic praise from Friedrich Bessel , to arrange for him the ...