By David E. Malach
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Additional info for Advances in Mechanical Engineering Research; Volume 2
Derivation of the Power Law The power law may represent any function f(x) as follows from the following derivation. 3). Any function f(x) always can be written in a reduced variable x/x0 30 T. A. C. M. 7) and can be given in the power of a function: f ( x) f1 ( x / x0 ) f ( x) f ( x0 ) f ( x / x ) 1/ n n 1 0 and expanded into the row: x x0 . ( x x0 ) 2 . f '( x0 ) f ''( x0 ) ....... 1! 2! giving: n x x x0 1 1/ n 1/ n 1 f ( x) f1 (1) f1 (1) . f1 (1).
And at the end of the crack a negative moment of about: M 2 M1 . Further is M 2 M1 V , thus M1 V / 2 . 1. Beam with crack by the dowel force of a joint and bending moment. 2) 42 T. A. C. M. 2. Statics of half the crack. 3) where Gc is the fracture energy. 6) which thus also applies for notched beams and for end-joints and verifies the lower bound of the strength, predicted by the theory of . This also indicates that only work by shear stresses contributes to fracture. 6(1 – α)α and also that β is about proportional to α and is of the same order.
5 nc and not splitting but flow of the connection is determining for failure reaching the in  theoretical explained high embedding strength by hardening as to be expected for the always sufficient high spreading possibility of one- (or two-) dowel joints. The same applies for the 1 and 2 dowel joints of the Karlsruhe investigation. Splitting then is not the cause of failure but the result of post-failure behaviour due to continued extension by the testing device. 1 of  shows that for series B, splitting of the beam is determining.
Advances in Mechanical Engineering Research; Volume 2 by David E. Malach