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Prediction of the cohesive crack growth in concrete beams in bending by mean of fracture mechanics and the finite element method

The text presents the theoretical base for the construction of the program CGPTROl. The fictitious crack model and the finite element method are employed for analyzing. This program is created to investigate two-dimensional models for the initiation and growth of the I-mode crack in notched beams in bending. The final result of the fradtu"e analysis is ·the load-deflection diagram for the prediction of the cohesive crack growth in concrete notched beam in bending. | T~p chi C. is constant and w in p. inch. Tran Tu and Ka.sperkiewicz (1994), jlOJ: !!._ = (1- A)(1- x') !t w w, ::t=-, + A(1- x) 1/k (4) k- .!I_ - 1-ST , Here, u is the crack opening displacement dependent tensile in the fracture process zone and- ft is the tensile strength of material, w is actual crack opening displacement, and We is critical va.Iue· of CTOD. ST is the quasi-brittle index, it has been considered to be a main parameter characterizing to the shape of the softening branch, JlOJ. According to Hordijk's opinion, J8J, Eq (2) may be the best approximation for all conc~ete mixes. It is however a little too complicated for determining the coefficients from measurements. In the case of approximation of the stress - crack opening curve by bilinear diagrams with a knee point at the coordinates ( a,j,, a2w, with a1 and a2 ::; 1): (1- a,)j, u= a2Wc w+ f when t a,j, ) (w-w,) 1- a2 We u= ( w :5 a2wc (5) when a2wc ::5 w :$ We this equation will be used to calculate the cohesive forces with the CGP-TR01 for examples in the text. 5. Numerical approach 5.1. Generation for the element mesh This is an important part in numerical approach to fracture mechanics when applying the fictitious crack model. The automatic mesh generation procedure can be briefly presented as follows, .