This explains why the obtained structural response is stiffer when a half-FE-model is employed, as just discussed. This analytical conclusion agrees with the results of a large number of bending tests on plain concrete beams, which have invariantly shown the beam failure to be the result of a single fracture. The numerical results of Case 4-1 and Case 4-2 with three notches: (a) load-displacement relation, (b) load-CMOD relation, and (c) crack propagation chart (after Shi et al., 2003 courtesy of ASCE).Īs demonstrated through all the beam cases studied, although multiple cracks were involved in the initial stage of crack propagation, only the dominant crack in each case became an open crack, while the others stopped propagating and closed eventually before reaching the peak load. It should be pointed out that by modifying crack paths and employing full FE models, the obtained structural deformation curves almost perfectly match the experimental curves in the postpeak regions.įigure 4.14. Obviously, the crack interactions, which will be the focus of study in Chapter 5, play an important role in causing these complicated cracking behaviors. This makes the prediction of cracking behavior in a real structure very difficult when multiple cracks are involved. As such, a small change in the sizes or positions of initial notches may completely alter the pattern of crack propagation. Reducing the initial size of notch C by only one centimeter, however, crack A of Case 4-2 easily becomes the most progressive crack, curbing the growth of crack B and crack C at an early stage.

Crack C becomes the dominant crack in the postpeak region, forcing the others to close eventually.

As shown in Figure 4.14, in Case 4-1, crack A and crack C compete for simultaneous propagation up to the peak load at the sixth step, reaching almost one-half of the beam depth.

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