טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentWerzberger Shmuel
SubjectQuantification of the Localization Phenomenon in
Fiber-Reinforced Concrete Beams with Conventional
Reinforcement
DepartmentDepartment of Civil and Environmental Engineering
Supervisors Professor Avraham Dancygier
Dr. Yuri Karinski
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


Abstract



Concrete that includes steel fibers is known to have increased toughness, exhibited in the material post-peak tensile behavior. Therefore, RC flexural elements that include steel fibers (RFRC elements) are expected to have enhanced structural ductility. However, relatively recent experiments have shown that both normal strength and high strength RFRC beams with minimum longitudinal reinforcement, exhibited a pronounced reduction in their flexural ductility .

This ductility reduction is associated with cracking localization phenomenon. The phenomenon is characterized by significant widening of one or only few cracks, compared with the other cracks. Yet, in design of RC beams and slabs, minimum longitudinal reinforcement ratio is determined a criterion that refers to flexural capacity, but not to the flexural ductility.

This work was aimed at developing, verifying and calibrating a probabilistic model for quantifying the phenomenon of cracking localization in beams. The analysis is based on measurements from seven RC (plain) and eighteen RFRC beam specimens that had been previously tested under four-point bending setup.

The model is based on measuring the level of cracking localization by the ratio m/n, where n is the total number of flexural cracks that develop in the beam, and m is the number of cracks that are significantly wider than the others.           
The work included a literature survey of the phenomenon and of models that predict the crack spacing in beams, where the latter is required for the evaluation of the expected number of cracks, n, (within a given beam length). One of these models includes as parameters, the fibrous concrete tensile and residual strengths (after cracking). For this purpose, the work included also bending tests that were conducted to measure these material properties of two types of concrete mixes with different amounts of fibers (which also yielded their stress-strain curves in tension).

In order to examine the various models for the crack spacing, a comparison was made with the experimental results.

The main part of the study was the development of a model to predict the number of wide cracks, m, that are expected to widen in beams, in order to quantify the localization phenomenon. This was done by expanding an existing probabilistic model of cracking localization in tensile RFRC bars. For the use of the tensioned bar model, adjustments and changes were made for beams.

The model was calibrated against measured results and then - verified against other experimental results of specimens with different reinforcement ratios.

This study contributes to knowledge and understanding of the localization phenomenon. The model that was developed in this study contributes to the knowledge and understanding of the localization phenomenon. It allows consideration of various parameters of the specimens and the concrete mixture. The quantitative relationship developed here between the conventional reinforcement ratio and the m / n ratio indicates the localization level. This development will allow quantitative determination of the minimum reinforcement ratio in FRC beams, which will ensure that there will be no decrease in the ductility due to the localization phenomenon.