טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentTom Eren
SubjectRevisiting criteria and calculation procedures of
deflections in reinforced concrete beams and slabs
DepartmentDepartment of Civil and Environmental Engineering
Supervisor Professor Dancygier Avraham
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


Abstract

This research is aimed at examining calculations of one-way beams and slabs deflections as part of the verification for SLS, under the pertinent design criteria. The work includes investigation of the detailed deflection calculations according to the American method (ACI318), which is adopted in the Israeli code, and according to the European code (EC2), which is about to be adopted in Israel. It also includes revisiting of the European and Israeli approaches for a simplified verification (by limiting the slenderness of the element) and development of a modified version for the Israeli simplified formula to ensure results that are conservative. Additionally, the deflection criterion in the case of a cantilever beam has been examined.

This research reviews the deflection criteria in main international design codes and it provides a detailed description of the calculations according to the European and north American methodologies, as well as the Israeli one. The methodology of this study is based on performing detailed calculations for a wide range of practical cases. comprising, different spans, simply-supported, fixed-fixed and cantilever static schemes and two regimes of loads that are typical of residential and public buildings.

These calculations have shown that for slabs, the three approaches yield similar required cross-section thicknesses. However, for beams there is a significant difference, where the European code requires cross-sections that are 50%-75% smaller than those required by ACI.  

In addition, comparison of the deflection predictions according to the approaches mentioned above with measured data was held.

The study also included examination of the effect of using reinforcing steel with 400 or 500 MPa yield strength.

As for the simplified calculation that sets a slenderness limit, it has been found that in most cases, both the European and Israeli formulas are not conservative with respect to their relevant detailed calculations. Consequently, a modification to the non-conservative simplified Israeli formulation was developed, such that it yields conservative (yet not too conservative) results. It is shown that the proposed formula enhances the predictions of the Israeli simplified design.

Finally, the study also included examination of the deflection criterion for cantilever beams. It was done by FE simulations of masonry walls that are supported by an internal span beam and by a cantilever beam. Results of these simulations indicate that in the case of cantilever the design criterion can refer to relative deflections that are larger than those in internal spans. This can be worked out by keeping the current criteria but multiplying the span of the cantilever by a factor larger than 1.0. Yet, the numerical results were not conclusive regarding the value of this factor.

Conclusions of this research show the theoretical evaluation of beams and slabs deflections - of their accuracy and their level of conservatism. This refers also to the simplified design approaches. Yet, it is noted that these calculations are done with reference to criteria that were set years ago. Therefore, the definition of the design criteria for limiting the deflections at the service state still requires their deeper study.