Evaluation of Relationships to Extrapolation Shear Strength of Reinforced Concrete Beams Without Stirrups
Keywords:
shear strength, fracture mechanics, database, determination coefficient, correlation coefficientAbstract
The shear strength of reinforced concrete beams without stirrups relates to several parameters the most important of which are the depth of the beam, the compressive strength of concrete, the ratio of the longitudinal reinforcement and finally shear span - effective depth ratio . Based on these parameters, relationships were suggested in the design codes and scientific references that take into account the set of parameters mentioned above. In this paper, a set of these relationships was tested using a database built by a research team (Collins, et al., 2008) by compiling the results of scientific research published over sixty years. In the first part of this research, the efficiency of the proposed relationships was statistically evaluated after the Outliers values were omitted by calculating the correlation coefficient and the determination coefficient to assess the correlation strength between experimental and analytical values. The proposed relationships in design codes CEB-FIP and EC2, in addition to the relationship of the researcher Bazant, gave high and close correlation coefficients (0.876-0.777-0.827), respectively, indicating the efficiency of these relationships in order to extrapolate shear strength. On the other hand, the statistical study gave a correlation coefficient equal to 0.631 for the relationship of the Syrian code SYR code and 0.643 for the American code ACI, and finally a value of 0.244 for the Canadian code CSA, which means that these relationships are not appropriate for assessing shear strength. In the second part of this research, a set of modified relationships based on the same database was proposed by reducing the differences between the analytical and experimental values using Excel. The modified set of relationships gave better correlation coefficients for SYR code, ACI, CSA and finally EC2 where correlation coefficient values (0.786, 0.824, 0.68, 0.8), respectively, while for CEB-FIP and Bazant relationships, correlation coefficient values ( 0.857, 0.824) respectively.
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