The failure behavior of a reinforced concrete corbel is complicated due to the shear span-to-effective depth ratio, reinforcement patterns, load conditions, and material properties. In this study, an optimum first-order indeterminate strut-and-tie model that reflects all characteristics of the failure behavior is proposed for the rational design of reinforced concrete corbels with a shear span-to-effective depth ratio of less than 1.0. A load distribution ratio that transforms the indeterminate strut-and-tie model into a determinate model is also developed to help structural designers design reinforced concrete corbels using the strut-and-tie model methods of current design codes. For the development of the load distribution ratio, a material nonlinear finite element analysis of the proposed first-order indeterminate strut-and-tie model was conducted repeatedly by changing the combination of primary design variables of the corbels. To examine the validity of our results, the ultimate strengths of 294 reinforced concrete corbels tested to failure by other investigators were predicted using the proposed strut-and-tie model with the load distribution ratio, the existing determinate strut-and-tie models representing arch and truss load transfer mechanisms, and the American Concrete Institute 318 conventional design method based on a shear friction theory. The ultimate strengths predicted by the proposed strut-and-tie model agreed fairly well with the experimental results. The ratio of the experimental strength to the predicted strength (and coefficient of variation) was 1.09 (28.0%), implying that the proposed strut-and-tie model can represent the load transfer mechanisms of corbels most appropriately.

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:The sectional methods of current design codes have been broadly used for the design of various kinds of reinforced concrete pile caps. Lately, the strut-tie model approach of current design codes also became one of the attracting methods for pile caps. However, since the sectional methods and the strut-tie model approach of current design codes have been established by considering the behaviors of structural concrete without D-regions and two-dimensional concrete structures with D-regions, respectively, it is inappropriate to apply the methods to the pile caps dominated by 3-dimensional structural behavior with disturbed stress regions. In this study, the refined 3-dimensional strut-tie models, which consider the strength characteristics of 3-dimensional concrete struts and nodal zones and the load-carrying capacity of concrete ties in tension regions, are proposed for the rational analysis and design of pile caps. To examine the validity of the proposed models and to verify the necessity of appropriate constituent elements for describing 3-dimensional structural behavior and load-transfer mechanism of pile caps, the ultimate strength of 78 reinforced concrete pile caps tested to failure was examined by the proposed models along with the sectional and strut-tie model methods of current design codes.

The ultimate behavior of reinforced concrete corbel is complicated due to the primary design variables including the shear span-to-effective depth ratio a/d, flexural reinforcement ratio, load condition, and material properties. In this study, a simple indeterminate strut-tie model reflecting all characteristics of the ultimate strength and complicated structural behavior is proposed for the design of the reinforced concrete corbels with shear span-to-effective depth ratio of a/d ≤ 1. A load distribution ratio, defined as the fraction of applied load transferred by horizontal truss mechanism, is also proposed to help structural designers perform the design of reinforced concrete corbels by using the strut-tie model approaches of current design codes. For the development of the load distribution ratio, numerous material nonlinear finite element analyses of the proposed indeterminate strut-tie model were conducted by changing primary design variables. The ultimate strengths of reinforced concrete corbels tested to failure were evaluated by incorporating the proposed strut-tie model and load distribution ratio into the ACI 318-11's strut-tie model method. The validity of the proposed model and load distribution ratio was examined by comparing the strength analysis results with those by the ACI 318-11's conventional design method and strut-tie model methods of current design codes.

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