Evaluating strut-and-tie models for concrete elements by nonlinear finite element analysis

Abstract

The strut-and-tie method (STM) has been acknowledged as one of the most reliable tools for designing discontinuity regions in structural concrete. It is capable of producing safe designs consistently since it was developed as an extension of the lower-bound theorem of plasticity theory. However, to aptly address a physical problem of a concrete element, STM often relies heavily on engineering experience and intuition. It is because the current STM has an inability to be transparent in informing the nonlinear consequences of choosing a certain ST model design, which make the method to be troublesome in more complicated design tasks.

In this thesis, a supplementary evaluation technique that employs nonlinear finite element analysis (NLFEA) is proposed as a solution. It is advantageous to incorporate NLFEA because it can provide nonlinear behavior of a structural concrete as objective insights for making a more informed decision in determining a suitable ST model. To incorporate NLFEA to STM, the concept of 'ties-as-extended-rebars' or TER model is introduced. A TER model is a numerical model used to assess the influence of a certain ST model design toward the nonlinear behavior of a concrete element. Through a TER model, an ST model is nonlinearly evaluated as a concrete element with embedded reinforcements. Additionally, to allow the TER model to generate a representative failure, the rebars in the TER model are extended with straight anchorage length. Then, the information generated by the model, i.e. failure mode and ultimate capacity, can be utilized as additional information to find a fitting ST model.

To assess its ability, the proposed technique was implemented on six ST models generated for two complex concrete beam elements. The implementation provided the TER model versions of the ST models. At the same time, the experimental results of the ST models were also validated using NLFEA. The validation attempt generated six numerical validation (NV) results, which were then compared with the TER model results. The result of the comparison indicated that five out of six TER models were able to suggest failure mode and ultimate capacity (RTER) that are comparable with the failure mode and ultimate capacity (RNV) from the NV results. In more detail, RNV to RTER ratio of models with similar failure mode has an average of 1.04 and a coefficient of variation of 11.1%, which suggests that the proposed technique can provide representative ultimate capacity value with relatively low variability.