The effect of reinforcement configuration on crack widths in concrete deep beams

Abstract: Reinforced concrete deep beams are known for applications in tall buildings, foundations and offshore structures. Deep beams are structural elements with length and height within the same magnitude and have significantly smaller thickness compared to a conventional concrete beam. Deep beams in bending have non-linear strain distribution compared to conventional beams where Bernoulli’s hypothesis is valid. Crack formation is a common problem in reinforced concrete structures, which reduce the durability of the structure. Once the concrete cracks the tension reinforcement carry the tensile forces instead of the concrete. Therefore, the design of tension reinforcement is important since the serviceability should be retained even after the structure cracks. The crack widths can be limited by using proper reinforcement and one alternative is to combine tensile reinforcement with crack reinforcement.  The function of the reinforcement is to distribute the cracks over the cross section which leads to that many smaller cracks occur instead of fewer, wider cracks. Small cracks are seen as less of a problem compared to large cracks since larger cracks reduce the durability significantly. For deep beams, there is at the present no well-substantiated analysis model for how crack widths shall be calculated when having reinforcement in multiple layers with different diameters. The use of crack reinforcement in the outer bottom layer has by tradition been considered as a cost efficient way to achieve small crack widths. In this work the crack width in deep beams have been analysed using the finite element program Atena 2D. The numerical results have been verified by analytical calculations based on Eurocode 2. The aim is to achieve reduced crack widths  by analysing the combination of crack- and tensile reinforcement compared to the case with tensile reinforcement only. Tensile reinforcement has a larger diameter, for example ø25 mm, and crack reinforcement has smaller diameters, often between ø10 and ø16 mm. The result from the calculations with Atena showed that there was an improvement regarding the reduction of crack widths when using crack reinforcement in combination with tensile reinforcement compared to using tensile reinforcement only. However, this improvement decreased by using reinforcement in multiple layers since a tensile reinforcement bar 1ø25 mm needed to be replaced by approximately six crack reinforcement bars 6ø10 mm in order to achieve the same total reinforcement area. The main disadvantage was that more space was required to place all reinforcement bars in the cross section, which reduced the lever arm. The reduction of the lever arm resulted in a reduced capacity for the reinforcement and the cracks might unintentionally become wider than expected. Furthermore, significant reduction of both crack widths and reinforcement stresses were obtained when the total area for a case with 7ø25 mm was increased to 9ø25 mm. The increased total area of only tensile reinforcement ø25 mm reduced the crack width more compared to using a combination of crack- and tensile reinforcement, which could simplify the construction work at building sites and minimize time consumption.