Engineering Models for Shear Crack Width and Shear Deflection in Slender Reinforced Concrete Beams

Shear cracking in slender reinforced concrete beams with thin webs can result in significant shear crack width and deflection which is usually ignored in practice due to lack of availability of the engineering models in design codes. This can lead to unconservative predictions of the crack width and total deflection in the SLS (Serviceability Limit State). The large crack widths can cause problems related to durability, aesthetic appeal, maintainability and fluid tightness of the structure. An inspection in 2001 reveals extensive shear cracks in Grondal and Alvik bridges in Sweden. The problem is so severe that the bridges are temporarily closed. Later, the investigations reveal that although the bridges are designed according to Swedish codes, the provided shear reinforcement is insufficient for crack width control under service loads on the bridge. Therefore, it becomes imperative to evaluate the available crack width models and develop robust models for shear crack width prediction. A literature review of the available models for shear crack width is performed to identify the crucial parameters influencing shear crack width. Shear crack width is influenced by several parameters, but the most critical parameters are shear crack spacing, shear stirrup strain, principle strain in the cracked concrete and diagonal compression strut angle. Thereafter, various models available to evaluate these parameters are reviewed to understand their applicability and limitations.This is followed by a study for the analysis of performance of the models with respect to the experimental observations. Based on the limited experimental dataset, it is found that the Zakaria et al. (2011) shear crack spacing model, and the fib MC 2010 (Model Code 2010) crack spacing model (for members with orthogonal reinforcement) provide a conservative estimate for the shear crack spacing in RC (reinforced concrete) beams. The predictions from the current EC2 crack spacing model are slightly unconservative. All the three crack spacing models take into account the influence of bond transfer length on the stress distribution in concrete and reinforcement. It is also found that the SMCFT (Simplified Modified Compression Field Theory), CFT (Compression Field Theory) and CCC (Compression Chord Capacity) model provide estimates for the shear crack angle with small deviations from the experimentally observed values. However, all these three models predict flatter (smaller) mean shear crack angles as compared to the experimentally observed values. The SMCFT and CFT determine the diagonal compression strut angle with a consideration of deformations of reinforcement (transverse and longitudinal) and diagonally cracked concrete. On the other hand, the CCC model predicts the diagonal shear crack angle based on the assumption that the horizontal projection of the first branch of flexural-shear crack is equal to 0.85d where d is the effective depth to the longitudinal tensile reinforcement. According to comparison with the experimental observations referred in this study, the CCC model provides a conservative estimate for the concrete contribution to shear resistance which is required to evaluate the shear stirrup strains. Using concrete contribution to shear resistance from this model, an engineering strategy to estimate the concrete contribution to shear resistance at service loads is proposed. Thereafter, five different models for mean shear crack width (the first three models with two variants each) and four different models for shear deflection are proposed. The comparison of the predictions from the mean shear crack width models with the experimental data reveals that a conservative estimate for the shear crack width can be made by equating shear crack width as the product of mean principle tensile strain in the cracked concrete and the shear crack spacing (ModelIIIB, Model-IV and Model-V). It is observed that the assumption of zero concrete contribution to shear resistance (shear-force transfer) at service loads (in B variants of Models-I, II and III) result in relatively higher predicted mean shear crack widths (as compared to the corresponding A variants) and therefore, more conservative estimates. Moreover, the assumption of mean shear crack angle equal to 45 degrees also leads to relatively more conservative estimates of mean shear crack width. Model-IV and Model-V seem to outperform other mean shear crack width models considering mean and consistency of the models together as a metric. The mean and SD of the predictions from Model-IV are 0.85 and 0.30 for the original formulation of the model. However, with the assumption of mean shear crack angle equal to 45 degrees, the mean and SD values are observed to be 0.37 and 0.13 respectively. It is found that a conservative estimate for shear deflection can be obtained by assuming a linear shear force versus deflection response for a slender reinforced concrete beam (Model-I). The ratio of the experimentally observed to predict shear deflection for Model-I is 0.85 with a SD (Standard Deviation) of 0.31. The proposed Models-IIIB, IV and V (in their original formulation) and Models- IB, IIA, IIB, IIIA, IIIB and IV (with an assumption of mean shear crack angle equal to 45 degrees) for the shear crack width and Model-I for shear deflection provide a conservative estimate for the range of experimental beam specimen data covered in this MSc thesis. These models (especially Model-IV for mean shear crack width and Model-I for shear deflection) seem to be potentially useful engineering models for use in engineering practice to evaluate mean shear crack width and shear deflection for slender beams with thin webs (for example slender webs of bridge girders). However, the models require further validation with an experimental study to assess and establish suitability for wider application in design practice