Evan C. Bentz

Simplified Modified Compression Field Theory for Calculating Shear Strength of Reinforced Concrete Elements

In this article, the authors propose a simplified MCFT (modified compression field theory) and demonstrate that this simplified MCFT is capable of predicting the shear strength of a wide range of reinforced concrete (RC) elements with almost the same accuracy as the full theory. The authors summarize the results of over 100 pure shear tests on reinforced concrete panels. The ACI approach for predicting shear strength as the sum of a diagonal cracking load and a 45-degree truss model predicts the strength of these panels poorly, with an average experimental-over-predicted shear strength ratio of 1.40 with a coefficient of variation of 46.7%. The modified compression field theory (MCFT), developed in the 1980s, can predict the shear strength of these panels with an average shear strength ratio of 1.01 and a coefficient of variation (COV) of only 12.2%. The authors contend that their new, simplified method gives an average shear strength ratio of 1.11 with a COV of 13.0%. They demonstrate the application of this new simplified method to panels with numerical examples. They conclude that, on many occasions, a full load-deformation analysis is not needed and this quick calculation of shear strength is appropriate and useful.

An overview and sensitivity study of a multimechanistic chloride transport model

Service life prediction models have been developed in order to ensure adequate durability of reinforced concrete structures in chloride environments. Many of the models currently available are overly simplistic, assuming chloride ingress occurs solely by diffusion and that boundary conditions and concrete properties (i.e., diffusivity) remain constant with time. This paper describes a recently developed model that considers multimechanistic transport, chemical binding, and the time-dependent nature of concrete properties. The results of a sensitivity analysis carried out on eight of the input parameters in the model are also reviewed.

EFFECT OF CONCRETE STRENGTH AND MINIMUM STIRRUPS ON SHEAR STRENGTH OF LARGE MEMBERS

There is currently a concern that ACI shear design procedures can be unconservative if applied to thick one-way slabs or large beams containing only minimum stirrups. This research discusses the results of 21 large beams tested to look into these concerns. Based on experimental results, this paper concludes that until the present ACI shear provisions are modified, it would be prudent to use the recent shear provisions of the AASHTO LRFD specifications as they provide a more consistent level of safety. A simple spreadsheet is described that allows these provisions to be conveniently applied.

Effect of Aggregate Size on Beam-Shear Strength of Thick Slabs

This study investigates the safety and accuracy of the American Concrete Institute shear design method when applied to thick slabs by focusing on the size effect in shear and the role played by the maximum coarse aggregate size in transferring shear stress across cracks. An experimental program was conducted in which 10 large-scale and 10 geometrically-similar, small-scale, shear-critical reinforced concrete slab-strip specimens were loaded to failure. It was found that the major mechanism of shear transfer in these element types is aggregate interlock, and that the maximum aggregate size plays an important role in beam-shear capacity of reinforced concrete members. The abilities of the ACI design method and a simplified design method based on the modified compression field theory (MCFT) to predict the failure loads are compared. Findings indicate that the ACI design method is unconservative when applied to thick slabs or large wide beams constructed without stirrups, but the simplified MCFT design method is both safe and accurate. The simplified method also can accurately predict the effects of decreasing the maximum aggregate size on the beam-shear behavior of lightly reinforced concrete members.

One-Way Shear Strength of Thick Slabs and Wide Beams

This paper discusses nine recent tests designed to investigate if current provisions for one-way shear in the ACI 318-05 Building Code are unconservative when applied to thick slabs or large, wide beams. The tests addressed the influence of member width and the presence of shrinkage and temperature reinforcement, which are two factors that may influence the shear capacity of slabs. Member width was observed to have no significant effect on the shear stress at failure for one-way slabs and for wide beams. The presence of shrinkage and temperature reinforcement also did not influence the one-way shear capacity. These findings indicate that ACI 318-05s provisions, which dictate different levels of useable shear capacity for slabs, wide beams and narrow beams, can result in inadequate levels of safety for both thick slabs and large wide beams. Because narrow design strips have been shown to behave in shear in a similar manner to wider members, the well-established size effect of decreasing shear stress at failure as the member depth increases also applies to wide beams and thick one-way slabs. The author recommends that ACI 318-05s basic expression for shear strength be reformulated to better predict the shear capacity of members regardless of depth or classification.

Shear Strength of Large Concrete Members with FRP Reinforcement

Increasing interest in the use of fiber-reinforced polymer (FRP) reinforcement for reinforced concrete structures has made it clear that insufficient information about the shear performance of such members is currently available to practicing engineers. This paper summarizes the results of 11 large shear tests of reinforced concrete beams with glass FRP (GFRP) longitudinal reinforcement and with or without GFRP stirrups. Test variables were the member depth, the member flexural reinforcement ratio, and the amount of shear reinforcement provided. Results showed that the equations of the Canadian CSA shear provisions provide conservative estimates of the shear strength of FRP-reinforced members. Recommendations are given along with a worked example on how to apply these provisions including to members with FRP stirrups. It was found that members with multiple layers of longitudinal bars appear to perform better than those with a single layer of longitudinal reinforcing bars. Overall, it was concluded that t...

Empirical Modeling of Reinforced Concrete Shear Strength Size Effect for Members without Stirrups

The reduction in shear stress at shear failure as member depth of beams and slabs not containing stirrups increases is known as the size effect in shear. While many theoretical models for this phenomenon have been proposed over the years, this paper provides a purely empirical study of the effect. Twenty-four different size effect series of shear experiments are examined, and curve fit parameters are calculated for three different equation formats. Equations to estimate the curve fit parameters are presented that may be useful in generating design specifications that include size effect. The conclusions include that a size effect equation based on a power equation is not as good as a 1/d-based equation with a depth offset. Aggregate size and longitudinal percentage of reinforcement were found to be important in the estimation of shear strength. No strong evidence was found that size effect data for shear in reinforced concrete beams without stirrups should be modeled with effective depth to the power of -0.5 as would be expected from linear elastic fracture mechanics.

ACI-DAfStb Databases for Shear Tests on Slender Reinforced Concrete Beams with Stirrups (with Appendix)

Nearly all code provisions for the shear capacity of structural concrete members without shear reinforcement have been empirically derived and some were calibrated decades ago. Since then, a significant volume of new test data has been generated that can aid in understanding. To address this issue, a database of 439 shear test results had been created in 2003 that contained the data of beams without shear reinforcement subjected to point loads. The 2003 database was considerably expanded in recent years by a joint ACI-DAfStb (American Concrete Institute - Deutscher Ausschuss fur Stahlbeton, German Committee for Structural Concrete) Group, with new test data including 40 tests on beams with uniformly distributed loads. The newly extended database now contains 784 tests that can be used for the evaluation of shear design provisions. A comparison of ACI 318-11 Eq. (11-3) with this extended database has revealed that current code provisions can be unconservative for large, lightly reinforced members and that the influences of important parameters are not adequately captured.

Repeating a classic set of experiments on size effect in shear of members without stirrups

The shear tests performed by Bazant and Kazemi in 1991 have been cited as strong evidence that the theory of fracture mechanics applies to the shear strength of beams without stirrups. It has also been noted in the past, however, that these results are not totally consistent with other size effect experimental series. This paper provides a detailed summary of duplicate experiments carried out to determine if the original 1991 results were reproducible. It was found that the repeat experiments were 31 to 70% stronger than the original results. All experimental results were stronger than the predictions of the ACI and CSA codes. Cracks patterns were observed to scale with the beam size. A comparison of historical data indicated that the higher strengths were likely not a result of random variation, but due to a systematic effect in the original testing, making them inconsistent with other tests. Potential reasons for the differences from the 1991 results are presented and discussed.

Shear Reinforcement Spacing in Wide Members

Many structural framing schemes use wide beams and thick slabs as primary transfer elements, especially where the total structural depth must minimized. For these wide members, design codes do not provide guidance on appropriate limits for spacing of the shear reinforcement legs across the member width. This paper presents the results of 13 experiments designed to investigate the influence of this spacing on the one-way shear capacity of wide reinforced concrete members. Members up to 1170 mm (46.1 in.) wide are presented, and the web reinforcement pattern within the cross section was a primary test parameter. Results showed that the capacity of members with well-distributed shear reinforcement could be safely predicted by the ACI 318 shear model, but stirrup efficiency decreased significantly as the stirrup leg spacing across the width increased. The transverse spacing of web reinforcement should be limited to the lesser of the effective member depth and 600 mm (24 in.) to ensure that the shear capacity of all members with web reinforcement are adequate.