Frank J. Vecchio

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.

A GENERAL SHEAR DESIGN METHOD

The authors present a simple, unified method for the shear design of both prestressed concrete members and nonprestressed concrete members. The method can treat members subjected to axial tension or axial compression and treats members with and without web reinforcement. The derivation of the method is summarized and the predictions of the method are compared with those of the current American Concrete Institute (ACI) Code.

NONLINEAR FINITE ELEMENT ANALYSIS OF REINFORCED CONCRETE MEMBRANES

A procedure is described whereby linear elastic finite element routines can be modified to enable nonlinear analysis of reinforced concrete membrane structures. The proposed procedure is based on an interative, secant stiffness formulation and employs constitutive relations for concrete and reinforcement based on the modified compression field theory. Predictions from the proposed procedure are compared against experimental results, as well as against more complex fourmulations, and excellent accuracy is found. Example analyses and potential applications of the nonlinear procedure are also described.

TOWARDS MODELING OF REINFORCED CONCRETE MEMBERS WITH EXTERNALLY BONDED FIBER-REINFORCED POLYMER COMPOSITES

Fiber-reinforced polymer (FRP) composites have been increasingly studied for their application in flexural or shear strengthening of reinforced concrete (RC) members. Although substantial increases in strength have been achieved, reductions in ductility have also been reported as a result of debonding failures near concrete-FRP interfaces. The debonding phenomenon is the focus of the experimental program described in this paper, which involved the strengthening of shear-critical beams using FRP (CFRP) strips. It was determined that the bond slip behavior at the bond interface must be considered in numerical modeling of externally reinforced members. The formulations of bond elements and their constitutive relations are essential to analyses using a finite element program. The implementation of link and contact elements, along with linear elastic and elastic-plastic bond laws, is shown to produce accurate predictions of member response.

Effects of Shear Mechanisms on Impact Behavior of Reinforced Concrete Beams

numerical methods for predicting the impact response. The test program was devised to observe the effects of the static shear capacity of the RC beams on the impact behavior, involving eight RC beams (four pairs), with varying static shear capacities, tested under free-falling impact weights. This paper documents the details of the test program, including specimen properties, test setup, instrumentation, and test procedures. Test results and major observations are also presented and discussed. The study presented in this paper constitutes the experimental phase of a wider study that also includes numerical and analytical investigations, which will be presented and discussed in papers to follow. RESEARCH SIGNIFICANCE Demand for impact-resistant RC structures is increasing and, thus, many recent experimental studies have been carried out aimed at developing analysis and design methods for such structures. In many of these studies, severe shear mechanisms, such as shear plugs, were observed. Little effort, however, was spent to explain their role in the overall impact behavior of the structure. This paper presents an experimental program with two major objectives: 1) understanding the effect of shear mechanisms in the overall impact behavior; and 2) supplying the literature with detailed impact test data that can assist further analytical and numerical studies in the area.

COMPRESSION FIELD MODELING OF REINFORCED CONCRETE SUBJECTED TO REVERSED LOADING: FORMULATION

Analysis of reinforced concrete (RC) structures subjected to general loading conditions requires realistic constitutive models and analytical procedures to produce reasonably accurate simulations of behavior. However, models reported that have demonstrated successful results under reversed cyclic loading are less common than models applicable to monotonic loading. This paper presents a unified approach to constitutive modeling of RC that can be implemented into finite element analysis procedures to provide accurate simulations of concrete structures subjected to reversed loading. Improved analysis and design can be achieved by modeling the main features of the hysteresis behavior of concrete and by addressing concrete in tension.

Behavior of Three-Dimensional Reinforced ConcreteShear Walls

Results from two large-scale flanged shear walls tested under static cyclic displacements are presented. The objectives of the tests were to provide insight into the behavior of shear walls under cyclic displacements, and more importantly, to provide data to help corroborate constitutive models for concrete exposed to arbitrary loading conditions. The results indicated that the presence of an axial load, although relatively small, and the stiffness of flange walls have a significant effect on the strength, ductility, and failure mechanisms of the shear walls. Finite element analyses using provisional constitutive models are also provided to show that the procedures employed are stable, compliant, and provide reasonably accurate simulations of behavior. The analyses presented also indicated that two-dimensional analyses capture main features of behavior, but three-dimensional analyses are required to capture some important second-order mechanisms.

Analysis of Shear-Critical Reinforced Concrete Beams

Recent experience among some researchers suggests that analysis methods based on the smeared rotating crack concept do not adequately model the response of shear-critical concrete beams containing little or no shear reinforcement. Application of the modified compression field theory (MCFT), one of the first such rotating crack models, to the analysis of shear beams is addressed in this paper. The original constitutive relations are reexamined, and a crack width limit and residual tension term are introduced. When incorporated into a nonlinear finite element procedure, the model is shown to adequately simulate the strength, stiffness, ductility, and failure mode of lightly reinforced shear-critical test beams. Sectional analysis procedures based on the same model are also shown to provide accurate predictions of response. Prevailing mechanisms are discussed, and aspects of the model in need of further refinement are also identified.

TOWARDS CYCLIC LOAD MODELING OF REINFORCED CONCRETE

The need for accurate methods of analysis of reinforced concrete structures under general loading conditions has been brought to the fore by structural failures sustained during the Northridge and Kobe earthquakes. This paper presents an alternative method by which finite element analysis procedures can be made to provide accurate simulations of reinforced concrete subjected to reversed cyclic loads. Emphasis is placed on developing simple, numerically stable formulations. Plastic offset strains are defined for concrete and reinforcement, and these are incorporated into the analysis through the use of prestrain forces. The elastic components of strain are then used to define effective secant stiffness factors. To provide a record of plastic offsets, and of maximum strain experienced during previous loading, strain envelopes are defined using a Mohrs circle construction. Provisional constitutive models are presented for the concrete, although further work is required in this area. An analysis of a shearwall shows the procedure to be stable and compliant and to provide reasonably accurate simulations of behavior. The results of a pilot series of panel tests are used to identify the aspects of concrete modeling that are in need of further study and refinement.

Cracking Behavior of Steel Fiber-Reinforced Concrete Members Containing Conventional Reinforcement

Uniaxial tension tests were conducted on 12 plain reinforced concrete (RC) and 48 large-scale steel fiber-reinforced concrete (SFRC) specimens, each containing conventional longitudinal reinforcement, to study their cracking and tension-stiffening behavior. The test parameters included fiber volumetric content, fiber length and aspect ratio, conventional reinforcement ratio, and steel reinforcing bar diameter. “Dog-bone” tension tests and bending tests were also performed to quantify the tensile properties of the concrete. It was found that the cracking behavior of SFRC was significantly altered by the presence of conventional reinforcement. Crack spacings and crack widths were influenced by the reinforcement ratio and bar diameter of the conventional reinforcing bar, as well as by the volume fraction and aspect ratio of the steel fiber. Details and results of the experimental investigation are provided and discussed.