Thomas T. C. Hsu

Concrete structural health monitoring using embedded piezoceramic transducers

Health monitoring of reinforced concrete bridges and other large-scale civil infrastructures has received considerable attention in recent years. However, traditional inspection methods (x-ray, C-scan, etc) are expensive and sometimes ineffective for large-scale structures. Piezoceramic transducers have emerged as new tools for the health monitoring of large-scale structures due to their advantages of active sensing, low cost, quick response, availability in different shapes, and simplicity for implementation. In this research, piezoceramic transducers are used for damage detection of a 6.1 m long reinforced concrete bridge bent-cap. Piezoceramic transducers are embedded in the concrete structure at pre-determined spatial locations prior to casting. This research can be considered as a continuation of an earlier work, where four piezoceramic transducers were embedded in planar locations near one end of the bent-cap. This research involves ten piezoceramic patches embedded at spatial locations in four different cross-sections. To induce cracks in the bent-cap, the structure is subjected to loads from four hydraulic actuators with capacities of 80 and 100 ton. In addition to the piezoceramic sensors, strain gages, LVDTs, and microscopes are used in the experiment to provide reference data. During the experiment, one embedded piezoceramic patch is used as an actuator to generate high frequency waves, and the other piezoceramic patches are used as sensors to detect the propagating waves. With the increasing number and severity of cracks, the magnitude of the sensor output decreases. Wavelet packet analysis is used to analyze the recorded sensor signals. A damage index is formed on the basis of the wavelet packet analysis. The experimental results show that the proposed methods of using piezoceramic transducers along with the damage index based on wavelet packet analysis are effective in identifying the existence and severity of cracks inside the concrete structure. The experimental results demonstrate that the proposed method has the ability to predict the failure of a concrete structure as verified by results from conventional microscopes (MSs) and LVDTs.

Constitutive Laws of Softened Concrete in Biaxial Tension Compression

A softened truss model was developed over the last 10 years at the University of Houston for predicting the behavior of reinforced concrete subjected to shear and torsion. The model, based on the conditions of equilibrium and compatibility, employs realistic constitutive laws for concrete and reinforcement. The required constitutive laws for concrete and reinforcement were examined by testing 22 full-size reinforced concrete panels. These large test panels were subjected to tension in one direction and compression in the perpendicular direction. Testing showed that the strength and stiffness of concrete in compression were softened primarily by the presence of tensile strains in the perpendicular direction. The effect of other parameters, e.g., load path, percentage of steel, and spacing of reinforcing bars, was assessed. Based on these tests, improved softened stress-strain relationships of concrete in compression were developed.

SOFTENED TRUSS MODEL THEORY FOR SHEAR AND TORSION

The softened truss model theory, which has recently been developed for shear and torsion of reinforced concrete members, is summarized in a systematic and unified manner. Eleven equations involving fourteen variables are derived from equilibrium, compatibility, and materials conditions to solve the shear problem. An additional six equations involving six more variables are required to treat the torsion problem. The theory was successfully applied to structures where shear behavior predominates, such as low-rise shearwalls, framed wall panels, deep beams, and shear transfer strengths. It also worked very well for members subjected to torsion. Efficient algorithms are proposed to solve the simultaneous equations for different types of structures. The theoretical predictions are in good agreement with the test results in all cases. The prediction includes not only the shear and torsional strengths, but also the deformations of structures throughout their post-cracking loading history.

Behavior of Reinforced Concrete MembraneElements in Shear

Thirteen full-size reinforced concrete panels were tested to determine the behavior of reinforced concrete elements subjected to membrane shear. The panels were designed to study three variables : 1) the percentage of reinforcement, 2) the ratio of transverse-to-longitudinal steel, and 3) the load path. The resulting load-deformation responses in the test panels were correctly predicted by a softened truss model. This rational model satisfies the three fundamental principles of the mechanics of materials : 1) stress equilibrium, 2) strain compatibility, and 3) the constitutive laws of materials. Three constitutive laws previously established from membrane elements subjected to biaxial tension-compression were applied to membrane elements subjected to shear. It was found that the constitutive law of reinforcing bars must be modified by a factor that takes into account the kinking of the reinforcing bars. Membrane elements subjected to shear may fail in four modes : I) under-reinforced, 2) partially under-reinforced in longitudinal steel, 3) partially under-reinforced in transverse steel, or 4) over-reinforced. These four failure modes are also correctly predicted by the softened truss model.

Fixed angle softened truss model for reinforced concrete

A softened truss model has previously been developed for reinforced and prestressed concrete membrane elements subjected to in-plane shear and normal stresses. This existing model satisfies the three principles of mechanics of materials : two-dimensional stress equilibrium, Mohrs circular strain compatibility, and the softened biaxial constitutive laws of concrete. That is, the model can predict the strength of a membrane element as well as its load-deformation history. However, this model cannot predict the contribution of concrete observed in tests, because it is based on the assumption that the direction of the cracks (and thus, the concrete struts) is inclined at the rotating angle following the postcracking principal stresses of the concrete. This paper presents a new and more general softened truss model in which the direction of the cracks is assumed to incline at the fixed angle following the principal stresses of the applied loading. This new model, although more complex, is capable of predicting the contribution of concrete. The fixed angle softened truss model requires four constitutive laws of materials. Three have been established previously for the rotating angle softened truss model (concrete in compression, concrete in tension, and steel embedded in concrete). This paper presents the fourth constitutive law relating the average shear stress of concrete to the average shear strain.

Softened Membrane Model for Reinforced Concrete Elements in Shear

This paper presents a rational and general theory, the softened membrane model, which is capable of predicting the entire shear behavior of membrane elements, including the postpeak response. The postpeak response is predicted by accounting for the Poisson effect. The Poisson effect of cracked reinforced concrete composites is characterized by 2 Hsu/Zhu ratios, given in a companion paper, that are determined experimentally using a unique panel testing facility with strain-control features.

Nonlinear finite element analysis of concrete structures using new constitutive models

Abstract Nonlinear finite element analysis was applied to various types of reinforced concrete structures using a new set of constitutive models established in the fixed-angle softened-truss model (FA-STM). A computer code FEAPRC was developed specifically for application to reinforced concrete structures by modifying the general-purpose program FEAP. FEAPRC can take care of the four important characteristics of cracked reinforced concrete: (1) the softening effect of concrete in compression, (2) the tension-stiffening effect by concrete in tension, (3) the average (or smeared) stress–strain curve of steel bars embedded in concrete, and (4) the new, rational shear modulus of concrete. The predictions made by FEAPRC are in good agreement with the experimental results of beams, panels, and framed shear walls.

RATIONAL SHEAR MODULUS FOR SMEARED-CRACK ANALYSIS OF REINFORCED CONCRETE

This paper presents a new rational shear modulus for the fixed-angle softened truss model (FA-STM) based on the smeared-crack concept. This rational, yet very simple, modulus not only greatly simplifies the solution of the FA-STM but also improves its accuracy. Moreover, this new shear modulus can be used widely to replace the many complicated empirical constitutive laws for shear of cracked concrete, as employed in the various nonlinear analyses of reinforced concrete structures. A notable example is the finite-element analysis.

TENSION STIFFENING IN REINFORCED CONCRETE MEMBRANE ELEMENTS

A rational prediction of the behavior of membrane elements requires a set of constitutive laws for materials. Three sets of constitutive laws of mild steel bars and concrete in tension were evaluated. In the first set of simplified constitutive equations, the tensile strength of concrete is neglected and the elastic-perfectly-plastic stress-strain relationship of bare mild steel bars is assumed. This set of simplified constitutive laws is shown to predict the correct yield strength, but will overestimate the deformations because the tension stiffening effect due to the tensile resistance of concrete is neglected. In the second set of modified constitutive equations, the average tensile stress-strain relationship of concrete is considered in addition to the stress-strain relationship of bare mild steel bars. This treatment produces a correct reduction in deformations due to the tension stiffening of concrete, but will result in an unwarranted increase in yield strength. The third set of accurate constitutive equations employs both the average tensile stress-strain relationship of concrete and the average stress-strain curve of mild steel bars stiffened by concrete. This third set of accurate constitutive equations is shown to provide good prediction for the entire load-deformation response of membrane elements.

Fresh and Hardened Properties of Self-Consolidating Fiber-Reinforced Concrete

Traditional fiber-reinforced concrete tensile and shear resistance has been known to be enhanced by the addition of steel fibers to a concrete mixture. Plain concrete workability, however, has also been known to be impeded by fibers. In this study, self-consolidating fiber-reinforced concrete (SCFRC) mixtures were developed to improve workability for prestressed concrete beam application. In this study, extensive SCFRC and traditional fiber-reinforced concrete mixture fresh and hardened properties have been produced through use of two different types and variable amounts of hooked steel fibers. The satisfactory workability and stability of the SCFRC mixtures were demonstrated at up to a fiber factor of 55. Greater normalized tensile strength has been proven in SCFRC mixtures in general than, for the same fiber factor, the traditional fibrous concrete mixtures. The concrete mixtures workability requirements were found to govern optimum fiber content.