Unified Theory of Concrete Structures
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LanguageEnglish
Pages517
FormatPDF
Size11.6 MB



Unified Theory of Concrete Structures



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The Authors of Unified Theory of Concrete Structures

Thomas T. C. Hsu and Y. L. Mo are the editors of Unified Theory of Concrete Structures eBook.

Preface to Unified Theory of Concrete Structures by Thomas T. C. Hsu and Y. L. Mo


Concrete structures are subjected to a complex variety of stresses and strains. The four basic actions are: bending, axial load, shear and torsion. Each action alone, or in combination with others, may affect structures in different ways under varying conditions.

The first two actions – bending and axial load – are one-dimensional problems, which were studied in the first six decades of the 20th century, and essentially solved by 1963 when the ultimate strength design was incorporated into the ACI Building Code.

The last two actions – shear and torsion – are two-dimensional and three-dimensional problems, respectively.

These more complicated problems were studied seriously in the second half of the 20th century, and continued into the first decade of the 21st century. By 1993, a book entitled Unified Theory of Reinforced Concrete was published by the first author.

At that time, the unified theory consisted of five component models:

(1) the struts-andties model for design of local regions;

(2) the equilibrium (plasticity) truss model for predicting the ultimate strengths of members under all four actions;

(3) the Bernoulli compatibility truss model for linear and nonlinear theories of bending and axial load;

(4) the Mohr compatibility truss model for the linear theory of shear and torsion; and

(5) the softened truss model for the nonlinear theory of shear and torsion. The first unified theory published in 1993 was a milestone in the development of models for reinforced concrete elements.


Nevertheless, the ultimate goal must be science-based prediction of the behavior of whole concrete structures. Progress was impeded because the fifth component model, the softened truss model, was inadequate for incorporation into the new finite element analysis for whole structures.

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An innovation in testing facility in 1995 allowed new experimental research to advance the nonlinear theory for shear and torsion.

This breakthrough was the installation of a ten-channel servo-control system onto the universal panel tester (UPT) at the University of Houston (UH), which enabled the UPT to perform strain-controlled tests indispensable in establishing more advanced material models.

The expanded testing capabilities opened up a whole new realm of research potentials. One fundamental advance was the understanding of the Poisson effect in cracked reinforced concrete and the recognition of the difference between uniaxial and biaxial strain.

The UPT, capable of performing strain-control tests, allowed UH researchers to establish two Hsu/Zhu ratios based on the smeared crack concept, thus laying the foundation for the development of the softened membrane model.

This new nonlinear model for shear and torsion constitutes the sixth component model of the unified theory. The second advance was the development of the fixed angle shear theory, much more powerful than the rotating angle shear theory because it can predict the ‘contribution of concrete’ (Vc).

Begun in 1995, the fixed angle shear theory gradually evolved into a smooth-operating analytical method by developing a rational shear modulus based on smeared cracks and enrichment of the softened coefficient of concrete.

This new fixed angle shear theory serves as a platform to build the softened membrane model, even though the term ‘fixed angle’ is not attached to the name of this model.

The third advance stemming from the expanded capability of the strain-controlled UPT was to obtain the descending branches of the shear stress versus shear strain curves, and to trace the hysteretic loops under reversed cyclic shear.

As a result, the constitutive relationships of the cracked reinforced concrete could be established for the whole cyclic loading.

These cyclic constitutive relationships, which constitute the cyclic softened membrane model (CSMM), opened the door to predicting the behavior of membrane elements under earthquake and other dynamic actions.

A concrete structure can be visualized as an assembly of one-dimensional (1-D) fiber elements subjected to bending/axial load and two-dimensional (2-D) membrane elements subjected to in-plane shear and normal stresses.

The behavior of a whole structure can be predicted by integrating the behavior of its component 1-D and 2-D elements. This ‘elementbased approach’ to the prediction of the responses of concrete structures is made possible by the modern electronic computer with its unprecedented speed,

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and the corresponding rapid development of analytical and numerical tools, such as the nonlinear finite element method. Finite element method has developed rapidly in the past decade to predict the behavior of structures with nonlinear characteristics, including concrete structures.

A nonlinear finite element framework OpenSees, developed during the past decade, is relatively easy to use. By building the constitutive model CSMM of reinforced concrete elements on the platform of OpenSees, a computer program, Simulation of Concrete Structures (SCS), was developed at the University of Houston.

Program SCS can predict the static, cyclic, and dynamic behavior of concrete structures composed of 1-D frame elements and 2-D wall elements.


The unified theory in this 2010 book covers not only the unification of reinforced concrete theories involving bending, axial force, shear and torsion, but also includes the integration of the behavior of 1-D and 2-D elements to reveal the actual behavioral outcome of whole concrete structures with frames and walls.

The universal impact of this achievement led to the title for the new book: Unified Theory of Concrete Structures, a giant step beyond the scope of Unified Theory of Reinforced Concrete. The many challenging goals of this new book are made possible only by the collaboration between the two authors.

The first eight chapters were prepared by Thomas T. C. Hsu, and the concluding two chapters by Y. L. Mo. In closing, this book presents a very comprehensive science-based unified theory to design concrete structures and infrastructure for maximum safety and economy.

In the USA alone, the value of the concrete construction industry is of the order of two hundred billion dollars a year.

Furthermore, the value of this body of work is also reflected by its incalculable human benefit in mitigating the damage caused by earthquakes, hurricanes and other natural or artificial disasters.

With this larger thought, the authors express their deep appreciation to all their colleagues, laboratory staff, and former/current, graduate/undergraduate students, who contributed greatly to the development of the unified theory.

A special acknowledgment goes to Professor Gregory L. Fenves and his co-workers for the development of the open-domain OpenSees.


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