Civil Engineering Reference
In-Depth Information
The three-dimensional (3-D) stress state of a member subjected to torsion must take into
account the 2-D shear action in the shear flow zone, as well as the bending action of the concrete
struts caused by the warping of the shear flow zone. Since both the 2-D shear action and the
bending action can be taken care of by the simultaneous applications of Mohr's compatibility
condition and Bernoulli's compatibility condition, the torsional action becomes, for the first
time, solvable in a scientific way. This topic provides all the necessary information leading up
to the rational solution of the problem in torsion.
Because each of the four basic actions experienced by reinforced concrete structures has
been found to adhere to the fundamental principles of the mechanics of materials, a unified
theory is developed encompassing bending, axial load, shear and torsion in reinforced as well
as prestressed concrete structures. This topic is devoted to a systematic integration of all the
individual theories for the various stress states. As a result of this synthesis, the new rational
theories should replace the many empirical formulas currently in use for shear, torsion and
membrane stress.
The unified theory is divided into six model components based on the fundamental principles
employed and the degree of adherence to the rigorous principles of mechanics of materials. The
six models are: (1) the struts-and-ties model; (2) the equilibrium (plasticity) truss model; (3) the
Bernoulli compatibility truss model; (4) the Mohr compatibility truss model; (5) the softened
truss model; and (6) the softened membrane model. In this topic the six models are presented
as rational tools for the solution of the four basic actions: bending, axial load, and particularly,
2-D shear and 3-D torsion. Both the four basic actions and the six model components of
unified theory are presented in a systematic manner, focusing on the significance of their
intrinsic consistencies and their inter-relationships. Because of its inherent rationality, this
unified theory of reinforced concrete can serve as the basis for the formulation of a universal
and international design code.
In Section 1.2, the position of the unified theory in the field of structural engineering
is presented. Then the six components of the unified theory are introduced and defined in
Section 1.3, including a historical review of the six model components, and an explanation of
how the topic's chapters are organized. The conceptual introduction of the first model - the
struts-and-ties model - is given in Section 1.4. Detailed study of the struts-and-ties model is
not included in this topic, but is available in many other textbooks on reinforced concrete.
Chapters 2-7 present a systematic and rigorous study of the last five model components of
the unified theory, as rational tools to solve the four basic actions (bending, axial load, shear and
torsion) in concrete structures. The last three chapters, 8-10, illustrate the wide applications of
the unified theory to prestressed I-beams, ductile frames, various types of framed shear walls,
bridge columns, etc., subjected to static, reversed cyclic, dynamic and earthquake loadings.
1.2 Structural Engineering
1.2.1 Structural Analysis
We will now look at the structural engineering of a typical reinforced concrete structure, and
will use, for our example, a typical frame-type structure for a manufacturing plant, as shown in
Figure 1.1. The main portal frame, with its high ceiling, accommodates the processing work.
The columns have protruding corbels to support an overhead crane. The space on the right,
