Introduction - Unified Theory of Concrete Structures - page 1

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Introduction

1.1 Overview
A reinforced concrete structure may be subjected to four basic types of actions: bending,
axial load, shear and torsion. All of these actions can, for the first time, be analyzed and
designed by a single unified theory based on the three fundamental principles of mechanics
of materials: namely, the stress equilibrium condition, the strain compatibility condition, and
the constitutive laws of concrete and steel. Because the compatibility condition is taken into
account, this theory can be used to reliably predict the strength of a structure, as well as its
load-deformation behavior.
Extensive research of shear action in recent years has resulted in the development of various
types of truss model theories. The newest theories for shear can now rigorously satisfy the
two-dimensional stress equilibrium, Mohr's two-dimensional circular strain compatibility and
the softened biaxial constitutive laws for concrete. In practice, this new information on shear
can be used to predict the shear load versus shear deformation histories of reinforced concrete
structures, including I-beams, bridge columns and low-rise shear walls. Understanding the
interaction of shear and bending is essential to the design of beams, bridge girders, high-rise
shear walls, etc.
The simultaneous application of shear and biaxial loads on a two-dimensional (2-D) ele-
ment produces the important stress state known as 'membrane stresses'. The 2-D element,
also known as 'membrane element', represents the basic building block of a large variety
of structures made of walls and shells. Such structures, including shear walls, submerged
containers, offshore platforms and nuclear containment vessels, can be very large with walls
several feet thick. The information in this topic provides a rational way to analyze and to
design these wall-type and shell-type structures, based on the three fundamental principles of
the mechanics of materials for two-dimensional stress and strain states.
The simultaneous application of bending and axial load is also an important stress state
prevalent in beams, columns, piers, caissons, etc. The design and analysis of these essential
structures are presented in a new light, emphasizing the three principles of mechanics of
materials for the parallel stress state, i.e. parallel stress equilibrium, the Bernoulli linear strain
compatibility and the uniaxial constitutive laws of materials.