Civil Engineering Reference
In-Depth Information
From a scientific point of view, a main region is one where the stresses and strains are
distributed so regularly that they can be easily expressed mathematically. That is, the stresses
and strains in the main regions are governed by simple equilibrium and compatibility con-
ditions. For columns that are under bending and axial load, the equilibrium equations come
from the parallel force equilibrium condition, while the compatibility equations are governed
by Bernoulli's hypothesis of the plane section remaining plane. In the case where beams are
subjected to shear and torsion, the stresses and strains should satisfy the two-dimensional
equilibrium and compatibility conditions, i.e. Mohr's stress and strain circles.
In contrast, a local region is one where the stresses and strains are so disturbed and irregular
that they are not amenable to mathematical solution. In particular, the compatibility conditions
are difficult to apply. In the design of the local regions the stresses are usually determined
by equilibrium condition alone, while the strain conditions are neglected. Numerical analysis
by computer (such as the finite element method), can possibly determine the stress and strain
distributions in the local regions, but it is seldom employed due to its complexity.
The local region is often referred to as the 'D region'. The prefix D indicates that the stresses
and strains in the region are
d
isturbed or that the region is
d
iscontinuous. Analogously, the
main region is often called the 'B region', noting that the strain condition in this bending region
satisfies
B
ernoulli's compatibility condition. This terminology does not take into account the
strain conditions of structures subjected to shear and torsion, which should satisfy
M
ohr's
compatibility condition. Therefore, the term 'B-M region' would be more general and tech-
nically more accurate, including both the Bernoulli and the Mohr compatibility conditions.
However, since the term 'B region' has been used for a long time, it could be thought of as a
simplification of the term 'B-M region'.
The second step of structural engineering is the division of the main regions and local
regions in a structure as indicated in row 2 of Table 1.1. On the one hand, the main regions
of a structure are designed directly by the four sectional actions,
M
,
N
,
V
and
T
, according to
the four sectional action diagrams obtained from structural analysis. On the other hand, the
local regions are designed by stresses acting on the boundaries of the regions. These boundary
stresses are calculated from the four action diagrams at the boundary sections. A local region
is actually treated as an isolated free body subjected to external boundary stresses.
The third step of structural engineering is the determination of the design actions for the
two regions. This third step of finding the sectional actions for main regions and the boundary
stresses for local regions is indicated in row 3 of Table 1.1. Once the diagrams of the four
actions are determined by structural analysis and the two regions are identified, all the main
regions and local regions can be designed.
1.2.3 Member and Joint Design
This fourth step of structural engineering is commonly known as the
member and joint design
.
More precisely, it means the
design and analysis of the main and local regions
. By this process
the size and the reinforcement of the members as well as the arrangement of reinforcement in
the joints are determined.
The unified theory aims to provide this fourth and most important step with a rational
method of design and analysis for all of the main and local regions in a typical reinforced
concrete structure, such as the one in Figure 1.1. It serves to synthesize all the rational theories
and to replace all the empirical design formulas for these regions.
