Civil Engineering Reference
In-Depth Information
The position of the unified theory in the scheme of structural engineering is shown in row
4 of Table 1.1. The six model components of the unified theory are distinguished by their
adherence to the three fundamental principles of the mechanics of materials (the equilibrium
condition, the compatibility condition and the constitutive laws of materials). The six models
are named to reflect the most significant principle(s) embodied in each as listed in the
following section.
1.3 Six Component Models of the Unified Theory
1.3.1 Principles and Applications of the Six Models
As shown in Table 1.1, some of the six models are intended for the main regions and some for
the local regions. Others may be particularly suitable for the service load stage or the ultimate
load stage. The six models are summarized below, together with their basic principles and the
scope of their applications:
1.3.1.1 Struts-and-ties Model
Principles:
Equilibrium
condition only
Applications:
Design of local regions
1.3.1.2 Equilibrium (Plasticity) Truss Model
Principles:
Equilibrium
condition and the theory of
plasticity
Applications:
Analysis and design of
M
,
N
,
V and T
in the main regions at the ultimate
load stage
1.3.1.3 Bernoulli Compatibility Truss Model
Principles:
1-D Equilibrium
condition,
Bernoulli compatibility
condition and
1-D
or
uni-
axial constitutive law
for concrete and reinforcement. The constitutive laws
may be linear or nonlinear
Applications:
Analysis and design of
M
and
N
in the main regions at both the serviceability
and the ultimate load stages
1.3.1.4 Mohr Compatibility Truss Model
Principles:
2-D Equilibrium
condition,
Mohr compatibilit
y
condition and
1-D
or
uniaxial
constitutive law
(
Hooke's Law
is preferred) for both concrete and reinforce-
ment
Applications:
Analysis and design of
V
and
T
in the main regions at the serviceability
load stage
