Finite Element Modeling of Frames and Walls - Unified Theory of Concrete Structures - page 385

formulation need to be set up as the first step. Then the equilibrium and compatibility equations
are derived, as shown in Section 6.1.1. Afterwards, the relationship between biaxial strains
and uniaxial strains is needed, as introduced in Section 6.1.4.4. Finally, uniaxial constitutive
relationships of the reinforced concrete materials developed in Section 6.1.6 to 6.1.10 are
employed, including uniaxial constitutive relationships of concrete in compression and tension,
uniaxial constitutive relationship of mild steel bars embedded in concrete, and constitutive
relationship of concrete in shear. The uniaxial constitutive relationships required for prestressed
concrete were derived by Wang (2006) and Laskar (2008).

9.2 Material Models for Concrete Structures
In both the fiber model (FM) and CSMM, all the required material models for concrete,
reinforcing bars and prestressing tendons of reinforced/prestressed concrete have been imple-
mented in OpenSees (Fenves, 2005). These material models are summarized in Table 9.1 and
are presented in the following section.

Table 9.1 Uniaxial material models employed

Model name Material type Source

Steel01 Steel Existing in OpenSees

Concrete01 Concrete Existing in OpenSees

SteelZ01 Steel Developed based on CSMM

TendonL01 Tendons Developed based on CSMM-PC

ConcreteL01 Concrete Developed based on CSMM-PC

9.2.1 Material Models in OpenSees
9.2.1.1 Steel01

The steel module Steel01 needed in the FM is based on a uniaxial bilinear material model as
shown in Figure 9.2. It has an elastic phase before yielding and a strain-hardening part after
yielding. The unloading and reloading paths follow a bilinear pattern in which the slopes of

Figure 9.2 Steel01 material model