Civil Engineering Reference
In-Depth Information
consider the softening effect on the compressive strain and stress due to the tensile strain
in the perpendicular direction. Also the tensile stress of concrete in Concrete01 is ignored.
2. Reinforced/prestressed concrete plane stress material is added to OpenSees for analysis
of reinforced/prestressed concrete plane stress structures such as panels, deep beams, and
walls.
3. In addition, the displacement control scheme implemented in OpenSees is only for mono-
tonic displacement control with uniform displacement increment. The displacement control
needs to be modified for reversed cyclic loading.
In order to perform analysis on reinforced/prestressed concrete plane stress structures several
new material classes are implemented into the OpenSees framework, and some analysis classes
in the OpenSees are modified. Details of the implementation and modification are presented
as follows:
Three uniaxial material classes, SteelZ01, TendonL01, and ConcreteL01 are created and
implemented into OpenSees. The features of these three material modules have been described
in Section 9.1. An object made of SteelZ01 needs four input parameters: yield stress, Young's
modulus, concrete compressive strength, and steel ratio. The latter two parameters are used to
calculate the smeared yield stress and strain of embedded rebars. In addition, the coefficients
A
and
R
that determine the shapes of unloading and reloading paths (Equations 9.13 and
9.14) are set as two additional input parameters. The default values are defined as 1.9 and
10. An object made of TendonL01 needs similar inputs and has similar attributes as that of
SteelZ01. In addition it also needs the initial prestressing strains in the tendons as input. An
object of ConcreteL01 needs two input parameters: ultimate compressive strength
f
c
and the
compressive strain
ε
0
corresponding to
f
c
.
A 2D material class, PCPlaneStress, is created and implemented into OpenSees. The PC-
PlaneStress is a class for plane stress concrete material using CSMM-PC. In PCPlaneStress,
the material constitutive matrix derived in this chapter is evaluated and the stress vector is
calculated. An object made of PCPlaneStress material needs the tags of the created uniaxial
steel and concrete objects of SteelZ01, TendonL01, and ConcreteL01, the directions of the
steel grids, and the steel ratio for the steel in each direction. Two uniaxial concrete objects
are needed in defining one PCPlaneStress object, which represents the concrete in the two
principal stresses directions. The steel orientations are not necessary in the horizontal and
vertical directions
,
and the user can define the arbitrary angles of the steel. The steel directions
are also not necessarily orthogonal. Users can define the steel in the reinforced/prestressed
concrete element in up to four directions.
The implementation of the PCPlaneStress into OpenSees is shown in Figure 9.13. The
Analysis and Recorder objects in OpenSees are omitted in this figure. The PCPlaneStress is
implemented with the Quadrilateral element to represent the PC plane stress four node ele-
ments. The PCPlaneStress is related with SteelZ01, TendonL01 and ConcreteL01 to determine
the tangent material constitutive matrix and to calculate the stress of the elements. For each
trial displacement increment in the analysis procedure, PCPlaneStress will receive the strains
of the elements, determine the uniaxial strains of the concrete, tendons and steel - then send
the uniaxial strain of concrete and the tensile perpendicular strain to the two uniaxial concrete
objects. After receiving the uniaxial strain and corresponding tensile strain, the concrete object
will produce the tangent stiffness and stress and then send the values back to the PCPlaneStress
object. Similarly, PCPlaneStress will send the uniaxial strain of the steel and tendon to the
