1.1. The authors modeled the concrete beam using the

1.1.  Introduction


In order to simulate the behavior of corroded beams, the
authors developed a finite element model, and verified the results with the
available experimental data conducted by others. However, due to the limited
number of experimental data of RC beams with corroded compression reinforcement,
the model was compared to structurally sound beams and beams with corroded
tensile reinforcement. After being verified with preexisting experimental data,
the authors employed the FEA model to study a total of 36 beams subjected to
different compression reinforcement ratios and different unbond lengths between
compression steel reinforcement and adjacent concrete. The authors employed the
outcome of the above study to develop an analytical model to calculate the
ultimate flexural strength of RC beams with corroded compression reinforcement.

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1.2.  Element



The authors modeled the concrete beam using the 3-D SOLID65
Element. The element allows the modeling of nonlinear material properties. In addition,
it has the capability of crushing in compression and cracking tension. The
SOLID65 element is defined by eight nodes, each of these nodes have three
degrees of freedom; translations in the nodal x, y, and z directions. Moreover,
the above element is capable of cracking (in three orthogonal directions),
crushing, plastic deformation, and creep (ANSYS, 2013).

Steel Elements

The 3-D element LINK180 was used to model the steel
reinforcing bars. The element is a uniaxial spar capable of carrying tension
and compression. The element is defined by two nodes with three degrees of
freedom at each node: translations in the nodal x, y, and z directions. The
X-axis of the element is oriented along the length of the element from node I
to node J. The element does not allow bending. In addition, plasticity, creep,
rotation, large deflection, and large strain capabilities are considered (ANSYS,
2013). Link180 is used to model sound steel reinforcement as well as corroded
steel reinforcement.

Corroded Steel

The corroded steel elements were modeled using LINK180, the
same element that was used to model non-corroded steel elements. However. The
reduction in steel’s cross-sectional area and strength, due to corrosion, were
taken into account.

Spring Elements

Loss of bond between reinforcing steel and surrounding
concrete was modeled using vertical spring element COMBIN14. This element has longitudinal
or torsional capability in 1-D, 2-D, or 3-D applications. However, when the
longitudinal spring-damper option is activated, the element is considered as a
uniaxial tension-compression element with up to three degrees of freedom at
each node: translations in the nodal x, y, and z directions.  The element has no mass and the capability of
the spring or damper can be deactivated (ANSYS, 2013).


1.3.  Material
Properties and Real Constants



The authors used Von Mises failure criterion along with
William and Warnke’s (1974) constitutive model in order to define concrete
failure. The modified Hognestad stress-strain relationship defined multilinear
isotropic concrete stress-strain curves as shown in Fig.
The first point of the stress-strain diagram is defined as 0.30f’c and it represents the
linear branch of the stress strain diagram (Hook’s law) (Kachlakev et al. 2001, and Wolanski 2004). The
modified Hognestad stress-strain relationship defines the next six points until
?0. The last portion of
the curve is perfectly plastic since the most recent version of ANSYS do not accept
negative slopes in stress-strain diagrams.

The modulus of elasticity of concrete was 4,750 times the square
root of concrete cube strength, whereas the modulus of rupture (uniaxial
cracking stress) was 8.5% of the concrete compressive strength. Poisson’s ratio
was assumed to be 0.2. Shear transfer coefficients range from 0 to 1, with 0
representing a “smooth crack” (complete loss of shear transfer) and 1.0
representing a “rough crack” (no loss of shear transfer) (ANSYS, 2013). The shear
transfer coefficient for a closed crack was assumed 1, and the shear transfer
coefficient for an open crack was considered 0.3 (Kachlakev et al. 2001, Wolanski 2004, ad Dahmani et al. 2010). The uniaxial crushing
stress and the uniaxial cracking stress defined the concrete compressive
strength and the modulus of rupture respectively. The biaxial crushing stress,
hydrostatic pressure, hydro biax crush stress, hydro uniax crush stress, and
tensile crack factor were set equal to their default values determined by ANSYS,
which is zero. The authors performed a preliminary analysis to verify the
values of the above coefficients to the best agreement with the existing experimental

Steel Elements

The stress-strain curve for steel was elastic perfectly plastic
as shown in Fig. 1(b).
The steel yield stress varied based on each experiment. The modulus of elasticity
of steel was assumed 200,000 MPa, and Poisson’s ratio was considered 0.3. The
real constant R1, which represents the cross-sectional area of the steel
reinforcement, varied based on each experiment.