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.

1.2. Element

Types

Concrete

Elements

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

Elements

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

Concrete

Elements

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.

1(a).

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

data.

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.