Analytical Modeling


The three bridge decks were modeled using the finite element analysis program ?ANACAP? (Anat – ech Concrete Analysis Program) Version 3.0, (James, 2004). The concrete material model is based on smeared cracking methodology developed by Y. R. Rashid, 1960. Within the concrete constitutive

Fig. 20. Mesh used for modeling the three bridge decks.

model, cracking and all other forms of material non-linearity are treated at the finite element integ­ration points. Cracks are assumed to form perpendicular to the principal tensile strain direction in which the criterion is exceeded and they are allowed to from at each material point. When cracking occurs, the normal stress across the crack is reduced to zero and distribution of cracks around the crack is recalculated. Cracks may close or re-open under load reversals. Concrete modeling also included residual tension stiffness for the gradual transfer of load to the reinforcement during crack formation. In addition, the program accounts for the reduction in shear stiffness due to cracking and further decay as the crack opens. The reinforcement is modeled as individual sub-elements within the concrete elements. The stiffness of the bar sub-element is superimposed on the concrete element stiffness in which the bar resides. The anchorage loss is modeled as an effective stiffness degradation of the bar as a function of the concrete strain normal to the bar.

A 3-D analysis was conducted for the three bridge decks using 20-node hexahedral continuum elements. Only one quarter of the deck was modeled due to its symmetry about both axes. The depth of the deck was divided into five layers within its thickness with a total number of elements of 1040, as shown in Figure 20.