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corresponded to one rotational and two translational degrees of freedom for
each two nodes located at beam element ends and one relative translational
degree of freedom for the node situated at midlength of the beam element.
The introduction of the relative translational degrees of freedom for the
node at midlength of the beam element was necessary to account for the
strong variation of the centroid position when the behavior of the section
was not symmetrical. Such situation occurred for concrete sections when
cracking propagated. The authors showed that, as usual for fiber element,
the section forces at the element nodes were computed using both a longi-
tudinal and transversal integration scheme. The integration along the beam
length was performed using four integration points. For each longitudinal
integration point, a transversal integration was performed using a
multilayer-type scheme. The section was divided into a certain number
of layers, each of which was assumed to be in uniaxial stress state. At each
transversal integration point, the state of deformation and stress was com-
puted. The connection between the concrete beam element and the steel
beam element was introduced by means of specific connection elements
comprising two transversal springs and two rotational springs to avoid uplift.
Longitudinal springs were uniformly distributed along the element. The res-
olution of the nonlinear problem was performed using classical algorithms,
Newton-Raphson scheme with arc length method.
Zaforteza and Garlock [1.47] investigated numerically the fire response
of steel girder bridges by developing a 3-D numerical model for a typical
bridge of 12.20 m span length. A parametric study was performed consider-
ing different axial restraints of the bridge deck, different types of structural
steel for the girders, different constitutive models for carbon steel, different
live loads, and different fire loads. The numerical study showed that restraint
to deck expansion coming from an adjacent span or abutment should be
considered in numerical models. Also, times to collapse were very small
when the bridge girders are built with carbon steel (between 8.5 and
18 min), but they can almost double if stainless steel is used for the girders.
The authors recommended that stainless steel can be used as a construction
material for girder bridges in a high-fire-risk situation. It was also concluded
that the methodology developed in the study and the results obtained can be
useful for researchers and practitioners interested in developing and applying
a performance-based approach for the design of bridges against fire. The
numerical study was performed using ABAQUS [1.29]. Due to the symme-
try, only half of the bridge was modeled. An uncoupled thermomechanical
analysis was used, where in the first phase, a thermal heat transfer analysis
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