Finite Element Analysis of Steel and Steel-Concrete Composite Bridges - Finite Element Analysis and Design of Steel and Steel-Concrete Composite Bridges - page 481

isoparametric directions in the plane of the membrane, shell, or solid ele-
ments. Modelers can specify the desired isoparametric direction from which
the rebar angle will be measured (1 or 2). The rebar angle is measured from
the isoparametric direction to the rebar with a positive angle defined as a
counterclockwise rotation around the element's normal direction. The
default direction is the first isoparametric direction.
Bolted connections and shear connectors can be modeled using combina-
tions of spring elements. Spring elements available in ABAQUS [1.29] can
couple a force with a relative displacement and can couple a moment with
a relative rotation. Spring elements can be linear or nonlinear. Figure 5.9
shows the definition of symbols for spring elements. The terms “force” and
“displacement” are used throughout the description of spring elements. When
the spring is associated with displacement degrees of freedom, these variables
are the force and relative displacement in the spring. If the springs are associ-
ated with rotational degrees of freedom, they are torsional springs. In this case,
the variables will be the moment transmitted by the spring and the relative
rotation across the spring. Spring elements are used to model actual physical
springs as well as idealizations of axial or torsional components. They can also
model restraints to prevent rigid-body motion. They are also used to represent
structural dampers by specifying structural damping factors to form the
imaginary part of the spring stiffness. SPRING1, SPRING2, and SPRINGA
elements are available in ABAQUS [1.29]. SPRING1 is between a node
and ground, acting in a fixed direction. SPRING2 is between two nodes,
acting in a fixed direction. While, SPRINGA acts between two nodes, with
its line of action being the line joining the two nodes, so that this line of
action can rotate in large-displacement analysis. The spring behavior can be
linear or nonlinear in any of the spring elements. Element types SPRING1
and SPRING2 can be associated with displacement or rotational degrees
of freedom.
The relative displacement definition depends on the element type. The
relative displacement across a SPRING1 element is the i th component of
displacement of the spring's node, with i defined as shown in Figure 5.9 .
The relative displacement across a SPRING2 element is the difference

j

i

2

1

Figure 5.9 Definition of symbols for spring elements.