Civil Engineering Reference
In-Depth Information
Actual
Idealized complete
interaction k i = ∞
Shear load V i
Idealized partial
interaction k i = d V i /d u s
Idealized no
interaction k i = 0
Slip ( u s )
FIGURE 7.19 Stiffness of the interface connection.
7.4.1 F LEXURE IN C OMPOSITE S TEEL AND C ONCRETE S PANS
When a composite steel and concrete span bends, the horizontal shear at the steel
to concrete interface must be resisted in order that the materials act integrally. The
number and size of mechanical connectors governs the interface behavior in terms of
shear strength and stiffness of the connection. The allowable stress design method of
AREMA (2008) provides for a linear elastic analysis at service loads. Linear elastic
analysis may be used provided complete (or near complete) interaction (i.e., adequate
horizontal stiffness) occurs at the interface. The flexural stress is then
Mc
I ,
σ =
(7.96)
where M is the bending moment,
is the normal (flexural) stress, c is the distance
from the neutral axis to the extreme fiber, and I is the moment of inertia.
The horizontal stiffness of the interface connection, k i , is determined from the
horizontal shear load versus interface slip relationship ( Figure 7.19) . All connections
between concrete decks and steel superstructures will exhibit some degree of slip
or partial interaction. Partial interaction analysis requires consideration of nonlinear
behavior, although “equivalent” linear elastic analyses of partial interaction have
been developed (Newmark et al., 1951). Complete interaction enables a linear elastic
analysis to be performed with a connection stiffness, k i =∞
σ
.
The relationship between interface connection stiffness, slip, and slip strain in a
simply supported composite steel and concrete span is shown in Figure 7.20. With
k i =
complete interaction occurs. As indi-
cated above, practical structures will behave between these extremes and exhibit
partial interaction. However, because of the relatively large number of shear connec-
tors required for strength in railway girders, the connection stiffness will be very large
andmaybeidealizedasinfinitelystiffwithcompleteinteraction.Completeinteraction
strain compatibility indicates that, slip, u s = 0, and slip strain, d u s / d x = ε c − ε s = 0,
0 no interaction occurs and with k i =∞
Slippage must occur in order to mobilize shear connector resistance.
 
 
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