Strut-and-tie modeling - Computational Analysis and Design of Bridge Structures - page 399

Strut-and-tie modeling
13.1 PrinciPle of Strut-and-tie Model
Structural concrete members used in bridges can be subdivided into
two regions, B- and D-regions (Figure 13.1). In the B-region, Bernoulli's
hypothesis holds valid, where it is assumed that a normal cross-sectional
plane remains plane and normal to the reference lines when the beam
deforms. Bernoulli's hypothesis facilitates the flexural design of reinforced
concrete structures by allowing a linear strain distribution for all loading
stages, including an ultimate flexural capacity. Design of the B- (Bernoulli
or beam) region is well understood, and the entire flexural behavior can be
predicted by simple calculations. For torsion, the sectional shape and size
in its own sectional plane are assumed to be preserved during torsion, and
the cross section can warp freely out of its plane.
In the D-region (disturbed or discontinued portion), Bernoulli's hypothesis
does not apply. Some examples of D-regions are corbels, dapped beams, deep
beams, regions near the support or concentrated load, sudden changes of the
cross section, holes, joints, and so on. All these are considered two-dimen-
sional (2D) applications of the strut-and-tie model (STM). Three-dimensional
(3D) STM are required when the structure and loading are considerably spread
over all three dimensions, such as pile caps with two or more rows of piles.
According to St. Venant's principle, the localized effects caused by any
load acting on the body will dissipate or smooth out within regions that
are sufficiently far enough from the load location (Figure 13.2b). This is
applied in the analysis of D-regions.
Design of the B-region has long been established and can be easily calcu-
lated. However, even for the most common cases of D-regions, the ability
to predict capacity by traditional methods is either empirical or requires
finite element analysis to reach an estimation of capacity. An STM closes
this gap and offers engineers the ability to develop a conservative capacity
without sophisticated modeling. D-regions can be idealized as consisting of
concrete struts in compression, steel ties in tension, and nodes where more
than one member are joined together.
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