Shear Capacity of Large Structural Elements

Abstract

The concept
of shear loading and the shear resistance is well known for ‘regular’ sized
beams, meaning beams that can be characterized as a slender beam. However, once
the beam increases in size such that it is characterized as a deep beam or even
falls outside the range of the typical deep beam, less knowledge is available.
A case study of the Itaipu lock walls is used to compare three different
calculation methods for shear loading (sectional method, strut & tie
method, and a linear and nonlinear finite element model) to each other. The
calculation methods are applied to the large concrete lock walls in order to
determine which of these methods can best be used for shear calculations on
structural elements that fall out of the range of these so-called ‘regular’
sized beams.  The effect of increasing
thickness is studied and it can be concluded that the combination of a certain
crack width and the aggregate interlock mechanism, and thus the grain size of
the concrete mixture, play an important role in the shear capacity of beams.  The existing norms and guidelines, such as the
Eurocode and the American Concrete Institute codes, have been proven to be
inadequate for shear calculations on structural elements that surpass the
definition of a deep beam in size, such as the Itaipu lock walls. The sectional
calculation, which is based on these norms and guidelines is however still used
as a rough reference calculation in this research. The first calculation, which
is the sectional calculation, resulted in two alternative designs next to the
original lock wall design by Witteveen+Bos: total wall thickness original
design: 33m, total wall thickness alternative design 1 (i): 17m and total wall
thickness alternative design 2 (ii): 29m. The Strut & Tie calculation is
then performed for the original Witteveen+Bos design, resulting in a
reinforcement plan based on the normal forces in the ties. The third
calculation type consisted of three linear models (of the original design and
the two alternative designs) and one nonlinear model of the original
Witteveen+Bos design. The stress trajectories of the linear models illustrated
that the wall is predominantly stressed in compression, as a result of the
large self-weight of the wall. Only the lower part of the wall and the lock
floor connected to this wall are stressed in tension. The nonlinear model was
therefore reinforced only in the lock floor and the lower part of the wall
connected to the lock floor.  Because the
linear finite element approach does not include material behavior beyond the
elastic stage, this approach is not sufficient and does not provide the
necessary required insight for a shear resistance calculation. The nonlinear
finite element model has proven to be the most accurate and adequate calculation
method. The downside is that this method will take longer and requires more
background information about the materials used, the connection between
structural elements and the type of subsoil. The Strut & Tie approach, is a
good first design step. However, for a thorough tradeoff between wall
thickness, the complex connection between the floor and the wall, and the
amount of reinforcement necessary to prevent cracking, the nonlinear finite
element method gives the most accurate estimate.  From the calculation results, the conclusion
is drawn that the current wall design by Witteveen+Bos is an overly
conservative design. Decreasing the current total wall thickness and increasing
the amount of reinforcement in the lock floor and the lower part of the wall connected
to the lock floor, will also result in a design that is able to resist the
shear loading.