Shear Capacity of Large Structural Elements

Shear Capacity of Large Structural Elements: A case study of the shear behavior of the itaipu concrete lock walls

Demmerer, D'tasha (TU Delft Civil Engineering & Geosciences)

Jonkman, Sebastiaan N. (mentor)
Molenaar, W.F. (graduation committee)
Hendriks, M.A.N. (graduation committee)
de Waardt, H (graduation committee)

Delft University of Technology

Civil Engineering | Hydraulic Structures

2020-12-15

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.

Shear force
deep beam
DIANA FEA
strut and tie model

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Student theses

master thesis

© 2020 D'tasha Demmerer