Concrete structures are subjected to a complex variety of stresses and strains. The four basic
actions are: bending, axial load, shear and torsion. Each action alone, or in combination
with others, may affect structures in different ways under varying conditions. The first two
actions – bending and axial load – are one-dimensional problems, which were studied in the
first six decades of the 20th century, and essentially solved by 1963 when the ultimate strength
design was incorporated into the ACI Building Code. The last two actions – shear and
torsion – are two-dimensional and three-dimensional problems, respectively. These more
complicated problems were studied seriously in the second half of the 20th century, and
continued into the first decade of the 21st century.

The first unified theory published in 1993 was a milestone in the development of mod-
els for reinforced concrete elements. Nevertheless, the ultimate goal must be science-based
prediction of the behavior of whole concrete structures. Progress was impeded because the
fifth component model, the softened truss model, was inadequate for incorporation into the
new finite element analysis for whole structures. An innovation in testing facility in 1995
allowed new experimental research to advance the nonlinear theory for shear and torsion. This
breakthrough was the installation of a ten-channel servo-control system onto the universal
panel tester (UPT) at the University of Houston (UH), which enabled the UPT to perform
strain-controlled tests indispensable in establishing more advanced material models.


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