The boundary conditions used by Fattal are much more amenable to analytic modelling, since the half-round bars provide very little rotational resistance. The use of two tests per panel type is also beneficial, since the tests establish a range allowing more meaningful comparison with analytic results. The lack of solid masonry specimens is a drawback of the Fattal study, since it is awkward to model this effect in a non-linear analysis. For comparison purposes, this study chose a brick masonry unit with three round holes along the centerline, with the holes accounting for 20 percent of the gross area [Fattal 1976, p. 2, table 3.1]. The two identical tests were designated 4A13 and 4A14.
Two analytic models were created for comparison with experimental results: one with four lamination and one element layer per course, and one with four laminations and two element layers per course. In both models, the base boundary condition was modelled as a series of vertical displacement restraints along the centerline of the bottom of the wall, allowing free rotation of the base. The figure below shows the deformed shape of the 4-lamination, 2-layer model; the red triangles indicate displacement diagrams.
|The deformed shape of the 4-lamination, 2-layer model. The red triangles indicate displacement boundary conditions. Magnification factor = 20.|
|A load-displacement diagram comparing experimental results of Fattal with analytic results of the block-interface model. The experimental curve is the mean of two tests. (experimental curve from [ Fattal1976, figure 6.30, p. 26]|
The results of the Fattal comparison are similar to the brick wall study of Yokel. The analytic models tend to overestimate the stiffness in the elastic range, although increasing the number of element layers per course brings the elastic stiffness closer to the experimental value. Increasing the layers per course also decreases the strength. Note that this effect on strength was not true in the block-wall test of Yokel, which was much less slender.
In comparing the strength, it is important to consider the range of values established by the two tests performed by Fattal. The curve shows a maximum the pressure-displacement combination of 2.53 psi, 0.30 in. This curve is based on the mean of two tests whose maximum pressure-displacement combinations were 2.40 psi, 0.306 in. and 2.66 psi, 0.45 in [Fattal 1976, p. 25, table 6.5]. The two tests establish a range about the plotted curve which is not far from the results of the analytic model.
Another factor in the discrepancy between the model and the analytic results is the non-solid masonry. Since the holes are located on the centerline, they have little effect on the bending stresses, but effectively increase the axial prestress level by 20 percent, allowing the wall re resist greater moments without cracking. Taking into account the range of values in the test and the strengthening effect of the masonry voids, it is clear that the analytic models capture the strength behavior of wall with quite reasonable accuracy, although they tend to overestimate elastic stiffness.
Overall, the comparisons indicate that the block-interface model can reasonably predict the post-cracking behavior of unreinforced masonry under static compression and bending. Differences between the analytic and experimental results arise not only from limitations in the modelling method, but also in uncertainty in the physical characteristics of the experimental structure and its measuring devices. For the Yokel studies in particular, the degree of fixity provided by the boundary supports is unclear, as the authors admit themselves [Yokel 1971, p. 38]. The comparison of two identical tests by Fattal also reveals that there is a degree of uncertainty in the measured capacity of a particular assembly.
Examination of the parametric studies concerning the number of laminations and layers per course reveals that adequate results were achieved with six laminations, and when the courses and number of layers per course were arranged to provide at least 50 layers of elements along the entire span. These parameters will be the subject of further study.
In addition to analytic studies, the project is also investigating emperical studies to compare the relative strength of two-way spanning wall panels based on dimensions and material properties, based on published experimental results. The following discussion presents current results of these studies.
|Next: Empirical Studies of Relative Strength|