Empirical Studies of Relative Strength of Two-Way Panels
    Last updated Friday, June 20, 1997, at 9:43 AM Copyright © 1996, 1997 Kirk Martini

    Objectives

    In assessing the viability of a hypothesis concerning patterns of out-of-plane damage to masonry walls, it is important to be able to compare the relative vulnerability of various walls. If it's postulated that certain walls were damaged during an event while other walls survived, then it should follow that the surviving walls are less vulnerable to out-of-plane failure.

    A method for assessing the relative strengths of walls (e.g. assessing whether wall A is stronger than wall B) is nearly as useful as a method for assessing the absolute strengths of walls (e.g. what is the load required to induce failure in wall A), since there are so many unknowns concerning absolute load levels. For similar construction types and support conditions, a gross assessment of relative strength can be based on geometric proportions.

    The following discussion outlines studies to identify a simple parameter to compare the relative vulnerability of two-way-spanning unreinforced masonry walls to out-of-plane failure. The discussion begins with empirical studies.

    Empirical Studies

    There has been relatively little experimental work on two-way-spanning unreinforced masonry panels. Some of the best-documented work was done in Britain during the 1970s by Hendry [1973] and a two-part study by Haseltine [1977] & West [1977]. These studies include data concerning the dimensions, support conditions, and material properties of a variety of test panels. Reviewing the data and results presented in these studies, it appears that the following parameter is a reasonable measure of relative strength for two-way spanning walls of similar construction supported on three sides (sides and bottom).
    fxt2 / (L2h)

    where

    fx = Material flexural strength.
    t = Wall thickness.
    L = Wall length.
    h = Wall height.

    The data and analysis are presented below.

    The Haseltine-West Studies

    The Haseltine-West Studies [Haseltine 1977, West 1977] include a variety of tests on full-scale panels, including a range of length, height, and materials. The great majority of the tests used a support condition supported on two side edges and the bottom, with the bottom support being attached to a bituminous material that gave way in some tests, so that support was provided along the two sides only. Test panels were loaded to failure by uniform lateral pressure induced by an air-filled bag, and there was no vertical surcharge.

    Haseltine observed [1977, p. 427] the following linear relationship gave reasonable agreement with the data:

    p = (2.6/h)(1.8 + 12.7(fx/L2)) kN/m2

    where

    p = Lateral pressure inducing wall failure. (kN/m2)
    fx = Material flexural strength. (kN/mm2)
    L = Wall length. (m)
    h = Wall height. (m)

    For assessing relative strength, the constant terms can be neglected, simplifying the expression to say that the failure pressure increases with the following quantity:

    fx / (L2h)

    Note that this expression does not account for wall thickness, which was not necessary in Haseltine's study since all the walls studies had the same thickness. According to simple beam theory, strength varies with the square of the thickness, so the expression for the relative strength parameter can be modified as follows:

    fxt2 / (L2h)
    The graph below shows the relationship between this strength parameter and the failure pressure for several test panels from the Haseltine study. There is a three-part designation for each group: the first part is the number of the table in the paper where the data is listed (either 4 or 5); the second part is the designation for the type of brick and mortar listed in the paper (AX, BX, or BY for successively weaker combinations); and the third part indicates the dimension that was held constant in the data group (e.g. 2.6H for a 2.6 meter height, of 5.5L for a 5.5 meter length). Panels which failed in one-way action due to loss of bond along the bottom edge are not included here. The heights of the panels range from 1.3 to 3.6 meters, the lengths range from 2.44 to 5.5 meters. All panels have a thickness of 0.1025 meters.

    The relative strength parameter plotted against failure pressure for a variety of panels from the Haseltine-West study.

    The figure shows that the relative strength parameter is a reasonable indicator of panel strength and can be used a basis for approximate comparison of panel strength; however, it cannot be concluded that the parameter correctly accounts for the effect of varying thickness, since all test panels the same thickness. To investigate the effectiveness of the parameter in accounting for stiffness, it will be applied to a series of tests conducted by Hendry [1973].

    The Hendry Studies

    Hendry conducted an extensive series of tests on one-sixth-scale panels over a range dimensions and at thickness of 19 mm (0.75 in) and 38 mm (1.5"). The figure below shows the results of plotting the failure stress vs. the relative strength parameter. Panel lengths range from 203.2 mm (8 in) to 812.8 mm (32 in); the panel height is either 406.4 mm (16 in) or 431.8 mm (17 in); the panel thickness is either 19 mm (0.75 in) or 38 mm (1.5 in). The designations A through H are based on table 3 of the paper [Hendry 1973, p. 46].

    The relative strength parameter plotted against failure pressure for a variety of panels from the Hendry study.

    As with the plot of the Haseltine-West results, the figure above shows that the relative strength parameter provides a reasonable basis for comparing the lateral resisting capacity of unreinforced masonry walls in a two-way span condition, supported on the bottom and sides.

    Conclusions

    Although the relative strength parameter provides a reasonable basis for comparing similar walls, it must be used with caution. The figure below shows a plot including data points from both the Haseltine and Hendry studies. It is clear that the test panels from the Hendry tests have a consistently higher failure pressure at the same value of the relative strength parameter.

    The relative strength parameter plotted for tests panels by Hendry and by Haseltine. The parameter is useful for comparing panels within a given set of tests, but not between the two sets.

    The difference between the two test sets is probably due to variations in boundary conditions of the test panels. In particular, the bituminous material used on the bottom edge of panels in the Haseltine studies may have provided less restraint, resulting in generally lower strength values. The significant difference in scale (the Hendry tests are based on one-sixth scale panels) may also be a factor. The key point is that the relative strength parameter is useful for comparing the strength of two-way wall panels provided that the conditions of the panel are reasonably similar and that the proportions lie in the range spanned by these tests, with L/h ranging from 0.5 to 2.1; L/t ranging from 5 to 54; and h/t ranging from 11 to 35.

    Last updated Friday, June 20, 1997, at 9:43 AM
    Copyright © 1996, 1997 Kirk Martini
    Please send comments or questions to Martini@virginia.edu
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