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.
f_{x}t^{2} / (L^{2}h)where
f_{x} = Material flexural strength. t = Wall thickness. L = Wall length. h = Wall height.
The data and analysis are presented below.
Haseltine observed [1977, p. 427] the following linear relationship gave reasonable agreement with the data:
p = (2.6/h)(1.8 + 12.7(f_{x}/L^{2})) kN/m^{2}where
p = Lateral pressure inducing wall failure. (kN/m^{2}) f_{x} = Material flexural strength. (kN/mm^{2}) 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:
f_{x} / (L^{2}h)
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:
f_{x}t^{2} / (L^{2}h)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 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.
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.