Load capacity of perforated walls

Although it is common and necessary to use doors and windows in buildings, walls with openings are less experimentally evaluated than unperforated walls (without openings).

Hatzinikolas et al. (2015) comment that the behavior of masonry shear walls with openings is much more complex than that of unperforated walls.

Results of experimental tests (Calderón et al., 2017) have shown that the inclusion of openings significantly reduces the load capacity of masonry shear walls. If the mechanisms of lateral resistance depend on the second moment of area of the walls, it is evident that the decrease in stiffness due to the presence of openings will substantially alter the strength and, consequently, the behavior of the wall. Elshafie et al. (2002) state that for walls of equal dimensions, the stiffness reduction due to openings is comparable to the reduction in the load capacity, regardless of the size and location of the opening.

According to Voon and Ingham (2008), the lateral strength of walls is significantly affected by the height of the opening because the steeper the compression strut formed, the less efficient is the transfer of lateral forces. In contrast, Fortes and Parsekian (2017) and Calderón et al. (2017) concluded, based on the results of their tests, that for openings of similar length, differences in height do not affect the lateral capacity of the wall.

Walls are planar members that lose their continuity when openings are created and, thus, the general behavior of the walls becomes conditional on the behavior of the spandrels and piers defined by the dimensions of the openings (Carvalho and Oliveira, 1997). It is usual and relatively conservative to calculate the shear load capacity of masonry walls with openings as the sum of the capacity of its piers (Drysdale and Hamid, 2005; Voon and Ingham, 2008). Such an approach, however, ignores any frame action developed by the coupling of the piers and the spandrels (Calderón et al., 2019). In addition, that approach assumes that all piers reach their maximum capacity at the same displacement level, which can be adequate when the openings are identical and similar piers are formed. However, it may not be adequate when the piers have different aspect ratios and, consequently, different boundary conditions (Vargas et al., 2020).

Ingham et al. (2001) suggested that the identification of lateral load-bearing panels of walls with openings should be made according to illustrated in Figure 48. The hatched areas highlight the adopted piers with a height equal to the adjacent opening and whole panels since there is a shrinkage control joints over the entire height of the wall with a distance to the opening of more than 200 mm. The authors recommended ignoring the frame action imposed by the

beam's connection to treat the piers as individual cantilever walls. The authors cautioned that there was not enough experimental evidence that this approach could be suitable for walls with small openings.

Figure 48: Identification of load-bearing panels according to Ingham et al. (2001).

Source: Ingham et al. (2001).

Voon and Ingham (2008) tested eight shear walls with different types of openings and coupled with reinforced masonry beams. From the experimental results, the authors noticed that the available effective shear area of the piers directly affected the load distribution on the walls, increasing their capacity when the length of the piers was greater. The experimental results were used to check the approach recommended by NZS 4229 (1999) for calculating the lateral load capacity of walls. The standard says that the total capacity of a wall can be determined by the sum of the individual capacity of the piers with a vertical dimension limited to the smallest adjacent opening, as illustrated in Figure 49. The authors concluded that NZS 4229 (1999) failed to identify the resistant geometry of the wall panels, resulting in an overestimated load capacity for the wall with a small opening and more conservative as the opening height increased in the others. In walls with more than one opening, the standard underestimated the lateral load capacity by almost 90%, and, according to the authors, the extra capacity generated in the central pier should be added, given the connection made by the beam.

Yanez et al. (2004) developed an experimental study of confined masonry shear walls with different sizes of openings and reinforcement only around the openings, as shown in Figure 50. The authors concluded that the analysis methodology considering the lateral load capacity proportional to the net cross-sectional area of the walls is conservative.

Figure 49: Identification of piers on walls tested by Voon and Ingham (2008).

Source: Voon e Ingham (2008).

Figure 50: Arrangement of the walls tested by Yanez et al. (2004).

Source: Yanez et al. (2004).

Johnson and Schultz (2014) evaluated the expression of TMS 402/602 (2016) to predict the lateral load capacity of a wall experimentally tested by them. As seen in Figure 51, the wall was partially grouted with a centralized window opening, in addition to having flanges at both ends. The authors considered the total lateral capacity of the wall as the sum of the capacity of the two piers with a height equal to the opening. They did not include horizontal reinforcement because the bars were not positioned within this region. It was concluded that the standard equation adequately predicted the load capacity of the wall, presenting a ratio 𝑉_𝑒𝑥𝑝⁄𝑉_𝑛 = 1.003.

However, the authors clarify that the yielding of the horizontal bars was observed in the tests, which implies that they contributed to the capacity of the wall.

Figure 51: Detail of the wall tested by Johnson and Schultz (2014).

Source: Johnson e Schultz (2014).

Calderón et al. (2017) stated that the pier aspect ratio is the parameter that presented the best correlation with the results of their experimental and numerical studies. According to the authors, the lateral load capacity of walls with openings can be measured by an equivalent wall with an aspect ratio equal to that of their piers. It was observed that the shear load capacity of the walls decreased when the aspect ratio of the piers increased, but the capacity increased proportionally to the ratio of the horizontal reinforcement positioned in the region of the piers, regardless of their aspect ratio. In a later study, Calderón et al. (2019) evaluated the accuracy of the equations proposed by the CSA S304 (2014) and TMS 402/602 (2016) and by Shing et al. (1990), Psilla and Tassios (2009), and Aguilar et al. (2016) to predict the shear load capacity of the ten walls studied by them, of which three were experimentally tested, and seven were numerically modeled. The capacity of the piers, identified as depicted in Figure 52, was considered in calculating the total capacity of the walls. The authors concluded that the equation of Psilla and Tassios (2009) and TMS 402/602(2016) had the highest mean of the 𝑉_𝑒𝑥𝑝⁄𝑉_𝑛 ratio and the greatest variability, while the expressions of Shing et al. (1990) and Aguilar et al. (2016) were the ones that showed the best performance and acceptable deviation.

Figure 52: Identification of piers in walls studied by Calderón et al. (2019).

Source: Calderón et al. (2019).

Koutras and Shing (2018) commented that the equations of the American standard predicted the shear capacity of the walls of their experiment sufficiently well considering the sum of the capacity of the piers. However, the disparity between the stiffnesses of the piers and their brittle behavior can lead to an unsafe design.