# Active Confinement of Masonry Walls with Stainless Steel Straps: The Effect of Strap Arrangement on the in-Plane Behavior of Strength, Poisson’s Ratio, and Pseudo-Ductility

## Abstract

**:**

## 1. Introduction

#### 1.1. General Information on the CAM^{®} System

^{®}system (active confinement of masonry: CAM is the Italian acronym for active stitching of masonry) [16,17,18,19,20]. This system is an evolution of the strengthening method with post-tensioned horizontal and vertical tie rods [21,22,23,24,25,26,27]. The evolution consists of the strengthening elements of the CAM

^{®}system [28], which are stainless steel straps instead of metal bars. The stainless steel straps pass through the thickness of the masonry thanks to openings made in the masonry by core drilling. Special stainless steel elements protect the edges of the masonry [29] where the stainless steel straps turn around the edges of the wall (Figure S1a) and enter the perforations (Figure S1b). Since up to six stainless steel straps share the same perforation (Figure S2), the CAM

^{®}system is a continuous strengthening system (unlike the tie rods system and all other systems in the same strengthening category). This makes it possible to establish effective connections in three dimensions between all the construction elements (roof, floors, and walls)—starting from the foundations of the building—to obtain or re-establish the so-called box-type behavior (Figure S3).

^{®}system is an active strengthening system.

^{®}system replicates the reinforcement scheme with horizontal and vertical ties. In this case, known as a rectangular arrangement, the perforations divide the masonry wall into volume units in the shape of right parallelepipeds (Figure 1). The early studies on the CAM

^{®}system [16,17,18,19,20,30,31,32] assumed that the three-dimensional arrangement of the loops provided the parallelepiped volume units with an additional compressive stress field that is hydrostatic, by extension in the three dimensions of the stress transfer mechanism shown in Figure S4. However, further theoretical analyses [11,29] revealed that the CAM

^{®}system adds confinement forces only in the transverse direction (Figure 1), except for volume units located near the free ends of the masonry wall. Recently, the numerical results of a FEM simulation [15] also confirmed that the confinement provided by the CAM

^{®}system to the wall is not isotropic.

#### 1.2. The Idea behind the Experimental Program

^{®}system with a rectangular arrangement (Figure 1) is suitable for increasing the out-of-plane strength of masonry walls when used in conjunction with other strengthening systems [29,35,36]. In the plane of the wall, however, the rectangular arrangement does not bring any increase in strength or stiffness. Both in-depth experimental tests [37] and recent numerical analyses [38], in fact, have shown that the rectangular arrangement of the stainless steel straps leads to an almost negligible increase in the strength of the shear-loaded masonry panels while providing a significant increase in ductility. The use of steel grids on both faces of the masonry wall, conversely, increases both the shear strength and the ductility, but the ultimate displacement achieved with the steel grids is lower than that achieved with the CAM

^{®}system [38].

^{®}system depends on the arrangement of the perforations, which makes the strengthening system labile to horizontal loads [29]. On the two wall facings, in fact, the straps of the rectangular arrangement form unbraced rectangular frame structures with hinged nodes. Under the action of horizontal forces, these nodes sway laterally exactly like the nodes of the simplified mechanical model in Figure 3a. Therefore, the perforations for the common passage of the straps are cylindrical hinges (Figure 3b), around which the loops connecting the two wall facings can rotate freely.

^{®}system useless under horizontal loads. In order to allow the CAM

^{®}system with a rectangular arrangement to also improve the in-plane behavior of masonry walls subjected to seismic loads, it is therefore mandatory to eliminate its in-plane lability.

^{®}system, because even labile static schemes can be in equilibrium for certain load directions. In fact, there is at least one load direction (in the plane) that keeps a labile static (plane) scheme in equilibrium. When the load has a fixed direction—such as during a seismic event—it is therefore possible to rotate the labile system, in search of an equilibrium configuration. This suggests that it is possible to avoid (expensive) bracing of the CAM

^{®}system simply by arranging its straps along the most suitable directions in the plane of the wall [29]. The aim of this work was precisely to verify the relationship between the in-plane arrangement of the straps and the ultimate load in the horizontal direction.

^{®}system with a rectangular arrangement is actually unable to increase the ultimate load under horizontal loads. However, a 45° rotation of the straps makes the rectangular arrangement effective even in the plane of masonry walls. The paper also offers insight into the elastic moduli, Poisson’s ratio, and the pseudo-ductility factor. Finally, the experimental results provided the opportunity to review some of the most commonly adopted assumptions in the interpretation of diagonal compression tests.

## 2. Experimental Program

- Specimen M1-90: one strap per loop along the directions of the mortar head and bed joints (Figure 8a);
- Specimen M1-45: one strap per loop along the directions forming $\pm 45\xb0$ angles with the mortar head and bed joints (Figure 8b), that is, along the compressed and tensioned directions (Appendix A);

#### 2.1. Material Properties

#### 2.1.1. Bricks

#### 2.1.2. Mortar

#### 2.1.3. Stainless Steel Straps and Seals

^{®}system. Table 4 displays the mechanical properties declared by the manufacturer (Mauser) for the rolls of stainless steel straps.

^{®}-system-like reinforcements [29,30], one of the objectives of the experimental program was to verify how the sealing affects the strength and stiffness of the strapping system. Four specimens measuring 360 × 0.9 × 16 mm each were used for determining the tensile strength of clamped and unclamped straps:

- Specimen L2 consisted of a piece of steel tape (unclamped strap);
- Specimen L3 consisted of a piece of steel tape (unclamped strap);
- Specimen S2 consisted of two pieces of steel tape, fastened together by one seal (clamped strap);
- Specimen S3 consisted of two pieces of steel tape, fastened together by two seals (clamped strap).

^{®}system is brittle [29].

#### 2.1.4. Elements for the Protection of the Edges of Masonry Walls

^{®}system uses stainless steel rounded angles and funnel plates (Figure S1), which have the task of diffusing the action transmitted by the straps to the masonry. This experimental program replaced the stainless steel protective elements of the CAM

^{®}system with the same protective elements as in [29,35,36], that is, 3D-printed elements made from a PLA (polymerized lactic acid) filament. The PLA filament is one of the most eco-friendly filaments in FDM (fused deposition modeling) 3D printing. In fact, PLA comes from annually renewable resources (cornstarch, tapioca roots, sugarcane, or other sugar-containing crops) and requires less energy to process compared to traditional (petroleum-based) plastics. The amount of carbon dioxide released during the printing process is the same as that removed by the plants used to make the filament during their life cycle. Once discarded in an exposed natural environment, an object made from PLA filament will naturally decompose.

#### 2.2. Preparation of the Specimens

#### 2.3. Instrumentation and Test Setup

- LOSENHAUSEN hydraulic load frame with a load capacity of 200 kN, for specimen M1-90;
- LOSENHAUSEN UBP hydraulic load frame with a load capacity of 600 kN, for specimens M1-45 and M2-45.

- Strain gauges produced by Tokyo Sokki Kenkyujo Co., Ltd. (Tokyo, Japan);
- Potentiometers produced by Gefran SpA (Brescia, Italy);
- Linear variable differential transformers (LVDTs) produced by Gefran SpA (Brescia, Italy).

- ${u}_{2}$ is the displacement acquired by LVDT2 (positive values are downward displacements);
- ${u}_{3}$ is the displacement acquired by LVDT3 (positive values are downward displacements);
- ${d}_{23}$ is the distance between LVDT2 and LVDT3.

- ${u}_{1}$ is the displacement acquired by LVDT1 (positive values are downward displacements);
- ${d}_{12}$ is the distance between LVDT1 and LVDT2.

## 3. Failure Mode of the Specimens

#### 3.1. Specimen M1-90

#### 3.2. Specimen M1-45

#### 3.3. Specimen M2-45

- No primary cracks opened along the compressed diagonal;
- The maximum load ($202\mathrm{kN}$) increased by 30% compared to the maximum load of specimen M1-45 ($155\mathrm{kN}$);
- The high load values and the lack of cracks along the compressed diagonal meant that the failure occurred due to a combination of the punching effect of the load heads and boundary effects (Figure 27).

## 4. Analysis of the Results

- ${\left|P\right|}_{max}$ is the absolute value of the diagonal compression load, $P$, at collapse;
- ${A}_{n}$ is the net transversal area of the specimen.

^{®}system and the diagonal compression test on wallettes strengthened with other surface strengthening systems, such as FRCM (fiber-reinforced cementitious matrix) materials. In the latter case, in fact, the shear strength is the sum of two contributions [63]: the shear strength of the un-strengthened wallette—related to the diagonal tensile strength of masonry, ${f}_{dt}$ [64,65]—and the in-plane contribution of the FRCM reinforcement in terms of shear force [41,66].

#### 4.1. Shear Stress/Shear Strain Curves

- $\Delta V$ is the shortening in the direction parallel to loading (vertical direction);
- $\Delta H$ is the extension in the direction perpendicular to loading (horizontal direction);
- $g$ is the gage length in the direction parallel to loading (the gage length for the identification of $\Delta V$ must be equal to the gage length for the identification of $\Delta H$ [42]).

#### 4.1.1. Contribution of the Arrangement of the Straps to the Maximum Shear Stress

- As assumed in Section 1.2, the rectangular arrangement with straps parallel to the mortar joints (in both directions) is labile. In fact, after a short horizontal plateau at the maximum shear stress (Figure 30), specimen M1-90 undergoes a brittle failure. This means that the straps crossing the failure planes are unable to counteract the relative displacements activated by the failure process along the slip planes. Due to the forces acting orthogonally to their direction, these straps rotate around the hinged nodes of the CAM-like system, which activates the free nodal displacements of the unbraced scheme shown in Figure 3a. Consequently, the rectangular strengthening system with straps arranged along the mortar joints is ineffective in terms of increasing the maximum load. However, it is not entirely useless: keeping the various parts that make up the masonry wall together even after the activation of the slip planes prevents the debris from falling. In fact, the steel straps do not break at the maximum load. This allows them to act as a debris containment garrison, similar to rock-fall nets on rocky slopes. Furthermore, the box-type behavior created by the continuous strengthening system in a building (Figure S3) protects individual structural elements from out-of-plane overturning and prevents the entire structure from collapsing. Therefore, each structural element undergoes limited horizontal displacements after failure, which allows us to define a pseudo-ductility even for the building that has exceeded the shear strength. This makes the strap arrangement of specimen M1-90 a very useful tool for the (preventive) safety of the structures and, ultimately, for safeguarding the safety of the inhabitants. As a final remark, since specimen M1-90 deviates only slightly from linearity up to the maximum shear stress, it seems reasonable that the straps have no effect on the pre-peak behavior of specimen M1-90. Thus, the maximum shear stress of specimen M1-90 is, to a good approximation, the URM maximum shear stress.
- A $\pm 45\xb0$ rotation of the straps allows the rectangular arrangement to find equilibrium while remaining a labile configuration. The curves of specimens M1-45 and M2-45 in Figure 29 testify to the effectiveness of the $\pm 45\xb0$ arrangement, since they continue well beyond the first peak, caused by the initiation of the crisis in the masonry. This greatly increases the pseudo-ductility of the strengthened masonry wall (Section 4.4). The activation of the strengthening system allowed by the $\pm 45\xb0$ rotation of the straps therefore transforms the failure of the specimen from brittle to markedly ductile. The continuation of the curves beyond the peak of the first crack (first peak) is possible as the $\pm 45\xb0$ arrangement of the straps is labile but balanced, and therefore effective, given the particular load condition. Figure 31 provides an explanation in the Mohr plane of the effectiveness of the $\pm 45\xb0$ arrangement for an actual case of masonry subjected to horizontal (seismic) loading, using the pole method (Appendix A).

^{®}system. In particular, Figure 31a shows the actual loading condition—under horizontal seismic loading—that the diagonal compression test aims to simulate. The stress state at the center of gravity, $A$, of Figure 31a is a pure shear stress state (as assumed by the ASTM guidelines), much more similar to that produced at $A$ by the shear test than by the diagonal compression test. Therefore, the center of the Mohr circle for the actual load is at the origin of the Mohr plane (Figure 31b). As explained in Appendix A, however, the location of the center has no effect on the principal directions found with the RILEM and ASTM guidelines. Furthermore, the axes of Figure 31a make 45° angles with the axes of Figure A4a ($x$ and $y$ are parallel to the horizontal and vertical mortar joints, respectively, in both figures). This does not change the positions of the ${Q}_{x}^{\prime}$ and ${Q}_{y}^{\prime}$ stress points of Figure A4b, but moves the Mohr pole, ${Q}^{*}$, at the point of coordinates $\left(0,{\tau}_{yx}\right)$ (Figure 31b).

^{®}system compared to other strap arrangements.

#### 4.1.2. Contribution of the Number of Straps to the Maximum Shear Stress

^{®}system). The ultimate shear strain of specimen M1-45 is, in fact, about 81 times the ultimate shear strain of specimen M1-90 (Table 5). Furthermore, the action of the tensioned straps after the first peak ensures that the specimen has a residual shear load-bearing capacity, with a residual shear stress value of about $0.886\mathrm{MPa}$ (Figure 29, Table 5). This value is equal to about 63% of the maximum shear stress and 60% of the URM maximum shear stress (Table 5). The residual shear stress value remains nearly constant until the end of the test, which provides the specimen with a long pseudo-plastic branch after the activation of the slip planes in the masonry.

^{®}system. Since the continuity of the strengthening system contributes to decreasing the values of the horizontal displacements, we can conclude that even a single strap per loop is useful to increase the seismic resistance beyond the shear strength capacity of the masonry.

^{®}system with the traditional rectangular arrangement (specimen M1-90) increases ductility but not strength, bringing the structure to point (a) along the horizontal path in Figure 33. The $\pm 45\xb0$ orientation of the straps in the rectangular arrangement does not change this behavior as long as the number of straps per loop is low (specimen M1-45). However, it is possible to improve both ductility and strength by increasing the number of straps per loop in the $\pm 45\xb0$ arrangement (specimen M2-45). This makes the CAM

^{®}system a strengthening system capable of increasing both ductility and strength, which brings the structure to point (c) in Figure 33.

^{®}system and the early appearance of both the damage and the first crack confirms the findings of Reference [11], where this phenomenon finds a theoretical explanation in the Mohr plane.

#### 4.2. Stress/Strain Curves

- $E$ is the Young’s modulus;
- $\mathrm{G}$ is the shear modulus, defined by Equation (10).

- The stresses given by the principal stresses, ${\sigma}_{I}$ and ${\sigma}_{II}$, in the RILEM interpretation of the diagonal compression test (Equation (A24));
- The strains, ${\epsilon}_{h}$ and ${\epsilon}_{v}$, obtained as the ratios of the relative displacements between the ends of the horizontal and vertical potentiometers (Section 2.3) to the initial lengths of the potentiometers:

- The 0.3 ratio of the estimated diagonal tensile strength, ${f}_{dt}$:$${f}_{dt}={\sigma}_{{I}_{max}}=-{\sigma}^{*}{}_{{I}_{min}},$$$${f}_{dc}=-{\sigma}_{I{I}_{min}}={\sigma}^{*}{}_{I{I}_{max}},$$
- Since specimen M1-90 behaves like a URM specimen, the different values assumed by the initial slopes in the two opposite quadrants of Figure 34 would indicate that the tensile stiffness of the URMs is different from the compressive stiffness. In fact, even the difference between these slopes is too large to depend only on the approximations introduced. This would mean that there is no single Young’s modulus in tension and compression in the URMs, which is physically unacceptable. In particular, Figure 34 shows an estimated Young’s modulus in compression, ${E}_{c}$, that is significantly lower than the estimated Young’s modulus in tension, ${E}_{t}$ (Table 6).
- The details in Figure 35b and Figure 36b show that ${E}_{t}$ and ${E}_{c}$ take on different values in both specimen M1-45 and specimen M2-45 (Table 6), which is not evident from Figure 35a and Figure 36a. However, although it is reasonable to think that the straps modify the stiffness along the first principal stress direction, the inconsistencies that emerged regarding the discussion on the values of ${E}_{t}$ and ${E}_{c}$ for specimen M1-90 do not allow us to reach definitive conclusions on the elastic moduli for the RMs.

^{®}system with other uniaxially aligned reinforcement systems. Even the latter, in fact, lead to the anisotropy of strength and Young’s modulus [73].

#### 4.3. Poisson’s Ratio and Apparent Poisson’s Ratio

- Since the strengthening system of specimen M1-90 is labile (Section 4.1.1), the value $\mathsf{\nu}=0.130$ in Table 7 represents the URM Poisson’s ratio. This value is about 52% of the assumption $\mathsf{\nu}=0.25$, usually made to identify the Young’s modulus from the shear modulus with Equation (13). This constitutes a well-founded reason for uncertainty regarding the values of Young’s modulus obtained in the literature from the use of Equation (13) with $\mathsf{\nu}=0.25$, which leads to an overestimation of Young’s modulus equal to about 11%.
- The Poisson ratios of the specimens with effective strengthening (specimens M1-45 and M2-45) are lower than the Poisson ratio of the specimen with ineffective strengthening (specimen M1-90) and the difference is greater the greater the number of straps. The reason for this is twofold: the possible crushing of the walls of the micro-cavities during the pre-tensioning operations and the confining action of the straps arranged along the direction of the maximum principal stress (horizontal straps), which decreases the value of ${\mathsf{\epsilon}}_{\mathrm{h}}$. The decrease in Poisson’s ratio in RMs compared to URMs makes the use of Equation (13)—together with the hypothesis $\nu =0.25$—even more unacceptable in RMs than in URMs. In fact, the overestimations of Young’s modulus for specimen M1-45 and specimen M2-45 would be about 14% and 16%, respectively.

#### 4.4. Pseudo-Ductility

- The shear strain at the ultimate point of the shear stress–shear strain curve [69];
- The shear strain at the peak point of the shear stress–shear strain curve [77];
- The shear strain at the point on the descending branch of the shear stress–shear strain curve where the shear stress is 50% of the maximum shear stress, ${\tau}_{max}$ [79].

^{®}system to avoid the collapse of the structural element even for a high degree of damage (Section 4.1.1), it seems reasonable to assume that the value of ${\gamma}_{u}$ for the tests performed in this work is the shear strain at the ultimate point of the shear stress–shear strain curve.

- Where the tangent at the origin intersects the horizontal tangent at the peak point of the curve [77];
- Where the area under the experimental curve is equal to the area under the bilinear elastoplastic approximating relationship [68];
- Where [84]:
- the shear stress is 85% of the maximum shear stress, ${\tau}_{max}$, if:$${\gamma}_{u}^{2}\le \frac{2A}{{k}_{e}},$$
- the shear strain takes on the value:$${\gamma}_{y}={\gamma}_{u}-\sqrt{{\gamma}_{u}^{2}-\frac{2A}{{k}_{e}}}if{\gamma}_{u}^{2}\frac{2A}{{k}_{e}};$$

#### 4.5. Comparisons

- The residual shear stress at the end of the test (${\widehat{\tau}}_{u}$);
- The ultimate shear strain (${\widehat{\gamma}}_{u}$);
- The maximum shear stress (${\widehat{\tau}}_{max}$);
- The Poisson ratio ($\widehat{\nu}$);
- The shear stress at yielding (${\widehat{\tau}}_{y}$);
- The shear strain at yielding (${\widehat{\gamma}}_{y}$);
- The pseudo-ductility factor ($\widehat{\mu}$).

- The larger area covered by specimens M1-45 (Figure 41b) and M2-45 (Figure 41c) compared to specimen M1-90 (Figure 41a) along the axes of the variables $\widehat{\mu}$, ${\widehat{\tau}}_{u}$, ${\widehat{\gamma}}_{u}$, and ${\widehat{\tau}}_{max}$ is a measure of the increase in both shear strength and ductility, a specific feature of the CAM
^{®}system. Of particular relevance are the values along the ${\widehat{\tau}}_{u}$ axis. In fact, since in specimen M1-90 ${\widehat{\tau}}_{u}=0$, the strengthening gives the masonry walls a characteristic that the masonry does not possess, that is, the ability to withstand shear stresses even for large values of the shear strains, without ever reaching an actual failure. Therefore, the strengthening not only significantly increases the low values of some variables in the ultimate state, such as ${\widehat{\gamma}}_{u}$ and $\widehat{\mu}$, but also gives the masonry walls completely new characteristics. - The smaller area covered by specimens M1-45 (Figure 41b) and M2-45 (Figure 41c) compared to specimen M1-90 (Figure 41a) along the ${\widehat{\tau}}_{y}$ and ${\widehat{\gamma}}_{y}$ axes does not in itself have a negative meaning. It simply indicates that damage occurs earlier in RMs than in URMs, but this has no negative effect on the overall behavior at the ultimate state (governed by the variables $\widehat{\mu}$, ${\widehat{\tau}}_{u}$, and ${\widehat{\gamma}}_{u}$) and the shear strength (governed by the variable ${\widehat{\tau}}_{max}$).
- The variation in the values of $\widehat{\nu}$ indicates that the strengthening technique decreases the Poisson ratio, which requires evaluation of the single test setup.

## 5. Conclusions

- The straps parallel to the mortar joints (one strap per loop) provide no increase in either shear strength or ductility. However, they are helpful in preventing falling debris, which is a major cause of injury.
- The straps forming $\pm 45\xb0$ angles with the mortar joints (one strap per loop) do not increase the maximum shear stress but provide the masonry wall with the ability to withstand large shear strains without losing shear-bearing capacity.
- By increasing the number of straps per loop in the $\pm 45\xb0$ arrangement, both the maximum shear stress and the ductility increase. This means that the CAM
^{®}system is a strengthening system capable of increasing both ductility and shear strength.

^{®}system with a rectangular arrangement. Precisely the predictability of these results is indeed the main motivation of this work. Besides the expected results, however, the analysis of the experimental results performed in the Mohr plane and the concept of apparent Poisson’s ratio—introduced in previous works—provided some unexpected findings on the mechanical properties of both URMs and RMs. As far as the mechanical properties of the URMs are concerned:

- The static analysis performed in the Mohr plane according to the RILEM interpretation of the diagonal compression test leads to stress/strain curves that are not consistent with the experimental evidence, for the values assumed by both the ${f}_{dt}/{f}_{dc}$ ratio and the ${E}_{t}/{E}_{c}$ ratio. The reason for this seems to lie in the underestimation of the hydrostatic stress at the center of the specimen by the RILEM approach. Therefore, the interpretation of the diagonal compression test needs a more accurate analysis in the Mohr plane.
- The Poisson ratio, $\nu $, is much smaller than $0.25$, which is the value usually taken as a reference in interpreting the experimental results of masonry walls. The experimental program provided the value $\nu =0.13$, which is about 52% of the conventional value $\nu =0.25$.
- In the context of linear elasticity for homogeneous and isotropic materials, the usual overestimation of the Poisson ratio leads to an overestimation of Young’s modulus of about 11%, which gives rise to a well-founded doubt regarding the values of Young’s moduli obtained in the literature from diagonal compression tests.
- The apparent Poisson’s ratio decreases for low values of the applied load and increases for high values of the applied load. The reason for the initial decreasing behavior could be the presence of micro-cavities that collapse during the early stages of the load test.

^{®}system.

- The use of CAM-like strengthening systems anticipates the onset of damage and shortens the length of the initial linear branch.
- The value of $\nu $ depends on the percentage of reinforcement. In particular, the greater the percentage of reinforcement, the lower the value of $\nu $. This makes it impossible to use a single value for the Poisson ratio in RMs, which is in any case lower than that in URMs.
- Being a greater overestimation in RMs than in URMS, the value of 0.25 usually assumed for the Poisson ratio leads to even greater overestimations of Young’s modulus.
- The trend of the apparent Poisson’s ratio is different from the trend of the apparent Poisson’s ratio in diagonal compression tests performed on URMs since it gives rise to a monotonically non-decreasing function. This could be a consequence of the pre-tensioning of the straps, in particular of those arranged along the direction of the load. In fact, the pre-tension could cause the collapse of the micro-cavities before the start of the load test, which would eliminate the initial decreasing branch in the law of the apparent Poisson’s ratio.
- The experimental program provided evidence of a possible anisotropy caused by the use of straps in CAM-like strengthening systems.

## 6. Future Developments

^{®}system. Despite the ecological motivation underlying the use of PLA in this research, in future experiments, it will therefore be desirable to use steel elements, which will allow exploiting the full potential of the strengthening system. In addition to steel funnel elements such as those patented with the CAM

^{®}system, toroidal elements similar to those used in Reference [35] may be suitable for the purpose.

## Supplementary Materials

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Some Insights into the Interpretation of the Diagonal Compression Test

- P is the diagonal compression load applied during the test;
- α is the angle between the direction of loading and the horizontal mortar joints (bed joints);
- A is the center of gravity of the wall specimen and origin of the local reference frame;
- x and y are the axes (of the local reference frame of origin A) parallel, respectively, to the horizontal mortar joints (bed joints) and to the vertical mortar joints (head joints);
- σ
_{x}is the normal stress acting—in the x direction—on the planes of the infinitesimal neighborhood of A that are perpendicular to the x-axis; - σ
_{y}is the normal stress acting—in the y direction—on the planes of the infinitesimal neighborhood of A that are perpendicular to the y-axis; - τ
_{xy}is the shear stress—directed along the y-axis—acting on the planes of the infinitesimal neighborhood of A that are perpendicular to the x-axis (the x index designates the unit normal vector to the coordinate plane on which the shear stress acts, the y index identifies the coordinate direction along which the shear stress acts).

**Figure A1.**Normal and shear stresses in the infinitesimal neighborhood of point A, the center of gravity of the wall specimen.

**Figure A2.**Stress state for the infinitesimal neighborhood of point A: (

**a**) in the reference frame of Figure A1; (

**b**) in the modified Mohr plane, according to the ASTM and RILEM interpretations of the diagonal compression test.

**Figure A3.**Stress components acting on the plane with unit normal vector

**n**(the plane perpendicular to the outward-pointing line n) in the reference frame of Figure A1: (

**a**) for normal and shear stresses that are positive in the Mohr plane; (

**b**) for normal and shear stresses that are negative in the Mohr plane.

**Figure A4.**The pole method for the identification of the stress components in the infinitesimal neighborhood of point A: (

**a**) reference frame of Figure A1 for the association between planes with unit normal vector $n$ and points ${Q}_{n}^{\prime}$ of the Mohr plane; (

**b**) application of the method in the ASTM and RILEM interpretations of the diagonal compression test.

- The straight line connecting the Mohr pole with the stress point of coordinates $\left(0,{\tau}_{d0}\right)$ is not inclined by $-45\xb0$. Due to the Mohr pole property, this means that the stress point $\left(0,{\tau}_{d0}\right)$ does not provide the stress state acting on the bed joint passing through point A.
- Even if the straight line connecting the Mohr pole with the stress point $\left(0,{\tau}_{d0}\right)$ was at $-45\xb0$, the non-homogeneous stress state inside the specimen does not allow us to apply the results found for the neighborhood of A to other points and their neighborhoods. Thus, the stress state at the center of gravity A cannot provide information on the shear force applied to the upper and lower faces of the specimen.

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**Figure 1.**Stress transfer mechanism from the three-dimensional net of stainless steel loops placed in tension to the volume units of the masonry wall [11].

**Figure 2.**How a seismic event loads a wall (being oscillatory in nature, the seismic action acts, in an alternating manner, both in the direction of the load schematized as the action of a man on the wall, and in the opposite direction): (

**a**) in the plane of the wall (shear loading in the midplane); (

**b**) along the direction perpendicular to the plane of the wall (out-of-plane loading).

**Figure 3.**Lability of the CAM

^{®}system with a rectangular arrangement: (

**a**) in the wall plane, according to the simplified mechanical model of an unbraced rectangular frame structure with hinged nodes and load oriented as the red arrow; (

**b**) in the wall thickness, as represented by the orange element of the axonometric view (without the masonry blocks, to better appreciate the three-dimensional arrangement of the straps).

**Figure 4.**Bracing of a rectangle made of hinged strips: (

**a**) by adding a strip along a diagonal, which will prevent the rectangle from collapsing in the direction of the red arrow but not in the opposite direction; (

**b**) by adding strips along both diagonals, which will prevent the rectangle from collapsing in either direction.

**Figure 5.**Constraint conditions in the shear-compression test (shear load directed towards the left).

**Figure 6.**Vertical stresses and deformed configuration in a masonry wallette subjected to shear-compression testing [39] (shear load directed towards the left).

**Figure 7.**Geometric characteristics of the single-headed masonry specimens (all dimensions in mm): (

**a**) side view; (

**b**) front view.

**Figure 8.**The three specimens of the experimental program: (

**a**) specimen M1-90; (

**b**) specimen M1-45; and (

**c**) specimen M2-45.

**Figure 9.**Appearance of the specimen PC2: (

**a**) before the compression test and (

**b**) after the compression test.

**Figure 10.**Mechanical characterization of the mortar according to the UNI EN 1015-11:2019 standard: (

**a**) setup of the three-point bending flexural test (dimensions in mm); (

**b**) uniaxial compression test on one of the two half-prisms originating from the flexural test.

**Figure 11.**The elements of the active strengthening system: (

**a**) a stainless steel strap closed to form a ring (before tightening the seal); (

**b**) a stainless steel seal used for the strap ring closure.

**Figure 12.**Stress/strain diagrams of the four specimens for the mechanical characterization of the straps.

**Figure 14.**Failure modes of the clamped specimens: slipping out of the seal of one of the two fastened ends in (

**a**) specimen S2 and (

**b**) specimen S3.

**Figure 15.**Three-dimensional printed elements for the protection of (

**a**) the edges of the walls (rounded angles) and (

**b**) the new edges generated by the perforations for the passage of the straps (funnel plates).

**Figure 16.**The 3D-printed elements applied with mortar on the specimens: (

**a**) rounded angles; (

**b**) funnel plates.

**Figure 17.**Preparatory stages for laying bricks: (

**a**) core drilling of a brick; (

**b**) drying of bricks after core drilling.

**Figure 22.**Rotations undergone by specimen M1-45: positive values indicate anti-clockwise rotations on the front face and on the vertical cross-section, seen from the left side.

**Figure 23.**Rotations undergone by specimen M2-45: positive values indicate anti-clockwise rotations on the front face and on the vertical cross-section, seen from the left side.

**Figure 25.**Details of the broken funnel plates: (

**a**) funnel plate in the upper left corner of the mechanism; (

**b**) funnel plate in the lower right corner of the mechanism.

**Figure 26.**The failure mode of specimen M1-45: (

**a**) appearance of the specimen after its removal from the testing machine; (

**b**) detail of the crack along the compressed diagonal.

**Figure 28.**Shear stress/shear strain curves for specimen M1-90, according to ASTM and RILEM interpretations of the diagonal compression test.

**Figure 30.**Detail of Figure 29 for shear strain values between 0 and 0.001.

**Figure 31.**Straps activated by a seismic load: (

**a**) in the plane of the wall; (

**b**) as explained by the stress analysis performed in the Mohr plane for the infinitesimal neighborhood of point $A$.

**Figure 32.**Stress analysis performed in the Mohr plane for the infinitesimal neighborhood of point $A$ when the direction of the seismic load reverses.

**Figure 33.**Seismic retrofitting provided by different types of strengthening systems, which increase ductility but not strength (point a); increase strength but not ductility (point b); increase both strength and ductility (point c).

**Figure 35.**Uniaxial stress/strain relationships of specimen M1-45: (

**a**) until the end of the loading test; (

**b**) truncated, to highlight the difference in slope at the origin in the two quadrants.

**Figure 36.**Uniaxial stress/strain relationships of specimen M2-45: (

**a**) until the end of the loading test; (

**b**) truncated, to highlight the difference in slope at the origin in the two quadrants.

Specimen | Compressive Strength (MPa) | Normalized Compressive Strength (MPa) |
---|---|---|

PA1 | 36.43 | 30.96 |

PA2 | 36.18 | 30.75 |

PB1 | 35.30 | 30.01 |

PB2 | 33.27 | 28.28 |

PC1 | 37.87 | 32.19 |

PC2 | 38.31 | 32.57 |

Technical Characteristic | Value |
---|---|

Maximum grain size [46] | $3\mathrm{mm}$ |

Compressive strength—after 28 days [47] | $\ge 5.0\mathrm{MPa}$ |

Flexural strength—after 28 days [47] | $\ge 2.0\mathrm{MPa}$ |

Reaction to fire [48] | Euroclass A1: Non-combustible |

Shrinkage rate | $-0.4\mathrm{mm}/\mathrm{m}$ |

Bulk of hardened product | $1900\mathrm{kg}/{\mathrm{m}}^{3}$ |

Water vapor permeability coefficient [49] | $\mu <15/35$ |

Cement content by weight | $11\%$ |

Lime content by weight | $3\%$ |

Aggregate content by weight | $86\%$ |

Thermal conductivity [50] | $0.76\mathrm{W}/\mathrm{mK}$ |

Water absorption [51] | $W0\left(0.5\mathrm{kg}/{\mathrm{m}}^{2}{\mathrm{min}}^{1/2}\right)$ |

Hazardousness [52] | Eye Dam. 1, H318: Causes serious eye damage Skin Irrit. 2, H315: Causes skin irritation Skin Sens. 1, H317: May cause an allergic skin reaction |

Specimen | Flexural Strength (MPa) | Broken Half-Specimen | Compressive Strength (MPa) |
---|---|---|---|

P1 | 2.74 | P1A | 9.28 |

P1B | 9.93 | ||

P2 | 2.85 | P2A | 9.56 |

P2B | 9.50 | ||

P3 | 3.22 | P3A | 9.72 |

P3B | 9.59 | ||

P4 | 2.10 | P4A | 7.06 |

P4B | 6.83 | ||

P5 | 2.29 | P5A | 6.72 |

P5B | 6.96 | ||

P6 | 2.29 | P6A | 7.58 |

P6B | 7.03 |

Mechanical Property | Value |
---|---|

Yield strength $\left({f}_{yk}\right)$ | $240\mathrm{MPa}$ |

Breaking strength $\left({f}_{tk}\right)$ | $540\mathrm{MPa}$ |

Elongation at break (also called fracture strain, or tensile elongation at break) | $20\%$ |

Specimen | Shear Stress at the End of the Linear Range (MPa) | Shear Stress of First Peak (MPa) | Maximum Shear Stress (MPa) | Residual Shear Stress (MPa) | Shear Strain at the End of the Test (mm/mm) |
---|---|---|---|---|---|

M1-90 | 1.118 | 1.465 | 1.465 | / | 0.00047 |

M1-45 | 1.044 | 1.423 | 1.423 | 0.886 | 0.03806 |

M2-45 | 0.545 | 0.985 | 1.850 | 0.959 | 0.06469 |

Specimen | ${\mathit{E}}_{\mathit{c}}$ (MPa) | ${\mathit{E}}_{\mathit{t}}$ (MPa) | ${\mathit{E}}_{\mathit{t}}/{\mathit{E}}_{\mathit{c}}$ |
---|---|---|---|

M1-90 | 9551 | 22,676 | 2.37 |

M1-45 | 7385 | 23,375 | 3.17 |

M2-45 | 8080 | 31,496 | 3.90 |

Specimen | ν |
---|---|

M1-90 | 0.130 |

M1-45 | 0.098 |

M2-45 | 0.079 |

Specimen | ${\mathit{\gamma}}_{\mathit{u}}$ * (mm/mm) | ${\mathit{\nu}}_{\mathit{y}}$ | ${\mathit{\tau}}_{\mathit{y}}$ (MPa) | ${\mathit{\tau}}_{\mathit{y}}/{\mathit{\tau}}_{\mathit{m}\mathit{a}\mathit{x}}$ (%) | ${\mathit{\gamma}}_{\mathit{y}}$ (mm/mm) | $\mathit{\mu}$ |
---|---|---|---|---|---|---|

M1-90 | 0.00047 | 0.214 | 1.453 | 99 | 0.00035 | 1.34 |

M1-45 | 0.03806 | 0.210 | 1.369 | 96 | 0.00038 | 99.82 |

M2-45 | 0.06469 | 0.084 | 0.613 | 33 | 0.00013 | 513.97 |

_{u}and γ

_{y}.

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Ferretti, E.
Active Confinement of Masonry Walls with Stainless Steel Straps: The Effect of Strap Arrangement on the in-Plane Behavior of Strength, Poisson’s Ratio, and Pseudo-Ductility. *Buildings* **2023**, *13*, 3027.
https://doi.org/10.3390/buildings13123027

**AMA Style**

Ferretti E.
Active Confinement of Masonry Walls with Stainless Steel Straps: The Effect of Strap Arrangement on the in-Plane Behavior of Strength, Poisson’s Ratio, and Pseudo-Ductility. *Buildings*. 2023; 13(12):3027.
https://doi.org/10.3390/buildings13123027

**Chicago/Turabian Style**

Ferretti, Elena.
2023. "Active Confinement of Masonry Walls with Stainless Steel Straps: The Effect of Strap Arrangement on the in-Plane Behavior of Strength, Poisson’s Ratio, and Pseudo-Ductility" *Buildings* 13, no. 12: 3027.
https://doi.org/10.3390/buildings13123027