# Research on the Influence of Bed Joint Reinforcement on Strength and Deformability of Masonry Shear Walls

## Abstract

**:**

## 1. Introduction

## 2. Research Programme

- to use the most common materials in Poland to erect masonry structures,
- to use the minimum amount of reinforcement,
- to use squat walls with an h/l ratio close to real structures,
- to build a unique test stand to perform tests on shearing and compression at the same time in a partially fixed static scheme.

- ceramic solid brick (CB), calcium-silicate masonry units (Ca-Si) from group I, and AAC masonry units from 600 density class,
- cement-lime mortar with a cement:lime:sand ratio of 1:1:6 to make CB walls and the system mortar for thin joints for Ca-Si and AAC walls,
- two types of reinforcement for bed joints in walls made of solid brick: smooth rebars with a diameter of 6 mm and made of stainless steel and structural reinforcement in the form of steel, galvanized trusses, in which the strips were made of steel rebars with a diameter of 5 mm and the struts were made of rebars with a diameter of 3.75 mm as in Figure 1a,
- plastic meshes and steel trusses for thin joints as in Figure 1b.

^{®}RND/Z/200 (NV Bekaert SA, Zwevegem, Belgium). Those types of reinforcement were selected due to practical reasons. The reinforcement in the form of unbounded rebars, although not recommended by the standard [33], is the simplest type of reinforcement most commonly used for strengthening cracked walls. Moreover, that type of reinforcement was unlikely to cause any negative effects according to a few tests taken on walls, including horizontal shear walls [17,29]. One of currently recommended by the standard [33] types of structural reinforcement—welded trusses—was accepted for tests. The reinforcement in the form of steel trusses of type MURFOR

^{®}EFS/Z/140 intended for thin joints was used in models made of silicate masonry units. Steel trusses were composed of two stripes made of steel flat bars (8 × 1.5 mm) joined with diagonal struts with a diameter of 1.5 mm. Plastic meshes towards the wall length were composed of weft fibres, and that towards the wall thickness were composed of warp fibres. A waft comprised two strands; each of them had a cross section similar to a circle having a diameter of 0.3 mm, whereas a weft was formed from a single strand with a cross section similar to a rectangle with dimensions of 1.5 mm × 0.22 mm. Percentage contents of the reinforcement in brick models were ρ = 0.05% and ρ = 0.1% and in walls made of silicate and AAC masonry units was ρ = 0.07%. In the case of solid brick walls, the proportions of the wall dimensions were h/l ≈ 0.84, and for walls made of calcium silicate and AAC masonry units, those proportions were h/l ≈ 0.55.

#### 2.1. Masonry Walls Made of Clay Brick

_{b}= 28.8 N/mm

^{2}(acc. to PN-EN 772-1 [34]) with cement–lime mortar having compressive strength f

_{m}= 9.67 N/mm

^{2}(acc. to EN 1015-11:2001 [35]). Average compressive strength of masonry determined according to EN 1052-1 [36] was f

_{c,m}= 8.17 N/mm

^{2}, and the modulus of elasticity was E

_{cm}= 3110 N/mm

^{2}according to Reference [36]. The initial shear value determined according to PN-EN 1052-3 [37] was f

_{v,o}= 0.452 N/mm

^{2}. The average yield strength of smooth stainless-steel bars was f

_{y}= 592 N/mm

^{2}and of strips and struts in steel trusses were f

_{y}= 701 N/mm

^{2}(strips of 5 mm diameter) and f

_{y}= 625 N/mm

^{2}(bracking of 3.75 mm diameter), respectively.

#### 2.2. Masonry Walls Made of Calcium-Silicate (Ca-Si) Masonry Units

_{b}= 17.7 N/mm

^{2}(acc. to the standard [34]) with system mortar for thin joints having compressive strength f

_{m}= 18.20 N/mm

^{2}(acc. to the standard [35]). Head joints were not filled in models. The compressive strength of masonry determined according to the standard [36] was f

_{c,mv}= 11.3 N/mm

^{2}, and the modulus of elasticity was E

_{cm}= 7833 N/mm

^{2}. The initial shear value determined according to the standard [37] was f

_{v,o}= 0.70 N/mm

^{2}. The average yield strengths of strips and struts in steel trusses were f

_{y}= 685 N/mm

^{2}(flat bars 1.5 × 8 mm) and f

_{y}= 821 N/mm

^{2}(bracking of 1.5 mm diameter), respectively.

#### 2.3. Masonry Walls Made of Autoclaved Aerated Concrete (AAC) Masonry Units

_{b}= 3.65 N/mm

^{2}[34] with system mortar for thin joints having compressive strength f

_{m}= 6.10 N/mm

^{2}[35]. Head joints were not filled in models. The compressive strength of masonry was f

_{c,mv}= 2.97 N/mm

^{2}[36], and the modulus of elasticity was E

_{cm}= 2041 N/mm

^{2}. The initial shear value was f

_{vo}= 0.31 N/mm

^{2}[37]. Models were reinforced with steel trusses and plastic meshes having the same parameters as in the calcium silicate masonry units.

## 3. Test Stand and Testing Technique

_{c}. Both columns differed in shape and the method of fixing to the laboratory strong floor. Column 5 had a closed box section (2 × I 500), rigidly fixed with four screws (ø65 mm). Actuator 8 with the force of 3000 kN was fixed to the upper part of the column in a way ensuring the smooth change of its position. At the bottom part, there was a horizontally articulated support for spandrel beam 3. Two steel knee braces 11 were articulated with the column and the resistor fixed to the strong floor. Knee braces were used to neutralise the effect of column bending. Column 4 had a two-branch section (2 × [260). Their branches were joined in the upper part with a lacing, and in the bottom part, they were welded to the slab of the laboratory strong floor with two screws (ø65 mm). The openings were made in the column branches to stabilize the movable horizontal “crossbar” 10 (2 × I 300) using the vertical support (with the dynamometer). Horizontal spandrel beams 2, 3, and 7 also had different shapes and purposes. Spandrel beams 2 and 3 had closed box sections. Between their stripes, bars with a diameter of 20 mm were welded across (to assure the adhesion of the monolithic concrete). During tests, the support at column 5 precluded the horizontal movement of spandrel beam 3, and its vertical movement was precluded by support 12. Spandrel beam 2 placed in the upper part of the model surface was horizontally sliding, supported vertically on the bearer in column 4. At spandrel beam edge 2, there was a cylindrical joint responsible for transmitting horizontal load from spandrel beam 7 (through the steel pin ø100 mm) to the testing unit. Branches of spandrel beam 7 were made of channels [260 and closed transversely with the system 2 × I 300. From column side 5 within the longitudinal axis of actuator 8, spandrel beam 7 was equipped with dynamometer 9 with the working range of 3000 kN, used to transmit horizontal shearing forces.

_{c}during tests, both tendons from the set were equipped with a compensation spring to minimise the impact of steel relaxation in tensioned tendons and vertical deformations of the wall. When the test stand was set, each model was tested in a sequential mode (Figure 5c). The first part of the tests consisted of exerting compressive prestress σ

_{c}(N

_{c}) on test units perpendicularly to the plane of bed joints with tendon systems. In the second part, units under compressive prestress were loaded with horizontal force H. The loading programme for all models included three cycles of loading and unloading. The load of 10 kN, that is ca. 5% of predicted failure load H

_{u}, was exerted in two first cycles. At that time, readings from measuring instruments were controlled and mobile elements of the stand were adjusted to the starting positions. In the third failure cycle, models were temporarily loaded every time until the force increase was not recorded on dynamometer 9 and, simultaneously, an increase in horizontal displacements of spandrel beams 2 and 7 was observed. Loading was changed progressively by 10 kN every 2 minute, and readings from inductive displacement transducers in dynamometers were recorded with the automatic measurement stand. Forces generated by tendon systems 6 were measured with the dynamometer Utilcell 750 with an operating capacity of 250 kN and reading accuracy of 0.1 kN, whereas the horizontal force H and support reaction R

_{A}were measured with electro-resistant dynamometers CT 300 and CT 100, having an operating capacity of 3000 kN and 1000 kN, respectively, and an accuracy of 0.5 kN. A frame structure was used to measure shear strain and deformation angles. The structure was fixed to both sides of each test model. The frame measurement system was fixed in the central part of the model made of a solid brick wall and covered the substantial area of the wall made from silicate or AAC masonry units. The measurement system was firmly fixed to the wall surface using an epoxy adhesive. The system was symmetrically fixed to both sides of the test model such that the diagonal centre of the test model corresponded to the diagonal centre of the frame system; see Figure 6. Displacements Δ

_{c}, Δ

_{f}, Δ

_{i}, Δ

_{j}, Δ

_{g}, and Δ

_{h}were measured along each of four sides (c, f, i, and j) of the test model and along two diagonals (g and h) of the frame system, using inductive converters of displacement with the accuracy of 0.002 mm. The range of indications was ± 10 mm. Changes in the lengths of sides l

_{cc}, l

_{fc}, l

_{ic}, and l

_{jc}(at the ith level of loading) and diagonals l

_{gc}and l

_{hc}and partial angles of shear strain Θ

_{j}(j = 1, 2, 3, 4), theoretically separated from the deformed measurement system, were determined.

_{j}were determined according to the law of cosines, on the basis of average changes in the length of measuring bases (Figure 6b).

_{fc}, l

_{hc}, l

_{jc}in Equation (1):

_{ic}= l + Δ

_{i}, l

_{fc}= l

_{f}

_{0}+ Δ

_{f},

l

_{jc}= l

_{j}

_{0}+ Δ

_{j}, l

_{gc}= l

_{g}

_{0}+ Δ

_{g},

l

_{cc}= l

_{c}

_{0}+ Δ

_{c}, l

_{hc}= l

_{h}

_{0}+ Δ

_{h}.

_{j}in Equation (2):

_{j}(j = 1, 2, 3, 4) determined at the ith level of loading. The assumed critical statistical value of the questioned extreme value was t

_{4,0.05}= 1.46 after four observations in the specimen and at the significance level equal to 0.05. Maximum and minimum values of shear strain angles were found from Equations (3) and (4):

_{i}is the average value of shear strain angle at the ith level of loading and S is the standard deviation determined from (Θ

_{j}) shear strain angles at the ith level of loading.

_{i}was determined as the ratio of horizontal loading H

_{i}and the horizontal area of the masonry in accordance with Equation (5):

_{i}was the ratio of the applied force H

_{i}and the corresponding horizontal displacement u

_{i}according to Equation (6):

_{cr}was determined at the time of observing first cracks, and the initial stiffness K

_{o}was determined at the initial phase of loading under stresses 0 < τ ≤ 0.05 τ

_{u}. The measured force, at which the first crack was observed in the masonry units or mortar, was considered as the cracking force

_{Hcr}. The corresponding stresses τ

_{cr}were defined as cracking stresses, and the angle Θ

_{cr}was defined as the shear strain angle at the time of cracking. The width of 0.1 mm was regarded as the minimum width of the crack, neglecting all previously observed micro-cracks. A detailed list of existing and visible cracks in the masonry units was prepared to avoid any wrong interpretations of visible cracks. The measured force, at which the model was destroyed, was considered as the destructive force H

_{u}—an increase in force was not further recorded at increasing displacements. Stresses at the top edge of the wall, corresponding to the force H

_{u}, were regarded as ultimate stresses τ

_{cr}, and the angle Θ

_{u}was regarded as the shear deformation angle.

## 4. Test Results

#### 4.1. Morphology of Cracks in Walls

#### 4.1.1. Solid Brick Walls

_{c}= 0, the loss of load capacity was observed at the interface of bricks and mortar. Places where bonded masonry units were present were also cracked. A rapid loss in load capacity was observed at a specific length of the “stepped” cracking—considerably shorter than the diagonal length—see Figure 7a. A similar type of cracks was found in shear units at σ

_{c}= 0.5 N/mm

^{2}, and units exposed to shearing at σ

_{c}= 1.0 N/mm

^{2}and 1.5 N/mm

^{2}had cracks in masonry units and mortar layers. No loss in adhesion between masonry units and mortar was observed.

_{A}and R

_{B}took place, as the result of considerable compression. No significant difference was noticed in the cracking of walls unreinforced or reinforced with bars; see Figure 7b,c. A little higher number of cracks having a width of ca. 0.1–0.3 mm was only observed in the central part of shear masonry units at σ

_{c}= 1.5 N/mm

^{2}. Prior to the failure of reinforced units, gentle drops in forces read at the dynamometer and greater width of cracks were observed. No significant changes with reference to models reinforced with bars were observed in walls reinforced with trusses; see Figure 7d,e.

#### 4.1.2. Walls Made of Silicate Masonry Units

^{2}(Figure 8c,f). An intensive cracking of masonry units and simultaneous crushing of masonry units was found in the top layer, and the reinforcement was broken in the zone of the greatest damage (Figure 8h). Instead of two diagonal cracks running from support of unreinforced walls, only one diagonal crack was observed in reinforced walls. Also, the top layers of masonry units were crushed.

#### 4.1.3. Walls Made of AAC Masonry Units

^{2}had diagonal cracks at the moment of failure. However, vertical cracks predominated at the extension of head joints in masonry units (Figure 9b).

^{2}(Figure 9c,e). In this case, diagonal cracks did not run along the whole wall diagonal. Rapid breaking of reinforcement was observed at failure (Figure 9g). In reinforced elements subjected to compressive prestress equal to 1.0 N/mm

^{2}(Figure 9c,f), cracking was much more intensive than in case of units under minimum compression. In that case, diagonal cracks were predominating and individual masonry units were crushed. Also, the breaking of reinforcements was observed (Figure 9h). The intensity of cracking in reinforced walls at the time of failure was considerably greater when compared to unreinforced walls.

#### 4.2. Effect of Reinforcement

#### 4.2.1. Solid Brick Walls

_{c}= 0, stress increased by 40% for reinforcement with bars and by 120% for reinforcement with trusses in comparison to unreinforced walls. With increasing values σ

_{c}, the impact of reinforcement was clearly weakening in comparison to unreinforced walls. Only in walls with truss reinforcement, a 40% increase in stress values was observed at both levels of the reinforcement percentage. The biggest impact of the reinforcement at the time of failure was only observed in shear units. In comparison to unreinforced units, τ

_{u,mv}increased to 100% (ρ = 0.05%) and 110% (ρ = 0.10%) in walls reinforced with trusses and to 45% (ρ = 0.05%) and 40% (ρ = 0.10%) in walls reinforced with bars. When values σ

_{c}were increasing, the reinforcement impact was decreasing proportionally. An increase of 3% (ρ = 0.05%) and 20% (ρ = 0.10%) was found in masonry units with rebars under maximum compression and of 30% in walls with truss reinforcement at both types of reinforcement percentage. The results for shear stress at the time of cracking and failure as a function of initial compressive stresses are shown in Figure 11a.

_{cr,mv}determined at the time of cracking was increasing proportionally to an increase of initial compressive stress (σ

_{c}). For reinforced walls, those values were lower than values of shear strain angle Θ

_{cr,mv}obtained for unreinforced walls. The greatest decrease in angles was found in shear units in walls reinforced with bars at σ

_{c}= 0 by 50% and in walls with truss reinforcement by 30% (ρ = 0.05%) and 40% (ρ = 0.10%). Also, shear deformation of walls determined at the time of failure Θ

_{u,mv}increased with increasing compressive stresses. When compared to unreinforced units, values of Θ

_{u,mv}determined for reinforced walls were lower at σ

_{c}= 0 by 50–60% in case of rebar reinforcement and by 40/50% in the case of truss reinforcement. At the highest values σ

_{c}= 1.5 N/mm

^{2}, shear deformations of walls with truss reinforcement were greater by 8% (ρ = 0.10%), and those of walls with bar reinforcement were greater by 17% (ρ = 0.05%) and 49% (ρ = 0.10%) when compared to unreinforced units. Figure 11b shows the comparison of shear strain angles in reinforced walls Θ

_{cr,mv}at the time of cracking and failure Θ

_{u,mv}obtained from tests on unreinforced units. Determined values of shear strain angles at the time of cracking were required for verifying SLS for structures.

_{cr, mv}determined from tests on all unit series and the acceptable value equal to Θ

_{adm}= 0.5 mrad as specified in PN-B-03002:2007 [38] for unreinforced brick masonry to determine SLS. The diagram indicates that the limit value of an angle Θ

_{adm}was lower than that determined from tests on angle values Θ

_{cr}in all reinforced walls except for shear walls. Therefore, setting values Θ

_{adm}(specified in Reference [38]) for shear walls with reinforcement (infill walls) when no relevant regulations have been introduced can lead to dangerous underestimation of width of diagonal cracks.

#### 4.2.2. Walls Made of Calcium-Silicate Masonry Units

^{2}, an increase in shear–strain angle with a small increase in shear loading (slightly inclined plate on diagrams) was observed. A further increase in horizontal loading resulted in slight strengthening of the wall. The test results are presented in Table 5.

^{2}, cracking stresses in truss-reinforced units of series HOS-Z1-S were lower by 29% compared to unreinforced units. Failure stress increased at the time of failure by 12% in the wall under minimum compression and by 18% when initial compressive stresses were the highest; see Figure 13a. For models of series HOS-Z2-S reinforced with plastic mesh, cracking stresses in units under minimum compression only was only higher by 7% than in the same units without reinforcement. An increase in cracking stress in the unit under maximum compressive stress was lower by 6% when compared to the unreinforced model. Considering a failure stress increase with reference to unreinforced units, its increase was the greatest in the model under minimum compressive stress (by 21%) and lower by 2% in the unit under maximum compressive stress; see Figure 13a.

^{2}was exerted. Shear deformation in units reinforced with truss were higher by more than 79% than in unreinforced units in the model under minimum compressive stress and lower by 10% than in the unit under maximum compressive and shear stress.

^{2}was exerted. Shear deformation of units with plastic mesh reinforcement were greater by more than 38% in the model under minimum compressive and shear stress and lower by 48% in the unit under maximum compressive and shear stress; see Figure 13b. Figure 13b shows the comparison of test results with acceptable values of shear–strain angles equal to Θ

_{adm}= 0.4 mrad. Values of shear strain angle recommended by the standard [38] turned out to be a dangerous estimation for both unreinforced walls and walls with truss and plastic mesh reinforcement.

#### 4.2.3. Walls Made of AAC Masonry Units

^{2}, no strengthening was observed after cracking (slight breaking of the line on the graph); only values of shear strain angle increased. In the unit HOS-AAC-010/1 subjected to minimum compression, some strengthening occurred after cracking—Figure 14a. Consequently, an increase in load also led to an increase in shear deformation angle. Noticeable strengthening with simultaneously smaller shear deformation was observed in the unit HOS-AAC-10/2 under maximum compression—Figure 14b. The test results are presented in Table 6.

^{2}, whereas shear stress in the compressed element did not exceed 0.50 N/mm

^{2}. With reference to similar unreinforced elements, the increases in stress values were 6% and 30%, respectively.

^{2}) and 33% (0.5 N/mm

^{2}); see Figure 15b. An increase in compressive prestress was accompanied by increasing shear strain and deformation angles in walls compressed to 0.5 N/mm

^{2}, and those values were 94% and 69%, respectively. Angles of shear strain and deformation read at the time of cracking and failure in the wall reinforced with plastic mesh under minimum initial compressive stresses were lower by 18% compared to strains in the unreinforced wall. The shear angle increased to 72% in the wall under maximum compressive stress; see Figure 15b. Figure 15b shows the comparison of test results with acceptable values of shear–strain angle equal to Θ

_{adm}= 0.4 mrad. Considering unreinforced walls, the recommended angle value proved to be the safe estimation for all walls except for the unit under minimum compressive stress. Reinforced units demonstrated a similar tendency. Assuming values specified in the standard [38] for walls under initial compressive stress proved to be a safe limitation.

## 5. Analysis on Effects of Reinforcement in Bed Joints

#### 5.1. Cracking and Ultimate Shear Stresses

_{u,z}and the stress determined in unreinforced walls τ

_{u,n}. The achieved results were presented depending on the percentage of horizontal reinforcement ρ (values in brackets express the percentage of the horizontal reinforcement-ρ).

_{m}. For mortars having f

_{m}< 3 N/mm

^{2}, the failure stress in the reinforced wall (ρ = 0.168–0.301%) made of hollow bricks (Ančić, Steinman [29]) was significantly lower than in the unreinforced wall. An increase in failure stress was observed with an increase with the mortar strength 3 N/mm

^{2}< f

_{m}< 4.5 N/mm

^{2}(units from solid brick at ρ = 0.146–0.267%) when compared to unreinforced units. Units made of hollow brick tested by Ančić, Steinman [29], which had the lowest reinforcement percentage ρ = 0.112%, were an exception. For walls made with mortar f

_{m}> 4.5 N/mm

^{2}, an increase in failure stress (at ρ = 0.168–0.187%) was definitely higher in the majority of tests, except for one model (f

_{m}= 6.0 N/mm

^{2}, ρ

_{h}= 0.079%) tested by Ernst [18] and in tests performed by Sanpaelesi and Cieni [28] (f

_{m}= 13.7 N/mm

^{2}, ρ = 0.187%), in which a slight increase was only observed. The smooth bar and truss-type reinforcement was found to have a positive effect on tested brick walls with the mortar f

_{m}= 9.67 N/mm

^{2}. A proportional increase in failure stress was observed with an increasing percentage of reinforcement. The most positive increase in the load capacity was found in tests conducted by Haach, Vasconcelos, and Lourenço [23], in which the cement mortar having the strength f

_{m}= 18.77 N/mm

^{2}was used. Considering tests on calcium silicate made of silicate masonry units with the similar mortar strength f

_{m}= 18.2 N/mm

^{2}, an increase in failure stress was not significant when compared to unreinforced units. In tests on AAC masonry units [39,40] with the mortar strength of class M5, maximum values of failure stress were lower than in unreinforced walls. Exceptions were walls with truss reinforcement, in which the mortar was doubled on support areas of masonry units. The highest increase in stress, comparable to an increase in the strength of brick masonry, was achieved for the mortar of class M10 and truss-type reinforcement.

_{m}of mortar used in tested models. Those results were close to the ones achieved at failure. In the case of mortar with the strength f

_{m}< 3.5 N/mm

^{2}, values of cracking stress were considerably lower when compared to unreinforced walls (Ančić, Steinman [29])—solid and hollow brick (at ρ = 0.146–0.301%). Considering mortar with the strength 3.5 N/mm

^{2}< f

_{m}< 4.5 N/mm

^{2}, ratios τ

_{cr,z}/τ

_{cr,n}were higher or lower than one for models made of solid brick and hollow brick (at ρ = 0.112–0.267%). An increase in cracking stress was observed only at f

_{m}> 5.0 N/mm

^{2}and ρ = 0.125–0.187% (Ančić, Steinman [29]—solid and hollow brick, and Scrivener [17]—concrete units). An increase in cracking stress determined from tests on brick walls reinforced with bars was similar as in walls with the truss-type reinforcement and doubled mortar applied on bed joints in masonry units [39,40].

_{u,z}/τ

_{u,n}and τ

_{cr,z}/τ

_{cr,n}. There were 92 test results for failures stress, in which the average ratio between failure shear stress in reinforced walls and unreinforced walls was τ

_{u,z}/τ

_{u,n}= 1.373 and the corresponding standard deviation was σ = 0.468. The probability of reinforcement negative effect, determined on the above basis, was not greater than 21%. A similar analysis was performed for stress values at the time of cracking, and the available number of test results was 87. The average ratio between failure shear stress in reinforced walls and unreinforced walls was τ

_{u,z}/τ

_{u,n}= 1.363, and the corresponding standard deviation was σ = 0.692. The probability of a negative effect of the reinforcement was greater than at the time failure and was equal to 30%.

_{u,z}/τ

_{u,n}in Equation (8):

_{u,z}/τ

_{u,n}in Equation (9):

#### 5.2. Shear Strain and Stiffness

_{o}and stiffness at the time of cracking K

_{cr}were used to obtain the in Equations (13) and (14):

## 6. Conclusions

- Initial compressive stress was the factor affecting crack morphology. In walls subjected to minimum compressive stress, there was a predominant single crack running through head and bed joints, whereas in walls subjected to maximum compressive stress, including masonry units, there were many diagonal and even vertical cracks;
- horizontal reinforcement in bed joints constrained the number of cracks;
- differences in masonry behaviour were observed at the phase close to failure as unreinforced units or the ones with plastic mesh type reinforcement were gently wearing out, and masonry with truss type reinforcement were destroyed immediately by crushing with simultaneous reinforcement breaking.

_{c}and failure τ

_{u}, the following observations were made:

- the noticeable effect of compressive stress on values of shear stress at the time of cracking and failure was confirmed;
- steel reinforcement in the form of unbonded steel bars and trusses used in the minimum quantity in solid brick walls (acc. to PN-EN 1996-1-1 [32]) ρ
_{min}= 0.1%, and lower than minimum quantity did not result in an undesirable reduction of shear stress at the time of cracking and failure; - the average increases in cracking and failure stress were 25% and 34%, respectively;
- the conducted statistical analysis of our own tests and those by other authors indicated that the reinforcement placed in bed joints increases average values of cracking and failure stress by 22% and 28%, respectively.

_{cr}and failure Θ

_{u}, the following observations were made:

- a significant impact of initial compressive stress was found in all tested series of units, and the tendency was that an increase in initial compressive stress resulted in increased angles of shear strain;
- generally, at the time of cracking, reinforcement reduced angles of shear strain by 11% on average and increased angles of shear deformation by 7% on average;
- including statistical analyses, shear–strain angles decreased by 8%, and an increase of shear deformation was equal to 18%,
- limitations of shear–strain angle, accepted in Polish design rules PN-B-03002:2007 [38], which meet SLS conditions, were found to be dangerous for unreinforced and reinforced walls made of solid brick and AAC and evidently overestimated for Ca-Si walls.

_{o}and stiffness at the time of cracking K

_{cr}, it was the following were found:

- the highest increase in the initial stiffness and stiffness at the time of cracking was observed in walls under maximum compression;
- in reinforced walls, there was a noticeable increase in the initial stiffness K
_{o}and stiffness at the time of cracking K_{cr}by 70% and 58% on average; - after taking into account statistical analyses, reinforcement in bed joints caused an increase in average values of K
_{o}and K_{cr}by 52% and 36%.

## Funding

## Conflicts of Interest

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**Figure 1.**Reinforcements used in the tests: (

**a**,

**b**) reinforcement in solid brick walls and (

**c**,

**d**) reinforcement in a wall made of Ca-Si and autoclaved aerated concrete (AAC) masonry units; 1—stainless steel bars, 2—truss strips made of bars with a diameter of 5 mm, 3—truss struts made of bars with a diameter of 3.75 mm, 4—truss strips made of 8 × 1.5 mm flat bars, 5—truss struts with a diameter of 1.5 mm, 6—weft fibres, and 7—warp fibres.

**Figure 2.**Geometry of solid brick models: (

**a**) reinforced with bars and trusses of series HC-ZPI and HC-ZKI (ρ = 0.05%) and (

**b**) reinforced with bars and trusses of series HC-ZPII and HC-ZKII (ρ = 0.10%), dimensions are in centimeters.

**Figure 6.**Frame system for measuring strain and deformation angle: (

**a**) a wall made of calcium silicate units and (

**b**) determining measurement bases and partial strain angles.

**Figure 7.**Patterns of cracking clay brick masonry walls: (

**a**) unreinforced walls, (

**b**) walls reinforced with bars ρ = 0.05%, (

**c**) walls reinforced with bars ρ = 0.10%, (

**d**) walls reinforced with trusses ρ = 0.05%, and (

**e**) walls reinforced with trusses ρ = 0.10%.

**Figure 8.**Cracking patterns of HOS series walls at the time of failure: (

**a**) unreinforced shear wall at σ

_{c}= 0.1 N/mm

^{2}, (

**b**) unreinforced shear wall at σ

_{c}= 1.5 N/mm

^{2}, (

**c**) shear wall reinforced with steel trusses at σ

_{c}= 0.1 N/mm

^{2}, (

**d**) shear wall reinforced with steel trusses at σ

_{c}= 1.5 N/mm

^{2}, (

**e**) shear wall reinforced with plastic mesh at σ

_{c}= 0.1 N/mm

^{2}, (

**f**) shear wall reinforced with plastic mesh at σ

_{c}= 1.5 N/mm

^{2}, (

**g**) a broken truss, and (

**h**) a broken plastic grid in the crush zone of a wall.

**Figure 9.**Cracking patterns of HOS-AAC series walls at the time of failure: (

**a**) unreinforced shear wall at σ

_{c}= 0.1 N/mm

^{2}, (

**b**) unreinforced shear wall at σ

_{c}= 1.0 N/mm

^{2}, (

**c**) shear wall reinforced with steel trusses at σ

_{c}= 0.1 N/mm

^{2}, (

**d**) shear wall reinforced with steel trusses at σ

_{c}= 1.0 N/mm

^{2}, (

**e**) shear wall reinforced with plastic mesh at σ

_{c}= 0.1 N/mm

^{2}, (

**f**) shear wall reinforced with plastic mesh at σ

_{c}= 1.0 N/mm

^{2}, (

**g**) a broken truss, and (

**h**) a broken plastic grid in the crush zone of a wall.

**Figure 10.**Relationships τ − Θ for unreinforced and reinforced units made of solid brick tested at different values of initial compressive stress: (

**a**) σ

_{c}= 0, (

**b**) σ

_{c}= 0.5 N/mm

^{2}, (

**c**) σ

_{c}= 1.0 N/mm

^{2}, and (

**d**) σ

_{c}= 1.5 N/mm

^{2}.

**Figure 11.**Comparison of test results: (

**a**) shear stress at the time of cracking and failure and (

**b**) shear–strain angle at the time of cracking and shear deformation angle at the time of failure.

**Figure 12.**Relationships τ-Θ for unreinforced and reinforced units made of silicate masonry units tested at different values of initial compressive stress: (

**a**) σ

_{c}= 0.1 N/mm

^{2}and (

**b**) σ

_{c}= 1.5 N/mm

^{2}.

**Figure 13.**Comparison of test results: (

**a**) shear stress at the time of cracking and failure and (

**b**) shear–strain angle at the time of cracking and shear deformation angle at the time of failure.

**Figure 14.**Relationships τ

_{v,i}-Θ

_{i}for unreinforced and reinforced AAC masonry tested at different values of initial compressive stress: (

**a**) σ

_{c}= 0.1 N/mm

^{2}and (

**b**) σ

_{c}= 1.5 N/mm

^{2}.

**Figure 15.**Comparison of test results: (

**a**) shear stress at the time of cracking and failure and (

**b**) shear–strain angle at the time of cracking and shear deformation angle at the time of failure.

**Figure 16.**Summary of test results: (

**a**) failure shear stress value for reinforced wall τ

_{u,z}/failure shear stress value for unreinforced wall τ

_{u,n}—depending on percentage of horizontal reinforcement ρ—and (

**b**) ratio τ

_{u,z}/τ

_{u,n}—compressive strength of mortar f

_{m}.

**Figure 17.**Summary of test results: (

**a**) cracking stress value for reinforced wall τ

_{cr,z}/cracking shear stress value for unreinforced wall τ

_{cr,n}—depending on the percentage of horizontal reinforcement ρ—and (

**b**) ratio τ

_{cr,z}/τ

_{cr,n}—compressive strength of mortar f

_{m}

_{.}

Series Marking | Wall Dimensions h/l, m | Type of Reinforcement | Reinforcement % ρ, % | σ_{c}N/mm ^{2} | Number of Test Units | |
---|---|---|---|---|---|---|

at σ_{c} | Total | |||||

HC | 1.42/1.68 | Without reinforcement | - | 0 | 3 | 11 |

0.5 | 2 | |||||

1.0 | 2 | |||||

1.5 | 4 | |||||

HC-ZPI | Smooth bars ϕ 6 mm (Figure 1a) | 0.05 | 0 | 3 | 10 | |

0.5 | 2 | |||||

1.0 | 2 | |||||

1.5 | 3 | |||||

HC-ZPII | Smooth bars ϕ 6 mm (Figure 1a) | 0.10 | 0 | 3 | 10 | |

0.5 | 2 | |||||

1.0 | 2 | |||||

1.5 | 3 | |||||

HC-ZKI | Trusses (Figure 1b) | 0.05 | 0 | 3 | 10 | |

0.5 | 2 | |||||

1.0 | 2 | |||||

1.5 | 3 | |||||

HC-ZKII | Trusses (Figure 1b) | 0.10 | 0 | 3 | 10 | |

0.5 | 2 | |||||

1.0 | 2 | |||||

1.5 | 3 |

Series Marking | Wall External Dimensions h/l, m | Type of Reinforcement | Reinforcement % ρ, % | σ_{c}(N/mm ^{2}) | Number of Test Units | |
---|---|---|---|---|---|---|

at σ_{c} | Total | |||||

HOS | 2.45/4.50 | Without reinforcement | 0 | 0 | 1 | 3 |

0.1 | 1 | |||||

1.5 | 1 | |||||

HOS-Z1-S | Trusses (Figure 1c) | 0.07 | 0.1 | 1 | 2 | |

1.5 | 1 | |||||

HOS-Z2-S | Plastic meshes (Figure 1d) | 0.07 | 0.1 | 1 | 2 | |

1.5 | 1 |

Series Marking | Wall External Dimensions h/l, m | Type of Reinforcement | Reinforcement % ρ, % | σ_{c}(N/mm ^{2}) | Number of Test Units | |
---|---|---|---|---|---|---|

at σ_{c} | Total | |||||

HOS-AAC | 2.43/4.43 | Without reinforcement | 0 | 0.1 | 1 | 4 |

0.75 | 1 | |||||

1.0 | 2 | |||||

HOS-AAC-Z1 | Trusses (Figure 1c) | 0.07 | 0.1 | 1 | 2 | |

1.0 | 1 | |||||

HOS-AAC-Z2 | Plastic meshes (Figure 1d) | 0.07 | 0.1 | 1 | 2 | |

1.0 | 1 |

Type of Reinforcement | ρ,% | σ_{c}N/mm ^{2} | Stresses | Angles of Shear Strain (Deformation) | Total Stiffness | |||
---|---|---|---|---|---|---|---|---|

Cracking | Failure | Cracking | Failure | Initial | At the Time of Cracking | |||

τ_{cr,mv}N/mm ^{2} | τ_{u,mv}N/mm ^{2} | Θ_{cr,mv}mrad | Θ_{u,mv}mrad | K_{o}_{, mv}MN/m | K_{cr,mv}MN/m | |||

no reinforcement | 0 | 0 | 0.343 | 0.388 | 0.735 | 1.413 | 301 | 118 |

0.5 | 0.684 | 0.812 | 1.02 | 4.665 | 282 | 168 | ||

1.0 | 0.892 | 1.06 | 1.04 | 4.671 | 374 | 214 | ||

1.5 | 1.01 | 1.35 | 1.28 | 5.84 | 370 | 197 | ||

smooth rebars | 0.05 | 0 | 0.442 | 0.564 | 0.373 | 0.658 | 577 | 305 |

0.5 | 0.775 | 1.066 | 0.816 | 5.04 | 668 | 239 | ||

1.0 | 0.942 | 1.291 | 1.14 | 5.49 | 605 | 206 | ||

1.5 | 0.970 | 1.39 | 1.17 | 6.86 | 484 | 209 | ||

0.1 | 0 | 0.479 | 0.557 | 0.347 | 0.510 | 493 | 346 | |

0.5 | 0.798 | 1.132 | 0.739 | 5.94 | 539 | 273 | ||

1.0 | 0.988 | 1.392 | 0.888 | 6.17 | 624 | 264 | ||

1.5 | 1.05 | 1.59 | 1.32 | 8.72 | 453 | 199 | ||

truss | 0.05 | 0.0 | 0.739 | 0.794 | 0.523 | 0.827 | 732 | 353 |

0.5 | 0.930 | 1.10 | 0.638 | 3.43 | 700 | 364 | ||

1.0 | 1.22 | 1.59 | 0.994 | 4.84 | 593 | 308 | ||

1.5 | 1.38 | 1.76 | 1.02 | 4.71 | 751 | 340 | ||

0.1 | 0.0 | 0.764 | 0.829 | 0.445 | 0.717 | 740 | 430 | |

0.5 | 1.10 | 1.29 | 0.735 | 4.01 | 816 | 375 | ||

1.0 | 1.28 | 1.63 | 0.892 | 5.54 | 717 | 357 | ||

1.5 | 1.45 | 1.77 | 1.03 | 6.31 | 1095 | 353 |

Type of Reinforcement | ρ,% | σ_{c}N/mm ^{2} | Stresses | Angles of Shear Strain (Deformation) | Total Stiffness | |||
---|---|---|---|---|---|---|---|---|

Cracking | Failure | Cracking | Failure | Initial | At the Time of Cracking | |||

τ_{cr}N/mm ^{2} | τ_{u}N/mm ^{2} | Θ_{cr}mrad | Θ_{u}mrad | K_{o}MN/m | K_{cr}MN/m | |||

no reinforcement | 0 | 0 | 0.069 | 0.107 | 0.175 | 2.126 | 137 | 131 |

0.1 | 0.124 | 0.313 | 0.086 | 6.714 | 1378 | 477 | ||

1.5 | 0.346 | 0.954 | 0.197 | 2.182 | 1674 | 580 | ||

truss | 0.07 | 0.1 | 0.088 | 0.35 | 0.087 | 11.99 | 1039 | 333 |

1.5 | 0.324 | 1.13 | 0.169 | 1.968 | 1525 | 635 | ||

plastic mesh | 0.07 | 0.1 | 0.133 | 0.379 | 0.109 | 9.262 | 1478 | 403 |

1.5 | 0.326 | 0.939 | 0.143 | 1.125 | 1496 | 753 |

Type of Reinforcement | ρ,% | σ_{c}N/mm ^{2} | Stresses | Angles of Shear Strain (Deformation) | Total Stiffness | |||
---|---|---|---|---|---|---|---|---|

Cracking | Failure | Cracking | Failure | Initial | At the Time of Cracking | |||

τ_{cr}N/mm ^{2} | τ_{u}N/mm ^{2} | Θ_{cr}mrad | Θ_{u}mrad | K_{o}MN/m | K_{cr}MN/m | |||

no reinforcement | 0 | 0.1 | 0.196 | 0.235 | 0.281 | 0.97 | 932 | 229 |

0.75 | 0.372 | 0.426 | 0.724 | 2.44 | 1168 | 169 | ||

1.0 | 0.298 | 0.385 | 0.524 | 1.45 | 1541 | 187 | ||

1.0 * | 0.11 | 0.25 | 0.651 | 2.72 | 379 | 75 | ||

truss | 0.07 | 0.1 | 0.191 | 0.250 | 0.358 | 1.49 | 1262 | 175 |

1.0 | 0.350 | 0.50 | 0.695 | 2.52 | 1782 | 165 | ||

plastic mesh | 0.07 | 0.1 | 0.205 | 0.23 | 0.322 | 0.80 | 1193 | 208 |

1.0 | 0.338 | 0.46 | 0.649 | 2.50 | 1374 | 171 |

Wall Type | Type of Reinforcement | ρ,% | σ_{c}N/mm ^{2} | Stresses | Angles of Shear Strain (Deformation) | Total Stiffness | |||
---|---|---|---|---|---|---|---|---|---|

Cracking | Failure | Cracking | Failure | Initial | At the Time of Cracking | ||||

$\frac{{\mathit{\tau}}_{\mathit{cr},\mathit{z}}}{{\mathit{\tau}}_{\mathit{cr},\mathit{n}}}$ | $\frac{{\mathit{\tau}}_{\mathit{u},\mathit{z}}}{{\mathit{\tau}}_{\mathit{u},\mathit{n}}}$ | $\frac{{\mathsf{\Theta}}_{\mathit{cr},\mathit{z}}}{{\mathsf{\Theta}}_{\mathit{cr},\mathit{n}}}$ | $\frac{{\mathsf{\Theta}}_{\mathit{u},\mathit{z}}}{{\mathsf{\Theta}}_{\mathit{u},\mathit{n}}}$ | $\frac{{\mathit{K}}_{\mathit{o},\mathit{z}}}{{\mathit{K}}_{\mathit{o},\mathit{n}}}$ | $\frac{{\mathit{K}}_{\mathit{cr},\mathit{z}}}{{\mathit{K}}_{\mathit{cr},\mathit{n}}}$ | ||||

solid brick | smooth bars | 0.05 | 0 | 1.29 | 1.45 | 0.51 | 0.47 | 1.92 | 2.58 |

0.5 | 1.13 | 1.31 | 0.80 | 1.08 | 2.37 | 1.42 | |||

1.0 | 1.06 | 1.22 | 1.10 | 1.18 | 1.62 | 0.96 | |||

1.5 | 0.96 | 1.03 | 0.91 | 1.17 | 1.31 | 1.06 | |||

0.1 | 0 | 1.40 | 1.44 | 0.47 | 0.36 | 1.64 | 2.93 | ||

0.5 | 1.17 | 1.39 | 0.72 | 1.27 | 1.91 | 1.63 | |||

1.0 | 1.11 | 1.31 | 0.85 | 1.32 | 1.67 | 1.23 | |||

1.5 | 1.04 | 1.18 | 1.03 | 1.49 | 1.22 | 1.01 | |||

truss | 0.05 | 0.0 | 2.15 | 2.05 | 0.71 | 0.59 | 2.43 | 2.99 | |

0.5 | 1.36 | 1.35 | 0.63 | 0.74 | 2.48 | 2.17 | |||

1.0 | 1.37 | 1.50 | 0.96 | 1.04 | 1.59 | 1.44 | |||

1.5 | 1.37 | 1.30 | 0.80 | 0.81 | 2.03 | 1.73 | |||

0.1 | 0.0 | 2.23 | 2.14 | 0.61 | 0.51 | 2.46 | 3.64 | ||

0.5 | 1.61 | 1.59 | 0.72 | 0.86 | 2.89 | 2.23 | |||

1.0 | 1.43 | 1.54 | 0.86 | 1.19 | 1.92 | 1.67 | |||

1.5 | 1.44 | 1.31 | 0.80 | 1.08 | 2.96 | 1.79 | |||

wall made of silicate masonry units | truss | 0.07 | 0.1 | 0.71 | 1.12 | 1.01 | 1.79 | 0.75 | 0.70 |

1.5 | 0.94 | 1.18 | 0.86 | 0.90 | 0.91 | 1.09 | |||

plastic mesh | 0.07 | 0.1 | 1.07 | 1.21 | 1.27 | 1.38 | 1.07 | 0.84 | |

1.5 | 0.94 | 0.98 | 0.73 | 0.52 | 0.89 | 1.30 | |||

wall made of AAC masonry units | truss | 0.07 | 0.1 | 0.97 | 1.06 | 1.27 | 1.54 | 1.35 | 0.76 |

1.0 | 1.17 | 1.30 | 1.33 | 1.74 | 1.16 | 0.88 | |||

plastic mesh | 0.07 | 0.1 | 1.05 | 0.98 | 1.15 | 0.82 | 1.28 | 0.91 | |

1.0 | 1.13 | 1.19 | 1.24 | 1.72 | 0.89 | 0.91 | |||

Average value $\overline{x}$: | 1.25 | 1.34 | 0.89 | 1.07 | 1.70 | 1.58 | |||

Standard deviation S: | 0.355 | 0.287 | 0.244 | 0.419 | 0.648 | 0.801 |

© 2019 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Jasiński, R. Research on the Influence of Bed Joint Reinforcement on Strength and Deformability of Masonry Shear Walls. *Materials* **2019**, *12*, 2543.
https://doi.org/10.3390/ma12162543

**AMA Style**

Jasiński R. Research on the Influence of Bed Joint Reinforcement on Strength and Deformability of Masonry Shear Walls. *Materials*. 2019; 12(16):2543.
https://doi.org/10.3390/ma12162543

**Chicago/Turabian Style**

Jasiński, Radosław. 2019. "Research on the Influence of Bed Joint Reinforcement on Strength and Deformability of Masonry Shear Walls" *Materials* 12, no. 16: 2543.
https://doi.org/10.3390/ma12162543