9th Australasian Masonry ConferenceQueenstown, New Zealand

15 – 18 February 2011

STRENGTHENING UNREINFORCED MASONRY STRUCTURES USING EXTERNALLY BONDED FIBER REINFORCED POLYMER SYSTEMS: AN OVERVIEW OF THE AMERICAN CONCRETE INSTITUTE 440.7R DESIGN

APPROACH

J.J. MYERS

1 Associate Professor, Missouri University of Science and Technology, Rolla, Missouri, USA SUMMARY The use of unreinforced masonry (URM), particularly for infill walls, is a relatively common practice in building construction throughout the world. Typically, URM walls have very low flexural capacities and possess brittle modes of failure making them highly susceptible to damage when exposed to significant out-of-plane loads. In-plane behavior is also very important to resist lateral loads. Significant research has focused on improving both the out-of-plane and in-plane behavior of URM wall systems by using modern materials such as fiber-reinforced polymers (FRPs) to externally retrofit structures. The use of FRP to retrofit URM wall systems has been proven to be highly effective in improving both the load resistance and the deformability of URM walls subjected to out-of-plane loads and in-plane loads (Velazquez-Dimas et al., 2000; Tumialan et al., 2001; Carney, 2003; Hrynyk, 2008; Tanizawa, 2009). In 2010, the American Concrete Institute (ACI) published a new standard ACI 440.7R-10 entitled “Guide for the Design and Construction of Externally Bonded Fiber-Reinforced Systems for Strengthening Unreinforced Masonry System.” This paper will provide an overview of the ACI design procedures for in-plane and out-of-plane strengthening of URM wall systems. It will also provide two example case studies to further detail the design processes of the new standard in an effort to further disseminate the design standard. INTRODUCTION Masonry is a generic term used to describe a type of construction where clay, or concrete masonry units, or natural stones are bonded together to form a load-bearing structure or a component in a structure. Non-load-bearing masonry includes partitions and veneers (ACI 440.7R, 2010). The use of unreinforced masonry (URM) for walls has been and continues to be common practice in building construction throughout the United States and around the world. While unreinforced masonry structures are widely considered a highly sustainable material, they have shown their vulnerability to major events such as earthquakes, severe wind, blast,

and impact. Furthermore, factors such as change in occupancy, deterioration, or an increase in lateral-load demand, may generate the need to undertake structural retrofit. The 2008 joint TMS 402/ACI 530/ASCE 5 Building Code Requirements for Masonry Structures covers the design and construction of new masonry. Repair, retrofitting, and rehabilitation of masonry structures are not included in that code. Specifications for masonry structures are detailed in the joint TMS 405/ACI 530.1/ASCE 6 Specification for Masonry Structures document. Within the past two decades, fiber-reinforced polymer (FRP) systems have been developed for infrastructure applications and used for strengthening and repair of existing structures as an alternative to traditional strengthening methods, such as steel plate bonding, section enlargement, and external post-tensioning. The use of FRP to retrofit URM wall systems has been proven to be highly effective in improving both the load resistance and the deformability of URM walls subjected to out-of-plane loads and in-plane loads (Velazquez-Dimas, 2000; Tumialan, 2001; Carney, 2005; Hrynyk, 2008; Tanizawa, 2009). The initial attraction of using FRP in construction was because it did not experience the common durability problems that are typically associated with conventional steel reinforcement. Additionally, FRP reinforcement is lightweight and is available in multiple forms, many of which could easily be manipulated to match variable structural shapes and geometries (ACI 440.2R, 2002). FRP materials are readily available in several forms such as laminates, sheets, meshes, and bars (see Figure 1). They are relatively expensive at the present when compared to concrete and steel as strengthening materials, but labor and equipment costs to install FRP systems are often lower. FRP systems can also be used in areas with limited access where traditional techniques would be difficult to implement such as in tight confined areas where post cured systems allow for improved flexibility. Today significant research is still being carried out to assess the use of FRP as an alternative for steel reinforcement. However, in recent years, the focus of much of the research has shifted to the use of FRP as a means of retrofitting current infrastructure. As a result, the use of various externally bonded FRP systems and near surface mounted (NSM) systems continues to be studied extensively not only in concrete structures, but also in masonry, steel, and timber structures. The benefits of using FRP as opposed to conventional steel in structural retrofits are the same as those in new construction and in most cases externally bonded FRP systems are less intrusive to building occupants. This benefit is primarily because externally bonded FRP systems and NSM systems are typically easy to install and are less time consuming than conventional retrofit methods. There are several different retrofit methods that can be employed to increase the out-of-plane and in-plane load resistance and improve the behavior of URM wall systems including infill systems. Conventional masonry retrofitting methods, which typically involve the use of additional concrete and steel reinforcement, tend to not only add significant mass to a structure, but in many cases the methods result in a reduction of available space for building occupants. In addition to the effects on the building, conventional retrofit methods also tend to be both time consuming and expensive. The use of modern retrofit systems, which involve the use of fiber reinforced polymers (FRP) or elastomeric coatings, are aimed to address and improve upon the negative traits associated with conventional techniques of retrofitting masonry structures. The two most common retrofit techniques involve externally bonded FRP systems and NSM systems. Both of these techniques have demonstrated promise for upgrading the flexural and

shear strengthening of masonry systems. Figures 2 and 3 detail both of these systems. Externally bonded systems have demonstrated more robustness for extreme events, while NSM allows for the reinforcement to be installed near the surface within the existing bed joints and therefore impacts the aesthetics of the masonry wall to a lesser degree. More recently, new coating technologies such as elastomeric polyurea with and without discrete fibers, as shown in Figure 4, have also shown great promise for hardening of masonry systems, but the current ACI 440.7R document does not cover this technology at the present as it is still in the developmental stage. SCOPE OF ACI 440.7R-10 DOCUMENT This 440.7R guide offers general information on FRP systems use, a description of their unique material properties, and recommendations for the design, construction, and inspection of FRP systems for strengthening URM structures. The guidelines are based on knowledge gained from a comprehensive review of experimental and analytical investigations and field applications. At present the guide provides information on the selection and design of FRP systems limited to externally bonded FRP laminates and near-surface-mounted FRP bars/strips for increasing the in-plane and out-of-plane strength of existing ungrouted, grouted, or partially grouted URM walls; infill walls are not included in this guide. The guide is applicable to URM structures made of clay bricks, concrete masonry units, and natural stones using conventional types of mortar.

Figure 1. FRP products, CFRP and GFRP rods (left) and CFRP and GFRP laminates (right).

Figure 2. Externally bonded FRP laminate strengthening for masonry.

Figure 3. Near surface mounted (NSM) strengthening for masonry.

Figure 4. Discrete fiber polyurea retrofit for in-plane strengthening (Tanizawa, 2009).

For masonry with significant deterioration, questionable mortar bond, and cracking and/or element displacement, traditional procedures may be required as well as FRP strengthening. The evaluation for the need to apply traditional modes of strengthening is not covered in the guide (ACI 440.7R, 2010). FRP CONSTITUENT MATERIALS AND PROPERTIES The behavior of FRP-reinforced masonry structures depends on the physical and material properties of the existing masonry, as well as the FRP system. The physical and mechanical properties of the masonry should be investigated and known prior to the retrofit or repair design. The effects of factors such as loading history and duration, temperature, and moisture on the properties of FRP systems can influence the design and long-term service performance. Fiber-reinforced polymer systems are available in a variety of forms such as wet layup, prepreg, and procured systems. Factors such as fiber volume, type of fiber, type of resin, fiber orientation, dimensional effects, and quality control during manufacturing, all play a role in establishing characteristics of the FRP system (ACI 440.7R, 2010). Test methods according to ASTM standards should be used for material characterization; for test methods not included in ASTM standards, reference should be made to ACI 440.3R. Preconstruction quality assurance testing of the FRP strengthening system, hereby called FRP system or FRP reinforcement, is recommended. Physical Properties Fiber-reinforced polymer materials have densities ranging from1.2 to 2.1 g/cm3 (75 to 130 lb/ft3), which is four to six times less than that of steel, as indicated in Table 1 (ACI 440.7R). The material characteristics described in this section are generic and do not apply to all commercially available products. The coefficients of thermal expansion of unidirectional FRP materials differ in longitudinal and transverse directions, depending on the fiber type, resin type, and fiber content. Table 2 (ACI 440.7R) lists the longitudinal and transverse coefficients of thermal expansion for typical unidirectional FRP materials. Note that a negative coefficient of thermal expansion indicates the material contracts with increased temperature and expands with decreased temperature. For reference, concrete has a coefficient of thermal expansion that varies from 7x10–6 to 11x10–6/°C (4x10–6 to 6x10–6/°F) and is usually assumed to be isotropic (Young et al., 2002). Steel has an isotropic coefficient thermal expansion of 11.7x10–6/°C (6.5x10–6/°F). Mechanical Properties

When loaded in direct tension, FRP materials do not exhibit any plastic behavior, or yielding, before rupture. The tensile behavior of FRP materials consisting of one type of fiber material is characterized by a linear elastic stress-strain relationship until failure, which is sudden and without warning. The tensile strength and stiffness of a FRP material depends on several factors. Because the fibers in a FRP material are the main load-carrying constituent, fiber type, fiber orientation, fiber quantity, and method and conditions that the composite is manufactured affect the tensile properties of the FRP material. Due to the primary role of the fibers as tensile reinforcement and methods of application, the properties of a FRP system are sometimes reported based on the net-fiber area (Method 2 of 440.3R). In other examples, such as in pre-cured laminates, the reported properties are based on the gross-laminate area (Method 1 of 440.3R). Externally bonded FRP systems should not be used as compression reinforcement because of insufficient test results validating its use in this type of application (ACI 440.7R, 2010).

Table 1. Typical densities of materials, g/cm3 (lb/ft3).1

Steel GFRP CFRP AFRP 7.9 1.2 to 2.1 1.5 to 1.6 1.2 to 1.5

(490) (75 to 130) (90 to 100) (75 to 90) 1 Table adapted from ACI 440.7R-10.

Table 2. Typical coefficient of thermal expansion for FRP materials.1,2

Direction Coefficient of thermal expansion

x 10-6/ºC (x 10-6/ºF) GFRP CFRP AFRP

Longitudinal, αL 6 to 10

(3.3 to 5.6) -1 to 0

(-0.6 to 0) -6 to -2

(-3.3 to -1.1)

Transverse, αT 19 to 22

(10.4 to 12.6) 22 to 50

(12 to 27) 60 to 80

(33 to 44) 1 Table adapted from ACI 440.7R-10. 2 Typical values for fiber-volume fractions ranging from 0.5 to 0.7.

FRP materials subjected to a constant tensile load over time can suddenly fail after a time period called the endurance time. As the ratio of the sustained tensile stress to the short-term strength of the FRP laminate increases, endurance time decreases. The creep rupture time may also decrease under adverse environmental conditions, such as high temperature, ultraviolet radiation exposure, high alkalinity, wetting-and-drying cycles, or freezing-and-thawing cycles. In general, carbon fibers are the least susceptible to creep rupture, aramid fibers are moderately susceptible, and glass fibers are most susceptible. Therefore, the design guideline specifies stress limits of ultimate tensile capacity for carbon (55%), glass (20%) and aramid (30%) to prevent creep rupture of the FRP material while in service. The fatigue performance of the FRP system is generally considered a non-issue in URM structures that are typically strengthened with FRP systems because the systems are intended to resist loads with low cycle counts, such as earthquake, hurricane, and blast loads. ACI 440.2R provides more details regarding the fatigue sensitivity of FRP materials in fatigue sensitive applications.

It has been widely reported that many FRP systems exhibit reduced mechanical properties after exposure to certain environmental factors, including high temperature, humidity, and chemical exposure. The type of FRP strengthening technique may also affect the long-term durability performance of the strengthened system. The exposure environment, duration of the exposure, resin type and formulation, fiber type and volume fraction, and resin-curing method are some of the factors that influence the extent of the reduction in mechanical properties. GENERAL DESIGN CONSIDERATIONS The strength design approach taken in the ACI 440.7R document is a limit states approach to provide acceptable safety levels. All possible failure modes must be investigated to understand the controlling mechanism of failure. This is particularly critical when strengthening with FRP for a particular behavior such as flexure. The shear capacity after retrofit must be investigated to ensure the desirable mode of failure occurs at the desired strengthening level. The ACI 440.7R document provides guidance on strengthening a particular masonry element, but ASCE 41-06 is recommended to perform a global analysis of the overall structure to understand how component strengthening will affect the global behavior of a structure. For masonry structures, the ACI 440.7R document does not specify strengthening limits like the ACI 440.2R document does for concrete structures. The rational for this is that masonry structures are strengthened for special loading events such as earthquake, wind, hurricane, and blast loads. These loads are rare and typically not sustained. Therefore, the probability of simultaneous occurrence of damage to FRP, for example from vandalism or exposure to high temperatures and high short-term loads, like from earthquake or wind, is low; therefore, a strengthening limit for these applications is unnecessary (ACI 440.7R, 2010). However, the document does stipulate that strengthening limits should be considered for two specific cases; namely, cases that include masonry walls resisting out-of-plane loads due to earth pressure and walls that are part of the primary lateral load-carrying system resisting in-plane loads from wind. Design Material Properties Because long-term exposure to various types of environments can reduce the tensile properties and creep rupture / fatigue endurance of FRP laminates, the material properties used in design equations are reduced based on the environmental exposure condition. Eqs (1) through (3) give the tensile properties that are used in all design equations. The design tensile strength is determined using the environmental reduction factor given in Table 3 for the appropriate fiber type and exposure condition.

ffu = CE ffu* (1)

Similarly, the design rupture strain should also be reduced for environmental-exposure conditions.

εfu = CE εfu* (2)

Fiber-reinforced polymer materials consisting of one type of fiber oriented predominantly in one direction are practically linearly elastic until failure. Their modulus of elasticity does not

vary significantly with environmental exposure and loading history and can be computed according to Eq. [1].

Ef = ffu / εfu (3)

Constituent materials affect the durability and resistance to environmental exposure of a FRP system. The environmental-reduction factors given in Table 3 are estimates based on the relative durability of each fiber type. As more research information is developed and becomes available, these values may be refined. The relative durability of NSM systems versus surface applied laminates may be better. Given the lack of data, however, this guide conservatively recommends use of the same CE factors for both applications.

Table 3. Environmental reduction factors for various FRP systems and exposure systems.1

Exposure conditions Fiber type Environmental reduction

factor, CE

Interior exposure (for example, partitions)

Carbon 0.95 Glass 0.75

Aramid 0.85

Exterior exposure (including int. side walls of ext. walls)

Carbon 0.85 Glass 0.65

Aramid 0.75

Aggressive environmental (basement walls)

Carbon 0.85 Glass 0.50

Aramid 0.70 1 Table adapted from ACI 440.7R-10. Debonding of the FRP system can occur if the force in the FRP system at the strength limit state cannot be sustained by the masonry substrate. For a typical FRP system that is linear elastic until failure, the level of strain in the FRP system will dictate the level of stress developed in the system. To prevent debonding, a limitation is placed on the strain level developed in the FRP laminate. The maximum strain and corresponding stress that FRP systems can attain before debonding from the masonry substrate are defined as effective strain εfe and effective stress ffe. Effective Strain and Stress in FRP at the Strength Limit State: flexural-controlled failure mode The effective strain εfe and effective stress ffe used for the design of flexural out-of-plane and in-plane FRP strengthening of masonry walls can be computed according to Eq. (4) and (5), respectively:

εfe = κmεfu * ≤ CEεfu* (4)

ffe = Ef εfe (5)

where κm is a bond reduction coefficient calibrated using available experimental data (ACI 440.7R-10), defined as in Eq. (6). This coefficient is subject to force per unit widths as detailed in ACI 404.7R-10 since it is based upon current experimental data.

κm = 0.45 for surface mounted FRP systems; = 0.35 for NSM FRP systems (6)

Effective Strain and Stress in FRP at the Strength Limit State: shear-controlled failure mode The effective strain εfe and effective stress ffe to be used for the design of shear in-plane FRP strengthening of masonry walls can be computed according to Eq. (7) and (8), respectively:

εfe = κvεfu * ≤ CEεfu* (7)

ffe = Ef εfe (8) The bond reduction coefficient for shear-controlled failure modes κv depends on the FRP reinforcement index ωf , defined in Eq. (9).

'1000

1

mn

fff

fA

EA for in.-lb units or

'85

1

mn

fff

fA

EA for SI units (9)

For shear-controlled failure modes, the bond reduction coefficient is again calibrated based on experimental data (ACI 440.7R, 2010). The coefficient for shear-controlled failure modes is equal for both FRP laminates and NSM FRP systems and is given in Eq. (10). Similar to flexure-controlled failure modes, this coefficient is subject to force per unit widths as detailed in ACI 404.7R-10. (10) It is recognized by ACI 440.7R that in Eq. (4) and (7), the κ values will always control over the CE values. The κ values, however, were set as a lower bound from experimental data. It is expected that further experimental data added to the data base may result in higher κ values in the future. Limitation involving the CE value is presented to establish the design philosophy. Furthermore, if experimental data for a particular application is available, the designer may wish to incorporate different CE or κ values. In this case, it is recommended to follow the limitations given by Eq. (4) and (7). WALL STRENGTHENING FOR OUT-OF-PLANE LOADS A number of research projects involving out-of-plane strengthening have been conducted to study the use of FRP systems for flexural strengthening of masonry walls. The guide provides a literature overview of several of these studies and may be referenced for greater detail. Existing Wall Strength To determine whether FRP strengthening is needed, the existing out-of-plane strength of the wall should be evaluated first. Unreinforced masonry walls should be analyzed for out-of-plane seismic forces and wind pressures, or both, and earth pressures as isolated elements spanning between floor levels and spanning horizontally, or both, between columns or pilasters (TMS 402/ACI 530/ASCE 5; ASCE 41-06) and the applicable local building code, or both. This includes analyzing the system for flexural, shear, and axial strengths to determine what level of retrofit is required.

Nominal Flexural Strength of FRP-Reinforced Masonry Walls Subjected to Out-of-Plane Loads The strength design method requires that the flexural strength of the FRP-strengthened wall (Mn) times the phi factor exceeds the factored moment (Mu), as indicated by Eq. (11). ACI 440.7R-10 recommends a phi factor = 0.6, as required in TMS 402/ACI 530/ASCE 5 for URM walls subject to flexure load, axial load or a combination thereof. Assuming that the factored axial load Pu acts at t/2 (t = thickness of wall), the nominal flexural strength Mn of the FRP-strengthened masonry wall can be determined from Eq. (12) using strain compatibility, internal force equilibrium, and the controlling mode of failure.

un MM (11)

22211 ct

Pc

dfAM uffefn

(12)

where ffe represents the effective stress to be calculated according to Eq. (5) with the strain level εfe as defined in Eq. (13). The maximum strain level that can be achieved in the FRP reinforcement is determined by the strain developed in the FRP system at the ultimate limit state by either crushing of the masonry or FRP system debonding. The maximum strain or effective strain level in the FRP reinforcement may be calculated as defined in Eq. (13).

**min ,min fuEfumfe C

c

ct

(13)

The effective stress level in the FRP reinforcement is the maximum level of stress that can be developed in the FRP reinforcement before reaching the ultimate limit state. This effective stress can be calculated from the strain level in the FRP system, assuming perfectly elastic behavior as given in Eq. (5). The failure mode of that will control the behavior of URM walls strengthened with externally bonded FRP systems include (a) crushing of the masonry in compression or (b) debonding of the FRP system from the masonry substrate. Anchorage on the FRP system may delay or prevent the premature debonding of the external retrofit system. The ACI 440.7R-10 document provides information on details in this regard. WALL STRENGTHENING FOR IN-PLANE LOADS A number of research projects involving in-plane strengthening have been conducted to study the use of FRP systems for shear strengthening of masonry walls. The guide provides a literature overview of several of these studies and may be referenced for greater detail. Existing Wall Strength Similar to flexural strengthening, the existing in-plane strength of the wall should be evaluated first. The behavior of URM walls under in-plane loads depends on several parameters related to geometry including height, thickness, slenderness, and bond pattern as well as mechanical properties of the materials and the loading / support conditions. Three

failure modes may result from in-plane shear including joint sliding (Vjs), diagonal tension (Vdt), and toe-crushing (Vtc). Joint sliding and diagonal tension are shear-controlled failure modes while toe-crushing is a flexural-controlled failure mode. Each must be investigated and existing documents such as TMS 402/ACI 530/ASCE 5, ASCE 41-06, and FEMA 306 may be referenced. The nominal shear strength of URM walls should be computed as defined in Eq. (14)

tcdtbjsURM

n VVVV ,,min (14)

Nominal Shear Strength of FRP-Reinforced Masonry Walls Subjected to In-Plane Loads The strength design method requires that the shear strength of the FRP-strengthened wall (Vn) times the phi factor exceeds the factored shear (Vu), as indicated by Eq. (15). ACI 440.7R recommends a phi factor = 0.8, as required in TMS 402/ACI 530/ASCE 5 for URM walls subject to in-plane shear load.

un VV (15)

Unreinforced masonry walls requiring shear strengthening against in-plane loads are those walls whose failure mode is due to either stepped joint sliding or diagonal tension. A typical FRP strengthening scheme performed either with wet layup or NSM systems is indicated in Fig. 5 (a) and (b), respectively. Other layouts, including fibers placed diagonally, have been used, but they are not covered in the scope of the ACI 440.7R guide. The design method is based on the assumption that FRP debonding governs the behavior of the FRP-strengthened wall. Bonding the FRP into boundary elements such as beams or columns can help reduce the risk of wall overturning due to out-of-plane excitations. In several situations, however, extension of FRP may not be practical due to existing field conditions. For example, intersecting walls, slabs, or columns with dimensions larger than the wall thickness can preclude extending the FRP beyond the wall. In such cases, other mechanical anchors should be considered. The in-plane performance of FRP-strengthened walls is highly dependent on the type of masonry construction and the FRP strengthening layout. Experimental investigations have shown that FRP systems can significantly increase the shear capacity of URM walls when the original shear strength of the wall is not large (for example, single-wythe or ungrouted walls). Contrarily, when the shear strength of the URM wall is large (for example, multi-wythe or grouted walls), the contribution of FRP has been observed to be marginal in some situations. Test results also indicate that the FRP layout influences the wall’s structural performance. For instance, in thick walls, FRP placed on the two wall sides has been shown to be more effective than FRP placed on one side. In the absence of project specific experimental evidence, the guide recommends FRP strengthening layouts based on the masonry construction as shown in the guide, where the wall thicknesses are given in nominal dimensions (ACI 440.7R, 2010). The nominal shear strength of the FRP-strengthened wall can be computed by adding the FRP contribution Vf to the nominal strength of the URM wall, computed according to the provisions discussed in Eq. (14); Vn

URM in Eq. (16). The nominal in-plane flexural strength of the FRP-strengthened wall is the minimum of the nominal shear strength given in Eq. (16) and the nominal lateral strength corresponding to toe-crushing of the URM wall. The FRP contribution to the shear strength Vf can be determined from Eq. (17a or 17b) based upon the strengthening system.

a) Horizontal strips b) horizontal bars

Figure5. FRP strengthening of shear-controlled walls (adapted from ACI 440.7R).

fURM

nsn VVV , (16)

f

vffvf s

dV (surface mounted FRP) or

f

vfvf s

dV (NSM FRP systems) (17)

where pfv is computed according to limits specified in ACI 440.7R-10, wf is the width of the FRP laminates, sf is the center-to-center spacing between each strip, and dv is the effective masonry depth for shear calculations given by

),(min LHdv (18)

Nominal Flexural Strength of FRP-Reinforced Masonry Walls Subjected to In-Plane Loads The strength design method requires that the flexural strength of the FRP-strengthened wall exceeds the factored flexural demand, as indicated by Eq. (19). ACI 440.7R-10 recommends a phi factor = 0.6, as required in TMS 402/ACI 530/ASCE 5 for URM walls under combination of axial load and bending. Unreinforced masonry walls requiring flexural strengthening are those walls whose failure mode is due to toe crushing, as discussed previously. Assuming that the factored axial load Pu acts at L/2 (L = length of the wall), the nominal moment capacity Mn of a FRP-strengthened masonry wall subjected to in-plane loading can be calculated from Eq. (20) according to the assumptions and provisions given in the guide.

un MM (19)

222

11 cLP

cdFM uiin

(20)

where Fi is the force acting on the i-th FRP strip located at a distance di from the extreme compression fiber. In cases where Pu does not act at L/2, Eq. (20) should account for the eccentricity of the axial load by inserting an appropriate value instead of L/2. The nominal lateral strength corresponding to flexural failure of the FRP-strengthened wall can be obtained as

eff

nn hk

MV

(21)

where k is the coefficient that accounts for the boundary condition of the wall, k (k = 0.5 and k = 1.0 for a fixed-fixed and fixed-free wall, respectively), and heff is the wall height. The nominal lateral strength of the FRP-strengthened wall is the minimum of the nominal lateral strength corresponding to flexural failure given in Eq. (21) and the nominal lateral strength corresponding to shear failure of the URM wall (that is, minimum between joint sliding and

diagonal tension). Similar considerations and identical procedures may be repeated in the case of NSM FRP systems installed on a wall as an alternative to the wet layup system. SUMMARY This paper provides an overview of the ACI 440.7R-10 design procedures for in-plane and out-of-plane strengthening of URM wall systems. The reader may be referred to that document for greater details on anchoring of these repair systems, drawings, specifications, submittals, and a series of design examples for both out-of-plane and in-plane strengthening. REFERENCES American Concrete Institute 440.2R-02, “Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures,” ACI, 2002. American Concrete Institute 440.3R Guide Test Methods for Fiber-Reinforced Polymers (FRPs) for Reinforcing or Strengthening Concrete Structures,” ACI 2003. American Concrete Institute 530/530.1, The Masonry Society 402/405 and ASCE 5/6, Joint Document, “Building Code Requirements for Masonry Structures,” ACI, TMS, and ASCE, 2008. American Concrete Institute 440.7R, “Guide for the Design and Construction of Externally Bonded Fiber-Reinforced Systems for Strengthening Unreinforced Masonry System,” ACI, 2010. American Society of Civil Engineers 41-06, “Seismic Rehabilitation of Existing Buildings,” ASCE, 2006. Carney, P., Myers, J.J., “Static and Blast Resistance of Unreinforced Masonry Wall Connections Strengthened with Fiber Reinforced Polymers,” American Concrete Institute Special Publication-230, FRPRC-7, November 2005, pp. 229-248. Hrynyk, T., Myers, J.J., “Out-of-Plane Behavior of URM Arching Walls with Modern Blast Retrofits: Experimental Results and Analytical Model,” American Society of Civil Engineering–Journal of Structural Engineering, Vol. 134, No. 10, Oct. 2008, pp. 1589-1597. Young, J.F., Mindness, S., and Darwin, D., “Concrete,” Prentice Hall, 2nd Edition, 2002. Tanizawa, Y., Myers, J.J. Sinclair, R. “In-Plane Response on an Alternative URM Infill Wall System with and without a Polyurea Retrofit,” 9th International Symposium on Reinforced Polymer Reinforcement for Concrete Structures,” Sydney, Australia, 2009, 4p. Tumialan J. G., 2001, “Strengthening of Masonry Structures with FRP Composites,” Doctoral Dissertation, University of Missouri-Rolla, Rolla, MO, 186 pp. Velazquez-Dimas, J.; Ehsani, M.; and Saadatmanesh, H., 2000, “Out-of-Plane Behavior of Brick Masonry Walls Strengthened with Fiber Composites,” American Concrete Institute Structural Journal, V. 97, No. 3, May-June, pp. 377-387.