EVALUATION OF DESIGN PROVISIONS FOR IN-PLANE SHEAR IN MASONRY WALLS COURTNEY LYNN DAVIS

Transcription

1 EVALUATION OF DESIGN PROVISIONS FOR IN-PLANE SHEAR IN MASONRY WALLS By COURTNEY LYNN DAVIS A thesis subitted in partial fulfillent of the requireents for the degree of MASTER OF SCIENCE IN CIVIL ENGINEERING WASHINGTON STATE UNIVERSITY Departent of Civil and Environental Engineering DECEMBER 2008

2 To the Faculty of Washington State University: The ebers of the Coittee appointed to exaine the thesis of COURTNEY LYNN DAVIS find it satisfactory and recoend that it be accepted. Chair ii

3 ACKNOWLEDGMENTS I would like to express y sincere gratitude to Dr. David McLean for all of his guidance and advice throughout y graduate school experience. I feel fortunate to have worked with such a successful and knowledgeable entor who has assisted e with y research projects and encouraged e to share y work professionally. He has dedicated countless hours to support y efforts, and I appreciate his constant leadership and backing. Thank you to Dr. David Pollock and Dr. Mohaed ElGawady for serving on y coittee. Thank you for your guidance with y thesis as well as your instruction both in and out of the classroo over the last several years. Thank you also to y fellow Enginerds! I could not have ade it through graduate school without you. Thanks for taking y ind off of work when needed and for telling e to get back to work when I needed to as well. You are soe of y best friends: Haley Falconer, Jennifer Allen, Katie Schaffnit, Steve Greenwood, Aaron John Booker, Alan Kuper, Karl Olsen, Guillaue Paternostre, Antoine Cordray, Joe Schidt, and Diana Worthen. I appreciate all of your support! Last, but not least, I would like to thank y faily. Mo, Dad, and Kelsie - thank you for your invaluable support. I could not have coe this far without you. iii

4 EVALUATION OF DESIGN PROVISIONS FOR IN-PLANE SHEAR IN MASONRY WALLS Abstract by Courtney Lynn Davis, MS. Washington State University Deceber 2008 Chair: David I. McLean This research investigated current and proposed design procedures for in-plane shear in asonry walls. Procedures considered include both strength design and allowable stress design provisions in the 2008 MSJC Building Code Requireents and Specifications for Masonry Structures, the New Zealand asonry design standard NZS 4230:2004, the Canadian asonry design standard CSA S , provisions in the 1997 Unifor Building Code, and proposed design equations developed by Shing et al in 1990 and by Anderson and Priestley in Predicted shear strengths fro the various procedures were copared with results fro a wide range of tests of asonry walls failing in in-plane shear. The test data encopassed both concrete asonry walls and clay asonry walls, all of which were fully grouted. Statistical analyses were perfored to copare the overall effectiveness of each set of provisions or proposed equation. Paraetric studies were also perfored to evaluate the ability of the provisions and equations to account for the effects of specific paraeters. The current MSJC strength design provisions were found to provide the best shear predictions over a wide range of wall paraeters. Based on the results of this study, recoendations were ade to iprove the current MSJC strength design and allowable stress design provisions. iv

5 TABLE OF CONTENTS Page ACKNOWLEDGMENTS... iii ABSTRACT... iv LIST OF TABLES... viii LIST OF FIGURES... ix CHAPTER 1 - INTRODUCTION Background Scope and Objectives Organization... 2 CHAPTER 2 - REVIEW OF CODE PROVISIONS MSJC Building Code MSJC Allowable Stress Design (ASD) Unreinforced Masonry Reinforced Masonry MSJC Strength Design (SD) Unreinforced Masonry Reinforced Masonry MSJC Notation Unifor Building Code UBC Working Stress Design (WSD) v

6 Unreinforced Masonry Reinforced Masonry UBC Strength Design (SD) Unifor Building Code Notation New Zealand Standard 4230: New Zealand Standard Notation Canadian Standards Association S Unreinforced Masonry Reinforced Masonry Canadian Standard Notation Shing et al Shing et al. Notation Anderson and Priestley (1992) Anderson and Priestley Notation CHAPTER 3 - SHEAR WALL TEST DATA Shing et al Matsuura Sveinsson et al Voon and Ingha CHAPTER 4 - ANALYSIS vi

7 4.1 Interpretation of Shear Equations Statistical Evaluations Test Paraeter Evaluations CHAPTER 5 - CONCLUSIONS AND RECOMMENDATIONS Suary Conclusions Recoendations Future Work APPENDIX A APPENDIX B vii

8 LIST OF TABLES Table 2.1 Type Dependent Noinal Strengths Table 2.2 Observation Types, Adissible Use and Noinal Strengths Table 4.1 Shear Prediction Equations Table 4.2 Statistical Coparisons of Design Equations viii

9 LIST OF FIGURES Figure 2.1 Effective Areas for Shear Figure 2.2 Contribution of Axial Load to Wall Shear Strength Figure 3.1 Shing et al.- Test Apparatus and Setup Figure 3.2 Matsuura - Test Apparatus and Setup Figure 4.1 Effectiveness of MSJC SD Shear Provisions Figure 4.2 Effectiveness of MSJC ASD V Shear Provisions Figure 4.3 Effectiveness of MSJC ASD V s Shear Provisions Figure 4.4 Effectiveness of UBC SD Shear Provisions Figure 4.5 Effectiveness of NZS Shear Provisions Figure 4.6 Effectiveness of CSA Shear Provisions Figure 4.7 Effectiveness of Shing Shear Prediction Equation Figure 4.8 Effectiveness of Anderson and Priestley Predictive Equations Figure 5.1 Ductility Reduction Factor α ix

10 CHAPTER 1 INTRODUCTION 1.1 Background Design provisions for shear in asonry structures vary widely in building standards existing around the world. Variations in the provisions include differences in forat, assuptions of structural behavior under shear loadings, separate provisions for unreinforced and reinforced eleents, treatent of in-plane and out-of-plane shear loading, accounting for partial and full grouting, factors of safety, and reductions in shear strength in plastic hinging regions. In the US design standard Building Code Requireents and Specifications for Masonry Structures (MSJC, 2008), which provides separate design provisions for allowable stress design and for strength design, fundaental differences in the two sets of shear provisions can produce substantially different designs. In response to the variations in the shear provisions, a nuber of experiental studies on the shear perforance of asonry walls and other structural eleents has been conducted over the last 25 years. Current and proposed design ethods were evaluated for their effectiveness to predict easured shear strengths. Two coprehensive studies (NEHRP, 2000; Voon and Ingha, 2007) collected shear data fro around the world and copared the data with predicted strengths fro a broad collection of existing and proposed shear provisions. The NEHRP study provided recoendations for shear design that were largely based on the equations developed in the National Science Foundation (NSF) - funded Technical Coordinating Coittee for Masonry Research (TCCMaR) progra. The TCCMaR equations are the basis for the strength design provisions in the MSJC Code. The Voon and Ingha study also found that the TCCMaR 1

11 equations provided a good prediction of the collected shear strengths. However, Voon and Ingha proposed several odifications to the TCCMaR equations, and their final recoendations for shear design were incorporated into the 2004 New Zealand Standard (NZS, 2004). The research reported in this thesis builds upon the previous studies by NEHRP and Voon and Ingha. The shear data collected in both previous studies is incorporated into this research, and the ethods for evaluating the effectiveness of the various provisions closely reseble those used in those studies. This research expands on this previous work to include consideration of additional codes as well as the allowable stress provisions of previously evaluated codes. The goal of this research is to provide recoendations for iproveents to the existing MSJC shear provisions. 1.2 Scope and Objectives The priary objective of this research is to evaluate the accuracy of various code provisions and proposed equations for predicting the in-plane shear strength of asonry walls. Statistical analysis of each equation was perfored, and evaluations isolating the effects of wall paraeters were ade. The paraeters exained include asonry copressive strength, aount of shear reinforceent, level of axial copressive stress, aount of vertical reinforceent, displaceent ductility, and wall aspect ratio. 1.3 Organization This thesis is coprised of five chapters. Chapter 2 contains a review of current and past code shear provisions as well as predictive equations. The review includes a detailed description 2

12 of each set of provisions. Chapter 3 provides a short suary of previous laboratory tests of asonry shear walls producing shear failures, including presentation of the test setup and data. Data fro four different sources is included. Chapter 4 reports on a statistical analysis and coparison of the various provisions and equations with respect to predicting the shear strengths in the collected data set. Chapter 4 also provides an evaluation of the ability of the provisions and equations to account for various test paraeters. Chapter 5 presents conclusions reached in this study along with recoendations for iproveents in the current MSJC shear provisions. 3

13 CHAPTER 2 REVIEW OF CODE PROVISIONS 2.1 MSJC Building Code The Masonry Standards Joint Coittee (MSJC) Building Code Requireents and Specification for Masonry Structures (MSJC, 2008) contains two sets of provisions for shear design. Provisions based on Allowable Stress Design (ASD) are given in MSJC Chapter 2, and provisions based on Strength Design (SD) are given in MSJC Chapter 3. The MSJC SD provisions for shear design are the sae as those developed through the National Earthquake Hazards Reduction Progra (NEHRP, 2003) MSJC Allowable Stress Design (ASD) The MSJC ASD shear design provisions are specified separately for unreinforced asonry and for reinforced asonry Unreinforced Masonry ASD shear design provisions for unreinforced asonry are given in MSJC Section Shear stresses in unreinforced asonry due to applied service loads are calculated using Equation 2-1. VQ f (2-1) v I b n For in-plane loading, the calculated shear stresses, f v, shall not exceed any of the allowable stress liits (a), (b) and the applicable condition of (c) through (f) as listed below. (a) 1.5 ƒ' 4

14 (b) 120 psi (c) For running bond asonry, not grouted solid: 37 psi N 0.45 A v n (d) For stack bond asonry with open end units and grouted solid: 37 psi N 0.45 A v n (e) For running bond asonry grouted solid: 60 psi N 0.45 A v n (f) For stack bond asonry other than open end units grouted solid: 15 psi No allowable stress liits are specified in Section for out-of-plane shear stresses Reinforced Masonry ASD shear design provisions for reinforced asonry are given in MSJC Section Separate provisions for reinforced asonry are provided for ebers that are subjected to flexural tension and for those without flexural tension. Reinforced asonry ebers that are subjected to flexural tension are to be designed in accordance with MSJC Sections and Shear stresses due to service loads are calculated using Equation 2-2. V ƒ v (2-2) bd Note that the area used to calculate the shear stress does not distinguish between fully and partially grouted sections. The calculated shear stresses, f v, shall not exceed the applicable 5

15 allowable stress liit, F v, given in MSJC Section and as listed below. For flexural ebers (i.e., for beas), F v is given by Equation 2-3. For shear walls with M/Vd ratios less than 1, F v is given by Equation 2-4. For shear walls with M/Vd ratios greater than or equal to 1, F v is given by Equation 2-5. F v ƒ' 50 psi (2-3) F v M Vd ƒ' M psi (2-4) Vd F v ƒ' 35 psi (2-5) If f v is less than or equal to the applicable F v liit, the asonry is assued to provide the entire shear strength and shear reinforceent is not required. If f v is greater than the applicable F v liit, the asonry is assued to carry no shear and shear reinforceent ust be provided in accordance with MSJC Section For reinforced asonry subjected to flexural tension, and where it has been deterined that shear reinforceent is required, the shear reinforceent is to coply with MSJC Section The iniu area of shear reinforceent, A v, at a spacing, s, shall be deterined using Equation 2-6. Vs Av (2-6) F d s The shear reinforceent is to be provided parallel to the direction of the applied shear force with a spacing not to exceed the lesser of d/2 or 48 in. Reinforceent is also required perpendicular to the shear reinforceent with an area equal to at least 1/3A v and with a spacing not to exceed 8 ft. 6

16 When shear reinforceent is provided, the shear stress under service loads, f v, calculated using Equation 2-2, shall not exceed the applicable allowable stress liit, F v, as given in MSJC Section and as listed below. For flexural ebers (i.e., for beas), F v is given by Equation 2-7. For shear walls with M/Vd ratios less than 1, F v is given by Equation 2-8. For shear walls with M/Vd ratios greater than or equal to 1, F v is given by Equation 2-9. In effect, these liits provided an upper bound on the shear strength peritted in reinforced asonry ebers, no atter the aount of shear reinforceent that is provided. F.0 ƒ' 150 psi (2-7) v 3 F v M Vd ƒ' M (2-8) Vd F v 1.5 ƒ' 75 psi (2-9) Reinforced asonry ebers that are not subjected to flexural tension are to be designed in accordance with either the requireents of MSJC Section for unreinforced asonry or with the requireents of MSJC Section This latter section requires that shear reinforceent coplying with MSJC Section be provided and that the allowable stress liits of MSJC Section be et. The MSJC ASD provisions for reinforced asonry do not distinguish between in-plane shear and out-of-plane shear MSJC Strength Design (SD) The MSJC SD shear design provisions are specified separately for unreinforced asonry and for reinforced asonry. 7

17 Unreinforced Masonry SD shear design provisions for unreinforced asonry are given in MSJC Section The noinal shear strength, V n, is specified as the sallest of (a), (b) and the applicable condition of (c) through (f) as listed below: (a) 3.8A n ƒ' (b) 300 An (c) For running bond asonry not solidly grouted: 56 A n N u (d) For stack bond asonry with open end units and grouted solid: 56 A n N u e) For running bond asonry grouted solid: 90 A n N u (f) For stack bond other than open end units grouted solid: 23 A n For design, the factored shear force, V u, shall not exceed the noinal shear strength, V n, ties the strength- reduction factor, ϕ, for shear of The MSJC SD provisions for unreinforced asonry do not distinguish between in-plane shear and out-of-plane shear Reinforced Masonry SD shear design provisions for reinforced asonry are given in MSJC Section The noinal shear strength, V n, is given as the su of the noinal shear strength provided by the 8

18 asonry, V n, and the noinal shear strength provided by the shear reinforceent, V ns, as shown in Equation V n = V n + V ns (2-10) For design, the factored shear force, V u, shall not exceed the noinal shear strength, V n, ties a shear strength- reduction factor, ϕ, of The noinal shear strength, V n, is given by Equation The first ter in this equation represents the strength contribution fro the asonry, and the second ter represents the shear strength contribution fro the applied axial copressive load. The third ter represents the noinal shear strength provided by the shear reinforceent, V ns. M V 5 n u v An ƒ' 0. 25Pu 0. f yd (2-11) v Vud v s A The noinal shear strength, V n, shall not exceed 6.0A f ' for walls with values of n M u /V u d v less than or equal to A liit on V n of 4.0A f ' applies for values of M u /V u d v n greater than or equal to 1.0. For M u /V u d v values between 0.25 and 1.0, the axiu value of V n is linearly interpolated. Values for M u /V u d v need not be taken greater than 1.0 and shall be taken as a positive nuber. The MSJC SD provisions for reinforced asonry do not distinguish between in-plane shear and out-of-plane shear MSJC Notation A n = net cross-sectional area of a eber A v = cross-sectional area of shear reinforceent b = width of section 9

19 d = distance fro extree copression fiber to centroid of tension reinforceent d v = actual depth of a eber in direction of shear considered F s = allowable tensile or copressive stress in reinforceent F v = allowable shear stress in asonry f = specified copressive strength of asonry f v = calculated shear stress in asonry f y = specified yield strength of steel for reinforceent or anchors I n = oent of inertia of net cross-sectional area of a eber M = axiu oent at the section under consideration M u = factored oent N u = factored copressive force acting noral to the shear surface that is associated with the V u loading cobination case under consideration N v = copressive force acting noral to the shear surface P u = factored axial load Q = first oent about the neutral axis of an area between the extree fiber and the plane at which the shear stress is being calculated s = spacing of reinforceent V = shear force V n = noinal shear strength V u = factored shear force ϕ = strength-reduction factor 10

20 2.2 Unifor Building Code The Unifor Building Code (UBC) (ICBO, 1997) contains two sets of provisions for shear design. Provisions based on working stress design (WSD), equivalent to ASD, are given in UBC Section 2107, and provisions based on SD are given in UBC Section UBC Working Stress Design (WSD) The UBC WSD shear design provisions are specified separately for unreinforced asonry and for reinforced asonry Unreinforced Masonry WSD shear design provisions for unreinforced asonry are given in UBC Section Shear stresses in beas and shear walls due to service loads are calculated using Equation V f v (2-12) A e This shear stress, f v, shall not exceed the applicable allowable stress liit, F v, given in UBC Sections and and as listed below. For flexural ebers (i.e., for beas), F v is given by Equation F v ƒ' 50 psi (2-13) For shear walls, F v is given by the applicable condition of Equations 2-14 through Clay units: F.3 ƒ' 80 psi (2-14) v 0 Concrete units, Type M or S ortar: Fv 34 psi (2-15) Concrete units, Type N ortar: Fv 23 psi (2-16) 11

21 In addition, the allowable shear stress, F v, in unreinforced asonry ay be increased by 0.2 ties the coputed copressive stress due to dead load. The UBC WSD provisions for unreinforced asonry do not distinguish between in-plane shear and out-of-plane shear Reinforced Masonry WSD shear design provisions for reinforced asonry are given in UBC Section Shear stresses in beas and shear walls due to service loads are calculated using Equation V ƒ v (2-17) bjd For ebers of T or I section, the width of the web, b, shall be substitute for the width, b. This shear stress, f v, shall not exceed the applicable allowable stress liit, F v, given in UBC Sections and and as listed below. For flexural ebers (i.e., for beas), F v is given by Equation F v ƒ' 50 psi (2-18) For shear walls with M/Vd ratios of less than 1, F v is given by Equation For shear walls with M/Vd ratios greater or equal to 1, F v is given by Equation F v M Vd ƒ' M psi (2-19) Vd F v ƒ' 35 psi (2-20) If f v is less than or equal to the applicable F v liit, the asonry is assued to provide the entire shear strength and shear reinforceent is not required. If f v is greater than the applicable F v 12

22 liit, the asonry is assued to carry no shear and shear reinforceent ust be provided in accordance with UBC Section For reinforced asonry sections where it has been deterined that shear reinforceent is required, the shear reinforceent is to coply with UBC Section The area required for shear reinforceent placed perpendicular to the longitudinal reinforceent is coputed by Equation Vs Av (2-21) F d s The shear reinforceent is to be spaced so that every 45-degree line extending fro a point at d/2 to the longitudinal tension bars shall be crossed by at least one line of web (shear) reinforceent. When shear reinforceent is provided, the shear stress under service loads, f v, calculated using Equation 2-17, shall not exceed the applicable allowable stress liit, F v, as given in UBC Section and as listed below. For flexural ebers (i.e., for beas), F v is given by Equation F.0 ƒ' 150 psi (2-22) v 3 For shear walls with M/Vd ratios less than 1, F v is given by Equation For shear walls with M/Vd ratios greater than or equal to 1, F v is given by Equation In effect, these liits provided an upper bound on the shear strength peritted in reinforced asonry ebers, no atter the aount of shear reinforceent that is provided. F v M Vd ƒ' M (2-23) Vd F v 1.5 ƒ' 75 psi (2-24) 13

23 The UBC WSD provisions for reinforced asonry do not distinguish between in-plane shear and out-of-plane shear UBC Strength Design (SD) The UBC SD shear design provisions are given in UBC Section 2108 and apply only to reinforced asonry. The noinal shear strength, V n, is generally given as the su of the noinal shear strength provided by the asonry, V, and the noinal shear strength provided by the shear reinforceent, V s, as shown in Equation V n = V + V s (2-25) For design, the factored shear force, V u, shall not exceed the noinal shear strength, V n, ties the strength-reduction factor, ϕ, for shear of However, the value of ϕ ay be taken as 0.80 for any shear wall when its noinal shear strength exceeds the shear corresponding to developent of its noinal flexural strength for the factored load cobination. The UBC SD shear provisions for beas are given in UBC Section , for walls under out-of-plane loads in UBC Section , and for walls under in-plane loads in UBC Section For beas, the strength contribution fro the asonry, V, is given by Equation The noinal shear strength coefficient, C d, is dependent on the M/Vd ratio. When M/Vd is less than or equal to 0.25, then C d is =2.4. If M/Vd is greater than or equal to 1.00, then C d is 1.2. For M/Vd values between 0.25 and 1.00, C d is interpolated. The strength provided by the shear reinforceent, V s, is given by Equation The value of V n shall not exceed 6.0A f' 380 A for beas with values of M/Vd less than or equal to 0.25, the axiu e e value of V n is 4.0A f' 250 A for values of M/Vd greater than or equal to 1.0, and the e e 14

24 axiu value of V n is linearly interpolated for M/Vd values between 0.25 and 1.0. Additionally, the value of V is taken as zero for any bea region subjected to net tension factored loads. V C A f 63C A (2-26) d e d e V A ρ f (2-27) s e n y Transverse (shear) reinforceent is required in beas when V u exceeds V. When transverse reinforceent is required, the following provisions apply: Shear reinforceent shall be a single bar with a 180-degree hook at each end. Shear reinforceent shall be hooked around the longitudinal reinforceent. The iniu transverse shear reinforceent ratio shall be The first transverse bar shall not be ore than one fourth of the bea depth fro the end of the bea. The axiu spacing shall not exceed half the depth of the bea nor 48 in. For out-of-plane loads on walls which have vertical load stresses under unfactored loads greater than 0.04 f but less than 0.2 f, and with a wall slenderness ratio h /t that does not exceed 30, the noinal shear strength, V n, is given by Equation V 2A f (2-28) n v For in-plane loads on walls, the noinal shear strength, V n, is given by Equation The first ter in this equation represents the strength contribution fro the asonry, V, and the second ter represents the noinal shear strength provided by the shear reinforceent, V s. The noinal shear strength coefficient, C d, is 2.4 for M/Vd less than or equal to 0.25, C d is 1.2 for 15

25 M/Vd greater than or equal to 1.00, and C d is interpolated for M/Vd values between 0.25 and V C A f A f (2-29) n d v v n y The value of V n shall not exceed 6.0A f' 380 A for walls with values of M/Vd less e e than or equal to 0.25, the axiu value of V n is 4.0A f' 250 A for values of M/Vd greater e e than or equal to 1.0, and the axiu value of V n is linearly interpolated for M/Vd values between 0.25 and 1.0. In the case that a shear wall has a noinal shear strength which exceeds the shear corresponding to the developent of its noinal flexural strength, two shear regions exist. For all cross sections within the region defined by the base of the shear wall and a plane at a distance L w above the base of the shear wall, the shear contribution fro the asonry is taken as zero and the noinal shear strength shall be deterined by Equation The required shear strength for this region shall be calculated at a distance L w /2 above the base of the shear wall, but not to exceed one half story height. For the other region, the noinal shear strength of the wall shall be deterined by Equation V A ρ f (2-30) n v n y Unifor Building Code Notation A e = effective area of asonry A v = net area of asonry section bounded by wall thickness and length of section in direction of shear force considered A v = cross-sectional area of shear reinforceent 16

26 b = effective width of rectangular section or width of flange for T and I sections b = width of web in T or I section C d = noinal shear strength coefficient d = distance fro copression face of flexural eber to centroid of longitudinal tensile reinforceent F s = allowable tensile or copressive stress in reinforceent F v = allowable shear stress in asonry f = specified copressive strength of asonry f v = coputed shear stress due to design load f y = specified yield strength of steel for reinforceent or anchors h = effective height of wall j = ratio or distance between centroid of flexural copressive forces and centroid of tensile forces of depth, d M = axiu oent at the section under consideration s = spacing of reinforceent t = effective thickness of wall V = total design shear force V n = noinal shear strength V u = factored shear force ρ n = ratio of distributed shear reinforceent on plane perpendicular to plane A v ϕ = strength-reduction factor 17

27 2.3 New Zealand Standard 4230:2004 The New Zealand Standard Design of Reinforced Concrete Masonry Structures (NZS, 2004) provisions for shear design are given in Section The design shear force fro ultiate liit state loads, V *, shall not exceed the noinal shear strength, V n, ties the strength-reduction factor, ϕ, for shear of The noinal shear strength is given as the specified shear stress, v n, ties the effective area of the section, as given by Equation The effective area, b w d, is defined in Figure 2.1 for in-plane and out-of-plane loadings and for full and partial grouting. Vn vnbwd (2-31) The specified shear stress v n consists of a contribution fro the asonry, v, a contribution fro any axial load, v p, and a contribution fro the shear reinforceent, v s. The three coponents are defined by Equations 2-32, 2-33 and 2-34, respectively. The total shear stress, v n, ay not exceed the stress liit, v g, as defined in Table 2.1. v C C2 v b 1 (2-32) N * v p 0.9 tan (2-33) b d w Av f y vs C3 (2-34) b s w The shear strength coefficient C 1 in the v equation accounts for the shear contribution fro dowel action of the longitudinal steel and is defined by Equation 2-35 for longitudinal reinforcing ratios greater than 0.07%. The shear coefficient C 2 is a function of the wall aspect ratio. For h e /L w less than 0.25, C 2 is equal to 1.5. For h e /L w greater than one, C 2 is equal to 1.0. For h e /L w greater than or equal to 0.25 and less than or equal to 1.0, C 2 is define by Equation 2-18

28 37. Beas and coluns have a C 2 value equal to 1.0. Values for the basic shear stress, v b, are given in Table 2.1 as a function of observation type and stress condition. Observation type refers to the level of inspection specified during construction (see Table 2.2). The shear stress contribution fro axial load, v p, ust be less than or equal to 0.1f. In addition, the value of N* ust be less than or equal to 0.1f A g. The α ter accounts for differences in the effective location of the axial load in walls subjected to single or double bending (see Figure 2.2) The coefficient C 3 in the v s equation is defined as 0.8 for walls and 1.0 for beas and coluns. The spacing of the shear reinforceent, s, ust not exceed 0.5L w for walls and not exceed 0.5d nor 600 for beas and coluns. A iniu area of shear reinforceent, defined by Equation 2-38, ust be provided. C1 33 w f y 300 (2-35) As Aps w b d (2-36) w C h e 2 Lw (2-37) A v 0.15bws f y (2-38) New Zealand Standard Notation A ps = area of prestressed reinforceent in flexural tension zone A s = area of nonprestressed reinforceent A v = area of shear reinforceent within a distance, s 19

29 b w = effective web width C 1, C 2, C 3 = shear strength coefficient d = distance fro extree copression fibre to centroid of longitudinal tension reinforceent, but needs not be less than 0.8Lw for walls and 0.8h for prestressed coponents f y = lower characteristic yield strength of non-prestressed reinforceent h e = effective wall height in the plane of applied loading L w = horizontal length of wall, in direction of applied shear force N* = design axial load in copression at given eccentricity s = spacing of shear reinforceent in direction parallel to longitudinal reinforceent V* = design shear force at section v b = basic type-dependent shear strength of asonry v g = axiu peritted type-dependent total shear stress V n = noinal shear strength of section v n = total shear stress corresponding to V n α = angle fored between lines of axial load action and resulting reaction on a coponent ϕ = strength reduction factor ρ w = ratio of longitudinal reinforceent in a wall 20

30 Figure 2.1 Effective Areas for Shear 21

31 Table 2.1 Type Dependent Noinal Strengths Figure 2.2 Contribution of Axial Load to Wall Shear Strength 22

32 Table 2.2 Observation Types, Adissible Use and Noinal Strengths 23

33 2.4 Canadian Standards Association S The shear design provisions in the Canadian Standards Association Design of Masonry Structures (CSA S304.1, 2004) are given in Section 7.10 and are specified separately for unreinforced asonry and for reinforced asonry Unreinforced Masonry The factored shear resistance, V r, for unreinforced asonry walls is given by Equation The first ter defines the shear strength contribution fro the asonry, and the second ter is the shear strength increase due to axial stress. The strength reduction factor for asonry, ϕ, is specified as For use in the equation, the ratio M f /V f d v is restricted to be greater than 0.25 and less than 1.0. For fully grouted walls, γ g is equal to 1.0. For partially grouted walls, γ g is equal to A e /A g but ay not be greater than 0.5. M f Vr f ' bwd v 0.25Pd g 0. 4 ƒ' bwd v g (2-39) V d f v For squat walls with aspect ratios, h w /l w, between 0.5 and 1.0, the axiu factored shear resistance ay be increased to the value defined by Equation h w 0.4 ƒ' bwd v g 2 (2-40) lw For out-of-plane loading of unreinforced walls and coluns, the factored shear resistance is defined by Equation V 0.16 ƒ' A 0.25P 0.4 ƒ' A (2-41) r e d e 24

34 2.4.2 Reinforced Masonry The factored shear resistance, V r, for reinforced asonry walls is given by Equation The first two ters in the equation, accounting for the asonry and axial stress contributions to shear strength, are the sae as those used for unreinforced asonry. The third ter represents the contribution due to shear reinforceent. The strength reduction factor for asonry, ϕ, is specified as 0.60, and the strength reduction factor for steel, ϕ s, is specified as For squat walls with aspect ratios of between 0.5 and 1.0, the liit on factored resistance is defined by Equation For out-of-plane loading of reinforced walls and coluns, the shear resistance is the sae as that for unreinforced sections, as defined by Equation M f v Vr f ' bwdv 0.25Pd g 0.60 s Av f y 0. 4 V f dv s d ƒ' b w d v g V (2-42) M f f ' bd 0.25Pd 0. ƒ' bd (2-43) V d r 4 f v Canadian Standards Notation A e = effective cross-sectional area of asonry A v = cross-sectional area of shear reinforceent b w = overall web width d v = effective depth for shear calculations, which need not be taken as less than 0.8 L w for walls f = copressive strength of asonry noral to bed joint at 28 days f y = yield strength of reinforceent h w = total wall height 25

35 l w = wall length M f = factored oent P d = axial copressive load on the section under consideration, based on 0.9 ties dead load plus any factored axial load arising fro bending in coupling beas where applicable s = spacing of shear reinforceent easured parallel to the longitudinal axis of the eber V f = shear under factored loads V r = factored shear resistance γ g = factor to account for partially grouted walls or coluns or ungrouted walls and coluns when calculating shear resistance ϕ = resistance factor for asonry ϕ s = resistance factor for reinforcing bars 2.5 Shing et al. Shing et al (1990a) developed a shear strength prediction equation based on laboratory tests producing shear failures in asonry walls. Shing s equation, given in Equation 2-44, accounts for the shear contributions fro the asonry, axial load and shear reinforceent. In addition, the shear strength contribution fro dowel action of vertical reinforceent is accounted for by the ρ v f y ter in the equation. L 2d Vn ( v f y c ) 2 A f 1 Ah f y (2-44) s 26

36 2.5.1 Shing et al. Notation A = the net horizontal cross-sectional area A h = area of a horizontal reinforcing bar d = the distance of the extree vertical steel fro the edge of a wall f = copressive strength of asonry f y = yield strength of the steel L = the horizontal length of a wall s = the vertical spacing of the horizontal reinforceent V n = noinal shear strength ρ v = the ratio of the vertical steel σ c = axial copressive stress 2.6 Anderson and Priestley (1992) Anderson and Priestley developed an epirical equation to predict the ultiate shear strength of asonry walls. Anderson and Priestley s equation, given in Equation 2-45, includes the ter b to account for the type of asonry used and the ter k to account for strength degradation due to cyclic loading of walls. The b factor is specified as 0.24 for walls constructed out of concrete asonry units and as 0.12 for clay brick walls. The k factor is based on the flexural ductility ratio. For a ductility ratio less than 2.0, k is specified as 1.0, indicating that the wall has not suffered significant shear strength degradation. The k factor linearly decreases fro 1.0 to zero as the ductility ratio increases fro 2.0 to 4.0. When the flexural ductility ratio has reached a value of 4.0, the asonry has endured significant degradation and the asonry contribution is assued to be negligible. 27

37 Vn kb f wt 0.25P 0.5Ah f yh d s (2-45) Anderson and Priestley Notation A h = area of a single horizontal reinforcing steel bar b = coefficient to account for the type of asonry used in construction d = distance fro copression face to extree tension bar f = asonry copressive strength f yh = yield strength of horizontal reinforcing steel k = ductility coefficient P = axial load s = spacing of horizontal shear reinforceent t = wall thickness V n = noinal shear strength w = wall width (length) 28

38 CHAPTER 3 SHEAR WALL TEST DATA Available results fro laboratory tests of asonry walls failing in shear were collected fro researchers fro around the world. Much of the data was collected previously by NERHP (2000) and Voon (2007). For the selected data, all walls were fully grouted, subjected to in-plane shear loading, and the failure ode was deterined to be shear. The data set include walls constructed of clay asonry and concrete asonry, resulting fro tests perfored by Shing et al (1990a), Masuura (1987), Sveinsson et al (1985) and Voon and Ingha (2006). 3.1 Shing et al. Shing et al. (1990a) tested 22 asonry walls with diensions of 72 in. by 72 in. The walls were subjected to a single bending loading arrangeent, shown in Figure 3.1. Ten of the walls failed in shear, and it is the results for those tests that were included in the shear data set for this study. Eight wall speciens were constructed of noinal 6 in. x 8 in. x 16 in. concrete blocks, and the other two wall speciens were constructed of noinal 4 in. x 6 in. x 16 in. clay units. All walls were fully grouted and contained uniforly distributed horizontal and vertical reinforceent. The wall aspect ratio, h e /L w, was kept constant at 1.0. The copressive strength of asonry, f, values were between 2,500 psi and 3,800 psi. The horizontal reinforcing ratio, ρ h, varied fro to The vertical reinforcing ratio, ρ v, ranged fro to The axial stresses on the wall speciens varied fro 0 psi to 280 psi. The reported displaceent ductility at failure, µ, ranged fro 2.0 to Data fro the wall tests by Shing et al are given in Appendix A. 29

39 Figure 3.1 Shing et al.- Test Apparatus and Setup 3.2 Matsuura Matsuura (1987) tested 80 asonry wall speciens, 18 of which failed in shear and were fully grouted. These walls included 14 walls constructed of concrete asonry and 4 walls constructed of clay asonry. The wall heights varied fro 1700 to 1800 (67 in. to 71 in.), and the wall lengths ranged fro 790 to 1590 (31 in. to 63 in.). The wall speciens were tested as cantilevers and subjected to horizontal shear loads. Figure 3.2 illustrates the test apparatus. The aspect ratio, h e /L w, varied fro 0.57 to The asonry copressive strength f, values were between 21.8 MPa to 31.4MPa (3160 psi to 4550 psi). The horizontal and vertical reinforcing ratios ranged fro 0 to and fro to , respectively. The axial stresses on the wall speciens varied fro 0.49 MPa to 1.96 MPa (71 psi to 284 psi). The reported displaceent ductility, µ, ranged fro 0.95 to Data fro the wall tests by Matsuura are given in Appendix A. 30

40 Figure 3.2 Matsuura - Test Apparatus and Setup 3.3 Sveinsson et al. Sveinsson et al. (1985) tested twenty wall speciens that were all fully grouted and failed in shear. Half of the walls were constructed out of concrete asonry, and the other half were constructed of clay asonry. The wall speciens were loaded in double bending, resulting in an effective wall height, h e, equal to half of the actual wall height. The wall aspect ratio, h e /L w, was kept constant at The asonry copressive strength f, values were between 2190 psi and 4000 psi. The horizontal and vertical reinforcing ratios ranged fro to and fro to , respectively. The axial stresses on the wall speciens varied fro 272 psi to 437 psi. The reported displaceent ductility, µ, ranged fro 2.2 to Data fro the wall tests by Sveinsson et al. are given in Appendix A. 31

41 3.4 Voon and Ingha Voon and Ingha (2003) conducted tests on seven concrete asonry wall speciens. The walls were fully grouted and failed in shear when subjected to a horizontal shear force in single bending. The test setup is shown in Figure 3.3. The asonry copressive strength f, values were between 17.0 MPa and 24.3MPa (2470 psi and 3520 psi). The horizontal and vertical reinforcing ratios ranged fro 0 to and fro to , respectively. The axial stresses on the wall speciens varied fro 0 MPa to 0.5 MPa (0 psi to 72 psi). The reported displaceent ductility, µ, ranged fro 1.33 to Data fro the wall tests by Voon and Ingha are given in Appendix A. Figure 3.3 Voon and Ingha - Test Apparatus and Setup 32

42 CHAPTER 4 ANALYSIS 4.1 Interpretation of Shear Equations To facilitate the evaluation of the effectiveness of the various code provisions and strength predication equations, consistent definitions of the equation variables were used. In addition, one set of units was also used for perforing the coparisons (English units were chosen). In soe cases, the original equations were odified to accoodate the consistent definitions of the variables. However, the resulting predicted shear strengths and allowable shear stresses are consistent with those produced by the original equations. Several odifications were ade to the variable definitions used in the MSJC shear provisions. The M u /V u d v ter in the MSJC equations was replaced with the ratio of the effective wall height to the wall length, h e /L w. The effective wall height takes into account whether the wall is loaded in double bending or single bending. The variable P u was also replaced with the level of axial stress, n, ultiplied by the wall cross-sectional area, A n, defined as wall thickness, t, ties the total wall length, L w. The area of shear reinforceent, A v, was relabeled as A h. The spacing of the shear reinforceent, s, was relabeled as s h. The yield stress in the shear reinforceent was labeled f yh, rather than f y. The variable d v, which is defined by MSJC as the actual depth of a eber in the direction of shear considered, was relabeled as the wall length, L w. The MSJC ASD shear provisions utilize allowable stresses rather than noinal strengths. The allowable stresses incorporate additional safety factors for application to service loads. In addition, the MSJC ASD provisions specify that, depending upon the level of service loads, either the asonry alone or the shear reinforceent alone ust provide the needed shear 33

43 capacity. Since design service loads are not applicable to the reported failure loads, the ASD asonry design stress and the shear reinforceent design stress were each deterined separately. A corresponding allowable shear force was then calculated by ultiplying the specified allowable shear stress, F v, by the applicable wall cross-sectional area, A n, and then copared to the reported shear failure loads fro the laboratory tests. The UBC WSD shear provisions are the sae as the MSJC ASD shear provisions, and thus these provisions were not considered in the evaluations. Variables in the UBC SD provisions were odified as follows. The variable A v in the UBC equations is the net area of the wall and was relabeled as A n. The ter in the shear reinforceent contribution, A v n f y, was relabeled as A h (L w /s h )f yh. The asonry, axial load and shear reinforceent contributions to shear strength in NZS 4230:2004 are specified in ters of stresses. The noinal shear strength is then obtained by ultiplying the total shear stress by the effective wall area, td. The axial load ter N* was relabeled as is the applied axial stress, σ n, ultiplied by the wall cross-sectional area, A n. Several variables in the shear contribution were relabeled: A h for A v, f yh for f y, and s h for s. The NZS 4230:2004 is written for SI units. In order to utilize the NZS tables and figures, all calculations were first deterined in SI units, and the resulting design strength was then converted into English units. The shear provisions in CSA S include the ter M f /V f d v to account for wall aspect ratio. Siilar to the change ade for the MSJC, this ter was replaced with the ratio of the effective wall height, h e, to the effective wall depth, d, defined as the distance fro the copression face of wall to the extree vertical reinforceent but not less than 0.8L w. The variable b w is equivalent to t, and d v was relabeled as d. The axial force P u was represented as the 34

44 applied axial stress, n, ultiplied by a noinal area, A n. The g variable is equal to 1.0 for fully grouted walls, so this variable thus drops out for the walls considered. As before, A h is equivalent to A v, and s is equivalent to s h. The ϕ factors were reoved fro the equations in order to copare a noinal strength to another noinal strength without application of aterial resistance factors. Finally, CSA provisions are specified in SI units, and in order to use English units, a 1 conversion factor was applied to all ters with ƒ' The only changes in the shear strength prediction equation developed by Shing et al. were associated with changes in the subscripts of the variables while aintaining the sae definition. The yield stress in the reinforceent was taken as f yv for vertical reinforceent and f yh for horizontal reinforceent, instead of f y used in the original equation. The wall area, A, in Shing s equation is relabeled as A n, L is relabeled as L w, and s is relabeled as s h in the adapted equation. The wt ters in the Anderson and Priestley equation were replaced with A n, aintaining the sae eaning. The axial load ter P, was exchanged with σ n A n. The horizontal spacing was defined with a s h ter rather than s. The equations used to deterine the asonry, axial load, and shear reinforceent contributions as specified by the various code provisions and strength prediction equations are suarized in Table 4.1 The calculated values resulting fro the evaluated equations are given in Appendix B. 35

45 Table 4.1 Shear Prediction Equations Source Masonry Horizontal Steel Axial Stress Equation h A e MSJC SD A ƒ' 0.5 h f L (4-1) L n 0.25σ A yh w w s h n n he 1 he 1 4 ƒ' Lw 3 0.8Lw MSJC ASD V (4-2) MSJC ASD V s A hfs (4-3) s t UBC SD h L e w 1 C d A n ƒ' f L A f w h yh s h (4-4) 0.8L w NZ-2004 C1 C2 vb t 0.8L w C3A hf yh (4-5) s 0.9 n An tan h h CANADIAN STANDARD SHING ET AL h v e d f y f ' 2 A t 0.8L n f ' w 0.60A L w s h h f 2d yh 0.8L s h 1 A w h f yh 0.25 (4-6) A n n n A n f (4-7) ANDERSON AND PRIESTLEY bk f A d 0.5A f 0.25 A n h yh n n (4-8) s h 4.2 Statistical Evaluations All of the various code and proposed equations were evaluated based on how well they predicted the reported shear capacities of the walls. The first ethod explored for evaluating the effectiveness of the various equations was a statistical evaluation and coparison. The ratio of test strength to the predicted strength (V test/ V n ) was calculated for each of the walls in the 36

46 copiled data set. A ratio of one indicates that the equation does a perfect job of predicting the wall shear capacity. A value greater than one eans that the equation is conservative, and a ratio less than one indicates that the equation is unconservative. For the MSJC ASD equations, the ratios should be larger than one because they include a factor of safety for application to design using service loads. Table 4.2 lists the ean, standard deviation, coefficient of variation, iniu value, axiu value and 5 th percentile value obtained for each of the various code and predicted strength equations. The fifth percentile values were calculated assuing a norally distributed data set. Table 4.2 Statistical Coparisons of Design Equations Shear Equation MSJC SD/ NEHRP Mean Standard Deviation Coeff. Of Variation Miniu Value Maxiu Value 5th Percentile MSJC ASD V MSJC ASD V s UBC CSA Shing et al NZS Anderson and Priestley V test /V n The ean values fro the MSJC SD and Shing equations are the closest to 1.0, indicating that these equations provide the best predictions of ean shear strength. The MSJC ASD ean values exceeded 8.5, which is higher than would be expected even taking into account the additional factor of safety present with allowable stress design. The sallest 37

47 standard deviation value, and therefore least varying equation, was the MSJC SD, with the CSA, Shing, and the NZS equations also having low values. The coefficient of variation (COV) was also calculated to quantify the true scatter. The lowest COV values were the MSJC SD and the CSA. The COV values for the MSJC ASD equations were aong the largest, indicating significant variation in the accuracy of the ASD equations. The fifth percentile value is the ratio whereby 95 percent of the walls failed at loads equal to or higher than are predicted by code or proposed equation. The fifth percentile value for the MSJC SD provisions is 0.88, which is above the aterial resistance factor value of ϕ = 0.8 specified by the MSJC. The fifth percentile values for the UBC, NZS, and CSA equations also are at or above 0.8. As an overall assessent of the statistics shown in Table 4.2, the best perforance of the various code and proposed equations is obtained using the MSJC SD equation. 4.3 Test Paraeter Evaluations After the statistics were calculated and the general behavior of the equation was better understood, plots were created to isolate the effects of individual specien paraeters. These plots illustrate the relationship between a particular variable and the ratio of test strength to predicted strength by the various code and predictive equations. The paraeters evaluated were: asonry copressive strength (f ), aount of shear reinforceent ( h f yh ), level of axial copressive stress ( n ), aount of vertical reinforceent ( v f yv ), displaceent ductility ( ), and wall aspect ratio (h e /L w ). The ideal equation will have data points aligned along the horizontal line of V test /V n =1.0. This situation is the result of an equation that predicts the test value accurately and handles the 38