Lecture Handouts Thursday, 20th Feb, 2014

Transcription

1 Lecture Handouts Thursday, 20 th Feb, 2014

2 Confined Masonry Buildings: Key Components and Performance in Past Earthquakes Dr. Svetlana Brzev BCIT, Vancouver, Canada IIT Gandhinagar, India Short Course on Seismic Design of Reinforced and Confined Masonry Buildings February 17-21, 2014, IIT Gandhinagar, India 1 Acknowledgments Earthquake Engineering Research Institute (SPI Projects Fund) Maximiliano Astroza and Maria Ofelia Moroni, Professors, Department of Civil Engineering, Universidad de Chile (members of the EERI team) Roberto Meli and 12 other co-authors of the EERI s Confined Masonry Guide 2 1

3 Topics Confined masonry: key concepts Lessons learned from the past earthquakes 3 Why Confined Masonry? Poor performance of unreinforced masonry and nonductile reinforced concrete (RC) frame construction caused unacceptably high human and economic losses in past earthquakes This prompted a need for developing and/or promoting alternative building technologies The goal is to achieve enhanced seismic performance using technologies which require similar (preferably lower) level of construction skills and are economically viable 4 2

4 CONFINED MASONRY: an opportunity for improved seismic performance both for unreinforced masonry and reinforced concrete frame construction in low- and medium-rise buildings 5 Confined Masonry Construction: An Alternative to RC Frame Construction 6 3

5 Confined Masonry Construction: An Alternative to Unreinforced Masonry Construction 7 Confined Masonry: Beginnings Evolved though an informal process based on its satisfactory performance in past earthquakes The first reported use in the reconstruction after the 1908 Messina, Italy earthquake (M 7.2) - death toll 70,000 Practiced in Chile and Columbia since 1930 s and in Mexico since 1940 s Currently practiced in several countries/regions with high seismic risk, including Latin America, Mediterranean Europe, Middle East (Iran), South Asia (Indonesia), and the Far East (China). 8 4

6 Confined Masonry and RC Frame Construction: Performance in Recent Earthquakes January 2010, Haiti M ,000 deaths February 2010, Chile M deaths (10 due to confined masonry construction) 9 Global Confined Masonry Initiative An International Strategy Workshop on the Promotion of Confined Masonry organized in January 2008 at Kanpur, India Confined Masonry Network established as a project of the World Housing Encyclopedia with two major objectives: To improve the design and construction quality of confined masonry where it is currently in use; and To introduce it in areas where it can reduce seismic risk. 10 5

7 Confined Masonry Design Codes Available at 11 Key Components of a Confined Masonry Building : Masonry walls made either of clay brick or concrete block units Tie-columns = vertical RC confining elements which resemble columns in reinforced concrete frame construction. Tie-beams = horizontal RC confining elements which resemble beams in reinforced concrete frame construction. 12 6

8 Components of a Confined Masonry Building: 13 Reinforced Concrete Frame Construction 14 7

9 Confined Masonry Construction 15 Confined Masonry versus Infilled RC frames: -construction sequence - integrity between masonry and frame Confined Masonry Walls first Concrete later Reinforced Concrete Infilled Frame Concrete first Walls later Source: Tom Schacher 16 8

10 Confined Masonry: Construction Process Source: Tom Schacher 17 Confined Masonry vs RC Frames with Infills Key Differences 18 9

11 A comparison: confined masonry and RC frames with infills Youtube videos developed by a Calpoly student, USA ned%20masonry&source=video&cd=9&cad=rja& ved=0cfgqtwiwca&url=http%3a%2f%2fwww.y outube.com%2fwatch%3fv%3d3czsuhywrek&e i=hkz3ufmze4_xrqfbzoa4&usg=afqjcnhmmfkf xipzbalyxiw3jwj4zeydew No. 19 Location of Confining Elements is Very Important! 20 10

12 Key Elements Layout Rules 21 Typical Floor Plans Examples from Chile Source: O. Moroni and M. Astroza 22 11

13 V Confined Masonry Panel Under Lateral Loading: Shear Failure P P P V m V c V ' m V c V m Shear force V ' m V c Displacement 23 Confined Masonry Panel Under Lateral Loading: Shear Failure Three stages: 1- Onset of diagonal cracking 2 Cracking propagated through RC tie-columns 3 Failure Note: internal stress redistribution starts at Stage

14 Confined Masonry Panel Bending Stress Distribution Source: EERI Guide (2011) 25 Strut-and-Tie Model for a Confined Masonry Panel B C B str ut no de C tie A D A D 26 13

15 Seismic Design Objectives RC confining elements must be designed to prevent crack propagation from the walls into critical regions of RC confining elements. This can be achieved if critical regions of the RC tie-columns are designed to resist the loads corresponding to the onset of diagonal cracking in masonry walls. 27 Mechanism of Seismic Response in a Confined Masonry Building Masonry walls Critical region Diagonal cracking Source: M. Astroza lecture notes,

16 Failure Mechanism: Key Stages Onset of Diagonal cracking Damage in critical regions Masonry walls 29 This condition should be avoided! 30 15

17 Confined Masonry Construction: Toothing at the Wall-to-Tie-Column Interface Toothing enhances interaction between masonry walls and RC confining elements 31 Seismic Performance Confined masonry construction is found in countries/regions with very high seismic risk, for example: Latin America (Mexico, Chile, Peru, Argentina), Mediterranean Europe (Italy, Slovenia), South Asia (Indonesia), and the Far East (China). In some countries (e.g. Italy) for almost 100 years If properly built, shows satisfactory seismic performance EXTENSIVE ENGINEERING INPUT NOT REQUIRED! 32 16

18 Oaxaca quake, September 1999 ecomán earthquake, January Earthquake Performance Confined masonry construction has been exposed to several destructive earthquakes: 1985 Lloleo, Chile (magnitude 7.8) 1985 Mexico City, Mexico (magnitude 8.0) 2001 El Salvador (magnitude 7.7) 2003 Tecoman, Mexico (magnitude 7.6) 2007 Pisco, Peru (magnitude 8.0) 2003 Bam, Iran (magnitude 6.6) 2004 The Great Sumatra Earthquake and Tsunami, Indonesia (magnitude 9.0) 2007 Pisco, Peru (magnitude 8.0) 2010 Maule, Chile earthquake (magnitude 8.8) 2010 Haiti earthquake (magnitude 7.0) Confined masonry buildings performed very well in these major earthquakes some buildings were damaged, but no human losses 34 17

19 Confined Masonry Performed Very Well in Past Earthquakes A six-storey confined masonry building remained undamaged in the August 2007 Pisco, Peru earthquake (Magnitude 8.0) while many other masonry buildings experienced severe damage or collapse 35 Seismic Performance of Confined Masonry Buildings in the February 27, 2010 Chile Earthquake Confined masonry (CM) used for construction of low-rise single family dwellings and medium-rise apartment buildings (up to four-story high). CM construction practice started in the 1930s, after the 1928 Talca earthquake (M 8.0). Good performance reported after the 1939 Chillan earthquake (M 7.8) and this paved the path for continued use of CM in Chile

20 Confined Masonry Construction in Chile (Cont d) Good performance track record in past earthquakes based on single family (one- to two-storey) buildings. Three- and four-storey confined masonry buildings exposed to severe ground shaking for the first time in the February 2010 earthquake (construction of confined masonry apartment buildings in the earthquake-affected area started in 1990s). Modern masonry codes first issued in 1990s prior to that, a 1940 document Ordenanza General de Urbanismo y Construcción had been followed 37 Low-Rise Confined Masonry Construction Single-storey rural house 38 19

21 Low-Rise Confined Masonry Construction Two-storey townhouses (semi-detached): small plan dimensions (5 m by 6 m per unit) 39 Performance of Confined Masonry Construction By and large, confined masonry buildings performed well in the earthquake. Most one- and two-story single-family dwellings did not experience any damage. Large majority of three- and four-story buildings remained undamaged A few buildings suffered severe damage, and two three-story buildings collapsed 40 20

22 Damage Observations: Topics Masonry damage (in- and out-of-plane) RC tie-columns Tie-beam-to-tie-column joints Confining elements around openings Construction materials Collapsed buildings 41 In-plane shear failure of masonry walls at the base level - hollow clay blocks (Cauquenes) 42 21

23 In-plane shear failure of masonry walls at the base level (cont d) 43 In-plane shear failure: hollow clay block masonry 44 22

24 Same failure mechanism as infill masonry in RC frames! Diagonal Tension (INPS-2), FEMA 306 p In-plane shear failure: clay brick masonry 46 23

25 Same failure mechanism as infill masonry in RC frames! Bed Joint Sliding (INPS-3), FEMA 306 p Out-of-Plane Wall Damage Damage at the 2 nd floor level An example of out-of-plane damage observed in a threestorey building The damage concentrated at the upper floor levels The building had concrete floors and timber truss roof The same building suffered severe in-plane damage 48 24

26 Out-of-Plane Damage (cont d) Damage at the 3 rd floor level 49 Floor and Roof Diaphragms Wood floors in single-family buildings (two-storey high) Concrete floors in three-storey high buildings and up (either cast-in-situ or precast) Precast concrete floors consist of hollow masonry blocks, precast RC beams, and concrete overlay ( Tralix system) 50 25

27 Discussion on Out-of-Plane Wall Failure Source: EERI Confined Masonry Guide 51 Tie-Column Failure 52 26

28 Buckling of a RC Tie-Column due to the Toe Crushing of the Masonry Wall Panel 53 Shear Failure of RC Tie-Columns 54 27

29 Same failure mechanism as columns in RC frames with infills! Column Snap Through Shear Failure (INF1C1), FEMA 306 p How to prevent buckling and shear failure of RC tie-columns? All surveyed buildings in Chile had uniform tie spacing 200 mm Tie size 6 mm typical, in some cases 4.2 mm (when prefabricated cages were used) Closer tie spacing at the ends of tie-columns (200 mm regular and 100 mm at ends) 56 28

30 How to Prevent Shear Failure? Must check shear capacity of tiecolumns! V p V r /2 V r V r = wall shear resistance Same approach like RC frames with infills! Note: an increase of tie-column length may be required in some cases! 57 Inadequate Anchorage of Tie-Beam Reinforcement 58 29

31 Inadequate Anchorage of Tie-Beam Reinforcement (another example) 59 Tie-Beam Connection: Drawing Detail Tie-Beam Intersection: Plan View 60 30

32 Tie-beam Tie-Column-to-Tie-Beam Connection: Drawing Detail (prefabricated reinforcement) Note additional reinforcing bars at the tie-beam-to-tiecolumn joint Tie-column (in this case, prefabricated reinforcement cages were used for tie-beams and tiecolumns) 61 Tie-Column-to-Tie-Beam Reinforcement: Anchorage Alternative anchorage details involving 90 hooks (tie-column and tie-beam shown in an elevation view) note that no ties in the joint area were observed 62 31

33 Deficiencies in Tie-Beam-to-Tie-Column Joint Reinforcement Detailing 63 RC Tie-Columns: Absence of Ties in the Joint Area 64 32

34 Tie-column Vertical Reinforcement & Tie-Beam Longitudinal Reinforcement It is preferred to place beam reinforcement outside the column reinforcement cage NO YES 65 Tie-Column Reinforcement: Drawing Detail (Chile) Note prefabricated tiecolumn reinforcement: 8 mm longitudinal bars and 4.2 mm ties at 150 mm spacing Additional ties to be placed at the site per drawing specifications 66 33

35 Absence of Confining Elements at the Openings 67 In-Plane Shear Cracking the Effect of Confinement Unconfined openings Confined openings 68 34

36 Recommendation Unconfined and confined openings - criteria specified in the Guide 69 Building Materials: Hollow Concrete Blocks??? Concrete blocks are widely used for masonry construction in North America and The quality is very good due to advanced manufacturing technology Quality of blocks in other countries often not satisfactory due to low-tech manufacturing technology and an absence of quality control 70 35

37 A severely damaged confined masonry concrete block wall in Chile In spite of poor seismic performance, it is impossible to avoid the use of concrete blocks for masonry construction in many countries 71 Masonry Units Confined Masonry Guide The guide permits the use of concrete blocks, but restricts the percentage of perforations and minimum compressive strength: 4 MPa (bricks) and 5 MPa (blocks-gross area) 72 36

38 Haiti Blocks Block D (215 psi) Block C (1000 psi) 73 Engineered Confined Masonry Buildings Evidence of Collapse Two 3-storey confined masonry buildings collapsed in the February 2010 Chile earthquake (Santa Cruz and Constitución) Most damage concentrated in the first storey level 74 37

39 Simulated Seismic Response: Shake-Table Testing Questions: 1. Which analysis approach is able to simulate seismic response in the most accurate manner? 2. Which approach is most suitable for practical design applications? Sources: Alcocer, Arias, and Vazquez (2004) Juan Guillermo Arias (2005) 75 A Possible Collapse Mechanism for Multi-storey Confined Masonry Buildings 76 38

40 Seismic Performance of Confined Masonry Buildings: Shake-Table Studies Shake-Table Testing of a 3-storey Confined Masonry Building at UNAM, Mexico (Credit: Sergio Alcocer and Juan Arias) Building #1: Building Complex in Constitución (Cerro O Higgins) N C B A Note a steep slope on the west and north sides! 78 39

41 Three Building Blocks: A, B and C A B C damaged collapsed 79 Building Plan Collapsed Building RC Tie-Columns: P1= 15x14 cm P2 = 20x14 cm P4 = 15x15 cm P5 = 70x15 cm P6 = 90x14 cm 80 40

42 Building C Collapse Building C collapsed at the first floor level and moved by approximately 1.5 m towards north 81 Building C Collapse (cont d) C 82 41

43 Probable Causes of Collapse 1. Geotechnical issues: a localized influence of the unrestrained slope boundary and localized variations in sub-surface strata caused localized variations of horizontal (and possibly vertical) ground accelerations 2. Inadequate wall density (less than 1% per floor) 83 Building #2: A Three-Storey Building in Santa Cruz 84 42

44 Collapsed Three-Storey Building 85 Probable Causes of Collapse Poor quality of construction (both brick and concrete block masonry) Low wall density (less than 1% per floor) Note: only one (out of 28) buildings in the same complex collapsed! 86 43

45 Key Causes of Damage 1. Inadequate wall density 2. Poor quality of masonry materials and construction 3. Inadequate detailing of reinforcement in confining elements 4. Absence of confining elements at openings 5. Geotechnical issues 87 Prescriptive international guide endorsed by EERI and IAEE Available online at

46 Short Course on Seismic Design of Reinforced and Confined Masonry Buildings February 17-21, 2014, IIT Gandhinagar, India Acknowledgments Kiran Rangwani, IIT Gandhinagar, India EERI Confined Masonry Network authors of the confined masonry guide: Roberto Meli and others 1

47 Topics Part 1: Simplified Method (Svetlana Brzev) Part 2: Wide Column Model (J.J. Perez Gavilan) The Simplified Method (SM) Based on an idealized distribution of lateral seismic forces in regular shear wall structures with rigid diaphragms. Shear strength of all walls at any floor level is required to exceed the seismic demand (applied shear force due to earthquake ground shaking) 2

48 Assumptions 1.It is assumed that all walls at each floor level fail simultaneously. 2.The walls have shear-dominant behaviour (the effect of bending is ignored). 3.The method assumes rigid diaphragm behaviour. 4.The method ignores torsional effects. The goal: Theoretical Background Shear strength of all walls at any floor level (V R ) should exceed the seismic shear force demand (V x ) at the same level 3

49 Seismic Shear Force Demand Interstorey shear force V x V x Q i Seismic Force Distribution to Individual Walls Wall shear demand V jx 4

50 Seismic Force Distribution to Individual Walls V jx k jx D x k jx N j 1 k jx V x k jx G F H AEj j A j V jx V x N F j 1 AE j F AEj A j A j Storey Shear Resistance Wall resistance V Rj Wall cross-section A j Ap Aw Seismic load 5

51 Storey Shear Resistance V Rj f s A j F AE H F AE 1 when L 2 L H F AE 1.33 when H L Wall Density Index (d) One of the key indicators of seismic resistance d A A w p Ap Aw Seismic load 6

52 Wall Density Index Derivations Goal: resistance greater than demand V R f N s j 1 A j f A s w VR V B V B A h W T W nwa T p d A h n w f s Wall Density Index India Allowable shear stress (N/mm 2 ) Floor weight (kn/m 2 ) Number of storeys Seismic Zone III IV V

53 Assumptions =2.5 for confined masonry (currently not addressed by IS 1893) = 2.5 assuming the fundamental period range from 0.1 to 0.4 sec 3. Importance factor =1 assuming regular importance 4. Allowable masonry shear stress (f s ): from 0.3 to 0.5 N/mm 2 5. Floor weight (w) two values: 6.0 kn/m 2 (light-weight floor structure) and 8.0 kn/m 2 (heavy-weight floor structure e.g. RC slab). Attached writeup (document) on the Simplified Method Seismic Design Guide for Low-Rise Confined Masonry Buildings, EERI, 2011 Further Reading 8

54 1 Simplified Method for Seismic Design of Confined Masonry Buildings by Svetlana Brzev, Juan Jose Perez Gavilan, and Kiran Rangwani 1.1 Introduction The Simplified Method (SM) can be used for quick and simple evaluation of overall seismic resistance for confined masonry buildings. The method is not intended for design of individual walls and it is considered as an approximate method. The SM is intended for application to regular buildings with symmetrical wall layout where torsional effects are not significant because the method cannot take into account additional shear stresses due to torsional effects. Due to its limitations, the method is intended for applications to low-rise confined masonry buildings (up to three storeys high). A few limitations of the SM are summarized below: 1. It is assumed that all walls at each floor level fail simultaneously. 2. The walls have shear-dominant behaviour (the effect of bending is ignored). 3. The method assumes rigid diaphragm behaviour. 4. The method ignores torsional effects. The SM has been used for seismic design of confined masonry buildings in Latin America for several decades. For example, the SM has been included in the Mexico City Masonry Code (NTC- M) since However, Mexican experience shows that the method has been misused, in the sense that it has been applied to structures that do not comply with its requirements (in some cases). For that reason, the revised Mexican Masonry Code NTC-M (to be issued in 2014) will no longer include SM as the method which can be solely used to design a confined masonry building. However, the SM has been recognized as a simple means for evaluating approximate lateral resistance of a masonry structure, thus the SM will still be used for checking the required minimum seismic resistance of confined masonry buildings (although detailed analysis and design will be performed using other methods). This paper presents the key concepts of the SM, including the requirements for its application, theoretical basis, and the wall density index. 1.2 Requirements for the SM Application There are eight requirements related to the SM application. The method can be safely applied provided that the building under consideration complies with these requirements. The requirements are summarized next. 1. Wall distribution must be uniform over the building height. 2. The distribution of walls in plan must be as symmetric as posible, but some assymetry is allowed. The walls should be laid symmetrically with respect to two orthogonal axes in plan. This requirement is met when the torsional static eccentricity at level j (e sj ) does not exceed ten per cent of the floor dimension (B i ) measured perpendicular to the direction of analysis, that is, e 0. 1 sj B j 1-1

55 Figure 1-1. Definition of static eccentricity (e sj ) at interstorey level j. The static eccentricity is given by (Figure 1-1): N i 1 i 1 x F i AEi esj 0. 1B N F A AEi A i i j where x = the distance from the shear center (center of mass) to the axis of the wall parallel to the i analysis direction A = cross-sectional area of the wall i (including RC tie-columns) i F AEi = the effective area factor for wall i N = total number of walls at level j 3. There are at least two lines of walls in each orthogonal direction of the building plan, and the walls along each line extend over at least 50% of the building dimension in the direction of analysis at each storey level. This requirement is illustrated in Figure 1-2 and it is intended to provide adequate torsional resistance. L 1 Dirección Analysis del Direction análisis L 3 L L 2 L 1 +L 2 0.5L L 3 0.5L Figure 1-2. At least two parallel lines of walls are required in each plan direction. 1-2

56 4. At least 75% of the building weight is supported by confined masonry walls. At each floor level, including the foundation level, at least 75 percent of vertical gravity loads are resisted by continuous walls that are inter-connected through monolithic slabs or other systems with adequate shear resistance. This requirement warranties that loadbearing walls compose the main structural system. 5. Floors and roofs must act as rigid diaphragms. In general, reinforced concrete floors and roofs can be treated as rigid diaphragms, provided that transverse walls are not too far apart and that the wall thickness is sufficiently large. Reinforced concrete slabs should be minimum 10 cm thick. 6. The plan aspect ratio of a building should not exceed two (L/W 2.0). The ratio of length to width (L/W) of the building plan should not be greater than 2.0 to reduce chances for flexible diaphragm amplification in RC slab systems (see Figure 1-3). 7. The ratio of the height of the building and the shorter plan side should not exceed 1.5 (H/W 1.5). This requirement limits the possibility of significant overturning moments and second order effects (P- ) (see Figure 1-3). 8. The building should not be higher than three storeys or 9 meters, whichever is smaller. The SM is intended for seismic design of low-rise confined masonry buildings. Current Mexican masonry code (NTC-M 2004) permits the application of this method to buildings of 13 m height or maximum 5 storeys. However, some Mexican masonry experts suggest to restrict the application of the SM to low-rise buildings (three-storey high or less). Figure 1-3. Building dimensions. 1.3 Theoretical Background The SM is based on an idealized distribution of lateral seismic forces in regular shear wall structures with rigid diaphragms. The method compares the shear strength of all walls at any floor level (V R ) and the seismic shear force demand (V x ) at the same level, that is, VR V x (1) 1-3

57 Note that V R depends on the sum of cross-sectional areas of all walls at level x and their shear strength or allowable shear stress (which depends on the type of masonry used). On the other hand, the shear force demand V x depends on applied seismic forces at the same level x in the building. The interstorey shear force at level x is calculated as the sum of all forces above that level, as follows: n X Q i i x V (2) where n = total number of floors x = interstorey level under consideration Note that is seismic inertial force at floor i which is determined in accordance with Indian Standard IS 1893 (Cl. 7.7), as follows (see Figure 1-4): Q V i B n j 1 2 i i W h W h j 2 j (3) where Q = lateral design force for floor i, i W = weight for floor i i h = height of floor i measured with respect to the base of the building i Figure 1-4. Seismic force distribution up the building height. 1-4

58 Design base shear force ( V B ) is determined from the following equation (IS 1893 Cl ): V B A W (4) h T where (IS 1893 Cl. 6.4) Z I Sa Ah (5) 2 R g Z = the zone factor (IS 1893 Table 2), Z 2 is the Design Basis Earthquake (the 2 in the denominator is the Maximum Earthquake reduction factor) I = the importance factor (IS 1893 Table 6) R = the response reduction factor ( I R 1. 0 ) S a g = the average response acceleration (IS 1893 Cl 6.4.5), based on natural period of the structure, and W = the total weight of the structure for seismic analysis (IS 1893 Cl. 7.4) T Consider an n-storey confined masonry building subjected to applied seismic force (interstorey shear force) V x at level x. Due to force V x, the floor and all walls at that level experience uniform lateral displacement D x (rigid diaphragm assumption). Let us assume that there are N walls at level x. Each wall j at level x (denoted by subscript jx) resists a fraction of the interstorey shear force V x in proportion to its stiffness, as follows, V x hence D N j 1 j 1 V V x x N k jx jx N j 1 k jx D x (6) (7) The equation for internal shear force in wall j at level x (spring force) is as follows k jx V jx k jx Dx V N x (8) k j 1 jx Basically, internal force in a wall (e.g. Vj x ) is proportional to its stiffness relative to the total stiffness of all walls at the level under consideration. 1-5

59 Figure 1-5. Seismic force distribution to individual walls at a storey level considering rigid diaphragm and ignoring torsional effects. The SM is intended for seismic design of low-rise wall buildings, and it is assumed that wall deformation is governed by shear, thus the stiffness equation is as follows G FAEj Aj k jx (9) H j where G = shear modulus of the wall material (e.g. masonry) A = cross-sectional area of wall j at level x j F AE j = lateral strength reduction factor for wall j at level x H j = height of wall j at level x Note that F AE depends on the wall height/length (H/L) ratio, where H is the clear wall height and L is the wall length. Since slender walls (H/L>1.33 aspect ratio) can undergo larger lateral 1-6

60 deformations (drift) at failure compared to squat walls, follows: H F AE 1 when L 2 L H F AE 1.33 when H L Therefore, shear force resisted by wall j at level x is equal to FAE A j j V jx Vx (10) N F A j 1 AEj j F AE factor is applied to these walls, as The lateral load resistance at level x can be determined as the sum of the wall resistances projected in the direction where seismic loading is being considered. An individual wall resistance can be estimated as follows: VRj f s Aj FAE (11) where f s is the allowable shear stress for specific type of masonry units and mortar. Indian masonry design standard IS 1905 (Cl ) prescribes the following equation for shear stress in unreinforced masonry walls: f f 0.5 (N/mm 2 ) (12) S d where is compressive stress due to dead loads in N/mm 2 The above equation assumes that the masonry mortar is not leaner than Grade M1 (mortar designations are included in IS 1905 Table 1). As IS 1905 refers to allowable stresses no load factors should be used. An average compressive stress due to gravity loads in walls at level x can be estimated as follows W x f d (13) Ax where Ax is the total cross-sectional area of walls at the floor level being studied, and Wx is the accumulated weight above interstorey x, that is, N A x A i i 1 (assuming N walls at level x) and n W x W i i x (considering n floors in total) 1-7

61 1.4 Wall Density Index Wall density is a key indicator of safety for low-rise confined masonry buildings subjected to seismic and gravity loads (EERI, 2011). Evidence from past earthquakes shows that confined masonry buildings with adequate wall density were able to resist the effects of major earthquakes without collapse. The wall density is quantified through the wall density index, d, which is equal to A w d (14) Ap where A p = area of the building floor plan, as shown in Figure 1-6, and A w = the cross-sectional area of all walls in one direction, that is, a product of the wall length and thickness. It is not necessary to deduct the area of tie-columns and the area of voids in hollow masonry units for the A calculations. w It is very important to note that the wall cross-sectional area should be disregarded in the calculation in the following cases: a) walls with openings, in which the area of an unconfined opening is greater than 10% of the wall surface area, and b) walls characterized by the height-to-length ratio greater than 1.5. The d value should be determined for both directions of the building plan (longitudinal and transverse). Aw Ap Aw Figure 1-6. Wall density index: parameters (EERI, 2011) Seismic load The SM is intended to verify the overall seismic resistance of a building. For that reason, we need to compare the seismic base shear force and the shear resistance (capacity) at the base level of the building, that is, VR V B (15) The total shear resistance at the base of the building can be calculated as follows: V R N j 1 V Rj N j 1 ( f A s j F AE ) 1-8

62 The above equation can be simplified if we assume that the walls have H/L ratio less than 1.33, thus F 1. Also, allowable shear stress ( f s ) is constant. Therefore, V AE R f Where N s j 1 w A j f s A w (16) A denotes the sum of cross-sectional areas for all walls at the base level of the building. On the other hand, the seismic base shear force is equal to V A W B h T where WT nwa p where w = average weight of floor or roof per unit area (N/m 2 ) A = building plan area (m 2 ) p Thus V A n w A (17) B h p Let us compare shear strength (equation 16) with the seismic base shear force (equation 17), as follows: f s A w A n w A h p thus A A w p A n w f h (18) s The above relation can be expressed in terms of the wall density index (d), as follows d A n w h (19) f s The minimum wall density index, d, required for a given building can be determined by applying the Simplified Method outlined in this paper. Equation (19) can be used to find the required wall density index for a building, given masonry properties ( f s ), number of storeys ( n ), estimated weight ( w ), and seismic design parameters for the building site and structural system ( A h ). In the absence of detailed design calculations, minimum recommended values for wall density index in India are summarized in Table 1. Note that the following assumptions have been made regarding the design parameters for the seismic coefficient A : h 1. =2.5 for confined masonry (currently not addressed by IS 1893) 2. = 2.5 assuming the fundamental period range from 0.1 to 0.4 sec 1-9

63 3. Importance factor =1 assuming regular importance In terms of the allowable masonry shear stress ( f s ), the range from 0.3 to 0.5 N/mm 2 was considered in Table 1. Two values for floor weight ( w ) were considered: 6.0 kn/m 2 (light-weight floor structure) and 8.0 kn/m 2 (heavy-weight floor structure e.g. RC slab). Table 1. Wall Density Index d (%) for each direction of the building plan Allowable shear stress f (N/mm 2 ) s Floor weight w (kn/m 2 ) Number of storeys n Seismic Zone III IV V Example 1: CALCULATION OF THE REQUIRED WALL DENSITY INDEX FOR A GIVEN BUILDING Consider a confined masonry residential building built using 230 mm thick clay brick masonry walls and Type M1 mortar. Assume a heavy floor and roof system for this building ( w of 8.0 kn/m 2 ). Consider allowable shear stress f s of 0.5 N/mm 2. The building is located in seismic zone V of India. Find the required wall density index for this building for the following two cases: a) single-storey building, and b) two-storey building. SOLUTION: Find the seismic coefficient ( ): 1-10

64 Z I Sa Ah = R g where = 0.36 (Zone V) =1 =2.5 = 2.5 a) Single-storey building The required wall density index (d) can be found from equation (19) as follows d Ah n w % f 0.5 s b) Two-storey building The required wall density index (d) can be found from equation (19) as follows d Ah n w % f 0.5 s Note that the obtained wall density index values, that is, 2.9 and 5.8% for single-storey and twostorey building respectively, are the same as shown in Table 1 for the same design parameters. References EERI (2011). Seismic Design Guide for Low-Rise Confined Masonry Buildings, Earthquake Engineering Research Institute, Oakland, California ( IS 1905 (2002). Indian Standard Code of Practice for Structural Use of Unreinforced Masonry (Third Revision), IS 1905:1987, Bureau of Indian Standards, New Delhi, India. IS 1893 (2005). Indian Standard Criteria for Earthquake Resistant Design of Structures, Part 1 General Provisions and Buildings (Fifth Revision), IS 1893 (Part 1):2002, Edition 6.1 ( ), Bureau of Indian Standards, New Delhi, India. NTC-M (2004). Normas Técnicas Complementarias para Diseño y Construcción de Estructuras de Mampostería (Technical Norms for Design and Construction of Masonry Structures), Mexico D.F. (in Spanish and English). SMiE (2011). Guía para el Análisis de Estructuras de Mampostería, J.J. Pérez Gavilán E. (Editor), Sociedad Mexicana de Ingeniería Estructural, Mexico, pp.114 (in Spanish). 1-11

65 Tena-Colunga, A., and Cano-Licona,J. (2010). Simplified Method for the Seismic Analysis of Masonry Shear-Wall Buildings, Journal of Structural Engineering, ASCE, Vol. 136, No. 5, pp

66 Analysis of Confined Masonry Buildings: Part 2 Short Course on Seismic Design of Reinforced and Confined Masonry Buildings February 17-21, 2014, IIT Gandhinagar, India Wide column Effective width 1

67 Modelling parapets hinge Modelling in 3D 2

68 Modelling example Axis 1 3

69 Axis 2 4

70 Axis A Axis B 5

71 Axis C Sections 6

72 Final model Finite elements 7

73 FE Axis 1 FE Axis 2 8

74 FE Axis 3 FE Axes A and C 9

75 FE Axes B Floor Diaphragm can be modelled as rigid in its plane Using SAP2000, select all the nodes at the level floor, then use Constraint, Diaphragm option. Reduces all degrees of freedom in the plane of the floor to just 3: two displacements in the plane of the floor and a rotation about an axis that is perpendicular to the plane. Out of plane degrees of freedom are preserved in each node. 10

76 Numerical experiments Control sections 11

77 Reference model For the complete set of numerical experiments see Taveras 2008 Rigid elements shown with thicker lines M1 FR1 M1 FR2 M1 FR3 M1 FR4 12

78 Shear force Control section Shear Large error show up using model FR 3 Model M1 FR1 seems to be more consistent. All models give good results for total shear in sections S1 and S2 (M1 FR4 the worst) For the wall segments around the windows larger errors were found. Left segments underestimated the shear force and the right segments overestimate it 13

79 Moment Control section Moment Large errors were found using model FR 3. This result is attributed to the fact that the model does not take into account the first parapet connected to the foundation (as is currently in the NTCM) Model M FR4 seems to be the more consistent, followed by M FR1 All models give good results for complete sections S1 and S2, however, for the control sections in the wall segments to the side of the windows considerable errors were found 14

80 Axial force Control section New recommendation The recommendation takes into account numerical experiments for coupling walls not shown in the preceding slides 15

81 Sections Wall division for modelling H/L having and error equal to 20% G=0.4 E G=0.2 E Fixed cantilever Dividing is ok if L/H >

82 Finite elements M1 EF1 M1 EF2 Tie columns are included as frame elements The frame elements should follow the discretization of the grid Same effective with as in wide columns models should be used M1 EF3 M1 EF4 33 Shear force More consistent than FR models Control section 17

83 Shear Errors were up to 12%, smaller than with FR models Model M1 EF2 seems to be more consistent Finite element models appear more robust as they can recover the shear forces in the wall segments at both sides of the windows. Moment Control section 18

84 Moment Errors less than 35% were obtained with all models In all control sections the model that produced the best results is the one with coarsest gird (M1 EF1) It seems that because the frame and finite elements are not compatible, regarding the rotational degrees of freedom, an error is always included, that may grow as the grid is subdivided When continually subdividing the mesh eventually there is convergence on displacements, but to a wrong value Axial force Control section 19

85 Axial force Axial force appears to be very difficult to recover accurately, specially in the wall segments at each side of the windows In all control sections the model that produced the best results is the one with coarsest gird (M1 EF1) Displacements Height (m) Displacements (cm) FR3, which do not consider the parapet of first floor overestimates the displacements 40 Considerably. FR4 are quite good, and with FE models are, in general, larger than expected 20

86 Summary/comments Wide column models (FR) cannot deal with complex force transmission they do well for uniform frames and walls with no windows Not shown above, however by enforcing the flat section in walls in 3D sometimes gives unexpected effects, for example when modelling T shaped walls, the effect of the flange is exaggerated when considering analysis in the direction of the web. An effective flange width should be considered but FR models cant. FE models in the other hand are much more flexible and do not impose artificial hypothesis Tie columns should be modelled. In case tie columns are not included in the model, one may expect a similar distributions of forces in the walls, however, the displacements are much larger and the period is increased, consequently the design will be conservative, as larger period usually means larger shear forces, for masonry structures. Parapets play an important role on the behaviour of a frame with windows, they should be modelled, specially the one of the first floor. FE vs FR Finite element models Are more robust The model preparation is time consuming and error prone. It take much time to recover the element forces for the design Wide column models Give good results for shear and are less accurate for moment and axial forces, specially around windows Models are relatively simple to prepare Recovering of the element forces is immediate 21

87 Questions? 22

88 Example: Seismic Analysis of a Medium rise Confined Masonry Building Short Course on Seismic Design of Reinforced and Confined Masonry Buildings February 17-21, 2014, IIT Gandhinagar, India Analysis example 1

89 Parameters Vertical loads NTC code specifies and extra 0.4 kn/m2 to account for Non uniform thickness of the slab plus the mortar used For the floor tiling 2

90 Wall weight Tie columns, tie beams and beam 3

91 Loads for dynamic analysis Detailed roof loads should be calculated, including water sealant materials For SAP only floor load should be specified, all others are self weight calculated by the program Approximate period Fundamental period (Cl.7.6.2) s 5m overall building height 6m plan dimension 4

92 Period approximation Using the approximation derived when we obtained the seismic forces 2 so There is no need to know, we are interested in the shape only Stiffness

93 Approximated periods Axis 1 Releases (pinned connection), only in first floor parapets Wide columns 6

94 Axis 2 Section includes Slab effective width and tiebeam if any Axis 3 Transformed section includes parapet, slab effective width And tie beam Section includes slab effective width and tiebeam if any 7

95 Rigid elements (R) Material for rigid elements 8

96 Axis A Axis B 9

97 Axis C Section properties cm 2 cm 4 cm 4 cm 4 C C E C C C T T T T

98 Mode 1 Tx=.0835 Tx approx.= Tx approx.= Mode 2 Ty=

99 Final remarks, wide column Advantages Using wide column method for analysis is simple and straight forward Can be time consuming Can retrieve directly the element forces for design Disadvantages Enforces plane sections which is not always a good hypothesis specially in 3D and long walls Questions? 12

100 Short Course on Seismic Design of Reinforced and Confined Masonry Buildings February 17-21, 2014, IIT Gandhinagar, India Acknowledgement Structural Designer and Architect involved in the project Short Course on Seismic Design of Reinforced and Confined Masonry Buildings 1

101 Building Layout Housing Type-1 Short Course on Seismic Design of Reinforced and Confined Masonry Buildings 2

102 Design Unit Y X Preliminary Checking for Confining Elements Short Course on Seismic Design of Reinforced and Confined Masonry Buildings 3

103 Preliminary Checking Building Dimension Along x-direction: 12.43m Along y-direction: 10.86m Floor area: m 2 Confined Wall Length X-direction: 24.78m Y-direction: 27.53m Confined Wall area X-Direction: x 0.23 = 5.699m 2 Y-Direction: x 0.23 = 6.332m 2 Preliminary Checking Wall Density X-direction: (5.699/ ) x 100 % = 4.22% Y-direction: (6.332/ ) x 100 % = 4.69% Ahmedabad (Zone III) PGA: 0.16g Campus sight: Moderately Stiff Soil Type-B Number of story: 3 Minimum Required Wall Density: 3% Hence, Wall Density Check is OK for both X and Y Directions Short Course on Seismic Design of Reinforced and Confined Masonry Buildings 4

104 EERI Guidelines on Wall Density Design Base Shear Calculation Short Course on Seismic Design of Reinforced and Confined Masonry Buildings 5

105 Lumped Mass Calculation Slab Load Ground Floor Load, kn/m² Floor Area,m² Load,kN 150thk slab Floor Finish Live Load Sunk Load Water proofing Load Total 786 First Floor Load, kn/m² Floor Area,m² Load,kN 150thk slab Floor Finish Live Load Sunk Load Water proofing Load Total 786 Gravity Load Calculation Second Floor Load, kn/m² Floor Area,m² Load,kN 150thk slab Floor Finish Live Load Sunk Load Water proofing Load Total 902 Short Course on Seismic Design of Reinforced and Confined Masonry Buildings 6

106 Gravity Load.. Wall Thickness, m Length, m Height, Load, kn Thickness, Length, Height, Load, kn m m m m Ground floor First floor Second floor Parapet Total Load Total Wall load kN Total Weight of Building, kn 5133 kn Seismic Weight and Base Shear Dead Live Load Lump Mass, Lump Mass Load (25%) Wall Load kn Height, m WiHi² Qi, kn Slab Over Ground Slab Over First Slab Over Second Total Seismic Weight of Building with Reduced Live Load, kn 4206 kn Base Shear Calculation Zone Factor, Z 0.16 Importance Factor, I 1 Response Reduction Factor, R 2.5 Sa/g 2.5 Ah 0.08 Base Shear Vb kn Short Course on Seismic Design of Reinforced and Confined Masonry Buildings 7

107 Design of A Typical Wall Along X- Direction Checking Against Gravity Load Load Consideration Slab Thickness 0.15 m Self Wt kn/m² Live load For room 2 kn/m² Live load for corridor 0 kn/m² Live load on terrace floor 1.5 kn/m² Floor Finish 1 kn/m² Water Proofing on terrace 1.5 kn/m² Short Course on Seismic Design of Reinforced and Confined Masonry Buildings 8

108 Gravity Check Load on wall slab load on typical floor DEAD LOAD LIVE LOAD load from bedroom,kn/m load from master bedroom,kn/m slab load on terrace floor load from bedroom,kn/m load from master bedroom,kn/m Thickness with Height Self Weight of Wall plaster Height of ground floor including plinth, m Height of First floor, m Height of second floor, m Wall Thickness considered to resist load 0.23 Wall wt kn/m Total Load on wall kn/m Stress Check at Plinth 0.44 N/mm² Length of Wall 3.88 m Thickness of wall 0.23 m Gravity Check Area of wall m² Slenderness Check Height of Floor 3.15 m Thickness of Wall 0.23 m H/T L/T For Whichever is Less Slenderness Stress Reduction Factor for slenderness as per Table 9 IS Permissible compressive stress as per Report of IITK For ordinary Masonry Permissible compressive stress with cement : lime: sand mortar (1:1:6) as per Report of IITK Allowable stress with stress reduction factor as per IIK-Recommendation 1.83 N/mm² N/mm² Stress Check at Plinth 0.44 N/mm² (OK) Short Course on Seismic Design of Reinforced and Confined Masonry Buildings 9

109 Check Against Shear Permissible Shear strength as per Report of IITK Minimum of 0.5MPa σ = f m = N/mm² Calculation for % lateral force distribution Length of wall 3.88 m Thickness of Wall 0.23 m Height of wall 3.15 m Inertia of Wall 1.12 m⁴ Total length of wall m % Partcipation of Wall % Area Of Wall 0.89 m² Section Modulus of Wall, Z 0.58 m³ Shear Check Base Shear and Overturning Moment Floors Story Force in Height, Base Force, kn Wall, kn m M, kn-m Slab over Second Slab over First Slab Over Ground Total Over Turning Moment Total Base Shear in wall Shear stress at Base, MPa 0.06 Mpa Amplification due to Shear stress at base = 1.2*0.6=0.72 torsion (20%) Mpa. AND SAFE Short Course on Seismic Design of Reinforced and Confined Masonry Buildings 10

110 Check for Tension in Wall Stress Check (P/A)+(M/Z) Load P 351 kn Moment, M kn-m Lever Arm 3.88 m Coupling Force kn Allowable Stress(0.6fy as per IITGn recommendation) 300 N/mm2 Ast(r)=force/stress 3.65 cm2 Ast provided 4 no. 16 dia mi. as per mexican code 8 cm2 OK Moment Capacity of Boundary Element Ast Provided in Each Boundary Element 8 cm2 Allowable Stress(0.6fy as per IITGn 300 recommendation) N/mm2 Allowable Axail force Cap. Of Each Boundary Element 240 kn Moment Capacity of Boundary Element kn-m NO MOMENT TRANSFERRED TO WALL-HENCE NO TENSION IN WALL Tension Check Stress in WALL Total Vertical Load,P 351 KN Total Moment transferred to Wall(M-Mb) 0.00 kn-m P/A + M/Z 0.39 N/mm2 OK P/A - M/Z 0.39 N/mm2 OK Short Course on Seismic Design of Reinforced and Confined Masonry Buildings 11

111 Questions? Short Course on Seismic Design of Reinforced and Confined Masonry Buildings 12