SEISMIC DESIGN GUIDE FOR MASONRY BUILDINGS

Transcription

1 SEISMIC DESIGN GUIDE FOR MASONRY BUILDINGS Secon Eition Svetlana Brzev Donal Anerson Canaian Concrete Masonry Proucers Association 2018

2 TABLE OF CONTENTS CHAPTER 1 1 SEISMIC DESIGN PROVISIONS OF THE NATIONAL BUILDING CODE OF CANADA Introuction Design an Performance Objectives Seismic Hazar Effect of Site Soil Conitions Methos of Analysis Base Shear Calculations- Equivalent Static Analysis Proceure Force Reuction Factors R an R o Higher Moe Effects ( M v factor) Vertical Distribution of Seismic Forces Overturning Moments ( J factor) Torsion Torsional effects Torsional sensitivity Determination of torsional forces Fleible iaphragms Configuration Issues: Irregularities an Restrictions Irregularities Restrictions Deflections an Drift Limits Dynamic Analysis Metho Soil-Structure Interaction A Comparison of NBC 2005 an NBC 2015 Seismic Design Provisions /1/

3 1 Seismic Design Provisions of the National Builing Coe of Canaa Introuction This chapter provies a review of the seismic esign provisions in the 2015 National Builing Coe of Canaa (NBC 2015) as they pertain to masonry. Reference will be mae here to NBC 2005 where appropriate to point out changes. Appeni A contains an introuction to the ynamic analysis of structures to assist in unerstaning the NBC provisions. The original eition of this guieline (Anerson an Brzev, 2009) was prouce to aress the many funamental changes in how seismic risk was evaluate between NBC 2005 an CSA S , an their previous versions. The seismic response of a builing structure epens on several factors, such as the structural system an its ynamic characteristics, the builing materials an esign etails, an most importantly, the epecte earthquake groun motion at the site. The epecte groun motion, terme the seismic hazar, can be estimate using probabilistic methos, or be base on eterministic means if there is an aequate history of large earthquakes on ientifiable faults in the region of the site. Canaa generally uses a probabilistic metho to assess the seismic hazar, an over the years, the probability has been ecreasing, from roughly a 40% chance (probability) of being eceee in 50 years in the 1970s (corresponing to 1/100 per annum probability, also terme the 100- year earthquake), to a 10% in 50-year probability in the 1980s (the 475-year earthquake), to finally a 2% in 50-year probability (the 2475-year earthquake) use for NBC The change was mae so that the risk of builing failure in eastern an western Canaa woul be roughly the same (Aams an Atkinson, 2003), as well as to eplicitly recognize that an acceptable probability of severe builing amage in North America from seismic activity is about 2% in 50 years. Despite the large changes over the years in the probability level for the seismic hazar etermination, the seismic esign forces have not change appreciably because other multiplier factors in the NBC esign equations have change to compensate for these higher hazar values. Thus, while the coe seismic esign hazar has been rising over the years, the average seismic risk of failure of builings esigne accoring to the coe has not change greatly, although there can be substantial changes for certain builings in certain cases. Seismic esign of masonry structures became an issue following the 1933 Long Beach, California earthquake in which school builings suffere amage that woul have been fatal to stuents ha the earthquake occurre uring school hours. At that time, a seismic lateral loa equal to the prouct of a seismic coefficient an the structure weight ha to be consiere in those areas of California known to be seismically active. Strong motion instruments that coul measure the peak groun acceleration or isplacement were evelope aroun that time, an in fact, the first strong motion accelerogram was recore uring the 1933 Long Beach earthquake. However, in this era the most wiely use strong groun motion acceleration recor was measure at El Centro uring the 1940 Imperial Valley earthquake in southern California. The 1940 El Centro recor became famous an is still use by many researchers stuying the effect of earthquakes on structures. However, toay there are thousans of recors to use, an the choice of how many an which ones to consier, an whether to scale the recors or moify them somewhat to match the esign spectrum is a major consieration in any seismic risk analysis. 9/1/

4 With the availability of groun motion acceleration recors (also known as acceleration time history recors), it was possible to etermine the response of simple structures moelle as single egree of freeom systems. After computers became available in the 1960s it was possible to evelop more comple moels for analysing the response of larger structures. The availability of computers has also ha a huge impact on the ability to preict the groun motion hazar at a site, an in particular, on probabilistic preictions of hazar on which the NBC seismic hazar moel is base. They also enhance the ability of engineers to analyse structures both for linear an nonlinear response. 1.2 Design an Performance Objectives For many years, seismic esign philosophy has been foune on the unerstaning that it woul be too epensive to esign most structures to remain elastic uner the forces that the earthquake groun motion creates. Accoringly, most moern builing coes allow structures to be esigne for forces lower than the elastic forces, with the result that such structures may suffer inelastic strains an be amage in an earthquake, but they shoul not collapse, an the occupants shoul be able to safely evacuate the builing. The past an present NBC eitions follow this philosophy, an allow for lateral esign forces smaller than the elastic forces, but they also impose etailing requirements so that the inelastic response remains uctile an a brittle failure is prevente, even for larger than epecte events. Research stuies have shown that for most structures the lateral isplacements or rifts are about the same, irrespective of whether the structure remains elastic or is allowe to yiel an eperience inelastic (plastic) eformations. This is known as the equal isplacement rule, an it will be iscusse later in this chapter as it forms the basis for many of the coe provisions. A comparison of builing esigns performe accoring to the NBC 2005 an the NBC 2015 will show an increase in esign level forces in some areas of Canaa, an a ecrease level in others. However, it is epecte that the overall ifference between these esigns is not significant. The NBC 2015 approach to seismic esign follows that of previous eitions, but its probability seismic hazar has been etermine at many more perios, incluing perios as long as 10 secons. Previously the hazar for perios longer than 2 or 4 secons was base on a conservative empirical ecay relation. Thus, the probability of severe amage or near collapse remains about 1/2475 per annum, or about 2% in the preicte 50-year life span of the structure, but hopefully with the NBC 2015 spectral values some esigns will be more economical. Work on new moel coes aroun the worl is leaing to what is escribe as Performance Base Design, a concept that is alreay being applie by some esigners working with private or public owners who have concerns that builing amage will have an averse effect on their ability to maintain their business or operations. NBC 2015 only aresses one performance level, that of collapse prevention an life safety, an is essentially mute on serviceability after smaller seismic events that are epecte to occur more frequently. Performance base esign attempts to minimize the cost of earthquake losses by weighing the costs of repair an lost business against an increase cost of construction. But this usually requires a nonlinear analysis utilizing many earthquake recors. 9/1/

5 1.3 Seismic Hazar (1) The NBC 2015 seismic hazar is base on a 2% in 50 years probability (corresponing to 1/2475 per annum), an it is represente by the 5% ampe spectral response acceleration, S a (T ), as was the NBC 2005, but the values have change to reflect new information on the hazar an on spectral values. The response spectrum for each perio has the same probability of eceeance, an as such is terme a Uniform Hazar Spectrum, or UHS. For a specifie location NBC 2015 gives the UHS values at nine perios an approimates with straight lines to construct a spectrum, S a (T ), which is terme the hazar spectrum. For many locations in the country, these values are specifie in Table C-3, Appeni C to the NBC 2015, along with the peak groun acceleration (PGA) an peak groun velocity (PGV). For other Canaian locations, it is possible to fin the values online at: by entering the coorinates (latitue an longitue) of the location. The program oes not irectly calculate the S a (T ) values, but instea, interpolates them from the known values at several surrouning locations. For etaile information on the moels use as the basis for the NBC 2015 seismic hazar provisions, the reaer is referre to Aams et al. (2015), Halchuk et al. (2014), an Atkinson an Aams (2013). As an eample, Table 1-1 provies nine spectral acceleration values S a(t), plus values for PGA an PGV for a Vancouver site. The S a values an PGA, plotte as the S a value at T= 0, are shown in Figure 1-1. Table 1-1. S a spectral values for Vancouver for the reference groun conition S a values for Vancouver (Coorinates , ) Site Class C T PGA PGV S a S a(t) is efine for Site Class C which consists of very ense soil or soft rock. For other site conitions a Design Spectrum S(T) = F(T) Sa(T) is efine. F(T) is iscusse more fully in the net section. 9/1/

6 Figure 1-1. Uniform Hazar Spectrum S a(t) for Vancouver (2% in 50 years probability, 5% amping, Site Class C) There are limits impose on the esign base shear as iscusse in Section 1.6 (NBC 2015 Cl (2)), which can be emonstrate by plotting S(T) an S a(t) for Site Class C, as shown in Figure 1-2. These limits affect both the short an long perio response an also epen on the type of structure. 9/1/

7 Figure 1-2. Log plot of the UHS Sa(T) an the Design Spectrum S(T) spectrum for Vancouver with limits in the short an long perio regions. The cut off at low perios may appear to be very conservative, but there are other reasons relate to the inelastic response of such short-perio structures for the esign loas to be conservative in this region. Note that many low-rise masonry builings may have a funamental perio in the orer of 0.2 to 0.3 sec. 1.4 Effect of Site Soil Conitions In NBC 2015, the seismic hazar given by the S a (T ) spectrum has been evelope for a site that consists of very ense soil or soft rock, referre to as Site class C by NBC If the structure is to be locate on soil that is softer than this, the groun motion may be amplifie, or in the case of rock or har rock sites, the motion may be e-amplifie. NBC 2015 introuces a new site coefficient F(t) which is applie to the Site Class C S a (T ) spectrum to account for the local groun conitions. The coefficient epens on the builing perio an level of seismic hazar, as well as on the site properties, which are escribe in terms of site classes. The NBC 2015 site coefficient is more etaile than the founation factors, F a an F v, provie in previous coe eitions, but shoul better represent the effect of the local soil conitions on the seismic response. Table 1-2 ecerpte from NBC 2015, escribes five site classes, labelle from A to E, which correspon to ifferent soil profiles (note that a sith class, F, is one that fits none of the first five an woul require a special investigation). The site classes are base on the properties of the soil or rock in the top 30 m. Site Class C is the base class for which the site coefficients are unity, i.e. it is the type of soil on which the seismic ata use to generate the S a T spectrum is base. The table ientifies three soil properties that can be use to ientify the site class; the best one being the average shear wave velocity, V s, which is a parameter that irectly affects the ynamic response. The other classes are Average Stanar Penetration Resistance N 60, an the Soil Unraine Shear Strength s u. NBC 2015 an Commentary J (NRC, 2006) o not iscuss the level from which the 30 m shoul be measure. For builings on shallow founations, the 30 m shoul be measure from the bottom of the founation. However, if the builing has a very eep founation where the groun motion forces transferre to the builing may come from both friction at the base an soil pressures on the sies, the answer is not so clear an may require a site-specific investigation. 9/1/

8 Table 1-2. NBC 2015 Site Classification for Seismic Response (NBC 2015 Table A) Site Class Groun Profile Name Average Properties in Top 30 m, as per NBC Note A (3) an Table A Average Shear Wave Velocity, V s (m/s) Average Stanar Penetration Resistance, N 60 Soil Unraine Shear Strength, s u A Har rock (1)(2) V s > 1500 Not applicable Not applicable B Rock (1) 760 < V s 1500 Not applicable Not applicable C Very ense soil an soft rock 360 < V s < 760 N 60 > 50 su > 100kPa D Stiff soil 180 < V s < < N 60 < < su 100kPa V s <180 N 60 < 15 su < 50kPa E Soft soil Any profile with more than 3 m of soil with the following characteristics: plasticity ine: PI > 20 moisture content: w 40%; an unraine shear strength: su < 25 kpa F Other soils (3) Site-specific evaluation require Reprouce with the permission of the National Research Council of Canaa, copyright holer Notes: (1) Site Classes A an B, har rock an rock, are not to be use if there is more than 3 m of softer materials between the rock an the unersie of footing or mat founations. The appropriate Site Class for such cases is etermine on the basis of the average properties of the total thickness of the softer materials (see Note A (3) an Table A) (2) Where V s30 has been measure in-situ, the F(T) values for Site Class A erive from Tables B to G are permitte to be multiplie by the factor 0.04+(1500/ V s30) 1/2. (3) Other soils inclue: a) liquefiable soils, quick an highly sensitive clays, collapsible weakly cemente soils, an other soils susceptible to failure or collapse uner seismic loaing, b) peat an/or highly organic clays greater than 3 m in thickness, c) highly plastic clays (PI>75) more than 8 m thick, an ) soft to meium stiff clays more than 30 m thick. NBC 2015 Tables B to -G efine a function F(T) for each soil class an earthquake strength in terms of PGA. Because of ifferent shapes of the S a(t) spectrum, mainly between eastern an western sites, the coe uses PGA ref rather than PGA in etermining the F(T) values (NBC Cl ): PGA ref = 0.8 * PGA when the ratio S a(0.2)/pga < 2.0, otherwise PGA ref =PGA. Note that the founation factors, F a an F v, which were use in NBC 2005 an are still neee for some seismic esign parameters, are relate to the F(T) as follows (NBC Cl ): F a = F(0.2) an F v = F(1.0) Values of F(T) factor as a function of the site class an PGA ref are given in the following tables for T values of: 0.2, 0.5, 1.0, 2.0, 5.0, an 10.0 sec. 9/1/

9 Table 1-3. Values of F(0.2) as a Function of Site Class an PGA ref (NBC 2015 Table B) F(0.2) Site class PGA ref 0.1 PGA ref = 0.2 PGA ref = 0.3 PGA ref = 0.4 PGA ref 0.5 A B C D E F (1) (1) (1) (1) (1) Table 1-4. Values of F(0.5) as a Function of Site Class an PGA ref (NBC 2015 Table C) F(0.5) Site class PGA ref 0.1 PGA ref = 0.2 PGA ref = 0.3 PGA ref = 0.4 PGA ref 0.5 A B C D E F (1) (1) (1) (1) (1) Table 1-5. Values of F(1.0) as a Function of Site Class an PGA ref (NBC 2015 Table D) F(1.0) Site class PGA ref 0.1 PGA ref = 0.2 PGA ref = 0.3 PGA ref = 0.4 PGA ref 0.5 A B C D E F (1) (1) (1) (1) (1) Table 1-6. Values of F(2.0) as a Function of Site Class an PGA ref (NBC 2015 Table E) F(2.0) Site class PGA ref 0.1 PGA ref = 0.2 PGA ref = 0.3 PGA ref = 0.4 PGA ref 0.5 A B C D E F (1) (1) (1) (1) (1) 9/1/

10 Table 1-7. Values of F(5.0) as a Function of Site Class an PGA ref (NBC 2015 Table F) F(5.0) Site class PGA ref 0.1 PGA ref = 0.2 PGA ref = 0.3 PGA ref = 0.4 PGA ref 0.5 A B C D E F (1) (1) (1) (1) (1) Table 1-8. Values of F(10.0) as a Function of Site Class an PGA ref (NBC 2015 Table G) F(10.0) Site class PGA ref 0.1 PGA ref = 0.2 PGA ref = 0.3 PGA ref = 0.4 PGA ref 0.5 A B C D E F (1) (1) (1) (1) (1) Table 1-9 an 1-10 present values of F(PGA) an F(PGV) as a function of the site class an PGA ref. Table 1-9. Values of F(PGA) as a Function of Site Class an PGA ref (NBC 2015 Table H) F(PGA) Site class PGA ref 0.1 PGA ref = 0.2 PGA ref = 0.3 PGA ref = 0.4 PGA ref 0.5 A B C D E F (1) (1) (1) (1) (1) Notes: (1) See Sentence (6). 9/1/

11 Table Values of F(PGV) as a Function of Site Class an PGA ref (NBC 2015 Table I) F(PGV) Site class PGA ref 0.1 PGA ref = 0.2 PGA ref = 0.3 PGA ref = 0.4 PGA ref 0.5 A B C D E F (1) (1) (1) (1) (1) Notes: (1) See Sentence (6). Reprouce with the permission of the National Research Council of Canaa, copyright holer Note that the F(T), F(PGA), an F(PGV) values epen on the level of seismic hazar as well as the site soil class. For soft soil sites (site classes D an E), motion from a high hazar event woul lea to higher shear strains in the soil, which gives rise to higher soil amping an results in reuce site coefficients. The softer the soil, as given by a higher site classification, the larger the site coefficients. For rock an har rock, the site coefficients will generally be less than unity an are not much affecte by the seismic hazar level. The calculation of S(T) values will be illustrate with an eample an the resulting spectra for site Classes C an E are given in Table Figure 1-3 shows the esign seismic hazar spectrum, S a(t), for Vancouver for a firm groun site, Class C, an a soft soil site, Class E. Since soil Class C is the reference soil class the F(T) values are all unity an the S(T) values are the same as the S a(t) values. The F(T) values of site Class E must be interpolate from Tables B to -G. The calculations to etermine S a(t) for the Class E site in Vancouver are shown below (see NBC Clause )): For T 0.2 sec: S(0.2) = F(0.2)*S a(0.2) or F(0.5)Sa(0.5), whichever is larger For T= 0.5 sec: S(0.5) = F(0.5)*S a(0.5) For T= 1.0 sec: S(1.0) = F(1.0)*S a (1.0) For T= 2.0 sec: S(2.0) = F(2.0)*S a(2.0) For T= 5.0 sec: S(5.0) = F(5.0)*S a(5.0) For T 10.0 sec: S(10.0) = F(10.0)*S a(10.0) 9/1/

12 Table Design Spectral Values an F(T) Values for Site Class C an E in Vancouver S=S a values for Vancouver (Coorinates , ), Site Class C T PGA PGV S=Sa F(T) values for Site Class E T PGA PGV F(T) S(T) values for Vancouver, Site Class E S The resulting S(T) esign spectra for soil Classes C an E for Vancouver are plotte in Figure 1-3. Note that since F(0.2)*S(0.2) is less than F(0.5)*S(0.5), for Site Class E the S(T) spectra for T 0.2 is the F(0.5)*S(0.5) value. Figure 1-3. NBC 2015 esign spectra for Vancouver for site Classes C an E. 9/1/

13 1.5 Methos of Analysis NBC 2015 prescribes two methos of calculating the esign base shear for a structure. The ynamic metho is the efault metho, but the equivalent static metho can be use if the structure meets any of the following criteria: (a) is locate in a region of low seismic activity where I E Fa S a ( I E is the earthquake importance factor of the structure as efine in Clause (1)), or (b) is a regular structure less than 60 m in height with perio, T a, less than 2 secons in either irection ( T a is efine as the funamental lateral perio of vibration of the structure in the irection uner consieration, as efine in Clause (3)), or (c) is an irregular structure, but oes not have Type 7 or Type 9 irregularity, an is less than 20 m in height with perio, T a, less than 0.5 secons in either irection. The equivalent static metho will be escribe in this section because it likely can be use on the majority of masonry builings given the above criteria, an notwithstaning, if the ynamic metho is use, it must be calibrate back to the base shear etermine from the equivalent static analysis proceure. Basic concepts of the moal ynamic analysis metho are presente in Appeni A, an further iscussion is offere in Section Base Shear Calculations- Equivalent Static Analysis Proceure The lateral earthquake forces use for esign are specifie in the NBC 2015, an are base on the maimum (esign) base shearv of the structure as given by Clause , an is the e base shear if the structure were to remain elastic. Design base shear,v, is equal to V reuce e by the force reuction factors, R an R o, (relate to uctility an overstrength, respectively; iscusse in Section 1.7), an increase by the importance factor I E (see Table 1-12 for a escription of parameters use in these relations), thus; VeI E V R R o where V ST M W, represents the elastic base shear, e a v v M is a multiplier that accounts for higher moe shears, an W is the ea loa attache to the SFRS, as efine in Table The relationship between V an e V is shown in Figure 1-4. Note that the actual strength of the structure is greater than the esign strength because of the overstrength factor R o. T a enotes the funamental perio of vibration of the builing or structure in secons in the irection uner consieration. The funamental perio of wall structures is given in the NBC 2015 by: a) 3 4 Ta 0.05 hn, where h n is the height of the builing in metres (Cl (c)), or 9/1/

14 b) other establishe methos of mechanics, ecept that T a shoul not be greater than 2.0 times that etermine in (a) above (Sub Cl ()(iii). Note the 4 secon floor in Fig 1-3. Figure 1-4. Relation between esign base shear,v, an elastic base shear, V. e The perio given by the NBC 2015 in (a) is a conservative (short) estimate base on measure values for eisting builings. Using metho (b) will generally result in a longer perio, with resulting lower forces, an shoul be base on stiffness values reflecting possible cracke sections an shear eformations. For the purpose of calculating eflections, there is no limit on the calculate perio as a longer perio results in larger isplacements (a conservative estimate), but it shoul never be less than that perio use to calculate the forces. NBC 2015 Clause (2) prescribes the following lower an upper bouns for the esign base shear, V ; a) Lower boun: Because of uncertainties in the hazar spectrum, S a T, for perios greater than 2 secons, the minimum esign base shear for walls, couple walls an wall frame systems shoul not be taken less than: S4.0M vi EW Vmin R Ro For moment resisting frames, brace frames, an other systems, the minimum base shear shoul not be taken less than: S2.0M v I EW Vmin R R o b) Upper boun: Short perio structures have small isplacements, an there is not a huge boy of evience of failures for very low perio structures, provie the structure has some uctile capacity. Thus an upper boun on the esign base shear, provie R 1. 5, nee not be greater than the larger of: 9/1/

15 2S 0.2 I EW V ma an 3 R Ro I EW V ma S(0.5) R Ro M is not inclue in the above equations as M 1 for short perios. v Table NBC 2015 Seismic Design Parameters v Design parameter S T the esign spectral acceleration that inclues the site soil coefficient F(T) For T 0.2 sec: whichever is larger For T= 0.5 sec: S(0.5) = F(0.5)*S a(0.5) For T= 1.0 sec: S(1.0) = F(1.0)*S a (1.0) For T= 2.0 sec: S(2.0) = F(2.0)*S a(2.0) For T= 5.0 sec: S(5.0) = F(5.0)*S a(5.0) For T 10.0 sec: S(10.0) = F(10.0)*S a(10.0) S(0.2) = F(0.2)*S a(0.2) or F(0.5)Sa(0.5), NBC reference Cl (9) M higher moe factor (see Section 1.8) Cl (6) v Cl (8) Table I E W R = R o = importance factor for the esign of the structure: 1.5 for post-isaster builings, 1.3 for high importance structures, incluing schools an places of assembly that coul be use as refuge in the event of an earthquake, 1.0 for normal builings, an 0.8 for low importance structures such as farm builings where people o not spen much time. See Table in NBC 2015 Part 4 for more complete efinitions of the importance categories. There are also requirements for the serviceability limit states for the ifferent categories. ea loa plus some portion of live loa that woul move laterally with the structure (also known as seismic weight). Live loas consiere are 25% of the esign snow loa, 60% of storage loas for areas use for storage, an the full contents of any tanks. uctility relate force moification factor that represents the capability of a structure to issipate energy through inelastic behaviour (see Table 1-13 an Section 1.7); ranges from 1.0 for unreinforce masonry to 3.0 for uctile masonry shear walls. overstrength relate force moification factor that accounts for the epenable portion of reserve strength in the structure (see Table 1-13 an Section 1.7); equal to 1.5 for all reinforce masonry walls. Cl (1) Table Cl Table Table /1/

16 Note that the esign base shear force,v, correspons to the esign force at the ultimate limit state, where the structure is assume to be at the point of collapse. Consequently, seismic loas are esigne with a loa factor value of 1.0 when use in combination with other loas (e.g. ea an live loas; see Table A, NBC 2015). It is also useful to recall that while V represents the esign base shear, iniviual members are esigne using factore resistances, R, an since the nominal resistance, R, is greater than the factore resistance, the actual base shear capacity will be approimately equal to VR, as shown in Figure 1-4. o 1.7 Force Reuction Factors R an Table 1-13 (NBC 2015 Table ) gives the R an R o values for the ifferent types of lateral loa-resisting systems, which are terme the Seismic Force Resisting Systems, SFRS(s), by NBC 2015 Cl The SFRS is that part of the structural system that has been consiere in the esign to provie the lateral resistance to the earthquake forces an effects. In aition to proviing the R an R values, the table lists height limits for the ifferent o systems, epening on the level of seismic hazar an importance factor, I E. Table Masonry (1) R an R o R o Factors an General Restrictions (1) - Forming Part of Sentence Height Restrictions (m) (2) Cases where I EF as a(0.2) Type of SFRS R R o <0.2 to to < Masonry Structures Designe an Detaile Accoring to CSA S >0.75 Cases where I EF vs a(1.0) >0.3 Ductile shear walls NL NL Moerately Ductile shear NL NL walls Conventional construction NL shear walls Conventional construction NL 30 NP NP NP moment resisting frames Unreinforce masonry NP NP NP Other masonry SFRS(s) not liste above NP NP NP NP Reprouce with the permission of the National Research Council of Canaa, copyright holer Notes: (1) See Article (2) NP = system is not permitte. NL = system is permitte an not limite in height as an SFRS; height may be limite in other parts of the NBC. Numbers in this Table are maimum height limits above grae in m. The most stringent requirement governs. 9/1/

17 Commentary NBC 2015 Table ientifies the following five SFRS(s) relate to masonry construction: 1. Ductile shear walls (new SFRS introuce in NBC 2015) 2. Moerately Ductile shear walls 3. Conventional construction: shear walls an moment resisting frames 4. Unreinforce masonry 5. Other unefine masonry SFRS(s) Note that Ductile shear walls are assigne the highest R value of 3.0, leaing to the lowest esign forces for masonry structures. The etailing requirements, given in CSA S304-14, are the most restrictive of all the masonry shear wall types. However, the height limitations impose by the NBC 2015 are the most liberal, allowing structures up to 60 m in height (approimately 20 storeys) in moerately high seismic regions, an up to 40 m in higher seismic regions. Moerately Ductile shear walls, R = 2.0, have the same height restrictions as Ductile shear walls. They have less restrictive etailing requirements, but have to be esigne for larger forces, generally resulting in a stiffer structure with less uctility eman. Moerately uctile shear walls are require for masonry SFRS(s) use in post-isaster builings, ue to the NBC requirement for an R = 2.0 for these structures. Moerately Ductile squat shear walls, those with a height-to-length ratio less than 1, are a separate class of Moerately uctile shear wall. They are allowe higher shear resistance, an less restrictive requirements on the height-to-thickness ratio, when compare to regular Moerately Ductile shear walls. Conventional construction shear walls an moment-resisting frames both have R =1.5, with more onerous height restrictions, but less stringent etailing requirements than Moerately Ductile walls. Masonry moment-resisting frames are limite to low seismic regions an are not iscusse in CSA S Conventional construction is the most common type of shear wall use in typical masonry structures. Unreinforce masonry construction is only allowe where I F S E a a. It is limite to a height of 15 or 30 m epening on the level of seismic hazar. Unreinforce masonry oes not have a goo recor in past earthquakes, an is assigne R R o 1. 0 values, as there is usually no uctility an brittle failures are a possibility. The R o factor in NBC 2015 is an overstrength factor to account for the real resistance capacity of the structure when compare to the factore esign resistance. It is mae up of 3 components: i) 1/ , ii) a factor that accounts for the epecte yiel strength of the reinforcement being above the specifie yiel strength, an iii) a factor of about 1.1 that recognizes that because of restrictions on possible core locations for the reinforcement in moular masonry walls, the amount of reinforcement is in most cases larger than require. This results in an R 1. 5 after some rouning of the factors (Mitchell et al., 2003). o A comparison of masonry wall classes containe in NBC 2015 an NBC 2005 is presente in Table The class Limite uctility shear walls no longer eists in NBC 2015, an a new class (Ductile shear walls) has been introuce. 9/1/

18 Table A comparison of NBC 2015 an NBC 2005 Classes of Masonry Walls Base on Seismic Performance Requirements NBC 2005 Table an CSA S Unreinforce masonry R =1.0 R =1.0 o Shear walls with conventional construction R =1.5 R =1.5 o Limite uctility shear walls R =1.5 R o =1.5 Moerately Ductile shear walls R =2.0 R o =1.5 Moerately Ductile squat shear walls R =2.0 R =1.5 o Not inclue NBC 2015 Table an CSA S Unreinforce masonry R =1.0 R =1.0 Shear walls with conventional construction R =1.5 R =1.5 o o Does not eist Moerately Ductile shear walls R =2.0 R o =1.5 Moerately Ductile squat shear walls R =2.0 R =1.5 Ductile shear walls R =3.0 R =1.5 o o Comments Slight ifference in where unreinforce masonry coul be use Changes in seismic reinforcement requirements epening on seismic hazar in S This class was remove from S Seismic esign requirements relae for low-rise walls in S No major changes in seismic reinforcement requirements in S New class introuce in NBC 2015 an S Higher Moe Effects ( M v factor) (6) In the etermination of elastic base shear, V, only the first moe spectral value S T is use. In e longer perio structures, higher moes will also contribute to the base shear, an to account for this the M v factor is introuce. M v is epenent on the type of SFRS, the funamental perio T a, an the ratio S ( 0.2) S(5.0), an its values are given in Table Part of the base shear is assigne to the top moes to ensure that the shear forces in the top of the structure are aequate. Applying larger loas to the top of the structure results in the moments along the height being too large, an so a secon factor, J, is introuce to reuce the calculate moments in the lower portion of the structure. A iscussion about the base overturning reuction factor, J, (also shown in Table 1-15) is provie in Section /1/

19 Table Higher Moe Factor, M v, an Base Overturning Reuction Factor, J (1)(2)(3)(4), for Walls an Wall Frame Systems (an ecerpt from NBC 2015 Table ) S(0.2)/S(5.0) Mv for Ta 0.5 Mv for Ta=1.0 Mv for Ta=2.0 Mv for Ta 5.0 J for Ta 0.5 J for Ta=1.0 J for Ta=2.0 J for Ta (7) (8) (7) (8) (7) (8) (7) (8) Reprouce with the permission of the National Research Council of Canaa, copyright holer Notes: (1) For intermeiate values of the spectral ratio S(0.2)/S(5.0), Mv an J shall be obtaine by linear interpolation. (2) For intermeiate values of the funamental lateral perio Ta, S(Ta)*Mv shall be obtaine by linear interpolation using the values of Mv obtaine in accorance with Note (1). (3) For intermeiate values of the funamental lateral perio Ta, J shall be obtaine by linear interpolation using the values of J obtaine in accorance with Note (1). (4) For a combination of ifferent seismic force resisting systems (SFRS) not given in Table that are in the same irection uner consieration, use the highest Mv factor of all the SFRS an the corresponing value of J. (7) For funamental lateral perios, Ta, greater than 4.0 s, use the 4.0s values of S(Ta)*Mv obtaine by interpolation between 2.0s an 5.0s using the value of Mv obtaine in accorance with Note (1). See (2)(a). (8) For funamental lateral perios, Ta, greater than 4.0 s, use the 4.0s values of J obtaine by interpolation between 2.0s an 5.0s using the value of J obtaine in accorance with Note (1). See Clause (2)(a). Commentary For structures with perios T a greater than 1.0 s (typically, builings of 10 storeys or higher), the contribution of higher moes to the base shear becomes increasingly important. In the eastern part of Canaa, where S 0.2) S (5.0) tens to be larger than in the west, an where T a ( a the S a spectrum ecreases sharply with perios beyon 0.2 secons, the spectral acceleration for the secon an thir moes can be high compare to the first moe, hence these moes make a substantial contribution to the base shear. In western Canaa, the spectrum oes not ecrease as sharply with increasing perio, an the higher moe shears are less important. The M v factor is largest for wall structures, ranging in value up to This is relevant for high-rise masonry wall structures when compare to frames, because their moal mass for the higher moes is larger an because the ifference in perios between the moes is larger. For perios that fall between the publishe T a values it is important to note that interpolation between the two perios shoul be one on the prouct ST M v, an not on the iniviual terms. Beyon perios of 5 secons, M v is assume constant, although it theoretically coul be larger. However, since V is conservatively base on the S 4.0 spectral value, it is appropriate to use e the 5 secon value of M. v 9/1/

20 1.9 Vertical Distribution of Seismic Forces (7) The total lateral seismic force,v, is to be istribute such that a portion, F t, is assume to be concentrate at the top of the builing; the remainer V F t is to be istribute along the height of the builing, incluing the top level, in accorance with the following formula (see Figure 1-5): F V where F seismic force acting at level F t a portion of the base shear to be applie, in aition to force F n, at the top of the builing h height from the base of the structure up to the level (base of the structure enotes level at which horizontal earthquake motions are consiere to be imparte to the structure - usually the top of the founations) W - a portion of seismic weight, W, that is assigne to level ; that is, the weight at level which inclues the floor weight plus a portion of the wall weight above an below that level. The seismic weight W is the sum of the weights at each floor; normally this woul be the weight of the floors, walls an other rigily attache masses that woul move with the SFRS, hence (Clause (5)) W F n Commentary 1 W i The above formula for the force istribution is base on a linear first moe approimation for the acceleration at each level. The purpose of applying force F t at the top of the structure is to increase the storey shear forces in the upper part of longer perio structures where the first moe approimation is not correct. For perios less than 0.7 sec, shear is ominate by the first moe an so F t 0. The F t force is etermine as follows, see Clause (7): F 0 for T 0. 7 sec t Ft 0. 07TaV for 0.7 < T a 3. 6 sec F t 0. 25V for T a > 3.6 sec The remaining force, V height from the base. t W h n i1 i W h i Ft a, is istribute assuming the floor accelerations vary linearly with 9/1/

21 Figure 1-5. Vertical force istribution Overturning Moments ( J factor) (6) (8) While higher moe forces can make a significant contribution to the base shear, they make a much smaller contribution to the storey moments. Thus, moments at each storey level etermine from the seismic floor forces, which inclue the higher moe shears in the form of the F t factor, result in overturning moments that are too large. Previous eitions of the NBC have traitionally use a factor, terme the J factor, to reuce the moments. The value of the J factor an how it is applie over the height of the structure is substantially the same in NBC 2015, but the values are now epenent on T a. The J factor values are given in Table 1-15 an illustrate in Figure 1-6. The overturning moment at any level shall be multiplie by the factor J where J 1.0 for h 0. 6hn an, J J 1 J h 0. 6h n for h 0. 6hn 9/1/

22 Figure 1-6. Distribution of the J factor over the builing height.. Commentary How the J factor an reuce overturning moments are incorporate into a structural analysis is not always straightforwar, an it epens on the structural system. For shear wall structures, the overturning moments can be calculate using the floor forces from the lateral force istribution, an then reuce by the J factor at each level to give the esign overturning moments. Without applying the J factor, the wall moment capacity woul be too high, leaing to higher shears when the structure yiels, an coul result in a shear failure. For frames, the beam shears an moments an aial loas, resulting from applying the coe lateral seismic forces at each floor level, will be too large; but the column shears woul not increase. This woul essentially result in higher aial loas in the columns, but not increase the shear eman on the structure, an so woul be conservative in that the columns woul be stronger than necessary, especially in the lower levels. The J factor for frames is usually small, an it is believe that many esigners ignore it as it is conservative to o so Torsion Torsional effects (9) Torsional effects, that are concurrent with the effects of the lateral forces, F, an that are cause by the following torsional moments nee to be consiere in the esign of the structure: a) torsional moments introuce by eccentricity between the centre of mass an the centre of resistance, an their ynamic amplification, or b) torsional moments ue to acciental eccentricities. 9/1/

23 In etermining the torsional forces on members, the stiffness of the iaphragms is important. The iscussion in Sections to consiers rigi iaphragms only, while fleible iaphragms are iscusse in Section Commentary Torsional effects have been associate with many builing failures uring earthquakes. Torsional moments, or torques, arise when the lateral inertial forces acting through the centre of mass at each floor level o not coincie with the resisting structural forces acting through the centres of resistance. The centre of mass, C M, is a point through which the lateral seismic inertia force can be assume to act. The seismic shear is resiste by the vertical elements, an if the resultant of the shear forces oes not lie along the same line of action as the inertia force acting through the centre of mass, then a torsional moment about a vertical ais will be create. The centre of resistance, C R, also known as the centre of stiffness, is a point through which the resultant of all resisting forces act provie there is no torsional rotation of the structure. If the centre of mass at a certain floor level oes not coincie with its centre of resistance, the builing will twist in the horizontal plane about C R. Torsion generates significant aitional forces an isplacements for the vertical elements (e.g. walls) furthest away from C R. Ieally, C R shoul coincie with, or be close to C M, an sufficient torsional resistance shoul be available to keep the rotations small. Figure 1-7 shows two ifferent plan configurations, one of which has a nonsymmetric wall layout (a), an the other a symmetric layout (b). Both plans have approimately the same amount of walls in each irection, but the symmetric builing will perform better. The location of the shear walls etermines the torsional stiffness of the structure; wiely space walls provie high torsional stiffness an consequently small torsional rotations. Walls place aroun the perimeter of the builing, such as shown in Figure 1-7b), have very high torsional stiffness an are representative of low-rise or single-storey builings. Taller builings, which often have several shear walls istribute across the footprint of the structure, can also give satisfactory torsional resistance (see Section for a iscussion on torsional sensitivity). Figure 1-7. Builing plan: a) non-symmetric wall layout (significant torsional effects), an b) symmetric wall layout (minor torsional effects). Figure 1-8a) shows a builing plan (of a single storey builing, or one floor of a multi-storey builing), for which the centre of mass, C M, an the centre of resistance, C R, o not coincie. The istance between C R (at each floor) an the line of action of the lateral force (at each floor), which passes through C M is terme the natural floor eccentricity, e (note that the eccentricity is measure perpenicular to the irection of lateral loa). The effect of the lateral seismic force, F, which acts at point C M, can be treate as the superposition of the following two loa cases: a force F acting at point C R (no torsion, only translational isplacements, see Figure 1-8b), an pure torsion in the form of torsional moment, T, about the point C R, as 9/1/

24 shown in Figure 1-8c). The torsional moment, T, is calculate as the prouct of the floor force, F, an the eccentricity e. In aition to the natural eccentricity, the NBC requires consieration of an aitional eccentricity, terme the acciental eccentricity, e a. Acciental eccentricity is consiere because of possible errors in etermining the natural eccentricity, incluing errors in locating the centres of mass as well as the centres of resistance, aitional eccentricities that might come from yieling of some elements, an perhaps from some torsional groun motion. Figure 1-8. Torsional effects a), can be moelle as a combination of a seismic force, F, at point C R (causing translational isplacements only) b), an a torsional moment, T F e (causing rotation of builing plan) about point CR c). Fining the centre of resistance, C R, may be a comple task in some cases. For single-storey structures it is possible to etermine a centre of stiffness, which is the same as the C R. However, in multi-storey structures, C R is not well efine. For a given set of lateral loas, it is possible to fin the location on each floor through which the lateral loa must pass, so as to prouce zero rotation of the structure about a vertical ais. These points are often calle the centres of rigiity, rather than centres of stiffness or resistance, but they are a function of the loaing as well as the structure, an so centres of rigiity are not a unique structural property. A ifferent set of lateral loas will give ifferent centres of rigiity. Earlier versions of the NBC (before 2005) require the etermination of the C R location so as to eplicitly etermine e, as it was necessary to amplify e (by factors of 1.5 or 0.5) to etermine the esign torque at each floor level. NBC 2015 oes not require this amplification, so the effect of the torque from the natural eccentricities can come irectly from a 3-D lateral loa analysis, without the aitional work of eplicitly etermining e. However, NBC 2015 requires a comparison of the torsional stiffness to the lateral stiffness of the structure to evaluate the torsional sensitivity, an so requires increase computational effort in this regar Torsional sensitivity (10) NBC 2015 requires the etermination of a torsional sensitivity parameter, B, which is use to etermine allowable analysis methos. To etermine B, a set of lateral forces, F, is applie at a istance of 0.1Dn from the centre of mass C M, where D n is the plan imension of the builing perpenicular to the irection of the seismic loaing being consiere. The set of lateral loas, F, to be applie can either be the static lateral loas or those etermine from a 9/1/

25 ynamic analysis. A parameter, B, evaluate at each level,, shoul be etermine from the following equation) (Figure 1-9): ma B ave where ma - the maimum storey isplacement at level at one of the etreme corners, in the irection of earthquake, an ave - the average storey isplacement, etermine by averaging the maimum an minimum isplacements of the storey at level. Figure 1-9. Torsional isplacements use in the etermination of The torsional sensitivity, B, is the maimum value of B for all storeys for both orthogonal irections. Note that B nee not be consiere for one-storey penthouses with a weight less than 10% of the level below. Commentary A structure is consiere to be torsionally sensitive when the torsional fleibility compare to the lateral fleibility is above a certain level, that is, when B Torsionally sensitive builings are consiere to be torsionally vulnerable, an NBC 2015 in some cases requires that the effect of natural eccentricity be evaluate using a ynamic analysis, while the effect of acciental eccentricity be evaluate statically. Structures that are not torsionally sensitive, or locate in a low seismic region where I EFa Sa , can have the effects of torsion evaluate using only the equivalent static analysis. If the structure is torsionally sensitive an locate in a high seismic region, a ynamic analysis must be use to etermine the effect of the natural eccentricity, but the acciental eccentricity effects must be evaluate statically, an the results then combine as iscusse in the net section. A static torsional analysis of the acciental eccentricity, on a torsionally fleible builing, will lea to large torsional isplacements, an generally to large torsional forces in the elements, an thus may require a change in the structural layout so that the structure is not so torsionally sensitive. B. 9/1/

26 Determination of torsional forces (11) Torsional effects shoul be accounte for as follows: a) if B 1. 7 (or B 1. 7 an I EFa Sa ), the equivalent static analysis proceure can be use, an the torsional moments, T, about a vertical ais at each level throughout the builing, shoul be consiere separately for each of the following loa cases: T F e 0. 1D, an i) n ii) T F e 0. 1D. n The analysis require to etermine the element forces, for both the lateral loa an the above torques, is ientical to that require to etermine the B factor, where the lateral forces are applie at a istance 0.1Dn from the centre of mass, C M, as shown by the ashe arrows in Figure b) if B 1. 7, an I EFa Sa , the ynamic analysis proceure must be use to etermine the effects of the natural eccentricities, e. The results from the ynamic analysis must be combine with those from a static torsional analysis that consiers only the acciental torques given by T F 0. 1D, or T F 0. 1D In this analysis, analysis. n n F can come from either the equivalent static analysis or from a ynamic c) If B 1.7 it is permitte to use a 3-D ynamic analysis with the centres of mass shifte by a istance of 0.05D n (see Clause (4)(b). Figure Torsional eccentricity accoring to NBC /1/