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Seismic Design of Timber Structures

Tomi Toratti

Cover page figure source: Destruction of a residential house /Filmore, Northridge earthquake 1994. FEMA news photo, http://www.fema.gov/library. Federal Emergency Management Agency

Abstract Wooden buildings have a good reputation when subjected to seismic events. Experience from North America and Japan shows that wooden buildings can resist catastrophic earthquakes while sustaining only minimal damage. Many modern timber buildings have even survived showing no visible signs of damage. The advantage of wooden buildings is based on low selfweight, ductile joints and in general very regular building geometry. An effective way to design for lateral loads, including seismic loads, in residential wooden houses, is the use of plywood panels in shear walls. These shear walls have a high lateral force-resisting capacity and the joints are in general very ductile. The ductility of the joints is very critical as it also affects the level of shear force to which the wall is subjected. The high performance of plywood shear walls is based on the ductility and energy dissipative characteristics of nailed or screwed joints on plywood in shear walls. Based on previous experience, modern design codes perform well for earthquakes. In the European region, Eurocode 5, design of timber structures, and Eurocode 8, design provisions for earthquake resistance of structures, are new design codes and these may be applied, for example, in the exportation of wooden buildings and building expertise to seismic areas. This report explains the use of Eurocodes in the seismic design of wooden residential buildings. Wooden buildings are usually regular, both in plane and in height, and in such cases, a simplified modal response spectrum analysis may be used. The body forces created by the ground acceleration on the building are converted to a base shear force imposed in both principal directions. EC8 gives the methods to calculate this shear force. The structures resisting these lateral forces such as shear walls, floor diaphragms and anchorages are then designed against this base shear force.

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Preface This final report belongs to a Tekes research project lead by Wood Focus Oy 'Seismic design of Timber Structures - prestudy'. The project has been funded by the companies and institutions represented in the management committee. The project was initiated in February 2000 and it ended in December 2000. The research was carried out by VTT/Building and Transport. The work was done primarily as a literature survey and as interviews with experts. Significant contributions are those of Prof. Ario Ceccotti, University of Florence, Mr. Onur Önal, Schauman Wood Oy office in Turkey, Dr. Erol Karacabeyli, Forintek Corp., and many other members of the COST action E5 'Timber frame systems' management committee. The COST E5 programme organised a seminar on the seismic behaviour of timber structures in Venice in September 2000. This was very valuable to the present study. The management committee of this research project consisted of the following experts: Ilmari Absetz, Tekes, Jouni Hakkarainen, Finnforest Oy Keijo Kolu, UPM-Kymmene Wood Products, Kari Liikanen, Porvoon Puurakennus Oy Alpo Maunu, Maunu-Talot Oy Pekka Nurro, Wood Focus Oy Hannu Pellikka, Sepa Oy Jouni Turunen, Kontiotuote Oy Mikko Viljakainen, Wood Focus Oy

chairman

I wish to thank the experts who have contributed to the present study.

Espoo, April 2001 Tomi Toratti

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1. Table of contents

Abstract Preface 1. Table of contents 2. Introduction 3. Seismic design of timber houses according to Eurocode 8 3.1 Introduction 3.2 The structure of Eurocode 8 3.3 Analysis methods for seismic design 3.4 Simplified modal response spectrum analysis 3.5 Response spectrum 3.6 Vertical loads in seismic design 3.7 Combination of actions 3.8 Calculation of the seismic load, summary 4. Seismic design 4.1 Introduction 4.2 Ultimate limit state 4.3 Serviceability limit state 4.4 Special rules for timber structures 4.5 Lateral stability of the building 4.6 Floor diaphragms 4.7 Shear walls 4.8 The anchorage of the building 5. Connections of timber structures under seismic loads 5.1 Introduction 5.2 Ductility of connections 5.3 Performance under cyclic load 5.4 Performance of different types of connections 5.5 Performance of mechanical connectors under seismic load 5.6 Requirements of Eurocode 8 6. Conclusion Appendix 1 Earthquake magnitude, M Appendix 2 Example cases of seismic load calculation and design Appendix 3 A summary of the procedure to evaluate the seismic load according to Eurocode 8 References

1 2 3 4 6 6 6 7 9 10 13 14 15 16 16 16 17 18 19 20 23 29 33 33 33 34 37 40 41 42 43 44 - 52 53- 56

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2. Introduction Due to recent catastrophic earthquakes, for example in Turkey in 1999, it has been questioned whether timber houses would be safer to live in, in seismic areas, compared to traditional heavier houses. Based on the experience of the West Coast of North America, timber houses are in fact very safe when designed properly. The exportation of timber houses and structures to seismic areas requires knowledge of seismic design so that the safety of these products can be demonstrated. Acquiring knowledge of seismic design methods is thus of great importance to timber exporting companies. The prime objective of this report is to describe the seismic design of timber houses according to the Eurocodes. This report concentrates mainly on Eurocode 8 design provisions for earthquake resistance of structures, where the procedures to determine the seismic loads and the parts giving requirements for timber structures are described. The design procedures are applied here to a wooden residential house. Eurocode 8 (EC8) is a modern design standard for the determination of seismic loads and structural details. In Finland there are no major earthquakes and for this reason expertise in this field is not widespread. For the exportation industry, however, knowledge of EC8 is often important. The Eurocode 5 and 8 versions referred to in this report are the versions given in the references. Some details may change since these Eurocodes are not yet finalised but major changes should not be expected. The sources of information for this report are given in the list of references. The main sources have been Eurocodes 5 and 8 and the STEP lectures B13 and C17. The effect of earthquakes on buildings The soil movements induced by earthquakes produce vibrations in buildings and, thus, inertial forces in the structures also. These forces are called seismic loads. To bear seismic loads, the building should be able to withstand vertical movements without loosing strength. Stiff and brittle structures usually do not perform well against seismic loads, since in this case only a small deformation may cause failure. However, ductile structures or structures containing ductile joints perform well during seismic events. These possess an ability to withstand deformations without developing high stress concentrations. Most seismic design standards, including EC8, allow a significant reduction of seismic loads for ductile structures. This reduction takes into account the ability of the structure to deform during seismic events. For brittle structures, such reduction of seismic loads is not allowed. Timber structures Timber houses have a good reputation for performance in seismic events. This is based on the low weight of timber structures, ductility of joints, clear layout of timber houses and good lateral stability of the house as a whole. As in any kind of building it is usually the inadequate structural design or inadequate supervision during the building process that causes the damages induced by seismic events. For wooden houses vulnerable parts are: the anchorage of the house, the diaphragm action of floors and the first soft storey which sometimes has been left without sufficient lateral bracing (for example crawl spaces, garages). Timber behaves in a ductile manner when loaded under compression, especially compression perpendicular to the grain. This is advantageous in seismic design as, for example, in the side of the shear wall where the compression of the stud is applied to the bottom plate. Timber is brittle

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in tension, especially when the tension is perpendicular to the grain. Therefore, perpendicular tension stresses should be avoided. The joints of timber structures are normally more ductile than the timber parts themselves and this is, in most cases, the reason for the overall ductile behaviour of timber houses and their good seismic performance, (see Buchanan & Dean, 1988 and Ceccotti, 2000). The table below shows the casualties of some past earthquakes and how many of these occurred in timber houses (Karacabeyli, 2000). These data support the theory that timber buildings are safer than non-timber ones. Table 2.1 Numbers of casualties during past earthquakes and how many occurred in timber houses (Karacabeyli, 2000)

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3. Seismic design of timber houses according to Eurocode 8 3.1 Introduction Eurocode 8 (EC8) gives instructions on how the seismic loads are to be calculated. In addition, several structural and detail requirements are given on the lateral bracing structures and on the load-bearing joints. The part on timber structures is 9 pages long. This report deals with only those parts of EC8 which concern timber structures. Buildings built in seismic areas should be designed and built so that there is no danger of collapse. Only limited damages may be accepted with the building staying intact. The main emphasis in EC8 is on the security of human beings, limited damages and that those buildings, which are important in the community (hospitals, fire station, etc.), remain functional. Nuclear power plants and dam structures are outside the scope of EC8. 3.2 The structure of Eurocode 8 EC8 is divided into three parts as follows: Eurocode 8 part 1-1, General rules - Seismic actions and general requirements for structures. In this part, the general requirements and definitions of seismic-resistant buildings are stated. Also, the calculation method of seismic loads and relevant load combinations are given Eurocode 8 part 1-2, General rules for buildings. This part outlines the general rules regarding seismic resistance. Eurocode 8 part 1-3, Specific rules for various materials and structures. This part handles the different building materials (concrete, steel, timber and masonry) and gives detailed structural requirements as well as detailing the specifications for buildings made of these materials. The part describing timber structures is in Chapter 4, on pages 89-97. In addition to the above, EC8 includes part 2 specific provisions for bridges, part 3 provisions for towers, masts and chimneys, part 4 specific provisions with respect to tanks, silos and pipelines, and part 5 specific provisions relevant to foundations, retaining structures and geotechnical aspects. These parts will not be considered in this report.

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Ground acceleration National authorities may put restrictions on the building height or any other building property for seismic areas in their countries. This may depend on the seismicity, the nature of the building, the surrounding infrastructure or the foundation conditions. To determine the seismic load, it is necessary to know the peak ground acceleration value, ag. This depends on the seismicity of the area and is given, by the national authorities, on a country by country basis in the relevant national application documents, NAD. EC8 does not contain these acceleration values, but shows the methods to determine the seismic loads with the acceleration value. The dimensioning of the structures is based on Eurocode 5 (EC5). The design philosophy for seismic events is that the building should withstand a so-called 'service earthquake' without serious movements or damage. In this case, an acceleration value is normally used which has a return period of about 50 years, Ay. Additionally, the building should resist a so-called 'ultimate earthquake' without collapsing, but damages are allowed in this case. The return period of such earthquakes is around 475 years (EC8). The acceleration value is then Au. The ability of a structure to develop plastic strains and dissipate strain energy is central when determining its seismic performance (Ceccotti, 1989). Structures that have joints possessing plastic behaviour and energy dissipation can withstand much higher seismic events than structures with stiff and brittle joints. This applies to all building materials. For this reason, structures are classified in EC8 to several groups depending on their ability to deform and dissipate energy. This property is given by the 'action reduction factor' or 'behaviour factor' termed q. This factor lies in the range q = 13 for timber structures. When a building is designed so that the structures enter a plastic zone with a ground acceleration Au, it would withstand a q times higher acceleration without collapse, so Au = q Ay. In this way, the structure could be designed elastically, q=1.0, for the ground acceleration Ay considering building damages and the building would resist a q times higher acceleration without collapse. The ground acceleration value of EC8, ag, is for the ultimate earthquake and its numerical value as well as its return period is given by the national authorities in the relevant national application documents as mentioned above.

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3.3 Analysis methods for seismic design The seismic design of buildings may be carried out using several different methods of analysis. Such analyses are listed below. 1. Simplified modal response spectrum analysis 2. Multi-modal response spectrum analysis 3. Power spectrum analysis 4. Time-history analysis 5. Frequency domain analysis EC8 permits the use of these analysis methods with certain restrictions. From these analysis methods, only method 1, 'Simplified modal response spectrum analysis', can be carried out on hand using the rules set by EC8. The other analysis methods are more complex and need special expertise; usually finite element methods are then needed which possess routines for dynamic analysis. Table 3.1 gives the minimum requirements of the method of analysis, which depends on the regularity of the building. Table 3.1 The significance of the building regularity (EC8) Building regularity Plan yes yes no no Elevation yes no yes no Simplification allowed Model planar planar spatial spatial Analysis simplified multi-modal multi-modal multi-modal Behaviour factor, q reference decreased reference decreased

According to EC8, a building may be considered regular in plan if the following conditions apply: · The building is approximately symmetrical in plan in the two principal directions concerning lateral stiffness and mass distribution. · The plan configuration is compact, it does not contain divided shapes as H, I tai X. The total dimension of re-entrant corners and recesses in one direction does not exceed 25% of the overall external dimension of the building in that direction. · The in-plane stiffness of the floors is sufficiently high in comparison to the shear walls. The deformation of the floor has a minor effect on the distribution of forces to the vertical stiffening elements. · With the given seismic load distribution, the lateral displacement of any storey does not exceed the mean storey displacement by 20%. According to EC8, that building may be considered regular in elevation if the following conditions apply: · All lateral load-resisting systems run without interruption from the foundations to the top of the building or building part. · Both the lateral stiffness and the mass of the individual storeys remain constant or reduce gradually, without abrupt changes, from the base to the top. · Considering setbacks on load bearing structures the following apply: - in case of gradual setbacks preserving axial symmetry, the setback at any floor is not greater than 20% of the previous plan dimension in the direction of the setback. - In case of a single setback in the lower 15% of the total height of the building, the setback is not greater than 50% of the previous plan dimension. (Some additional rules for setbacks are given in EC8).

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It may be assumed that in most cases timber houses fulfil the requirements set on building regularity presented above. Thus, according to Table 3.1, these may be designed using the simplified modal response spectrum analysis. 3.4 Simplified modal response spectrum analysis The simplified modal response spectrum analysis may be used, according to Table 3.1, when the building is regular as defined by EC8. In this case, only the lowest natural frequency of the building needs to be considered. The natural frequency should be lower than two seconds (or 4 × Tc). Timber houses usually satisfy these conditions. Base shear force The seismic base shear force, for both main directions, is determined as follows: (1.a) Fb = Se(T0) W/q or = Sd(T0) W (1.b)

Where T0 is the fundamental period of the building Se is the ordinate of the elastic response spectrum Sd is the ordinate of the design spectrum W is the total weight of the building (see Chapter 6) q is the behaviour factor (or action reduction factor) The fundamental period of the building For the fundamental period of the building, T0, EC8 gives an approximate formula, which may be applied here. This gives values on the safe side and it may be used if other more exact methods are not available. For timber houses it is as follows: (2) T0 = 0.05 H0.75 Where the units of the building height H is given in metres and the result will be in seconds. Distribution of the horizontal seismic forces If the floor masses of the different storeys are equal, the base shear force is distributed triangularly on the building in a manner that the forces increase going upwards. z iWi (3) Fi = Fb å j ziWi Where Fi is the shear force in storey i Fb is the base shear force zi is the height of the storey from the ground Wi is the mass of the floor (see chapter 6) Subsoil conditions The influence of the local ground conditions on the seismic action is accounted for by considering three subsoil classes as follows: · Subsoil class A: Rock or firm deposits of sand, gravel or over-consolidated clay at least several tens of metres thick. Shear wave velocity vs at least 800 m/s or 400 m/s at a 10-m depth. · Subsoil class B: Deep deposits of medium dense sand, gravel or medium firm clay. Shear wave velocity vs at least 200 m/s at a 10-m depth increasing to 350 m/s at a 50-m depth. · Subsoil class C: Loose cohesionless soil deposits with or without some cohesive soil layers. Shear wave velocity vs below 200 m/s in the uppermost 20 m. 3.5 Response spectrum

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Nations exposed to earthquakes are subdivided into different seismic areas by their national authorities. The peak ground acceleration value, ag, with a chosen return period is given for these areas in the national application documents, NAD. EC8 does not contain such information. If the peak ground acceleration value in a chosen seismic area is below 0.04 g, then according to EC8 there is no need to design for seismic activity . Elastic response spectrum In the equation for the base shear, eq. (1.a), the value of the elastic response spectrum is evaluated from the equation set out below, depending on the fundamental period of the building. For timber houses, the equation to be used is normally eq. (4.b), when the fundamental period is calculated by eq. (2). é T ù (4.a ) S e = a g S ê1 + 0 ( - 1)ú jos T < Tb ë Tb û

S e = a g S

jos Tb < T0 < Tc

(4.b) ( 4.c)

æT ö S e = a g S ç c ÷ çT ÷ è 0ø

k1

jos Tc < T0 < Td

k1 k2

æT ö æT ö S e = a g S ç c ÷ ç d ÷ jos Td < T0 (4.d ) çT ÷ çT ÷ è dø è 0ø Where ag : Peak ground acceleration value T0 : Fundamental period of the building Tb, Tc, Td : time parameters S: soil parameter : damping correction factor, with reference value 1.0 (5% damping) ( = 7 /(2 + ) 0.7 , where damping coeff. 5%) k1 and k2 exponent parameters Depending on the subsoil class, the parameters for the elastic response spectrum are given as in Table 3.2. Table 3.2 Elastic response spectrum parameters for the different subsoil classes (EC8). Tc Td Subsoil S k1 k2 Tb [s] [s] [s] class A 1.0 2.5 1 2 0.10 0.40 3.00 B 1.0 2.5 1 2 0.15 0.60 3.00 C 0.9 2.5 1 2 0.20 0.80 3.00

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Se =ag S

0.563 0.6

0.4 SE T 0.2

0

0

0 0

1

2 T

3

4 4

Fig 3.1 Elastic response spectrum for subsoil class C when ag is 0.25 g

Design spectrum Usually the capacity of structures to resist seismic actions is higher than that based on the elastic response spectrum. For this reason, the base shear value eq. (1.a) is divided by q, the behaviour factor (or the action reduction factor). Alternatively one could use eq. (1.b) directly, where the behaviour factor q is included. The end result is the same. This latter method is called the design spectrum. The design spectrum value needed in the base shear eq.(1.b) is evaluated from the equations below. For timber structures eq.(5.b) is most relevant. é T æ öù S d = S ê1 + 0 ç - 1÷ú jos T < Tb (5.a) Tb ç q ÷û è ø ë

Sd = S

q

jos Tb < T0 < Tc

kd1

(5.b) (5.c)

æT ö Sd = S ç c ÷ q ç T0 ÷ è ø æT Sd = S ç c q ç Td è

( 0.2 )

kd 1

jos Tc < T0 < Td jos Td < T0

ö ÷ ÷ ø

æ Td ç çT è 0

ö ÷ ÷ ø

k 21

( 0.2 )

(5.d )

In eq.(5) the term is defined as the peak ground acceleration divided by the gravity acceleration g ( = ag/g). This of course does not have units. Table 3.3 Design spectrum parameters (otherwise as in Table 3.2). Subsoil kd1 kd2 class A 2/3 5/3 B 2/3 5/3 C 2/3 5/3 The existence of a behaviour factor, q, makes it possible to apply an elastic design method for seismic actions. This term takes into account the plastic properties of the structure. It defines the relationship between an acceleration causing collapse and an acceleration causing the

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strain to enter a plastic region from an elastic region. The ability of the structure to bear plastic strains without loosing strength is of high significance considering its seismic capacity. If the structure is fully elastic until failure then q = 1, otherwise q > 1. For timber structures, q is between 1 and 3. EC8 gives the behaviour factor q values for different structural types as below: q = 1.0 Non-dissipative structures: Class A Structures with no mechanical connections, hinged arches, cantilever structures with rigid connections at base q = 1.5 Structures having low capacity of energy dissipation: Class B Structures with few mechanical connections, cantilever structures with semi-rigidly fixed base connections q = 2.0 Structures having medium capacity of energy dissipation: Class C Frames, and beam-column structures with semi-rigid joints Log houses Gypsum board shear walls (Ceccotti & Karacabeyli 1998) q = 3.0 Structures having good capacity for energy dissipation: Class D Shear walls using wood-based boards and mechanical fasteners for example platform frame timber house (also multi-storey) Horizontal diaphragms may be glued or nailed. In case the building is stabilised for lateral loads with different structural types in the two main directions, each one can be treated separately and a different behaviour factor for the two directions may be applied. An example of this kind of building could be a three-hinged arch hall, which is braced with a truss (using mechanical connections) in the direction perpendicular to the arches. The behaviour factor would be q = 1 in the direction of the arch and q = 2 in the perpendicular direction. 3.6 Vertical loads in seismic design Equations (1) and (3) contain the mass of the structure. This mass is calculated from the gravity loads (dead load, live load, snow load) as follows. The effect of the seismic event on the building is computed considering the masses in the different storeys of the house: W = å Gkj + å EI Qki (6) Gkj is the characteristic dead load and EIQki is the probable live load during an earthquake. EI = 2i (7) 2i is the long-term value 0.3 for live loads, or 0.2 for snow loads (EC1 and EC5), is 0.5 for all storeys except the top storey for which it is 1.0 (no correlation between storey loads). (EC8) is 1.0 for storage loads (EC8) 3.7 Combination of actions The design loads needed in seismic design consist of dead loads and seismic loads. Wind loads do not need to be considered. E d = å Gkj + Fb + å 2i Qki (8)

is the importance factor (I = 1.4 hospitals, fire stations, power stations; II = 1.2 schools, cultural buildings; III = 1.0 residential and commercial buildings; IV = 0.8 agricultural buildings). Gkj and Qki are the characteristic values of the dead and live load. 2i is the combination coefficient of the quasi-permanent value of the live load.

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The above calculation method refers to the lateral loads during a seismic event. This is usually the most important loading direction. During a seismic event, however, the ground vibrates in all directions and for certain structures such as structures with long cantilevers, the vertical loading components may also be of importance. The vertical loading components may be determined by multiplying the lateral loads by the following factors: 0.7 when the fundamental period of the structure T0 < 0.15 s 0.5 when the fundamental period of the structure T0 > 0.50 s for values where 0.15 s < T0 < 0.5 the factor may be interpolated.

3.8 Calculation of the Seismic load, summary Timber houses are usually regular, both in plan and in elevation. Thus, according to Table 3.1, the simplified modal response spectrum analysis method may be used. If a multi-modal analysis is required, the simplified analysis may then be used as a first approximation. In any case, according to EC8 this method is, as previously stated, usually sufficient for timber houses. The calculation of the seismic load, in the simplest form, follows the list below: Calculation of the seismic load: 1. Determine the subsoil class according to the local ground conditions (class A, B or C). 2. Determine the peak ground acceleration value, ag, according to local seismicity as given by the local authorities (NAD). 3. Calculate the fundamental period of the building using eq. (2) or another method. 4. Determine the behaviour factor q of the building depending on the structure (q = 3 for shear wall braced houses, q = 2 for beam-column frames, q = 1 for arches, etc.). 5. Determine the ordinate of the design spectrum eq. (5). Using eq. (2) to estimate the period, one normally ends up using eq. (5.b), which gives the maximum value and is on the safe side. 6. Calculate the seismic mass according to eq. (6). 7. Calculate the base shear force according to eq. (1) and its distribution according to eq. (3). In order to keep the units consistent, it is good practice to express the peak ground acceleration as normalised by g (for example ag = 0.25[g] and not 2.45 [m/s2]), and the seismic mass as a force unit [N]. The base shear force will then also be [N]. After the seismic loads are determined, the dimensioning of the structures can be carried out according to EC5. In the next chapter, the main parts of structural design and dimensioning of the structures is explained.

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4. Seismic design 4.1 Introduction In this report, the seismic design is considered for residential or office buildings with load bearing walls only (as for example, a platform frame house). The seismic design of timber houses is very similar to the design for other lateral loads such as wind loads. The lateral loads are transferred to the foundations via the floor diaphragms and the shear walls. The difference compared to wind loads is that the wind action is a pressure on the external wall whereas with seismic action the loads are connected with the masses (either dead or live) of the building and mainly directed to the floors. The seismic action is cyclic and loading directions change constantly and simultaneously in horizontal and vertical directions. Therefore, the structures should be firmly tied to each other and the floors or beams should not be able to slide from their supports. The platform frame is very effective in this sense as the floor slab extends all the way through the external wall to the outer edge. The load-bearing wall supports the floor and the floor supports the upper edge of the lower floor. Also fire safety should be considered in seismic design, as fires may occur during a seismic event due to the cutting of electric wires or gas pipes. However, EC8 does not give instructions on how to do this. Local fire safety rules and standards should be applied. The lateral stabilisation of the whole building should be designed so that the lateral loads from the different parts of the building are directed to the foundations. The centre of the stiffness inertia and the centre of mass should coincide as closely as possible to avoid a torsion effect on the building. This will depend on the layout of the building and on the placement of the shear walls. The building layout should be regular in elevation and in plan regarding mass and rigidity distributions. The rules of EC8 for regularity were given in Section 3.3. The lateral stability (or bracing) design of the building concerns the design of the floor diaphragms, the shear walls and the anchorage to the foundations. These will be considered in the following chapters. 4.2 Ultimate limit state The safety of the structure for seismic events can be considered sufficient if the following conditions of resistance, ductility and equilibrium apply. Resistance The following condition should apply for all structures and connections f E d = f {å Gkj , Fb , å 2 i Qki } Rd = R{ k } (9) M The design resistance of the structures is determined so that the material strength corresponds to the instantaneous load duration class and the material safety factor is M = 1.3, when the structure dissipates energy (or q > 1) and M = 1.0 when the structure does not dissipate energy (q = 1). So in most cases the material safety factor is 1.3 as in ordinary structural design even though a seismic event could be considered an accidental load. The importance factor, , was described in eq. (8), for residential buildings this has a value of 1.0.

Ductility The structures and the building as a whole should be adequately ductile. The ductility should be considered in the design where it is taken into account as a load reducing factor, the behaviour factor q was explained previously. Equilibrium The building should be stable during a seismic event. The seismic load combinations should be considered when designing for the anchorage of the building for the following two cases: - anchorage for overturning: upward tension at ends of shear walls, - anchorage for sliding, base shear at the bottom of shear walls

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In a multi-storey building the anchorages should be considered at every storey level. Naturally the anchorage forces decrease at higher storey levels. The anchorage for overturning is usually resolved either with bolted hold-downs or with nailed metal straps. Also a shear panel crossing the storey level may be applied as an anchorage from store to storey, in this case the shear panel is in the outer edge of the wall as otherwise the floor would be in its way. The anchorage for sliding is usually resolved with bolts or wedge anchors in the bottom plate of the shear wall in the lowest storey. In the upper storeys, the nailing of the wall bottom plates should normally be strong enough to withstand the anchorage forces. 4.3 Serviceability limit state In order to avoid excessive damage, EC8 gives rules for the inter-storey drift during a seismic event. The design earthquake may be one, which is more likely (lower return period), and the peak ground acceleration is lower than for the ultimate limit state. The inter-storey drift is limited to the following values: , buildings having non-structural elements of brittle dr/ 0.004 h or materials attached to the structure 0.006 h , buildings having non-structural elements fixed in a way as not to interfere with structural deformations is the inter-storey drift Where dr h is the storey height reduction factor having values between 2.02.5. This takes into account the lower return period of the seismic event during the serviceability limit state.

4.4 Special rules for timber structures For the different building materials, in addition to normal structural design, EC8 gives some additional rules and restrictions on the design of structures, which are applied for seismic actions. In the following, the most important rules and restrictions are given. The behaviour factor q obtains the value between 1 and 3 for timber structures. EC8 gives this value depending on the structure (Section 3.5): · Type A, q = 1.0 : three hinged arches, cantilevered structures, shear walls without mechanical fasteners. · Type B, q = 1.5 : structure with few dissipative joints. · Type C, q = 2.0 : trusses with mechanical fasteners, log houses, · Type D, q = 3.0 shear walls with mechanical fasteners and wood-based panels. If the building is irregular in elevation (see 3.3), the behaviour factor q should be decreased by 20%, but not to below a value of 1.0. For the mechanical connections to be able to dissipate energy and to be able to use the behaviour factor values described above, certain restrictions apply to the mechanical fasteners: For wood-to-wood and metal-to-wood joints, the parts must be at least 8 d (d: connector diameter) thick and the diameter of the connector is limited to 12 mm. The minimum requirements set on shear panels of shear walls are: - the minimum thickness of plywood plates is 9 mm.

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- the minimum density of particleboard panels is 650 kg/m3 - the minimum thickness of particleboard and fibreboard sheathing is 13 mm. It should be emphasised, that EC5 does state restrictions on the use of board materials for different humidity conditions: · Plywood boards may be used in service classes 1, 2 and 3, · Particleboards, and certain OSB- and fibreboards may be used in service classes 1 and 2, · Certain gypsum boards may be used only in service class 1 and others also in the other service classes. One should check with the manufacturer where the board can be used.

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4.5 Lateral stability of the building

The lateral loads are transferred to the foundations with structures providing lateral bracing. In a platform frame building, the most appropriate manner to provide the bracing is by using shear walls. Usually plywood or OSB boards are used as shear resisting panels in shear walls. Gypsum boards may also be used. The use of structural panels is, in most cases, the most effective and economic manner to provide the lateral stability for a residential house. The following text is based on references EC5 and STEP B13. A schematic diagram of the functioning of structural panels against lateral loads is shown in Fig. 4.1, where a simple 'box-like' building is loaded laterally. The floor diaphragm is assumed to behave as a high beam and this is loaded by a seismic action depending on the floor mass and on the ground acceleration. The floor diaphragm is supported at the ends by shear walls, which in turn transfer the load to the foundations. Such structural configurations may be side by side or one on top of the other as in a multi-storey house. In multi-storey houses the lateral loads cumulate to the lower storeys.

Direction of ground acceleration

Fig. 4.1 A schematic diagram of the path of lateral forces in a simple building, where the floor diaphragm acts as a high beam supported by shear walls.

The structural parts should, of course, be properly attached to each other in order to ensure that an intact path for the lateral forces does exist. This includes the connection of the board materials to the timber frame (floors and walls), the connection between the floors and supporting shear walls and between the shear walls and the foundations. The anchorage of the building as well as the connection details will be described later in this report.

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4.6 Floor diaphragms

The floors may be used to transfer lateral loads to the shear walls. In timber houses, the floors are usually constructed with timber joists, which are connected to a structural panel of some kind. Plywood, particleboard and OSB-board are widely used as structural floor panel materials. The boards are connected to the floor joists by nails or screws. In a platform frame house, where the floor also performs as a working plane during construction, the moisture content of the panel and weather resistance should be considered. During construction the floor may be exposed to rain and panels meant for interior use should be avoided. Exterior plywood (EN 636-3) is the only structural wood-based board, which may be used in service class 3 conditions (EC5). The floor diaphragms may be assumed to perform as a high I-beam, which is supported by walls that are lined in the direction of the lateral force. According to EC5, this applies when the floor span (distance between shear walls) is longer than two and shorter than six times the height of the floor, (2b < l < 6b). The static behaviour is simplified so that the panelling performs as the web of the I-beam taking on all of the shear forces and the flanges take the compressive and tensile forces at the floor top and bottom edges, chords, caused by the bending moment.

b

l

18

Shear force d

Compressive force Fc b

Tensile force Ft l Shear walls

Fig. 4.2 The floor diaphragm and its static behaviour.

When the floor performs as an I-beam, the chord (flange part) is usually taken to be either the bottom or top plate of the wall frame or the end joist of the floor which runs in the direction of the wall and perpendicular to the main floor joists. The bottom plate is usually composed of two timber sections on top of each other, having overlapped and staggered end joints and these are nailed together and to the floor. The chord takes care of the bending moment and these are designed, in a simple single span case, for the compression and tension forces as follows:

Ft,d = Fc,d = Mmax, d / b

(10)

Where Mmax is the maximum bending moment and b is the width. The shear force qf,d (per length) between the sheathing and the chords may be calculated as

qf,d = Fv,d / bc

(11)

Where Fv,d is the total shear force and bc is the centre to centre distance between adjacent chords. The sheathing is designed to resist the shear force per length of:

vd = Fv,d / b

(12)

Where Fv,d is the total shear force and b is the width. The spacing of the fasteners connecting the sheathing to the joists is calculated from:

s = Rd / vd

(13)

Where Rd is the design capacity of a single fastener and vd is the calculated shear per length.

19

According to EC5 the fastener spacing should be, at most, 150 mm along the edges and 300 mm elsewhere. The fastener design capacity is thus the dominating property concerning the shear capacity of the floor. The fastener design capacity between the sheathing and the floorsupporting member is calculated from the EC5 eq. 8.3 as below:

ply ì f hd t1 d ï solid ï f hd t 2 d ï 2 ü ply é t æ t ö2 ù ï f hd t1d ì æ t 2 öï ï 2 3 æ t2 ö 2 2 ï í + 2 ê1 + + ç ÷ ú + ç ÷ - ç1 + ÷ý ç t ÷ çt ÷ ç ÷ 1+ ï ê t1 è t1 ø ú 1 øï è è 1ø ï û ë î þ ï nail ï ply é ù ï Rd = min í f hd t1d ê 2 (1 + ) + 4 ( 2 + ) M yd - ú (14) ply f hd t12 d ï 2+ ê ú ë û ï nail ï f ply t d é ù 4 (1 + 2 ) M yd ï hd 2 ê 2 2 (1 + ) + -ú ply 2 ï 1 + 2 ê f hd t 2 d ú ë û ï ï 2 nail ply 2M yd f hd d ï ï 1+ î

the

panel

increased

Where fplyhd and fsolidhd are the design embedment strength values of the sheathing panel and wood, Mnailyd is the design value of the yield moment of the fastener, t1 and t2 are the thickness of the sheathing and the penetration depth of fastener into the wood, d is the diameter of the fastener and is the ratio between the embedment strength values of the sheathing and wood (In the case of a shear wall, the design capacity value Rd may be

by a factor of 1.2)

For simply supported diaphragms, as in Fig. 4.2, the shear force is transferred to the shear walls at the edges. The shear force is assumed to be distributed evenly along the edge, in case the shear wall extends all through the floor depth. To ensure the path of forces from the floor to the supporting shear walls, the diaphragm supports, acting as the chords, are connected to the top plate of the shear wall. Alternatively some other means of load transfer should be provided. The seismic action is directed to the floor diaphragm in both plane directions (including vertical ) as a force alternating in direction. For this reason, all the floor edges should be dimensioned as chords acting both in compression and in tension and also for shear transfer in case the forces are transferred to a shear wall below. Using this simple static floor model, the sheathing performs as a single membrane. The individual panels should then be adequately attached to the supporting structure. The best performance is achieved when the panels are staggered rather than being on the same line. As staggering is not possible in two directions, this should be done against the principal loading direction (in the direction of the shorter floor dimension) as in Fig. 4.2.

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In case the floor has a large opening, it is important to ensure that it is possible to transfer the loads around the opening. The compression and tension forces should be transferred with joists or metal straps along the sides. The fastening of the sheathing to the supporting joists ensures the transfer of shear forces. The detailing of the fasteners of the shear panels is crucial.

Rules given by EC8 on the seismic design of floor diaphragms Floor diaphragms and shear walls may be designed in the same way as other lateral loads, such as wind loads, according to the procedures described in EC5 with certain exceptions. The following parts are different than given in EC5: · · · · · For floor diaphragms the increase in the fastener design capacity, by a factor of 1.2, may not be used. The shear forces may not necessarily be distributed evenly over the floor area ( EC5 5.4.2 P(5) ), and the in-plan position of the vertical shear walls should be considered. All edges of the sheathing panel should be supported and connected by blocking. The continuity of joists and headers should be ensured in places of diaphragm disturbances. The slenderness of the joists is restricted to h/b < 4. In seismic zones where ag > 0.2 g, the spacing of the fasteners in areas of discontinuity, such as panel corners, should be reduced by dividing it by a factor of 1.3. This should, however, not result in a spacing less than the minimum spacing given in EC5. If the floor diaphragm is assumed to be perfectly rigid in-plan, the direction of the floor joists should not change, for example over the supporting shear walls.

·

Fig. 4.3. Supporting and fastener spacing at the edges of sheathing panels according to EC8 (EC8).

4.7 Shear walls

21

In a wooden house, with a load-bearing wall frame, the lateral stability of the house is most effectively provided by the use of shear walls with panel sheathing. Usually wooden loadbearing walls consist of vertical struts, equally spaced, which are connected to top and bottom plates. To this frame, a sheathing panel is attached by nails or screws, on one or both sides of the frame. From a structural point of view, a shear wall may be regarded as a cantilever where a vertical load is located at the top plate. The sheathing transfers this vertical load to the foundations. The following text is based on references EC5 and STEP B13. Wood-based boards are often used as the sheathing panel, plywood or OSB. Gypsum boards may also be used. According to EC5, the shear capacity of the shear wall is based on the shear capacity of the fasteners as according to a lower bound plastic model. It is good practice to use the walls between attached dwellings and the walls next to corridors as shear walls; these may be sheathed on both sides and contain few interruptions from doors or windows.

y y

F

c

Top plate wall strut

H

H

Sheathing panel

t

Bottom plate (or sill plate)

F N B N

x

z

Fig. 4.4 Basic shear wall and its static model.

The wall struts are connected to the top and bottom plates with nails or with different types of metal connectors. These connections may be assumed to perform mechanically as a hinge. For this reason, the frame has to be braced with a sheathing panel, which is attached to the frame. The most loaded fasteners of the panel are located at the corners, where the displacement between the wooden frame and the panel is highest. The vertical struts are then designed only for the compression and tension forces along the edge of the shear wall. When panels of recommended thickness are connected to all the struts of the wooden frame with the usual strut spacing of K600 mm, the capacity to resist lateral loads is dependent on the fastener strength. Only in special cases, such as when using thin panels or having wide strut spacing, might the shear capacity of the panel or the shear buckling of the panel become decisive.

22

According to EC5 the shear capacity of a shear wall is dependent on the fasteners capacity. When the fasteners are at equal spacing all over the panel and the panel width is at least h/4, the shear capacity may be calculated from (EC5 9.18):

F v ,di =

F f ,d bi s ci

(15)

Where Ff,d is the design capacity of a single fastener, bi is the panel thickness, s is the fastener spacing along the panel edge (same on all edges) ci = 1 if bi b0 ci = bi / b0 if bi < b0 b0 = h/2, h is the height of panel The design capacity of the fastener, Ff,d (given in eq. 14) can be increased by a factor of 1.2 ( Ff,d = 1.2 Rd). The fastener spacing should be at the most 150 mm in the case of nails and 200 mm in the case of screws along the edges of the panel. In the central part of the panel, the spacing may be up to 300 mm, but never more than twice the spacing along the edges. The fasteners in the centre do not affect the shear capacity, except in reinforcing the panel against shear buckling. According to EC5 the shear buckling analysis does not need to be carried out if the following condition holds:

bnet/t < 100

(16)

Where bnet is the free distance between struts and t is the panel thickness. So if the struts are spaced at K600, the buckling analysis need not be done because t > 5.95 mm. The total shear capacity of the shear wall may be calculated as the sum of the shear capacities of the panels (EC5 9.19):

F v ,d = å F v ,di

i

(17)

It is assumed here that the shear force is equally distributed along the fasteners connecting the panel to the wooden frame. The tension and compression struts at the sides of the shear wall have to be designed for the forces and the tension force has to be adequately anchored (EC5 9.20):

Ft,d = Fc,d = Fv,d h/b

(18)

The capacity of a shear wall composed of different panel elements may be calculated as the sum of the element capacities (eq. 16), even in the case where the panel material or fastener type is different. If a wall has the same panel sheathing and fasteners on both sides, the capacities of the two sheathings may be added together. If different panel materials are used, EC5 allows that 75% of the weaker panel capacity may be used, if the fastener strength-deformation curves are similar for the two panels, then only 50% of the weaker panel capacity may be utilised. If the

23

wall contains a window, door or other opening, the shear capacities of these sections are omitted in the addition. The end struts of shear walls, as well as the bottom plate, should be anchored to the foundations to resist uplift forces (upwards) and sliding forces (horizontal). In a multi-storey house these anchoring forces should be considered from storey to storey as these accumulate towards the bottom storeys. Inner walls The distribution of lateral loads to several shear walls depends on the rigidity of the floor and the rigidity of the shear wall. A rigid floor with flexible shear walls is one extreme case and a flexible floor with rigid shear walls is another extreme case. In the first case, the lateral force is distributed to the shear walls depending on their relative levels of rigidity. In a case where the floor is supported by three shear walls of equal rigidity, each of these walls carries a third of the lateral load. However, if the inner wall is not located at the centre, a torsion component is also developed. In the other extreme case, the floor may be regarded as a continuous multi-span beam over the supporting shear walls or two non-continuous single-span beams extending between two shear walls. To be on the safe side, it may be good practice to design the outer shear walls assuming a single floor span supporting conditions and the inner shear walls assuming continuity of the floor. The assumption of a perfectly rigid floor should only be used if the floor plan dimension ratio is close to one. Calculated capacities of shear walls with plywood sheathings The following table contains calculated shear capacities, which may be used in the seismic design of timber buildings braced with shear walls. Calculated cases with several different plywood and LVL sheathing panels and different fasteners are given. These values are based on eq. 14 and on eq. 16. These design values were calculated for an instantaneous load duration and using a normal material safety factor, as EC8 assumes an energy dissipative structure.

24

Table 4.1 Shear design capacity with different panels and fasteners [KN/m] in seismic design, note the following: 1) kmod = 1.1, M = 1.3 , 2) values are for only one panel on one side, 3) the fastener spacing is constant all around the panel, in the inner part the spacing may be up to double ( and < 300 mm).

Spruce plywood 9 [mm] nail (helically threaded) 25x45 Fastener spacing [mm] K150 K100 K70 K50 Spruce plywood 12 [mm] 25x45 Fastener spacing [mm] K150 K100 K70 K50 Spruce plywood 15 [mm] 25x45 Fastener spacing [mm] K150 K100 K70 K50 LVL 21 [mm] 25x45 Fastener spacing [mm] K150 K100 K70 K50 LVL 27 [mm] 25x45 Fastener spacing [mm] K150 K100 K70 K50 3.73 5.59 7.98 11.18 4.49 6.74 9.63 13.48 6.49 9.74 13.91 19.48 8.33 12.50 17.85 25.00 28x60 d = 3.5 d = 4.5 3.73 5.59 7.98 11.18 4.49 6.74 9.63 13.48 5.90 8.85 12.65 17.71 7.33 11.00 15.71 21.99 28x60 d = 3.5 d = 4.5 3.63 5.44 7.78 10.89 4.13 6.19 8.85 12.38 5.43 8.14 11.63 16.28 6.93 10.39 14.84 20.78 28x60 d = 3.5 d = 4.5 3.24 4.86 6.95 9.72 3.74 5.61 8.01 11.22 5.06 7.59 10.84 15.18 6.60 9.90 14.15 19.81 28x60 d = 3.5 d = 4.5 2.93 4.39 6.28 8.79 3.44 5.16 7.38 10.33 4.81 7.22 10.32 14.44 6.42 9.63 13.76 19.27 28x60 d = 3.5 screw d = 4.5

25

Shear capacity of different sheathing panels in seismic design

12

Fasteners screw 3.5 (3.9x29 Gyprocille) K100 mm 27 mm Kerto-Q LVL

10

21 mm Kerto-Q LVL 15 mm spruce plywood

Shear capacity [KN/m]

8

9 mm spruce

12 mm spruce plywood

6

4

Gypsum board (Gyproc GN13)

2

0 1 2 3 4 5 6

Fig. 4.5 A comparison of shear capacity per wall length of different sheathing panels.

Table 4.2 A comparison of the shear capacity of spruce plywood panel (9 mm) and gypsum board (13 mm) in seismic design.

Shear capacity per shear wall length KN/m

K150 Spruce plywood panel 9 mm q = 3.0 nail 25x45 28x60 screw 3.5 screw 4.5 Gypsum board, GN13 and GEK13 q = 2.0 T 29 screw 3.9x29 GN13 TR 29 screw 4.2x29 GEK13 Reduced by q=2/3 (takes into account the different behaviour factors) Capacity of gypsum boards in relation to plywood panel of 9 mm [%] T 29 screw 3.9x29 GN13 TR 29 screw 4.2x29 GEK13 2.51 4.07 1.65 2.69 3.76 6.11 2.48 4.03 5.37 8.73 3.55 5.76 7.52 12.22 4.96 8.07 2.93 3.44 4.81 6.42 4.39 5.16 7.22 9.63 6.28 7.38 10.32 13.76 8.79 10.33 14.44 19.27 Fastener spacing K100 K70 K50

34% 42%

(compared to screw 3.5 case) (compared to screw 4.5 case)

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4.8 The anchorage of the building

In order to transfer the lateral loads to the foundations, the building has to be anchored to the storey below and then on to the foundations. Anchoring is normally required at the ends of shear walls to account for the uplift forces (due to overturning when the building's own weight does not compensate for the effects of the lateral load) and at the bottom plate to account for the sliding (slip from base shear), see Fig. 4.6. The uplift and sliding forces are anchored independently of each other with special connectors.

Fig. 4.6 The two anchoring cases: sliding caused by base shear and uplift caused by overturning ( APA 1997a,b)

Fig. 4.7 Anchorages of a shear wall (APA 1997a,b)

Figure 4.7 demonstrates the anchoring of a shear wall of a single storey house and Fig. 4.9 the anchoring of a multi-storey house. The basic principle is as follows.

27

- To withstand overturning, both sides of a shear wall are anchored to the storeys below and to the foundations to account for uplift forces. The connection is fastened to the frame strut and this transfers the tensile forces downward to the struts below or to the foundations. The connection cannot be attached only to the panelling or only to the frame plate. The fastener may be a hold-down bolt with metal end-plates or a metal strap that is nailed to the frame, Fig. 4.8. The anchorage uplift force may be calculated from eq. 17. In the case of a loadbearing wall, the self-weight may be subtracted from the uplift force. - To prevent sliding, shear anchor bolts are usually used to connect the bottom plate (sill plate) to the foundations. The spacing of these bolts will result from the calculations. For upper storeys, the nailing of the bottom plate to the flooring or to the wall section below is usually sufficient to account for the shear forces at these upper levels. The shear force acting on a single fastener is:

F = Fv,d s l

(19) Where Fv,d is the shear force (lateral load) acting on a shear wall

s is the spacing and l is the length of the shear wall

Fig. 4.8 The anchoring of uplift forces is handled with metal straps or hold-down bolts (SECBC 1997).

28

Fig. 4.9 Anchoring details in a multi-storey house case (SECBC 1997)

29

Fig. 4.10 Anchoring details where a metal strap is used on top of panelling (Secbc 1997)

30

5. Connections of timber structures under seismic actions 5.1 Introduction

The behaviour of timber structures during seismic events is fully dependent on the behaviour of the joints under cyclic loading. The detailing of joints is thus very important in seismic design. The source of this chapter is mainly the STEP lectures dealing with the design of connections for seismic actions. Under cyclic actions, wood usually performs linearly and elastically. Failures are brittle in nature and these are caused by natural defects in wood, such as knots. Wood in itself has a low capability for dissipating energy, except for compression loading perpendicular to the grain. Glued joints perform linearly and elastically. These do not involve plastic deformations and they do not dissipate energy. For this reason, timber structures with glued joints as well as structures that have hinges, should be classified as structures that do not dissipate energy and possess no plastic strains; therefore, the behaviour factor for these structures is q=1.0 (class A). The plasticity and energy dissipation property can be introduced to the connections, if the connections are "semi-rigid" as most mechanical connections used for timber structures are, instead of perfectly rigid joints as, for example, glued joints. Well-designed mechanical connections perform usually in a semi-rigid manner. If the forces caused by static loads are greater than those caused by seismic events (when q=1), there is no necessity to carry out any ductility analysis of the connections. This might be the case for large structures under high snow loads. In this case, the normal static analysis of the structures is sufficient and no seismic or experimental analysis are needed. With a few exceptions, it is usually beneficial to view the behaviour factor, q, as a loadreducing factor. In this case, there is a need to demonstrate that the connections are sufficiently plastic and energy dissipating to cope with the q value initially assumed. This may be demonstrated by experimentation or, in the case of those connection types where q is known , by following certain rules in building specifications.

5.2 Ductility of connections

Mechanical joints in timber structures usually perform in a semi-rigid manner and plastic strains may develop, if the fastener spacing and the end distances are according to the design rules. The force-deformation curve is initially steep under ramp loading (Fig. 5.1a, I). After the fastener or the wood embedment stress reaches its elastic limit, the force-deformation curve becomes non-linear and less steep reaching a peak, where the maximum connection capacity may be found Fmax (Fig. 5.1a, II). After this stage, the curve slopes down (Fig. 5.1a, III), which means that the connection has failed, maybe because the wood has split or the fastener strength has been reached. The determination of ductility is presented in Fig. 5.1. Two cases are given, one composed of two linear curves and the other of one fully non-linear curve.

31

Fig 5.1 Definition of ductility, examples of different force-deformation curves. (a) Two linear curves with different slopes (b) a non-linear curve with a constantly changing slope. Ds is the ductility, u is the deformation at failure and y is the deformation at the yield point. (STEP C17).

5.3 Performance under cyclic loading

Figure 5.1 presents a ramp loading case, with a monotonic increasing force. Under seismic actions, the loading is more complex and the loading reverses in direction within a few seconds. Figure 5.2 shows a nail being exposed to a regular cyclic loading. During the first loading, the wood fibres around the nail are compressed and a cavity is formed at the edges of the jointed material. This cavity leaves the nail without support for the subsequent loading cycles, if the deformations are within previous limits. Residual strength is given solely by the nail acting as a cantilever over the cavity distance. As the previous displacement is exceeded, the nail is supported by the wood again and the loading proceeds approximately following the parent curve.

Fig 5.2 Plywood connected to a wood frame showing the cavity caused by cyclic loading (STEP C17)

The force-deformation loops are usually quite narrow, Fig. 5.3, whether the deformations are low or high. These differ from the wide loops typical in mild steel.

32

Fig 5.3 Typical force-deformation loops for different load levels of dowelled joints under cyclic loading (STEP C17).

Figure 5.4a presents the shape of a well-designed dowelled connection, where the energy is dissipated through the embedment of wood and through the plasticity of the connection. If the fastener is so strong and rigid that it does not bend, the energy dissipation is solely given by the embedment of the wood. In this case the force-deformation curve is as shown in Fig. 5.4b.

Fig 5.4 Dissipation for different connections (t is tension, c is compression). (STEP C17)

Mechanical connections are not usually sensitive to fatigue failure, although there are some exceptions. As an example, there are several types of steel plates with punched teeth, where the failure may occur as a pull-out of the teeth or brittle failure of the steel plate. Another example is a shear wall made of a brittle panel sheathing, in which case a cyclic loading might cause a brittle failure of the wall. In order to have harmonised procedures to develop connections for seismic design, CEN is preparing a standard, where a simple method of testing connections is given by a quasi-static method. In the following, the test procedure is briefly described. Figure 5.5 shows a threecycle load loading pattern, where the amplitudes are multiples of the yield slip y .

33

Fig 5.5 Recommended cyclic loading pattern in tests. (STEP C17)

In Fig. 5.6, F describes the impairment of the strength between the first and the third load cycles, when the connection is loaded to the same deformation.

Fig 5.6 Impairment of strength between first (a) and third load cycle. (STEP C17)

The energy dissipated in a half cycle through plastic strains in the non-linear zone is measured as the shaded Ed area shown in Fig. 5.7. The ratio between the dissipated energy and the potential energy Ep is called the 'hysteresis equivalent viscous damping ratio' eq. The amount of dissipated energy increases as the amplitude increases, but eq remains more or less constant. For well-designed connections between plywood and the timber frame in shear walls the value of eq is about 8-10%.

Fig 5.7 Dissipation of energy in a loading cycle. (STEP C17)

34

In the elastic zone, the hysteresis damping is, in principle, zero, Fig. 5.3a. However, in the elastic zone some energy may also be dissipated. In small amplitude dynamic vibrations, less than 1% viscous damping may be measured if secondary structures are not connected. If secondary structures are connected, due to friction in connections and compression perpendicular to the grain, values exceeding 4% are easily obtained. This is often the case for redundant building elements and contact points in buildings. For these reasons, a damping ratio value of 5% is assumed for the elastic zone.

5.4 Performance of different types of connections

As previously mentioned, the successful performance of mechanical connections is due to high ductility, lack of sensitivity to cyclic loads and their ability to dissipate energy. In order to avoid splitting of wood and brittle failures, EC5 states the minimum end and side and spacing distances of the fasteners and these should be obeyed. They are given to ensure that the connection failure is not brittle. Splitting may also be prevented by using reinforcing materials in the connection areas, which give higher tension strength in the direction perpendicular to the grain of the wood. Such reinforcing materials are, for example, plywood panels and densified veneers. In addition to preventing the wood from splitting, the reinforcement ensures the yielding of the fasteners and thus enhancing connection ductility. To ensure the dissipation of energy, it is possible to take advantage of the slenderness of the fastener. The slenderness is defined as the ratio between the wood member thickness and the fastener diameter. Fasteners with high slenderness ratios dissipate more energy since the plastic yield points are, in this case, always formed in the fastener. Fasteners with low slenderness ratios perform more elastically and do not dissipate as much energy. In addition, the wood splitting may be prevented by increasing the member thickness in comparison to the fastener diameter. To avoid an unacceptable strength loss in cyclic loading, three general principles should be followed. Details should be designed so that the elements cannot easily pull out, brittle material failures should be avoided and materials should be used which retain their mechanical properties during cyclic loading.

Dowel-type fasteners

Nails, staples and screws Nails, staples and screws are usually made of hardened steel. In spite of this they perform plastically in a mechanical connection when designed appropriately. The nail length should be increased if there is a risk of pull-out. Smooth nails are not recommended for this reason. If the slenderness ratio of the nail is higher than 8, good ductility may be expected.

35

Fig. 5.8 Typical performance of a nailed connection under cyclic loading (nail slenderness 8.5). (STEP C17)

A ductile connection between plywood and wood may be ensured if the slenderness of the nails is at least 4d. Experiments show that nailed shear walls with plywood sheathing possess high ductility and a high ability to dissipate energy as may be seen in Fig. 5.9. Figure 5.9 presents a full-scale seismic experiment on a three-storey timber house, the experimental set-up, the loading scheme and the test results of the lateral displacement of the building top (Yasumura et al., 1988). The building is braced with shear walls with 9-mm plywood panels on the external walls and 12-mm gypsum boards on the internal walls. The result shows that these shear walls dissipate energy well and that the building as a whole has a high ability to deform without losing strength.

36

Test set-up

Load

Lateral deformation [mm]

Fig. 5.9 Full-scale seismic experiment of a three-storey timber house braced with nailed shear walls (Yasumura et al., 1988).

Dowels Slender dowels in connections may yield both from the steel and from the wood and these dissipate energy well. If the dowel length in the wood is higher than 8d, the connection performs in a ductile manner. If the connection is made of thick dowels and the fastener spacing complies with EC5, the plastic behaviour is only dependent on the performance of the embedment of the wood. Since the energy dissipation is low in this case, tests are usually recommended to evaluate the ductility property of such a connection. Bolts Bolted connections have oversized holes due to the production technique and this may result in an unequal distribution of forces under loading. This may cause the overstressing of certain fasteners and thus cause local splitting of the wood at these fasteners and prevent the redistribution of forces within the connection. For this reason, bolted connections for seismic zones should be precisely constructed and the bolts should have a high slenderness ratio. Thick bolts (d > 16 mm) are usually not able to deform and do not dissipate energy. For this

37

reason these should only be used in combination with other fastener types such as toothed ring connectors. (EC8 recommends the diameter of dowel type fasteners to be less than 16 mm). Split ring and shear plate connectors These are not recommended for use in energy dissipating parts of structures as they have low plasticity values. Toothed plate connectors With good design, toothed plate connectors may have good plastic performance. Spacing and end distances, particularly, should be considered in order to prevent the splitting of wood. Nailplates Although the force-deformation curves of nailplate connections typically show some plastic behaviour, it is recommended that prototype tests should be carried out if these connections are intended as energy dissipating connections. This is to avoid potential failure such as brittle metal plate failure and nail pull-out failure. In Helsinki University of Technology, TKK (1995), experiments were carried out to test nailplates of the 'Träforband T150' type to determine their performance against seismic actions. The tests were done on cyclic loading using tension-compression, shear and bending loading modes. The nail length was 14.3 mm. The conclusion of this study was that these nailplates may be designed as energy dissipating connectors (class D, q=3), provided that the anchorage failure mode is dominant and that the anchorage strength is designed in accordance with a medium-term load duration class.

5.5 Performance of mechanical connectors under seismic loading

Until now, the loading on connections has been considered to be a quasi-static cyclic action. The true loading under an earthquake is different, however. The influence of the loading rate, for example, cannot be taken into account in the cyclic loading. Also, the frequency of the cyclic loading varies in time and it is different for different earthquakes and in most cases it is also unknown. It seems, however, that a cyclic load test, as previously described, is sufficient in order to estimate the seismic performance of a connection. The true performance under an 'instantaneous' load is less flexible and more resistant than under a 'medium-term' load. There is no evidence that a seismic loading of high velocity would alter the ductility of the structure. Cyclic tests are considered to be sufficiently accurate to determine the parameters and to reveal the true performance of the connection under a seismic event. When the shape of the force-deformation loop is known under cyclic loading (RILEM, 1994), it is possible to model the structure by a non-linear seismic analysis computation to estimate the strength of the structure under a given earthquake. Another point to emphasise is that a true earthquake loading scheme is random and irregular. There is a low number of cycles causing high deformations and a much higher number of cycles causing lower deformations. In Fig. 5.10, an example is given of a test of a portal frame corner connected with dowels during similar conditions to those of the El Centro earthquake. The moment-rotation results are based on numerical calculations. The earthquake was amplified by a factor of 1.5.

38

5.6 Requirements of Eurocode 8

In EC8, structures are classified according to their ductility and to their energy dissipative property. In certain cases, it is recommended to design the structure to be sufficiently rigid to fulfil the serviceability criteria. For structures designed to dissipate energy, that is q > 1, the strength of the wooden parts should be higher than the strength of the connections. The connections should also be able to deform to the plastic range.

Fig 5.10 The moment-rotation curve of a portal frame corner under the El Centro earthquake. (STEP C17)

The ability to dissipate the energy of the connections under seismic actions should usually be demonstrated by tests following internationally recognised experimental procedures. The test shows that the connection is ductile and the properties are stable under a rather high deformation or a stress level cyclic load. To ensure ductility, it is required that the ductility under a cyclic load is at least three times the q value. This multiplier is reduced to two for panel structures. Additionally, the connections should be able to deform plastically for at least three full cycles at the above ductility ratio without a 20% reduction in strength. Satisfying these conditions, the designer may calculate the strength and rigidity of the connection following the normal procedures in EC5.

39

6. Conclusion

Timber houses are usually regular, both in plan and in elevation. The seismic design may then be carried out using the simplified modal response spectrum analysis, which returns a single base shear value acting on the building. EC8 gives the rules on how this base shear is calculated. The bracing of the building is designed in both principal directions against this base shear load. When the seismic load is calculated, the bracing is designed according to EC5. However, some restrictions on the detailing of floor diaphragms and shear walls are given in EC8. In the case of multi-storey timber houses, the seismic loads are about twice the magnitude of the wind loads in high seismic zones. Therefore, the lateral loads should be taken into account early in the design process when planing the layout and the frame. In the simplest case, the seismic loads are determined following the list below: 1. Determine the subsoil class according to local conditions (A, B or C) 2. Determine the peak ground acceleration value, ag, to be used in the design from local authorities. 3. Estimate the natural period of the building using eq. 2. 4. Determine the behaviour factor q according to the structure class. 5. Calculate the ordinate of the design spectrum from eq. 5. 6. Calculate the loads using eq. 6. 7. Calculate the base shear force with eq. 1. and its distribution using eq. 3. 8. When the seismic loads are determined, the dimensioning of the structures may be done following EC5. The following are some aspects in need of further study: The seismic design should be carried out by computer. The equations presented in this text to determine these loads as well as the equations needed for the dimensioning of the structures should be implemented in a computer-based design program. The calculation routines are rather simple, but can be laborious, especially when the shear walls are not situated symmetrically in a building and torsion effects are produced. Seismic design expertise should also be widely known in countries such as Finland, which do not have earthquakes, but which do have a timber house exporting industry. In this way, the local requirements for houses can be better fulfilled. The good seismic performance of timber buildings should be used in the marketing aimed at seismic areas of the world. Also, local authorities should be better informed on the performance of timber houses. Usually, in areas of high seismic activity, buildings are made of concrete or masonry and these are very dangerous if not properly designed for seismic actions.

40

References

APA, (1997a) Earthquake safeguards; Introduction to lateral design, wood design concepts. Seattle USA APA (1997b) Introduction to lateral design, wood design concepts. Seattle USA 1997 Buchanan, A., Dean, J. (1988) Practical design of timber structures to resist earthquakes. International Timber Engineering Conference, Seattle, 1988: 813-822. Ceccotti, A. (2000) Seismic behaviour of timber buildings, introduction. COST E5 Workshop on Seismic behaviour of Timber Structures. September 28-29 2000 Venice Italy. Ceccotti, A., Karacabeyli, E. (1998) Seismic design considerations on the multi-storey woodframe structures. Cost E5 workshop on constructional aspects of multi-storey timber buildings. June 1998 UK. Ceccotti, A., editor, (1989) Structural Behaviour of Timber Constructions in Seismic Zones. Proc. of the relevant CEC DG III - Univ. of Florence Workshop, Florence, Italy. EUROCODE 8 (1994) ENV 1998-1-1. Design provisions for earthquake resistant structures. European prestandard. TC 250 of CEN, Brussels, Belgium. EUROCODE 5 (1995) ENV 1995-1-1. Design of timber structures. European prestandard. TC 250 of CEN, Brussels, Belgium. (Version 29.06.1999) Karacabeyli, E. (2000) Performance of North American platform frame wood construction in earthquakes. COST E5 Workshop on Seismic behaviour of Timber Structures. September 2829 2000 Venice Italy. RILEM TC 109 TSA (1994) Timber structures in seismic regions. RILEM State-of-the-Art Report. Material and Structures 27: 157-184. SECBC (1997) Updated seismic design of buildings. Structural Engineering Consultants of British Columbia, Wood Frame Committee. STEP B13 Diaphragms and shear walls, Thomas Alsmarker. STEP 1 Timber Engineering, Basis of design, material properties, structural components and joints. Centrum Hout 1995 STEP C17 Timber connections under seismic actions, Ario Ceccotti. STEP 1 Timber Engineering, Basis of design, material properties, structural components and joints. Centrum Hout 1995 TKK (1995) Träförband T150 naulalevyliitosten käyttäytyminen seismisessä kuormituksessa. Tutkimusselostus TRT0595AK. Talonrakennustekniikka TKK, 1995. (The performance of the T150 nailplate under seismic loading, test report in Finnish) Yasumura, M. et al. (1988) Experiment on a three-storied wooden frame building subjected to horizontal load. In: International Timber Engineering Conference, Seattle, 1988: 262-275.

41

Material suppliers Anchorage connectors

Simpson strong-tie connectors Bulldog-Simpson GMBH Boschstrasse 9 D-28857 Syke, Germany tel. + 49 4242 95940 fax + 49 4242 60778 http://www.strongtie.com MGA connectors MGA 11476 Kinston St. Maple Ridge B.C. V2X O45 Canada tel. + 1 604 465 0296 fax. + 1 604 465 0297

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43

Plywood WISA - special plywoods Schauman Wood OY PL 203 FIN-15141 Lahti, Finland tel. 0204 15113 fax. 0204 15112 http://www.schaumanwood.fi/tuotteet/vanerit/ index.html

Finnforest Oy PL 50 FIN-02020 Metsä tel. 010 4605 fax. 01 4694863 http://www.finnforest.fi/pages/products/ plywood2.htm

In Turkey: WISA - special plywoods Schauman Wood OY Istanbul Branch Office Bagdat Cad. Yesilbahar Sk. No. 1/10 TR-81060 Ciftehavuzlar/Istanbul, Turkey tel.+90(0)2163854610, 3860831 fax.+90(0)2163856558.

43

44

Earthquake magnitude, M

To assess the magnitude of earthquakes, a scale to describe the energy released during an earthquake was developed by Richter in the 1930s. This is named the Richter scale and it is the most common scale used today to describe earthquakes. The magnitude of an earthquake on the Richter scale is determined by a so-called Wood-Anderson seismograph maximum amplitude, where M = log(a), and a is the maximum amplitude [µm] at a 100 km distance from the epicentre. The magnitude may also be assessed at other distances using special conversion tables. The magnitude measures the amount of released energy and a unit increase of magnitude signifies a 32-fold energy release. There exists a physical upper limit above which elastic energy cannot be stored without being released; this limit is approximately M = 8.9 . Buildings usually do not suffer severe damages when M < 5 . The seismic action on buildings cannot be described by the Richter scale magnitude and this may not be used in the design. However, Housner in 1970 developed empirical relationships between the magnitude, the duration and the peak ground acceleration to be used in design, see Table L1 below.

Table L1. Relationships between the magnitude, peak ground acceleration and the duration of the most intense phase of the earthquake (Housner, 1970)

Magnitude on the Richter scale 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 Peak ground acceleration (% g) 9 15 22 29 37 45 50 50 Duration (s) 2 6 12 18 24 30 34 37

44

45

Example cases of seismic load calculation and design Example 1, Seismic load for a small one-storey house Input values: Building area 9.3 × 16.8 m2 Ground acceleration = 0.35 g H Subsoil class C Importance factor = 1.0 (residence)

45

46

Dead load g: 0.8 KN/m2 Snow load q: 1.8 KN/m2 Building height H: 3.5 m Subsoil class C Building fundamental period, T0 Shear walls as vertical diaphragms, q = 3.0 H 3.5 ( m) 0.35

3 4.

2.5

Tb

0.2. s

Tc ag g

0.8.s

Td kd1 S

3 .s 2 3 0.9 q kd2 5 3 3.0

Relative acceleration =

T0

0.05. H s

T 0 = 0.128 s Sd T .S . 1 .S . q . Tb q T 1 if T < T b

if T b < T < T c

kd1

Tc .S . . q T Tc .S . . q Td

if T c < T < T d

kd1

.

Td T

kd2

if T d < T

S d T 0 = 0.281

0.4

0.3

Sd T

0.2

0.1

0

0

1

2 T

3

4

Vertical load for seismic design W = (G+ Ei Qki) x building area W ( 0.8 0.2.1.8) . 9.3. 16.8 W .S d T 0 Fb = 51.003 KN Fb Importance factor = 1.0 Comparison to the wind force below Qwind = 3.5 x 16.8 x 0.7 KN/m 2 = 41 KN W = 181.238 KN Base shear force

46

47

Example 2, A four-storey timber house case, calculation of the seismic load and design of some details

Input values: Ground acceleration = 0.35 g, Subsoil class B Floor dead load 1 KN/m2 (the weight of the walls is assumed to be included in this figure) Roof dead load 0.75 KN/m2 Live load qh = 2.0 KN/m2 Importance factor = 1.0 (residence) The seismic load is determined considering the vertical loads present in the different storeys of the building. This load is calculated using eq. 6:

åG

kj

+ å EI Qki

(6)

Gkj is the characteristic dead load and EIQki is the probable live load during a seismic event. Combination coefficient: EI = 2i 2i is 0.3 (the quasi-permanent value of the live load (EC1 and EC5) , is 0.5 except for the top storey for which it is 1.0 (EC8)

Table L2.1 combining the loads in the different storeys.

Storey Gkj Qki

2i

EI

Gkj + EIQki

Roof Storey 4 Storeys 2 and 3 Storey 1

0.75 1.0 1.0 2.0 2.0 0.3 0.3 1 0.5 0.30 0.15

0.75 1.60 1.30

Loads transferred directly to the foundations

Following the table above, the total vertical load is:

åG

· · · ·

kj

+ å EI Qki = 0.75 + 1.60 + 1.30 + 1.30 = 4.95 KN/m2

Ground acceleration is ag = 0.35 g Subsoil class B Building braced with shear walls of plywood sheathing and mechanical fasteners, q = 3 . Building area: 288 m2

47

48

Building height H: 12 m Building fundamental period T 0 H 12 0.35

3

kd1

2.5 2 3

Tb

0.15. s 5 3

Tc S

0.6. s 1

Td q

3 .s 3.0

kd2

T0

4 0.05. H . s

T 0 = 0.322 s Sd T .S . 1 .S . q . Tb q T 1 if T < T b

if T b < T < T c

kd1

Tc .S . . q T Tc .S . . q Td S d T 0 = 0.292

if T c < T < T d

kd1

.

Td T

kd2

if T d < T

0.4

Sd T

0.2

0

0

1

2 T

3

4

Vertical load , W = (G+ Ei Qki) x building area W ( 0.75 1.6 1.3 1.3) . 288 KN

Base shear load Fb W .S d T 0 KN Importance factor = 1.0 Comparison to the wind load below Qwind = 20 x 12 x 0.7 KN/m 2 = 168 KN

Fb = 415.8

48

49

The base shear force is distributed in elevation according to eq. 3 :

Fi = Fb z iWi å ziWi

j

(3)

Fb is the base shear force The shear force acting on the shear walls of each storey Froof Froof+F4 Froof+F4+F3 Froof+F4+F3+F2 2/3 x H Fb = F2+F3+F4+Froof The force distribution according to eq. 3

Fb = Froof+F4+F3+F2

Table L2.2 The design shear forces in the different storeys

Storey, i

Height of storey from ground zi [m]

The load on each floor (Table L2.1) Wi [KN] 0.75×288 = 216 1.6×288 = 461 1.3×288 = 375 1.3×288 = 375

Fi , shear force in the storey level zW Fi = Fb i i å ziWi

j

Cumulative shear force acting on the shear walls at the different storey levels

Fv = å Fi

i

4

[KN] 107 171 93 46

[KN] 107 278 371 416

Roof 4 3 2

12 9 6 3

ziWi = 10116 KNm ;

Fb 416 KN

49

50

The shear walls will be composed of 9-mm-thick plywood panels connected with threaded nails 28×60 k70. In this case the shear wall capacity per length (from Table 4.1) is Fv,d = 7.38 KN/m. This means that the lengths of shear walls needed in the different storeys are: - first storey at least 416/7.38 = 56 m - second storey at least 371/7.38 = 50 m - third storey at least 278/7.38 = 38 m - fourth storey at least 107/7.38 = 14 m The sheathing panel is nailed along all edges to the timber frame at spacing k70 and to the middle of the panel at spacing k300. A schematic diagram of the shear walls in the first storey of the building

7000 4000 7000

3500

2500

2500

3500

8500 Apartment A Corridor Apartment B

Apartment C Y X

Apartment D

8500

shear wall

The total length of shear walls in X-direction - internal walls 18 m × 2 3 × 1.2 m (doors) = 32.4 m - external walls (3.5 m + 2.5 m + 2.5 m + 3.5 m) × 2 = 24 m total 56.4 m ( > 56 m ) OK The total length of shear walls in Y-direction 63.2 m - internal walls 17 m × 4 4 × 1.2 (doors) = - external walls (3.5 m + 2.5 m + 2.5 m + 3.5 m) x 2 = 24 m

50

51

total 56 m ) OK

87.2 m ( >

It is advantageous to use the walls between apartments and corridors as shear walls with panelling on both sides of the wall. In this example, the shear walls are situated symmetrically to avoid a torsion effect (for simplicity). In practice, gypsum boards could also be used as an additional reinforcement for the shear walls. EC5 allows the use of two different panels in shear walls, but only 50% of the capacity of the weaker gypsum panel could be included.

Anchoring the building against uplift The example below concerns only the anchorage of the first storey to the foundations. Only the anchoring of one shear wall, the shortest shear wall of 2.5 m, is shown. The anchoring analysis should be carried out on all of the storeys and all of the other shear walls in a similar manner. Below the vertical load is calculate. The dead load is advantageous so the partial safety factor is 1.0 . Wind and live loads are not included. Vertical load: p Hd = g [ g roof + g 2- storey + g 3- storey + g 4- storey ] x Building area + g g wall

= 1.0 x [0.75 + 1.0 + 1.0 + 1.0] x 288 + 1.0 x 0.5 x ( 4 x17.0 + 3 x18.0) x12 = 1812 KN From this load, the portion affecting the 2.5 m long shear wall is approximately: · PHd,wall = 1812 × 2.5 × 8.5 × 0.5 × 0.5/288 = 33.4 KN The lateral load affects at height 2/3 × H: Fb = 416 KN From this load, the portion affecting the 2.5-m long shear wall is approximately: · Fb,wall = 416 × 2.5/56.4 = 18.4 KN Distribution of vertical load by eq. (9) : Fi = Fb z iWi å ziWi

j

Fb,wall

2/3 x H PHd,wall

51

52

2.5 m

Anchoring for uplift force, AHd

AHd =

Fb ,seinä x12 x

2 - PHd ,seinä x1.25 3 = 42,2 KN 2.5

Both sides of the shear wall are anchored for an uplift force of 42.2 KN.

The anchorage is made of 10 pieces of lag screws of size 10×55 and a metal plate folded to a 90-degree angle with a cross-section size of 80×5 mm2 and a bolt of size M12 connected to the foundations. First let us analyse the connection of the anchorage to the wooden frame. The metal plate is of thickness t1 = 5 mm and the penetration of the screw into the wood is t2 = 50 mm .

75 5 50 20 40 20 20 70 d = 10mm 70 70 70 75 5

d = 12mm

solid The characteristic embedment strength of wood is f hk (EC5):. solid f hk = 0.082(1 - 0.01d ) ksolid = 0.082 x (1 - 0.01 x10mm) x 350kg / m 3 = 25.8 N / mm 2

The characteristic tension strength of steel is f uk = 500 N / mm 2

screw The yield moment of the lag screw 10x55 is M yk (EC5):

M

screw yk

0.8 f uk d 3 0.8 x 500 N / mm 2 x (10mm) 3 = = = 66667 Nmm 6 6

screw The characteristic shear strength of the screw 10x55 is Fvk (EC5).

52

53

solid ì0.4 f hk t 2 d = 0.4 x 25.8 x 50 x10 = 5166 N ï F = min í screw solid ï 2M yk f hk d = 2 x 66667 x 25.8 x10 = 5869 N î screw Þ Fvk = 5166 N screw vk

For the service class 1 and load duration class "instantaneous" the design shear strength of the screw is:

screw Fvd = k mod screw Fvk

M

= 1.1 x

5166 N = 4371N 1.3

The load acting on the screw is Fvscrew :

Fvscrew = AHd 42200 screw = = 4220 N < Fvd , 10 n OK

Under service class 1 and load duration class "instantaneous", the design strength of the metal plate and bolt is: f uk 500 N / mm 2 f ud = f hd 1 = = = 454.5 N / mm 2 1.1 M The design tension capacity of the plate 5x80 is Ftdplate : Ftdplate = f ud A = 454.5 N / mm 2 x 5mm x 80mm = 181800 N < AHd ,

bar The design tension capacity of the bolt M12 is Ftd : bar Ftd = f ud A = 454.5 x x 6 2 = 51400 N < AHd ,

OK

OK

The tension force acting on the wooden frame strut (T24) 42.2 KN ftk 14 = 8.4 N / mm 2 < k mod = 1.1 = 11.8 N / mm 2 2 50 x100 mm 1.3 Anchoring the building against sliding Next, the anchorage calculation against sliding is carried out. The vertical loads are not necessary in this case as the effects of friction cannot be considered. OK

53

54

In the first storey, the building had a total of 56.4 m (weakest lateral direction) of shear walls and the base shear force is FB=416 KN. Therefore, the anchoring force against sliding is as follows: AVd = Fb = 7.4 KN / m 56.4

Bolts of size M10 × 120 are used, with a design shear capacity of Fvd= 9.4 KN. Therefore, the bolt spacing in the bottom plate (sill plate) is as follows: s= Fb = 1.3 m AVd

The shear walls are anchored for sliding in the first storey with bolts connected to the foundation of type M10 × 120 and with a spacing of, let's say, k1000.

Vertical section

54

55

Bolts M10*120 k1000 Shear wall edges anchored by a bolt M12

Horizontal section

Anchorage for sliding Bolts M10x120 k1000 Plywood panel sheathing 9 mm

Shear wall length 2500 mm

Anchorage for uplift forces bolt M12 Wall opening Screws 10 x 55 10 pieces metal plate

55

56

A summary of the procedure to evaluate the seismic load according to Eurocode 8 The seismic design of a building starts with an evaluation of the regularity of the building in both layout and elevation compared with the requirements mentioned in section 3.3 (EC8 part 1-2, 2.2 Structural regularity). Generally regularity increases the seismic resistance of the building. Usually timber residential buildings are regular in plan and in height. The initial values are given, the subsoil class (section 3.4) according to the ground conditions and the peak ground acceleration value, ag, according to the site seismicity. It should be noted that for a different country, the authorities may enforce values or parameters different from the ones given in EC8, which are so-called boxed values. The values given in this report are the ones recommended by EC8. Such information is given in the national application documents. Base shear force The base shear force acts in both principal directions of the building. (1.a, b) (EC8 part 1-2 eq. 3.3) Fb = Se(T0) W/q = Sd(T0) W

Where T0 is the fundamental period of the building Se is the ordinate of the elastic response spectrum Sd is the ordinate of the design response spectrum W is the vertical load q is the behaviour factor Fundamental period To estimate the fundamental period, T0, of the building, EC8 has a simple procedure: (2) (EC8 part 1-2 eq. C1) T0 = 0.05 H0.75 Where the building height is in metres and the time in seconds. Distribution of the base shear force in elevation If the floor loads are equal in the different storeys, the base shear force is distributed in a triangular manner so that higher forces are higher up. This is given by the equation: z iWi Fi = Fb (3) (EC8 part 1-2 eq. 3.5) å j ziWi Where Fi is the lateral load in storey i Fb is the base shear force zi is the distance of the floor from the ground Wi is the vertical load on the floor Design spectrum é T æ öù S d = S ê1 + 0 ç - 1÷ú ç ÷ ë Tb è q øû Sd = S q

jos T < Tb jos Tb < T0 < Tc ( 0.2 ) jos Tc < T0 < Td jos Td < T0

(5.a) (5.b) (EC8 part 1-1 eq. 4.7(5.c)

æT ö Sd = S ç c ÷ q ç T0 ÷ è ø æT Sd = S ç c q ç Td è 4.10)

kd1

ö ÷ ÷ ø

kd 1

æ Td ç çT è 0

ö ÷ ÷ ø

k 21

( 0.2 )

(5.d )

56

57 Where = ag/g , ag is the peak ground acceleration value T0 : is the fundamental period of the building Tb, Tc, Td : are time parameters S: soil parameter kd1 = 2/3 , kd2 = 5/3, exponent parameters According to the subsoil class, the parameter values are as in the following table. Table L3.1 Parameters for the spectrum equations. (EC8 part 1-1 Table 4.1) Tc [s] Td [s] Subsoil class S Tb [s] A 1.0 2.5 0.10 0.40 3.00 B 1.0 2.5 0.15 0.60 3.00 C 0.9 2.5 0.20 0.80 3.00 Se =ag S

0.563 0.6

0.4 SE T

Fig L3.1 An example of an elastic design spectrum, subsoil class C and ag = 0.25g

0.2

EC8 gives the behaviour factor q values for different structural types as below: (EC8 part 1-3 fig. 4.1) 0 Class A Non-dissipative structures: 0 0 1 2 3 4 q = 1.0 Structures with no mechanical connections, hinged arches, cantilever structures 0 T 4 with rigid connections at base Class B Structures having a low capacity for energy dissipation: q = 1.5 Structures with few mechanical connections, cantilever structures with semi-rigidly fixed base connections Class C Structures having a medium capacity for energy dissipation: q = 2.0 Frames, and beam-column structures with semi-rigid joints Log houses Gypsum board shear walls (Ceccotti & Karacabeyli, 1998) Class D Structures having a good capacity for energy dissipation: q = 3.0 Shear walls using wood-based boards and mechanical fasteners for example platform frame timber houses (also multi-storey) Horizontal diaphragms may be glued or nailed. The mass in seismic design W = å Gkj + å EI Qki (6) (EC8 part 1-1 eq. 4.12) Gkj is the characteristic dead load and EIQki is the probable live load during an earthquake. EI = 2i (7) (EC8 part 1-2 eq. 3.15) 2i is the long-term value 0.3 for live loads, or 0.2 for snow loads (EC1 and EC5), is 0.5 for all storeys except the top storey for which it is 1.0 (no correlation between storey loads). (EC8) is 1.0 for storage loads (EC8)

57

58

Combining loads in seismic design The design loads needed in seismic design consist of dead loads and seismic loads. Wind loads do not need to be considered. E d = å Gkj + Fb + å 2 i Qki (8) (EC8 part 1-1 eq. 4.11) Where, is the importance factor (I = 1.4 hospitals, fire stations, power stations; II = 1.2 schools, cultural buildings; III = 1.0 residential and commercial buildings; 0.8 agricultural buildings), IV = Gkj and Qki are the characteristic values of the dead and live load, 2i is the combination coefficient of the quasi-permanent value of the live load. The vertical loading components may be determined by multiplying the lateral loads by the following factors: 0.7 when the fundamental period of the structure T0 < 0.15 s 0.5 when the fundamental period of the structure T0 > 0.50 s for values where 0.15 s < T0 < 0.5 the factor may be interpolated. Seismic design Ultimate limit state f E d = f {å Gkj , Fb , å 2 i Qki } Rd = R{ k } (9) (EC8 part 1-2 eq. 4.1) M The load duration class is 'instantaneous' and such kmod values are used. The material safety factor is M = 1.3, when the structure is energy dissipative (or q > 1) and M = 1.0, when the structure is non-dissipative (or q = 1). The importance factor, , in the above equation is as given for eq. 8. Ductility The structures and the building as a whole should be adequately ductile. The ductility should be as considered in the design, where it is taken into account as a load reducing factor, the behaviour factor q was explained previously. Equilibrium The building should be stable during a seismic event. The seismic load combinations should be considered when designing for the anchorage of the building in the following two cases: - anchorage for overturning: upward tension at ends of shear walls, - anchorage for sliding, base shear at the bottom of shear walls Serviceability limit state In order to avoid excessive damage, EC8 gives rules for the inter-storey drift during a seismic event. The design earthquake may be one, which is more likely (lower return period), and the peak ground acceleration is lower than for the ultimate limit state. The inter-storey drift is limited to the following values: , buildings having non-structural elements of brittle dr/ 0.004 h or materials attached to the structure 0.006 h , buildings having non-structural elements fixed in a way as not to interfere with structural deformations Where dr is the inter-storey drift h is the storey height reduction factor having values between 2.0 2.5 . Takes into account the lower return period of the seismic event during the serviceability limit state.

58

59

JULKAISUN ESITTELYTEKSTI englanniksi

Takakannessa julkaistaan esittelyteksti [X] (tutkimusyksikön) julkaisujen luettelo [ ] Viimeisellä sivulla julkaistaan (tutkimusyksikön) uusimpien julkaisujen luettelo [ ] Lomake tai mahdollinen erillinen esittelyteksti lähetetään valmiin käsikirjoituksen mukana.

Sarjanimeke

Sarjanumero

Vuosi

VTT Tiedotteita

Tekijät

2001

Tomi Toratti

Julkaisun nimi

Seismic design of timber structures

Sivuja

52

Liitesivuja

16

ISBN

Esittelyteksti

This report describes the seismic design of timber structures according to Eurocode 8. The calculation procedures to obtain the seismic loads are given and these are illustrated with examples. The dimensioning of the structure is carried out according to Eurocode 5 in a similar manner as for other lateral loads, for example wind loads, with a few minor exceptions. This report is written in a practical level so that also designers inexperienced with seismic analysis would be able to carry out a seismic design of a timber building.

59

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