seismic design of timber structures
TRANSCRIPT
Seismic Design of Timber Structures
Tomi Toratti
Cover page figure source: Destruction of a residential house /Filmore, Northridge earthquake 1994. FEMAnews photo, http://www.fema.gov/library. Federal Emergency Management Agency
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Abstract
Wooden buildings have a good reputation when subjected to seismic events. Experience fromNorth America and Japan shows that wooden buildings can resist catastrophic earthquakeswhile sustaining only minimal damage. Many modern timber buildings have even survivedshowing no visible signs of damage. The advantage of wooden buildings is based on low self-weight, ductile joints and in general very regular building geometry.
An effective way to design for lateral loads, including seismic loads, in residential woodenhouses, is the use of plywood panels in shear walls. These shear walls have a high lateralforce-resisting capacity and the joints are in general very ductile. The ductility of the joints isvery critical as it also affects the level of shear force to which the wall is subjected. The highperformance of plywood shear walls is based on the ductility and energy dissipativecharacteristics of nailed or screwed joints on plywood in shear walls.
Based on previous experience, modern design codes perform well for earthquakes. In theEuropean region, Eurocode 5, design of timber structures, and Eurocode 8, design provisionsfor earthquake resistance of structures, are new design codes and these may be applied, forexample, in the exportation of wooden buildings and building expertise to seismic areas. Thisreport 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, asimplified modal response spectrum analysis may be used. The body forces created by theground acceleration on the building are converted to a base shear force imposed in bothprincipal directions. EC8 gives the methods to calculate this shear force. The structuresresisting these lateral forces such as shear walls, floor diaphragms and anchorages are thendesigned 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 designof Timber Structures - prestudy'. The project has been funded by the companies andinstitutions represented in the management committee. The project was initiated in February2000 and it ended in December 2000.
The research was carried out by VTT/Building and Transport. The work was done primarilyas a literature survey and as interviews with experts. Significant contributions are those ofProf. Ario Ceccotti, University of Florence, Mr. Onur Önal, Schauman Wood Oy office inTurkey, Dr. Erol Karacabeyli, Forintek Corp., and many other members of the COST actionE5 'Timber frame systems' management committee. The COST E5 programme organised aseminar on the seismic behaviour of timber structures in Venice in September 2000. This wasvery valuable to the present study.
The management committee of this research project consisted of the following experts:
Ilmari Absetz, Tekes,Jouni Hakkarainen, Finnforest OyKeijo Kolu, UPM-Kymmene Wood Products, chairmanKari Liikanen, Porvoon Puurakennus OyAlpo Maunu, Maunu-Talot OyPekka Nurro, Wood Focus OyHannu Pellikka, Sepa OyJouni Turunen, Kontiotuote OyMikko Viljakainen, Wood Focus Oy
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 1
Preface 2
1. Table of contents 3
2. Introduction 4
3. Seismic design of timber houses according to Eurocode 8 63.1 Introduction 63.2 The structure of Eurocode 8 63.3 Analysis methods for seismic design 73.4 Simplified modal response spectrum analysis 93.5 Response spectrum 103.6 Vertical loads in seismic design 133.7 Combination of actions 143.8 Calculation of the seismic load, summary 15
4. Seismic design 164.1 Introduction 164.2 Ultimate limit state 164.3 Serviceability limit state 174.4 Special rules for timber structures 184.5 Lateral stability of the building 194.6 Floor diaphragms 204.7 Shear walls 234.8 The anchorage of the building 29
5. Connections of timber structures under seismic loads 335.1 Introduction 335.2 Ductility of connections 335.3 Performance under cyclic load 345.4 Performance of different types of connections 375.5 Performance of mechanical connectors under seismic load 405.6 Requirements of Eurocode 8 41
6. Conclusion 42
Appendix 1 Earthquake magnitude, M 43
Appendix 2 Example cases of seismic load calculation and design 44 - 52
Appendix 3 A summary of the procedure to evaluate the seismic load 53- 56according to Eurocode 8
References 57
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2. Introduction
Due to recent catastrophic earthquakes, for example in Turkey in 1999, it has been questionedwhether timber houses would be safer to live in, in seismic areas, compared to traditionalheavier houses. Based on the experience of the West Coast of North America, timber houses arein fact very safe when designed properly. The exportation of timber houses and structures toseismic areas requires knowledge of seismic design so that the safety of these products can bedemonstrated. Acquiring knowledge of seismic design methods is thus of great importance totimber exporting companies.
The prime objective of this report is to describe the seismic design of timber houses accordingto the Eurocodes. This report concentrates mainly on Eurocode 8 design provisions forearthquake resistance of structures, where the procedures to determine the seismic loads andthe parts giving requirements for timber structures are described. The design procedures areapplied here to a wooden residential house.
Eurocode 8 (EC8) is a modern design standard for the determination of seismic loads andstructural details. In Finland there are no major earthquakes and for this reason expertise in thisfield is not widespread. For the exportation industry, however, knowledge of EC8 is oftenimportant. The Eurocode 5 and 8 versions referred to in this report are the versions given in thereferences. Some details may change since these Eurocodes are not yet finalised but majorchanges should not be expected. The sources of information for this report are given in the listof references. The main sources have been Eurocodes 5 and 8 and the STEP lectures B13 andC17.
The effect of earthquakes on buildings
The soil movements induced by earthquakes produce vibrations in buildings and, thus, inertialforces in the structures also. These forces are called seismic loads. To bear seismic loads, thebuilding should be able to withstand vertical movements without loosing strength. Stiff andbrittle structures usually do not perform well against seismic loads, since in this case only asmall deformation may cause failure. However, ductile structures or structures containingductile joints perform well during seismic events. These possess an ability to withstanddeformations without developing high stress concentrations. Most seismic design standards,including EC8, allow a significant reduction of seismic loads for ductile structures. Thisreduction takes into account the ability of the structure to deform during seismic events. Forbrittle 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 thelow weight of timber structures, ductility of joints, clear layout of timber houses and goodlateral stability of the house as a whole. As in any kind of building it is usually the inadequatestructural design or inadequate supervision during the building process that causes the damagesinduced 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 withoutsufficient lateral bracing (for example crawl spaces, garages).
Timber behaves in a ductile manner when loaded under compression, especially compressionperpendicular to the grain. This is advantageous in seismic design as, for example, in the side ofthe 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, perpendiculartension stresses should be avoided. The joints of timber structures are normally more ductilethan the timber parts themselves and this is, in most cases, the reason for the overall ductilebehaviour of timber houses and their good seismic performance, (see Buchanan & Dean, 1988and Ceccotti, 2000).
The table below shows the casualties of some past earthquakes and how many of these occurredin timber houses (Karacabeyli, 2000). These data support the theory that timber buildings aresafer than non-timber ones.
Table 2.1 Numbers of casualties during past earthquakes and how many occurred in timberhouses (Karacabeyli, 2000)
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3. Seismic design of timber houses according to Eurocode 83.1 IntroductionEurocode 8 (EC8) gives instructions on how the seismic loads are to be calculated. Inaddition, several structural and detail requirements are given on the lateral bracing structuresand on the load-bearing joints. The part on timber structures is 9 pages long. This report dealswith 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 ofcollapse. Only limited damages may be accepted with the building staying intact. The mainemphasis in EC8 is on the security of human beings, limited damages and that thosebuildings, which are important in the community (hospitals, fire station, etc.), remainfunctional. Nuclear power plants and dam structures are outside the scope of EC8.3.2 The structure of Eurocode 8EC8 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 givenEurocode 8 part 1-2, General rules for buildings. This part outlines the general rules regardingseismic resistance.Eurocode 8 part 1-3, Specific rules for various materials and structures. This part handles thedifferent building materials (concrete, steel, timber and masonry) and gives detailed structuralrequirements as well as detailing the specifications for buildings made of these materials. Thepart 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 provisionsfor towers, masts and chimneys, part 4 specific provisions with respect to tanks, silos andpipelines, and part 5 specific provisions relevant to foundations, retaining structures andgeotechnical aspects. These parts will not be considered in this report.
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Ground accelerationNational authorities may put restrictions on the building height or any other building propertyfor seismic areas in their countries. This may depend on the seismicity, the nature of thebuilding, 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 acountry by country basis in the relevant national application documents, NAD. EC8 does notcontain these acceleration values, but shows the methods to determine the seismic loads withthe 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 valueis normally used which has a return period of about 50 years, Ay. Additionally, the buildingshould resist a so-called 'ultimate earthquake' without collapsing, but damages are allowed inthis case. The return period of such earthquakes is around 475 years (EC8). The accelerationvalue is then Au.The ability of a structure to develop plastic strains and dissipate strain energy is central whendetermining its seismic performance (Ceccotti, 1989). Structures that have joints possessingplastic behaviour and energy dissipation can withstand much higher seismic events thanstructures 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 anddissipate energy. This property is given by the 'action reduction factor' or 'behaviour factor'termed q. This factor lies in the range q = 1–3 for timber structures. When a building isdesigned so that the structures enter a plastic zone with a ground acceleration Au, it wouldwithstand a q times higher acceleration without collapse, so Au = q Ay. In this way, thestructure could be designed elastically, q=1.0, for the ground acceleration Ay consideringbuilding 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 numericalvalue as well as its return period is given by the national authorities in the relevant nationalapplication documents as mentioned above.
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3.3 Analysis methods for seismic designThe seismic design of buildings may be carried out using several different methods ofanalysis. Such analyses are listed below.1. Simplified modal response spectrum analysis2. Multi-modal response spectrum analysis3. Power spectrum analysis4. Time-history analysis5. Frequency domain analysisEC8 permits the use of these analysis methods with certain restrictions. From these analysismethods, only method 1, 'Simplified modal response spectrum analysis', can be carried out onhand using the rules set by EC8. The other analysis methods are more complex and needspecial expertise; usually finite element methods are then needed which possess routines fordynamic analysis.Table 3.1 gives the minimum requirements of the method of analysis, which depends on theregularity of the building.
Table 3.1 The significance of the building regularity (EC8)
Building regularity Simplification allowed Behaviour factor,q
Plan Elevation Model Analysisyes yes planar simplified referenceyes no planar multi-modal decreasedno yes spatial multi-modal referenceno no spatial multi-modal decreased
According to EC8, a building may be considered regular in plan if the following conditionsapply:• 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% ofthe 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 verticalstiffening elements.
• With the given seismic load distribution, the lateral displacement of any storey does notexceed the mean storey displacement by 20%.
According to EC8, that building may be considered regular in elevation if the followingconditions 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 theprevious plan dimension in the direction of the setback. - In case of a single setback in thelower 15% of the total height of the building, the setback is not greater than 50% of theprevious 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 buildingregularity presented above. Thus, according to Table 3.1, these may be designed using thesimplified modal response spectrum analysis.3.4 Simplified modal response spectrum analysisThe simplified modal response spectrum analysis may be used, according to Table 3.1, whenthe building is regular as defined by EC8. In this case, only the lowest natural frequency ofthe 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 forceThe seismic base shear force, for both main directions, is determined as follows:
Fb = Se(T0) W/q or (1.a)
= Sd(T0) W (1.b)
Where T0 is the fundamental period of the buildingSe is the ordinate of the elastic response spectrumSd is the ordinate of the design spectrumW is the total weight of the building (see Chapter 6)q is the behaviour factor (or action reduction factor)
The fundamental period of the buildingFor the fundamental period of the building, T0, EC8 gives an approximate formula, whichmay be applied here. This gives values on the safe side and it may be used if other more exactmethods are not available. For timber houses it is as follows:
T0 = 0.05 H0.75 (2)Where the units of the building height H is given in metres and the result will be
inseconds.
Distribution of the horizontal seismic forcesIf the floor masses of the different storeys are equal, the base shear force is distributedtriangularly on the building in a manner that the forces increase going upwards.
�=
j ii
iibi Wz
WzFF (3)
Where Fi is the shear force in storey iFb is the base shear forcezi is the height of the storey from the groundWi is the mass of the floor (see chapter 6)
Subsoil conditionsThe influence of the local ground conditions on the seismic action is accounted for byconsidering 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-mdepth.
• Subsoil class B: Deep deposits of medium dense sand, gravel or medium firm clay. Shearwave 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 soillayers. 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 nationalauthorities. The peak ground acceleration value, ag, with a chosen return period is given forthese areas in the national application documents, NAD. EC8 does not contain suchinformation. 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 spectrumIn the equation for the base shear, eq. (1.a), the value of the elastic response spectrum isevaluated from the equation set out below, depending on the fundamental period of thebuilding. For timber houses, the equation to be used is normally eq. (4.b), when thefundamental period is calculated by eq. (2).
( )
).4(
).4(
).4(
).4(11
00
00
0
0
21
1
dTTjosT
T
T
TSaS
cTTTjosT
TSaS
bTTTjosSaS
aTTjosT
TSaS
d
k
d
k
d
cge
dc
k
cge
cbge
bb
ge
<���
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�=
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����
�=
<<=
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�
�−+=
ηβ
ηβ
ηβ
ηβ
Where ag : Peak ground acceleration valueT0 : Fundamental period of the buildingTb, Tc, Td : time parametersS: soil parameterη: damping correction factor, with reference value 1.0 (5% damping)
( 7.0)2/(7 ≥+= ξη , where ξ damping coeff. ≈5%)
k1 and k2 exponent parametersDepending on the subsoil class, the parameters for the elastic response spectrum are given asin Table 3.2.Table 3.2 Elastic response spectrum parameters for the different subsoil classes (EC8).Subsoilclass
S β k1 k2 Tb
[s]Tc
[s]Td
[s]A 1.0 2.5 1 2 0.10 0.40 3.00B 1.0 2.5 1 2 0.15 0.60 3.00C 0.9 2.5 1 2 0.20 0.80 3.00
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Fig 3.1 Elastic response spectrum for subsoil class C when ag is 0.25 g
Design spectrumUsually the capacity of structures to resist seismic actions is higher than that based on theelastic response spectrum. For this reason, the base shear value eq. (1.a) is divided by q, thebehaviour 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 iscalled the design spectrum.The design spectrum value needed in the base shear eq.(1.b) is evaluated from the equationsbelow. For timber structures eq.(5.b) is most relevant.
).5()2.0(
).5()2.0(
).5(
).5(11
00
00
0
0
211
1
dTTjosT
T
T
T
qSS
cTTTjosT
T
qSS
bTTTjosq
SS
aTTjosqT
TSS
d
k
d
k
d
cd
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cd
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d
d
<≥���
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�−+=
αβα
αβα
βα
βα
In eq.(5) the term α is defined as the peak ground acceleration divided by the gravityacceleration g (α = ag/g). This of course does not have units.
Table 3.3 Design spectrum parameters (otherwise as in Table 3.2).Subsoilclass
kd1 kd2
A 2/3 5/3B 2/3 5/3C 2/3 5/3
The existence of a behaviour factor, q, makes it possible to apply an elastic design method forseismic actions. This term takes into account the plastic properties of the structure. It definesthe relationship between an acceleration causing collapse and an acceleration causing the
0 1 2 3 40
0.2
0.4
0.60.563
0
S E T
40 T
Se =ag S η β
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strain to enter a plastic region from an elastic region. The ability of the structure to bearplastic 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, qis 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 structureswith
rigid connections at baseq = 1.5 Structures having low capacity of energy dissipation:Class B Structures with few mechanical connections, cantilever structures with
semi-rigidly fixed base connectionsq = 2.0 Structures having medium capacity of energy dissipation:Class C Frames, and beam-column structures with semi-rigid joints
Log housesGypsum 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 twomain directions, each one can be treated separately and a different behaviour factor for thetwo directions may be applied. An example of this kind of building could be a three-hingedarch hall, which is braced with a truss (using mechanical connections) in the directionperpendicular to the arches. The behaviour factor would be q = 1 in the direction of the archand q = 2 in the perpendicular direction.3.6 Vertical loads in seismic designEquations (1) and (3) contain the mass of the structure. This mass is calculated from thegravity loads (dead load, live load, snow load) as follows. The effect of the seismic event onthe building is computed considering the masses in the different storeys of the house:
� �+= kiEIkj QGW ψ (6)
Gkj is the characteristic dead load andψEIQki is the probable live load during an earthquake.
iEI 2ϕψψ = (7)
ψ2i is the long-term value 0.3 for live loads,or 0.2 for snow loads (EC1 and EC5),
ϕ is 0.5 for all storeys except the top storey for which it is 1.0(no correlation between storey loads). (EC8)
ϕ is 1.0 for storage loads (EC8)3.7 Combination of actionsThe design loads needed in seismic design consist of dead loads and seismic loads. Windloads do not need to be considered.
� �++= kiibkjd QFGE 2ψγ (8)
γ is the importance factor (γI = 1.4 hospitals, fire stations, power stations; γII = 1.2 schools,cultural buildings; γIII = 1.0 residential and commercial buildings; γIV = 0.8 agriculturalbuildings).Gkj and Qki are the characteristic values of the dead and live load.ψ2i 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 usuallythe most important loading direction. During a seismic event, however, the ground vibrates inall directions and for certain structures such as structures with long cantilevers, the verticalloading components may also be of importance. The vertical loading components may bedetermined by multiplying the lateral loads by the following factors:
0.7 when the fundamental period of the structure T0 < 0.15 s0.5 when the fundamental period of the structure T0 > 0.50 sfor values where 0.15 s < T0 < 0.5 the factor may be interpolated.
3.8 Calculation of the Seismic load, summaryTimber 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-modalanalysis is required, the simplified analysis may then be used as a first approximation. In anycase, according to EC8 this method is, as previously stated, usually sufficient for timberhouses. 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 ison 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 groundacceleration as normalised by g (for example ag = 0.25[g] and not 2.45 [m/s2]), and theseismic 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 outaccording to EC5. In the next chapter, the main parts of structural design and dimensioning ofthe structures is explained.
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4. Seismic design4.1 IntroductionIn this report, the seismic design is considered for residential or office buildings with loadbearing 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 suchas wind loads. The lateral loads are transferred to the foundations via the floor diaphragmsand the shear walls. The difference compared to wind loads is that the wind action is apressure on the external wall whereas with seismic action the loads are connected with themasses (either dead or live) of the building and mainly directed to the floors. The seismicaction is cyclic and loading directions change constantly and simultaneously in horizontal andvertical directions. Therefore, the structures should be firmly tied to each other and the floorsor beams should not be able to slide from their supports. The platform frame is very effectivein 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 lowerfloor.Also fire safety should be considered in seismic design, as fires may occur during a seismicevent due to the cutting of electric wires or gas pipes. However, EC8 does not giveinstructions 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 loadsfrom the different parts of the building are directed to the foundations. The centre of thestiffness inertia and the centre of mass should coincide as closely as possible to avoid atorsion effect on the building. This will depend on the layout of the building and on theplacement of the shear walls. The building layout should be regular in elevation and in planregarding mass and rigidity distributions. The rules of EC8 for regularity were given inSection 3.3. The lateral stability (or bracing) design of the building concerns the design of thefloor diaphragms, the shear walls and the anchorage to the foundations. These will beconsidered in the following chapters.4.2 Ultimate limit stateThe safety of the structure for seismic events can be considered sufficient if the followingconditions of resistance, ductility and equilibrium apply.ResistanceThe following condition should apply for all structures and connections
{ } }{,, 2M
kdkiibkjd
fRRQFGfE
γψγ =≤= � � (9)
The design resistance of the structures is determined so that the material strength correspondsto the instantaneous load duration class and the material safety factor is γM = 1.3, when thestructure dissipates energy (or q > 1) and γM = 1.0 when the structure does not dissipateenergy (q = 1). So in most cases the material safety factor is 1.3 as in ordinary structuraldesign even though a seismic event could be considered an accidental load. The importancefactor, γ, was described in eq. (8), for residential buildings this has a value of 1.0.
DuctilityThe structures and the building as a whole should be adequately ductile. The ductility shouldbe considered in the design where it is taken into account as a load reducing factor, thebehaviour factor q was explained previously.EquilibriumThe building should be stable during a seismic event. The seismic load combinations shouldbe 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. Naturallythe anchorage forces decrease at higher storey levels.The anchorage for overturning is usually resolved either with bolted hold-downs or withnailed metal straps. Also a shear panel crossing the storey level may be applied as ananchorage from store to storey, in this case the shear panel is in the outer edge of the wall asotherwise the floor would be in its way.The anchorage for sliding is usually resolved with bolts or wedge anchors in the bottom plateof the shear wall in the lowest storey. In the upper storeys, the nailing of the wall bottomplates should normally be strong enough to withstand the anchorage forces.4.3 Serviceability limit stateIn order to avoid excessive damage, EC8 gives rules for the inter-storey drift during a seismicevent. The design earthquake may be one, which is more likely (lower return period), and thepeak ground acceleration is lower than for the ultimate limit state.The inter-storey drift is limited to the following values:
dr/ν ≤ 0.004 h , buildings having non-structural elements of brittleor materials attached to the structure
≤ 0.006 h , buildings having non-structural elements fixed in away as not to interfere with structural deformations
Where dr is the inter-storey drifth is the storey heightν reduction factor having values between
2.0- 2.5. This takes into account the lowerreturn
period of the seismic event during theserviceability limit state.
4.4 Special rules for timber structuresFor the different building materials, in addition to normal structural design, EC8 gives someadditional rules and restrictions on the design of structures, which are applied for seismicactions. 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 thisvalue depending on the structure (Section 3.5):
• Type A, q = 1.0 : three hinged arches, cantilevered structures, shear wallswithout 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 decreasedby 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 thebehaviour factor values described above, certain restrictions apply to the mechanicalfasteners:For wood-to-wood and metal-to-wood joints, the parts must be at least 8 d (d: connectordiameter) 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 fordifferent 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 aplatform frame building, the most appropriate manner to provide the bracing is by using shearwalls. 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 mosteffective and economic manner to provide the lateral stability for a residential house. Thefollowing text is based on references EC5 and STEP B13.
A schematic diagram of the functioning of structural panels against lateral loads is shown inFig. 4.1, where a simple 'box-like' building is loaded laterally. The floor diaphragm is assumedto behave as a high beam and this is loaded by a seismic action depending on the floor mass andon the ground acceleration. The floor diaphragm is supported at the ends by shear walls, whichin turn transfer the load to the foundations. Such structural configurations may be side by sideor one on top of the other as in a multi-storey house. In multi-storey houses the lateral loadscumulate to the lower storeys.
Direction of groundacceleration
Fig. 4.1 A schematic diagram of the path of lateral forces in a simple building, where the floordiaphragm 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 thatan intact path for the lateral forces does exist. This includes the connection of the boardmaterials to the timber frame (floors and walls), the connection between the floors andsupporting shear walls and between the shear walls and the foundations. The anchorage of thebuilding as well as the connection details will be described later in this report.
18
4.6 Floor diaphragms
The floors may be used to transfer lateral loads to the shear walls. In timber houses, the floorsare usually constructed with timber joists, which are connected to a structural panel of somekind. 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, wherethe floor also performs as a working plane during construction, the moisture content of the paneland weather resistance should be considered. During construction the floor may be exposed torain and panels meant for interior use should be avoided. Exterior plywood (EN 636-3) is theonly 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 bywalls that are lined in the direction of the lateral force. According to EC5, this applies when thefloor span (distance between shear walls) is longer than two and shorter than six times theheight of the floor, (2b < l < 6b). The static behaviour is simplified so that the panellingperforms as the web of the I-beam taking on all of the shear forces and the flanges take thecompressive and tensile forces at the floor top and bottom edges, chords, caused by the bendingmoment.
l
b
19
Tensile force Ft
b
l
Shear force νd
Compressive force Fc
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 thebottom or top plate of the wall frame or the end joist of the floor which runs in the direction ofthe wall and perpendicular to the main floor joists. The bottom plate is usually composed of twotimber sections on top of each other, having overlapped and staggered end joints and these arenailed together and to the floor. The chord takes care of the bending moment and these aredesigned, in a simple single span case, for the compression and tension forces as follows:
Ft,d = Fc,d = Mmax, d / b (10)
WhereMmax 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 andbc 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 andb 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 andvd is the calculated shear per length.
20
According to EC5 the fastener spacing should be, at most, 150 mm along the edges and 300 mmelsewhere. The fastener design capacity is thus the dominating property concerning the shearcapacity of the floor. The fastener design capacity between the sheathing and the floor-supporting member is calculated from the EC5 eq. 8.3 as below:
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+
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−
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+
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+
=
dfM
dtf
Mdtf
dtf
Mdtf
t
t
t
t
t
t
t
tdtf
dtf
dtf
R
plyhd
nailyd
plyhd
nailyd
plyhd
plyhd
nailyd
plyhd
plyhd
solidhd
plyhd
d
212
)21(4)1(2
21
)2(4)1(2
2
1121
min
22
22
21
1
1
2
2
1
23
2
1
2
1
221
2
1
ββ
βββ
βββ
βββ
βββ
βββββ
(14)
Where fplyhd and fsolidhd are the design embedment strength values of thesheathing panel and wood,Mnail
yd 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
the fastener into the wood,d is the diameter of the fastener andβ is the ratio between the embedment strength values of the sheathing
panel and wood(In the case of a shear wall, the design capacity value Rd may be
increasedby a factor of 1.2)
For simply supported diaphragms, as in Fig. 4.2, the shear force is transferred to the shear wallsat the edges. The shear force is assumed to be distributed evenly along the edge, in case theshear wall extends all through the floor depth. To ensure the path of forces from the floor to thesupporting shear walls, the diaphragm supports, acting as the chords, are connected to the topplate 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 aschords acting both in compression and in tension and also for shear transfer in case the forcesare transferred to a shear wall below.
Using this simple static floor model, the sheathing performs as a single membrane. Theindividual panels should then be adequately attached to the supporting structure. The bestperformance is achieved when the panels are staggered rather than being on the same line. Asstaggering is not possible in two directions, this should be done against the principal loadingdirection (in the direction of the shorter floor dimension) as in Fig. 4.2.
21
In case the floor has a large opening, it is important to ensure that it is possible to transfer theloads around the opening. The compression and tension forces should be transferred with joistsor metal straps along the sides. The fastening of the sheathing to the supporting joists ensuresthe 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, suchas wind loads, according to the procedures described in EC5 with certain exceptions. Thefollowing parts are different than given in EC5:
• For floor diaphragms the increase in the fastener design capacity, by a factor of 1.2, may notbe 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, suchas 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 floorjoists should not change, for example over the supporting shear walls.
Fig. 4.3. Supporting and fastener spacing at the edges of sheathing panels according toEC8
(EC8).
4.7 Shear walls
22
In a wooden house, with a load-bearing wall frame, the lateral stability of the house is mosteffectively provided by the use of shear walls with panel sheathing. Usually wooden load-bearing walls consist of vertical struts, equally spaced, which are connected to top and bottomplates. To this frame, a sheathing panel is attached by nails or screws, on one or both sides ofthe frame. From a structural point of view, a shear wall may be regarded as a cantilever where avertical load is located at the top plate. The sheathing transfers this vertical load to thefoundations. 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 boardsmay also be used. According to EC5, the shear capacity of the shear wall is based on the shearcapacity of the fasteners as according to a lower bound plastic model. It is good practice to usethe walls between attached dwellings and the walls next to corridors as shear walls; these maybe sheathed on both sides and contain few interruptions from doors or windows.
H
x
F
F
H
t
NN
z
cTop plate
wall strut
Sheathing panel
Bottom plate(or sill plate)
B
yy
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 ofmetal connectors. These connections may be assumed to perform mechanically as a hinge. Forthis 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 displacementbetween the wooden frame and the panel is highest. The vertical struts are then designed onlyfor 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 framewith the usual strut spacing of K600 mm, the capacity to resist lateral loads is dependent on thefastener strength. Only in special cases, such as when using thin panels or having wide strutspacing, might the shear capacity of the panel or the shear buckling of the panel becomedecisive.
23
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, theshear capacity may be calculated from (EC5 9.18):
i
idfdiv
cs
bF=F
,, (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 ≥ b0ci= bi / b0 if bi < b0b0 = 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 200mm in the case of screws along the edges of the panel. In the central part of the panel, thespacing may be up to 300 mm, but never more than twice the spacing along the edges. Thefasteners in the centre do not affect the shear capacity, except in reinforcing the panel againstshear buckling. According to EC5 the shear buckling analysis does not need to be carried out ifthe following condition holds:
bnet/t < 100 (16)
Where bnet is the free distance between struts andt is the panel thickness.
So if the struts are spaced at K600, the buckling analysis need not be done because t > 5.95mm.
The total shear capacity of the shear wall may be calculated as the sum of the shear capacities ofthe panels (EC5 9.19):
�i
divdv F=F ,, (17)
It is assumed here that the shear force is equally distributed along the fasteners connecting thepanel to the wooden frame.
The tension and compression struts at the sides of the shear wall have to be designed for theforces 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 sumof the element capacities (eq. 16), even in the case where the panel material or fastener type isdifferent. If a wall has the same panel sheathing and fasteners on both sides, the capacities of thetwo sheathings may be added together. If different panel materials are used, EC5 allows that75% of the weaker panel capacity may be used, if the fastener strength-deformation curves aresimilar for the two panels, then only 50% of the weaker panel capacity may be utilised. If the
24
wall contains a window, door or other opening, the shear capacities of these sections are omittedin the addition.
The end struts of shear walls, as well as the bottom plate, should be anchored to the foundationsto resist uplift forces (upwards) and sliding forces (horizontal). In a multi-storey house theseanchoring forces should be considered from storey to storey as these accumulate towards thebottom storeys.
Inner walls
The distribution of lateral loads to several shear walls depends on the rigidity of the floor andthe rigidity of the shear wall. A rigid floor with flexible shear walls is one extreme case and aflexible floor with rigid shear walls is another extreme case. In the first case, the lateral force isdistributed to the shear walls depending on their relative levels of rigidity. In a case where thefloor is supported by three shear walls of equal rigidity, each of these walls carries a third of thelateral load. However, if the inner wall is not located at the centre, a torsion component is alsodeveloped. In the other extreme case, the floor may be regarded as a continuous multi-spanbeam over the supporting shear walls or two non-continuous single-span beams extendingbetween two shear walls.
To be on the safe side, it may be good practice to design the outer shear walls assuming asingle floor span supporting conditions and the inner shear walls assuming continuity of thefloor. The assumption of a perfectly rigid floor should only be used if the floor plan dimensionratio 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 seismicdesign of timber buildings braced with shear walls. Calculated cases with several differentplywood and LVL sheathing panels and different fasteners are given. These values are basedon eq. 14 and on eq. 16. These design values were calculated for an instantaneous loadduration and using a normal material safety factor, as EC8 assumes an energy dissipativestructure.
25
Table 4.1 Shear design capacity with different panels and fasteners [KN/m]in seismic design, note the following:1) kmod = 1.1, γM = 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 thespacing may be up to double ( and < 300 mm).
Spruce plywood 9 [mm] nail (helically threaded) screw
25x45 28x60 d = 3.5 d = 4.5
Fastener spacing [mm]
K150 2.93 3.44 4.81 6.42
K100 4.39 5.16 7.22 9.63
K70 6.28 7.38 10.32 13.76
K50 8.79 10.33 14.44 19.27
Spruce plywood 12 [mm]
25x45 28x60 d = 3.5 d = 4.5
Fastener spacing [mm]
K150 3.24 3.74 5.06 6.60
K100 4.86 5.61 7.59 9.90
K70 6.95 8.01 10.84 14.15
K50 9.72 11.22 15.18 19.81
Spruce plywood 15 [mm]
25x45 28x60 d = 3.5 d = 4.5
Fastener spacing [mm]
K150 3.63 4.13 5.43 6.93
K100 5.44 6.19 8.14 10.39
K70 7.78 8.85 11.63 14.84
K50 10.89 12.38 16.28 20.78
LVL 21 [mm]
25x45 28x60 d = 3.5 d = 4.5
Fastener spacing [mm]
K150 3.73 4.49 5.90 7.33
K100 5.59 6.74 8.85 11.00
K70 7.98 9.63 12.65 15.71
K50 11.18 13.48 17.71 21.99
LVL 27 [mm]
25x45 28x60 d = 3.5 d = 4.5
Fastener spacing [mm]
K150 3.73 4.49 6.49 8.33
K100 5.59 6.74 9.74 12.50
K70 7.98 9.63 13.91 17.85
K50 11.18 13.48 19.48 25.00
26
Shear capacity of different sheathing panels in seismic design
0
2
4
6
8
10
12
1 2 3 4 5 6
Shearcapacity[KN/m] 9 mm spruce
Gypsum board(Gyproc GN13)
Fasteners screw 3.5 (3.9x29 Gyprocille) K100 mm
21 mm Kerto-Q LVL
27 mm Kerto-Q LVL
12 mm spruce plywood15 mm spruce plywood
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 gypsumboard (13 mm) in seismic design.
Shear capacity per shear wall length KN/m Fastener spacing
K150 K100 K70 K50
Spruce plywoodpanel 9 mm
q = 3.0
nail 25x45 2.93 4.39 6.28 8.79
28x60 3.44 5.16 7.38 10.33
screw 3.5 4.81 7.22 10.32 14.44
screw 4.5 6.42 9.63 13.76 19.27
Gypsum board, GN13 and GEK13
q = 2.0
T 29 screw 3.9x29 GN13 2.51 3.76 5.37 7.52
TR 29 screw 4.2x29 GEK13 4.07 6.11 8.73 12.22
1.65 2.48 3.55 4.96Reduced by q=2/3(takes into account thedifferent behaviour factors)
2.69 4.03 5.76 8.07
T 29 screw 3.9x29 GN13 34% (compared to screw 3.5 case)Capacity of gypsumboards in relation toplywood panel of 9 mm
[%]
TR 29 screw 4.2x29 GEK13 42% (compared to screw 4.5 case)
27
4.8 The anchorage of the building
In order to transfer the lateral loads to the foundations, the building has to be anchored to thestorey below and then on to the foundations. Anchoring is normally required at the ends ofshear walls to account for the uplift forces (due to overturning when the building’s ownweight does not compensate for the effects of the lateral load) and at the bottom plate toaccount for the sliding (slip from base shear), see Fig. 4.6. The uplift and sliding forces areanchored independently of each other with special connectors.
Fig. 4.6 The two anchoring cases: sliding caused by base shear and uplift caused byoverturning
( 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 theanchoring of a multi-storey house. The basic principle is as follows.
28
- To withstand overturning, both sides of a shear wall are anchored to the storeys below and tothe foundations to account for uplift forces. The connection is fastened to the frame strut andthis transfers the tensile forces downward to the struts below or to the foundations. Theconnection cannot be attached only to the panelling or only to the frame plate. The fastenermay 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 load-bearing 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 (sillplate) to the foundations. The spacing of these bolts will result from the calculations. Forupper storeys, the nailing of the bottom plate to the flooring or to the wall section below isusually sufficient to account for the shear forces at these upper levels.
The shear force acting on a single fastener is:
l
sF=F
dv,
(19)
Where Fv,d is the shear force (lateral load) acting on ashear wall
s is the spacing andl is the length of the shear wall
Fig. 4.8 The anchoring of uplift forces is handled with metal straps or hold-down bolts (SECBC1997).
29
Fig. 4.9 Anchoring details in a multi-storey house case (SECBC 1997)
30
Fig. 4.10 Anchoring details where a metal strap is used on top of panelling (Secbc 1997)
31
5. Connections of timber structures under seismic actions
5.1 Introduction
The behaviour of timber structures during seismic events is fully dependent on the behaviourof the joints under cyclic loading. The detailing of joints is thus very important in seismicdesign. The source of this chapter is mainly the STEP lectures dealing with the design ofconnections for seismic actions.
Under cyclic actions, wood usually performs linearly and elastically. Failures are brittle innature and these are caused by natural defects in wood, such as knots. Wood in itself has alow capability for dissipating energy, except for compression loading perpendicular to thegrain. Glued joints perform linearly and elastically. These do not involve plastic deformationsand they do not dissipate energy. For this reason, timber structures with glued joints as well asstructures that have hinges, should be classified as structures that do not dissipate energy andpossess no plastic strains; therefore, the behaviour factor for these structures is q=1.0 (classA).
The plasticity and energy dissipation property can be introduced to the connections, if theconnections are "semi-rigid" as most mechanical connections used for timber structures are,instead of perfectly rigid joints as, for example, glued joints. Well-designed mechanicalconnections perform usually in a semi-rigid manner.
If the forces caused by static loads are greater than those caused by seismic events (whenq=1), there is no necessity to carry out any ductility analysis of the connections. This might bethe case for large structures under high snow loads. In this case, the normal static analysis ofthe 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 load-reducing factor. In this case, there is a need to demonstrate that the connections aresufficiently plastic and energy dissipating to cope with the q value initially assumed. Thismay be demonstrated by experimentation or, in the case of those connection types where q isknown , 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 plasticstrains may develop, if the fastener spacing and the end distances are according to the designrules. The force-deformation curve is initially steep under ramp loading (Fig. 5.1a, I). Afterthe fastener or the wood embedment stress reaches its elastic limit, the force-deformationcurve becomes non-linear and less steep reaching a peak, where the maximum connectioncapacity 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 thefastener strength has been reached.
The determination of ductility is presented in Fig. 5.1. Two cases are given, one composed oftwo linear curves and the other of one fully non-linear curve.
32
Fig 5.1 Definition of ductility, examples of different force-deformation curves. (a) Two linearcurves with different slopes (b) a non-linear curve with a constantly changing slope. Ds is theductility, νu is the deformation at failure and ν 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 seismicactions, the loading is more complex and the loading reverses in direction within a fewseconds. Figure 5.2 shows a nail being exposed to a regular cyclic loading. During the firstloading, the wood fibres around the nail are compressed and a cavity is formed at the edges ofthe jointed material. This cavity leaves the nail without support for the subsequent loadingcycles, if the deformations are within previous limits. Residual strength is given solely by thenail 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 theparent 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 arelow or high. These differ from the wide loops typical in mild steel.
33
Fig 5.3 Typical force-deformation loops for different load levels of dowelled joints undercyclic loading (STEP C17).
Figure 5.4a presents the shape of a well-designed dowelled connection, where the energy isdissipated through the embedment of wood and through the plasticity of the connection. If thefastener is so strong and rigid that it does not bend, the energy dissipation is solely given bythe 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 someexceptions. As an example, there are several types of steel plates with punched teeth, wherethe failure may occur as a pull-out of the teeth or brittle failure of the steel plate. Anotherexample is a shear wall made of a brittle panel sheathing, in which case a cyclic loading mightcause a brittle failure of the wall.
In order to have harmonised procedures to develop connections for seismic design, CEN ispreparing a standard, where a simple method of testing connections is given by a quasi-staticmethod. In the following, the test procedure is briefly described. Figure 5.5 shows a three-cycle load loading pattern, where the amplitudes are multiples of the yield slip ν y .
34
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 loadcycles, 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 measuredas the shaded Ed area shown in Fig. 5.7. The ratio between the dissipated energy and thepotential energy Ep is called the 'hysteresis equivalent viscous damping ratio' νeq. The amountof dissipated energy increases as the amplitude increases, but νeq remains more or lessconstant. For well-designed connections between plywood and the timber frame in shear wallsthe value of νeq is about 8-10%.
Fig 5.7 Dissipation of energy in a loading cycle. (STEP C17)
35
In the elastic zone, the hysteresis damping is, in principle, zero, Fig. 5.3a. However, in theelastic zone some energy may also be dissipated. In small amplitude dynamic vibrations, lessthan 1% viscous damping may be measured if secondary structures are not connected. Ifsecondary structures are connected, due to friction in connections and compressionperpendicular to the grain, values exceeding 4% are easily obtained. This is often the case forredundant building elements and contact points in buildings. For these reasons, a dampingratio 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 tohigh 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 sideand spacing distances of the fasteners and these should be obeyed. They are given to ensurethat the connection failure is not brittle.
Splitting may also be prevented by using reinforcing materials in the connection areas, whichgive higher tension strength in the direction perpendicular to the grain of the wood. Suchreinforcing materials are, for example, plywood panels and densified veneers. In addition topreventing the wood from splitting, the reinforcement ensures the yielding of the fastenersand thus enhancing connection ductility.
To ensure the dissipation of energy, it is possible to take advantage of the slenderness of thefastener. The slenderness is defined as the ratio between the wood member thickness and thefastener diameter. Fasteners with high slenderness ratios dissipate more energy since theplastic yield points are, in this case, always formed in the fastener. Fasteners with lowslenderness 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 thefastener diameter.
To avoid an unacceptable strength loss in cyclic loading, three general principles should befollowed. Details should be designed so that the elements cannot easily pull out, brittlematerial failures should be avoided and materials should be used which retain theirmechanical 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 performplastically in a mechanical connection when designed appropriately. The nail length should beincreased if there is a risk of pull-out. Smooth nails are not recommended for this reason. Ifthe slenderness ratio of the nail is higher than 8, good ductility may be expected.
36
Fig. 5.8 Typical performance of a nailed connection under cyclic loading (nail slenderness8.5).
(STEP C17)
A ductile connection between plywood and wood may be ensured if the slenderness of thenails is at least 4d. Experiments show that nailed shear walls with plywood sheathing possesshigh 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, theexperimental set-up, the loading scheme and the test results of the lateral displacement of thebuilding top (Yasumura et al., 1988). The building is braced with shear walls with 9-mmplywood panels on the external walls and 12-mm gypsum boards on the internal walls. Theresult shows that these shear walls dissipate energy well and that the building as a whole has ahigh ability to deform without losing strength.
37
Fig. 5.9 Full-scale seismic experiment of a three-storey tshear walls (Yasumura et al., 1988).
Dowels
Slender dowels in connections may yield both from the stedissipate energy well. If the dowel length in the wood isperforms in a ductile manner. If the connection is made ospacing complies with EC5, the plastic behaviour is only depembedment of the wood. Since the energy dissipation is lorecommended to evaluate the ductility property of such a con
Bolts
Bolted connections have oversized holes due to the productin an unequal distribution of forces under loading. This mayfasteners and thus cause local splitting of the wood atredistribution of forces within the connection. For this reasozones should be precisely constructed and the bolts shoulThick bolts (d > 16 mm) are usually not able to deform and
Test set-up
Ld ]
Load
ateraleformation [mm
imber house braced with nailed
el and from the wood and thesehigher than 8d, the connectionf thick dowels and the fastenerendent on the performance of thew in this case, tests are usuallynection.
ion technique and this may resultcause the overstressing of certainthese fasteners and prevent then, bolted connections for seismicd have a high slenderness ratio.do not dissipate energy. For this
38
reason these should only be used in combination with other fastener types such as toothedring connectors. (EC8 recommends the diameter of dowel type fasteners to be less than 16mm).
Split ring and shear plate connectors
These are not recommended for use in energy dissipating parts of structures as they have lowplasticity values.
Toothed plate connectors
With good design, toothed plate connectors may have good plastic performance. Spacing andend 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 plasticbehaviour, it is recommended that prototype tests should be carried out if these connectionsare intended as energy dissipating connections. This is to avoid potential failure such as brittlemetal plate failure and nail pull-out failure.
In Helsinki University of Technology, TKK (1995), experiments were carried out to testnailplates of the 'Träforband T150' type to determine their performance against seismicactions. The tests were done on cyclic loading using tension-compression, shear and bendingloading modes. The nail length was 14.3 mm. The conclusion of this study was that thesenailplates may be designed as energy dissipating connectors (class D, q=3), provided that theanchorage failure mode is dominant and that the anchorage strength is designed in accordancewith 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 thecyclic loading varies in time and it is different for different earthquakes and in most cases it isalso unknown.
It seems, however, that a cyclic load test, as previously described, is sufficient in order toestimate 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. Thereis 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 toreveal 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 estimatethe strength of the structure under a given earthquake. Another point to emphasise is that atrue earthquake loading scheme is random and irregular. There is a low number of cyclescausing 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 dowelsduring similar conditions to those of the El Centro earthquake. The moment-rotation resultsare based on numerical calculations. The earthquake was amplified by a factor of 1.5.
39
5.6 Requirements of Eurocode 8
In EC8, structures are classified according to their ductility and to their energy dissipativeproperty. In certain cases, it is recommended to design the structure to be sufficiently rigid tofulfil the serviceability criteria. For structures designed to dissipate energy, that is q > 1, thestrength of the wooden parts should be higher than the strength of the connections. Theconnections 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 bedemonstrated by tests following internationally recognised experimental procedures. The testshows that the connection is ductile and the properties are stable under a rather highdeformation or a stress level cyclic load. To ensure ductility, it is required that the ductilityunder a cyclic load is at least three times the q value. This multiplier is reduced to two forpanel structures.
Additionally, the connections should be able to deform plastically for at least three full cyclesat 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 normalprocedures in EC5.
40
6. Conclusion
Timber houses are usually regular, both in plan and in elevation. The seismic design may thenbe carried out using the simplified modal response spectrum analysis, which returns a singlebase shear value acting on the building. EC8 gives the rules on how this base shear iscalculated. The bracing of the building is designed in both principal directions against thisbase 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 ofthe wind loads in high seismic zones. Therefore, the lateral loads should be taken into accountearly 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 localauthorities.
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 donefollowing 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 todetermine these loads as well as the equations needed for the dimensioning of the structuresshould be implemented in a computer-based design program. The calculation routines arerather simple, but can be laborious, especially when the shear walls are not situatedsymmetrically in a building and torsion effects are produced.
Seismic design expertise should also be widely known in countries such as Finland, which donot have earthquakes, but which do have a timber house exporting industry. In this way, thelocal requirements for houses can be better fulfilled. The good seismic performance of timberbuildings should be used in the marketing aimed at seismic areas of the world. Also, localauthorities should be better informed on the performance of timber houses. Usually, in areasof high seismic activity, buildings are made of concrete or masonry and these are verydangerous if not properly designed for seismic actions.
41
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 Workshopon Seismic behaviour of Timber Structures. September 28-29 2000 Venice Italy.
Ceccotti, A., Karacabeyli, E. (1998) Seismic design considerations on the multi-storey wood-frame structures. Cost E5 workshop on constructional aspects of multi-storey timberbuildings. 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 inearthquakes. COST E5 Workshop on Seismic behaviour of Timber Structures. September 28-29 2000 Venice Italy.
RILEM TC 109 TSA (1994) Timber structures in seismic regions. RILEM State-of-the-ArtReport. Material and Structures 27: 157-184.
SECBC (1997) Updated seismic design of buildings. Structural Engineering Consultants ofBritish 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 TimberEngineering, Basis of design, material properties, structural components and joints. CentrumHout 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 tohorizontal load. In: International Timber Engineering Conference, Seattle, 1988: 262-275.
42
Material suppliers
Anchorage connectors
Simpson strong-tie connectorsBulldog-Simpson GMBHBoschstrasse 9D-28857 Syke, Germanytel. + 49 4242 95940fax + 49 4242 60778http://www.strongtie.com
MGA connectorsMGA11476 Kinston St.Maple Ridge B.C.V2X O45 Canadatel. + 1 604 465 0296fax. + 1 604 465 0297
43
43
PlywoodWISA - special plywoodsSchauman Wood OYPL 203 FIN-15141 Lahti, Finlandtel. 0204 15113fax. 0204 15112http://www.schaumanwood.fi/tuotteet/vanerit/index.html
Finnforest OyPL 50 FIN-02020 Metsätel. 010 4605fax. 01 4694863http://www.finnforest.fi/pages/products/plywood2.htm
In Turkey:WISA - special plywoodsSchauman Wood OYIstanbul Branch OfficeBagdat Cad. Yesilbahar Sk. No. 1/10TR-81060 Ciftehavuzlar/Istanbul, Turkeytel.+90(0)2163854610, 3860831fax.+90(0)2163856558.
44
44
Earthquake magnitude, M
To assess the magnitude of earthquakes, a scale to describe the energy released during anearthquake was developed by Richter in the 1930s. This is named the Richter scale and it isthe most common scale used today to describe earthquakes. The magnitude of an earthquakeon the Richter scale is determined by a so-called Wood-Anderson seismograph maximumamplitude, where M = log(a), and a is the maximum amplitude [µm] at a 100 km distancefrom the epicentre. The magnitude may also be assessed at other distances using specialconversion tables. The magnitude measures the amount of released energy and a unit increaseof magnitude signifies a 32-fold energy release. There exists a physical upper limit abovewhich 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 thismay not be used in the design. However, Housner in 1970 developed empirical relationshipsbetween 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 ofthe
most intense phase of the earthquake (Housner, 1970)
Magnitude on theRichter scale
Peak groundacceleration (% g)
Duration (s)
5.0 9 25.5 15 66.0 22 126.5 29 187.0 37 247.5 45 308.0 50 348.5 50 37
45
45
Example cases of seismic load calculation and design
Example 1, Seismic load for a small one-storey houseInput values:Building area 9.3 × 16.8 m2
Ground acceleration = 0.35 gSubsoil class CImportance factor γ= 1.0 (residence)
H
46
46
Dead load g: 0.8 KN/m2Snow load q: 1.8 KN/m2Building height H: 3.5 mSubsoil class CBuilding fundamental period, T0Shear walls as vertical diaphragms, q = 3.0
H 3.5 m( ) β 2.5 T b 0.2 s. T c 0.8 s. T d 3 s.
kd12
3kd2
5
3α 0.35 Relative acceleration α =a g
gS 0.9 q 3.0
T 0 0.05 H
3
4. s.
T 0 0.128 s=
S d T α S. 1T
T b
βq
1.. T T b<if
α S. βq
. T b T< T c<if
α S. βq
.T c
T
kd1
. T c T< T d<if
α S. βq
.T c
T d
kd1
.T d
T
kd2
. T d T<ifS d T 0 0.281=
0 1 2 3 40
0.1
0.2
0.3
0.4
S d T
T
Vertical load for seismic design W = Σ (G+ψEiQki) x building area
W 0.8 0.2 1.8.( ) 9.3. 16.8.
W 181.238= KNImportance factor = 1.0
Base shear force Fb W S d T 0.
Comparison to the wind force below
Qwind = 3.5 x 16.8 x 0.7 KN/m 2 = 41 KNFb 51.003= KN
47
47
Example 2, A four-storey timber house case, calculation of the seismic load and design ofsome details
Input values:Ground acceleration = 0.35 g,Subsoil class BFloor 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 γ= 1.0 (residence)
The seismic load is determined considering the vertical loads present in the different storeysof the building. This load is calculated using eq. 6:
� �+ kiEIkj QG ψ (6)
Gkj is the characteristic dead load andψEIQki is the probable live load during a seismic event.
Combination coefficient: iEI 2ϕψψ =
ψ2i is 0.3 (the quasi-permanent value of the live load (EC1 and EC5) ,ϕ 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 ψψψψ2i ϕϕϕϕ ψψψψEI Gkj + ψψψψEIQki
Roof 0.75 0.75
Storey 4 1.0 2.0 0.3 1 0.30 1.60
Storeys 2 and 3 1.0 2.0 0.3 0.5 0.15 1.30
Storey 1 Loads transferred directly to the foundations
Following the table above, the total vertical load is:
� �+ kiEIkj QG ψ = 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
48
48
Building height H: 12 mBuilding fundamental period T0
H 12 β 2.5 T b 0.15 s. T c 0.6 s. T d 3 s.
α 0.35kd1
2
3kd2
5
3S 1 q 3.0
T 0 0.05 H
3
4. s.
T 0 0.322 s=
S d T α S. 1T
T b
βq
1.. T T b<if
α S. βq
. T b T< T c<if
α S. βq
.T c
T
kd1
. T c T< T d<if
α S. βq
.T c
T d
kd1
.T d
T
kd2
. T d T<if
0 1 2 3 40
0.2
0.4
S d T
T
S d T 0 0.292=
Vertical load , W = Σ (G+ψEiQki) x building area
W 0.75 1.6 1.3 1.3( ) 288. KN
Base shear load
Fb W S d T 0. Importance factor = 1.0
Comparison to the wind load below
Qwind = 20 x 12 x 0.7 KN/m2 = 168 KNFb 415.8= KN
49
49
The base shear force is distributed in elevation according to eq. 3 :
�=
jii
iibi Wz
WzFF (3)
Fb is the base shear force
Table L2.2 The design shear forces in the different storeys
Storey,i
Height ofstorey fromground zi
[m]
The load oneach floor(Table L2.1)
Wi
[KN]
Fi , shear force in thestorey level
�=
jii
iibi Wz
WzFF
[KN]
Cumulative shethe shear wall
storey
=vF
[K
Roof 12 0.75×288 = 216 107 1
4 9 1.6×288 = 461 171 2
3 6 1.3×288 = 375 93 3
2 3 1.3×288 = 375 46 4
Σ ziWi = 10116 KNm ;Fb ≅ 416 KN
The shear force acting onthe shear walls of eachstorey
The force distributionaccording to eq. 3
Fb = F2+F3+F4+Froof
Fb = Froof+F4+F3+F2
Froof+F4+F3+F2
Froof+F4+F3
Froof+F4
Froof
2/3 x H
ar force acting ons at the differentlevels
�4
iiF
N]
07
78
71
16
50
50
The shear walls will be composed of 9-mm-thick plywood panels connected with threadednails 28×60 k70. In this case the shear wall capacity per length (from Table 4.1) is Fv,d = 7.38KN/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 themiddle of the panel at spacing k300.
A schematic diagram of the shear walls in the first storey of the building
8500
8500
Apartment A Corridor
7000 4000 7000
2500 2500 35003500
Apartment B
Apartment DApartment C
X
Y
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- internal walls 17 m × 4 – 4 × 1.2 (doors) = 63.2 m- external walls (3.5 m + 2.5 m + 2.5 m + 3.5 m) x 2 = 24 m
shear wall
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51
total 87.2 m ( >56 m ) OK
It is advantageous to use the walls between apartments and corridors as shear walls withpanelling on both sides of the wall. In this example, the shear walls are situated symmetricallyto avoid a torsion effect (for simplicity). In practice, gypsum boards could also be used as anadditional reinforcement for the shear walls. EC5 allows the use of two different panels inshear 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. Onlythe anchoring of one shear wall, the shortest shear wall of 2.5 m, is shown. The anchoringanalysis should be carried out on all of the storeys and all of the other shear walls in a similarmanner.
Below the vertical load is calculate. The dead load is advantageous so the partial safety factoris 1.0 . Wind and live loads are not included.
Vertical load:
wallgstoreystoreystoreyroofgHd gareaBuildingxggggp γγ ++++= −−− ][ 432
12)0.1830.174(5.00.1288]0.10.10.175.0[0.1 xxxxxxx +++++== 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 KNFrom this load, the portion affecting the 2.5-m long shear wall is approximately:• Fb,wall = 416 × 2.5/56.4 = 18.4 KN
�=
jii
iibi Wz
WzFF
Distribution of verticalload by eq. (9) :
H
2/3 x PHd,wallFb,wall
52
xxFA
seinäb
Hd 5.232
12, −=
Both sides of the shear
The anchorage is made90-degree angle with athe foundations.
First let us analyse thethicknesst1 = 5 mm and the pene
5 5075
d mm= 10
d mm= 12
The characteristic emb
01.01(082.0 df solidhk −=
The characteristic tens
The yield moment of t
dfM ukscrew
yk
.06
8.0 3
==
The characteristic shea
m Anchoring for uplift force, AHd
2.552
KNxP seinäHd
2,4225.1,
=
wall are anchored for an uplift force of 42.2 KN.
of 10 pieces of lag screws of size 10×55 and a metal plate folded to across-section size of 80×5 mm2 and a bolt of size M12 connected to
connection of the anchorage to the wooden frame. The metal plate is of
tration of the screw into the wood is t2 = 50 mm .
20 40 20
70
70
70
20
755
70
edment strength of wood is solidhkf (EC5):.
23 /8.25/350)1001.01(082.0) mmNmkgxmmxxsolidk =−=ρ
ion strength of steel is 2/500 mmNfuk =
he lag screw 10x55 is screwykM (EC5):
NmmmmxmmNx
666676
)10(/5008 32
=
r strength of the screw 10x55 is screwvkF (EC5).
53
53
��
���
==
===
NxxxdfM
NxxxdtfF
solidhk
screwyk
solidhkscrew
vk5869108.256666722
516610508.254.04.0min
2
NF screwvk 5166=�
For the service class 1 and load duration class "instantaneous" the design shear strength of thescrew is:
NN
xF
kFM
screwvkscrew
vd 43713.1
51661.1mod ===
γ
The load acting on the screw is Fvscrew :
screwvd
Hdscrewv FN
n
AF <=== 4220
1042200
, OK
Under service class 1 and load duration class "instantaneous", the design strength of the metalplate and bolt is:
22
1 /5.4541.1/500
mmNmmNf
ffM
ukhdud ====
γThe design tension capacity of the plate 5x80 is F
td
plate :
Hdudplatetd ANmmxmmxmmNAfF <=== 181800805/5.454 2 , OK
The design tension capacity of the bolt M12 is Ftd
bar :
Hdudbartd ANxxAfF <=== 5140065.454 2π , OK
The tension force acting on the wooden frame strut (T24)
2mod
22
/8.113.1
141.1/4.8
100502.42
mmNftk
kmmNmmx
KN ==<=γ
OK
Anchoring the building against sliding
Next, the anchorage calculation against sliding is carried out. The vertical loads are notnecessary in this case as the effects of friction cannot be considered.
54
54
In the first storey, the building had a total of 56.4 m (weakest lateral direction) of shear wallsand the base shear force is FB=416 KN. Therefore, the anchoring force against sliding is asfollows:
mKNFb
AVd /4.74.56
==
Bolts of size M10 × 120 are used, with a design shear capacity of Fvd= 9.4 KN. Therefore, thebolt spacing in the bottom plate (sill plate) is as follows:
mA
Fbs
Vd
3.1==
The shear walls are anchored for sliding in the first storey with bolts connected to thefoundation of type M10 × 120 and with a spacing of, let’s say, k1000.
Vertical section
55
55
Bolts M10*120 k1000
Shear wall edges anchored by a bolt M12
Horizontal section
bolt M12Wall openingScrews 10 x 55 10 piecesmetal plate
Bolts M10x120 k1000
Shear wall length2500 mm
Anchorage for uplift forces
Anchorage for sliding
Plywood panel sheathing 9 mm
56
56
A summary of the procedure to evaluate the seismic load according to Eurocode 8The seismic design of a building starts with an evaluation of the regularity of the building inboth layout and elevation compared with the requirements mentioned in section 3.3 (EC8 part1-2, 2.2 Structural regularity). Generally regularity increases the seismic resistance of thebuilding. 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 conditionsand 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 orparameters different from the ones given in EC8, which are so-called boxed values. Thevalues given in this report are the ones recommended by EC8. Such information is given inthe national application documents.Base shear forceThe base shear force acts in both principal directions of the building.
Fb = Se(T0) W/q = Sd(T0) W (1.a, b) (EC8 part 1-2 eq. 3.3)
Where T0 is the fundamental period of the buildingSe is the ordinate of the elastic response spectrumSd is the ordinate of the design response spectrumW is the vertical loadq is the behaviour factor
Fundamental periodTo estimate the fundamental period, T0, of the building, EC8 has a simple procedure:
T0 = 0.05 H0.75 (2) (EC8 part 1-2 eq. C1)Where the building height is in metres and the time in seconds.
Distribution of the base shear force in elevationIf the floor loads are equal in the different storeys, the base shear force is distributed in atriangular manner so that higher forces are higher up. This is given by the equation:
�=
j ii
iibi Wz
WzFF (3) (EC8 part 1-2 eq. 3.5)
Where Fi is the lateral load in storey iFb is the base shear forcezi is the distance of the floor from the groundWi is the vertical load on the floor
Design spectrum
).5()2.0(
).5()2.0(
).5(
).5(11
00
00
0
0
211
1
dTTjosT
T
T
T
qSS
cTTTjosT
T
qSS
bTTTjosq
SS
aTTjosqT
TSS
d
k
d
k
d
cd
dc
k
cd
cbd
bb
d
d
d
<≥���
����
����
����
�=
<<≥���
����
�=
<<=
<��
�
����
����
�−+=
αβα
αβα
βα
βα
(EC8 part 1-1 eq. 4.7-
4.10)
57
57
Where α = ag/g , ag is the peak ground acceleration valueT0 : is the fundamental period of the buildingTb, Tc, Td : are time parametersS: soil parameterkd1 = 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)
Subsoil class S β Tb [s] Tc [s] Td [s]A 1.0 2.5 0.10 0.40 3.00B 1.0 2.5 0.15 0.60 3.00C 0.9 2.5 0.20 0.80 3.00
Fig L3.1 An example of an elastic design spectrum, subsoil class C and ag = 0.25g
EC8 gives the behaviour factor q values for different structural types as below:(EC8 part 1-3 fig. 4.1)Class A Non-dissipative structures:q = 1.0 Structures with no mechanical connections, hinged arches, cantilever structureswith
rigid connections at baseClass B Structures having a low capacity for energy dissipation:q = 1.5 Structures with few mechanical connections, cantilever structures with
semi-rigidly fixed base connectionsClass C Structures having a medium capacity for energy dissipation:q = 2.0 Frames, and beam-column structures with semi-rigid joints
Log housesGypsum 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
� �+= kiEIkj QGW ψ (6) (EC8 part 1-1 eq. 4.12)
Gkj is the characteristic dead load andψEIQki is the probable live load during an earthquake.
iEI 2ϕψψ = (7) (EC8 part 1-2 eq. 3.15)
ψ2i is the long-term value 0.3 for live loads,or 0.2 for snow loads (EC1 and EC5),
ϕ is 0.5 for all storeys except the top storey for which it is 1.0(no correlation between storey loads). (EC8)
ϕ is 1.0 for storage loads (EC8)
0 1 2 3 40
0.2
0.4
0.60.563
0
S E T
40 T
Se =ag S η β
58
58
Combining loads in seismic designThe design loads needed in seismic design consist of dead loads and seismic loads. Windloads do not need to be considered.
� �++= kiibkjd QFGE 2ψγ (8) (EC8 part 1-1 eq. 4.11)
Where, γ is the importance factor (γI = 1.4 hospitals, fire stations, powerstations; γII = 1.2 schools, cultural buildings; γIII = 1.0 residential and commercial buildings;γIV = 0.8 agricultural buildings),
Gkj and Qki are the characteristic values of the dead and live load,ψ2i 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 thefollowing factors:
0.7 when the fundamental period of the structure T0 < 0.15 s0.5 when the fundamental period of the structure T0 > 0.50 sfor values where 0.15 s < T0 < 0.5 the factor may be interpolated.
Seismic designUltimate limit state
{ } }{,, 2M
kdkiibkjd
fRRQFGfE
γψγ =≤= � � (9) (EC8 part 1-2 eq. 4.1)
The load duration class is 'instantaneous' and such kmod values are used. The material safetyfactor is γM = 1.3, when the structure is energy dissipative (or q > 1) and γM = 1.0, when thestructure is non-dissipative (or q = 1). The importance factor, γ, in the above equation is asgiven for eq. 8.DuctilityThe structures and the building as a whole should be adequately ductile. The ductility shouldbe as considered in the design, where it is taken into account as a load reducing factor, thebehaviour factor q was explained previously.EquilibriumThe building should be stable during a seismic event. The seismic load combinations shouldbe 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 stateIn order to avoid excessive damage, EC8 gives rules for the inter-storey drift during a seismicevent. The design earthquake may be one, which is more likely (lower return period), and thepeak ground acceleration is lower than for the ultimate limit state. The inter-storey drift islimited to the following values:
dr/ν ≤ 0.004 h , buildings having non-structural elements of brittleor materials attached to the structure
≤ 0.006 h , buildings having non-structural elements fixed in away as not to interfere with structural deformations
Where dr is the inter-storey drifth is the storey heightν reduction factor having values between
2.0 - 2.5 . Takes into account the lowerreturn
period of the seismic event during theserviceability limit state.
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JULKAISUN ESITTELYTEKSTI englanniksi
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Viimeisellä sivulla julkaistaan (tutkimusyksikön) uusimpien julkaisujen luettelo [ ]Lomake tai mahdollinen erillinen esittelyteksti lähetetään valmiin käsikirjoituksen mukana.
Sarjanimeke Sarjanumero Vuosi
VTT Tiedotteita 2001
Tekijät
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. Thecalculation procedures to obtain the seismic loads are given and these are illustrated withexamples. The dimensioning of the structure is carried out according to Eurocode 5 in asimilar manner as for other lateral loads, for example wind loads, with a few minorexceptions. This report is written in a practical level so that also designers inexperienced withseismic analysis would be able to carry out a seismic design of a timber building.