In EC8, structures are classified according to their ductility and to their energy dissipative property. In certain cases, it is recommended to design the structure to be sufficiently rigid to fulfil the serviceability criteria. For structures designed to dissipate energy, that is q > 1, the strength of the wooden parts should be higher than the strength of the connections. The connections should also be able to deform to the plastic range.
Fig 5.10 The moment-rotation curve of a portal frame corner under the El Centro earthquake.
(STEP C17)
The ability to dissipate the energy of the connections under seismic actions should usually be demonstrated by tests following internationally recognised experimental procedures. The test shows that the connection is ductile and the properties are stable under a rather high deformation or a stress level cyclic load. To ensure ductility, it is required that the ductility under a cyclic load is at least three times the q value. This multiplier is reduced to two for panel structures.
Additionally, the connections should be able to deform plastically for at least three full cycles at the above ductility ratio without a 20% reduction in strength. Satisfying these conditions, the designer may calculate the strength and rigidity of the connection following the normal procedures in EC5.
6 . Conclusion
Timber houses are usually regular, both in plan and in elevation. The seismic design may then be carried out using the simplified modal response spectrum analysis, which returns a single base shear value acting on the building. EC8 gives the rules on how this base shear is calculated. The bracing of the building is designed in both principal directions against this base shear load.
When the seismic load is calculated, the bracing is designed according to EC5. However, some restrictions on the detailing of floor diaphragms and shear walls are given in EC8.
In the case of multi-storey timber houses, the seismic loads are about twice the magnitude of the wind loads in high seismic zones. Therefore, the lateral loads should be taken into account early in the design process when planing the layout and the frame.
In the simplest case, the seismic loads are determined following the list below:
1. Determine the subsoil class according to local conditions (A, B or C)
2. Determine the peak ground acceleration value, ag, to be used in the design from local authorities.
3. Estimate the natural period of the building using eq. 2.
4. Determine the behaviour factor q according to the structure class.
5. Calculate the ordinate of the design spectrum from eq. 5.
6. Calculate the loads using eq. 6.
7. Calculate the base shear force with eq. 1. and its distribution using eq. 3.
8. When the seismic loads are determined, the dimensioning of the structures may be done following EC5.
The following are some aspects in need of further study:
The seismic design should be carried out by computer. The equations presented in this text to determine these loads as well as the equations needed for the dimensioning of the structures should be implemented in a computer-based design program. The calculation routines are rather simple, but can be laborious, especially when the shear walls are not situated symmetrically in a building and torsion effects are produced.
Seismic design expertise should also be widely known in countries such as Finland, which do not have earthquakes, but which do have a timber house exporting industry. In this way, the local requirements for houses can be better fulfilled. The good seismic performance of timber buildings should be used in the marketing aimed at seismic areas of the world. Also, local authorities should be better informed on the performance of timber houses. Usually, in areas of high seismic activity, buildings are made of concrete or masonry and these are very dangerous if not properly designed for seismic actions.
References
APA, (1997a) Earthquake safeguards; Introduction to lateral design, wood design concepts.
Seattle USA
APA (1997b) Introduction to lateral design, wood design concepts. Seattle USA 1997
Buchanan, A., Dean, J. (1988) Practical design of timber structures to resist earthquakes.
International Timber Engineering Conference, Seattle, 1988: 813-822.
Ceccotti, A. (2000) Seismic behaviour of timber buildings, introduction. COST E5 Workshop on Seismic behaviour of Timber Structures. September 28-29 2000 Venice Italy.
Ceccotti, A., Karacabeyli, E. (1998) Seismic design considerations on the multi-storey wood-frame structures. Cost E5 workshop on constructional aspects of multi-storey timber buildings. June 1998 UK.
Ceccotti, A., editor, (1989) Structural Behaviour of Timber Constructions in Seismic Zones.
Proc. of the relevant CEC DG III - Univ. of Florence Workshop, Florence, Italy.
EUROCODE 8 (1994) ENV 1998-1-1. Design provisions for earthquake resistant structures.
European prestandard. TC 250 of CEN, Brussels, Belgium.
EUROCODE 5 (1995) ENV 1995-1-1. Design of timber structures. European prestandard.
TC 250 of CEN, Brussels, Belgium. (Version 29.06.1999)
Karacabeyli, E. (2000) Performance of North American platform frame wood construction in earthquakes. COST E5 Workshop on Seismic behaviour of Timber Structures. September 28-29 2000 Venice Italy.
RILEM TC 109 TSA (1994) Timber structures in seismic regions. RILEM State-of-the-Art Report. Material and Structures 27: 157-184.
SECBC (1997) Updated seismic design of buildings. Structural Engineering Consultants of British Columbia, Wood Frame Committee.
STEP B13 Diaphragms and shear walls, Thomas Alsmarker. STEP 1 Timber Engineering, Basis of design, material properties, structural components and joints. Centrum Hout 1995 STEP C17 Timber connections under seismic actions, Ario Ceccotti. STEP 1 Timber Engineering, Basis of design, material properties, structural components and joints. Centrum Hout 1995
TKK (1995) Träförband T150 naulalevyliitosten käyttäytyminen seismisessä kuormituksessa.
Tutkimusselostus TRT0595AK. Talonrakennustekniikka TKK, 1995.
(The performance of the T150 nailplate under seismic loading, test report in Finnish)
Yasumura, M. et al. (1988) Experiment on a three-storied wooden frame building subjected to horizontal load. In: International Timber Engineering Conference, Seattle, 1988: 262-275.
Material suppliers
Anchorage connectors Simpson strong-tie connectors Bulldog-Simpson GMBH Boschstrasse 9
D-28857 Syke, Germany tel. + 49 4242 95940 fax + 49 4242 60778 http://www.strongtie.com MGA connectors
MGA
11476 Kinston St.
Maple Ridge B.C.
V2X O45 Canada tel. + 1 604 465 0296 fax. + 1 604 465 0297
43
Plywood
WISA - special plywoods Schauman Wood OY
PL 203 FIN-15141 Lahti, Finland tel. 0204 15113
fax. 0204 15112
http://www.schaumanwood.fi/tuotteet/vanerit/
index.html Finnforest Oy
PL 50 FIN-02020 Metsä tel. 010 4605
fax. 01 4694863
http://www.finnforest.fi/pages/products/
plywood2.htm
In Turkey:
WISA - special plywoods Schauman Wood OY Istanbul Branch Office
Bagdat Cad. Yesilbahar Sk. No. 1/10 TR-81060 Ciftehavuzlar/Istanbul, Turkey tel.+90(0)2163854610, 3860831
fax.+90(0)2163856558.
44
Earthquake magnitude, M
To assess the magnitude of earthquakes, a scale to describe the energy released during an earthquake was developed by Richter in the 1930s. This is named the Richter scale and it is the most common scale used today to describe earthquakes. The magnitude of an earthquake on the Richter scale is determined by a so-called Wood-Anderson seismograph maximum amplitude, where M = log(a), and a is the maximum amplitude [µm] at a 100 km distance from the epicentre. The magnitude may also be assessed at other distances using special conversion tables. The magnitude measures the amount of released energy and a unit increase of magnitude signifies a 32-fold energy release. There exists a physical upper limit above which elastic energy cannot be stored without being released; this limit is approximately M = 8.9 . Buildings usually do not suffer severe damages when M < 5 .
The seismic action on buildings cannot be described by the Richter scale magnitude and this may not be used in the design. However, Housner in 1970 developed empirical relationships between the magnitude, the duration and the peak ground acceleration to be used in design, see Table L1 below.
Table L1. Relationships between the magnitude, peak ground acceleration and the duration of the
most intense phase of the earthquake (Housner, 1970) Magnitude on the
Richter scale
Peak ground acceleration (% g)
Duration (s)
5.0 9 2
5.5 15 6
6.0 22 12
6.5 29 18
7.0 37 24
7.5 45 30
8.0 50 34
8.5 50 37
45
Example cases of seismic load calculation and design Example 1, Seismic load for a small one-storey house Input values:
Building area 9.3×16.8 m2 Ground acceleration = 0.35 g Subsoil class C
Importance factorγ= 1.0 (residence)
H
46
Dead load g: 0.8 KN/m2 Snow load q: 1.8 KN/m2 Building height H: 3.5 m Subsoil class C
Building fundamental period, T0
Shear walls as vertical diaphragms, q = 3.0
H 3.5 ( )m β 2.5 T b 0.2 s. T c 0.8 s. T d 3 s.
Importance 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/ m2= 41 KN Fb= 51.003 KN
47
Example 2, A four-storey timber house case, calculation of the seismic load and design of some details
Input values:
Ground acceleration = 0.35 g, Subsoil class B
Floor dead load 1 KN/m2 (the weight of the walls is assumed to be included in this figure) Roof dead load 0.75 KN/m2
Live load qh= 2.0 KN/m2
Importance factorγ= 1.0 (residence)
The seismic load is determined considering the vertical loads present in the different storeys of the building. This load is calculated using eq. 6:
å
Gkj +å
ψEIQki (6)Gkjis the characteristic dead load and
ψEIQkiis the probable live load during a seismic event.
Combination coefficient:ψ =EI ϕψ2i ψ2iis 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:
å
Gkj +å
ψEIQki= 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
Building height H: 12 m Building fundamental period T0
H 12 β 2.5 T b 0.15 s. T c 0.6 s. T d 3 s.
Comparison to the wind load below Qwind = 20 x 12 x 0.7 KN /m2= 168 KN Fb= 415.8 KN
49
The base shear force is distributed in elevation according to eq. 3 :
=
å
Fbis the base shear force
Table L2.2 The design shear forces in the different storeys Storey,
Cumulative shear force acting on the shear walls at the different
storey levels
Roof 12 0.75×288 = 216 107 107
4 9 1.6×288 = 461 171 278
3 6 1.3×288 = 375 93 371
2 3 1.3×288 = 375 46 416
Σ
ziWi= 10116 KNm ; Fb≅416 KNThe shear force acting on the shear walls of each storey
The force distribution according to eq. 3
2/3 x H
50
The shear walls will be composed of 9-mm-thick plywood panels connected with threaded nails 28×60 k70. In this case the shear wall capacity per length (from Table 4.1) is Fv,d= 7.38 KN/m.
This means that the lengths of shear walls needed in the different storeys are:
- first storey at least 416/7.38 = 56 m - second storey at least 371/7.38 = 50 m - third storey at least 278/7.38 = 38 m - fourth storey at least 107/7.38 = 14 m
The sheathing panel is nailed along all edges to the timber frame at spacing k70 and to the middle of the panel at spacing k300.
A schematic diagram of the shear walls in the first storey of the building
8500
8500 Apartment A Corridor
7000 4000 7000
2500 2500 3500
3500
Apartment B
Apartment D Apartment 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
51
total 87.2 m ( >
56 m ) OK
It is advantageous to use the walls between apartments and corridors as shear walls with panelling on both sides of the wall. In this example, the shear walls are situated symmetrically to avoid a torsion effect (for simplicity). In practice, gypsum boards could also be used as an additional reinforcement for the shear walls. EC5 allows the use of two different panels in shear walls, but only 50% of the capacity of the weaker gypsum panel could be included.
Anchoring the building against uplift
The example below concerns only the anchorage of the first storey to the foundations. Only the anchoring of one shear wall, the shortest shear wall of 2.5 m, is shown. The anchoring analysis should be carried out on all of the storeys and all of the other shear walls in a similar manner.
Below the vertical load is calculate. The dead load is advantageous so the partial safety factor is 1.0 . Wind and live loads are not included.
Vertical load:
From this load, the portion affecting the 2.5 m long shear wall is approximately:
• PHd,wall= 1812×2.5×8.5×0.5×0.5/288 = 33.4 KN The lateral load affects at height 2/3×H:
Fb= 416 KN
From this load, the portion affecting the 2.5-m long shear wall is approximately:
• Fb,wall = 416×2.5/56.4 = 18.4 KN Distribution of vertical F
load by eq. (9) :
2/3 x H PHd,wall
Fb,wall
52
Both sides of the shear wall are anchored for an uplift force of 42.2 KN.
The anchorage is made of 10 pieces of lag screws of size 10×55 and a metal plate folded to a 90-degree angle with a cross-section size of 80×5 mm2 and a bolt of size M12 connected to the foundations.
First let us analyse the connection of the anchorage to the wooden frame. The metal plate is of thickness
The characteristic embedment strength of wood is fhksolid (EC5):.
2
The characteristic tension strength of steel is fuk =500N/mm2 The yield moment of the lag screw 10x55 is Mykscrew (EC5):
mm Nmm
The characteristic shear strength of the screw 10x55 is Fvkscrew (EC5).
2.5 m Anchoring for uplift force, AHd
53
For the service class 1 and load duration class "instantaneous" the design shear strength of the screw is:
Under service class 1 and load duration class "instantaneous", the design strength of the metal plate and bolt is:
2
The design tension capacity of the plate 5x80 is F
td
The design tension capacity of the bolt M12 is F
td
The tension force acting on the wooden frame strut (T24)
2
Anchoring the building against sliding
Next, the anchorage calculation against sliding is carried out. The vertical loads are not necessary in this case as the effects of friction cannot be considered.
54
In the first storey, the building had a total of 56.4 m (weakest lateral direction) of shear walls and the base shear force is FB=416 KN. Therefore, the anchoring force against sliding is as follows:
m Fb KN
AVd 7.4 /
4 . 56 =
=
Bolts of size M10×120 are used, with a design shear capacity of Fvd= 9.4 KN. Therefore, the bolt spacing in the bottom plate (sill plate) is as follows:
A m s Fb
Vd
3 .
=1
=
The shear walls are anchored for sliding in the first storey with bolts connected to the foundation of type M10×120 and with a spacing of, let’s say, k1000.
Vertical section
55
Bolts M10*120 k1000 Shear wall edges anchored by a bolt M12
Horizontal section
bolt M12 Wall opening
Screws 10 x 55 10 pieces metal plate Bolts M10x120 k1000
Shear wall length 2500 mm
Anchorage for uplift forces Anchorage for sliding
Plywood panel sheathing 9 mm
56
A summary of the procedure to evaluate the seismic load according to Eurocode 8 The seismic design of a building starts with an evaluation of the regularity of the building in both layout and elevation compared with the requirements mentioned in section 3.3 (EC8 part 1-2, 2.2 Structural regularity). Generally regularity increases the seismic resistance of the building. Usually timber residential buildings are regular in plan and in height.
The initial values are given, the subsoil class (section 3.4) according to the ground conditions and the peak ground acceleration value, ag, according to the site seismicity.
It should be noted that for a different country, the authorities may enforce values or parameters different from the ones given in EC8, which are so-called boxed values. The values given in this report are the ones recommended by EC8. Such information is given in the national application documents.
Base shear force
The base shear force acts in both principal directions of the building.
Fb= Se(T0) W/q = Sd(T0) W (1.a, b) (EC8 part 1-2 eq. 3.3) Where T0is the fundamental period of the building
Seis the ordinate of the elastic response spectrum Sdis the ordinate of the design response spectrum W is the vertical load
q is the behaviour factor Fundamental period
To estimate the fundamental period, T0, of the building, EC8 has a simple procedure:
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 elevation
If the floor loads are equal in the different storeys, the base shear force is distributed in a triangular manner so that higher forces are higher up. This is given by the equation:
=
å
Where Fiis the lateral load in storey i Fbis the base shear force
ziis the distance of the floor from the ground Wiis the vertical load on the floor
Design spectrum
57
Whereα= ag/g , agis the peak ground acceleration value T0: is the fundamental period of the building
Tb, Tc, Td: are time parameters S: soil parameter
kd1= 2/3 , kd2= 5/3, exponent parameters
According to the subsoil class, the parameter values are as in the following table.
Table L3.1 Parameters for the spectrum equations. (EC8 part 1-1 Table 4.1)
Subsoil class S β Tb[s] Tc[s] Td[s]
A 1.0 2.5 0.10 0.40 3.00
B 1.0 2.5 0.15 0.60 3.00
C 0.9 2.5 0.20 0.80 3.00
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 structures with
rigid connections at base
Class B Structures having a low capacity for energy dissipation:
q = 1.5 Structures with few mechanical connections, cantilever structures with semi-rigidly fixed base connections
Class C Structures having a medium capacity for energy dissipation:
q = 2.0 Frames, and beam-column structures with semi-rigid joints Log houses
Gypsum board shear walls (Ceccotti & Karacabeyli, 1998) Class D Structures having a good capacity for energy dissipation:
q = 3.0 Shear walls using wood-based boards and mechanical fasteners for example platform frame timber houses (also multi-storey) Horizontal diaphragms may be glued or nailed.
The mass in seismic design
å
+å
= Gkj EIQki
W ψ (6) (EC8 part 1-1 eq. 4.12)
Gkjis the characteristic dead load and
ψEIQkiis the probable live load during an earthquake.
i
EI ϕψ2
ψ = (7) (EC8 part 1-2 eq. 3.15)
ψ2iis 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) ϕis 1.0 for storage loads (EC8)
0 1 2 3 4
58
Combining loads in seismic design
The design loads needed in seismic design consist of dead loads and seismic loads. Wind loads do not need to be considered.
å
+ +å
= kj b i ki
d G F Q
E γ ψ2 (8) (EC8 part 1-1 eq. 4.11)
Where,γis 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 agricultural buildings),
Gkjand Qkiare the characteristic values of the dead and live load,
ψ2iis the combination coefficient of the quasi-permanent value of the live load.
The vertical loading components may be determined by multiplying the lateral loads by the following factors:
0.7 when the fundamental period of the structure T0< 0.15 s 0.5 when the fundamental period of the structure T0> 0.50 s for values where 0.15 s < T0< 0.5 the factor may be interpolated.
Seismic design
The load duration class is 'instantaneous' and such kmod values are used. The material safety factor isγM= 1.3, when the structure is energy dissipative (or q > 1) andγM= 1.0, when the structure is non-dissipative (or q = 1). The importance factor,γ, in the above equation is as given for eq. 8.
Ductility
The structures and the building as a whole should be adequately ductile. The ductility should be as considered in the design, where it is taken into account as a load reducing factor, the behaviour factor q was explained previously.
Equilibrium
The building should be stable during a seismic event. The seismic load combinations should be considered when designing for the anchorage of the building in the following two cases:
- anchorage for overturning: upward tension at ends of shear walls, - anchorage for sliding, base shear at the bottom of shear walls Serviceability limit state
In order to avoid excessive damage, EC8 gives rules for the inter-storey drift during a seismic event. The design earthquake may be one, which is more likely (lower return period), and the peak ground acceleration is lower than for the ultimate limit state. The inter-storey drift is limited to the following values:
dr/ν ≤ 0.004 h , buildings having non-structural elements of brittle or materials attached to the structure
≤0.006 h , buildings having non-structural elements fixed in a
way as not to interfere with structural deformations
Where dr is the inter-storey drift h is the storey height
ν reduction factor having values between
2.0 - 2.5 . Takes into account the lower
return
period of the seismic event during the serviceability limit state.
59