seismic response of mid-rise wood- frame buildings on podium

Seismic Response of Mid-Rise Wood-Frame Buildings on Podium Date: March 2017

By: Zhiyong Chen, Ph.D., P.Eng., Scientist, Advanced Building System Chun Ni, Ph.D., P.Eng., Principal Scientist, Advanced Building System

Natural Resources Canada Canadian Forest Service

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301011233: Enhancements in mid-rise

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ACKNOWLEDGEMENTS This project was financially supported by the Canadian Forest Service under the Contribution Agreement existing between the Government of Canada and FPInnovations.

The authors would like to thank Prof. Robert Tremblay, Dr. Poulad Daneshvar, Prof. Najib Bouaanani and Prof. Pierre Leger, Polytechnique Montreal, Canada, and Prof. Katsu Goda, University of Bristol, United Kingdom, for their guidance on the selection of earthquake ground motions for this study.

REVIEWERS Marjan Popovski, Ph.D., P.Eng., Principal Scientist, Advanced Building Systems

CONTACT Chun Ni, Ph.D., P.Eng. Principal Scientist Advanced Building Systems 604-222-5647 [email protected]

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SUMMARY

An analytical study to examine the seismic performance of wood-frame podium buildings up to 8 storeys is presented in this report. Simple archetype podium buildings of 5 to 8 storeys in total height were designed in accordance with the two-step analysis procedure given in 2015 NBCC or ASCE 7-10. Nonlinear time-history dynamic analyses were conducted using earthquake ground motions selected and scaled based on the guidelines proposed by Tremblay et al. to match the reference design spectra in NBCC. Using the performance-based seismic design criteria established in the NEESWood project, it was found that:

• Podium buildings with a building period ratio of 1.1 (ASCE 7-10) did not meet the performance criteria, thus the period ratio requirement of 1.1 was not appropriate.

• A stiffness ratio of not less than 10 times (ASCE 7-10) was more appropriate as a requirement of using two-step analysis procedure for wood-frame podium buildings up to 8 storeys, compared to that of not less than 3 times (NBCC Commentary). With a higher stiffness ratio, the seismic response of the upper wood-frame structure of podium building was closer to that of the pure wood-frame structure.

The results of this study will be used to guide the assessment of the feasibility of constructing wood-frame podium buildings of 8 storeys in height and the development of design guidelines. This would also guide the longer-term goal of proposing changes to the building codes.

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Table of contents

Summary ............................................................................................................................................... 3

1. Introduction ..................................................................................................................................... 7

2. Current Design Provisions for Podium Structures ........................................................................... 8

3. Objectives ....................................................................................................................................... 9

4. Staff ................................................................................................................................................ 9

5. Archetypes of Wood-frame Podium Buildings ................................................................................. 9

5.1 Design Information ....................................................................................................................... 9

5.2 Seismic Design .......................................................................................................................... 10

5.2.1 Pure Mid-Rise Wood-Frame Buildings ................................................................................. 10

5.2.2 Mid-Rise Wood-Frame Buildings on Podium ........................................................................ 12

6. Model Developement .................................................................................................................... 14

6.1 Model for Mid-Rise Wood-Frame Buildings on Podium............................................................... 14

6.2 Model Properties ........................................................................................................................ 16

7. Selection and Scaling of Ground Motions ..................................................................................... 19

8. Results and Discussions ............................................................................................................... 23

8.1 Pure Mid-Rise Wood-Frame Buildings ........................................................................................ 23

8.2 Wood-Frame Podium Buildings of Cases I and II ....................................................................... 24

8.3 Wood-Frame Podium Buildings of Cases III and IV .................................................................... 24

8.4 Effect of Ground Motions on Inter-Storey Drifts .......................................................................... 28

9. Conclusions and Recommendations ............................................................................................. 28

10. References ................................................................................................................................ 29

Appendix I Maximum Inter-Storey Drift of Building Models ................................................................... 31

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List of figures

Figure 1 Example of podium building (Courtesy of BC Wood WORKS!) ................................................ 7

Figure 2 Two-step analysis procedure according to ASCE 7-10 ............................................................ 9

Figure 3 Numerical model of a podium building with 4-storey wood-frame structure on 2-stroey podium ............................................................................................................................................................ 15

Figure 4 Hysteresis loops of shear wall at the 6th storey of 6-storey wood-frame buildings ................. 17

Figure 5 Target response spectrums for the three scenarios ............................................................... 20

Figure 6 Spectra of scaled ground motion time histories of crustal scenario (0.2 to 0.8 s) ................... 22

Figure 7 Spectra of scaled ground motion time histories of in-slab scenario (0.3 to 1.5 s) ................... 22

Figure 8 Spectra of scaled ground motion time histories of subduction scenario (1.0 to 3.0 s) ............. 23

Figure 9 Inter-storey drift of pure wood-frame buildings under fifteen scaled ground motions .............. 24

Figure 10 Inter-storey drift of 4-storey pure wood-frame building vs podium buildings on 1-storey (a) and 2-storey (b) podium ....................................................................................................................... 25



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List of tables

Table 1. 2014 Canada New Construction (in 000’s ft2, Source: Reed/CMD) .......................................... 8

Table 2. Number of storeys in wood-frame podium buildings analysed in this study ............................ 10

Table 3. Building periods, seismic weight and base shear per shear wall ............................................ 10

Table 4. Construction details of shear walls of each storey for wood buildings .................................... 12

Table 5. Stiffness, weight and period ratio for different building cases ................................................. 13

Table 6. Stiffness, weight and period of wood-frame buildings on 1-storey podium .............................. 13

Table 7. Stiffness, weight and period of wood-frame buildings on 2-storey podium .............................. 14

Table 8. Model Parameters .................................................................................................................. 16

Table 9. Model parameters and vertical-spring stiffness for 4-storey wood-frame buildings ................. 18

Table 10. Model parameters and vertical-spring stiffness for 5-storey wood-frame buildings ............... 18

Table 11. Model parameters and vertical-spring stiffness for 6-storey wood-frame buildings ............... 18

Table 12. Earthquake records .............................................................................................................. 21

Table 13. Inter-storey drift [%] of 4-storey wood-frame buildings .......................................................... 31



Table 16. Inter-storey drift [%] of 4+1 podium buildings with a stiffness ratio of 3 ................................. 32

Table 17. Inter-storey drift [%] of 4+1 podium buildings with a stiffness ratio of 10 ............................... 32











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1. INTRODUCTION

In North America, wood-frame construction is the dominant type for single-family housing and for multi-family housing in low-rise (up to 4 storeys) buildings (Ni and Popovski 2015). In 2009, British Columbia became the first province in Canada to amend its building code to allow mid-rise (5- and 6-storeys) wood-frame construction (Ministry of Housing and Social Development 2009a & 2009b). The amendment brought the BC Building Code more closely in line with the states of California, Washington, and Oregon, where mid-rise wood construction was permitted as an acceptable solution. Later in 2013, Régie du Bâtiment du Québec introduced 5- and 6-storey wood construction (RBQ 2013). Subsequently in 2015, Ontario and Alberta allowed mid-rise wood-frame construction in their provincial building codes (Ministry of Municipal Affair and Housing 2014; NRC 2014). On the national level, the Canadian Commission on Building and Fire Codes (CCBFC) accepted the code change proposal to allow 5- and 6-storey wood-frame construction in the 2015 edition of the National Building Code of Canada (NBCC) (NRC 2015).

Wood-frame podium buildings usually refer to several storeys of wood-frame construction built over one or more storeys of elevated concrete or steel podium, with concrete being the predominant. On the west coast of the United States, wood-frame podium buildings can be built up to 7 storeys with 5-storey wood-frame on 2-storey concrete podium in building height, as shown in Figure 1 (Triggs 2015). In Canada, the wood-frame podium buildings are permitted up to 6 storeys. Increasing the cumulative height to a possible maximum of 8 storeys could bring significant potential to the wood building market. In Canada, maximum market opportunity for apartments could increase by 42% from 6.6 million ft2 (5-6 storey class), to 9.3 million ft2 (combined opportunities for both 5-6 and 7-8 storey class), as shown in Table 1.

Figure 1 Example of podium building (Courtesy of BC Wood WORKS!)

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Table 1. 2014 Canada New Construction (in 000’s ft2, Source: Reed/CMD)

Storey Building Type BC Province Canadian Total Summary

5-6 Apartments 3,468 6,563

9,738 Non-residential 577 3,175

7-8 Apartments 352 2,745

4,324 Non-residential 1,071 1,579

Total 5,467 14,062 14,062

2. CURRENT DESIGN PROVISIONS FOR PODIUM STRUCTURES

Neither the 2015 NBCC nor the CSA O86 (CSA 2014) explicitly provides seismic design guidelines for podium buildings (Newfield 2015). In the Commentary J of the 2010 NBCC Structural Commentaries (Part 4 of Division B) (NRC 2010), a two-step analysis procedure which uses the Equivalent Static Force Procedure can be used for podium building with a ductile wood-frame shear wall structure above a stiff, normally ductile one- or two-storey concrete structure, provided the stiffness of the lower storey(s) is greater than three times that of each of the upper storeys. For podium buildings meeting the above requirements, the upper structure can be treated as a separate building with a fixed base starting at the top of the lower structure; and the lower structure can be treated as a separate “short” building with the forces from the upper structure applied at the top. Either the upper or the lower structure can be analysed with the corresponding RdRo value and the appropriate period for its height. In the 2010 edition of ASCE-7 (ASCE 2010), a simple two-step equivalent lateral force procedure can be used for the seismic design of podium buildings regardless the building height, if it meets stiffness and building period requirements. Clause 12.2.3.2 in ASCE-7 states that a two-step equivalent lateral force procedure may be used for structures having a flexible upper portion above a rigid lower portion, provided that the design of the structure complies with all of the following (as shown in Figure 2): a) The stiffness of the lower portion must be at least 10 times the stiffness of the upper portion; b) The period of the entire structure must not be greater than 1.1 times the period of the upper portion considered as a separate structure supported at the transition from the upper to the lower portion; c) The upper portion must be designed as a separate structure using the appropriate values of R and ρ, where R is the seismic response modification coefficient for the upper portion and ρ is a redundancy factor based on the extent of structural redundancy present in the upper portion; d) The lower portion must be designed as a separate structure using the appropriate values of R and ρ. The reactions from the upper portion must be those determined from the analysis of the upper portion amplified by the ratio of the R/ρ of the upper portion over the R/ρ of the lower portion. This ratio must not be less than 1.0; and e) The upper portion is analysed with the equivalent lateral force or modal response spectrum procedure, and the lower portion is analysed with the equivalent lateral force procedure.

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Figure 2 Two-step analysis procedure according to ASCE 7-10

3. OBJECTIVES

The requirements for using two-step analysis procedure are different in NBCC Commentary than those of ASCE 7-10. For example, the ratio of the stiffness of the lower portion to the upper portion is required to be more than three compared to not less than ten in ASCE 7-10. So far no study has been carried out to examine which criterion is more appropriate for the design of wood-frame podium buildings. This research project will investigate the seismic response of wood-frame podium buildings of 5 to 8 storeys designed with two-step analysis procedure in accordance with NBCC or ASCE 7-10. It is an initial step towards assessing the feasibility of constructing 8-storey wood-frame podium buildings and subsequently towards the development of design guidelines. Where appropriate, code change proposals will be considered for inclusion in building codes and CSA Standard O86.

4. STAFF

Chun Ni, Ph.D., P.Eng., Principle Scientist, Advanced Building Systems

Zhiyong Chen, Ph.D., P.Eng., Scientist, Advanced Building Systems

Marjan Popovski, Ph.D., P.Eng., Principle Scientist, Advanced Building Systems

5. ARCHETYPES OF WOOD-FRAME PODIUM BUILDINGS

5.1 Design Information Nine buildings were selected for this investigation. Table 2 lists the number of storeys in the upper and lower structure for each building case. A storey height of 2.74 m (9 ft) was used for both wood and

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podium portion in each building. For the upper wood-frame structure, 6.1 m (20 ft) long shear walls were used spaced at 4.27m (14 ft).

Table 2. Number of storeys in wood-frame podium buildings analysed in this study

Index 4 4+1 4+2 5 5+1 5+2 6 6+1 6+2

Upper structure (wood-frame)

4 5 6

Lower structure (concrete) 0 1 2 0 1 2 0 1 2

Total 4 5 6 5 6 7 6 7 8

These buildings were assumed to be located in the City Hall area in Vancouver, B.C. According to NBCC, the spectral response acceleration of Sa(0.2), Sa(0.5), Sa(1.0), Sa(2.0), Sa(5.0) and Sa(10.0) is 0.848 g, 0.751 g, 0.425 g, 0.257 g, 0.08 g and 0.029 g, respectively. Stiff soil condition (Site Class D) was selected. It was assumed that a uniformly seismic weight of 1.36 kPa (including 25% snow load) and 1.80 kPa was applied to the roof and wood floor, respectively.

5.2 Seismic Design

5.2.1 Pure Mid-Rise Wood-Frame Buildings Fundamental natural period of the pure wood-frame buildings, Ta, was estimated using the code formula in accordance with NBCC Clause 4.1.8.11.(3)(c). Also the mechanics-based method specified in FEMA 450 Commentary (BSSC 2003) was used to estimate the period, Tm. The estimated building periods are listed in Table 3. Since the estimated building periods based on the mechanics-based method were greater than two times of those calculated using the code formula, 2Ta was used to determine the earthquake force in accordance with NBCC Clause 4.1.8.11.(3).(d).(iii).

Table 3. Building periods, seismic weight and base shear per shear wall

Building 4-Storey 5-Storey 6-Storey

Ta [s] 0.301 0.356 0.409

2Ta [s] 0.603 0.713 0.817

Tm [s] 0.782 0.910 1.003

Seismic Weight [kN]* 175.8 222.7 269.5

Base Shear [kN] 31.1 38.2 41.9

Base Shear / Seismic Weight [%] 17.7 17.2 15.5

Note: * It was calculated assuming that the attributed area of shear wall has a length and a width that are equal to the length and spacing of the shear wall, respectively.

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According to NBCC, the ductile- and over-strength related force modification factor, Rd and Ro, were taken as 3.0 and 1.7 for nailed wood shear walls, respectively. Equivalent static force method was used to determine the minimum lateral earthquake force applied on the pure wood-frame buildings. The seismic weight and base shear per shear wall of the buildings are also listed in Table 3. It shows that the percentage of base shear over the seismic weight was smaller for 6-storey building due to its longer period. The lateral seismic force was distributed along the height of the buildings in accordance with NBCC Clause 4.1.8.11.(7). In this study, the shear walls of the wood-frame buildings were designed so that the factored shear resistance is equal to the lateral earthquake force determined in accordance with NBCC. The shear walls consisted of Douglas Fir-Larch (D.Fir-L) No.2 framing members (used as studs and plates), Oriented-Strand-Board (OSB) sheathing panels, and common wire nails. The shear resistance of shear walls was determined in accordance with CSA O86-14. Anchor Tie-Down System of Simpson Strong-Tie was used to resist the overturning of the shear walls. The construction details of shear walls for the pure wood-frame buildings are given in Table 4.

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Table 4. Construction details of shear walls of each storey for wood buildings

Storey No.

Construction Details 4-Storey 5-Storey 6-Storey

6th

Hold-down End stud each end Sheathing Nail Nail spacing

SR6 1-2x6 12.5 mm 8d (63.5 mm x 3.25 mm) 408 mm

5th


SR5 1-2x6 12.5 mm 8d (63.5 mm x 3.25 mm) 398

SR6 1-2x6 12.5 mm 8d (63.5 mm x 3.25 mm) 218

4th


SR5 1-2x6 12.5 mm 8d (63.5 mm x 3.25 mm) 453

SR6 1-2x6 12.5 mm 8d (63.5 mm x 3.25 mm) 211

SR7 2-2x6 12.5 mm 8d (63.5 mm x 3.25 mm) 159

3rd


SR5 1-2x6 12.5 mm 8d (63.5 mm x 3.25 mm) 227

SR6 2-2x6 12.5 mm 8d (63.5 mm x 3.25 mm) 156

SR7 2-2x6 12.5 mm 8d (63.5 mm x 3.25 mm) 132

2nd


SR6 2-2x6 12.5 mm 8d (63.5 mm x 3.25 mm) 171

SR7 2-2x6 12.5 mm 8d (63.5 mm x 3.25 mm) 133

SR8 3-2x6 12.5 mm 8d (63.5 mm x 3.25 mm) 118

1st


SR6 2-2x6 12.5 mm 8d (63.5 mm x 3.25 mm) 152

SR7 3-2x6 12.5 mm 8d (63.5 mm x 3.25 mm) 124

SR9 3-2x6 12.5 mm 8d (63.5 mm x 3.25 mm) 112

5.2.2 Mid-Rise Wood-Frame Buildings on Podium The same construction details of the pure wood-frame buildings shown in Table 4 were used for the upper structure (wood-frame) of the wood-frame podium buildings. For each podium building, four different cases, Table 5, were studied in this project. Case I met the minimum stiffness ratio requirement in NBCC Commentary, with additional building period requirement in accordance with ASCE 7-10. Case II met the minimum stiffness ratio and building period requirements in ASCE 7-10. The Cases III and IV met the minimum stiffness ratio requirement in NBCC Commentary and ASCE 7-10, respectively, with a more realistic weight ratio between wood-frame and concrete structure. It is

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worth pointing out that neither NBCC Commentary not ASCE 7-10 has clearly defined the stiffness ratio. In this study, a lateral stiffness ratio of the top-storey of concrete-podium structure and the bottom-storey of upper wood-frame structure was used. The actual stiffness, weight and building period of the pure wood-frame buildings and the wood-frame podium buildings are provided in Tables 6 and 7.

Table 5. Stiffness, weight and period ratio for different building cases

Case I II III IV

Kc / Kw 3 10 3 10

Wc / Ww - - 5 5

Ttol / Tw 1.1 1.1 - -

Note: Kc and Kw are the lateral stiffness of the top-storey of concrete-podium structure and the bottom-storey of upper wood-frame structure, respectively; Wc and Ww are the seismic weight of each storey in the concrete podium and upper wood-frame structure, respectively; Ttol is the fundamental period of the overall wood-frame podium building, and Tw is the period of the upper wood-frame structure.

Table 6. Stiffness, weight and period of wood-frame buildings on 1-storey podium

Building 4+1 5+1 6+1

Case I II III IV I II III IV I II III IV

Kw [kN/mm] 3.5 4.0 4.4

Kc [kN/mm] 10.4 34.8 10.4 34.8 12.1 40.2 12.1 40.2 13.1 43.7 13.1 43.7

Kc / Kw 3 10 3 10 3 10 3 10 3 10 3 10

Ww [kN] 46.8

Wc [kN] 1405 6790 234 234 2107 9833 234 234 3278 14281 234 234

Wc / Ww 30 145 5 5 45 210 5 5 70 305 5 5

Tw [s] 0.86 0.95 1.10

Ttol [s] 0.94 0.94 0.89 0.87 1.04 1.05 0.99 0.96 1.20 1.20 1.13 1.10

Ttol / Tw 1.1 1.1 1.04 1.01 1.1 1.1 1.04 1.01 1.1 1.1 1.03 1.01

Note: Kw and Kc were taken as the initial stiffness of the hysteresis loops of the wood-frame shear wall model and the elastic stiffness of the concrete shear wall model; Tw and Ttol were derived by performing frequency analysis on pure wood-frame building and wood-frame podium building using the finite element models developed below.

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Table 7. Stiffness, weight and period of wood-frame buildings on 2-storey podium

Building 4+2 5+2 6+2

Case I II III IV I II III IV I II III IV

Kw [kN/mm] 3.5 4.0 4.4

Kc [kN/mm] 10.4 34.8 10.4 34.8 12.1 40.2 12.1 40.2 13.1 43.7 13.1 43.7

Kc2 [kN/mm] 12.8 50.2 12.4 41.3 15.2 58.1 13.9 46.2 16.8 63.3 14.7 49.0

Kc / Kw 3 10 3 10 3 10 3 10 3 10 3 10

Ww [kN] 46.8

Wc [kN] 328 3044 234 234 609 4448 234 234 936 6555 234 234

Wc / Ww 7 65 5 5 13 95 5 5 20 140 5 5

Tw [s] 0.86 0.95 1.10

Ttol [s] 0.94 0.94 0.94 0.88 1.05 1.05 1.02 0.97 1.19 1.20 1.16 1.11

Ttol / Tw 1.1 1.1 1.09 1.02 1.1 1.1 1.07 1.02 1.1 1.1 1.06 1.02

Note: Kc2 was obtained based on the shear ratio between the first and second storey of concrete podium where the shears were derived in accordance with 4.1.8.11.(7) of NBCC using weight and high ratio.

It is noticed that in cases I and II, the weight of lower structure (concrete podium) needed to be dramatically increased to achieve the building period ratio of 1.1, in particular for higher stiffness ratio. As the weight ratios in cases I and II were probably unrealistic, cases III and IV which had a more realistic weight ratio between wood-frame and concrete structure were also studied. In cases III and IV, the building period ratios were far less than 1.1. This indicates that the criterion of period ratio (not greater than 1.1) was not necessary in most cases.

6. MODEL DEVELOPEMENT

6.1 Model for Mid-Rise Wood-Frame Buildings on Podium Two-dimensional modelling approach was adopted in this study. General purpose finite element software ABAQUS was used to model the behaviour of pure wood-frame buildings and wood-frame podium buildings. A macro-element model, originally developed by Xu and Dolan (2009b) and further modified by Chen et al. (2014) to consider the rotational effect, was used to simulate the wood-frame shear walls. The modified macro-element model is composed of three rigid boundary-framing members, one diagonal modified Bouc-Wen-Baber-Noori (BWBN) hysteretic spring, and two vertical translational (uplift or compression) springs. The vertical translational springs are restrained to have only vertical deformation. The shear wall of lower structure (concrete podium) was assumed to behave elastically, and thus it was modelled by using a macro-element mode including three rigid boundary-framing members and an elastic spring. Figure 3 illustrates a model for a 4+2 wood-frame podium building.

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Note: All the springs are zero-length and wood-frame storeys were intentionally elevated to illustrate the vertical elastic springs only.

Figure 3 Numerical model of a podium building with 4-storey wood-frame structure on 2-stroey podium

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The modified BWBN hysteretic spring, representing the hysteretic behaviour of wood-based shear wall, is governed by 13 different identifiable parameters, shown in Table 8 (Xu and Dolan 2009a). The modified BWBN hysteretic spring was built as a user-defined element (UEL) subroutine in ABAQUS/Standard. More details can be found from the study by Xu and Dolan (2009a, b) and Chen et al. (2014). The rotation induced by the elongation of hold-downs, compression of end studs, anchorage slip and compression of top and bottom plates was simulated via the two translational springs that deform vertically under the overturning moment. The load-deformation response of the translational springs was assumed to be linear elastic with different tension and compression stiffness, kt and kc.

Table 8. Model Parameters

6.2 Model Properties The hysteresis loops of shear walls in pure wood-frame buildings (or wood-frame structure of podium buildings) were obtained by scaling the load of the hysteretic loops of specimen SW-01 tested by Chen et al. (2016). The scaling is determined as follow:

According to Commentary J of NBCC, lower-bound strength properties shall be used for the modelling of nonlinear seismic force resisting system elements when determining structure displacement demands or forces or deformations designated as deformation-controlled actions. Based on Sentence 7.5.1.4 of ASCE 41 (ASCE 2013), the lower-bound resistance of nailed shear walls can be determined as the mean value of tested material properties minus one standard deviation. Assuming the coefficient

Parameter Unit Influence on the hysteretic shape

p mm-1 Determines the developing grate of 𝒛𝟏, the pinching stiffness factor, with M_Dis, the maximum experienced displacement.

Q None Determines the peak pinching location and effects the residual force.

α None Determines the ratio of the final asymptote tangent stiffness to the initial stiffness.

β mm1/n

Act as a couple and determine whether the curve is hardening or softening, also affects the ultimate hysteretic spring force. γ mm1/n

ω [kN/mm]1/2 Determines the initial stiffness of the system.

ζo None Basic value of 𝒛𝟏, the pinching stiffness factor.

n None Determines the sharpness of the transition from initial slope to the slope of the asymptote.

ψo mm2/3 Basic value of 𝒛𝟐, the pinching range factor.

δψ mm-1/3 Determines the developing rate of 𝒛𝟐, the pinching range factor, with M_Dis, the maximum experienced displacement.

δυ [kN•mm]-1 Determines the strength degradation rate.

ξo [kN•mm]1/2/s The linear viscous damping ratio.

δη [kN•mm]-1 Determines the stiffness degradation rate.

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of variation of shear wall strength to be 20%, the lower-bound resistance of shear wall was taken as 0.8 times the mean value of test results. As the mean resistance of shear wall is approximately twice the factored resistance of the shear wall based on the commentary of CSA O86, the lower-bound resistance of a shear wall was approximately 1.6 times the factored resistance of the shear wall. Therefore for each shear wall, the maximum load (or resistance) of the input hysteresis loops used in the finite element model was 1.6 times the factored resistance of the shear wall in CSA O86-14.

The 13 parameters (Table 8) for each shear wall used in the LWFB models were derived by data fitting to the scaled hysteretic loops. Figure 4 shows a comparison of hysteresis loops between macro-element response and scaled test data. The stiffness of the two vertical translational springs of the macro-element model was determined based on the properties of hold-down connection and framing members. The input parameters and spring stiffness of the macro-element model for each wood-frame shear wall are given in Tables 9 to 11. The horizontal stiffness of the elastic spring in the macro-element model for each shear wall of lower structure (concrete podium) is provided in Tables 6 and 7.

Figure 4 Hysteresis loops of shear wall at the 6th storey of 6-storey wood-frame buildings

-20

-15

-10

-5

0

5

10

15

20

-150 -120 -90 -60 -30 0 30 60 90 120 150

Load

[kN

]

Displacement [mm]

Scaled test data

FEA data

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Table 9. Model parameters and vertical-spring stiffness for 4-storey wood-frame buildings

Storey # 1st 2nd 3rd 4th

ω 1.635 1.545 1.335 0.945

ζo 0.972 0.976 0.976 0.978

Q 0.115 0.115 0.120 0.125

kc [kN/mm] 91.3 91.3 45.7 45.7

kt [kN/mm) 58.8 41.0 25.7 24.4

Note: ξo=0.000015, α=0.0001, β=0.065, γ=-0.03, n=1.108, δυ=0.0000005, δη=0.000004, p=0.06, ψo=0.96, δψ=0.175 for all the shear walls.


Storey # 1st 2nd 3rd 4th 5th

ω 1.820 1.758 1.616 1.390 1.010

ζo 0.974 0.974 0.975 0.976 0.978

Q 0.112 0.112 0.115 0.120 0.125

kc [kN/mm] 137 91.4 91.3 45.7 45.7

kt [kN/mm] 67.4 43.8 27.2 25.7 16.7



Storey # 1st 2nd 3rd 4th 5th 6th

ω 1.900 1.850 1.760 1.600 1.37 0.995

ζo 0.973 0.973 0.975 0.976 0.978 0.978

Q 0.112 0.112 0.112 0.115 0.120 0.125

Kc [kN/mm] 137 137 91.4 91.4 45.7 45.7

Kt [kN/mm] 92.2 57.3 35.5 32.3 22.5 22.0


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7. SELECTION AND SCALING OF GROUND MOTIONS

Guidelines proposed by Tremblay et al. (2015) for selection and scaling of ground motion time histories for linear or nonlinear dynamic response history analysis of structures designed in accordance with the 2015 edition of NBCC was adopted in this study. Below are the steps for selection and scaling of ground motion time histories.

Step 1 – Determination of period range To involve sufficient high vibration modes in the analysis which can significantly contribute to the inelastic seismic response of the structure, it is recommended that the lower period Tmin is therefore set equal to the period of the highest vibration mode required to cumulate a minimum participating mass of 90% of the structural mass, T90%. Tmin shall not exceed 0.2 times the period of the fundamental period, Ta, and the upper period Tmax is equal to two times the fundamental period Ta. In addition, the upper period Tmax shall not be less than 1.5 s so that the ground motion records for the analysis of stiff structures reflect the seismic demand over the period range where a large portion of the energy of typical seismic motions lies. In this study, the fundamental period of the analysed archetypes was in the range of 0.86 ~ 1.32 s with an average of 1.04 s. A period range, TR, of 0.2 to 3.0 s was selected accordingly.

Step 2 – Determination of target spectrum A reference design response spectrum reflected actual spectral acceleration demand was developed based on the design spectrum of Vancouver using the information provided by NBCC and Geological Survey of Canada (www.earthquakecanada.ca). S(T) for periods shorter than 0.5 s was obtained by using linear interpolation between F(PGA)PGA, F(0.05)Sa(0.05), F(0.1)Sa(0.1), F(0.2)Sa(0.2), F(0.3)Sa(0.3), and F(0.5)Sa(0.5).

The hazard in south western British Columbia comes from movements of tectonic plates along the Pacific Ocean plate, more specifically from: (a) crustal (or shallow) earthquakes in the North American plate, (b) deep in-slab (sub-crustal) events within the down-going Juan de Fuca plate, at a depth of 50 km or more, and (c) large magnitude subduction (or interface) earthquakes occurring at the boundary of the two plates, away from the coast at a depth of approximately 20 km. According to Tremblay et al. (2015), the scenario-specific period ranges are 0.2 ~ 0.8 s for crustal evens, 0.3 ~ 1.5 s for in-slab events, and 1.0 ~ 3.0 s for subduction earthquakes. The Mean M–R (moment magnitude – Closest distance to fault, km) scenarios are 6.7–14 for crustal earthquakes, 7.0–52 for in-slab earthquakes, and 8.6–141 for subduction earthquakes (Tremblay et al. 2015), respectively. These parameters are served as a basis for ground motion selection. A target response spectrum composed of three target spectra (ST1, ST2, and ST3) at scenario-specific period ranges (TRS1, TRS2, and TRS3) is shown in Figure 5.

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Figure 5 Target response spectrums for the three scenarios

Step 3 – Selection of the ground motions Using the mean M–R scenarios parameters discussed in Step 2, the ground motions were selected from the databases of earthquake: the PEER-NGA database for the crustal events, and the K-NET and KiK-net databases for the in-slab and the subduction events. Only the records at sites with shear wave velocity between 180 and 360 m/s corresponding to site class D were retained. In the NBCC Guidelines, at least eleven (11) ground motion time histories is required for dynamic analysis to achieve statistically reliable estimates of mean structural responses while keeping the computational effort within practical limits. In this study, a total of fifteen (15) ground motion time histories were selected, with five (5) ground motions selected from each M-R scenario. Details of the selected ground motion time histories were provided in Table 12.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Spec

tral

Acc

eler

atio

n [g

]

Period [s]

Target Response Spectrum90% LimitCrustal EarthquakeIn-slab EarthquakeSubduction Earthquake

TRS1

(0.2-0.8 s) TRS2

(0.3-1.5 s) TRS3

(1.0-3.0 s)

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Table 12. Earthquake records

No. Event Name or Record Name* Year Magnitude Recording station PGA [g] SF**

CR1 Iprina Italy 1980 6.90 ENEL 99999 Calitri 0.132 2.64

CR2 Imperial Valley 1979 6.53 UNAMUSCD 6621 Chihuahua 0.270 1.41

CR3 Gazli USSR 1976 6.80 9201 Karakyr 0.608 0.79

CR4 San Fernando 1971 6.61 CDMG 24271 Lake Hughes 0.145 3.00

CR5 Northridge 1994 6.69 UCSB 78 Stone Canyon 0.252 1.25

IN1 EHM0160103241528.NS 2001 6.80 EHM016 0.248 1.63

IN2 YMG0180103241528.EW 2001 6.80 YMG018 0.229 1.43

IN3 IWTH200305261824.EW2 2003 6.99 IWTH20 0.323 1.43

IN4 MYG0131104072332.NS 2011 7.11 MYG013 0.570 0.78

IN5 MYG0101104072332.EW 2011 7.11 MYG010 0.274 1.31

SD1 CHB0241103111446.NS 2011 9.08 CHB024 0.229 2.08

SD2 MYG0151103111446.NS 2011 9.08 MYG015 0.434 0.95

SD3 HKD0670309260450.EW 2003 8.26 HKD067 0.355 1.60

SD4 HDKH040309260450.EW2 2003 8.26 HDKH04 0.203 1.44

SD5 KSRH010309260450.EW2 2003 8.26 KSRH01 0.162 1.49

Note: * The even name is unavailable by K-NET and KiK-net databases for the selected in-slab and subduction ground motion records. ** SF is the scaling factor to target response spectrum for Vancouver, BC.

Step 4 – Scaling of the ground motions According to the NBCC Guidelines, each ground motion must be scaled such that its response spectrum Sg(T) generally equals or exceeds the target spectrum ST(T) over the appropriate period range. Scaling factor was established by equalling the area under Sg(T) to that under ST(T). Scaling was performed for each period range TRSi of the M-R scenario considered for the selection of the ground motion. The spectra of the scaled ground motions for each earthquake type are shown in Figures 6 to 8, and the corresponding mean spectra are plotted in Figure 5. Moreover, the NBCC Guidelines require that the mean response spectrum of each scenario-specific suite of time histories does not fall more than 10% below ST(T) over the corresponding period range. To achieve this, the mean response spectrum was further adjusted by a factor of 1.04 for crustal earthquake, 1.06 for in-slab earthquake and 1.21 for subduction earthquake, respectively. The errors between the final mean and target spectra over each period range are plotted in Figure 5. Final scaling factor for each ground motion is listed in Table 12.

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Figure 6 Spectra of scaled ground motion time histories of crustal scenario (0.2 to 0.8 s)

Figure 7 Spectra of scaled ground motion time histories of in-slab scenario (0.3 to 1.5 s)

0.0

0.4

0.8

1.2

1.6

2.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Spec

tral

Acc

eler

atio

n [g

]

Period [s]

0.0

0.4

0.8

1.2

1.6

2.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Spec

tral

Acc

eler

atio

n [g

]

Period [s]

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Figure 8 Spectra of scaled ground motion time histories of subduction scenario (1.0 to 3.0 s)

8. RESULTS AND DISCUSSIONS

The seismic response of the mid-rise wood-frame podium buildings under Maximum Considered Earthquake (MCE) level events was analysed in ABAQUS using implicitly dynamic analysis method through direct integration (Hibbit et al. 2011). The seismic response, in terms of the inter-storey drift, is discussed below.

In this study, performance-based seismic design criteria used in NEESWood project was adopted. The building is considered meeting the performance objective if the inter-storey drift of the building is within 4% with a non-exceedance probability of 80% under MCE, which is earthquake having 2% exceedance probabilities in 50 years (van de Lindt et al. 2010; Pang et al. 2010). Since the storey height is 2.74 m and fifteen scaled seismic ground motion time histories were used in the nonlinear time history analysis, the performance objective is met if no more than three scaled earthquakes resulted in maximum inter-storey drift greater than 110 mm.

8.1 Pure Mid-Rise Wood-Frame Buildings Pure mid-rise wood-frame buildings designed in accordance with the latest NBCC and CSA O86 were analysed under MCE level events. They were used as benchmark cases for evaluating the seismic performance of mid-rise wood-frame buildings on podium designed with two-step analysis procedure.

The maximum inter-storey drift of pure wood-frame buildings is shown in Figure 9. The results show that 3 scaled earthquakes exceeded the 4% inter-story drift in 4-storey building, and 2 scaled earthquakes exceeded the 4% inter-story drift in 5- and 6-storey buildings, respectively. It indicates that the seismic response of the pure mid-rise wood-frame buildings met the seismic performance objective. All maximum inter-storey drifts that exceeded 4% occurred in the top storey and were significantly

0.0

0.4

0.8

1.2

1.6

2.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Spec

tral

Acc

eler

atio

n [g

]

Period [s]

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larger than those in other storeys. More details related to the maximum inter-storey drift can be found in the tables of Appendix I.

Figure 9 Inter-storey drift of pure wood-frame buildings under fifteen scaled ground motions

8.2 Wood-Frame Podium Buildings of Cases I and II The results show that the maximum inter-storey drift of all podium buildings in cases I and II, which had a period ratio of 1.1, exceed the deformation criterion of 4%. As it did not meet the performance criteria, it is not presented. However, it indicates that all mid-rise wood-frame buildings on podium with a period ratio of 1.1 collapsed during MCE level events, thus the period ratio of 1.1 was unsuitable. As noticed, in order to achieve the building period ratio of 1.1, the storey weight of lower structure has to be dramatically larger than the storey weight of upper structure, as listed in Tables 6 and 7. As the weight ratios were unrealistic, it seems to indicate that the building period ratio requirement is unnecessary.

8.3 Wood-Frame Podium Buildings of Cases III and IV The maximum inter-storey drifts of cases III and IV podium buildings are shown in Figures 10 to 12. For mid-rise wood-frame structure on 1-storey concrete podium, the inter-storey drifts were close to those of pure wood-frame buildings, as shown in Figures 10a, 11a and 12a. Except the 4+1 podium buildings with a stiffness ratio of 3 which marginally failed to meet the inter-storey drift criterion, the rest of podium buildings with 1-storey podium met the seismic performance objective. This indicates that the two-step analysis procedure can be used for 5- and 6-storey wood-frame buildings on 1-storey podium with a stiffness ratio of not less than 3. The two-step analysis procedure can be applied to 4-storey wood-frame building on 1-storey podium when the stiffness ratio is not less than 10.

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(a)

(b)

Figure 10 Inter-storey drift of 4-storey pure wood-frame building vs podium buildings on 1-storey (a) and 2-storey (b) podium

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(a)

(b)


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Figures 10b, 11b and 12b show the inter-storey drifts of mid-rise wood-frame structure on 2-storey podium. The results indicate that only 5- and 6-storey wood-frame structures on 2-storey podium with a stiffness ratio of 10 met the inter-storey drift criterion. As a result, the two-step analysis procedure can be used for 5+2 and 6+2 wood-frame podium buildings with a stiffness ratio of not less than 10. The results also indicate that if the two-step analysis procedure is used to design 4+2 wood-frame podium building, a higher stiffness ratio should be required to meet the inter-storey drift criterion.

8.4 Effect of Ground Motions on Inter-Storey Drifts As shown in Figures 9 to 12, greater inter-storey drifts were obtained for both pure mid-rise wood-frame buildings and podium buildings under subduction earthquakes. It was due to the fact that a factor of 1.21 was applied to the subduction ground motions (1.04 and 1.06 were used for crustal and in-slab ground motions, respectively) so that the mean response spectrum did not fall more than 10% below ST(T) over the corresponding period range, as shown in Figure 5. This results in higher mean response spectrum of subduction ground motions than those of crustal and in-slab ground motions. Meanwhile, it is worthwhile pointing out that the scaled subduction ground motions had higher spectral acceleration than crustal and in-slab ground motions between 0.1 and 0.9 s, Figures 10 to 12. This could be another reason for most of the building models had higher seismic response under subduction ground motions.

If the ground motions had not been scaled up to make the mean response spectrum not fall more than 10% below ST(T) over the corresponding period range, or all ground motions were scaled in the three scenario-specific period ranges rather than just one of them, the seismic response of the pure mid-rise wood-frame buildings and podium buildings under subduction earthquake events would be smaller and close to that under crustal and in-slab earthquake events.

9. CONCLUSIONS AND RECOMMENDATIONS

Seismic responses of mid-rise wood-frame structures on 1- or 2-storey podium structure were studied. The podium buildings were designed with two-step analysis procedure in accordance with NBCC or ASCE 7-10. Nonlinear time history dynamic analysis was conducted using the test data scaled according to the latest version of NBCC, with earthquake ground motions selected and scaled based on the guidelines proposed by Tremblay et al. (2015). Using the performance-based seismic design criteria established in the NEESWood project, it was found that:

• Mid-rise buildings on podium with a building period ratio of 1.1 (ASCE 7-10) did not meet the performance criteria, thus the period ratio requirement of 1.1 was not appropriate.

• A stiffness ratio of not less than 10 times (ASCE 7-10) was more appropriate as a requirement of using two-step analysis procedure for mid-rise wood-frame buildings on one or two-storey podium, compared to that of not less than 3 times (NBCC Commentary). With a higher stiffness ratio, the seismic response of the upper wood-frame structure of podium building was closer to that of the pure wood-frame structure.

It is noticed that most podium buildings that had larger inter-storey drifts were shaken by subduction ground motions. It was due to the fact that higher mean response spectrum of subduction ground

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motions was used so that the mean response spectrum did not fall more than 10% below the target response spectrum.

It is suggested that in future the following studies be conducted:

• evaluate the seismic performance of wood-frame podium buildings designed with linear dynamic analysis method. This is to verify whether linear dynamic analysis method can be used to design wood-frame podium buildings up to 8 storeys.

• investigate the seismic response of wood-frame podium buildings with concrete podium having moderate ductility. This is to investigate the impact of non-linear behaviour of concrete podium on the performance of upper wood-frame structure.

10. REFERENCES

ASCE (2010). ASCE/SEI 7-10 Minimum Design Loads For Buildings and Other Structures. American Society of Civil Engineers, Reston, Virginia.

ASCE (2013). ASCE/SEI 41-13 Seismic Evaluation and Retrofit of Existing Buildings. American Society of Civil Engineers, Reston, Virginia.

BSSC (2003). Recommended provisions for seismic regulations for new buildings and other structures – Part 2: Commentary (FEMA 450). Washington, DC: National Institute of Building Sciences, Building Seismic Safety Council (BSSC).

Chen, Z., Chui, Y. H., Ni, C., and Xu, J. (2013). “Seismic response of midrise light wood-frame buildings with portal frames.” J. Struct. Eng., 140(8): A4013003.

Chen, Z., Chui, Y. H., Doudak, G., and Nott, A. (2016). “Contribution of Type-X Gypsum Wall Board to the Racking Performance of Light-Frame Wood Shear Walls.” J. Struct. Eng., 142(5): A4016008.

Chen, Z., Chui Y. H., Doudak, G., Ni, C., and Mohammad, M. (2014). Simulation of the lateral drift of multi-storey light wood frame buildings based on a modified macro-element model. The 13th World Conference on Timber Engineering (WCTE 2014), Quebec City, Canada, Aug. 10-14.

CSA (Canadian Standards Association). (2014). “Engineering design in wood”. CSA O86-14, Mississauga.

Goda, Katsuichiro, and Atkinson, G. M. (2011). “Seismic performance of wood-frame house in south-western British Columbia.” Earthquake Engineering and Structural Dynamics, 40(8): 903-924.

Hibbitt, D., Karlsson, B., and Sorensen, P. (2011). ABAQUS Analysis User’s Manual (Version 6.11), Dassault Systems Simulia Corp., Pawtucket, RI.

Ministry of Housing and Social Development, (2009a). Ministerial Order No. M008, Regulation of the Minister of Housing and Social Development, Province of British Columbia, Victoria, British Columbia, Canada.

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Ministry of Housing and Social Development, (2009b). Ministerial Order No. M121, Regulation of the Minister of Housing and Social Development. Province of British Columbia, Victoria, British Columbia, Canada.

Ministry of Municipal Affair and Housing. (2014). Ontario Regluation 191/14. Regulation of the Minister of Municipal Affair and Housing, Province of Ontario, Canada.

Newfield, G. (2015). Seismic analysis of wood-frame buildings on concrete podium. BC Advisory Group on Advanced Wood Design Solutions.

Ni, C., and Popovski, M. (2015). Mid-rise Wood-Frame Construction Handbook. Special Publication SP57. FPInnovations, Pointe-Claire, QC, Canada.

NRC (2015). National Building Code of Canada. National Research Council of Canada, Ottawa, Ontario.

NRC (2010). User’s Guide – NBCC 2010 Structural Commentaries (Part 4 of Division B). National Research Council of Canada, Ottawa, Ontario.

Pang, W., Rosowsky, D. V., Pei, S., and van de Lindt, J.W. (2010). “Simplified direct displacement design of six-story woodframe building and pretest seismic performance assessment.” J. Struct. Eng., 136(7), 813–825.

RBQ (2013). Construction d’habitations en bois de 5 ou 6 étages. Régie du bâtiment du Québec, QC.

Tremblay, R., Atkinson, G. M., Bouaanani, N., et al. (2015). Selection and scaling of ground motion time histories for seismic analysis using NBCC 2015. The 11th Canadian Conference on Earthquake Engineering (11CCEE), Victoria, Canada, July. 21-24.

Triggs, G. (2015). Review of building code approaches for podium structures – Western US examples. BC Advisory Group on Advanced Wood Design Solutions.

van de Lindt, J. W., Pei, S., Pryor, S. E., Shimizu, H., and Isoda, H. (2010). “Experimental seismic response of a full-scale six-storey light-frame wood building.” J. Struct. Eng., 136(10): 1262-1272.

Xu, J., and Dolan, J. D. (2009a). “Development of nailed wood joint element in ABAQUS.” J. Struct. Eng., 135(8), 968-976.

Xu, J., and Dolan, J. D. (2009b). “Development of a wood-frame shear wall model in ABAQUS.” J. Struct. Eng., 135(8), 977-984.

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APPENDIX I MAXIMUM INTER-STOREY DRIFT OF BUILDING MODELS

The maximum inter-storey drift of each storey of analysed building models were listed.

Table 13. Inter-storey drift [%] of 4-storey wood-frame buildings

Earthquake CR1 CR2 CR3 CR4 CR5 IN1 IN2 IN3 IN4 IN5 SD1 SD2 SD3 SD4 SD5

W4 4.6 1.7 2.0 1.6 1.4 1.5 2.9 1.8 2.9 2.8 7.6 4.6 1.2 2.0 2.4

W3 1.9 1.0 1.2 2.0 1.0 1.4 1.3 1.2 1.2 1.4 2.7 2.0 1.3 1.8 1.2

W2 1.4 0.7 1.1 2.2 0.7 1.3 1.1 1.1 1.1 1.1 2.0 1.5 1.6 1.8 1.2

W1 1.5 0.7 1.3 2.9 0.8 1.5 1.2 1.3 1.0 1.0 3.3 2.4 2.3 1.9 1.5

Max 4.6 1.7 2.0 2.9 1.4 1.5 2.9 1.8 2.9 2.8 7.6 4.6 2.3 2.0 2.4

Note: The highlighted maximum inter-storey drifts are greater than the criterion of 4% storey height, 110 mm.



W5 3.6 1.2 1.3 1.1 1.2 1.1 1.7 1.7 2.0 2.5 5.6 5.9 1.2 1.4 1.9

W4 1.9 1.0 1.1 1.6 1.0 1.3 1.6 1.1 1.6 1.5 2.5 1.8 1.1 1.6 1.5

W3 1.4 0.8 1.0 1.9 0.6 1.3 1.1 1.0 1.0 1.0 1.9 1.4 1.1 1.7 1.4

W2 1.3 0.6 1.2 2.0 0.6 1.3 1.0 0.9 1.1 1.1 2.1 1.4 1.6 1.5 1.6

W1 1.3 0.5 1.3 2.3 0.8 1.4 0.9 1.0 1.0 1.0 2.2 1.9 2.1 1.8 1.6

Max 3.6 1.2 1.3 2.3 1.2 1.4 1.7 1.7 2.0 2.5 5.6 5.9 2.1 1.8 1.9



W6 3.1 1.3 1.2 1.2 1.1 1.2 1.3 1.4 1.6 1.9 3.6 5.7 1.5 1.8 4.3

W5 1.8 1.0 1.0 1.4 1.1 1.5 1.4 1.0 1.6 2.2 2.7 2.0 1.2 1.3 2.3

W4 1.3 0.8 1.0 1.6 0.6 1.6 1.0 1.0 1.0 1.4 2.0 1.5 1.2 1.7 1.5

W3 1.1 0.5 1.0 1.5 0.7 1.2 1.0 0.8 0.9 1.0 1.7 1.3 1.1 1.8 1.3

W2 1.3 0.6 1.1 1.8 0.7 1.1 0.9 0.9 0.9 1.1 1.7 1.8 1.5 1.5 1.1

W1 1.1 0.6 1.1 2.0 0.8 1.4 0.8 0.9 0.8 1.0 2.1 1.9 2.9 1.5 1.8

Max 3.1 1.3 1.2 2.0 1.1 1.6 1.4 1.4 1.6 2.2 3.6 5.7 2.9 1.8 4.3

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Table 16. Inter-storey drift [%] of 4+1 podium buildings with a stiffness ratio of 3


W4 4.2 1.9 1.9 1.7 1.9 2.0 1.7 2.0 2.9 2.5 6.4 6.0 2.2 3.7 3.2

W3 2.1 1.3 2.3 1.5 1.0 1.4 1.4 1.6 1.9 1.5 3.5 3.5 3.2 2.3 1.6

W2 2.0 1.0 1.7 2.5 1.8 1.7 1.2 1.6 1.7 1.7 3.3 3.8 2.3 1.7 1.5

W1 3.2 1.0 1.5 3.0 1.8 1.9 1.3 2.1 2.0 1.8 3.6 4.5 4.5 1.9 2.3

C1 0.7 0.6 0.8 0.7 0.7 0.8 0.6 0.8 0.8 0.8 0.6 0.9 1.1 0.5 0.3

Max 4.2 1.9 2.3 3.0 1.9 2.0 1.7 2.1 2.9 2.5 6.4 6.0 4.5 3.7 3.2



W4 4.2 1.4 2.1 1.5 1.3 2.0 2.1 1.2 3.2 3.1 7.2 4.9 2.9 2.1 1.8

W3 2.0 1.0 1.7 2.1 0.9 1.7 1.4 1.2 1.2 1.6 2.7 2.5 2.0 2.1 1.4

W2 1.4 0.9 1.2 2.2 0.8 1.2 1.3 1.5 1.0 1.6 2.4 1.8 2.3 1.8 1.2

W1 1.8 0.9 2.9 2.7 1.1 1.7 1.5 2.7 1.1 2.4 3.6 3.0 3.9 2.1 1.9

C1 0.2 0.2 0.3 0.2 0.2 0.2 0.2 0.4 0.2 0.5 0.2 0.2 0.7 0.1 0.1

Max 4.2 1.4 2.9 2.7 1.3 2.0 2.1 2.7 3.2 3.1 7.2 4.9 3.9 2.1 1.9



W4 4.8 1.6 1.5 3.8 2.5 2.4 2.8 4.2 2.7 3.9 4.7 9.7 5.2 4.9 2.3

W3 3.0 1.9 1.5 2.6 1.8 2.2 2.4 3.1 2.4 3.0 4.2 6.6 3.2 2.9 2.0

W2 4.8 1.5 2.1 3.4 1.6 3.6 2.6 2.0 2.3 3.6 4.1 5.5 3.1 2.5 2.5

W1 6.1 2.6 7.0 5.8 2.5 3.0 3.2 2.9 3.8 4.1 7.9 7.8 3.8 6.8 5.6

C1 0.9 0.7 0.7 0.7 0.8 0.8 0.8 1.0 1.3 1.2 1.0 2.6 0.9 0.6 0.4

C2 1.1 0.8 0.8 0.9 1.2 1.1 1.0 1.6 1.3 1.3 1.3 3.1 1.0 0.8 0.5

Max 6.1 2.6 7.0 5.8 2.5 3.6 3.2 4.2 3.8 4.1 7.9 9.7 5.2 6.8 5.6

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W4 3.9 1.6 2.8 3.8 1.9 1.8 1.7 1.4 1.9 2.2 6.8 5.1 2.4 2.9 4.4

W3 2.5 1.3 1.7 1.9 1.1 1.9 1.7 1.9 1.7 1.8 4.0 3.5 2.5 2.1 1.5

W2 2.3 1.1 1.2 1.4 1.0 1.8 1.7 1.6 1.4 2.0 2.7 2.9 3.0 2.3 1.4

W1 2.3 1.7 1.5 2.9 1.2 2.6 1.9 3.5 2.7 2.8 2.8 4.1 8.3 2.3 1.9

C1 0.3 0.4 0.3 0.2 0.3 0.3 0.3 0.5 0.5 0.6 0.3 0.2 0.6 0.1 0.1

C2 0.4 0.4 0.3 0.3 0.4 0.4 0.4 0.7 0.6 0.6 0.4 0.3 0.8 0.2 0.2

Max 3.9 1.7 2.8 3.8 1.9 2.6 1.9 3.5 2.7 2.8 6.8 5.1 8.3 2.9 4.4



W5 3.4 1.6 1.5 1.6 1.5 1.5 1.9 1.8 1.8 1.9 4.4 4.8 1.6 2.3 2.5

W4 2.0 1.1 1.4 2.0 1.2 1.1 1.3 1.4 1.3 1.6 4.5 2.5 1.7 2.2 2.6

W3 1.7 0.9 1.2 2.4 1.1 1.4 1.3 1.4 1.2 1.5 2.0 2.0 1.6 1.8 1.5

W2 1.7 0.9 1.1 1.9 0.9 1.3 1.2 1.6 1.4 1.7 2.0 2.6 2.3 1.3 1.5

W1 1.8 1.1 1.3 2.1 1.1 1.9 1.4 2.1 1.5 1.6 2.7 3.0 4.7 1.9 2.1

C1 0.7 0.6 0.6 0.5 0.6 0.7 0.5 0.6 0.7 0.6 0.4 0.6 1.0 0.4 0.3

Max 3.4 1.6 1.5 2.4 1.5 1.9 1.9 2.1 1.8 1.9 4.5 4.8 4.7 2.3 2.6



W5 3.9 1.4 1.4 1.4 1.3 1.2 2.0 1.2 2.1 2.0 2.5 4.1 2.2 1.6 1.9

W4 1.8 1.0 1.1 1.7 1.0 1.4 1.3 1.2 1.3 1.4 2.9 2.4 1.9 1.8 1.5

W3 1.3 0.7 1.0 1.8 0.6 1.3 1.1 1.3 1.0 1.3 2.0 1.7 1.7 3.3 1.6

W2 1.2 0.6 1.3 2.0 0.8 1.1 1.0 1.3 0.9 1.5 1.5 1.6 1.7 1.3 1.5

W1 1.3 0.6 1.6 2.6 0.8 1.6 1.0 2.0 1.0 2.0 2.2 2.2 3.5 1.8 1.9

C1 0.2 0.1 0.3 0.2 0.1 0.2 0.2 0.3 0.2 0.3 0.2 0.1 0.6 0.1 0.1

Max 3.9 1.4 1.6 2.6 1.3 1.6 2.0 2.0 2.1 2.0 2.9 4.1 3.5 3.3 1.9

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W5 3.6 2.2 4.6 3.7 1.6 2.3 2.7 2.2 2.1 3.0 5.4 4.7 3.1 2.9 4.8

W4 2.5 1.4 1.9 3.0 1.5 2.3 1.5 1.8 2.0 2.6 3.1 6.9 2.7 2.6 2.2

W3 2.5 1.4 1.1 2.0 1.4 2.1 1.8 1.5 1.6 3.3 2.9 4.8 2.5 2.4 1.6

W2 2.1 1.1 1.2 1.9 1.8 2.4 1.5 2.0 2.0 2.8 3.3 4.2 2.8 2.1 1.8

W1 3.2 1.6 1.8 2.3 2.2 2.1 2.2 4.0 2.6 3.4 3.6 9.1 4.9 3.4 1.7

C1 0.8 0.6 0.7 0.6 0.7 0.7 0.7 0.8 0.9 1.1 0.8 1.6 1.0 0.5 0.3

C2 1.0 0.8 0.8 0.7 1.1 1.0 0.9 1.2 1.3 1.3 1.0 2.4 1.0 0.7 0.5

Max 3.6 2.2 4.6 3.7 2.2 2.4 2.7 4.0 2.6 3.4 5.4 9.1 4.9 3.4 4.8



W5 2.2 1.5 1.5 3.0 1.6 1.8 1.4 1.6 1.3 1.8 4.1 3.6 1.9 1.6 3.2

W4 1.7 1.1 1.2 2.4 1.0 1.3 1.1 1.5 1.3 1.8 3.6 2.3 1.6 1.8 1.6

W3 1.5 0.9 1.1 2.2 1.0 1.4 1.0 2.2 1.2 1.7 1.8 2.6 1.9 1.8 1.3

W2 1.7 1.0 1.6 1.8 0.8 1.8 1.2 2.3 1.4 1.9 2.0 2.1 3.0 2.0 1.4

W1 2.2 1.3 1.7 2.2 0.8 2.2 1.5 2.9 1.8 2.2 2.3 3.4 6.3 2.2 1.9

C1 0.3 0.2 0.3 0.2 0.2 0.3 0.3 0.3 0.3 0.4 0.2 0.2 0.5 0.1 0.1

C2 0.3 0.3 0.3 0.2 0.3 0.4 0.4 0.4 0.5 0.5 0.3 0.3 0.6 0.2 0.1

Max 2.2 1.5 1.7 3.0 1.6 2.2 1.5 2.9 1.8 2.2 4.1 3.6 6.3 2.2 3.2

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W6 2.5 1.6 1.6 2.3 1.7 1.7 1.2 1.4 1.7 1.9 3.4 3.7 1.7 1.8 4.7

W5 1.7 1.4 1.1 2.0 1.0 1.6 1.1 1.0 1.3 1.8 2.7 2.6 1.7 1.9 2.7

W4 1.4 1.3 1.3 1.5 0.8 1.2 0.9 1.0 1.1 1.3 2.3 2.4 1.8 1.7 1.8

W3 1.5 1.1 1.1 1.4 0.9 1.3 1.1 1.5 1.1 1.3 2.2 2.0 1.8 1.7 1.6

W2 1.8 1.0 1.1 1.3 0.9 1.5 1.0 1.7 1.2 1.4 2.1 2.6 2.6 1.7 1.7

W1 2.1 1.1 1.1 1.5 0.9 1.9 1.1 2.6 1.3 1.7 2.8 3.9 4.5 2.1 1.7

C1 0.6 0.5 0.5 0.5 0.5 0.6 0.5 0.7 0.6 0.6 0.4 0.5 1.0 0.4 0.3

Max 2.5 1.6 1.6 2.3 1.7 1.9 1.2 2.6 1.7 1.9 3.4 3.9 4.5 2.1 4.7



W6 3.2 1.3 1.0 1.4 1.2 1.4 1.7 1.4 1.8 1.6 3.1 4.9 1.6 1.6 3.5

W5 1.5 1.0 0.9 1.3 1.1 1.6 1.2 0.9 1.4 1.3 2.2 2.1 1.6 1.5 2.5

W4 1.3 0.7 1.0 1.4 0.6 1.2 1.2 0.9 1.0 1.3 1.8 1.6 1.5 1.6 1.5

W3 1.2 0.6 1.0 1.5 0.7 1.1 1.0 1.0 0.9 1.0 1.6 1.4 1.9 1.7 1.2

W2 1.0 0.6 1.2 1.7 0.8 1.1 1.0 1.5 0.9 1.5 1.7 2.0 2.4 1.5 1.7

W1 1.2 0.7 2.2 2.1 0.9 1.7 0.9 2.5 0.9 1.6 1.8 2.4 3.6 1.6 2.0

C1 0.1 0.1 0.2 0.1 0.1 0.2 0.1 0.2 0.2 0.3 0.2 0.1 0.4 0.1 0.1

Max 3.2 1.3 2.2 2.1 1.2 1.7 1.7 2.5 1.8 1.6 3.1 4.9 3.6 1.7 3.5

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W6 3.4 2.2 1.9 2.9 1.7 1.5 1.9 1.7 1.7 2.4 4.5 7.2 3.3 3.4 7.1

W5 2.6 1.6 1.4 2.2 1.1 1.8 1.7 1.3 1.5 2.0 3.1 2.5 2.0 2.0 2.3

W4 2.0 1.2 1.3 1.9 1.6 1.7 1.6 1.9 1.7 2.3 2.5 3.4 2.0 1.8 1.6

W3 1.7 1.1 1.2 1.6 1.4 1.7 1.6 1.9 1.7 2.3 2.8 3.8 2.2 1.8 1.8

W2 2.3 1.3 1.4 1.8 1.6 1.7 1.7 2.0 1.8 3.1 3.2 3.8 3.0 2.1 1.5

W1 2.7 1.3 1.5 1.8 2.1 2.1 1.3 4.1 2.2 3.5 5.7 5.4 5.0 4.3 1.8

C1 0.7 0.5 0.7 0.5 0.7 0.5 0.6 0.9 0.9 0.9 0.7 1.2 0.9 0.4 0.3

C2 0.9 0.8 0.7 0.6 1.0 0.8 0.7 1.1 1.2 1.1 1.0 1.7 1.0 0.6 0.4

Max 3.4 2.2 1.9 2.9 2.1 2.1 1.9 4.1 2.2 3.5 5.7 7.2 5.0 4.3 7.1



W6 1.7 1.4 1.3 2.1 1.6 1.9 1.4 1.5 1.3 2.2 2.7 3.1 1.6 1.8 4.8

W5 1.6 1.3 1.1 1.6 1.0 1.4 1.0 1.5 1.3 1.5 2.2 2.1 1.6 1.5 2.4

W4 1.2 1.0 1.0 1.5 0.8 1.3 1.1 1.5 1.1 1.6 2.3 2.2 1.8 1.7 1.9

W3 1.5 0.8 1.2 1.3 0.9 1.3 1.1 1.5 1.1 1.6 2.1 1.6 1.7 1.8 1.6

W2 1.7 1.1 1.1 1.4 0.9 1.4 1.2 2.2 1.2 1.6 2.1 2.2 2.6 1.8 1.6

W1 1.7 1.3 1.2 1.7 0.9 1.7 1.5 2.7 1.3 1.9 2.3 3.8 6.0 1.9 1.6

C1 0.3 0.2 0.2 0.1 0.2 0.2 0.2 0.3 0.3 0.3 0.2 0.2 0.4 0.1 0.1

C2 0.3 0.3 0.3 0.2 0.3 0.3 0.3 0.5 0.4 0.5 0.3 0.2 0.6 0.2 0.1

Max 1.7 1.4 1.3 2.1 1.6 1.9 1.5 2.7 1.3 2.2 2.7 3.8 6.0 1.9 4.8

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seismic response of mid-rise wood- frame buildings on podium

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