Department of Architecture and Civil Engineering Division of Structural engineering Steel and timber structures CHALMERS UNIVERSITY OF TECHNOLOGY Master’s Thesis ACEX30-18-54 Gothenburg, Sweden 2018 Horizontal stabilization of a trä8 building using glulam trusses Finite element analysis of a multiple storey building in timber Master’s thesis in the Master’s Programme Structural Engineering and Building Technology STINA ÅKESSON MASTER’S THESIS ACEX30-18-54 Horizontal stabilization of a trä8 building using glulam trusses Finite element analysis of a multiple storey building in timber Master’s Thesis in the Master’s Programme Structural Engineering and Building Technology STINA ÅKESSON Department of Architecture and Civil Engineering Division of Structural engineering Steel and timber structures CHALMERS UNIVERSITY OF TECHNOLOGY Göteborg, Sweden 2018 I Horizontal stabilization of a trä8 building using glulam trusses Finite element analysis of a multiple storey building Master’s Thesis in the Master’s Programme Structural Engineering and Building Technology STINA ÅKESSON © STINA ÅKESSON, 2018 Examensarbete ACEX30-18-54 Institutionen för arkitektur och samhällsbyggnadsteknik Chalmers tekniska högskola, 2018 Department of Architecture and Civil Engineering Division of Structural engineering Research Group Name Chalmers University of Technology SE-412 96 Göteborg Sweden Telephone: + 46 (0)31-772 1000 Cover: The eigenmode of the building modelled with six storeys and floor stiffness of 80 %. Additional trusses A, B and C are added to the structure. See Appendix B, page B87. Department of Architecture and Civil Engineering Göteborg, Sweden, 2018 I Horizontal stabilization of a trä8 building using glulam trusses Finite element analysis of a multiple storey building in timber Master’s thesis in the Master’s Programme Structural Engineering and Building Technology STINA ÅKESSON Department of Architecture and Civil Engineering Division of Structural engineering Steel and timber structures Chalmers University of Technology ABSTRACT Due to an increasing environmental awareness along with a need of building high-rise buildings the demand of multiple storey timber buildings has reached its highest yet. Trä8 is a construction method for constructing multiple storey timber buildings developed by Moelven Töreboda. As timber is a light-weight construction material stability is often a concern for high-rise timber buildings. Frostaliden 3 is a newly built residential building in Skövde which was constructed using the trä8 method. This thesis refers to investigate the horizontal stability of this building modelled with four and six storeys. For the purpose of the thesis the glulam trusses were designed, and the complete structure of the building was modelled in a finite element software, RFEM, in order to investigate its static and dynamic behaviour. The stiffness of the floor is not yet established. The stiffness has been estimated to between 35 and 80 % of the stiffness of one floor element. The modelling in this thesis was therefore done including two cases of floor stiffness, within which range the actual stiffness will be. For the static behaviour of the structure the horizontal displacements were examined and compared to the limit set at L/500 for the four- and the six-storey model. The results showed to be within limits for both heights and both modelled stiffnesses. For the dynamic analysis guidelines are provided in ISO 10137 in terms of fundamental eigenfrequency and wind peak acceleration. For the six-storey model the results exceeded the guidelines except for the most favourable case with stiffness of 80 % and wind acting on the short side. For the four-storey building all cases showed to be within the limits except for the worst case, 35 % stiffness and wind on the long side. The analysis further showed that the importance of additional trusses and floor stiffnesses decreases with increasing building height. For tall buildings it is not enough to add trusses or stiffer floor elements, other measures need to be taken in order to increase the fundamental frequency, such as increasing the structures stiffness or adding dampers. Key words: timber engineering, trä8, tall timber buildings II Horisontell stabilisering av en trä8-byggnad med hjälp av limträfackverk FE-analys på ett flervåningshus i trä Examensarbete inom masterprogrammet Structural Engineering and Building Technology STINA ÅKESSON Institutionen för arkitektur och samhällsbyggnadsteknik Avdelningen för Konstruktionsteknik Stål- och träbyggnad Chalmers tekniska högskola SAMMANFATTNING På grund av dagens miljömedvetenhet samt det ökande behovet av att bygga på höjden har efterfrågan på flervåningshus i trä nått sin högsta nivå hittills. Trä8 är en byggnadsmetod, för att konstruera flervåningshus i trä, som är framtagen av Moelven Töreboda. Eftersom trä har en låg egenvikt kan stabiliteten utgöra problem för höga träbyggnader. Frostaliden 3 är ett nybyggt lägenhetshus i Skövde som är konstruerat med trä8- metoden. Projektet avser att undersöka den horisontella stabiliteten i denna byggnad modellerad med fyra respektive sex våningar. I detta syfte har limträfackverken designats och den sammansatta stommen har vidare modelleras i RFEM, ett program baserat på finita elementmetoden, där dess statiska och dynamiska egenskaper undersökts. Styvheten på golvet är ännu inte fastställd. Styvheten har estimerats till mellan 35 och 80 % av styvheten för ett golvelement. Modelleringen i detta projekt kommer därför göras för två fall som representerar lägsta och högsta möjliga styvheten. För den statiska analysen undersöktes byggnadens horisontella förskjutningar vilka jämfördes med gränsvärdet på L/500 för fyra- och sexvåningsmodellen. Resultaten visade sig vara inom gränsvärdena för bägge byggnadshöjderna och för bägge modellerade styvheter. För den dynamiska analysen ges riktlinjer i ISO 10137 som involverar första egenfrekvensen samt maximala vind accelerationen. För sexvåningsmodellen överstiger resultaten riktlinjerna för alla fall utom det mest fördelaktiga med styvhet på 80 % och vind mot kortsidan. För modellen med fyra våningar var samtliga fall inom riktlinjerna förutom det mest kritiska med styvhet på 35 % och vind mot långsidan. Analysen visade vidare att effekten från ytterligare fackverk samt styvhet i golvelementen minskar då byggnadshöjden ökar. För höga byggnader räcker det inte med extra fackverk eller styvare golvelement, för att uppnå riktlinjerna krävs åtgärder för att öka egenfrekvensen genom att göra stommen styvare eller lägga in dämpare. Nyckelord: träkonstruktioner, trä8, höga trähus CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 III Contents ABSTRACT I SAMMANFATTNING II CONTENTS III PREFACE V 1 INTRODUCTION 1 1.1 Background 1 1.2 Aim 2 1.3 Research questions 2 1.4 Limitations and assumptions 2 1.5 Disposition 2 2 THEORETICAL BACKGROUND 4 2.1 Horizontal stabilization of structures 4 2.2 Dynamic behaviour of structures 6 2.2.1 Recommended guidelines 7 2.3 Finite element modelling 8 2.4 Timber as a construction material 9 2.4.1 Glulam 9 2.4.2 LVL 12 2.5 The construction method trä8 12 3 BASIS OF ANALYSIS 14 3.1 Frostaliden 3 14 3.1.1 Modifications in the building model 15 3.2 Computational aids 16 3.2.1 RFEM 17 3.2.2 Statcon 17 4 METHOD 18 4.1 Literature study 18 4.2 Design of glulam trusses 18 4.2.1 Calculation of forces 18 4.2.2 Dimensioning of glulam components 18 4.2.3 Design of dowelled connections 19 4.3 Analysis of the complete structure 20 4.3.1 Modelling of building structure 20 4.3.2 Static analysis 21 CHALMERS, Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 IV 4.3.3 Dynamic analysis 21 5 RESULTS 23 5.1 Static analysis 23 5.2 Dynamic analysis 24 6 DISCUSSION 29 6.1 Analysis of static results 29 6.2 Analysis of dynamic results 29 6.3 Method and assumptions 30 7 CONCLUSIONS 32 7.1 Suggestions on further research 32 REFERENCES 33 APPENDIX A – Drawings APPENDIX B – Results from computational software APPENDIX C – Hand calculations CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 V Preface This master thesis was carried out as the concluding part of the master programme Structural Engineering and Building Technology which is part of the five-year civil engineering programme at Chalmers University of Technology. The thesis was carried out at Moelven Töreboda from January 2018 to June 2018. I want to thank my colleagues at Moelven Töreboda for all help and support throughout this thesis, especially Fredrik Morell for initiating the project and Thomas Johansson who has been the supervisor. Further thanks to my supervisor at Chalmers Rasoul Atashipour and examiner Mohammad Al-Emrani, and lastly opponents Hanna Närhi and Viktor Wiberg. Töreboda, June 2018 Stina Åkesson CHALMERS, Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 VI CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 1 1 Introduction A challenge when constructing high-rise timber buildings is to ensure the stability. Compared to its load carrying capacity timber has a light self-weight. This is regarded as one of the many advantages of timber as a construction material as it facilitates erection. However, regarding dynamic performance a light self-weight is not favourable and as a result the stability, with regard to dynamic motions, can become an issue for high-rise timber buildings. The focus of this project is to investigate how horizontal stability against wind forces can be achieved in trä8 buildings using glulam trusses. 1.1 Background A reason behind the increasing popularity of timber constructions, is that timber in many ways can be regarded as an environmentally friendly construction material. In the Report of the World Commission on Environment and Development: Our Common Future the term sustainable development is explained as a development in order to meet today’s needs without compromising future generations ability to meet theirs (NGO Committee on Education, 1987). Consequently, with timber being a renewable resource (Svenskt trä, 2003), usage of timber goes in line with what is stated as a sustainable development. Furthermore, a big threat to our environment is the increasing global warming (Naturvårdsverket, 2017). The reason for the rising temperatures is a number of greenhouse gases which has increased in quantity due to human impact. The foremost greenhouse gas is carbon dioxide and with timber being part of the natural carbon cycle, it is not considered as a contributor to the increasing carbon dioxide in our atmosphere. Further proving timber to be a good choice of material with regard to the environment. As the populations continues to rise in the big cities of Sweden (Statistiska centralbyrån, 2018) so does the demand of constructing high-rise buildings. High-rise buildings have been constructed for centuries (Guinness World Records, 2018) although construction of high-rise buildings made of timber is comparatively new. In fact, constructing timber buildings of more than two storeys were prohibited in Sweden until the mid 90’s (Näringsdepartementet, 2004). Today due to the increasing environmental awareness the demand of high-rise buildings constructed in timber has reached its highest yet. However, construction of high-rise timber buildings is not a matter of course, but by overcoming the challenges of the material a step towards sustainable building is ensured. Trä8 is a construction method used for construction of high-rise timber buildings developed by Moelven Töreboda (Moelven Töreboda AB, n.d.). Trä8 refers to a post beam structure that was originally stabilized by shear walls and rigid floor elements made of timber. It has been found that the capacity of the shear walls was not adequate (Tlustochowicz, Johnsson, & Girhammar, 2010) and these walls are now commonly replaced by glulam trusses. The trusses have shown to perform better than the shear walls, but further research of the trusses has not currently been made1. 1 Thomas Johansson, Structural engineer at Moelven Töreboda. Interview 2018-01-22. CHALMERS, Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 2 1.2 Aim This project aims to investigate the horizontal stability, with regard to wind forces, of a trä8 building stabilized by glulam trusses. Investigations are carried out for a six- and a four-storey model of the building Frostaliden 3 in Skövde. For the purpose of the thesis the glulam trusses are designed regarding sizing and connections to withstand the vertical and horizontal forces they are exposed to. By modelling the complete structure of the building, the response is examined through a finite element analysis regarding horizontal static displacements and further the dynamic performance involving eigenfrequency and peak acceleration. 1.3 Research questions Following questions are to be answered in the thesis. • Does the four- and six-storey building fulfil the demands regarding static behaviour? • Does the four- and six-storey building fulfil the demands regarding dynamic behaviour? • How does the difference in building height affect the results? 1.4 Limitations and assumptions Calculations of dimensions and connections of this building are limited to the trusses. Other components such as beams, columns and floor- and roof elements and also the connections between them is not considered in design and when modelling the complete structure, the dimension of these members are taken from the original design performed by the responsible engineer. As the actual stiffness of the floor construction is yet to be determined the precise behaviour of the building cannot be established. The rigidity of each floor element is provided by a Kerto Q board and for this thesis the rigidity of the floor has been modelled by 35 % and 80 % of the stiffness of the board, within which range the actual stiffness is approximated to according to engineers involved with the particular floor elements. As a result, the actual behaviour of the building cannot be determined, the findings will rather circle the range of which the performance vary with respect to the stiffness of the floor construction. Furthermore, also the stiffness of the connections between the glulam members is unknown. The connections, consisting of steel plates and dowels, will in reality have some resistance regarding moment but for this thesis all joints have been modelled as moment free as the actual stiffness is not determined. This applies not only for the trusses, but for all members of the structure. The performance of the building model is only analysed with regard to wind induced motions. Motions and vibrations due to other sources such as footsteps, earthquakes and accidents is not considered. Moreover, other aspects such as durability, fatigue, manufacturing, foundation work or economic concerns is not covered. 1.5 Disposition Following of this introduction is a theory chapter that describes some background and theory on which this thesis is based. Thereafter comes a chapter describing the considered object and the aids of the project and later a chapter describing the CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 3 methods used for achieving the aims. Further the results are presented and discussed and in the last chapter the conclusions are drawn. In the following appendixes drawings, output data and calculations are gathered. CHALMERS, Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 4 2 Theoretical background This chapter consists of gathered information that describes the theory on which this project is based. The knowledge of this chapter was obtained as a result of an initial literature study. 2.1 Horizontal stabilization of structures In order to make a structure stable it needs to be able to resist horizontal forces. A regular frame with moment free joints is not stable in its plane, see Figure 2.1A. In order to obtain stability there are a few possible alternatives: either by adding a diagonal, Figure 2.1B, adding stiff connections , Figure 2.1C and Figure 2.1D, or by adding a rigid plate, Figure 2.1E (Swedish wood, 2015). Figure 2.1. Methods on creating a stable frame construction. To obtain horizontal stability for a building, one of these methods, see Figure 2.1, or combinations of them must be included in the structure (Swedish wood, 2015). Dependent on how the stabilizing frames are placed with regard to each other, the response of the building will differ. Considering the roof as rigid in its plane stability can be obtained as long as there are at least three stabilizing elements that are not parallel and does not meet in one common point (Svenskt trä, 2016b). In Figure 2.2 this is illustrated. Figure 2.2A shows the case where all elements are parallel, this only gives stability in one direction which is not sufficient. In Figure 2.2B all the elements have a common meeting point, this will cause rotation around this point which makes the construction unstable. By using only two elements, the elements will either be parallel or have a common meeting point, which means that two elements are too few. Figure 2.2C and Figure 2.2D fulfils all the criteria for a horizontally stable construction. However, the arrangement in Figure 2.2C cause torsional forces (Swedish wood, 2015). The size of the torsional forces depends on the size and shape of the building. If these forces become too large problems with regard to deformation might occur. A way to overcome the torsional forces is to place the stabilizing elements symmetrically in the structure as seen in Figure 2.2D. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 5 Figure 2.2 How the location of the stabilizing elements will affect the buildings behaviour. For large buildings, requiring several stabilizing elements in the same direction, the force distribution will depend on the rigidity of the elements and the roof (Swedish wood, 2015). In Figure 2.3 models of a simple rectangular building with four equally spaced stabilizing elements is illustrated. In Figure 2.3A the model consists of a rigid roof and four, comparatively less rigid, stabilizing units. As the stabilizing units are of equal stiffness the same force will be acting in each of these units. In Figure 2.3B the roof is identical as in Figure 2.3A but the rigidity of the two middle units is decreased, due to less rigidity these will uptake less load linearly dependent of their rigidity. In Figure 2.3C the roof is flexible compared to the stabilizing units. This gives that the load resisted by each unit is dependent on the span length between them and not their rigidity. So in Figure 2.3A and Figure 2.3B the roof is considered as infinitely rigid compared to the stabilizing elements and in Figure 2.3C they are considered as infinitely rigid compared to the flexible roof. In reality there will obviously occur cases that are between these two extremes. CHALMERS, Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 6 Figure 2.3 Distribution of reaction forces between stabilizing elements. 2.2 Dynamic behaviour of structures A mass-spring system can be used to illustrate a dynamic behaviour (Strømmen, 2014). A mass attached to a spring set in motion will start to oscillate, however this oscillation will in reality eventually die out leaving the system at rest once again. This damping that occurs in reality is modelled by adding a damper to the system, see Figure 2.4. Figure 2.4 Simple mass-spring system with damper and an external time dependent force. The dynamic equilibrium for the system presented in Figure 2.4 can be described by the equation of motion, see Equation (2.1) (Strømmen, 2014). For the equation of motion 𝑚 denotes the mass in kg, 𝑐 is the damping coefficient in Ns/m and 𝑘 is the elastic spring constant in N/m. 𝐹(𝑡) is an external force in N and �̈�(𝑡), �̇�(𝑡) and 𝑢(𝑡) describes acceleration, velocity and displacement in m/s2, m/s and m respectively. 𝑚�̈�(𝑡) + 𝑐�̇�(𝑡) + 𝑘𝑢(𝑡) = 𝐹(𝑡) (2.1) The eigenfrequency, or the natural frequency, of a system is a frequency for which the system will oscillate without any driving forces. This means that very small forces applied with this frequency can cause vibrations of great amplitude. For an undamped system the eigenfrequency can be determined by using Equation (2.2) (Strømmen, 2014). CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 7 𝜔𝑛 = √𝑘 𝑚⁄ (2.2) Using the eigenfrequency for the undamped case, the damping ratio can be determined for damped systems by Equation (2.3) (Strømmen, 2014). 𝜁𝑛 = 𝑐2𝑚𝜔𝑛 (2.3) If the value of the damping ratio, 𝜁𝑛, is equal to or greater than one this means that no oscillations will occur (Strømmen, 2014). Therefore, no eigenfrequency can be obtained for such systems. When 𝜁𝑛<1 the damped eigenfrequency can be calculated using Equation (2.4). 𝜔𝑑 = 𝜔𝑛√1 − 𝜁𝑛2 (2.4) Once the eigenfrequency of a given system is obtained the corresponding eigenmode, 𝜑, can be determined from Equation (2.5) (Strømmen, 2014). The eigenmode is also called the shape mode and describes the shape of the oscillating system. (𝑘 − 𝜔2𝑚)𝜑 = 0 (2.5) In this chapter the equation of motion is described for a system with only one degree of freedom, it is however applicable for all kind of systems (Strømmen, 2014). For multiple degree of freedom systems, the factors for mass, damping and stiffness will be arranged in matrices with number of columns and rows corresponding to the degrees of freedom and �̈�(𝑡), �̇�(𝑡), 𝑢(t) and 𝐹(𝑡) becomes vectors of equal length. Consequently, this results in multiple eigenfrequencies and corresponding eigenmodes, and the resulting shape of motion is usually a combination of all or some of the eigenmodes. The lowest eigenfrequency is the most critical and is referred to as the fundamental frequency. From these equations it can be read that the eigenfrequencies are dependent on the stiffness, the mass and the damping of the structure. Measures to be taken in order to increase the eigenfrequency is to increase the stiffness or decrease the mass. However, decreasing the mass will cause increased accelerations according to Newton’s second law, see Equation (2.6), which is not preferable for a building structure. 𝐹 = 𝑚𝑎 (2.6) 2.2.1 Recommended guidelines According to Eurocode (European Commitee for Standardization, 2002) the comfort criteria should be evaluated if the fundamental frequency, i.e. the lowest eigenfrequency, is lower than 5 Hz in vertical vibration and lower than 2,5 Hz for horizontal and torsional vibrations. Further the comfort criteria can be stated individually for given projects however a recommended maximum value is stated at 0,7 m/s2 for vertical vibrations and 0,2 m/s2 for horizontal vibrations. CHALMERS, Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 8 In ISO 10137 guidelines are provided with regard to wind-induced motions (Swedish Standards Institute, 2008) with respect to peak accelerations and the fundamental frequency of the building. The guidelines are based upon humans’ perception of the vibrations; however, it is stated that humans’ perception vary with individuals, activity and context. An article by Kwok, Hitchcock and Burton reviews tests done on humans’ interpretation of vibration and conclusions are drawn that both psychological and physiological factors affect the response (Kwok, Hitchcock, & Burton, 2009). Due to difference in activity ISO 10137 provide guidelines of different magnitude dependent on if the facility is used for offices or residences as seen in Figure 2.5. The guidelines for residences constitutes of 2/3 of what is accepted for offices. Figure 2.5 Guidelines of vibrations from ISO 10137 (Swedish Standards Institute, 2008). 2.3 Finite element modelling The finite element method is a calculation method used to solve complicated problems in a simplified manner. Differential equations are widely used to describe the behaviour of structures and materials and when the analytical solution of these equations become too complicated the finite element method provides an approximate numerical solution (Ottosen & Petersson, 1992). A finite element analysis consists of dividing the considered structure or member into small regions, finite elements, and then perform a numerical approximation over each of these elements (Ottosen & Petersson, 1992). The division in elements is called the finite element mesh, and the size of the mesh determines the accuracy of the approximation. Boundary conditions are set at points where the output is known, and the behaviour of adjacent elements follows from given conditions. An example of how to use finite element approximation is shown in Figure 2.6. In this example the temperature varies non-linearly over a rod. In the finite element analysis, the temperature is approximated to vary linearly over the finite elements, and as seen in Figure 2.6 the accuracy of the approximation rises with the number of elements used. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 9 Figure 2.6 Example of how to use finite element modelling. Approximation of the temperature distribution over a rod divided in three respectively four elements. 2.4 Timber as a construction material Many devastating city fires occurred in Sweden during the 1800s and as a result of that it was stated in 1874 that no more than two storeys were allowed for timber constructions (Näringsdepartementet, 2004). When Sweden later joined EU the regulations changed. In 1995 Boverket (National Board of Housing, Building and Planning) gave restrictions with regard to functionality of the construction rather than choice of material. This allowed for timber to become an alternative construction material for multiple storey buildings. Usage of timber in construction has many advantages, especially regarding environmental issues as timber is renewable and carbon neutral but also regarding its self-weight putting less pressure on the foundation than a corresponding concrete structure would. However, ordinary timber logs have some limitations. Since timber is a natural material it is obvious that variations in quality will occur from log to log. The timber logs also have limitations regarding size and shape (Svenskt trä, 2016a). To overcome these limitations engineered wood products have become a solution (Swedish wood, 2015). Engineered wood products, EWP, consists of wooden parts that are put together with adhesives. 2.4.1 Glulam Glulam, which refers to glued laminated timber, was the first EWP to be developed (Swedish wood, 2015). It was the German Otto Hetzer who was the first to introduce glulam as a feasible construction material (Svenskt trä, 2016a). By gluing wooden CHALMERS, Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 10 lamellas together, he was able to achieve large cross-sections which ensured enough capacity for long span structures. Hetzer also created curved beams, which he got the patent for in 1906. Economically glulam showed to be advantageous compared to steel and reinforced concrete regarding great span structures, and as a result glulam became a popular construction material for railway buildings and hangars. In Sweden the first glulam factory was established in 1919 in Töreboda, and it provided glulam for the constructions of the central stations in Stockholm, Gothenburg and Malmö, which was all constructed during the 1920s (Svenskt trä, 2016b) and are still standing today, see Figure 2.7 and Figure 2.8. Figure 2.7 Stockholm central station with glulam frames manufactured during the 1920s. Figure 2.8 Malmö central station (left) and Gothenburg central station (right) with glulam manufactured during the 1920s. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 11 Glulam consists of lamellas of timber that are finger jointed and glued together to the dimension and length of choice. The lamellas are usually sawn from fir but also pine can be used (Svenskt trä, 2016a). Before the different lamellas are joint they are graded with regard to strength (Swedish wood, 2015). Depending on the strength of the lamellas the strength of the composed glulam beam can differ, the standard strength class of glulam beams manufactured for the Swedish market is GL30 (Svenskt trä, n.d.). The number 30 corresponds to the characteristic bending strength in N/mm2 (Svenskt trä, 2016a). The strength class is usually followed by a letter c for combined or h for homogeneous. The combined beams have lamellas of higher strength in the upper and lower parts of the cross-section while lamellas placed in the middle are of less strength. The reason for this arrangement is that the maximum stresses from bending will occur in the top and bottom parts while the stresses in the middle part will be of less magnitude (Svenskt trä, n.d.). By limiting the high strength lamellas to where the maximum stress occurs an efficient use of material is achieved. The homogeneous beams have same strength lamellas throughout the cross-section, which is suitable for columns where the stress is more evenly distributed (Svenskt trä, 2016a). Comparing the strength of glulam with ordinary solid timber beams of the same size, the difference is neglectable (Swedish wood, 2015). What is obvious is though that the variation in strength is smaller for glulam. An explanation for this is that since the wood is cut in pieces the imperfections will be spread throughout the beam. One bigger defect localised to one area of a solid timber beam is likely to cause early failure in that point, however for glulam each imperfection has less effect on the strength since they are smaller and evenly distributed over the whole beam. Considering the effects of moisture in wood, glulam will expand and shrink with differing moisture content in the same way as a solid timber beam. Though, since glulam consists of lamellas originating from different parts of the log, the glulam beam is less likely to bend and turn like an ordinary timber beam might. Glulam can be made in straight and curved beams (Svenskt trä, 2016a). The straight beams have a lamella thickness of 45 mm and curved beams at 33 mm. The available heights of glulam beams are generally multiples of the lamella thickness. The maximum height is dependent of the machinery at manufacturing and is often around 2 m. The width is dependent on the available width of lamellas and the maximum is usually at 215 mm. If a wider beam is desired the lamellas can be glued together which will give widths up to 430 mm. Sizing is also limited with regard to transportation, and the maximum length of beams is normally restricted to 30 m and for curved beams also the width and height must be taken into account. 2.4.1.1 Material properties The building investigated in this project will have beams, columns and trusses made of glulam of class GL30c. The material properties of GL30c can be found in Table 2.1. CHALMERS, Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 12 Table 2.1 Material properties of glulam GL30c. GL30c Modulus of elasticity E 13 000 MPa Shear modulus G 650 MPa Poisson’s ratio ν 9 Specific weight ϒ 4,3 kN/m3 2.4.2 LVL LVL stands for laminated veneer lumber and is a material made from thin veneer sheets, 2-4 mm, glued together (Swedish wood, 2015). LVL can be made into beams or boards depending on the direction of the fibres (Moelven Töreboda AB, n.d.). Kerto S is the name of the beam material with all fibres in the same direction and Kerto Q has an 80/20 distribution of fibres which makes it suitable for boards. 2.4.2.1 Material properties In this project Kerto Q boards will be used in the floor and roof. The material properties of Kerto Q can be found in Table 2.2. Table 2.2 Material properties of Kerto Q. Kerto Q Modulus of elasticity, x Ex 10 500 MPa Modulus of elasticity, y Ey 2 000 MPa Shear modulus, yz Gyz 22,0 MPa Shear modulus, xz Gxz 120 MPa Shear modulus, xy Gxy 600 MPa Poisson’s ratio νxy 0 Poisson’s ratio νyx 0 2.5 The construction method trä8 Trä8 was the name of a construction method in timber that was launched in 2009 by Moelven Töreboda (Moelven Töreboda AB, n.d.). It was a system for buildings up to four storeys consisting of columns and beams, and with floor elements that could span up to eight metres. The columns and beams of the system was made of glulam and for floor, roof and shear walls prefabricated elements were used consisting of LVL and glulam. The roof and floor elements consisted of beams and boards both in LVL. The stabilization elements where made in shapes of L and T which made them stable on their own. The stabilization elements consisted of LVL boards mounted on glulam frames. The stabilizing system developed for the trä8 system was only used in two projects2, this was due to insufficient capacity. A report by Tlustochowicz, Johnsson and Girhammar (2010) shows that the failing mechanism originates from the glued in rods at the foundation. To solve the problems the stabilizing elements were replaced by 2 Thomas Johansson, Structural engineer at Moelven Töreboda. Interview 2018-01-22 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 13 glulam trusses. The construction of the floor elements has also changed in construction since the launch of the trä8 system1. Today the LVL beams of the floors has been replaced by glulam, and the reason for that is mainly in order to favour the factory in Töreboda as the Kerto beams are imported. Even though the construction methods used today have developed from the original idea of trä8 the term is still used today, but today the term is referring to Moelven Töreboda’s gathered methods of building high timber buildings rather than the system developed in 2009 (Moelven, n.d.). These methods include some standardizations as the continuous tall glulam columns with standardized footings as well as standardized joist hangers on which the beams are fastened to the columns1. Furthermore, the rigid floor elements are common for all trä8 houses built today and the horizontal stability is usually achieved by trusses and is sometimes complemented by a concrete core for stairwells. Another common way of stabilization of just high-rise timber buildings is usage of cross laminated timber, CLT (Mills, 2017), which is rigid wall elements made of offcuts from sawmills that are glued together (Svenskt trä, 2017). The advantage of these components is that they are very rigid and also made from waste products. However, the use of material is inefficient compared to glulam trusses and further since it requires a sawmill nearby the factory it is not an option for Moelven Töreboda’s way of construction3. 3 Thomas Johansson, Structural engineer at Moelven Töreboda. Interview 2018-01-22. CHALMERS, Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 14 3 Basis of analysis This chapter refers to describing the building to be analysed and also the aides used for analysis. 3.1 Frostaliden 3 The building to be examined in this thesis is Frostaliden 3 located in Skövde. The building is part of the residential area Frostaliden which will be the biggest residential area consisting of high-rise timber buildings in Sweden once it is finalised (Skövde Kommun, 2017). The area is part of a national project called Trästad 2012, whose purpose is to develop the commonly used construction methods of today and promote usage of timber as a construction material (Länsstyrelsen Dalarnas län, n.d.). The Frostaliden area is aimed to serve as inspiration regarding its environmentally friendly attributes, encouraging sustainable construction (Skövde Kommun, 2017). Figure 3.1 The considered building, Frostaliden 3. Frostaliden 3, see Figure 3.1, was finalised around the turn of the year 2017-2018 and is a six-storey apartment building by the developer Götenehus (Götenehus, n.d.). The floors consist of two, three and four room apartments of 64-91 m2 with accompanying balconies and the top floor apartments also have roof terraces. The height between each floor is approximately 3 m. The architect for the building was Staffan Morud from CH Arkitekter (Götenehus, 2016) and the building structure was developed by Moelven Töreboda AB. The structure follows the trä8 concept and is further stabilized by a concrete core for the staircase, see plan in Figure 3.2. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 15 Figure 3.2 Original layout of Frostaliden. 3.1.1 Modifications in the building model This thesis refers to examine the wind induced motions of a four- and a six-storey building. For the four-storey building the two bottom floors of Frostaliden 3 was removed but otherwise the building was modelled the same way. Changes were also made regarding the stabilizing system. In order to obtain a building with timber as the only construction material the concrete core was removed and replaced by additional trusses. The layout of the additional trusses was established in agreement with a qualified engineer regarding number and placement. The layout was modelled as shown in Figure 3.3 and Figure 3.4, describing the placement of trusses as well as orientation of floor elements and measurements. CHALMERS, Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 16 Figure 3.3 Numbering and position of original trusses and the added ones compensating for the concrete core. Figure 3.4 Outer measurements and orientation of floor elements. 3.2 Computational aids For the purpose of this thesis, trusses should be designed, and the structure should be modelled and analysed with regard to its performance regarding horizontal wind CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 17 forces through a finite element analysis. This was done using computational softwares which are described below. 3.2.1 RFEM Dlubal RFEM is a structural analysis program which allows the user to model complete 3D structures of plates, shells, walls and members (Dlubal, 2018). The output on the analysed structure involves deformations, internal forces, stresses and support reactions. For this thesis RFEM was used both in order to get the appropriate dimensions of the glulam trusses and later when analysing the complete structure with regard to statics and dynamics. When designing the trusses, the add-on module RF- TIMBER Pro was used, which provides the utility of the timber components. For the dynamic analysis the add-on module RF-DYNAM Pro was used to get the natural frequencies. 3.2.2 Statcon Statcon is a computational software developed by Elecosoft (Elecosoft, 2017). For this thesis the version Statcon connections was used for designing the connections between the glulam members of the trusses. By using the forces of the members of the truss obtained from RFEM, the connections were designed with regard to the capacity of the connectors as well as the capacity of the glulam members. CHALMERS, Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 18 4 Method The methodology for this thesis can be divided in three parts; the initial literature study, designing of trusses and lastly, modelling and analysis of the complete structure, see further below. 4.1 Literature study The project was initiated by a study of literature in order to gain knowledge about the area to be analysed. This was done by studying released books, searching information through online databases and also by discussing with professionals in the area. By initiating the project with gathering of information a deepened understanding for the theory behind the calculations and analysis was gained which increased efficiency and reduced the risk of mistakes during calculation and analysis. 4.2 Design of glulam trusses Before any calculations were initiated the arrangement of trusses was set with regard to the floor plan. This was done by identifying sections in the building where the trusses could be placed without interfering with the floor plan or the outlook of the facades. The width of the trusses was set around 4-6 m wide. 4.2.1 Calculation of forces In order to design the trusses, the horizontal forces acting on the building must be determined. In this case the horizontal forces were determined from wind and initial imperfections. Calculations of wind was done according to Eurocode 1 Part 1-4 (European Committee for Standardization, 2010). Calculations of the initial imperfections include vertical loads regarding self-weight, snow and imposed loads. The snow load was taken from Swedish Eurocode 1 Part 1-3 (Swedish Standards Institute, 2015) and the values for imposed loads was taken from the Swedish Eurocode 1 Part 1-1 (Swedish Standards Institute, 2009), see calculations in Appendix C.1. When the total horizontal force, acting on each storey of the building, was determined, the force was distributed on the trusses resisting force in that direction. This was done by modelling a continuous beam of same length as the building in that direction and with supports acting at the same distances as the trusses were placed. By comparing the reaction forces the distribution factors could be determined, see Appendix C.2. Since the trusses, additionally to the diagonal struts, consists of beams and columns they are also responsible for vertical load carrying. Load carrying beams are mounted on the columns of the truss and in some cases the horizontal members of the truss have floor and roof elements resting on them. Therefore, also vertical forces must be taken into account while designing. Calculations of all the loads acting on the trusses can be found in Appendix C.3. 4.2.2 Dimensioning of glulam components The design of the trusses was carried out using the software RFEM, based on SS-EN 14080:2013-08. 2D models of all the trusses was made and the previously calculated forces, both horizontal and vertical, was applied to the structures. The add-on module RF-TIMBER Pro was used in order to examine the utility of the members and the consequence class was set to three. The connections consist of slotted steel plates CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 19 fastened with dowels, and since parts of the glulam needs to be cut out in order to make this kind of connection the capacity of the glulam is slightly lowered. To account for this the maximum utility was set at 70 % in ULS. Moreover, the displacements of the truss must be considered, and limits were set at L/500 for horizontal displacements and L/300 for vertical deformations. By ensuring that these criteria were fulfilled the preliminary dimensions of the glulam components could be determined, see Appendix B.1. 4.2.3 Design of dowelled connections The connections were designed using the computer software Statcon, based on EKS10. This was done by modelling each connection for all of the trusses and adding the loads in each member obtained from the RFEM models. Two load cases were applied to each connection representing forces acting from the left and right side of the truss, see Figure 4.1. Figure 4.1 Load cases for design of connections. The connections consist of 8 mm thick steel plates and dowels of 12 mm in diameter both of quality S355. The spacing of the dowels was set according to Eurocode 5 (Swedish Standards Institute, 2004) which gave limits at 48 mm perpendicular to the fibres and 80 mm parallel to the fibre direction. At the edges the limits were 84 mm parallel to the fibres and 48 mm perpendicular, see Figure 4.2. Figure 4.2 Arrangement of dowels. CHALMERS, Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 20 The design of the connections was made with the following criteria: • As few steel plates as possible, and maximum three • Maximum five dowels in a row parallel to the fibres • Minimum four dowels in each member • Maximum 70 % utility In cases were all these criteria could not be met the dimensions of the glulam was enlarged in order to fit more dowels. The result of the design of connections can be seen in Appendix B.2, and drawings of the final design of trusses can be seen in Appendix A.2 and Appendix A.3. 4.3 Analysis of the complete structure For analysis of the static and dynamic behaviour of the building, models of the entire structure of the building were made, incorporating the trusses that previously was designed. 4.3.1 Modelling of building structure The structures of the two buildings were modelled in RFEM. The floor elements were modelled only by the Kerto Q board which constitutes the rigidity of the elements. Two cases were modelled for each building, one with 35 % stiffness of the Kerto Q board and one case with 80 % stiffness. As the floors and roof only where modelled with regard to rigidity and not load carrying, the loads acting on the elements were distributed directly on the beams on which they rest. Calculations of loads acting on the FE model can be found in Appendix C.4. Load combinations of the applied loads were generated by RFEM for SLS. The modelled structures consist of nodes, lines and surfaces meaning that all components are modelled centre to centre. This cause problems at places where the columns have large cross sections and the centre of the column doesn’t line up with where the beam should attach. This was the case especially for the columns of the trusses and was solved by making rigid couplings from the node of the column to a node where the beam should be fastened. A picture of the modelled structure for Frostaliden 3 with six storeys can be seen in Figure 4.3. The pink and blue colours of the floors correspond to the direction of the floor elements as the Kerto Q board have different material properties in x- and y- direction. In Figure 4.4 the finite element mesh is shown for the same model, the length was set to 0,5 m. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 21 Figure 4.3 Structural model of Frostaliden. Figure 4.4 Illustration of the FE-mesh for Frostaliden. 4.3.2 Static analysis The static behaviour of the structure was examined with regard to horizontal displacements at SLS. The displacements were obtained from RFEM and was compared to the limit of L/500, see outputs in Appendix B.3. 4.3.3 Dynamic analysis The dynamic response of the building consists of determining eigenfrequencies and peak accelerations in SLS and comparing them to the recommended guidelines set in ISO 10137, see Figure 2.5. The eigenfrequencies were obtained in RFEM using the add-on module RF-DYNAM Pro and the peak accelerations were determined by calculations following Eurocode (European Committee for Standardization, 2010), EKS 10 (Boverket, 2016) and BSV 97 (Boverket, 1997). See full calculations in Appendix C.5. After determining eigenfrequencies and peak accelerations for the original design idea additional trusses was added in order to investigate the importance of each truss, see layout in Figure 4.5. Placements of these trusses were set by studying the fundamental eigenmode of the building and placing trusses to prevent the particular movement, see Appendix B.4. All of the additional trusses were set to the same dimensions, see Table 4.1, and no calculations were carried out regarding design. As these trusses are mainly to describe the approximate behaviour additional calculations were assumed to CHALMERS, Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 22 be unnecessary. Some of these trusses also interfere with the placements of windows in the façade design, which makes them unfeasible in reality. Figure 4.5 Layout of Frostaliden along with additional trusses A-D. Table 4.1 Dimensions of the components of the additional trusses. Additional trusses Six-storey model Four-storey model Vertical members 280x540 215x360 Horizontal members 280x270 215x225 Diagonal members 280x360 215x225 Further analysis was made in order to investigate the impact of the height of the building. For this purpose, models were made with five, three and two floors as well and the obtained fundamental eigenfrequencies was compared. As also this was done just to analyse the approximate behaviour, and therefore no further calculations were carried out for the matter and this was only performed regarding the original design of truss layout. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 23 5 Results The results of the analysis for both buildings regarding statics and dynamics is presented below. The resulting design of trusses can be found in Appendix A.2 and Appendix A.3. 5.1 Static analysis Below the results from the static analysis will be presented. The defined coordinate system can be read in Figure 5.1. Figure 5.1 Description of the defined axes for the model of Frostaliden. The limit of L/500 for the six-storey model gives a maximum displacement of 36,8 mm. The horizontal displacements of the six-storey model are shown in Table 5.1 and further in Appendix B.3. Table 5.1 Horizontal displacements of Frostaliden, six floors, at static analysis. Six-storey model k=0,8 k=0,35 ux,max 5,9 mm 8,3 mm ux,min -6,1 mm -8,6 mm uy,max 13,7 mm 16,2 mm uy,min -8,6 mm -10,6 mm For the four-storey model the limit of L/500 gives maximum displacement at 24,8 mm. Results from the model are shown Table 5.2 and further in Appendix B.3. Table 5.2 Horizontal displacements of Frostaliden, four floors, at static analysis. Four-storey model k=0,8 k=0,35 ux,max 2,7 mm 6,1 mm ux,min -2,8 mm -6,3 mm uy,max 5,8 mm 11,6 mm uy,min -3,6 mm -6,8 mm The results are further illustrated and compared to the limit in Figure 5.2 and Figure 5.3. CHALMERS, Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 24 Figure 5.2 Comparison of the static response to the limit for the six-storey model. Figure 5.3 Comparison of the static response to the limit for the four-storey model. 5.2 Dynamic analysis The results from the dynamic analysis for the six-storey model can be read in Table 5.3 and the results from the four-storey model in Table 5.4. The different mode shapes are found in Appendix B.4. Table 5.3 Eigenfrequency and peak acceleration for different truss plans of Frostaliden, six floors. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 25 Six-storey model Wind on short side Wind on long side k=0,8 k=0,35 k=0,8 k=0,35 Original design Natural frequency 1,566 Hz 1,315 Hz 1,566 Hz 1,315 Hz Peak wind acceleration 0,036 m/s2 0,043 m/s2 0,058 m/s2 0,070 m/s2 Additional trusses: A, B Natural frequency 1,922 Hz 1,697 Hz 1,922 Hz 1,697 Hz Peak wind acceleration 0,028 m/s2 0,033 m/s2 0,047 m/s2 0,053 m/s2 Additional trusses: A, B, C Natural frequency 1,951 Hz 1,866 Hz 1,951 Hz 1,866 Hz Peak wind acceleration 0,028 m/s2 0,029 m/s2 0,046 m/s2 0,048 m/s2 Additional trusses: A, B, C, D Natural frequency 1,972 Hz 1,880 Hz 1,972 Hz 1,880 Hz Peak wind acceleration 0,028 m/s2 0,029 m/s2 0,045 m/s2 0,048 m/s2 Table 5.4 Eigenfrequency and peak acceleration for different truss plans of Frostaliden, four floors. Four-storey model Wind on short side Wind on long side k=0,8 k=0,35 k=0,8 k=0,35 Original design Natural frequency 2,575 Hz 1,543 Hz 2,575 Hz 1,543 Hz Peak wind acceleration 0,022 m/s2 0,038 m/s2 0,035 m/s2 0,062 m/s2 Additional trusses: A, B Natural frequency 3,031 Hz 2,159 Hz 3,031 Hz 2,159 Hz Peak wind acceleration 0,018 m/s2 0,026 m/s2 0,029 m/s2 0,043 m/s2 Additional trusses: A, B, C Natural frequency 3,042 Hz 2,315 Hz 3,042 Hz 2,315 Hz Peak wind acceleration 0,018 m/s2 0,024 m/s2 0,029 m/s2 0,040 m/s2 The results of the original design idea compared to the guidelines from ISO 10137 can be seen in Figure 5.4 for the six-storey model and Figure 5.5 for the four-storey model. CHALMERS, Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 26 Figure 5.4 The results of the original design idea for the six-storey model compared to the guidelines defined in ISO 10137. Figure 5.5 The results of the original design idea for the four-storey model compared to the guidelines defined in ISO 10137. The critical wind direction is wind acting on the long side. Comparison between the different truss layouts can be found in Figure 5.6 and Figure 5.7 regarding stiffnesses of 35-80 % with wind acting in the critical direction for the six- and the four-storey model. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 27 Figure 5.6 The result of the different layouts of trusses for the six-storey model compared to the guidelines. Only response to wind in the critical direction is displayed. Figure 5.7 The result of the different layouts of trusses for the four-storey model compared to the guidelines. Only response to wind in the critical direction is displayed. The change in fundamental eigenfrequency due to different truss designs are shown in Figure 5.8. CHALMERS, Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 28 Figure 5.8 The influence on the fundamental eigenfrequency when the additional trusses are added to the model. In Figure 5.9 the fundamental frequency is plotted towards the number of storeys for stiffnesses of 35 and 80 % of the Kerto Q board for the floor elements. Figure 5.9 Illustration on how the fundamental eigenfrequency changes depending on the number of storeys. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 29 6 Discussion This chapter handles evaluation on the results and methods used to reach them. The first sections involve analysis of the obtained results and further the used methods and assumptions are discussed. 6.1 Analysis of static results Considering horizontal displacements both building models fulfil the demands regarding all of the modelled cases, see Figure 5.2 and Figure 5.3. Each truss was designed in order to withstand the wind forces it was exposed to, hence each truss will keep within the limits of L/500 also when modelled in the complete structure. If the static displacement of the complete structure were to exceed the limits it should be due to insufficient stiffness of the floor elements, giving displacements similar to the ones illustrated in Figure 2.3C. Since the displacements were within limits for all modelled cases it seems that the floor elements provide sufficient rigidity. The case with wind acting in the y-direction, on the long side, gives larger displacements than the cases with wind acting in the other direction. In the y-direction there are three trusses withstanding the forces, see Figure 3.3, truss 1, 4 and 7. However, due to the shape of the building only truss 1 and 4 will cover the top floor. This gives that the distance between the trusses are larger in the top floor putting pressure on the elements of the roof to transfer the forces further. In this case the displacements are visibly larger at the roof level than the floor below, especially regarding wind in the positive y-direction, see Appendix B.3. When comparing the influence of the stiffness of floor elements, on the horizontal displacements it is seen that the difference is greater for the four-storey model than the six-storey. This is easily seen by comparing Figure 5.2 and Figure 5.3. This indicates that the importance of the stiffness decreases as the building height increases. Possibly since with a higher building comes additional instability due to more connections and taller columns. 6.2 Analysis of dynamic results The results from the dynamic analysis are less adequate compared to the static analysis. This means that even if the static response is satisfactory a dynamic analysis should be carried out before constructing high-rise buildings like the building considered in this thesis. In Figure 5.4 it can be read that the original design idea regarding placements and number of trusses do not perform well when modelled in the six-storey model. The only case that fulfils the demands stated in ISO 10137 is the most favourable case with wind on the short side and 80 % stiffness. In Figure 5.5 the corresponding results for the four-storey model can be read. In this case the demands are fulfilled for all cases except one, the most critical with wind acting on the long side and stiffness modelled at 35 %. Consequently, the dynamic performance differs quite a lot for the six- and the four-storey model. In order to improve the dynamic behaviour additional trusses were added to the structure and the contribution can be analysed from Figure 5.6 and Figure 5.7. For the six-storey model the demands for residential buildings are not fulfilled even when in total eight additional trusses are added to the structure. This indicates that the influence of the trusses is saturated, which is further illustrated in Figure 5.8 where CHALMERS, Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 30 the inclination of the curves markedly decreases. This implies that the given structure will not be able to fulfil the demands regardless of how many trusses are added, and this is the case regarding both modelled stiffnesses for the six-storey model. On the other hand, considering the four-storey model the additional trusses actually do help the dynamic performance to such length that the demands are fulfilled for all modelled cases for the four-storey model. It can be read from Figure 5.8 that the stiffness of the floor has higher influence on the eigenfrequency for the four-storey model compared to the six-storey. This is also confirmed in Figure 5.9, where the difference in fundamental frequency increases as the number of floor decreases. This indicates that the stiffness of the floor elements is of less importance when constructing high buildings. Similar findings were also obtained in the static analysis, as discussed in previous section. Consequently, both the number of trusses and the stiffnesses of the floor elements become irrelevant at certain building heights. This implies that in order to fulfil the dynamic demands other measures needs to be taken. The eigenfrequency depends on the mass, stiffness and damping following from Chapter 2.2. The peak accelerations depend on many factors such as fundamental eigenfrequency, wind speed, building’s geometry, see further Appendix C.5. The wind speed will increase with height and is something all high-rise buildings will be exposed to, however by altering the geometry the peak acceleration can be changed. A wide building will catch more wind than a narrow building structure. However, changes in geometry will also affect the eigenfrequency, a narrow building will be less rigid since the lever arm is decreased and also the weight of the building is decreased. Considering the eigenmodes, see Appendix B.4, it’s clear that the stiffness of the floor elements has an impact on the resulting fundamental eigenfrequency. From the figures in Appendix B.4 the floor modelled with 35 % stiffness appear flexible compared to the post beam structure and the floor with 80 % stiffness behaves rigidly in comparison. In this case it also appears that the eigenmodes are similar for the six- and the four-storey model regarding the different truss layouts modelled. This suggests that the eigenmode will look the same regardless of building height and is only dependent on the building’s geometry and layout of stabilization. The fundamental eigenfrequency is however lowered with increasing height. 6.3 Method and assumptions The disadvantages regarding the method lies in the uncertainties of the modelled structure. First and foremost, the stiffness of the floor elements is unknown, however by modelling the floor elements at the extremes of their assumed stiffness conclusions can be drawn within which span the actual results lie and also how the stiffness of the elements affects the total stability of the structure. Moreover, the stiffness of the connections in between glulam members is unknown. When modelling, all connections were assumed moment free in order to model the worst case as with semi-rigid couplings the structure would be stiffer. Nevertheless, even though the structure would be stiffer with semi-rigid couplings, the rigidity might cause other problems. As the members are not free to move, stresses will occur within the members which might cause problems regarding fatigue among others. The dynamic response of the structure is compared to guidelines set in ISO 10137. However, these guidelines are not compelled to be met as there are no definite rules regarding vibrations and motions of building structures. As the perception of CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 31 vibrations and motions varies with individuals it is possible that some people might feel uncomfortable in a building even though these guidelines have been met or maybe none of the residents would have noticed if these guidelines weren’t fulfilled. Meaning that a building which doesn’t fulfil the guidelines might still be serviceable in practice. The modelling was carried out for wind acting on the sides of the building. In reality the wind might blow at an angle on the building structure. However, wind acting on the sides of the building shows the worst case since if wind is blowing at an angle trusses in both directions will help take the wind forces down to the foundation, and with wind blowing straight at the building only the trusses oriented in that direction will be able to resist the forces. Further, as the analysis is only carried out for one particular building, no definite conclusions can be drawn regarding four- and six-storey buildings in general. In order to fully understand the importance of trusses and stiffness of floor elements analysis must be carried out for multiple geometries. Also, as the building was originally designed as a six-storey building and the dimensions of the four-storey model will be over-sized regarding columns as they carry less load and the wind forces decrease with decreasing height. CHALMERS, Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 32 7 Conclusions The static response of the building models is satisfactory regarding both modelled building heights and floor stiffnesses. Considering the dynamic response of the six-storey model, the guidelines set in ISO 10137 cannot be fulfilled, independently on the number of trusses and floor stiffness within the limits of 35-80 % of the stiffness of the Kerto Q board. In order to fulfil the guidelines for this specific building model measures needs to be taken in order to increase the eigenfrequency by increasing the stiffness or by adding damping mechanisms to decrease the amplitudes. The four-storey model shows better results regarding dynamics and fulfils the guidelines for a stiffness of the floor elements modelled to 80 % however not for the 35 %. In order to ensure the stability of this building model the stiffness of the floor elements needs to be established. If the established stiffness is not sufficient additional trusses can ensure that the guidelines are fulfilled. By comparing the behaviour of the four- and the six-storey model it is seen that the influence regarding number of trusses and stiffness of floor elements is larger for buildings of less height. Consequently, the remaining instability found in higher structures originates from other factors. 7.1 Suggestions on further research For further analysis of the trusses the stiffness of the floor elements needs to be determined. Furthermore, analysis regarding stiffness of the connections would give a more exact result. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 33 References Boverket. (1997). Boverkets handbok om Snö- och vindlaster - Utgåva 2 - BVS 97. Karlskrona: Boverket. Boverket. (2016, Januari). Boverkets konstruktions regler - EKS 10. Karlskrona: Boverket. Dlubal. (2018). RFEM - FEM Structural Analysis Software. 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Retrieved April 17, 2018, from Guinness World Records: http://www.guinnessworldrecords.com/world- records/first-skyscraper/ Kwok, K. C., Hitchcock, P. A., & Burton, M. D. (2009). Perceotion of vibration and occupant in wind-exited tall buildings. Journal of Wind Engineering and Industrial Aeorodynamics, 368-380. Länsstyrelsen Dalarnas län. (n.d.). Trästad 2012. Retrieved April 3, 2018, from Länsstyrelsen Dalarnas län: http://www.lansstyrelsen.se/Dalarna/Sv/naringsliv-och- foreningar/naringslivsutveckling/avslutade-projekt/Pages/trastad- 2012.aspx CHALMERS, Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 34 Mills, F. (2017). Top 5: The World's Tallest Timber Buildings. Retrieved May 14, 2018, from https://www.theb1m.com/video/top-5-the-world-s-tallest- timber-buildings Moelven. (n.d.). Flervåningshus - Trä8. Retrieved January 29, 2018, from Moelven: https://www.moelven.com/se/Produkter-och-tjanster/Limtra- Massivtra-och-Kerto/Var-projektverksamhet/Flervaningshus-i-Tra/ Moelven Töreboda AB. (n.d.). Trä8 Pelarbalksystem: Ett revolutionerande byggsystem helt i trä. Retrieved January 29, 2018, from https://www.moelven.com/Documents/Toreboda/Broschyren/TR%C3 %848.pdf Näringsdepartementet. (2004). Mer trä i byggandet: Underlag for en nationell strategi att främja anvädning av trä i byggandet . Retrieved January 29, 2018, from http://www.regeringen.se/49bbba/contentassets/622a4cddc02a4026a3 bc3c4f5d5b94aa/mer-tra-i-byggandet---underlag-for-en-nationell- strategi-for-att-framja-tra-i-byggandet-ds-20041 Naturvårdsverket. (2017, November 13). Därför blir det varmare. Retrieved February 26, 2018, from Naturvårdsverket: http://www.naturvardsverket.se/Sa-mar-miljon/Klimat-och- luft/Klimat/Darfor-blir-det-varmare/ NGO Committee on Education. (1987). Report of the World Commission on Environment and Development: Our Common Future. Geneva: UN Documents. Ottosen, N., & Petersson, H. (1992). Introduction to the Finite Element Method. New York: Prentice Hall. Skövde Kommun. (2017, November 13). Frostaliden. Retrieved April 3, 2018, from Skövde: https://www.skovde.se/bygga- bo/samhallsutveckling/frostaliden/ Statistiska centralbyrån. (2018, April 17). Excess of migration by region, sex and year. Retrieved April 17, 2018, from Statistiska centralbyrån: http://www.statistikdatabasen.scb.se/sq/49489 Strømmen, E. N. (2014). Springer series in Solid and Structural Mechanics 2: Structural dynamics (Vol. 2). Springer. Swedish Standards Institute. (2004). Eurokod 5: Dimensionering av träkonstruktioner - Del 1-1: Allmänt - Gemensamma regler och regler för byggnader (SS-EN 1995-1-1:2004). Stockholm: SIS Förlag AB. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30-18-54 35 Swedish Standards Institute. (2008). Grundläggande dimensioneringsregler för bärverk - Byggnaders samt gång- och cykelbroars brukbarhet med hänsyn till svängningar och vibrationer (ISO10137:2007, IDT). Stockholm: SIS Förlag AB. Swedish Standards Institute. (2009). Eurokod 1: Laster på bärverk - Del 1-1: Allmänna laster - Tunghet, egentyngd, nyttig last för byggnader (SS-EN 1991-1-1/AC:2009). Stockholm: SIS Förlag AB. Swedish Standards Institute. (2015). Eurokod 1 - Laster på bärverk - Del 1-3: Allmänna laster - Snölast (SS-EN 1991-1-3/A1:2015). Stockholm: SIS Förlag AB. Swedish wood. (2015). Design of timber structures: Structural aspects of timber construction (2 ed., Vol. 1). Stockholm: Swedish Forest Industries Federation. Svenskt trä. (2003, September 1). Miljöeffekter. Retrieved February 26, 2018, from Träguiden: https://www.traguiden.se/om-tra/miljo/miljoeffekter/ Svenskt trä. (2016a). Limträhandbok Del 1: Fakta om limträ (5 ed.). Stockholm: Föreningen Sveriges Skogsindustrier. Svenskt trä. (2016b). Limträhandbok Del 2: Projektering av limträkonstruktioner (5 ed.). Stockholm: Föreningen Sveriges Skogsindustrier. Svenskt trä. (2017). KL-trähandbok: Fakta och projektering av KL- träkonstruktioner. Stockholm: Föreningen Sveriges Skogsindustrier. Svenskt trä. (n.d.). Om limträ. Retrieved January 29, 2018, from Svenskt trä: https://www.svenskttra.se/om-tra/om-limtra/ Tlustochowicz, G., Johnsson, H., & Girhammar, U. (2010). Beam and post system for non-residential multi-storey timber buildings - Horizontal stabilising system. Luleå: World conference on timber engineering. Appendix A - Drawings A.1 Plan with dimensions ...................................................................................................................... A1 A.2 Trusses of six storey buidling .......................................................................................................... A2 Truss 1 ............................................................................................................................................... A2 Truss 2 ............................................................................................................................................... A3 Truss 3 ............................................................................................................................................... A4 Truss 4 ............................................................................................................................................... A5 Truss 5 ............................................................................................................................................... A6 Truss 6 ............................................................................................................................................... A7 Truss 7 ............................................................................................................................................... A8 Additional trusses .............................................................................................................................. A9 A.3 Trusses of four storey building ...................................................................................................... A10 Truss 1 ............................................................................................................................................. A10 Truss 2 ............................................................................................................................................. A11 Truss 3 ............................................................................................................................................. A12 Truss 4 ............................................................................................................................................. A13 Truss 5 ............................................................................................................................................. A14 Truss 6 ............................................................................................................................................. A15 Truss 7 ............................................................................................................................................. A16 Additional trusses ............................................................................................................................ A17 215x495 215x495 215x495 215x270 215x270 215x270 215x270 215x270 215x270 TR U SS 5 TR U SS 5 TRUSS 6 215x360 215x225 TRUSS 1 165X 585 165x405 215x225 215x360 215x360 215x495 215x360 165x405 215x225 165x405 215x225 215x225 165x405 215x360 215x315 215x315 215x360 215x360 215x360 140x360 215x270 165x540 TR U SS 2 165x405 215x225 215x360 215x225 215x315 215x315 215x360 165x405 215x225 215x360215x450 C olum n on the second highest floor 215x225 215x360 215x360 215x360 215x270 215x360 215x495 215x360 165x585 TRUSS 4 215x360 215x225 165x405 215x225 215x360 215x315 215x315 215x360 215x360 215x360 165x405 215x225 215x360 90x360 90X360 215x360 215x225 165x405 215x225 165x405 215x225 215x360 215x360 140x360 215x360 215x270 215x360 215x360 215x360 TR U SS 3 215x315 215x315 215x360 165x405165x540 C olum n on the second highest floor 215x225 C olum n on the second highest floor 215x225 C olum n on the second highest floor 215x225 215x360 215x360 215x360 115x495 90x495 32735 20740 A ppendix A A .1 P lan A 1 Truss 1 H orizontal: 280x270 V ertical: 280x675 D iagonal: 280x360 B A 3002 4686 C E G I K M D F H J L N 3002 3002 3002 3002 3361 48 80 84 52,8 48 58 48 80 84 D etail A 3 plates 61 dow els 48,25 12 8084 D etail B 3 plates 85 dow els D etail C 3 plates 81 dow els D etail D 1 plate 12 dow els D etail E 1 plate 12 dow els D etail F 2 plates 92 dow els D etail G 2 plates 73 dow els 48,25 8 D etail H 1 plate 12 dow els D etail I 1 plate 13 dow els D etail K 1 plate 57 dow els D etail M 1 plate 14 dow els D etail J 2 plates 57 dow els D etail L 1 plate 18 dow els D etail N 1 plate 25 dow els 8 8 Three plates Tw o plates O ne plate 70 70 70 70 80 A ppendix A A .2 Trusses of six storey building A 2 Truss 2 H orizontal: 215x270 V ertical: 215x540 D iagonal: 215x315 A 3002 3002 3002 3002 3002 B C D E F G H I J K L 4686 D etail A 3 plates 48 dow els 49,33 48 8084 12 54,7548 84 80 D etail C 2 plates 59 dow els D etail E 1 plate 8 dow els D etail K 1 plate 14 dow els D etail I 1 plate 8 dow els D etail G 1 plate 53 dow els D etail B 3 plates 63 dow els D etail D 1 plate 8 dow els D etail F 1 plate 69 dow els D etail L 1 plate 8 dow els D etail J 1 plate 34 dow els D etail H 1 plate 8 dow els 8 Three plates Tw o plates O ne plate 53,8 53,8 8 53,8 53,8 8 58 48 80 84 A ppendix A A .2 Trusses of six storey building A 3 Truss 3 H orizontal: 215x270 V ertical: 215x495 D iagonal: 215x270 A 3002 3002 3002 3002 3002 B C D E F G H I J K L 4686 58 48 80 84 48 12 84 49,88 80 49,88 58 48 D etail A 3 plates 51 dow els D etail C 1 plate 8 dow els D etail E 2 plates 46 dow els D etail K 1 plate 9 dow els D etail I 1 plate 32 dow els D etail G 1 plate 8 dow els D etail B 3 plates 41 dow els D etail D 2 plates 57 dow els D etail F 1 plate 8 dow els D etail J 1 plate 14 dow els D etail J 1 plate 8 dow els D etail H 1 plate 50 dow els 8 Three plates Tw o plates O ne plate 53,8 53,8 8 53,8 53,8 8 80 84 80 A ppendix A A .2 Trusses of six storey building A 4 Truss 4 H orizontal: 280x270 V ertical: 280x540 D iagonal: 280x360 B A 3002 4686 C E G I K M D F H J L N 3002 3002 3002 3002 3361 D etail A 2 plates 44 dow els D etail C 3 plates 78 dow els D etail E 1 plate 12 dow els D etail G 2 plates 72 dow els D etail M 1 plates 15 dow els D etail K 1 plate 50 dow els D etail I 1 plates 13 dow els D etail B 3 plates 70 dow els D etail D 1 plate 8 dow els D etail F 2 plates 90 dow els D etail H 1 plate 8 dow els D etail N 1 plate 20 dow els D etail L 1 plate 8 dow els D etail J 1 plate 91 dow els 8 8 8 Three plates Tw o plates O ne plate 70 70 70 70 58 48 80 84 48 52,8 48 12 84 49,33 80 8084 A ppendix A A .2 Trusses of six storey building A 5 Truss 5 H orizontal: 280x360 V ertical: 280x450 D iagonal: 280x270 B A 3002 4288,5 C E G I K M D F H J L N 3002 3002 3002 3002 3361 D etail A 3 plates 36 dow els D etail C 1 plate 26 dow els D etail E 1 plate 66 dow els D etail G 1 plate 26 dow els D etail M 1 plate 27 dow els D etail K 1 plate 26 dow els D etail I 1 plate 47 dow els D etail B 3 plates 40 dow els D etail D 1 plate 73 dow els D etail F 1 plate 26 dow els D etail H 1 plate 69 dow els D etail N 1 plate 20 dow els D etail L 1 plate 38 dow els D etail J 1 plate 26 dow els 8 8 Three plates O ne plate 70 70 48 12 84 50,57 80 50,57 58 48 80 84 52,8 48 80 84 80 A ppendix A A .2 Trusses of six storey building A 6 Truss 6 H orizontal: 280x360 V ertical: 280x360 D iagonal: 280x270 B A 3002 4288,5 C E G I K M D F H J L N 3002 3002 3002 3002 3361 8 8 8 Three plates Tw o plates O ne plate 70 70 70 70 D etail A 3 plates 30 dow els D etail C 2 plates 41 dow els D etail E 1 plate 24 dow els D etail G 1 plate 52 dow els D etail M 1 plate 18 dow els D etail K 1 plate 41 dow els D etail I 1 plate 23 dow els D etail B 3 plates 35 dow els D etail D 1 plate 24 dow els D etail F 1 plate 62 dow els D etail H 1 plate 24 dow els D etail N 1 plate 20 dow els D etail L 1 plate 24 dow els D etail J 1 plate 42 dow els 52,8 48 80 84 48 12 84 52,8 80 52,8 80 84 80 48 58 A ppendix A A .2 Trusses of six storey building A 7 Truss 7 H orizontal: 115x450 x2 H orizontal at roof level: 280x495 V ertical: 280x585 D iagonal: 280x360 A 3002 3002 3002 3002 3002 C E G I K B D F H J L 5859 D etail A 3 plates 55 dow els D etail C 2 plates 85 dow els D etail E 2 plates 35 dow els D etail K 2 plates 36 dow els D etail I 2 plates 31 dow els D etail G 2 plates 67 dow els D etail B 3 plates 66 dow els D etail D 2 plates 32 dow els D etail F 2 plates 86 dow els D etail L 2 plates 29 dow els D etail J 2 plates 58 dow els D etail H 2 plates 28 dow els 48 12 84 48,9 80 48,9 48 52,8 8084 50,57 48 80 84 49,88 48 80 84 8 Three plates Tw o plates Line A B -IJ 70 70 57,5115 115 50 57,5 Tw o plates Line K L 8 70 70 A ppendix A A .2 Trusses of six storey building A 8 3002 3002 3002 3002 3002 3002 3002 3002 3002 3002 3361 A dditional trusses H orizontal: 280x270 V ertical: 280x540 D iagonal: 280x360 A ppendix A A .2 Trusses of six storey building A 9 A B C D E F G H I J Truss 1 H orizontal: 215x225 V ertical: 215x360 D iagonal: 215x225 3002 3002 3002 3381 4686 D etail A 3 plates 27 dow els D etail C 2 plates 36 dow els D etail E 1 plate 8 dow els D etail I 1 plate 8 dow els D etail G 1 plate 24 dow els D etail F 1 plate 37 dow els D etail D 1 plate 8 dow els D etail B 3 plates 38 dow els D etail H 1 plate 8 dow els D etail J 1 plate 12 dow els 8 Three plates Tw o plates O ne plate 53,8 53,8 8 53,8 53,8 8 48 80 84 64,5 52,8 12 8084 52,8 80 48 A ppendix A A .3 Trusses of four storey building A 10 A B C D E F G H 3002 3002 3002 Truss 2 H orizontal: 215x225 V ertical: 215x270 D iagonal: 215x225 4686 D etail A 3 plates 18 dow els D etail C 1 plate 41 dow els D etail G 1 plate 13 dow els D etail E 1 plate 9 dow els D etail D 1 plate 8 dow els D etail B 3 plates 26 dow els D etail F 1 plate 27 dow els D etail H 1 plate 8 dow els 8 Three plates Tw o plates O ne plate 53,8 53,8 8 53,8 53,8 8 80 84 64,52 48 8084 80 48 58 58 12 A ppendix A A .3 Trusses of four storey building A 11 A B C D E F G H Truss 3 H orizontal: 215x225 V ertical: 215x270 D iagonal: 215x225 3002 3002 3002 4686 D etail A 3 plates 26 dow els D etail C 1 plate 8 dow els D etail G 1 plate 8 dow els D etail E 1 plate 26 dow els D etail D 1 plate 41 dow els D etail B 3 plates 18 dow els D etail F 1 plate 9 dow els D etail H 1 plate 12 dow els 8 Three plates Tw o plates O ne plate 53,8 53,8 8 53,8 53,8 8 48 8084 80 48 58 58 12 84 80 64,5 A ppendix A A .3 Trusses of four storey building A 12 A C E G B D F H I J Truss 4 H orizontal: 215x225 V ertical: 215x360 D iagonal: 215x225 3002 3002 3002 3381 4686 D etail A 3 plates 27 dow els D etail C 2 plates 37 dow els D etail E 1 plate 8 dow els D etail I 1 plate 8 dow els D etail G 1 plate 27 dow els D etail B 2 plates 37 dow els D etail D 1 plate 8 dow els D etail F 1 plate 36 dow els D etail J 1 plate 12 dow els D etail H 1 plate 8 dow els 8 Three plates Tw o plates O ne plate 53,8 53,8 8 53,8 53,8 8 8084 80 48 52,8 52,8 12 80 84 64,5 48 A ppendix A A .3 Trusses of four storey building A 13 A C E G I B D F H J Truss 5 H orizontal: 215x405 V ertical: 215x360 D iagonal: 215x225 3002 3002 3002 3381 4288,5 D etail A 3 plates 28 dow els D etail C 1 plate 21 dow els D etail E 1 plate 43 dow els D etail I 1 plate 21 dow els D etail G 1 plate 17 dow els D etail B 3 plates 27 dow els D etail D 1 plate 49 dow els D etail F 1 plate 21 dow els D etail J 1 plate 17 dow els D etail H 1 plate 33 dow els 84 8084 80 48 52,8 52,8 12 80 A ppendix A A .3 Trusses of four storey building A 14 A C E G I B D F H J Truss 6 H orizontal: 215x405 V ertical: 215x315 D iagonal: 215x225 3002 3002 3002 3381 4288,5 8 Three plates Tw o plates O ne plate 53,8 53,8 8 53,8 53,8 8 D etail A 3 plates 23 dow els D etail C 1 plate 45 dow els D etail E 1 plate 21 dow els D etail I 1 plate 17 dow els D etail G 1 plate 32 dow els D etail B 3 plates 29 dow els D etail D 1 plate 21 dow els D etail F 1 plate 41 dow els D etail J 1 plate 19 dow els D etail H 1 plate 21 dow els 8084 80 48 54,75 54,75 12 84 80 48 64,5 A ppendix A A .3 Trusses of four storey building A 15 A C E G 3002 3002 3002 B D F H Truss 7 H orizontal: 115x450 x2 H orizontal at roof level: 280x495 V ertical: 280x315 D iagonal: 280x270 5859 D etail A 3 plates 25 dow els D etail C 2 plates 44 dow els D etail G 2 plates 24 dow els D etail E 2 plates 25 dow els D etail B 3 plates 29 dow els D etail D 2 plates 25 dow els D etail H 2 plates 20 dow els D etail F 2 plates 41 dow els 8 Three plates Tw o plates Line A B-EF 70 70 57,5115 115 50 57,5 Tw o plates Line G H 8 70 70 8084 80 48 54,8 54,8 12 84 80 48 58 A ppendix A A .3 Trusses of four storey building A 16 A dditional trusses H orizontal: 215x225 V ertical: 215x360 D iagonal: 215x225 3002 3002 3002 3002 3002 3002 3381 A ppendix A A .3 Trusses of four storey building A 17 B0 Appendix B – Results from computational software B.1 Dimensioning of trusses .................................................................................................................. B1 Trusses of six storey building............................................................................................................. B1 Truss 1 ........................................................................................................................................... B1 Truss 2 ........................................................................................................................................... B2 Truss 3 ........................................................................................................................................... B2 Truss 4 ........................................................................................................................................... B3 Truss 5 ........................................................................................................................................... B3 Truss 6 ........................................................................................................................................... B4 Truss 7 ........................................................................................................................................... B4 Trusses of four storey building .......................................................................................................... B5 Truss 1 ........................................................................................................................................... B5 Truss 2 ........................................................................................................................................... B6 Truss 3 ........................................................................................................................................... B6 Truss 4 ........................................................................................................................................... B7 Truss 5 ........................................................................................................................................... B8 Truss 6 ........................................................................................................................................... B8 Truss 7 ........................................................................................................................................... B9 B.2 Design of connections ................................................................................................................... B10 Connections of six storey building .................................................................................................. B10 Truss 1 ......................................................................................................................................... B10 Truss 2 ......................................................................................................................................... B16 Truss 3 ......................................................................................................................................... B21 Truss 4 ......................................................................................................................................... B26 Truss 5 ......................................................................................................................................... B32 Truss 6 ......................................................................................................................................... B38 Truss 7 ......................................................................................................................................... B44 Connections of four storey building ................................................................................................ B52 Truss 1 ......................................................................................................................................... B52 Truss 2 ......................................................................................................................................... B56 Truss 3 ......................................................................................................................................... B60 Truss 4 ......................................................................................................................................... B64 Truss 5 ......................................................................................................................................... B68 Truss 6 ......................................................................................................................................... B72 Appendix B Truss 7 ......................................................................................................................................... B76 B.3 Results from static analysis ........................................................................................................... B81 Results from six storey building ...................................................................................................... B81 k=0,8 ............................................................................................................................................ B81 k=0,35 .......................................................................................................................................... B82 Results from four storey building .................................................................................................... B83 k=0,8 ............................................................................................................................................ B83 k=0,35 .......................................................................................................................................... B84 B.4 Results from dynamic analysis ...................................................................................................... B85 Results of six storey building ........................................................................................................... B85 Original design ............................................................................................................................. B85 Design AB ..................................................................................................................................... B86 Design ABC................................................................................................................................... B87 Design ABCD ................................................................................................................................ B88 Results of four storey building ........................................................................................................ B89 Original design ............................................................................................................................. B89 Design AB ..................................................................................................................................... B90 Design ABC................................................................................................................................... B91 Appendix B B1 B.1 Dimensioning of trusses Trusses of six storey building Truss 1 Max utility 47 % Global def, x: 30,6 mm Local def, z: - Appendix B B2 Truss 2 Max utility 45 % Global def, x: 15,6 mm Local def, z: - Truss 3 Max utility 49 % Global def, x: 17,3 mm Local def, z: - Appendix B B3 Truss 4 Max utility 56 % Global def, x: 36,4 mm Local def, z: - Truss 5 Max utility 50 % Global def, x: 16,7 mm Local def, z: 14,7 mm Appendix B B4 Truss 6 Max utility 50 % Global def, x: 10,0 mm Local def, z: 15,5 mm Truss 7 Max utility: 51 % Global def, x: 14,5 mm Local def, z: 16,4 mm Appendix B B5 Trusses of four storey building Truss 1 Max utility 50 % Global def, x: 9,0 mm Local def, z: - Appendix B B6 Truss 2 Max utility 43 % Global def, x: 5,4 mm Local def, z: - Truss 3 Max utility 43 % Global def, x: 5,4 mm Local def, z: - Appendix B B7 Truss 4 Max utility 42 % Global def, x: 10,4 mm Local def, z: - Appendix B B8 Truss 5 Max utility 41 % Global def, x: 7,4 mm Local def, z: 12,5 mm Truss 6 Max utility 51 % Global def, x: 3,6 mm Local def, z: 13,0 mm Appendix B B9 Truss 7 Max utility 42 % Global def, x: 3,9 mm Local def, z: 15,1 mm Appendix B B10 B.2 Design of connections Connections of six storey building Truss 1 Connection A Connection B, vertical Appendix B B11 Connection B, diagonal Connection C Connection D Appendix B B12 Connection E Connection F Connection G Appendix B B13 Connection H Connection I Connection J Appendix B B14 Connection K Connection L Connection M Appendix B B15 Connection N Appendix B B16 Truss 2 Connection A Connection B, vertical Appendix B B17 Connection B, diagonal Connection C Connection D Appendix B B18 Connection E Connection F Connection G Appendix B B19 Connection H Connection I Connection J Appendix B B20 Connection K Connection L Appendix B B21 Truss 3 Connection A, vertical Connection A, diagonal Appendix B B22 Connection B Connection C Connection D Appendix B B23 Connection E Connection F Connection G Appendix B B24 Connection H Connection I Connection J Appendix B B25 Connection K Connection L Appendix B B26 Truss 4 Connection A Connection B, vertical Appendix B B27 Connection B, diagonal Connection C Connection D Appendix B B28 Connection E Connection F Connection G Appendix B B29 Connection H Connection I Connection J Appendix B B30 Connection K Connection L Connection M Appendix B B31 Connection N Appendix B B32 Truss 5 Connection A, vertical Connection A, diagonal Appendix B B33 Connection B Connection C Connection D Appendix B B34 Connection E Connection F Connection G Appendix B B35 Connection H Connection I Connection J Appendix B B36 Connection K Connection L Connection M Appendix B B37 Connection N Appendix B B38 Truss 6 Connection A Connection B, vertical Appendix B B39 Connection B, diagonal Connection C Connection D Appendix B B40 Connection E Connection F Connection G Appendix B B41 Connection H Connection I Connection J Appendix B B42 Connection K Connection L Connection M Appendix B B43 Connection N Appendix B B44 Truss 7 Connection A Connection B, vertical Appendix B B45 Connection B, diagonal Connection C, horizontal member – 1 plate Connection C, vertical and diagonal members – 2 plates Appendix B B46 Connection D, horizontal member – 1 plate Connection D, vertical member – 2 plates Connection E, horizontal member – 1 plate Appendix B B47 Connection E, vertical member – 2 plates Connection F, horizontal member – 1 plate Connection F, vertical and diagonal members – 2 plates Appendix B B48 Connection G, horizontal member – 1 plate Connection G, vertical and diagonal members – 2 plates Connection H, horizontal member – 1 plate Appendix B B49 Connection H, vertical member – 2 plates Connection I, horizontal member – 1 plate Connection I, vertical member – 2 plates Appendix B B50 Connection J, horizontal member – 1 plate Connection J, vertical and diagonal members – 2 plates Connection K Appendix B B51 Connection L Appendix B B52 Connections of four storey building Truss 1 Connection A Connection B, vertical Appendix B B53 Connection B, diagonal Connection C Connection D Appendix B B54 Connection E Connection F Connection G Appendix B B55 Connection H Connection I Connection J Appendix B B56 Truss 2 Connection A Connection B, vertical Appendix B B57 Connection B, diagonal Connection C Connection D Appendix B B58 Connection E Connection F Connection G Appendix B B59 Connection H Appendix B B60 Truss 3 Connection A, vertical Connection A, diagonal Appendix B B61 Connection B Connection C Connection D Appendix B B62 Connection E Connection F Connection G Appendix B B63 Connection H Appendix B B64 Truss 4 Connection A Connection B, vertical Appendix B B65 Connection B, diagonal Connection C Connection D Appendix B B66 Connection E Connection F Connection G Appendix B B67 Connection H Connection I Connection J Appendix B B68 Truss 5 Connection A, vertical Connection A, diagonal Appendix B B69 Connection B Connection C Connection D Appendix B B70 Connection E Connection F