TECHNICAL DESIGN CALCULATION REPORT

Transcription

1 TECHNICAL DESIGN CALCULATION REPORT Design Of Timber Structures Project: Residential building Location: Villazzano City: Trento Address: Via della Villa, 22/A Province: Trento Client: Building company: Structural designer: Date: Thursday, July 2, 2015

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3 Design codes and standards 1. EN Eurocode 3 Design of steel structures - Part 1-1: General rules and rules for buildings 2. EN Eurocode 3 Design of steel structures - Part 1-8: Design of joints 3. EN Eurocode 5 Design of timber structures - Part 1-1: General - Common rules and rules for buildings 4. EN 338 Structural timber - Strength classes 5. EN 1194 Timber structures - Glued laminated timber - Strength classes and determination of characteristic values 6. EN Timber structures - Glued laminated timber and glued solid timber - Requirements

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5 General description of the building Location Region: Province: City: Place: Trentino-alto Adige Trento Trento Villazzano Address: Via della Villa, 22/A Latitude: Longitude: Elevation mamsl: 193 m Description Number of storeys: 2 Building length: Building width: Building height: m 17.3 m 7.7 m

6 Three-dimensional view Southeast

7 Three-dimensional view Northwest

8 Three-dimensional view South West

9 Three-dimensional view North East

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11 Calculation software used Calculation software features The software used is TimberTech Buildings, developed by Timber Tech s.r.l., start-up of the University of Trento (Italy). Technical specifications Name: Version: Software Producer: TimberTech Buildings R Timber Tech s.r.l. Via della Villa, 22/A I Villazzano Trento (TN) Italy License registered to Timber Tech s.r.l.

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13 Materials Wooden materials The materials used in the project are listed in the following tables. Descr. ff mm,kk ff tt,0,kk ff tt,90,kk ff cc,0,kk ff cc,90,kk ff vv,kk EE 0,mmmmmmmm EE 0,05 EE 90,mmmmmmmm GG mmmmmmmm ρρ kk Description Characteristic bending strength Characteristic tensile strength along the grain Characteristic tensile strength perpendicular to the grain Characteristic compressive strength along the grain Characteristic compressive strength perpendicular to the grain Characteristic shear strength Mean value of modulus of elasticity along the grain Fifth percentile value of modulus of elasticity along the grain Mean value of modulus of elasticity perpendicular to the grain Mean value of shear modulus Characteristic density ff vv,kk,iiiiiiiiiiiiii Characteristic in-plane shear strength of CLT panel ff RR,kk ff TT,kk GG RR,mmmmmmmm Characteristic rolling shear strength Torsional resistance of the glued interfaces Mean value of rolling shear modulus Homogeneous glued-laminated timber Descr. ff mm,kk [MPa] ff tt,00,kk [MPa] ff tt,9999,kk [MPa] ff cc,00,kk [MPa] ff cc,9999,kk [MPa] ff vv,kk [MPa] EE 00,mmmmmmmm [MPa] EE 00,0000 [MPa] EE 9999,mmmmmmmm [MPa] GG mmmmmmmm [MPa] ρρ kk [kg/m 3 ] GL 24h

14 CLT Descr ff mm,kk [MPa] ff tt,00,kk [MPa] ff tt,9999,kk [MPa] ff cc,00,kk [MPa] ff cc,9999,kk [MPa] ff vv,kk,pppppppppp [MPa] ff RR,kk [MPa] ff vv,kk,llllllllll [MPa] ff TT,kk [MPa] EE 00,mmmmmmmm [MPa] EE 00,0000 [MPa] EE 9999,mmmmmmmm [MPa] GG mmmmmmmm [MPa] GG RR,mmmmmmmm [MPa] ρρ kk [kg/m 3 ] C 24 LAM C 24 LAM Screws Manufacturer Code Descr. Type l [mm] d1 [mm] d2 [mm] ff uuuu [MPa] HBS 10 x 120 HBS10120 HBS 10 x

15 Calculation method and numerical model Model Description Hypothesis adopted for the elements The timber walls are constrained at the base by means of connection systems capable of transmitting both in-plane and out-of-plane actions. The floors are schematized simply supported by the walls or by the beams and the columns are modelled with hinged ends. The horizontal elements are considered infinitely rigid in their plane and with three degrees of freedom: two translational and one rotational. In the analysis, in presence of horizontal loads, some elements may be defined as secondary : this mean that their strength and stiffness are neglected in the calculation of the response of the building. In the model these elements are represented in terms of mass and they are designed only for vertical loads. Rigid body rocking Forces on hold-down / tie-down The hold-down or tie-down systems are used to prevent the rotation of the wall caused by the overturning moment of the horizontal force. The hold-down, placed on the in-tension edge of the wall, is loaded by a force equal to TT = MM 3 3 bb NN 2 1 ffffff aaaaaaaaaaaa hoooooo dddddddd nn aaaaaa 0 ffffff iiiiiiiiiiiiiiii hoooooo dddddddd where: bb NN is the lever arm for the internal couple, assumed equal to 0.9 ll, where ll is the length of the wall is the axial vertical load acting on the wall MM 3 3 is the moment acting in the plane of the wall nn aaaaaa is the number of connections present at each corner of the wall

16 Figure: Calculation model for determining the tensile force acting on the hold-down Structural elements The following table shows the positions of the individual walls. The last four columns show the coordinates of the corners of each wall. 1 e 1 indicate the coordinates of the starting point of the wall 2 e 2 indicate the coordinates of the end point of the wall Wall name Type of wall Element resistant to horizontal loads Height [m] Length [m] Altitude [m] 1 [m] 1 [m] 2 [m] 2 [m] Wall 1 CLT es Wall 11 CLT es Wall 13 CLT es Wall 14 CLT es Wall 15 CLT es Wall 20 CLT es Wall 21 CLT es Wall 22 CLT es Wall 23 CLT es Wall 25 CLT es Wall 26 CLT es

17 Wall 27 CLT es Wall 29 CLT es Wall 3 CLT es Wall 30 CLT No Wall 31 CLT es Wall 33 CLT es Wall 34 CLT es Wall 35 CLT es Wall 36 CLT es Wall 37 CLT No Wall 38 CLT es Wall 39 CLT es Wall 4 CLT es Wall 42 CLT es Wall 43 CLT es Wall 46 CLT es Wall 54 CLT es Wall 6 CLT es Wall 61 CLT es Wall 62 CLT es Wall 63 CLT es Wall 64 CLT No Wall 66 CLT es Wall 67 CLT es Wall 71 CLT es

18 Wall 72 CLT es Wall 72 CLT es Wall 73 CLT es Wall 74 CLT No Wall 75 CLT No Wall 76 CLT No Wall 77 CLT No Wall 78 CLT No Wall 8 CLT es Wall 9 CLT es Wall2 CLT No Wall3 CLT es The following table shows the positions of the columns. e are the coordinates of the point where the column is located Column name Height [m] Altitude [m] [m] [m] Column Column Column Column Column Column Column Column Column

19 Wall horizontal stiffness The wall stiffness can be estimated considering the contributions of all the components, as shown below. CLT walls The overall stiffness of CLTwalls is calculated taking into account the contribution of the following components: CLT panel (k LAM) shear connections angle s (k a) hold-down or tie-down (k h) Figure: Mechanical model for determining the CLT walls overall stiffness The following table indicates the positions of the walls and their equivalent shear stiffness. Wall name Type of wall Element resistant to horizontal loads Height [m] Length [m] Equivalent shear stiffness [kn/m] Wall 1 CLT es Wall 11 CLT es Wall 13 CLT es

20 Wall 14 CLT es Wall 15 CLT es Wall 20 CLT es Wall 21 CLT es Wall 22 CLT es Wall 23 CLT es Wall 25 CLT es Wall 26 CLT es Wall 27 CLT es Wall 29 CLT es Wall 3 CLT es Wall 30 CLT No Wall 31 CLT es Wall 33 CLT es Wall 34 CLT es Wall 35 CLT es Wall 36 CLT es Wall 37 CLT No Wall 38 CLT es

21 Wall 39 CLT es Wall 4 CLT es Wall 42 CLT es Wall 43 CLT es Wall 46 CLT es Wall 54 CLT es Wall 6 CLT es Wall 61 CLT es Wall 62 CLT es Wall 63 CLT es Wall 64 CLT No Wall 66 CLT es Wall 67 CLT es Wall 71 CLT es Wall 72 CLT es Wall 72 CLT es Wall 73 CLT es Wall 74 CLT No Wall 75 CLT No

22 Wall 76 CLT No Wall 77 CLT No Wall 78 CLT No Wall 8 CLT es Wall 9 CLT es Wall2 CLT No Wall3 CLT es Types of structural elements and sign conventions Linear elements The linear elements are used to model beams and columns. They have a local reference system with respect to which stress/force components are shown. The sign convention adopted is shown in the figure below. Force Description Unit of measure N Axial force kn M3-3 Bending moment about local axis 3 kn m V2 Shear along local axis 2 kn M2-2 Bending moment about local axis 2 kn m V3 Shear along local axis 3 kn

23 Figure: sign conventions for beams Figure: sign conventions for columns

24 Wall elements The walls, regardless of type, have the following sign conventions. In-plane stresses Out-of-plane stresses (plate) Stress Description Unit of measure n Axial stress (per unit length) kn/m m3-3 Bending moment about local axis 3 (per unit length) knm/m v2 Shear along local axis 2 (per unit length) kn/m m2-2 Bending moment about local axis 2 (per unit length) knm/m v3 Shear along local axis 3 (per unit length) kn/m In-plane stresses Out-of-plane stresses (plate) Force Description Unit of measure N Total axial force kn M3-3 Bending moment about local axis 3 knm V2 Shear along local axis 2 kn M2-2 Bending moment about local axis 3 knm V3 Shear along local axis 2 kn Figure: sign conventions for walls

25 Actions and design loads Self-weight of structural materials The weights of the structural materials are shown in the table below. Description Specific weight ɣ [kn/m 3 ] GL 24h 6 C 24 LAM 6 Snow loads The snow load is evaluated in accordance with the Italian Standard (3.4 - NTC 08). Snow load on the roof can be evaluated using expression NTC 08 where qq ss = μμ ii qq ssss CC EE CC tt qq ss μμ ii qq ssss CC EE CC tt is the value of the snow load on the roof is the shape coefficient is the characteristic ground snow load is the exposure coefficient is the thermal coefficient Characteristic ground snow load at the site Province: Trento Elevation mamsl: 193 m Snow load zone: Zone I - Alpine Characteristic ground snow load: 1.50 kn/m 2 Topographic category: Normal topography : Exposure coefficient: 1 Thermal coefficient: 1 Snow is not prevented from sliding off: No

26 Snow load on the roof The value of the snow load acting on each roof is shown in the following table. Roof name Snow load [kn/m 2 ] Floor Floor Wind actions The wind load is evaluated in accordance with the Italian standard (section 3.3 of NTC 08). The wind action is represented by a simplified set of pressures or forces whose effects are equivalent to the extreme effects of the turbulent wind. For the usual structures the wind action are considered as equivalent static actions evaluated as described in NTC 08. Project data Province: Trento Elevation mamsl: 193 m Wind load zone: Zone 1 Terrain roughness class: Distance from the coast: Exposure category: Class A Hinterland V Reference mean (basic) velocity The fundamental value of the basic wind velocity, vb, is the characteristic 10 minutes mean wind velocity, irrespective of wind direction and time of year, at 10 m above ground level in terrain with exposure category II (Tab. 3.3.II) and referring to a return period of 50 years. The value of the basic wind velocity vv bb is given by the expression: vv bb = vv bb,0 vv bb = vv bb,0 + kk aa (aa ss aa 0 ) for as a0 for a0 < as 1500 m where: vv bb,0, aa 0, kk aa aa ss vv bb,0 aa 0 are factors which are dependent on the site where the building is located (Fig ) is the altitude above sea level (in m) of the site where the building is located. 25 m/s 1000 m

27 kk aa /s Reference velocity: m/s Reference velocity pressure The reference velocity pressure qb (in N/m²) is given by the expression: where qq bb = 1 2 ρρ vv bb 2 vv bb is the reference velocity of the wind (in m/s); ρρ is the air density conventionally assumed constant and equal to 1,25 kg/m 3. So qq bb N/m 2 Wind pressure acting on the building surfaces The wind pressure acting on the building surfaces is given by the following expression where pp = qq bb cc ee cc pp cc dd qq bb cc ee is reference velocity pressure is the exposure factor depending on the height z on the ground; it can be calculated with the following expression: cc ee (zz) = kk rr 2 cc tt ln zz zz cc tt ln zz zz 0 cc ee (zz) = cc ee (zz min ) for z z min for z<z min where cc tt cc pp cc dd is the topography factor is the pressure coefficient is the dynamic factor which takes into account the increasing effect from vibrations due to turbulence The values assumed in the calculations for the coefficients mentioned above are reported in the following tables. Description Value Dynamic factor 1

28 Figure: Values of the coefficient c pe depending on the inclination of the surface. Below are the values of c pe e c pi. The internal pressure coefficient, which gives the effect of the wind on the internal surfaces of buildings, is equal to zero if the building is airtight, conversely it is equal to ±0.2 if the building has openings. Internal and external pressures are considered to act at the same time. The worst combination of external and internal pressures are considered for every combination of possible openings. Building element Inclined at an angle [ ] cpe Windward wall Leeward wall Leeward roof pitch Windward pitch Type of construction cpi Airtight 0

29 Loads acting on the walls The following table shows the loads acting on the walls. Load name: Position: g 1,k: g 2,k: q,wind,k: Load ID Position of the wall: internal or external Permanent action: self-weight Permanent action Variable actions: wind load Wall name Position Load name g1,k [kn/m 2 ] g2,k [kn/m 2 ] q,wind,k downwind [kn/m 2 ] q,wind,k windward [kn/m 2 ] Wall 1 External External wall load Wall 3 External External wall load Wall 4 External External wall load Wall 6 External External wall load Wall 8 External External wall load Wall 9 External External wall load Wall 11 External External wall load Wall 13 External External wall load Wall 14 External External wall load Wall 15 External External wall load Wall 20 External External wall load Wall 21 External External wall load Wall 22 External External wall load Wall 23 External External wall load Wall 25 External External wall load Wall 26 External External wall load Wall 27 External External wall load

30 Wall 29 External External wall load Wall 30 External External wall load Wall 31 External External wall load Wall 33 External External wall load Wall 34 External External wall load Wall 35 External External wall load Wall 36 External External wall load Wall 37 External External wall load Wall 38 External External wall load Wall 39 External External wall load Wall 42 External External wall load Wall 43 External External wall load Wall 46 External External wall load Wall 54 External External wall load Wall 61 External External wall load Wall 62 External External wall load Wall 63 External External wall load Wall 64 External External wall load Wall 66 External External wall load Wall 67 External External wall load Wall 71 External External wall load Wall 72 External External wall load Wall 72 External External wall load Wall 73 External External wall load Wall 74 External External wall load Wall 75 External External wall load

31 Wall 76 External External wall load Wall 77 External External wall load Wall 78 External External wall load Wall2 External External wall load Wall3 External External wall load Loads acting on the floors The following table shows the characteristic values of the loads acting on the decks. Load name: Position: Load ID Position of the floor: internal or external Environment: Load category α: Roof pitch angle g 1,k: g 2,k: q,k: q,snow,k: q,wind,k: Permanent action: self-weight Permanent action Variable actions Variable actions: snow load Variable actions: wind load Floor name Position α [ ] Load name Environment g1,k [kn/m 2 ] g2,k [kn/m 2 ] q,k [kn/m 2 ] q,snow,k [kn/m 2 ] q,wind,k leeward [kn/m 2 ] q,wind,k windward [kn/m 2 ] Floor 1 Internal floor 0 Residential environment load Live loads cat. A - Residential rooms and related services, hotels Floor 3 Roof 22 Roof load Live loads cat. H1 - Roofs accessible only for maintenance and repair Floor 12 Internal floor 25 Residential environment load Live loads cat. A - Residential rooms and related services, hotels Floor 13 Internal floor 25 Residential environment load Live loads cat. A - Residential rooms and related services, hotels Floor 14 Roof 22 Roof load Live loads cat. H1 - Roofs accessible only for maintenance and repair Floor 15 Internal floor 0 Residential environment load Live loads cat. A - Residential rooms and related services, hotels

32 action The seismic action was evaluated according to the Italian standard NTC '08. The response spectra are calculated using three parameters depending on the characteristic of the site in question: aa gg FF 0 TT CC is the design ground acceleration on type A ground (Peak Acceleration) is the horizontal spectral acceleration amplification factor is the period when the spectrum constant-velocity starts The main parameters regarding the structure and the seismic parameters of the site are summarized below with reference to different limit states. Type of construction: Ordinary structures Nominal service life of the structure: 50 Use Class: Class II Building with normal crowding, without hazardous contents to the environment and without essential public functions Use Class parameter C u: 1 Reference Service Life (VV RR = VV NN CC UU ): 50 Limit States PVR TR [years] ag [g] F0 TC* SLO Operational Limit State 81% SLD Damage Limit State 63% SLV Life Safety Limit State 10% SLC Collapse Prevention Limit State 5% The following are the parameters of the site affecting the local seismic response. type: B - Tab. 3.2.II Deposits of very dense sand, gravel, or very stiff clay, at least several tens of metres in thickness, characterised by a gradual increase of mechanical properties with depth Topographic category: isolated cliffs with average slope angles i 15 T1 - Tab. 3.2.IV Plains, slopes and Topographic amplification factor S T: Limit states SS CC S TB [s] TC [s] TD [s] SLO Operational Limit State SLD Damage Limit State SLV Life Safety Limit State SLC Collapse Prevention Limit State

33 where S S s C C TB TC TD is the Soil Factor stratigraphic amplification factor a coefficient depending on the category of subsoil is the period when the plateau at constant acceleration of the spectrum starts is the period when this plateau ends is the value defining the beginning of the constant displacement response range of the spectrum Horizontal elastic response spectra Horizontal elastic response spectra are reported below; they are calculated using the following values of the parameters η e ξ η 1.00 ξ 5% η is the damping correction factor with a reference value of η = 1 for 5% viscous damping. Design spectra ULS To avoid explicit inelastic structural analysis in design, the capacity of the structure to dissipate energy, through mainly ductile behaviour of its elements and/or other mechanisms, is taken into account by performing an elastic analysis based on a response spectrum reduced with respect to the elastic one, henceforth called a ''design spectrum''. This reduction is accomplished by introducing the behaviour factor q. The design spectrum for elastic analysis Sd(T) can be calculated by substituting η with 1/q in formulas NTC 08 where q is the behaviour factor.

34 qq = qq 0 KK RR K R is a reduction factor of the value of the behaviour factor q for buildings non-regular in elevation Below are the parameters relating to the characteristics of the building: Elevation Regularity: es K R: 1.0 Ductility class: Ductility class "B" Structural typology: Glued wall panels - Tab. 7.7.I Glued wall panels with glued diaphragms, connected with nails and bolts Base value of the behavior factor q 0: 2.00 Behaviour factor q: 2.00 The horizontal elastic response spectra and the horizontal design spectrum (Life Safety Limit State) are shown below.

35 Sections of the structural elements CLT walls The following table shows the CLT walls characteristics. Section name CLT 120 mm - 5 layers - vertical joints CLT 100 mm - 3 layers Manufacturer Panel name Material Layers number Thickness [mm] Predefinito 100 5s T C 24 LAM Layers Orientation of the outer layers Vertical Predefinito 100 3s T C 24 LAM Vertical The characteristics of the walls with vertical joints between the CLT panels are summarized below. Section name CLT 120 mm - 5 layers - vertical joints Type of joint between the panels Inclined screws Length of the single panel bp [mm] Metal fastener Spacing of the fasteners sc [mm] 1250 HBS 10 x Figure: Vertical wall panels joint joint with inclined screws

36 Floors with timber joists Elements geometric characteristics h b: b b: i b: Cross section height Cross section width Joists spacing Figure: geometric characteristics of the floor The following table sets out the details concerning the floor with joists. Section name Material Cross section height hb [mm] Cross section width bb [mm] Joists spacing ib [mm] Joist floor 160x240 GL 24h CLT floors Floor geometric characteristic h b: CLT panel thickness Figure: CLT floor geometric characteristics The following table sets out the details concerning the CLT floors. Section name Manufacturer CLT panel name Material Number of layers Thickness hb[mm] CLT floor Predefinito 140 5s L C 24 LAM Layers External layers orientation Parallel to the calculation direction

37 Cross section of timber linear elements The following table sets out the details concerning the cross section of every linear element. Section name Material Width b [mm] Height h [mm] Area A [mm 2 ] Jy-y [mm 4 ] Jz-z [mm 4 ] Section 200x240 GL 24h GL 24h E8 1.60E8 Section 200x440 GL 24h GL 24h E9 2.93E8 Section 200x520 GL 24h GL 24h E9 3.47E8 Figure: Geometric size of every timber cross section Connections Hold Down Figure: graphical representation of a hold-down in a base connection (timber wall foundation connection)

38 Connection name connection - hold down - shear angle connection - hold down - shear angle 3 connection - hold down - shear angle 2 connection - hold down - shear angle 4 Connection position connection connection connection connection Manufacture r Description Fasteners number Rotho Blass WHT Rotho Blass WHT Rotho Blass WHT Rotho Blass WHT Fastener typology Chiodi Anker 4,0 40 Chiodi Anker 4,0 60 Chiodi Anker 4,0 60 Chiodi Anker 4,0 60 Anchor M M M M Type of anchor Resina vinilestere ETA-09/0078 Resina vinilestere ETA-09/0078 Resina vinilestere ETA-09/0078 Resina vinilestere ETA-09/0078 Anchorage depth [mm] Number of hold-down at each wall end Timber-reinforced concrete connection Figure: graphical representation of the shear connection with angle s Connection name connection - hold down - shear angle connection - hold down - shear angle 3 connection - hold down - shear angle 2 connection - hold down - shear angle 4 Connection position connection connection connection connection Manufactur er Rotho Blaas Rotho Blaas Rotho Blaas Rotho Blaas Descripti on Titan TCN 200 WBR100 con rinforzo Titan TCN 200 Titan TCN 240 Fasteners number on the vertical plate Fastener typology Chiodi Anker 4,0 60 Chiodi Anker 4,0 60 Chiodi Anker 4,0 60 Chiodi Anker 4,0 60 Anchors number Anchor 2 M M M12 2 M16 Type of anchor Resina vinilestere ETA- 09/0078 Resina vinilestere ETA- 09/0078 Ancorante avvitabile SKR Ancorante pesante AB ETA- 07/0067 Number of sides Angle s spacing i [mm]

39 Double Hold Down Figure: graphical representation of the hold-down connection at the upper floors Connection name Connection position Manufacturer Description Fasteners number Fastener typology Bolt Number of connections at each wall end Upper level - 2 hold down - shear angle Upper level Rotho Blass WHT Chiodi Anker 4,0 60 M Upper level - User connection Upper level Rotho Blass WHT Chiodi Anker 4,0 60 M Angle - Timber to timber connection Figure: graphical representation of the timber to timber shear connection with angle s

40 Connection name Upper level - 2 hold down - shear angle Connection position Manufacturer Description Number of fasteners on the vertical plate Number of fasteners on the horizontal plate Upper level Rotho Blaas Titan TTN Fasteners typology vertical plate Chiodi Anker 4,0 60 Fasteners typology horizontal plate Chiodi Anker 4,0 60 SIdes number Angle s spacing i [mm] Upper level - User connection Upper level Definito da utente Definito da utente 1 1 Utente Utente 1 500

41 Combinations of actions For each critical load case, the design values of the effects of actions shall be determined by combining the values of actions that are considered to occur simultaneously. Combination of actions for persistent or transient design situations (fundamental combination - ULS): γγ GG1 GG 1 + γγ GG2 GG 2 + γγ PP PP + γγ QQ QQ kk1 + γγ QQ2 ψψ 02 QQ kk2 + γγ QQ3 ψψ 03 QQ kk3 + Combination of actions for seismic design situations E: being EE + GG 1 + GG 2 + PP + ψψ 21 QQ kk1 + ψψ 22 QQ kk2 + G1 G2 Q1 Qki γγ GG1 γγ GG2 permanent action: self weight permanent actions characteristic value of the main variable action characteristic value of the i-th variable action is the partial factor for the self-weight action is the partial factor for the permanent actions action The following are the values of the combination coefficients used. Snow/wind loads Load name Description Load-duration ψ0 ψ1 ψ2 Wind Wind pressure Instantaneous 0,6 0,2 0 Snow Snow load (altitude 1000 mamsl) Short-term 0,5 0,2 0 Snow Snow load (altitude> 1000 mamsl) Medium-term 0,7 0,5 0,2 Variable actions Recommended values of ψ factors for buildings Category name Description Load-duration ψ0 ψ1 ψ2 Live load cat.a Live load cat.a: domestic, residential areas Medium-term 0,7 0,5 0,3 Live load cat.b Live load cat.b: office areas Medium-term 0,7 0,5 0,3 Live load cat.c Live load cat.c: shopping areas Medium-term 0,7 0,7 0,6

42 Live load cat.d Live load cat.d: storage areas Medium-term 0,7 0,7 0,6 Live load cat.e Live load cat.f Live load cat.g Live load cat.h Live load cat.h2-a Live load cat.h2-b Live load cat.h2-c Live load cat.h2-d Live load cat.h2-e Live load cat.e: Libraries, archives, warehouses and industrial areas Live load cat.f: traffic area, vehicle weight 30kN Live load cat.g: traffic area, vehicle weight > 30 kn Live load cat.h: roofs accessible only for maintenance Live load cat.h2-a: Practicable roofs of category A areas Live load cat.h2-b: Practicable roofs of category B areas Live load cat.h2-c: Practicable roofs of category C areas Live load cat.h2-d: Practicable roofs of category D areas Live load cat.h2-e: Practicable roofs of category E areas Long-term 1,0 0,9 0,8 Long-term 0,7 0,7 0,6 Long-term 0,7 0,5 0,3 Medium-term Medium-term Medium-term Medium-term Medium-term Medium-term 0 0 0

43 Combinations of actions used Vertical ULS loads combinations The following table shows the ULS load combinations relevant for verifications in conditions of vertical load. The coefficient values listed correspond to the product of the partial safety factor γγ jj and the combination factors ψψ 0jj. The action of the wind is schematized with a uniform load orthogonal to each external wall. Nome Durata G1 G2 Variable Variable Orthogonal Wind Wind Snow cat.a cat.h wind ULS ULS SLS SLS ULS 1 Permanent ULS 2 Medium-term ULS 3 Short-term ULS 4 Instantaneous ULS 5 Instantaneous ULS 6 Medium-term ULS 7 Medium-term ULS 8 Short-term ULS 9 Short-term ULS 10 Instantaneous ULS 11 Instantaneous ULS 12 Instantaneous ULS 13 Instantaneous ULS 14 Short-term ULS 15 Short-term ULS 16 Instantaneous ULS 17 Instantaneous ULS 18 Instantaneous ULS 19 Instantaneous ULS 20 Instantaneous ULS 21 Instantaneous ULS 22 Permanent ULS 23 Medium-term ULS 24 Short-term ULS 25 Instantaneous ULS 26 Instantaneous ULS 27 Medium-term ULS 28 Medium-term ULS 29 Short-term ULS 30 Short-term ULS 31 Instantaneous ULS 32 Instantaneous ULS 33 Instantaneous ULS 34 Instantaneous ULS 35 Short-term ULS 36 Short-term ULS 37 Instantaneous ULS 38 Instantaneous ULS 39 Instantaneous ULS 40 Instantaneous ULS 41 Instantaneous ULS 42 Instantaneous ULS 43 Permanent ULS 44 Medium-term ULS 45 Short-term ULS 46 Instantaneous ULS 47 Instantaneous ULS 48 Medium-term ULS 49 Medium-term ULS 50 Short-term ULS 51 Short-term ULS 52 Instantaneous ULS 53 Instantaneous ULS 54 Instantaneous ULS 55 Instantaneous ULS 56 Short-term ULS 57 Short-term ULS 58 Instantaneous ULS 59 Instantaneous ULS 60 Instantaneous ULS 61 Instantaneous ULS 62 Instantaneous ULS 63 Instantaneous ULS 64 Permanent ULS 65 Medium-term ULS 66 Short-term ULS 67 Instantaneous ULS 68 Instantaneous ULS 69 Medium-term ULS 70 Medium-term ULS 71 Short-term ULS 72 Short-term ULS 73 Instantaneous ULS 74 Instantaneous ULS 75 Instantaneous

44 ULS 76 Instantaneous ULS 77 Short-term ULS 78 Short-term ULS 79 Instantaneous ULS 80 Instantaneous ULS 81 Instantaneous ULS 82 Instantaneous ULS 83 Instantaneous ULS 84 Instantaneous Horizontal ULS loads combinations The following table shows the ULS load combinations relevant for verifications in conditions of vertical load. The coefficient values listed correspond to the product of the partial safety factor γγ jj and the combination factors ψψ 0jj. The action of the wind is schematized with a uniform load orthogonal to each external wall and it acts separately in the directions x, -x, y, -y. Name Horizontal ULS 1 Horizontal ULS 2 Horizontal ULS 3 Horizontal ULS 4 Horizontal ULS 5 Horizontal ULS 6 Horizontal ULS 7 Horizontal ULS 8 Load-duration Variable Variable Orthogonal Wind Wind G1 G2 Snow class cat.a cat.h wind ULS ULS SLS SLS Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Combination of actions for rare SLS Name SLS characteristic 1 SLS characteristic 2 SLS characteristic 3 SLS characteristic 4 SLS characteristic 5 SLS characteristic 6 SLS characteristic 7 SLS characteristic 8 SLS characteristic 9 SLS characteristic 10 SLS characteristic 11 SLS characteristic 12 SLS characteristic 13 SLS characteristic 14 SLS characteristic 15 SLS characteristic 16 SLS characteristic 17 SLS characteristic 18 SLS characteristic 19 SLS characteristic 20 SLS characteristic 21 Load-duration Variable Variable Orthogonal Wind Wind G1 G2 Snow class cat.a cat.h wind ULS ULS SLS SLS Permanent Medium-term Short-term Instantaneous Instantaneous Medium-term Medium-term Short-term Short-term Instantaneous Instantaneous Instantaneous Instantaneous Short-term Short-term Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous

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46 load combinations The seismic load combination used are those proposed by Italian technical standards NTC 08. The action effects due to the combination of the horizontal components of the seismic action are computed using the following combinations: with rotation of the multipliers. 1,00 EE xx + 0,3 EE yy Combinations of actions for Life Safety Limit State (SLV) Name 1 ex+ ey+ 1 ex+ ey- 1 ex- ey+ 1 ex- ey- 2 ex+ ey+ 2 ex+ ey- 2 ex- ey+ 2 ex- ey- 3 ex+ ey+ 3 ex+ ey- 3 ex- ey+ 3 ex- ey- 4 ex+ ey+ 4 ex+ ey- 4 ex- ey+ 4 ex- ey- 5 ex+ ey+ 5 ex+ ey- 5 ex- ey+ 5 ex- ey- 6 ex+ ey+ 6 ex+ ey- 6 ex- ey+ 6 ex- ey- 7 ex+ ey+ 7 ex+ ey- 7 ex- ey+ 7 ex- ey- 8 ex+ ey+ 8 ex+ ey- 8 ex- ey+ 8 ex- ey- Load-duration Variable Variable Orthogonal Wind Wind G1 G2 Snow class cat.a cat.h wind ULS ULS SLS SLS Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous

47 Combinations of actions for Damage Limit State (SLD) Name SLS 1 ex+ ey+ SLS 1 ex+ ey- SLS 1 ex- ey+ SLS 1 ex- ey- SLS 2 ex+ ey+ SLS 2 ex+ ey- SLS 2 ex- ey+ SLS 2 ex- ey- SLS 3 ex+ ey+ SLS 3 ex+ ey- SLS 3 ex- ey+ SLS 3 ex- ey- SLS 4 ex+ ey+ SLS 4 ex+ ey- SLS 4 ex- ey+ SLS 4 ex- ey- SLS 5 ex+ ey+ SLS 5 ex+ ey- SLS 5 ex- ey+ SLS 5 ex- ey- SLS 6 ex+ ey+ SLS 6 ex+ ey- SLS 6 ex- ey+ SLS 6 ex- ey- SLS 7 ex+ ey+ SLS 7 ex+ ey- SLS 7 ex- ey+ SLS 7 ex- ey- SLS 8 ex+ ey+ SLS 8 ex+ ey- SLS 8 ex- ey+ SLS 8 ex- ey- Load-duration Variable Variable Orthogonal Wind Wind G1 G2 Snow class cat.a cat.h wind ULS ULS SLS SLS Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous

48

49 Horizontal actions analysis The analysis of the structure subject to seismic action is performed using linear equivalent static analysis which involves the application of equivalent static horizontal forces to all storeys. For buildings with heights of up to 40 m the value of T1 (in s) may be approximated by the following expression: where: TT 1 = CC 1 HH 3 4 HH CC 1 is the height of the building, in m, from the foundation or from the top of a rigid basement is 0,05 as proposed by NTC 08 for structures different from moment resistant space steel frames, moment resistant space concrete frames and eccentrically braced steel frames. The structure has a period TT 1 equal to 0.23 s. When the fundamental mode shape is approximated by horizontal displacements increasing linearly along the height, the horizontal forces Fi should be taken as being given by: where: FF h = SS dd (TT 1 ) WW λλ gg is the base shear force FF ii = FF h zz ii WW ii jj zz jj WW jj FF ii WW ii e WW jj zz ii e zz jj is the horizontal force acting on storey i are the storey weights are the heights, with respect to the foundation, of the masses i and j SS dd (TT 1 ) is the ordinate of the design spectrum at period T 1 WW λλ gg is the total weight of the construction is the correction factor, the value of which is equal to: λλ = 0,85 if T1 < 2 T C and the building has more than two storeys, or λλ = 1,0 otherwise is the acceleration of gravity

50 The inertial effects of the design seismic action shall be evaluated by taking into account the presence of the masses associated with all gravity loads appearing in the following combination of actions: G 1 + G 2 + ψ 2j Q kj The base shear forces for SLD and SLV and the respective acceleration values are given below. j Ordinate of the design spectrum SLV Sd (T 1): Total base shear force F h SLV: Ordinate of the spectrum SLD Sd (T 1): Total base shear force F h SLD: 0.12 g kn 0.11 g kn The table below illustrates the horizontal forces acting on the storeys due to the seismic action and the coordinates of their respective application points. Storey Height above foundation zi [m] xg [m] yg [m] Mass i [kg] Fi,SLV [kn] Fi,SLD [kn] Wind The table below illustrates the horizontal forces acting on the storeys due to the wind action and the coordinates of their respective application points. Storey Height above foundation [m] xg,wind [m] yg,wind [m] Fx [kn] Fy [kn]

51 The action effects In this chapter are reported the internal stresses present in the structural elements and their connections caused by the different loads. Walls Wall name: Wall ID N: Total axial force V2: Shear force (in-plane) V3: Shear force (out-of-plane) M2-2: M3-3: Va: Ta: dr: Bending moment (out-of-plane) Bending moment (in-plane) Shear force on the single connection Tensile force on the single anchor Interstory drift Load Wall name N [kn] V2 [kn] V3 [kn] G1 Wall G1 Wall G1 Wall G1 Wall G1 Wall G1 Wall G1 Wall G1 Wall G1 Wall G1 Wall G1 Wall G1 Wall G1 Wall G1 Wall G1 Wall G1 Wall G1 Wall G1 Wall G1 Wall N/D G1 Wall G1 Wall G1 Wall G1 Wall G1 Wall G1 Wall N/D G1 Wall G1 Wall G1 Wall G1 Wall G1 Wall G1 Wall G1 Wall G1 Wall G1 Wall G1 Wall N/D G1 Wall G1 Wall G1 Wall G1 Wall M2-2 [knm] M3-3 [knm] Va [kn] Ta [kn] dr [mm]

52 G1 Wall G1 Wall G1 Wall N/D G1 Wall N/D G1 Wall N/D G1 Wall N/D G1 Wall N/D G1 Wall N/D G1 Wall G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall N/D G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall N/D G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall N/D G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall G2 Wall N/D G2 Wall N/D G2 Wall N/D G2 Wall N/D G2 Wall N/D G2 Wall N/D G2 Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall

53 Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall N/D Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall N/D Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall N/D Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall Variable cat.a Wall N/D Variable cat.a Wall N/D Variable cat.a Wall N/D Variable cat.a Wall N/D Variable cat.a Wall N/D Variable cat.a Wall N/D Variable cat.a Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall N/D Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall N/D Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall N/D Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall Variable cat.h Wall N/D

54 Variable cat.h Wall N/D Variable cat.h Wall N/D Variable cat.h Wall N/D Variable cat.h Wall N/D Variable cat.h Wall N/D Variable cat.h Wall Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall N/D Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall N/D Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall N/D Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall Snow Wall N/D Snow Wall N/D Snow Wall N/D Snow Wall N/D Snow Wall N/D Snow Wall N/D Snow Wall Orthogonal wind Wall Orthogonal wind Wall Orthogonal wind Wall Orthogonal wind Wall Orthogonal wind Wall Orthogonal wind Wall Orthogonal wind Wall Orthogonal wind Wall Orthogonal wind Wall Orthogonal wind Wall Orthogonal wind Wall Orthogonal wind Wall Orthogonal Wall

55 wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Orthogonal wind Wall Wall Wall Wall Wall Wall N/D Wall Wall Wall Wall Wall Wall N/D Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall N/D Wall Wall Wall Wall Wall Wall Wall N/D Wall N/D Wall N/D Wall N/D Wall N/D Wall N/D Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall N/D Wind Wall

56 Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall N/D Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall N/D Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall N/D Wind Wall N/D Wind Wall N/D Wind Wall N/D Wind Wall N/D Wind Wall N/D Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall N/D Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall N/D Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall N/D Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall Wind Wall N/D Wind Wall N/D Wind Wall N/D Wind Wall N/D Wind Wall N/D

57 Wind Wall N/D Wind Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall N/D Wall Wall Wall Wall Wall Wall N/D Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall N/D Wall Wall Wall Wall Wall Wall Wall N/D Wall N/D Wall N/D Wall N/D Wall N/D Wall N/D Wall

58 Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall N/D Wall Wall Wall Wall Wall Wall N/D Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall N/D Wall Wall Wall Wall Wall Wall Wall N/D Wall N/D Wall N/D Wall N/D Wall N/D Wall N/D Wall

59 SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall N/D Wall Wall Wall Wall Wall Wall N/D Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall N/D Wall Wall Wall Wall Wall Wall Wall N/D Wall N/D Wall N/D Wall N/D Wall N/D Wall N/D Wall

60 SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS SLS Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall N/D Wall Wall Wall Wall Wall Wall N/D Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall N/D Wall Wall Wall Wall Wall Wall Wall N/D Wall N/D Wall N/D Wall N/D Wall N/D Wall N/D Wall

61 Columns Column name: Column ID N: Total axial force Load Column name N [kn] G1 Column G1 Column G1 Column G1 Column G1 Column G1 Column G1 Column G1 Column G1 Column G2 Column G2 Column G2 Column G2 Column G2 Column G2 Column G2 Column G2 Column G2 Column Variable cat.a Column Variable cat.a Column Variable cat.a Column Variable cat.a Column Variable cat.a Column Variable cat.a Column Variable cat.a Column Variable cat.a Column Variable cat.a Column Variable cat.h Column Variable cat.h Column Variable cat.h Column Variable cat.h Column Variable cat.h Column Variable cat.h Column Variable cat.h Column Variable cat.h Column Variable cat.h Column Snow Column Snow Column Snow Column Snow Column Snow Column Snow Column Snow Column Snow Column Snow Column Orthogonal wind Column Orthogonal wind Column Orthogonal wind Column Orthogonal wind Column Orthogonal wind Column Orthogonal wind Column Orthogonal wind Column Orthogonal wind Column Orthogonal wind Column Wind Column Wind Column Wind Column Wind Column Wind Column Wind Column Wind Column Wind Column

62 Wind Column Wind Column Wind Column Wind Column Wind Column Wind Column Wind Column Wind Column Wind Column Wind Column Column Column Column Column Column Column Column Column Column Column Column Column Column Column Column Column Column Column SLS Column SLS Column SLS Column SLS Column SLS Column SLS Column SLS Column SLS Column SLS Column SLS Column SLS Column SLS Column SLS Column SLS Column SLS Column SLS Column SLS Column SLS Column Floors Floor name: Floor ID V2: Maximum shear stress along the local axis 2 for the most stressed element of the floor M3-3: w ist: Maximum bending moment around local axis 3 for the most stressed element of the floor Maximum deformation for the most stressed element of the floor

63 Load Floor name V2 [kn] M3-3 [knm] wist [mm] G1 Floor G1 Floor G1 Floor G1 Floor G1 Floor G1 Floor G2 Floor G2 Floor G2 Floor G2 Floor G2 Floor G2 Floor Variable cat.a Floor Variable cat.a Floor Variable cat.a Floor Variable cat.a Floor Variable cat.a Floor Variable cat.a Floor Variable cat.h Floor Variable cat.h Floor Variable cat.h Floor Variable cat.h Floor Variable cat.h Floor Variable cat.h Floor Snow Floor Snow Floor Snow Floor Snow Floor Snow Floor Snow Floor Orthogonal wind Floor Orthogonal wind Floor Orthogonal wind Floor Orthogonal wind Floor Orthogonal wind Floor Orthogonal wind Floor Wind Floor Wind Floor Wind Floor Wind Floor Wind Floor Wind Floor Wind Floor Wind Floor Wind Floor Wind Floor Wind Floor Wind Floor Floor Floor Floor Floor Floor Floor Floor Floor Floor Floor Floor Floor SLS Floor SLS Floor SLS Floor SLS Floor SLS Floor SLS Floor

64 SLS Floor SLS Floor SLS Floor SLS Floor SLS Floor SLS Floor Beams Beam name: Beam ID V2: Maximum shear stress along the local axis 2 M3-3: Maximum bending moment around local axis 3 w ist: Maximum deformation for the most stressed element of the floor Load Beam name V2 [kn] M3-3 [knm] wist [mm] G1 Beam G1 Beam G1 Beam G1 Beam G1 Beam G1 Beam G1 Beam G1 Beam G1 Beam G1 Beam G1 Beam G1 Beam G1 Beam G1 Beam G1 Beam G1 Beam G1 Beam G1 Beam G1 Beam G1 Beam G1 Beam G1 Beam G1 Beam G1 Beam G1 Beam G2 Beam G2 Beam G2 Beam G2 Beam G2 Beam G2 Beam G2 Beam G2 Beam G2 Beam G2 Beam G2 Beam G2 Beam G2 Beam G2 Beam G2 Beam G2 Beam G2 Beam G2 Beam G2 Beam G2 Beam G2 Beam G2 Beam G2 Beam G2 Beam

65 G2 Beam Variable cat.a Beam Variable cat.a Beam Variable cat.a Beam Variable cat.a Beam Variable cat.a Beam Variable cat.a Beam Variable cat.a Beam Variable cat.a Beam Variable cat.a Beam Variable cat.a Beam Variable cat.a Beam Variable cat.a Beam Variable cat.a Beam Variable cat.a Beam Variable cat.a Beam Variable cat.a Beam Variable cat.a Beam Variable cat.a Beam Variable cat.a Beam Variable cat.a Beam Variable cat.a Beam Variable cat.a Beam Variable cat.a Beam Variable cat.a Beam Variable cat.a Beam Variable cat.h Beam Variable cat.h Beam Variable cat.h Beam Variable cat.h Beam Variable cat.h Beam Variable cat.h Beam Variable cat.h Beam Variable cat.h Beam Variable cat.h Beam Variable cat.h Beam Variable cat.h Beam Variable cat.h Beam Variable cat.h Beam Variable cat.h Beam Variable cat.h Beam Variable cat.h Beam Variable cat.h Beam Variable cat.h Beam Variable cat.h Beam Variable cat.h Beam Variable cat.h Beam Variable cat.h Beam Variable cat.h Beam Variable cat.h Beam Variable cat.h Beam Snow Beam Snow Beam Snow Beam Snow Beam Snow Beam Snow Beam Snow Beam Snow Beam Snow Beam Snow Beam Snow Beam Snow Beam Snow Beam Snow Beam Snow Beam Snow Beam Snow Beam Snow Beam Snow Beam Snow Beam Snow Beam Snow Beam Snow Beam Snow Beam

66 Snow Beam Orthogonal wind Beam Orthogonal wind Beam Orthogonal wind Beam Orthogonal wind Beam Orthogonal wind Beam Orthogonal wind Beam Orthogonal wind Beam Orthogonal wind Beam Orthogonal wind Beam Orthogonal wind Beam Orthogonal wind Beam Orthogonal wind Beam Orthogonal wind Beam Orthogonal wind Beam Orthogonal wind Beam Orthogonal wind Beam Orthogonal wind Beam Orthogonal wind Beam Orthogonal wind Beam Orthogonal wind Beam Orthogonal wind Beam Orthogonal wind Beam Orthogonal wind Beam Orthogonal wind Beam Orthogonal wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam Wind Beam

67 Wind Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam

68 SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam SLS Beam

69 Forces and moments acting on foundations In this chapter are reported the values of actions acting at the base of the walls and columns of the ground floor. They refer to the ULS combination that maximizes the axial loads and to the different loads considered individually. Walls Wall name: Wall ID N: Total axial force V2: Shear force (in-plane) V3: Shear force (out-of-plane) M2-2: M3-3: Bending moment (out-of-plane) Bending moment (in-plane) Wall name Length N V2 V3 M2-2 M3-3 Load / Comb. [m] [kn] [kn] [kn] [knm] [knm] Wall ULS G G Variable cat.a Variable cat.h Snow Orthogonal wind Wind Wind SLS SLS Wall ULS G G Variable cat.a Variable cat.h Snow Orthogonal wind Wind Wind SLS SLS Wall ULS G G Variable cat.a Variable cat.h Snow Orthogonal wind Wind Wind SLS SLS Wall ULS G G Variable cat.a Variable cat.h Snow Orthogonal wind Wind Wind SLS SLS Wall ULS G

70 G Variable cat.a Variable cat.h Snow Orthogonal wind Wind Wind SLS SLS Wall ULS G G Variable cat.a Variable cat.h Snow Orthogonal wind Wind Wind SLS SLS Wall ULS G G Variable cat.a Variable cat.h Snow Orthogonal wind Wind Wind SLS SLS Wall ULS G G Variable cat.a Variable cat.h Snow Orthogonal wind Wind Wind SLS SLS Wall ULS G G Variable cat.a Variable cat.h Snow Orthogonal wind Wind Wind SLS SLS Wall ULS G G Variable cat.a Variable cat.h Snow Orthogonal wind Wind Wind SLS SLS Wall ULS G G Variable cat.a Variable cat.h Snow Orthogonal wind Wind Wind SLS SLS

71 Wall ULS G G Variable cat.a Variable cat.h Snow Orthogonal wind Wind Wind SLS SLS Wall ULS G G Variable cat.a Variable cat.h Snow Orthogonal wind Wind Wind SLS SLS Wall ULS G G Variable cat.a Variable cat.h Snow Orthogonal wind Wind Wind SLS SLS Wall ULS G G Variable cat.a Variable cat.h Snow Orthogonal wind Wind Wind SLS SLS Wall ULS G G Variable cat.a Variable cat.h Snow Orthogonal wind Wind Wind SLS SLS Wall ULS G G Variable cat.a Variable cat.h Snow Orthogonal wind Wind Wind SLS SLS Wall ULS G G Variable cat.a Variable cat.h Snow Orthogonal wind Wind Wind SLS

72 SLS Wall ULS G G Variable cat.a Variable cat.h Snow Orthogonal wind Wind Wind SLS SLS Wall ULS G G Variable cat.a Variable cat.h Snow Orthogonal wind Wind Wind SLS SLS Columns Column name: Column ID N: Total axial force Column name Load / Comb. N [kn] Column 1 ULS G G Variable cat.a 6.86 Variable cat.h 0.00 Snow 0.00 Orthogonal wind 0.00 Wind 0.00 Wind SLS 0.00 SLS 0.00 Column 2 ULS G G Variable cat.a Variable cat.h 0.00 Snow 0.00 Orthogonal wind 0.00 Wind 0.00 Wind

73 SLS 0.00 SLS 0.00 Column 3 ULS G G Variable cat.a 6.91 Variable cat.h 0.00 Snow 0.00 Orthogonal wind 0.00 Wind 0.00 Wind SLS 0.00 SLS 0.00 Column 11 ULS G G Variable cat.a Variable cat.h 0.00 Snow 0.00 Orthogonal wind 0.00 Wind 0.00 Wind SLS 0.00 SLS 0.00

74

75 Design of the structural elements CLT floors The calculation model adopted for the design of CLT in bending out-of-plane is that of mechanically jointed beams with deformable connection in accordance with Appendix B of EN The shear flexibility of the transverse layers is considered using the γ-method (gamma): namely with Möhler theory for CLT panel having up to 3 layers oriented in the direction of calculation and with Shelling theory for CLT panel having more than 3 layers oriented in the direction of calculation. The effective bending stiffness is taken as: where: nn EEJJ eeeeee = EE ii JJ ii + γγ ii EE ii AA ii aa ii 2 ii=1 γγ ii = 1 + ππ2 EE ii AA ii GG RR bb dd ll 2 rrrrrr 1 JJ ii AA ii aa ii ll rrrrrr GG RR is the moment of inertia of layer i in reference to its neutral axis is the cross-sectional area of layer i is the distance between the centre of gravity of layer i and centre of gravity of the CLT element is the reference length of the span is the rolling shear modulus (mean value) The reference length of the spans (l ref) is taken, depending on the static scheme, as reported in the following table. Structural scheme Simply supported beam Span of a continuous beam Internal support of a continuous beam Cantilever Reference length of the span l ref = l l ref = 0.8 l l ref = 0.8 l min l ref = 2 l The following table shows, for each floor and relatively to the different spans, the values of the reference lengths of the spans, the effective moment of inertia of the cross-sections of the CLT floor and the structural scheme adopted.

76 Floor name Calculation width of the strip of floor [m] Reference length lref [m] Jeff [mm 4 ] Structural scheme Floor E E8 Floor E8 Bending strength The checks are conducted according to of EN The following expression shall be satisfied: being σσ mm,dd the design bending stress ff mm,dd the design bending strength σσ mm,dd ff mm,dd 1 The following table illustrates the structural schemes and the envelopes of the diagram of the bending moment for the part of each floor where the checks are more severe.

77 Floor name Combination Duration Diagram M3-3 Bending stresses Floor 1 ULS 65 Medium-term Floor 15 ULS 65 Medium-term The checks are summarized below. The values resulting from the calculations, relating to each verification, are reported in the form of a percentage. Floor name Section M3-3 [knm] Floor 1 CLT floor Floor 15 CLT floor 4.99 Jeff [mm 4 ] Comb. kmod γm fm,d [MPa] σm,d [MPa] Check ULS % ULS % Shear strength Shear strength of the layers parallel to the calculation direction The checks are conducted according to of EN The following expression shall be satisfied: being: ττ vv,dd the design shear stress ττ vv,dd ff vv,dd 1 ff vv,dd the design shear strength for the actual condition The maximum design shear stress in the longitudinal layers can be evaluated using the following expression: where: ττ vv,dd = VV dd SS mmmmmm JJ eeeeee bb

78 VV dd is the total shear force at the location in question SS mmmmmm is the first moment of area JJ eeeeee is the effective moment of inertia of the CLT element cross section bb is the width of the CLT element cross section (kk cccc = 1) Rolling shear strength of the transversal layers The checks are conducted according to of EN The following expression shall be satisfied: being: ττ RR,dd ff vv,rr,dd 1 ττ RR,dd ff vv,rr,dd the design rolling shear stress the design shear strength The maximum design shear stress in the transversal layers can be evaluated using the following expression: where: ττ RR,dd = VV dd SS RR,mmmmmm JJ eeeeee bb VV dd is the total shear force at the location in question SS RR,mmmmmm is the first moment of area JJ eeeeee is the effective moment of inertia of the CLT element cross section bb is the width of the CLT element cross section (kk cccc = 1) The following table illustrates the structural schemes and the envelopes of the diagram of the shear force for the part of each floor where the checks are more severe. Floor name Combination Duration Diagram V2 Shear stresses Floor 1 ULS 65 Medium-term

79 Floor 15 ULS 65 Medium-term The checks are summarized below. The values resulting from the calculations, relating to each verification, are reported in the form of a percentage. Floor name Cross section V2 [kn] Jeff [mm 4 ] Comb. kmod γm fv,d [MPa] τv,d [MPa] Check fr,d [MPa] τr,d [MPa] Check Floor 1 CLT floor ULS % % Floor 15 CLT floor ULS % %

80 Joist floors / Glued laminated timber floors Bending strength The checks are conducted according to of EN The following expression shall be satisfied: where: σσ mm,dd is the design bending stress ff mm,dd is the design bending strength σσ mm,dd kk cccccccc ff mm,dd 1 kk cccccccc is a factor which takes into account the reduced bending strength due to lateral buckling. k crit is assumed equal to 1.0 for beams in which the lateral displacement of the compressed edge is prevented over the entire length and the torsional rotation is prevented at the supports. Floor name Combination Duration Diagram M3-3 Floor 3 ULS 64 Permanent Floor 12 ULS 65 Medium-term

81 Floor 13 ULS 65 Medium-term Floor 14 ULS 64 Permanent The checks are summarized below. The values resulting from the calculations, relating to each verification, are reported in the form of a percentage. Floor name Floor 3 Floor 12 Floor 13 Floor 14 Section Joist floor 160x240 Joist floor 160x240 Joist floor 160x240 Joist floor 160x240 M3-3 max [knm] W [mm 3 ] kcrit Comb. kmod γm fm,d [MPa] σm,d [MPa] ULS % ULS % ULS % ULS % Check

82 Shear strength The checks are conducted according to of EN The following expression shall be satisfied: where: ττ dd ff vv,dd 1 ττ dd is the design shear stress ff vv,dd is the design shear strength for the actual condition For the verification of shear resistance of members in bending, the influence of cracks should be taken into account using an effective width of the member given as: bb eeee = kk cccc bb where b is the width of the relevant section of the member. The following value of k cr are used k cr = 0.67 for solid timber k cr = 0.67 for glued laminated timber The maximum design shear stress in a rectangular cross section can be evaluated using the following expression: where A is the area of a joist cross section. VV dd ττ dd = 3 2 kk cccc AA The following table illustrates the structural schemes and the envelopes of the shear force diagram for the joist of each floor where the checks are more severe. Floor name Combination Duration Diagram V2 Floor 3 ULS 64 Permanent

83 Floor 12 ULS 65 Medium-term Floor 13 ULS 65 Medium-term Floor 14 ULS 64 Permanent The checks are summarized below. The values resulting from the calculations, relating to each verification, are reported in the form of a percentage. Floor name Floor 3 Floor 12 Floor 13 Floor 14 Section Joist floor 160x240 Joist floor 160x240 Joist floor 160x240 Joist floor 160x240 V2 max [kn] Area [mm 2 ] kcr Comb. kmod γm fv,d [MPa] τ2,d [MPa] ULS % ULS % ULS % ULS % Check

84 Floors deflections (SLS) The deflection checks are carried out according to of EN The net deflection below a straight line between the supports, w net,fin, is taken as: where: ww nnnnnn,ffffff = ww iiiiiiii + ww cccccccccc ww cc = ww ffffff ww cc ww nnnnnn,ffffff ww iiiiiiii ww cccccccccc ww cc ww ffffff is the net final deflection is the instantaneous deflection is the creep deflection is the precamber (if applied) is the final deflection The limiting values for deflections of floors are assumed as shown in the following table. winst wnet,fin Beam on two supports l/300 l/250 Cantilevering beams l/150 l/125 Instantaneous deflection The instantaneous deflection winst is calculated for the characteristic (rare) combination of actions. The following table shows the deformation of each floor (relative to the element in which the deformation checks are more severe).

85 Floor name Combination Instantaneous deflection Floor 1 SLS characteristic 2 Floor 3 SLS characteristic 14 Floor 12 SLS characteristic 2 Floor 13 SLS characteristic 2

86 Floor 14 SLS characteristic 14 Floor 15 SLS characteristic 2 The table below shows the instantaneous deflection checks of the floor elements. Floor name Combination More restrictive check winst [mm] winst limit [mm] Check Floor 1 SLS characteristic 2 Internal span % Floor 3 SLS characteristic 14 Overhang % Floor 12 SLS characteristic 2 Internal span % Floor 13 SLS characteristic 2 Internal span % Floor 14 SLS characteristic 14 Overhang % Floor 15 SLS characteristic 2 Internal span % Final deflection For structures consisting of members, components and connections with the same creep behaviour and under the assumption of a linear relationship between the actions and the corresponding deformations the final deformation, wfin, may be taken as: ww ffffff = ww ffffff,gg + ww ffffff,qq1 + ww ffffff,qqqq

87 where: ww ffffff,gg = ww iiiiiiii,gg 1 + kk dddddd for a permanent action, G ww ffffff,qq,1 = ww iiiiiiii,qq,1 1 + Ψ 2,1 kk dddddd for the leading variable action, Q 1 ww ffffff,qq,ii = ww iiiiiiii,qq,ii Ψ 0,ii + Ψ 2,1 kk dddddd for accompanying variable actions, Q i (i>1) The following table shows the deformation of each floor (relative to the element in which the deformation checks are more severe). Floor name Combination Final deflection Floor 1 SLS characteristic 2 Floor 3 SLS characteristic 14 Floor 12 SLS characteristic 2

88 Floor 13 SLS characteristic 2 Floor 14 SLS characteristic 14 Floor 15 SLS characteristic 2 The table below shows the final deflection checks of the floor elements. Floor name Combination More restrictive check wfin [mm] wfin limit [mm] Check Floor 1 SLS characteristic 2 Internal span % Floor 3 SLS characteristic 14 Overhang % Floor 12 SLS characteristic 2 Internal span % Floor 13 SLS characteristic 2 Internal span % Floor 14 SLS characteristic 14 Overhang % Floor 15 SLS characteristic 2 Internal span %

89 Beams Bending strength The checks are conducted according to of EN The following expression shall be satisfied: where: σσ mm,dd is the design bending stress ff mm,dd is the design bending strength σσ mm,dd kk cccccccc ff mm,dd 1 kk cccccccc is a factor which takes into account the reduced bending strength due to lateral buckling. k crit is assumed equal to 1.0 for beams in which the lateral displacement of the compressed edge is prevented over the entire length and the torsional rotation is prevented at the supports. Beam name Combination Duration Diagram M3-3 Beam 2 ULS 64 Permanent Beam 3 ULS 64 Permanent

90 Beam 4 ULS 64 Permanent Beam 5 ULS 65 Medium-term Beam 6 ULS 65 Medium-term Beam 10 ULS 65 Medium-term

91 Beam 11 ULS 64 Permanent Beam 16 ULS 64 Permanent Beam 17 ULS 64 Permanent Beam 18 ULS 64 Permanent

92 Beam 19 ULS 64 Permanent Beam 20 ULS 65 Medium-term Beam 21 ULS 65 Medium-term Beam 37 ULS 43 Permanent

93 Beam 42 ULS 65 Medium-term Beam 47 ULS 65 Medium-term Beam 48 ULS 64 Permanent Beam 49 ULS 64 Permanent

94 Beam 50 ULS 65 Medium-term Beam 51 ULS 65 Medium-term Beam 52 ULS 43 Permanent Beam 53 ULS 65 Medium-term

95 Beam 54 ULS 65 Medium-term Beam 56 ULS 65 Medium-term Beam 57 ULS 64 Permanent The checks are summarized below. The values resulting from the calculations, relating to each verification, are reported in the form of a percentage. Beam name Beam 2 Beam 3 Beam 4 Beam 5 Beam 6 Beam 10 Section Section 200x240 GL 24h Section 200x240 GL 24h Section 200x240 GL 24h Section 200x240 GL 24h Section 200x440 GL 24h Section 200x520 GL 24h M3-3 max [knm] W [mm 3 ] kcrit Comb. kmod γm fm,d [MPa] σm,d [MPa] ULS % ULS % ULS % ULS % ULS % ULS % Check

96 Beam 11 Beam 16 Beam 17 Beam 18 Beam 19 Beam 20 Beam 21 Beam 37 Beam 42 Beam 47 Beam 48 Beam 49 Beam 50 Beam 51 Beam 52 Beam 53 Beam 54 Beam 56 Beam 57 Section 200x240 GL 24h Section 200x240 GL 24h Section 200x240 GL 24h Section 200x440 GL 24h Section 200x240 GL 24h Section 200x240 GL 24h Section 200x240 GL 24h Section 200x240 GL 24h Section 200x240 GL 24h Section 200x440 GL 24h Section 200x240 GL 24h Section 200x240 GL 24h Section 200x240 GL 24h Section 200x520 GL 24h Section 200x240 GL 24h Section 200x240 GL 24h Section 200x440 GL 24h Section 200x240 GL 24h Section 200x440 GL 24h ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS %

97 Shear strength The checks are conducted according to of EN The following expression shall be satisfied: where: ττ dd ff vv,dd 1 ττ dd is the design shear stress ff vv,dd is the design shear strength for the actual condition For the verification of shear resistance of members in bending, the influence of cracks should be taken into account using an effective width of the member given as: bb eeee = kk cccc bb where b is the width of the relevant section of the member. The following value of k cr are used k cr = 0.67 for solid timber k cr = 0.67 for glued laminated timber The maximum design shear stress in a rectangular cross section can be evaluated using the following expression: where A is the area of a joist cross section. VV dd ττ dd = 3 2 kk cccc AA The following table illustrates the structural schemes and the envelopes of the shear force diagram for each beam. Beam name Combination Duration Diagram V2 Beam 2 ULS 64 Permanent

98 Beam 3 ULS 64 Permanent Beam 4 ULS 64 Permanent Beam 5 ULS 65 Medium-term Beam 6 ULS 65 Medium-term

99 Beam 10 ULS 65 Medium-term Beam 11 ULS 64 Permanent Beam 16 ULS 64 Permanent Beam 17 ULS 64 Permanent

100 Beam 18 ULS 64 Permanent Beam 19 ULS 64 Permanent Beam 20 ULS 65 Medium-term Beam 21 ULS 65 Medium-term

101 Beam 37 ULS 43 Permanent Beam 42 ULS 65 Medium-term Beam 47 ULS 65 Medium-term Beam 48 ULS 70 Medium-term

102 Beam 49 ULS 70 Medium-term Beam 50 ULS 65 Medium-term Beam 51 ULS 65 Medium-term Beam 52 ULS 43 Permanent

103 Beam 53 ULS 65 Medium-term Beam 54 ULS 65 Medium-term Beam 56 ULS 65 Medium-term Beam 57 ULS 64 Permanent

104 The checks are summarized below. The values resulting from the calculations, relating to each verification, are reported in the form of a percentage. Beam name Beam 2 Beam 3 Beam 4 Beam 5 Beam 6 Beam 10 Beam 11 Beam 16 Beam 17 Beam 18 Beam 19 Beam 20 Beam 21 Beam 37 Beam 42 Beam 47 Beam 48 Beam 49 Beam 50 Beam 51 Beam 52 Beam 53 Beam 54 Beam 56 Beam 57 Section Section 200x240 GL 24h Section 200x240 GL 24h Section 200x240 GL 24h Section 200x240 GL 24h Section 200x440 GL 24h Section 200x520 GL 24h Section 200x240 GL 24h Section 200x240 GL 24h Section 200x240 GL 24h Section 200x440 GL 24h Section 200x240 GL 24h Section 200x240 GL 24h Section 200x240 GL 24h Section 200x240 GL 24h Section 200x240 GL 24h Section 200x440 GL 24h Section 200x240 GL 24h Section 200x240 GL 24h Section 200x240 GL 24h Section 200x520 GL 24h Section 200x240 GL 24h Section 200x240 GL 24h Section 200x440 GL 24h Section 200x240 GL 24h Section 200x440 GL 24h V2 max [kn] Area [mm 2 ] kcr Comb. kmod γm fv,d [MPa] τ2,d [MPa] ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % Check

105 Beams deflections (SLS) The deflection checks are carried out according to of EN The net deflection below a straight line between the supports, w net,fin, is taken as: where: ww nnnnnn,ffffff = ww iiiiiiii + ww cccccccccc ww cc = ww ffffff ww cc ww nnnnnn,ffffff ww iiiiiiii ww cccccccccc ww cc ww ffffff is the net final deflection is the instantaneous deflection is the creep deflection is the precamber (if applied) is the final deflection The limiting values for deflections of beams are assumed as shown in the following table. winst wnet,fin Beam on two supports l/300 l/250 Cantilevering beams l/150 l/125

106 Instantaneous deflection The instantaneous deflection winst is calculated for the characteristic (rare) combination of actions. The following table shows the deformation of each beam. Beam name Combination Instantaneous deflection Beam 2 SLS characteristic 1 Beam 3 SLS characteristic 1 Beam 4 SLS characteristic 15

107 Beam 5 SLS characteristic 2 Beam 6 SLS characteristic 3 Beam 10 SLS characteristic 2 Beam 11 SLS characteristic 15

108 Beam 16 SLS characteristic 14 Beam 17 SLS characteristic 14 Beam 18 SLS characteristic 14 Beam 19 SLS characteristic 14

109 Beam 20 SLS characteristic 2 Beam 21 SLS characteristic 2 Beam 37 SLS characteristic 1 Beam 42 SLS characteristic 2

110 Beam 47 SLS characteristic 2 Beam 48 SLS characteristic 15 Beam 49 SLS characteristic 15 Beam 50 SLS characteristic 2

111 Beam 51 SLS characteristic 3 Beam 52 SLS characteristic 1 Beam 53 SLS characteristic 2 Beam 54 SLS characteristic 2

112 Beam 56 SLS characteristic 2 Beam 57 SLS characteristic 15 The table below shows the instantaneous deflection checks of the beams. Beam name Combination More restrictive check winst [mm] winst limit [mm] Check Beam 2 SLS characteristic 1 Internal span % Beam 3 SLS characteristic 1 Internal span % Beam 4 SLS characteristic 15 Internal span % Beam 5 SLS characteristic 2 Internal span % Beam 6 SLS characteristic 3 Internal span % Beam 10 SLS characteristic 2 Internal span % Beam 11 SLS characteristic 15 Internal span % Beam 16 SLS characteristic 14 Overhang % Beam 17 SLS characteristic 14 Internal span % Beam 18 SLS characteristic 14 Overhang % Beam 19 SLS characteristic 14 Overhang % Beam 20 SLS characteristic 2 Overhang % Beam 21 SLS characteristic 2 Overhang % Beam 37 SLS characteristic 1 Internal span %

113 Beam 42 SLS characteristic 2 Internal span % Beam 47 SLS characteristic 2 Overhang % Beam 48 SLS characteristic 15 Internal span % Beam 49 SLS characteristic 15 Internal span % Beam 50 SLS characteristic 2 Internal span % Beam 51 SLS characteristic 3 Internal span % Beam 52 SLS characteristic 1 Internal span % Beam 53 SLS characteristic 2 Internal span % Beam 54 SLS characteristic 2 Internal span % Beam 56 SLS characteristic 2 Internal span % Beam 57 SLS characteristic 15 Internal span % Final deflection For structures consisting of members, components and connections with the same creep behaviour and under the assumption of a linear relationship between the actions and the corresponding deformations the final deformation, wfin, may be taken as: where: ww ffffff = ww ffffff,gg + ww ffffff,qq1 + ww ffffff,qqqq ww ffffff,gg = ww iiiiiiii,gg 1 + kk dddddd for a permanent action, G ww ffffff,qq,1 = ww iiiiiiii,qq,1 1 + Ψ 2,1 kk dddddd for the leading variable action, Q 1 ww ffffff,qq,ii = ww iiiiiiii,qq,ii Ψ 0,ii + Ψ 2,1 kk dddddd for accompanying variable actions, Q i (i>1)

114 The following table shows the deformation of each floor (relative to the element in which the deformation checks are more severe). Beam name Combination Final deflection Beam 2 SLS characteristic 1 Beam 3 SLS characteristic 1 Beam 4 SLS characteristic 15 Beam 5 SLS characteristic 2

115 Beam 6 SLS characteristic 3 Beam 10 SLS characteristic 2 Beam 11 SLS characteristic 15 Beam 16 SLS characteristic 14

116 Beam 17 SLS characteristic 14 Beam 18 SLS characteristic 14 Beam 19 SLS characteristic 14 Beam 20 SLS characteristic 2

117 Beam 21 SLS characteristic 2 Beam 37 SLS characteristic 1 Beam 42 SLS characteristic 2 Beam 47 SLS characteristic 2

118 Beam 48 SLS characteristic 15 Beam 49 SLS characteristic 15 Beam 50 SLS characteristic 2 Beam 51 SLS characteristic 3

119 Beam 52 SLS characteristic 1 Beam 53 SLS characteristic 2 Beam 54 SLS characteristic 2 Beam 56 SLS characteristic 2

120 Beam 57 SLS characteristic 15 The table below shows the final deflection checks for every beam. Beam name Combination More restrictive check wfin [mm] wfin limit [mm] Check Beam 2 SLS characteristic 1 Internal span % Beam 3 SLS characteristic 1 Internal span % Beam 4 SLS characteristic 15 Internal span % Beam 5 SLS characteristic 2 Internal span % Beam 6 SLS characteristic 3 Internal span % Beam 10 SLS characteristic 2 Internal span % Beam 11 SLS characteristic 15 Internal span % Beam 16 SLS characteristic 14 Overhang % Beam 17 SLS characteristic 14 Internal span % Beam 18 SLS characteristic 14 Overhang % Beam 19 SLS characteristic 14 Overhang % Beam 20 SLS characteristic 2 Overhang % Beam 21 SLS characteristic 2 Overhang % Beam 37 SLS characteristic 1 Internal span % Beam 42 SLS characteristic 2 Internal span % Beam 47 SLS characteristic 2 Overhang % Beam 48 SLS characteristic 15 Internal span % Beam 49 SLS characteristic 15 Internal span % Beam 50 SLS characteristic 2 Internal span % Beam 51 SLS characteristic 3 Internal span %

121 Beam 52 SLS characteristic 1 Internal span % Beam 53 SLS characteristic 2 Internal span % Beam 54 SLS characteristic 2 Internal span % Beam 56 SLS characteristic 2 Internal span % Beam 57 SLS characteristic 15 Internal span %

122 Columns Stability of columns The stability of columns subjected to compression is verified in accordance with of EN The relative slenderness ratios should be taken as: λλ rrrrrr,yy = λλ,yy ππ ff cc,0,kk EE 0,05 and λλ rrrrrr,zz = λλ,zz ππ ff cc,0,kk EE 0,05 where λλ,yy e λλ rrrrrr,yy are the slenderness ratios corresponding to bending about the y-axis (deflection in the z-direction); λλ,zz e λλ rrrrrr,zz are the slenderness ratios corresponding to bending about the z-axis (deflection in the y- direction); Where both λ rel,z 0,3 and λ rel,y 0,3, the stresses should satisfy the expressions (6.19) e (6.20) in of EN In all other cases the stresses, which will be increased due to deflection, should satisfy the following expressions: σσ cc,0,dd kk cc,yy ff cc,0,dd + σσ mm,yy,dd ff mm,yy,dd + kk mm σσ mm,zz,dd ff mm,zz,dd 1 where the symbols are defined as follows: σσ cc,0,dd kk cc,zz ff cc,0,dd + kk mm σσ mm,yy,dd ff mm,yy,dd + σσ mm,zz,dd ff mm,zz,dd 1 kk cc,yy = 1 kk yy + kk 2 2 yy λλ rrrrrr,yy kk cc,zz = 1 kk zz + kk 2 2 zz λλ rrrrrr,zz where: 2 kk yy = 0,5 1 + ββ cc λλ rrrrrr,yy 0,3 + λλ rrrrrr,yy 2 kk zz = 0,5 1 + ββ cc λλ rrrrll,zz 0,3 + λλ rrrrrr,zz

123 ββ cc is a factor for members within the straightness limits defined in Section 10 of EN and assumes the following values 0,2 ffffff ssssssssss tttttttttttt ββ cc = 0,1 ffffff gggggggggg llllllllllllllllll tttttttttttt aaaaaa LLLLLL The values of the actions in the tables below are related, for each pillar, to the more severe combination of load for the Ultimate Limit State of instability. Comb.: Dur.: More severe combination of load Load duration N: Axial force V 2: Shear force along the local axis 2 V 3: Shear force along the local axis 3 M 2-2: Bending moment about local axis 2 M 3-3: Bending moment about local axis 3 Column name Comb. Dur. N [kn] V2 [kn] V3 [kn] M2-2 [knm] M3-3 [knm] Column 1 ULS 65 Medium-term Column 2 ULS 65 Medium-term Column 3 ULS 65 Medium-term Column 6 ULS 64 Permanent Column 7 ULS 65 Medium-term Column 9 ULS 65 Medium-term Column 10 ULS 65 Medium-term Column 12 ULS 65 Medium-term Column 11 ULS 65 Medium-term The following table summarizes the stability checks for the columns. Sect.: Column cross section h: Column height Area: J y: J z: Cross sectional area of the column Area moment of inertia with respect to the y axis Area moment of inertia with respect to the z axis

124 Comb.: k mod: γ M: f c,0,k: σ c,0,d: More severe load combination Modification factor taking into account the effect of the duration of load and moisture content Partial factor for a material property Design compressive strength along the grain Design compressive stress along the grain Column name Column 1 Column 2 Column 3 Column 6 Column 7 Column 9 Column 10 Column 12 Column 11 Sect. Section 200x24 0 GL 24h Section 200x24 0 GL 24h Section 200x24 0 GL 24h Section 200x24 0 GL 24h Section 200x24 0 GL 24h Section 200x24 0 GL 24h Section 200x24 0 GL 24h Section 200x24 0 GL 24h Section 200x24 0 GL 24h h [m] Area [mm 2 ] Jy [mm 4 ] Jz [mm 4 ] kc,y kc,z Comb kmod γm fc,0,k σc,0,d [MPa] E8 1.60E ULS % E8 1.60E ULS % E8 1.60E ULS % E8 1.60E ULS % E8 1.60E ULS % E8 1.60E ULS % E8 1.60E ULS % E8 1.60E ULS % E8 1.60E ULS % Check

125 CLT walls Buckling of CLT walls The stability checks of CLT walls are conducted with reference to what reported in of EN The values of the actions in the table below are related, for each wall, to the more severe combination of load for the Ultimate Limit State of stability. Wall name Length [m] Comb. Dur. N [kn] M2-2 [knm] Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 65 Medium-term Wall ULS 65 Medium-term Wall ULS 64 Permanent Wall ULS 83 Instantaneous Wall ULS 83 Instantaneous Wall ULS 83 Instantaneous Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 82 Instantaneous Wall ULS 82 Instantaneous Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 81 Instantaneous Wall ULS 84 Instantaneous Wall ULS 83 Instantaneous Wall ULS 83 Instantaneous Wall ULS 83 Instantaneous

126 Wall ULS 64 Permanent Wall ULS 81 Instantaneous Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 83 Instantaneous Wall ULS 64 Permanent Wall ULS 84 Instantaneous Wall ULS 81 Instantaneous Wall ULS 64 Permanent Wall ULS 83 Instantaneous Wall ULS 82 Instantaneous Wall ULS 82 Instantaneous Wall ULS 64 Permanent Wall ULS 65 Medium-term Wall ULS 65 Medium-term Wall ULS 84 Instantaneous Wall ULS 81 Instantaneous Wall ULS 81 Instantaneous Wall ULS 81 Instantaneous Wall ULS 81 Instantaneous Wall ULS 81 Instantaneous Wall ULS 81 Instantaneous Wall ULS 64 Permanent The stability checks of the CLT panels are performed considering a wall portion of unitary length. Where both λ rel,z 0,3 and λ rel,y 0,3, the stresses should satisfy the expressions (6.19) and (6.20) in of EN In all other cases the stresses, which will be increased due to deflection, should satisfy the following expressions:

127 σσ cc,0,dd kk cc ff cc,0,dd + σσ mm,yy,dd ff mm,yy,dd 1 Mechanical model for the internal stress pattern in CLT elements The calculation model adopted for the design of CLT in bending out-of-plane is that of mechanically jointed beams with deformable connection in accordance with Appendix B of EN The shear flexibility of the transverse layers is considered using the γ-method (gamma): namely with Möhler theory for CLT panel having up to 3 layers oriented in the direction of calculation and with Shelling theory for CLT panel having more than 3 layers oriented in the direction of calculation. The effective bending stiffness is taken as: where: nn EEJJ eeeeee = EE ii JJ ii + γγ ii EE ii AA ii aa ii 2 ii=1 γγ ii = 1 + ππ2 EE ii AA ii GG RR bb dd h2 1 JJ ii AA ii aa ii h GG RR is the moment of inertia of layer i in reference to its neutral axis is the cross-sectional area of layer i is the distance between the centre of gravity of layer i and centre of gravity of the CLT element is the height of the wall is the rolling shear modulus (mean value) The results of the stability checks are reported below expressed as percentages. A net: J eff: Comb.: k mod: γ M: f c,0,k: f m,k: σ c,0,d: Cross sectional area of the wall portion considered in the verification (linear meter) Cross sectional effective moment of inertia of the wall portion More severe combination of load Modification factor taking into account the effect of the duration of load and moisture content Partial factor for a material property Design compressive strength along the grain Design bending strength Design compressive stress along the grain

128 Wall name Section h [m] Anet [mm 2 /m] Jeff [mm 4 /m] kc Comb. kmod γm fc,0,k [MPa] fm,k [MPa] σc,0,d [MPa] σm,d [MPa] Check Wall 1 CLT 120 mm - 5 layers - vertical joints ULS % Wall 3 CLT 120 mm - 5 layers - vertical joints ULS % Wall 4 CLT 120 mm - 5 layers - vertical joints ULS % Wall 6 CLT 120 mm - 5 layers - vertical joints ULS % Wall 8 CLT 120 mm - 5 layers - vertical joints ULS % Wall 9 CLT 120 mm - 5 layers - vertical joints ULS % Wall 11 CLT 120 mm - 5 layers - vertical joints ULS % Wall 13 CLT 120 mm - 5 layers - vertical joints ULS % Wall 14 CLT 120 mm - 5 layers - vertical joints ULS % Wall 15 CLT 120 mm - 5 layers - vertical joints ULS % Wall 20 CLT 120 mm - 5 layers - vertical joints ULS % Wall 21 CLT 120 mm - 5 layers - vertical joints ULS % Wall 22 CLT 100 mm - 3 layers ULS % Wall 23 CLT 100 mm - 3 layers ULS % Wall 25 CLT 100 mm - 3 layers ULS % Wall 26 CLT 100 mm - 3 layers ULS % Wall 27 CLT 100 mm - 3 layers ULS % Wall 29 CLT 100 mm - 3 layers ULS % Wall 30 CLT 100 mm - 3 layers ULS % Wall 31 CLT 100 mm - 3 layers ULS % Wall 33 CLT 100 mm - 3 layers ULS % Wall 34 CLT 100 mm - 3 layers ULS % Wall 35 CLT 100 mm - 3 layers ULS % Wall 36 CLT 100 mm - 3 layers ULS %

129 Wall 37 CLT 100 mm - 3 layers ULS % Wall 38 CLT 100 mm - 3 layers ULS % Wall 39 CLT 100 mm - 3 layers ULS % Wall 42 CLT 100 mm - 3 layers ULS % Wall 43 CLT 100 mm - 3 layers ULS % Wall 46 CLT 100 mm - 3 layers ULS % Wall 54 CLT 120 mm - 5 layers - vertical joints ULS % Wall 61 CLT 120 mm - 5 layers - vertical joints ULS % Wall 62 CLT 100 mm - 3 layers ULS % Wall 63 CLT 100 mm - 3 layers ULS % Wall 64 CLT 100 mm - 3 layers ULS % Wall 66 CLT 120 mm - 5 layers - vertical joints ULS % Wall 67 CLT 120 mm - 5 layers - vertical joints ULS % Wall 71 CLT 120 mm - 5 layers - vertical joints ULS % Wall 72 CLT 120 mm - 5 layers - vertical joints ULS % Wall 72 CLT 120 mm - 5 layers - vertical joints ULS % Wall 73 CLT 100 mm - 3 layers ULS % Wall 74 CLT 100 mm - 3 layers ULS % Wall 75 CLT 100 mm - 3 layers ULS % Wall 76 CLT 100 mm - 3 layers ULS % Wall 77 CLT 100 mm - 3 layers ULS % Wall 78 CLT 100 mm - 3 layers ULS % Wall2 CLT 100 mm - 3 layers ULS % Wall3 CLT 120 mm - 5 layers - vertical joints ULS %

130 Compression perpendicular to the grain In the area of wall support there are high local stresses perpendicular to the grain. The following expression shall be satisfied: σσ cc,90,dd kk cc,90,dd ff cc,90,dd with σσ cc,90,dd = FF cc,90,dd AA ffffffff where: σσ cc,90,dd FF cc,90,dd AA ffffffff ff cc,90,dd kk cc,90,dd is the design compressive stress in the contact area perpendicular to the grain is the design load of compression perpendicular to the grain is the contact area on which the compression load (perpendicular to the grain) acts is the design compressive strength perpendicular to the grain is a factor taking into account the load configuration, possibility of splitting and degree of compressive deformation The values of the actions in the table below are related, for each wall, to the more severe combination of load for the Ultimate Limit State. Wall name Length [m] Comb. Dur. N [kn] Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 65 Medium-term Wall ULS 65 Medium-term Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent 9.74

131 Wall ULS 64 Permanent 9.76 Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 65 Medium-term Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 65 Medium-term Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 64 Permanent Wall ULS 65 Medium-term Wall ULS 65 Medium-term Wall ULS 65 Medium-term Wall ULS 64 Permanent 4.07 Wall ULS 64 Permanent 2.35 Wall ULS 64 Permanent 2.35 Wall ULS 64 Permanent 2.69

132 Wall ULS 64 Permanent 2.91 Wall ULS 64 Permanent Wall ULS 64 Permanent The compression checks of the CLT panels are performed considering a wall portion of unitary length. Section: A full: Comb.: k mod: γ M: f c,90,k: σ c,90,d: CLT element section Contact area on which the compression load (perpendicular to the grain) acts More severe combination of load Modification factor taking into account the effect of the duration of load and moisture content Partial factor for a material property Design compressive strength perpendicular to the grain Design compressive stress in the contact area perpendicular to the grain Wall name Wall 1 Wall 3 Wall 4 Wall 6 Wall 8 Wall 9 Wall 11 Wall 13 Wall 14 Wall 15 Wall 20 Wall 21 Wall 22 Section CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 100 mm - 3 layers Afull [mm 2 /m] kc,90 Comb. kmod γm fc,90,k [MPa] σc,90,d [MPa] ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % ULS % Check

133 Wall 23 CLT 100 mm - 3 layers ULS % Wall 25 CLT 100 mm - 3 layers ULS % Wall 26 CLT 100 mm - 3 layers ULS % Wall 27 CLT 100 mm - 3 layers ULS % Wall 29 CLT 100 mm - 3 layers ULS % Wall 30 CLT 100 mm - 3 layers ULS % Wall 31 CLT 100 mm - 3 layers ULS % Wall 33 CLT 100 mm - 3 layers ULS % Wall 34 CLT 100 mm - 3 layers ULS % Wall 35 CLT 100 mm - 3 layers ULS % Wall 36 CLT 100 mm - 3 layers ULS % Wall 37 CLT 100 mm - 3 layers ULS % Wall 38 CLT 100 mm - 3 layers ULS % Wall 39 CLT 100 mm - 3 layers ULS % Wall 42 CLT 100 mm - 3 layers ULS % Wall 43 CLT 100 mm - 3 layers ULS % Wall 46 Wall 54 Wall 61 Wall 62 CLT 100 mm - 3 layers CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 100 mm - 3 layers ULS % ULS % ULS % ULS % Wall 63 CLT 100 mm - 3 layers ULS % Wall 64 Wall 66 Wall 67 Wall 71 Wall 72 Wall 72 Wall 73 CLT 100 mm - 3 layers CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 100 mm - 3 layers ULS % ULS % ULS % ULS % ULS % ULS % ULS %

134 Wall 74 CLT 100 mm - 3 layers ULS % Wall 75 CLT 100 mm - 3 layers ULS % Wall 76 CLT 100 mm - 3 layers ULS % Wall 77 CLT 100 mm - 3 layers ULS % Wall 78 CLT 100 mm - 3 layers ULS % Wall2 Wall3 CLT 100 mm - 3 layers CLT 120 mm - 5 layers - vertical joints ULS % ULS %

135 Shear (load in-plane) The internal stress pattern in a CLT element subjected to shear forces can lead to failure of the material in two different mechanisms: shear bearing (mechanism I) in the boards and torsion-like (mechanism II) in the gluing interfaces. The values of the actions in the table below are related, for each wall, to the more severe combination of load for the shear Ultimate Limit State. Wall name Length [m] Comb. Dur. V2 [kn] Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall exey+ 1 exey+ 6 exey- 5 exey+ 1 exey+ 6 exey- 6 exey- 6 exey- 1 exey+ 2 ex+ ey+ 2 ex+ ey+ 2 ex+ ey+ 1 exey+ 1 exey+ 1 exey+ 1 exey+ 1 exey+ 1 exey+ 5 exey+ 6 exey- 6 exey- 6 exey- 1 exey+ 1 exey+ Instantaneous 3.44 Instantaneous Instantaneous Instantaneous 8.02 Instantaneous 1.28 Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous 4.14 Instantaneous Instantaneous 7.50 Instantaneous 7.37 Instantaneous 8.73 Instantaneous 8.32 Instantaneous 9.60 Instantaneous Instantaneous Instantaneous Instantaneous 5.73 Instantaneous 14.44

136 Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall exey+ 2 ex+ ey+ 2 ex+ ey+ 5 exey+ 5 exey+ 6 exey- 5 exey+ 2 ex+ ey+ 1 exey+ 1 exey+ 1 exey+ 1 exey+ 1 exey+ 5 exey+ 5 exey+ Instantaneous 1.10 Instantaneous Instantaneous 6.14 Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous 7.11 Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous 7.37 Instantaneous Mechanism I - shear The internal shear stress can be evaluated as where [omissis] vv 2 tt ii,eeeeee tt ii,iiiiii ττ zz ττ yy is the shear force per linear metre acting on the CLT element is the thickness of the i-th layer having orientation parallel to the external layers is the thickness of the i-th layer having orientation parallel to the internal layers is the shear stress acting on the layers having orientation parallel to the external layers is the shear stress acting on the layers having orientation parallel to the internal layers The stress to be used in the checks is the maximum between the two: The following expression shall be satisfied ττ dd = mmmmmm(ττ zz ; ττ yy ) ττ dd ff vv,llllllllllll,dd

137 being ff vv,dd the shear strength calculated as ff vv,dd = kk mmmmmm ff vv,kk γγ MM Mechanism II torsion The internal torsional stress can be expressed as [omissis] being: MM TT WW the internal torsional moment the polar moment of resistance The polar moment of resistance is defined by the following expression [omissis] where a ref is the average width of the boards assumed equal to 150 mm. [omissis] The following expression shall be satisfied being ττ TT,dd ff TT,dd ff TT,dd the design value of the torsional strength of glued interfaces ff TT,dd = kk mmmmmm ff TT,kk γγ MM Below is the table with the shear checks for each CLT wall. The two different mechanisms (shear and torsion) are verified. Comb.: k mod: γ M: More severe combination of load Modification factor taking into account the effect of the duration of load and moisture content Partial factor for a material property f v,k: CLT characteristic shear strength (Mechanism I) τ d: Design shear stress in the layers

138 M T: Torsional moment on every glued interfaces W: Polar moment of resistance f T,k: τ T,d: Characteristic value of the torsional shear strength of the glued interfaces Design shear stress (due to torsion) in the external layers Wall name Wall 1 Wall 3 Wall 4 Wall 6 Wall 8 Wall 9 Wall 11 Wall 13 Wall 14 Wall 15 Wall 20 Wall 21 Wall 22 Wall 23 Wall 25 Wall 26 Wall 27 Wall 29 Section Comb. kmod γm CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 100 mm - 3 layers CLT 100 mm - 3 layers CLT 100 mm - 3 layers CLT 100 mm - 3 layers CLT 100 mm - 3 layers CLT 100 mm - 3 layers ULS 1 ex- ey+ ULS 1 ex- ey+ ULS 6 ex- ey- ULS 5 ex- ey+ ULS 1 ex- ey+ ULS 6 ex- ey- ULS 6 ex- ey- ULS 6 ex- ey- ULS 1 ex- ey+ ULS 2 ex+ ey+ ULS 2 ex+ ey+ ULS 2 ex+ ey+ ULS 1 ex- ey+ ULS 1 ex- ey+ ULS 1 ex- ey+ ULS 1 ex- ey+ ULS 1 ex- ey+ ULS 1 ex- ey+ fv,lastra,k [MPa] τd [MPa] Check - shear MT [Nmm] W [mm 3 ] ft,k [MPa] τt,d [MPa] % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % Check - torsion % %

139 Wall 31 Wall 33 Wall 34 Wall 35 Wall 36 Wall 38 Wall 39 Wall 42 Wall 43 Wall 46 Wall 54 Wall 61 Wall 62 Wall 63 Wall 66 Wall 67 Wall 71 Wall 72 Wall 72 Wall 73 Wall3 CLT 100 mm - 3 layers CLT 100 mm - 3 layers CLT 100 mm - 3 layers CLT 100 mm - 3 layers CLT 100 mm - 3 layers CLT 100 mm - 3 layers CLT 100 mm - 3 layers CLT 100 mm - 3 layers CLT 100 mm - 3 layers CLT 100 mm - 3 layers CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 100 mm - 3 layers CLT 100 mm - 3 layers CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 120 mm - 5 layers - vertical joints CLT 100 mm - 3 layers CLT 120 mm - 5 layers - vertical joints ULS 5 ex- ey+ ULS 6 ex- ey- ULS 6 ex- ey- ULS 6 ex- ey- ULS 1 ex- ey+ ULS 1 ex- ey+ ULS 1 ex- ey+ ULS 2 ex+ ey+ ULS 2 ex+ ey+ ULS 5 ex- ey+ ULS 5 ex- ey+ ULS 6 ex- ey- ULS 5 ex- ey+ ULS 2 ex+ ey+ ULS 1 ex- ey+ ULS 1 ex- ey+ ULS 1 ex- ey+ ULS 1 ex- ey+ ULS 1 ex- ey+ ULS 5 ex- ey+ ULS 5 ex- ey % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %

140 Vertical joints among CLT panels of a wall The values of the actions in the vertical joints are summarized in the table below. They are related, for each wall, to the more severe combination of load for the shear Ultimate Limit State. Wall name Wall height [m] Comb. Dur. V2 [kn] Vjoint,d [kn] Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall Wall exey+ 1 exey+ 6 exey- 5 exey+ 1 exey+ 6 exey- 6 exey- 6 exey- 1 exey+ 2 ex+ ey+ 2 ex+ ey+ 2 ex+ ey+ 5 exey+ 6 exey- 1 exey+ 1 exey+ 1 exey+ 1 exey+ 1 exey+ 5 exey+ Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Instantaneous Vertical joints in CLT walls Fasteners strength The resistance of vertical joints in CLT walls is calculated in accordance to EN The resistance of the joints of each wall can be calculated by the following formula where R v,k = F v,k h s

141 R v,k F v,k h s is the characteristic shear resistance of the vertical joints among CLT panels of a wall is the characteristic load-carrying capacity of a single fastener is the height of the wall in correspondence of the joint is the spacing of the vertical joint fasteners The characteristic shear resistance of the vertical joint is where RR vv,dd = kk mmmmmm R v,k γγ MM kk mmmmmm γγ MM is the modification factor taking into account the effect of the duration of load and moisture content is the partial factor for connections Characteristic load-carrying capacity of the fasteners The load-carrying capacity of the fasteners is calculated in accordance with Johansen theory (8.2.2 of EN ) for the case timber-to-timber connection in single shear. The characteristic load-carrying capacity per shear plane per fastener, should be taken as the minimum value found from the following expressions: - Single shear FF vv,rrrr,aa = ff h,1,kk tt 1 dd FF vv,rrrr,bb = ff h,2,kk tt 2 dd FF vv,rrrr,cc = ff h,1,kk tt 1 dd ββ + 2ββ 1 + ββ tt 2 + tt ββ 3 tt 2 2 ββ 1 + tt 2 tt 1 tt 1 tt 1 tt 1 FF vv,rrrr,dd = 1,05 ff h,1,kk tt 1 dd 2ββ(1 + ββ) + 4ββ(2+ββ)MM yy,rrrr 2+ββ ff h,1,kk dd tt2 ββ 1 FF vv,rrrr,ee = 1,05 ff h,1,kk tt 2 dd 2ββ 1 + 2ββ 2 (1 + ββ) + 4ββ(1 + 2ββ)MM yy,rrrr 2 ββ ff h,1,kk dd tt 2 FF vv,rrrr,ff = 1,15 2ββ 1 + ββ 2 MM yy,rrrr ff h,1,kk dd Figura: Failure modes for timber and panel connections (Single shear).

142 - Double shear FF vv,rrrr,gg = ff h,1,kk tt 1 dd FF vv,rrrr,h = 0.5 ff h,2,kk tt 2 dd FF vv,rrrr,jj = 1,05 ff h,1,kk tt 1 dd 2ββ(1 + ββ) + 4ββ(2 + ββ)mm yy,rrrr 2 ββ 2 + ββ ff h,1,kk dd tt 1 FF vv,rrrr,kk = 1,15 2ββ 1 + ββ 2 MM yy,rrrr ff h,1,kk dd Figura: Failure modes for timber and panel connections (Double shear). Below is the table with the characteristic load-carrying capacity of the fasteners. Section CLT 120 mm - 5 layers - vertical joints Fastener Kser [N/mm] Failure mode Fv,Rk [N] HBS 10 x c 4668 Vertical joints in CLT walls Fasteners strength check The table below illustrates the geometric characteristics of the panels of every wall and the shear bearing capacity R v,k of the vertical joints. Wall name Section Height of the joint [mm] sc [mm] Rv,k [kn] Wall 1 CLT 120 mm - 5 layers - vertical joints Wall 3 CLT 120 mm - 5 layers - vertical joints Wall 4 CLT 120 mm - 5 layers - vertical joints Wall 6 CLT 120 mm - 5 layers - vertical joints Wall 8 CLT 120 mm - 5 layers - vertical joints