2C09 Design for seismic and climate change

Transcription

1 2C09 Design for seismic and climate change Raffaele Landolfo Mario D Aniello CZ-ERA MUNDUS-EMMC

2 List of Tutorials 1. Design and verification of a steel moment resisting frame 2. Design and verification of a steel concentric braced frame 3. Assignment: Design and verification of a steel eccentric braced frame 2

3 Design and verification of a steel Concentric Braced Frames 1. Introduction 2. General for Concentric Braced Frames 3. Damage limitation 4. Structural analysis and calculation models 5. Verification 3

4 Introduction Building description Normative references The case study is a six storey residential building with a rectangular plan, m x m. The storey height is equal to 3.50 m with exception of the first floor, which is 4.00 m high Materials Actions 4

5 Introduction Building description Normative references Structural plan and configuration of the CBFs Materials Actions X Bracings V Bracings Direction X Direction Y 5

6 Introduction Building description Normative references Materials composite slabs with profiled steel sheetings are adopted to resist the vertical loads and to behave as horizontal rigid diaphragms. The connection between slab and beams is provided by ductile headed shear studs that are welded directly through the metal deck to the beam flange. Actions 6

7 Introduction Building description Normative references Materials Actions Apart from the seismic recommendations, the structural safety verifications are carried out according to the following European s: - EN 1990 (2001) Euro 0: Basis of structural design; - EN (2002) Euro 1: Actions on structures - Part 1-1: General actions -Densities, self-weight, imposed loads for buildings; - EN (2003) Euro 3: Design of steel structures - Part 1-1: General rules and rules for buildings; - EN (2004) Euro 4: Design of composite steel and concrete structures - Part 1.1: General rules and rules for buildings. In EU specific National annex should be accounted for design. For generality sake, the calculation examples are carried out using the recommended values of the safety factors 7

8 Introduction Building description Normative references Materials Actions It is well known that the standard nominal yield stress fy is the minimum guaranteed value, which is generally larger than the actual steel strength. Owing to capacity design criteria, it is important to know the maximum yield stress of the dissipative parts. This implies practical problems because steel products are not usually provided for an upper bound yield stress. Euro 8 faces this problem considering 3 different options: a) the actual maximum yield strength f y,max of the steel of dissipative zones satisfies the following expression f y,max 1.1g ov f y where f y is the nominal yield strength specified for the steel grade and g ov is a coefficient based on a statistic characterization of steel products. The Recommended value is 1.25 (EN (a)), but the designer may use the value provided by the relevant National Annex. 8

9 Introduction Building description Normative references Materials Actions b) this clause refers to a situation in which steel producers provide a seismic-qualified steel grade with both lower and upper bound value of yield stress defined. So if all dissipative parts are made considering one seismic steel grade and the non-dissipative are made of a higher grade of steel there is no need for g ov which can be set equal to 1. c) the actual yield strength f y,act of the steel of each dissipative zone is determined from measurements and the overstrength factor is computed for each dissipative zone as g ov,act = f y,act / f y, f y being the nominal yield strength of the steel of dissipative zones. 9

10 Introduction Building description Normative references Materials Actions In general at design stage the actual yield stress of the material is not known a-priori. So the case a) is the more general. Hence, in this exercise we use it. Grade f y f t g M g ov E (N/mm 2 ) (N/mm 2 ) (N/mm 2 ) S g M0 = 1.00 g M1 = 1.00 S g M2 =

11 Introduction Building description Normative references Materials Actions Characteristic values of vertical persistent and transient actions G k (kn/m 2 ) Q k (kn/m 2 ) Storey slab Roof slab (Snow) Stairs Claddings

12 Introduction Building description Normative references Materials Actions Seismic action A reference peak ground acceleration equal to a gr = 0.25g (being g the gravity acceleration), a type C soil and a type 1 spectral shape have been assumed. The design response spectrum is then obtained starting from the elastic spectrum using the following equations 0 T TB B T T T C T T T C S T T T D D S T T 2.5 Sd T ag S 1 1 TB q 2.5 Sd T ag S q d d 2.5 TC ag S q T ag 2.5 TC TD ag S 2 q T ag S = 1.15, T B = 0.20 s, T C = 0.60 s and T D = 2.00 s. The parameter β is the lower bound factor for the horizontal design spectrum, whose value should be found in National Annex. β = 0.2 is recommended by the (EN ) (3.2) 12

13 S e, S d (m/s 2 ) Introduction Building description Normative references Materials Actions Seismic action Elastic and design response spectra Elastic spectrum Design spectrum-x braces Design spectrum-inverted-v braces 1 lower bound = 0.2a g T (s) behaviour factor q was assigned according to EC8 (DCH concept) as follows: q 4 for X-CBFs q 2.5 for inverted V-CBFs 13

14 Introduction Building description Normative references Materials Actions Combination of actions In case of buildings the seismic action should be combined with permanent and variable loads as follows: G " " Q " " A k,i 2,i k,i Ed where G k,i is the characteristic value of permanent action I (the self weight and all other dead loads), A Ed is the design seismic action (corresponding to the reference return period multiplied by the importance factor), Q k,i is the characteristic value of variable action I and ψ 2,i is the combination coefficient for the quasi-permanent value of the variable action I, which is a function of the destination of use of the building Type of variable actions 2i Category A Domestic, residential areas 0.30 Roof 0.30 Snow loads on buildings 0.20 Stairs

15 Introduction Building description Normative references Materials Actions Masses In accordance with EN (2)P, the inertial effects in the seismic design situation have to be evaluated by taking into account the presence of the masses corresponding to the following combination of permanent and variable gravity loads: G " " Q k,i where E,i 2i is the combination coefficient for variable action i, which takes into account the likelihood of the loads Q k,i to be not present over the entire structure during the earthquake, as well as a reduced participation in the motion of the structure due to a non-rigid connection with the structure. E,i k,i Type of variable actions 2i Ei Category A Domestic, residential areas Roof Snow loads on buildings Stairs

16 Introduction Building description Normative references Materials Actions Seismic weights and masses in the worked example Storey G k Q k Seismic Weight Seismic Mass (kn) (kn) (kn) (kn/m 2 ) (kn s 2 /m) VI 3195, , V 3990, , IV 4087, , III 4106, , II 4187, , I 4261, ,

17 General for CBFs Basic principles of conceptual design Plan location of CBFs and structural regularity Damage limitation Basic principles of conceptual design - structural simplicity: it consists in realizing clear and direct paths for the transmission of the seismic forces - uniformity: uniformity is characterized by an even distribution of the structural elements both in-plan and along the height of the building. - symmetry : a symmetrical layout of structural elements is envisaged - redundancy: redundancy allow redistributing action effects and widespread energy dissipation across the entire structure - bi-directional resistance and stiffness: the building structure must be able to resist horizontal actions in any direction - torsional resistance and stiffness: building structures should possess adequate torsional resistance and stiffness to limit torsional motions - diaphragmatic behaviour at storey level: the floors (including the roof) should act as horizontal diaphragms, thus transmitting the inertia forces to the vertical structural systems - adequate foundation: the foundations have a key role, because they have to ensure a uniform seismic excitation on the whole building. 17

18 General for CBFs Basic principles of conceptual design CBFs are mainly located along the perimeter of the building. There is the same number of CBF spans in the 2 main direction of the 31 plan Plan location of CBFs and structural regularity Damage limitation X Bracings V Bracings Hence, the building is regular in-plan because it complies with the following (EN ): - The building structure is symmetrical in plan with respect to two orthogonal axes in terms of both lateral stiffness and mass distribution. - The plan configuration is compact; in fact, each floor may be delimited by a polygonal convex line. Moreover, in plan set-backs or re-entrant corners or edge recesses do not exist. 18

19 General for CBFs Basic principles of conceptual design Plan location of CBFs and structural regularity Damage limitation - The structure has rigid in plan diaphragms. - The in-plan slenderness ratio L max /L min of the building is lower than 4 (31000 mm / mm = 1.29), where L max and L min are the larger and smaller in plan dimensions of the building, measured in two orthogonal directions. - At each level and for both X and Y directions, the structural eccentricity e o (which is the nominal distance between the centre of stiffness and the centre of mass) is practically negligible and the torsional radius r is larger than the radius of gyration of the floor mass in plan 19

20 General for CBFs Basic principles of conceptual design Plan location of CBFs and structural regularity Damage limitation Regularity in elevation - All seismic resisting systems are distributed along the building height without interruption from the base to the top of the building. - Both lateral stiffness and mass at every storey practically remain constant and/or reduce gradually, without abrupt changes, from the base to the top of the building. - The ratio of the actual storey resistance to the resistance required by the analysis does not vary disproportionately between adjacent storeys. - There are no setbacks 20

21 General for CBFs Basic principles of conceptual design Plan location of CBFs and structural regularity Damage limitation damage limitation requirement is expressed by the following Equation: d r n h where: is the limit related to the typology of non-structural elements; d r is the design interstorey drift; h is the storey height; n is a displacement reduction factor depending on the importance class of the building, whose values are specified in the National Annex. In this Tutorial n = 0.5 is assumed, which is the recommended value for importance classes I and II (the structure calculated in the numerical example belonging to class II). 21

22 General for CBFs Basic principles of conceptual design Plan location of CBFs and structural regularity According to EN , If the analysis for the design seismic action is linear-elastic based on the design response spectrum (i.e. the elastic spectrum with 5% damping divided by the behaviour factor q), then the values of the displacements d s are those from that analysis multiplied by the behaviour factor q, as expressed by means of the following simplified expression: d s = q d d e Damage limitation where: d s is the displacement of the structural system induced by the design seismic action; q d is the displacement behaviour factor, assumed equal to q; d e is the displacement of the structural system, as determined by a linear elastic analysis under the design seismic forces. 22

23 Structural analysis and calculation models General features for X-CBFs for inverted V-CBFs In this Tutorial two separate calculation 2D planar models in the two main plan directions have been used, one in X direction and the other in Y direction. This approach is allowed by the EC8 (at clause 4.3.1(5)), since the examined building satisfies the conditions given by EN and (8) Modelling assumptions: for the gravity load designed parts of the frame (beam tocolumns connections, column bases) have been assumed as perfectly pinned, but columns are considered continuous through each floor beam. Masses are considered as lumped into a selected master-joint at each floor, because the floor diaphragms may be taken as rigid in their planes The models of X-CBFs and inverted V-CBFs need different assumption for the braced part. 23

24 Seismic action Structural analysis and calculation models General features for X-CBFs for inverted V-CBFs In 3D model, in order to account for accidental torsional effects the seismic effects on the generic lateral load-resisting system are multiplied by a factor δ where: L e G x is the distance from the centre of gravity of the building, measured perpendicularly to the direction of the seismic action considered; L e is the distance between the two outermost lateral load resisting systems. x L e x Seismic resistant system 24

25 Seismic action Structural analysis and calculation models General features In planar models, If the analysis is performed using two planar models, one for each main horizontal direction, torsional effects may be determined by doubling the accidental eccentricity as follows: for X-CBFs x L e for inverted V-CBFs L e G x Seismic resistant system 25

26 Structural analysis and calculation models General features for X-CBFs An important aspect to be taken into account is the influence of second order (P- ) effects on frame stability. Indeed, in case of large lateral deformation the vertical gravity loads can act on the deformed configuration of the structure so that to increase the level the overall deformation and force distribution in the structure thus leading to potential collapse in a sidesway mode under seismic condition for inverted V-CBFs 26

27 Structural analysis and calculation models General features for X-CBFs for inverted V-CBFs According to EN , (2) second-order (P- ) effects are specified through a storey stability coefficient (θ) given as: where: P tot is the total vertical load, including the load tributary to gravity framing, at and above the storey considered in the seismic design situation; V tot is seismic shear at the storey under consideration; h is the storey height; P V tot d r is the design inter-storey drift, given by the product of elastic interstorey drift from analysis and the behaviour factor q (i.e. d e q). tot d r h 27

28 Structural analysis and calculation models General features for X-CBFs for inverted V-CBFs Frame instability is assumed for θ 0.3. If θ 0.1, second-order effects could be neglected, whilst for 0.1 < θ 0.2, P- effects may be approximately taken into account in seismic action effects through the following multiplier: 1 1 Differently from MRFs, for CBFs it is common that the storey stability coefficient is < 0.1, owing to the large lateral stiffness of this type of structural scheme. Hence, CBFs are generally insensitive to P-Delta effects 28

29 Structural analysis and calculation models General features for X-CBFs for inverted V-CBFs X-CBFs According to EN (2)P, in case of X-CBFs the structural model shall include the tension braces only, unless a non-linear analysis is carried out. Then, the generic braced bay is ideally composed by a single brace (i.e. the diagonal in tension). Generally speaking, in order to make tension alternatively developing in all the braces at any storey, two models must be developed, one with the braces tilted in one direction and another with the braces tilted in the opposite direction F Ed, i G Q k i 2i ki G Q k i 2i ki F Ed, i a) b) 29

30 Structural analysis and calculation models General features for X-CBFs X-CBFs the diagonal braces have to be designed and placed in such a way that, under seismic action reversals, the structure exhibits similar lateral load-deflection response in opposite directions at each storey for inverted V-CBFs A A A A where A+ and A- are the areas of the vertical projections of the crosssections of the tension diagonals (Fig. 4.6) when the horizontal seismic actions have a positive or negative direction, respectively 30

31 Structural analysis and calculation models General features for X-CBFs X-CBFs The diagonal braces have also to be designed in such a way that the yield resistance N pl,rd of their gross cross-section is such that N pl,rd N Ed, where N Ed is calculated from the elastic model illustrated in Fig. 4.5 (Section 4.4.2). In addition, the brace slenderness must fall in the range for inverted V-CBFs being y 31

32 Structural analysis and calculation models General features for X-CBFs for inverted V-CBFs X-CBFs the restraint effect of the diagonal in tension has been taken into account in the calculation of the geometrical slenderness of X- diagonal braces. This effect halves the brace in-plane buckling length, while it is taken as inefficient for out-of-plane buckling Hence, the geometrical in-plane slenderness is calculated considering the half brace length, while the out-of-plane ones considering the entire brace length Lb Lb Out-of-plane buckling In-plane buckling 32

33 Structural analysis and calculation models General features for X-CBFs for inverted V-CBFs X-CBFs In order to force the formation of a global mechanism, which means maximizing the number of yielding diagonals, clause 6.7.4(1) of the EC8 imposes that the ratios Ω i = N pl,rd,i /N Ed,i, which define the design overstrength of diagonals, may not vary too much over the height of the structure. In practical, being Ω the minimum over-strength ratio, the values of all other Ω i should be in the range Ω to 1.25Ω 33

34 Structural analysis and calculation models General features for X-CBFs for inverted V-CBFs X-CBFs Once Ω has been calculated, the design check of a beamcolumn member of the frame is based on Equation N ( M ) N 1.1 g N pl, Rd Ed Ed, G ov Ed, E In case of columns, axial forces induced by seismic actions are directly provided by the numerical model. This does not apply to beams 34

35 Structural analysis and calculation models General features for X-CBFs X-CBFs In the numerical model, floors are usually simulated by means of rigid diaphragms. In such a way the relative in-plane deformations are eliminated and the numerical model gives null beam axial forces. it is possible to calculate the beam axial forces by simple hand calculations: for inverted V-CBFs 35

36 Structural analysis and calculation models General features for X-CBFs Inverted V-CBFs Differently from the case of X bracings, Euro 8 states that the model should be developed considering both tension and compression diagonals for inverted V-CBFs 36

37 Structural analysis and calculation models General features for X-CBFs for inverted V-CBFs Inverted V-CBFs Differently from X-CBFs, in frame with inverted-v bracing compression diagonals should be designed for the compression resistance in accordance to EN 1993:1-1 (EN (6)). This implies that the following condition shall be satisfied the following condition: N pl, Rd N where is the buckling reduction factor (EN 1993: Ed (1)) and N Ed,i is the required strength 37

38 Structural analysis and calculation models General features for X-CBFs for inverted V-CBFs Inverted V-CBFs Differently from the case of X-CBFs, the does not impose a lower bound limit for the non-dimensional slenderness, while the upper bound limit ( 2 ) is retained. Also in this case it is compulsory to control the variability of the over-strength ratios Ω i = N pl,rd,i /N Ed,i in all diagonal braces. However, it should be noted that, differently from the case of X- CBFs, the design forces N Ed,i are calculated with the model where both the diagonal braces are taken into account 38

39 Structural analysis and calculation models General features for X-CBFs for inverted V-CBFs Inverted V-CBFs Vertical component of the force transmitted by the tension and compression braces: Static balance of horizontal forces: F(1-0.3)N i = (1+0.3)(N pl,rd,i sen pl,rd,(i+1) i cos (i+1) - N pl,rd,i cos i ) F Ed,i+1 F Ed,i i L N pl,rd,i N pl,rd,(i+1) N pl,rd,(i+1) cos (i+1) V Ed,E =(N pl,rd,i -0.3N pl,rd,i )(sen i )/2 0.3N pl,rd,i N pl,rd,i + Bending moment Axial force diagram diagram G 0.3N pl,rd,i q i =F i /L k i 2i ki 0.3N pl,rd,(i+1) Q 0.3N pl,rd,(i+1) cos i+1) M(N Ed,E pl,rd,i =(N- pl,rd,i 0.3N-0.3N pl,rd,i pl,rd,i )(sen )(sen i )(L/4) i )(L/4) N pl,rd,(i+1) cos (i+1) +q i L/2 V Ed,E =(N pl,rd,i -0.3N pl,rd,i )(sen i i )/2 Static balance of horizontal forces: F i = (1+0.3)(N Shear force pl,rd,(i+1) diagram cos (i+1) - N pl,rd,i cos i ) Shear force diagram Static balance of horizontal forces: F Ed,i = (1+0.3)(N pl,rd,(i+1) cos (i+1) - N pl,rd,i cos i ) F Ed,i+1 39

40 General features for X-CBFs i N pl,rd,(i+1) cos (i+1) Structural analysis and calculation models L V Ed,E =(N pl,rd,i -0.3N pl,rd,i )(sen i )/2 Bending moment Axial force diagram diagram Inverted V-CBFs 0.3N pl,rd,(i+1) cos i+1 M(N Ed,E pl,rd,i =(N- pl,rd,i 0.3N-0.3N pl,rd,i pl,rd,i )(sen )(sen i )(L/4 i N pl,rd,(i+1) cos (i+1) +q i L/2 V Ed,E =(N pl,rd,i -0.3N pl,rd,i )(sen i i ) ce of horizontal forces: F i = (1+0.3)(N Shear force pl,rd,(i+1) diagram cos (i+1) - N pl,rd,i cos i ) Shear force diagram Static balance of horizontal forces: F Ed,i = (1+0.3)(N pl,rd,(i+1) cos (i+1) - N pl,rd,i cos i ) q i =F i /L N pl,rd,(i+1) 0.3N pl,rd,(i+1) for inverted V-CBFs i L N pl,rd,i 0.3N pl,rd,i 0.3N pl,rd,(i+1) cos i+1) N pl,rd,(i+1) cos (i+1) N pl,rd,(i+1) cos (i+1) +q i L/2 Axial force diagram 40

41 Verifications Numerical dynamic properties Numerical models for X-CBFs numerical models of the calculation example with single diagonals tilted in +X direction (a) and in X direction (b). P- effects X-CBFs Inverted V- CBFs Connections Damage limitation a) b) 41

42 Verifications Numerical dynamic properties Numerical models for inverted V-CBFs P- effects X-CBFs Inverted V- CBFs Connections Damage limitation 42

43 Verifications Numerical dynamic properties P- effects X-CBFs Inverted V- CBFs T 1 = 0.874s; M 1 = T 2 = 0.316s; M 2 =0.161 Dynamic properties in X direction Connections Damage limitation T 1 = 0.455s; M 1 = T 2 = 0.176s; M 2 =0.156 Dynamic properties in Y direction 43

44 Verifications Numerical dynamic properties P- effects X-CBFs Inverted V- CBFs Connections Damage limitation The effects of actions included in the seismic design situation have been determined by means of a linear-elastic modal response spectrum analysis. The first two modes have been considered because they satisfy the following criterion: the sum of the effective modal masses for the modes taken into account amounts to at least 90% of the total mass of the structure. Since the first two vibration modes in both X and Y direction may be considered as independent (being T2 0.9T1, EN , ) the SRSS (Square Root of the Sum of the Squares) method is used to combine the modal maxima 44

45 Verifications Numerical dynamic properties P- effects X-CBFs Inverted V- CBFs the coefficient θ are lesser than 0.1 for both X-CBFs and inverted V-CBFs. Hence, the structure is not sensitive to second order effects that can be neglected in the calculations. This result is generally common for CBFs Connections Damage limitation 45

46 Verifications Numerical dynamic properties Circular hollow sections and S 235 steel grade are used for X braces. The brace cross sections are class 1. P- effects X-CBFs Inverted V- CBFs Connections Damage limitation Storey Brace cross section d x t d t d/t.50 2 (mm x mm) (mm) (mm) - VI 114.3x V 121x IV 121x III 121x II 133x I 159x

47 Verifications Numerical dynamic properties P- effects X-CBFs Inverted V- CBFs Connections Damage limitation The circular hollow sections are suitable to satisfy both the slenderness limits (1.3 < 2.0) and the requirement of minimizing the variation among the diagonals of the overstrength ratio Ω i, whose maximum value (Ω max ) must not differ from the minimum one (Ω min ) by more than 25%.. Storey Brace cross section (d x t) N pl,rd N Ed i = N pl,rd i min (x 100) (mm x mm) (kn) (kn) N Ed min VI 114.3x V 121x IV 121x III 121x II 133x I 159x

48 Verifications Numerical dynamic properties Verification of beams IPE 360 IPE 360 IPE 360 IPE 360 P- effects X-CBFs IPE 360 IPE 360 Inverted V- CBFs IPE 360 IPE 360 IPE 360 IPE 360 Connections IPE 360 IPE 360 Damage limitation 48

49 Verifications Numerical dynamic properties P- effects X-CBFs Inverted V- CBFs Connections Damage limitation Verification of beams Storey Section N Rd N Ed,G N Ed,E N Ed =N Ed,G +1.1g ov N Ed,E N Rd (kn) (kn) (kn) (kn) N Ed VI IPE V IPE IV IPE III IPE II IPE I IPE N Ed = M Ed = Storey N Ed,G N Ed,E N Ed,G +1.1g ov N Ed,E M Ed,G M Ed,E M Ed,G +1.1g ov M Ed,E M N,Rd M Rd (kn) (kn) (kn) (knm) (knm) (knm) (knm) M Ed VI V IV III II I

50 Verifications Numerical dynamic properties Verification of columns HE 180 A HE 180 A HE 180 A P- effects HE 180 A HE 180 A HE 180 A X-CBFs HE 240 B HE 240 B HE 240 B Inverted V- CBFs HE 240 B HE 240 B HE 240 B Connections HE 240 M HE 240 M HE 240 M Damage limitation Z HE 240 M HE 240 M HE 240 M X (a) (b) (b) (a) 50

51 Verifications Numerical dynamic properties P- effects X-CBFs Inverted V- CBFs Connections Damage limitation Verification of columns Axial strength checks for columns in + X direction column type a Storey Section A N pl,rd N Ed,G N Ed,E N Ed,G +1.1g ov N Ed,E N Ed = (mm 2 ) (kn) (kn) (kn) (kn) N Ed VI HE180A V HE180A N pl,rd IV HE240B III HE240B II HE240M I HE240M column type b VI HE180A V HE180A IV HE240B III HE240B II HE240M I HE240M

52 Verifications Numerical dynamic properties Inverted V-CBFs Similarly to the X-bracing, for the inverted-v braces circular hollow sections and S235 steel grade are used. The adopted brace cross sections belong to class 1 P- effects X-CBFs Inverted V- CBFs Connections Damage limitation Storey Brace cross section d x t d t d/t.50 2 (mm x mm) (mm) (mm) - VI 127x V 193.7x IV 244.5x III 244.5x II 273x I 323.9x

53 Verifications Numerical dynamic properties Inverted V-CBFs Because of the presence of vertical loads and the different deformations of columns, the brace axial force is slightly different for braces D1 and D2 P- effects X-CBFs D1 D2 D2 D1 Inverted V- CBFs Connections Damage limitation 53

54 Verifications Numerical dynamic properties P- effects X-CBFs Inverted V- CBFs Connections Inverted V-CBFs Inverted V-braces (D1 members) design checks in tension Storey Brace cross N section (d x t) pl,rd N Ed, D1 N pl,rd i i = (x 100) (mm x mm) (kn) (kn) N Ed d,d1 VI 127x V 193.7x IV 244.5x III 244.5x II 273x I 323.9x Damage limitation 54

55 Verifications Numerical dynamic properties P- effects X-CBFs Inverted V- CBFs Connections Inverted V-CBFs Inverted V-braces (D1 members) design checks in compression Storey Brace cross section (d x t) N b,rd N Ed, D1 N b,rd (mm x mm) (kn) (kn) N Ed,D1 VI 127x V 193.7x IV 244.5x III 244.5x II 273x I 323.9x Damage limitation 55

56 Verifications Numerical dynamic properties Verification of beams Inverted V-CBFs HE 320 B HE 320 B P- effects HE 320 M HE 320 M X-CBFs Inverted V- CBFs HE 360 M HE 450 M HE 360 M HE 450 M Connections HE 500 M HE 500 M Damage limitation HPE 550 M HPE 550 M 56

57 Verifications Numerical dynamic properties Verification of beams Inverted V-CBFs Static balance of horizontal forces: F i = (1+0.3)(N pl,rd,(i+1) cos (i+1) - N pl,rd,i cos i ) F Ed,i+1 Axial forces due to the seismic effects in beams of inverted-v CBFs q i =F i /L P- effects N pl,rd,(i+1) 0.3N pl,rd,(i+1) X-CBFs F Ed,i N pl,rd,i 0.3N pl,rd,i N C N D Inverted V- CBFs i L N A N B Axial force diagram Connections Damage limitation Storey N pl,rd q i N A N B N C N D (kn) (kn/m) (kn) (kn) (kn) (kn) VI V IV III II I

58 Verifications Numerical dynamic properties P- effects X-CBFs Inverted V- CBFs Connections Verification of beams Inverted V-CBFs Axial strength checks in beams of inverted-v CBFs N Ed = Storey Section A N pl,rd N Ed,G N Ed,E = N A N Ed,G +N Ed,E N pl,rd (mm 2 ) (kn) (kn) (kn) (kn) N Ed VI HE320 B V HE320 M IV HE360 M III HE450 M II HE500 M I HE550 M Damage limitation 58

59 Verifications Numerical dynamic properties P- effects X-CBFs Inverted V- CBFs Connections Verification of beams Inverted V-CBFs Combined bending-axial force checks in beams of inverted-v CBFs Storey Section N Ed M Ed,G M Ed,E M Ed M Rd M Rd (kn) (knm) (knm) (knm) (knm) M Ed VI HE320 B V HE320 M IV HE360 M III HE450 M II HE500 M I HE550 M Damage limitation 59

60 Verifications Numerical dynamic properties P- effects X-CBFs Inverted V- CBFs Connections Verification of beams Inverted V-CBFs Shear force checks in beams of inverted-v CBFs Storey Section A A v V pl,rd V Ed,G V Ed,E V Ed V pl,rd (mm 2 ) (mm 2 ) (kn) (kn) (kn) (kn) V Ed VI HE320B V HE320M IV HE360M III HE450M II HE500M I HE550M Damage limitation 60

61 Verifications Numerical dynamic properties Verification of columns HE 180 A Inverted V-CBFs HE 180 A HE 180 A P- effects HE 180 A HE 180 A HE 180 A X-CBFs HE 240 M HE 240 M HE 240 M Inverted V- CBFs HE 240 M HE 240 M HE 240 M Connections HE 320 M HE 320 M HE 320 M Damage limitation HE 320 M HE 320 M HE 320 M 61

62 Verifications Numerical dynamic properties Verification of columns Inverted V-CBFs P- effects X-CBFs Inverted V- CBFs Storey Section A N pl,rd N Ed,G N Ed,E N Ed = N Ed,G +1.1g ov N Ed,E N pl,rd (mm 2 ) (kn) (kn) (kn) (kn) N Ed VI HE180A V HE180A IV HE240M III HE240M II HE320M I HE320M Connections Damage limitation 62

63 Verifications Numerical dynamic properties P- effects X-CBFs Inverted V- CBFs Connections Damage limitation Connections Connections have to satisfy the given in EN In particular, the following connection overstrength criterion must be applied: R d 1.1 γ ov R fy where R d is the resistance of the connection, R fy is the plastic resistance of the connected dissipative member based on the design yield stress of the material, γ ov is the material overstrength factor. In addition, Euro 8 introduces an additional capacity design criterion for bolted shear connections. Indeed, the design shear resistance of the bolts should be at least 1.2 times higher than the design bearing resistance. 63

64 Verifications Numerical dynamic properties P- effects Beams Columns In the calculation example ductile non-structural elements have been hypothesized. Hence, the intestorey drift limit to be satisfied is equal to 0.75%h. Moreover, for what concerns the displacement reduction factor ν, it was assumed the recommended value that is ν = 0.5 (being the structure calculated in the numerical example belonging to class II) 0.10m max = 0.54% Connections Damage limitation a) 0.04m 64

65 Verifications max = 0.54% Numerical dynamic properties P- effects Beams Columns In the calculation example ductile non-structural elements have been hypothesized. Hence, the intestorey drift limit to be satisfied is equal to 0.75%h. Moreover, for what concerns the displacement reduction factor ν, it was assumed the recommended value that is ν = 0.5 (being the structure calculated in the numerical example belonging to class II) a) 0.04m max = 0.54% Connections Damage limitation b) 65

66 Thank you for your attention