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 moment resisting frame 1. Introduction 2. General for Moment-Resisting 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 6,00 12,00 5,10 Introduction Building description Structural plan and configuration of the MRFs Normative references 18,50 4,00 4,25 4,20 4,55 Materials Actions Y X 4,00 3,45 2,00 2,70 4,55 18,50 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 In order to avoid the composite action, the shear connectors are applied only on the beams of the gravity load designed bays and in the moment-resisting parts a gap was kept from both sides of both column flanges, or from other protruding elements associated with the beam-to-column joints, and the structural slab. according to AISC , it was widely demonstrated that this type of detailing is sufficient to inhibit the load transfer from the slab to the column. In such a way, the all-steel beam-to-column hierarchy criterion is not modified. 7

8 Introduction Building description Normative references Materials Actions Disconnecting the slab from the beam around the column is also a recommended option in Section 7 of EN (Clause 7.7.5), where it is clearly stated that to avoid the composite action it is sufficient to guarantee no contact between slab and any vertical side of any steel element in a circular zone around a column of diameter 2b eff, with b eff being the larger of the effective widths of the beams connected to that column 8

9 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 9

10 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. 10

11 Introduction Building description Normative references Materials 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. Actions 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. 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 =

12 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 =

13 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

14 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) 14

15 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 for MRFs 1 lower bound = 0.2a g T (s) behaviour factor q was assigned according to EN (6.3.2) as follows: u q q o

16 Introduction Building description Normative references Materials Actions Behaviour factor u q q o where q o is the reference value of the behaviour factor for systems regular in elevation, while α u /α 1 is the plastic redistribution parameter. The parameter α 1 is the multiplier of the horizontal seismic design action to reach the first plastic resistance in the structure and α u is the multiplier of the horizontal seismic design action necessary to form a global mechanism. The ratio α u /α 1 may be obtained from nonlinear static pushover global analysis according to EN ( ), but is limited to 1.6. In the worked example described within this Tutorial the EC8 suggested values of α u /α 1 = 1.3 was used. 16

17 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

18 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

19 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 V IV III II I

20 General for MRFs Basic principles of conceptual design Plan location of MRFs 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. 20

21 6,00 12,00 5,10 General for MRFs Basic principles of conceptual design Plan location of MRFs and structural regularity MRFs are mainly located along the perimeter of the building. There is the same number of MRF spans in the 2 main direction of the plan. 18,50 4,00 4,25 4,20 4,55 Damage limitation Y X 4,00 3,45 2,00 2,70 4,55 18,50 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. 21

22 General for MRFs Basic principles of conceptual design Plan location of MRFs 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 22

23 General for MRFs Basic principles of conceptual design Plan location of MRFs 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 23

24 General for MRFs Basic principles of conceptual design Plan location of MRFs 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). 24

25 General for MRFs Basic principles of conceptual design Plan location of MRFs and structural regularity Damage limitation 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 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. 25

26 Structural analysis and calculation models General features for beam-tocolumn joints for beams and columns 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 to-columns connections, column bases) have been assumed as perfectly pinned, but columns are considered continuous through each floor beam. All connections of the members belonging to the MRF have been considered full strength and full rigid. In addition, the flexibility of the panel zone has not been taken into account in the elastic models Masses have been considered as lumped into a selected master-joint at each floor, because the floor diaphragms are rigid in their planes. 26

27 Structural analysis and calculation models General features planar models for beam-tocolumn joints for beams and columns Gravity load resisting frame Moment Resisting frame 27

28 Seismic action Structural analysis and calculation models General features for beam-tocolumn joints for beams and columns 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 28

29 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 beam-tocolumn joints x L e for beams and columns L e G x Seismic resistant system 29

30 Structural analysis and calculation models General features for beam-tocolumn joints 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 beams and columns 30

31 Structural analysis and calculation models General features for beam-tocolumn joints for beams and columns 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 31

32 Structural analysis and calculation models General features for beam-tocolumn joints for beams and columns 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 In case of MRFs it is common that the storey stability coefficient could exceed 0.1, owing to the lateral flexibility of this type of structural scheme. In addition, it is typical of MRFs the need to increase the need to increase the lateral stiffness to fulfill the stability. 32

33 Structural analysis and calculation models General features for beam-tocolumn joints for beams and columns For full strength joints, the following overstrength criterion must be applied: R d 1.1g ov R fy where R d is the resistance of the connection, R fy is the plastic resistance of the connected dissipative member (namely M pl,rd for beams in MRFs) based on the design yield stress of the material, γ ov is the material overstrength factor. 33

34 Structural analysis and calculation models General features for beam-tocolumn joints for beams and columns for non-dissipative joints the is oriented to avoid inelastic deformations between beams and panel zones. Indeed, EN , 6.6.3(6) requires that the shear strength of web panels in beam-tocolumn connections should satisfy the following expression: V V wp,ed wp,rd

35 Structural analysis and calculation models General features V wp,ed the design shear force in the web panel due to the plastic resistance of the beam: for beam-tocolumn joints V wp,ed M z pl,rd,i for beams and columns where z = d b -t f, being d b is the beam depth and t f the flange thickness 35

36 Structural analysis and calculation models General features for beam-tocolumn joints for beams and columns V wp,rd is the shear strength of web panel, given by : 0.9 f A 4M Vwp,Rd Vwc,Rd Vwp,add,Rd d y,wc vc pl,fc,rd 3 g M 0 s V wc,rd the design plastic shear resistance of the unstiffened column web panel and V wc,rd the overstrength contribution due to mechanism involving the plastic moment capacity of column flanges M pl,fc,rd 36

37 Structural analysis and calculation models General features In MRFs with full strength full rigid joints, beams are the dissipative elements of the structure. for beam-tocolumn joints for beams and columns the states that the the following inequalities should be verified at the location where the formation of hinges: M M V V N Ed pl,rd Ed pl,rd N Ed pl,rd

38 Structural analysis and calculation models General features for beam-tocolumn joints In beam, shear force demand at both beam ends should be calculated using capacity design principles as follows: V V V Ed Ed,G Ed,M for beams and columns Mpl VED,G VED,G Mpl VED,M = 2Mpl/L VED,M 38

39 Structural analysis and calculation models General features for beam-tocolumn joints Beams should be verified as having sufficient resistance against lateral and lateral torsional buckling in accordance with EN 1993, assuming the formation of a plastic hinge at one end of the beam. Composite slab for beams and columns Beam of gravity load design frame Considering the span length of the common MRF structure, which ranging from 5 m to 10 m, it necessary to introduce stability bracing to satisfy this requirement Stability bracing Beam of MRF 39

40 Structural analysis and calculation models General features for beam-tocolumn joints for beams and columns the forces acting on columns calculated by the elastic model have to be amplified by the magnification coefficient Ω, defined as: pl,rd,i min M M Ed,i the columns should be verified against all resistance checks including those for element stability, according to the provisions of EC3 for the most unfavourable combination of bending moments M Ed, the shear force V Ed and axial forces N Ed, based on the following M M 1.1g M Ed Ed,G ov Ed,E V V 1.1g V Ed Ed,G ov Ed,E N N 1.1g N Ed Ed,G ov Ed,E 40

41 Structural analysis and calculation models General features for beam-tocolumn joints for beams and columns In addition to the member checks based on the Ω criterion, following condition should be satisfied: where: M Rc M Rb 1.3 SM Rc is the sum of the design values of the moments of resistance of the columns framing the joint. SM Rb is the sum of the design values of the moments of resistance moments of the beams framing the joint 41

42 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 Verifications Numerical dynamic properties IPE 550 IPE 550 IPE 550 IPE 550 IPE 550 IPE 550 IPE 550 IPE 550 P- effects IPE 600 IPE 600 IPE 600 IPE 600 Beams IPE 600 IPE 600 IPE 600 IPE 600 Columns Connections HEA 600 HEA 600 HEA 600 HEA 600 Damage limitation HEA 600 HEA 600 HEA 600 HEA

43 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 HEM 600 Verifications Numerical IPE 550 dynamic properties IPE 550 P- effects IPE 600 Beams IPE 600 Columns IPE 550 IPE 550 IPE 600 IPE 600 IPE 550 IPE 550 IPE 600 IPE 600 Connections HEA 600 Damage limitation HEA 600 HEA 600 HEA 600 HEA 600 HEA

44 Verifications Numerical dynamic properties P- effects Beams Columns Connections Damage limitation a) b) Numerical models of the worked example in X (a) and in Y (b) direction. 44

45 Verifications Numerical dynamic properties P- effects Beams Columns T 1 = 1.089s; M 1 = T 2 = 0.356s; M 2 =0.131 Dynamic properties in X direction Connections Damage limitation T 1 = 1.067s; M 1 = T 2 = 0.349s; M 2 =0.131 Dynamic properties in Y direction 45

46 Verifications Numerical dynamic properties P- effects Beams Columns 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 46

47 Verifications Numerical dynamic properties P- effects the coefficient θ ranges within at the lower storeys (namely those indicated in bold, which are from storey 1 to 4). Hence, to take into account second order effects the seismic effects were magnified through the relevant multiplier a, which is calculated at each storey having θ > 0.1 Beams Columns Connections Damage limitation 47

48 Verifications Numerical dynamic properties P- effects Beams Columns Connections Damage limitation The beam cross sections are class 1, as defined by EN 1993: which requires to satisfy the following conditions: d 2r 2t b f t w b 2r t t f f w 72 9 Storey cross section d 2r 2t VI IPE b t w f for web for flange 72 b 2r t f t f 4.39 V IPE IV IPE III IPE II HEA I HEA w

49 Span B-C Span A-B Storey Verifications Numerical dynamic properties P- effects Beams Columns Connections Damage limitation flexural checks for beams belonging to MRF in X direction: Left end Right end M Ed,G M Ed,E M Ed i M Ed,G M Ed,E M Ed i (knm) (knm) (knm) (knm) (knm) (knm) VI V IV III II I VI V IV III II I min MEd MEd,G MEd,E 76.72kNm knm knm

50 bottom end top end storey Verifications Numerical dynamic properties P- effects Beams Columns Connections Damage limitation flexural checks for columns belonging to MRF in X direction: M Ed,G M Ed,E M Ed N Ed,G N Ed,E N Ed M M NRd, M Ed (knm) (knm) (knm) (kn) (kn) (kn) (knm) Ed Ed,G 1.1gov Ed,E VI M M M 12.06kNm kNm kNm V IV EdIII Ed,G gov Ed,E II N N N kN kN kN I N Rd VI V IV III II I

51 storey Verifications Numerical dynamic properties P- effects Beams Columns Connections Damage limitation Local hierarchy criterion for external and inner columns in X direction: VI M 2 M kNm kNm Rc Rc M 2 M kNm kNm M M Rb Rb External joints (Vertical A) Inner joints (Vertical B) Rc M Rc 2.12 M Rb 1.3 M Rc M Rc M Rb, left side M Rb, right side M Rc (knm) Rb (kn) M Rb (knm) (knm) (knm) M Rb V IV III II I

52 Verifications Numerical dynamic properties P- effects Beams Columns Connections Damage limitation Panel Zone of Beam-to-Column Connections external joint: V V V wp,ed wp,rd wp,rd M pl,rd,i kN z f 3 y,wc Avc g 3 V wp,ed M 0 additional web plates are required kN the minimum thickness of supplementary web plate is given by: V wp,rd kN fy kN tp dwc kN 3 being d the column web depth wc t 4.44mm t 5 mm 1 plate 5mm thick p p 52

53 Verifications Numerical dynamic properties Panel Zone of Beam-to-Column Connections Strengthening solutions P- effects Beams Columns Connections Damage limitation 53

54 Verifications Numerical dynamic properties P- effects Beams 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) 0.12m Columns Connections Damage limitation max = 0.71% b) 54

55 Thank you for your attention