Seismic response of steel Moment Resisting Frames equipped with friction beam-to-column joints

Soil Dynamics and Earthquake Engineering 119 (2019) 144–157

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Seismic response of steel Moment Resisting Frames equipped with friction beam-to-column joints

T

Elide Nastrib, , Mario D’Anielloa, Mariana Zimbrua, Simona Strepponeb, Raffaele Landolfoa, Rosario Montuorib, Vincenzo Pilusob ⁎

a b

University of Naples “Federico II”, Department of Structures for Engineering and Architecture, Naples, NA, Italy University of Salerno, Department of Civil Engineering, Fisciano, SA, Italy

ABSTRACT

The use of supplementary dissipative devices is an effective design strategy to improve the seismic response of structures. Friction devices inserted into beam-tocolumn joints can be a viable solution to optimize the seismic performance of steel Moment Resisting Frames (MRFs). The joints equipped with such devices are full rigid but very ductile partial strength, whose resistance can be easily calibrated to match the EC8 design moments with negligible overstrength. On the contrary, EC8compliant MRFs equipped with traditional full-strength joints are often characterized by large beam overstrength due to the need to satisfy both serviceability and stability checks that lead largely oversizing the columns. In this paper, three design criteria for MRFs equipped with friction beam-to-column joints are described and examined by means non-linear static and dynamic analyses. The discussion of the results highlights the benefits of friction joints as well as the effectiveness of the examined design criteria.

1. Introduction Supplementary energy dissipation devices are largely used to mitigate the earthquake-induced effects on structures as well as to control the structural response under wind actions. Among the large variety of passive systems, friction devices are effective and low-cost systems that can be easily maintainable and replaceable if damaged. Another advantage of friction devices is their versatility, since they can be easily integrated in both braced and unbraced frames, providing wide and stable hysteresis loops [1,2] by exploiting the tribological properties of materials, [2–4]. The Pall-type friction damper is the pioneering patent that was used in several buildings in Canada [5] while other frictional devices are recently incorporated in several buildings in Japan [6] and in New Zealand [7–9]. In Europe, the use of friction devices in Moment Resisting Frames (MRFs) has been recently investigated with reference to both new [10–14] and existing [15] buildings. In fact, friction devices can be suitable also for the retrofitting of existing buildings giving the possibility to opportunely calibrate the bending resistance of members thus allowing the existing column to fulfil the hierarchy criterion requirements. In this study, friction devices incorporated into beam-to-column joints are investigated to enhance the design and the performance of steel moment-resisting frames (MRFs). The examined moment resisting friction connections are conceived to dissipate energy through the slip occurring between the devices (which are located below a haunch

⁎

stiffener connected to the lower beam flange) and two L-Stubs connected to the column flange (Fig. 1). The upper flange of the beam is connected to the column by means of a bolted T-Stub. The cover plate connecting the upper beam flange is arranged to allow moderate plastic deformations that accommodate the joint rotation following the sliding of the device. This arrangement is set to form an ideal center of rotation into the T-stub that prevents the damage of the slab. In order to prevent any interaction with the slab and to avoid any modification of the internal lever arm of the connection, a gap (e.g. about 25 mm in accordance with the typical detail of AISC 358 seismic prequalified joints) is assumed between the slab and any protruding part of the connection The depth of the haunch stiffener ranges within 2/3 and 1 times the beam depth, thus significantly increasing the internal lever arm of the connection [16–19]. The friction properties are given by the friction pads with surface treatments giving desired tribological properties. The slipping part is made of stainless steel, due to its higher superficial hardness. The hysteretic response of this joint typologies is strictly related with the material of the friction pads, but typically they exhibit wide and stable hysteresis loops, without appreciable stiffness and strength degradation [16–18]. The supplementary energy dissipation provided by such devices permits the control of the interstorey drifts and, consequently, the reduction of the structural damage occurring at the beam ends. Furthermore, the reduction of lateral drifts is also beneficial to mitigate of damage of non-structural components. Lastly, joints equipped with friction devices can be also easily replaceable after

Corresponding author. E-mail address: [email protected] (E. Nastri).

https://doi.org/10.1016/j.soildyn.2019.01.009 Received 10 May 2018; Received in revised form 5 January 2019; Accepted 6 January 2019 0267-7261/ © 2019 Elsevier Ltd. All rights reserved.

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Soil Dynamics and Earthquake Engineering 119 (2019) 144–157

resistance of the friction joints, even though different thresholds of friction resistance are assumed. In addition, TPMC has been also used since this method allows controlling the optimal dissipation mechanism more effectively than code-compliant procedures. The main features of each design approach are summarized hereinafter. 2.1. EC8 compliant FD-A design approach In the case of FD-A method, the flexural resistance MFD . Rd of the friction joints is set equal to the design plastic moment Mpl . b . Rd of the connected beam with the aim to exploit the maximum capacity of the connection. Under this assumption, the design procedure is very similar to the current EC8, and the nominal resistance of the frames with friction joints is close to those with conventional ones. Hence, the mechanical properties of the friction device can be easily obtained d as function of the capacity of the connected beam, thus the friction connection is designed for a value of the slip force given in Eq. (1)

Fig. 1. Example of haunched connection equipped with friction device.

Fslip =

severe seismic events, since the entire beam-to-column assembly is almost elastic in the aftermath of an earthquake. The use of friction beam-to-column joints can also overcome one of the main criticisms widely recognized for EC8-compliant steel MRFs, namely the large overdesign of the members due to the stringent requirements on P-Delta effects and serviceability checks [20–25]. Hence, to optimize the performance of MRFs, a viable option can be using friction beam-to-column joints able to exhibit a fully rigid behaviour but partial strength, the latter properly designed to match the design bending moments that come from the structural analysis. Under this assumption, the design overstrength of the dissipative component (i.e. the ratio between the bending resistance over the moment due to seismic actions) is close to 1, thus making less stringent the capacity design requirements for the columns. This feature is highly beneficial because it allows decoupling the lateral stiffness of the frame (which is mostly given by the second moment of area of the beam) from its resistance (which is given by the friction connection, differently from the cases of conventional MRFs where the beams are devoted to give both strength and stiffness). In line with this concept, two design criteria (hereinafter referred as FD-A and FD-B, where FD stands for Friction Device) are investigated in the framework of current EC8 and their effectiveness is compared as respect to the design procedure of Theory of Plastic Mechanism Control (TPMC), which is a well-established methodology that guarantees the complete formation of the overall ductile mechanism [26,27]. With this regard, the effectiveness of these design procedures to decouple the lateral strength and stiffness of MRFs by means of the use of friction joints is herein investigated with reference to a structural prototype that is alternatively designed with conventional and friction joints according to each design approach. In addition, three levels of the seismic intensity are considered: Medium (M), High (H) and Very High (VH), to which reference peak ground acceleration agR equal to 0.25 g, 0.35 g and 0.45 g are respectively associated. The structural response was analysed by means of both nonlinear static and dynamic analyses.

Mpl . b . Rd

(1)

z

where z is the connection lever arm, namely the distance from the center of rotation (Fig. 1) to the middle of the flange of the haunch. Once designed the devices, the required resistance for the non-dissipative elements can be evaluated based on the ultimate bending strength of the joint that is associated to the slip resistance of the device (previously defined), which is magnified by the factors µ that accounts for the design overstrength and variability of dynamic and static friction coefficient (μ) as well as the clamping forces in the bolts. The overstrength coefficient is consistent with EC8 definition and it is given as the minimum value of the (z Fslip/MEd)i ratios that should be computed for all friction connections, where MEd is the design bending moment at the end of the i-th beam due to seismic action. The overstrength coefficient µ is defined as follows: µ

=

µst .95% Nb .95% µdyn .5% Nb.5%

(2)

where μdyn,5%, Nb,5% are the lower-bound values of the dynamic friction coefficient and tightening force, respectively; μst,95%, Nb,95% are the upper-bound values of the static friction coefficient and tightening force, respectively. The values of both static and dynamic friction coefficients as well as the tightening forces were derived on the basis of previous experimental studies [14], which addressed aspects related to the friction properties of the coating material and the covered surfaces, the preloading level, creep phenomena, loss of preloading and high velocity load application. The design forces for the non-dissipative elements are evaluated based on Eq. (3)

Ed = Ed . G +

µ Ed . E

(3)

where Ed is the design value of the internal forces for non-dissipative elements, Ed . G is the effect coming from gravitational loads and Ed . E is the effect coming from the seismic action. The resistance and stability checks for the members (beams and columns) and the design of connections, must be done according to EN 1993 1-1 and 1-8, respectively. In the end, the beam-column hierarchy criterion at the node must be checked, again, as recommended by EC8. It is also worth noting that the design of haunch stiffener also depends on the verification checks of the beam strength. Indeed, to guarantee that the beam is kept in elastic range, the dimension and the length of the haunch are given by the condition that the bending and shear resistance of the unstiffened segment of the beam exceed the forces computed according to Eq. (3).

2. Design approaches adopted for the structures The main difference between MRFs equipped with conventional beam-to-column joints and those equipped with friction devices (FDMRFs) is the source of energy dissipation, i.e. the beam for the former case, while the friction device for the latter. In the light of this distinction, two design criteria in the framework of EC8 philosophy have been proposed, hereinafter referred as FD-A and FD-B approaches. Both methods set the capacity design rules on the basis of the flexural 145

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Fig. 2. TPMC statement.

Fig. 4. Elevation configuration of the building prototype.

Table 1 Characteristic values of loads and combination factors. Location

Type

Load [kN/m2]

ψ2,ia

ψE,ia

Roof

Permanent Variable

4.5 2

0.3

0.24

Intermediate stories

Permanent Variable

4.5 2

0.3

0.15

a

Coefficients reported in EC8 to combine loads and masses.

Fig. 3. Plan configuration of the building prototype with the evidence of the tributary area of masses (shaded area) for the seismic resistant structure.

columns and shorter haunch stiffeners for the beams. 2.2. EC8 compliant FD-B design approach

2.3. TPMC design approach

The FD-B approach follows the same algorithm for the initial design of the structure i.e. once the geometrical configuration is established and the forces are applied (considering the EC1 recommendations) the Serviceability Limit State limitations are verified. This will be the condition that primarily dictates the beam and column member profiles. The following step consists in the design of the dissipative element (the friction connection) for the design forces coming from the combination accounting for the seismic actions. In particular, the bending resistance of the friction joints and the relevant slip force (Fslip ) are calibrated to resist the bending moments MEd at the ends of each beam calculated from the loading combination accounting for the seismic actions. Hence, the required slip design force for the friction connection is computed as follows.

The Theory of Plastic Mechanism Control is a design approach based on a rigorous theoretical background. It assures the development at collapse of a mechanism of global type [26,27]. TPMC exploits the kinematic theorem of plastic collapse extended to the concept of mechanism equilibrium curve:

Fslip

M = Ed z

=

where, following the theory of rigid-plastic analysis, 0 is the first order collapse multiplier of horizontal forces, is the slope of the linearized mechanism equilibrium curve due to second order effects and is the plastic top sway displacement. It means that in the case of the global mechanism Eq. (6) becomes: (g )

(4)

µ Ed . E

=

(g ) 0

(g )

(7)

while in the case of undesired mechanism becomes:

Subsequently, the non-dissipative elements (beams, columns, connections) are designed to resist both gravity and seismic induced effects, the latter computed considering solely the overstrength factor µ (i.e. defined in Eq. (2)), namely as follows:

Ed = Ed . G +

(6)

0

(t ) im

=

(t ) 0. im

(t ) im

(8)

where 0(g ) and 0.(ti)m are the first order collapse mechanism multipliers for global and undesired mechanism, respectively; (g ) and i(mt ) are the collapse multiplier of horizontal force for the global and undesired (t ) mechanism, respectively and (g ) and im are the slope of mechanism equilibrium curve for the global and undesired mechanism, respectively. TPMC states that the mechanism equilibrium curve

(5)

The capacity design requirements given by Eq. (5) are less stringent than the previous case, thus leading to design lighter sections of the 146

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Table 2 Base shear, beams and column sections of the designed structure. Structures

Base shear

Columns

Beams

Vd (kN)

Columns

1st to 3rd floor

4th floor

5th to 6th floor

1st to 2rd floor

3th floor

4th floor

5th to 6th floor

FD-A 6-3-6 M

457

IPE 360

IPE 600

IPE 550

IPE 550

IPE 450

1044

HEB 400 HEB 360 HRB 500 HEB 450 HEM 450 HEM 400

IPE 500

FD-A 6-3-6 VH

HEM 450 HEB 400 HEM 550 HRB 500 HD 400 × 509 HEM 450

IPE 500

802

HEM 500 HEM 450 HEM 600 HEM 550 HD 400 × 551 HD 400 × 509

IPE 550

FD-A 6-3-6 H

Internal External Internal External Internal External

IPE 750 × 147

IPE 600

IPE 600

IPE 500

FD-B 6-3-6 M

407

IPE 360

IPE 600

IPE 550

IPE 550

IPE 450

970

HEB HEB HEB HEB HEB HEB

IPE 500

FD-B 6-3-6 VH

HEB HEB HEB HEB HEB HEB

IPE 500

710

HEB HEB HEB HEB HEB HEB

IPE 550

FD-B 6-3-6 H

Internal External Internal External Internal External

IPE 750 × 147

IPE 600

IPE 600

IPE 500

TPMC 6-3-6 M TPMC 6-3-6 H TPMC 6-3-6 VH

491 687 883

Both Both Both

HEB 500 HEB 500 HEB 650

IPE 400 IPE 400 IPE 500

IPE 400 IPE 400 IPE 500

IPE 360 IPE 400 IPE 450

IPE 360 IPE 360 IPE 450

450 400 500 450 600 550

400 360 450 400 550 500

HEB 450 HEB 500 HEB 650

360 320 400 36–0 500 450

HEB 450 HEB 450 HEB 600

a global collapse mechanism are the unknowns of the design problem, while the dissipative zones are preliminarily designed according to the first principle of capacity design. In this paper, the ultimate design displacement u is computed as: u

(9)

= hns

where is the target rotation of the plastic hinge that is assumed equal to 0.04 rad, and hns is the building height. The plastic hinge rotation is set equal to the interstorey drift ratio, since the idealized behaviour of the structure is rigid-plastic. Hence, the target rotation is assumed equal to the performance limit for the prequalified joints in accordance with AISC341-16 [28]. It is worth noting that P-Delta second order effects are taken into account using the TPMC design approach and, as a consequence, does not deeply affect the design as the use of the factor proposed in the framework of Eurocode 8 [21], thus allowing to optimize the design overstrength of the structure and the non-linear response as well. 3. Parametric analysis The building prototype of this study is a 6-storey 3-bay MRF, whose plan configuration is reported in Fig. 3. MRFs are located in longitudinal direction (x), while concentrically braced frames are considered in the transverse direction (y). The terms “hinged” and “braced” indicate the bay in transversal direction with pins at the end of the beams and braces, respectively. In addition, Fig. 4 shows the elevation configuration of the structure. Permanent (Gk ) and live (Qk ) loads considered for the structural analysis and evaluation of masses corresponding to the gravitational part, chosen within a practical range, are delivered in Table 1. All structural members were designed with cross section class 1 and S355 steel grade (it means that the characteristic yield strength is

Fig. 5. Node modelling scheme.

corresponding to the global mechanism (Eq. (7)) has to be located below those corresponding to all the undesired mechanisms (Eq. (8)) until a design displacement u compatible with the local ductility supply [27] (Fig. 2). The column sections at each storey that guarantee

Table 3 First-class parameters (strength, stiffness and ductility parameters) of the “Multilinear” spring element adopted for modelling the friction device. Initial rotational stiffness EI (kN/m2)

First yielding moment PCP/PCN (kN m)

Plastic moment PYP/PYN (kN m)

Yield rotation UYP/UYN (rad)

Ultimate rotation UUP/UUN (rad)

Post yield stiffness ratio as % of elastic EI3P/EI3N (–)

1.00E + 06

540/− 621

594/− 683.1

0.00054/0.000621

0.05/− 0.05

0.001/0.001

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Table 4 Second-class parameters (hysteresis shape parameters) of the “Multilinear” spring element adopted for modelling the friction device. Stiffness degradation parameter

Hysteretic energy based strength decay parameter HBF (–)

Slip parameter

Bilinear model parameter

HC (-)

Ductility based strength decay parameter HBD (–)

HS (–)

BM (–)

200

0.001

0.001

1

1

Fig. 7. Monitored parameters in capacity curves.

corresponding TPMC compliant structures due to the EC8 stringent requirements on second order effects that are accounted for by means of the stability coefficient . On the contrary, TPMC rigorously considers the second order effects by means of the concept of collapse mechanism equilibrium curve.

Fig. 6. Calibration using MULTICAL software and Multilinear spring in Seismostruct.

fyk = 355 MPa) . The beams of the prototype were designed to withstand vertical loads accounting also for serviceability requirements. The design horizontal forces are determined according to EC8, assuming three values of peak ground acceleration equal to 0.25, 0.35 and 0.45 g for M, H and VH seismic intensity, respectively. For the sake of generality, no specific site is considered. In line with that, the Type 1 elastic spectrum and soil Type C according to Eurocode 8 are assumed with 2% damping. The design spectrum was built by assuming a behaviour factor equal to 6.5. The effects of second order (P-Δ) are accounted for in the design as well as the accidental torsional effects. The assumed limits for interstorey drift ratios was set equal to 1.0% at damage limitation state. Global and local ductility requirements were checked according to EN 1998-1 [21]. The designed cross sections for beams and columns are summarized in Table 2 where also the computed base shear (Vd) is reported. It should be noted that the structures designed by means of TPMC approach are calculated considering the lateral force method, where the first vibration period is computed according to T1 = CH 3/4 (where C is a parameter equal to 0.085 and H is the structure height) formula given by EN 1998-1 [21]. The structures designed with Eurocode compliant approaches are calculated considering the response spectrum modal analysis. For the sake of comparison, the first and the second periods of vibration are reported in Table 7 for all examined structures. Both FD-B and TPMC design process resulted in similar consumption of steel at the same design parameters, while FD-A procedure leads to the larger structural weight. The larger profiles of the columns used for the FD-A set of structures (especially if compared to the FD-B) result from the more demanding design condition in terms of local hierarchy criteria between the column and the ductile element (the friction device). From the comparison between FD-B and TPMC procedures it can be observed that FD-B compliant structures have larger beam sections than the

4. Modelling assumptions To assess the seismic behaviour of structures, both non-linear static and dynamic analyses are performed using SeismoStruct [29] computer program. Force-based (FB) beam-column elements with distributed inelasticity [30,31] are assumed considering 5 integration sections and 150 section fibres subdivided automatically by the SeismoStruct between web and flanges with at least 2 fibres across the thickness. These elements account for distributed inelasticity through integration of material response over the cross section and integration of the section response along the length of the element. The cross-section behaviour is reproduced by means of the fibre approach, assigning a uniaxial stress–strain relationship at each fibre. The stress–strain relationship assumed for the steel modelling is Menegotto and Pinto [32] with a hardening parameter equal to 0.005. The calibration parameters for the transition curve are equal to 18.50 and 0.15, while, the isotropic hardening transition parameters are equal to 0 and 1. The average values of steel yield stress is used, considering an overstrength factor accounting for the random material variability ov equal to 1.25. The numerical integration method is based on the Gauss–Lobatto distribution [33,34], which includes monitoring points at each end of the element. Such feature allows each structural member to be modelled with a single finite element, thus elements do not need to be meshed. The panel zone is assumed full strength and rigid, and it is modelled by rigid elements converging in the node joint (see Fig. 5). Dissipative zones are modelled by means lumped non-linear springs. The moment-rotation behaviour of these springs is modelled by Multilinear (multi_lin) constitutive law [33]. Second order effects in large displacement are accounted in all analyses presented in this paper. In particular, the influence of gravity load resisting part masses is considered through the 148

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Fig. 8. Pushover curves of all examined structures.

leaning column, which is modelled by rigid elements with pinned end sections. The validity of the assumptions made for the hinge model adopted are verified against the experimental results of tests made in the framework of the research project FREEDAM, financially supported by the RFCS of the European Community. The parameters for the calibration of the multilinear rotational spring representing the nonlinear behaviour of the joints with friction devices are provided by the software MULTICAL [34,35] and are reported in Table 3 and Table 4. In particular the first-class parameters related to the strength, stiffness and rotation are reported in Table 3, while the second-class parameters related to the cyclic behaviour are reported in Table 4. The comparison between experimental and numerical response of moment-rotation curves of beam-to-column connections equipped with friction device is depicted in Fig. 6, where it can be noted the satisfactory accuracy of the implemented numerical models. However, it is also important to highlight the limits of the adopted modelling assumptions. Indeed,

since the present study is not devoted to investigating the ultimate response at collapse of the structures, the adopted models have not been set to capture the performance beyond the available ultimate rotation of the friction joint ( ± 0.06 rad) in accordance with the experimental pre-qualification tests carried out by Latour et al. [18]. In the examined range of behaviour, these types of joints do not experience any damage and the column web panel can be assumed as rigid [18]. In addition, since the sliding of the friction device develops at the lower flange of the beam, no interaction with the slab can be activated. It is also worth noting that the interior gravity part is not considered, but their contribution is generally negligible at the significant damage limit state, and it becomes significant for relevant seismic intensity, at which the ultimate response of the structure is assessed [36,37]. Anyway, this task was kept out of the scope of the present study.

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Table 5 Strength parameters and ductility factors for both uniform and 1st mode load patterns. Structures

Load pattern

FD-A 6-3-6 M FD-A 6-3-6 H FD-A 6-3-6 VH

Uniform Uniform Uniform

3.88 2.93 2.85

5.84 4.25 4.55

1.51 1.45 1.60

8.28 10.44 11.19

FD-A 6-3-6 M FD-A 6-3-6 H FD-A 6-3-6 VH

1st Mode 1st Mode 1st Mode

3.59 2.62 2.67

4.84 3.66 3.78

1.35 1.40 1.41

6.75 8.81 8.95

FD-B 6-3-6 M FD-B 6-3-6 H FD-B 6-3-6 VH

Uniform Uniform Uniform

1.42 1.22 1.49

2.81 2.23 2.48

1.98 1.83 1.67

22.52 23.42 23.43

FD-B 6-3-6 M FD-B 6-3-6 H FD-B 6-3-6 VH

1st Mode 1st Mode 1st Mode

1.34 1.06 1.40

2.23 1.82 2.04

1.66 1.71 1.45

15.29 20.78 17.55

TPMC 6-3-6 M TPMC 6-3-6 H TPMC 6-3-6 VH

Uniform Uniform Uniform

1.30 1.12 1.28

1.97 1.71 1.76

1.52 1.52 1.38

10.19 7.52 6.84

TPMC 6-3-6 M TPMC 6-3-6 H TPMC 6-3-6 VH

1st Mode 1st Mode 1st Mode

1.03 1.02 1.01

1.60 1.39 2.15

1.55 1.36 2.13

11.63 8.25 11.69

Structures

Sa (g)

2

1 0.5 0 0.5

1

1.5

2

2.5

FD-A 6-3-6 M FD-A 6-3-6 H FD-A 6-3-6 VH

0.96 0.778 0.66

0.37 0.28 0.24

FD-B 6-3-6 M FD-B 6-3-6 H FD-B 6-3-6 VH

1.07 0.89 0.68

0.41 0.32 0.25

TPMC 6-3-6 M TPMC 6-3-6 H TPMC 6-3-6 VH

1.27 1.24 0.88

0.38 0.37 0.28

Pushover analyses are carried out on the model previously described for each designed structure. They are performed in displacement control considering both geometrical and mechanical nonlinearities under two lateral load patterns, as suggested by EC8: a load distribution corresponding to the fundamental mode shape and a uniform distribution proportional to the seismic masses at each floor. The response parameters monitored by the performed pushover analyses are illustrated in Fig. 7. In particular, u is the lateral load multiplier corresponding to the maximum plastic capacity of the structure, 1 is the lateral load multiplier at the formation of the first plastic hinge; 1 and max are the roof displacements corresponding to the formation of the first plastic hinge and to the first occurrence of an interstorey drift ratio equal to 4%, respectively. Fig. 8 shows the capacity curves for both first mode and uniform lateral load patterns in terms of collapse multiplier (α = V/Vd) vs. displacement (δ) for structures designed according to TPMC and FD-A and FD-B code compliant approaches. It can be observed that all structures exhibit lateral capacity considerably higher than the one assumed in design, especially the FD-A set. This effect is due to the design procedure governed by the requirements to satisfy both interstorey drift limits and to control stability coefficient. In the case of FD-A approach the strength and the stiffness of the beams are not effectively decoupled, since the bending

1.5

0

T2

5.1. Non-linear static analyses results

EC8 i-th record Mean Spec Mean Spec + StDev Mean Spec - StDev

2.5

T1

5. Numerical results

3.5 3

Period of vibration

µ

u/ 1

u

1

Table 7 First and second periods of vibration.

3

T (sec) Fig. 9. Response spectra of selected accelerograms vs. EC8 response spectra for a PGA = 0.35 (H).

Table 6 Selected ground motion records. Earthquake name

Station name

Country

Date

Magnitude [Mw]

PGA [m/s2]

Length [s]

Alkion Montenegro Izmit Izmit Faial L'Aquila Aigion Alkion Umbria-Marche Izmit Izmit Ishakli Olfus Olfus

Xylokastro-O.T.E. Bar-Skupstina Opstine Yarimca (Eri) Usgs Golden Station Kor Horta L'Aquila - V. Aterno - Aquila Park In Aigio-OTE Korinthos-OTE Building Castelnuovo-Assisi Heybeliada-Senatoryum Istanbul-Zeytinburnu Afyon-Bayindirlik ve Iskan Ljosafoss-Hydroelectric Power Selfoss-City Hall

Greece Montenegro Turkey Turkey Portugal Italy Greece Greece Italy Turkey Turkey Turkey Iceland Iceland

24/02/1981 24/05/1979 13/09/1999 13/09/1999 09/07/1998 06/04/2009 15/06/1995 24/02/1981 26/09/1997 17/08/1999 17/08/1999 03/02/2002 29/05/2008 29/05/2008

6.6 6.2 5.8 5.8 6.1 6.3 6.5 6.6 6.0 7.4 7.4 5.8 6.3 6.3

6.69 6.95 4.46 7.07 9.58 3.36 3.22 4.47 7.46 5.29 7.54 6.05 5.63 6.26

17.49 41.87 40.03 55.31 105.30 114.39 124.01 40.01 30.02 47.34 48.20 9.34 93.13 40.03

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Fig. 10. Interstorey Drift Ratio (IDR) for MRFs designed according to FD-A approach.

strength of the friction joints are set equal to the strength of the connected beams, thus also leading to design large cross sections for the columns to satisfy the local hierarchy of resistances. On the contrary, in the structures compliant with FD-B approach the friction joints are designed to match the seismically induced forces, while the required lateral stiffness is guaranteed by the beam inertia, thus allowing to decouple the strength and the stiffness of the beams and leading to smaller overstrength and lower weight of steel respect to FD-A cases. As it can be also observed the response curves of FD-B structures is like those of TPMC structures, which are the cases with the lower overall overstrength and the larger ductility. As a general observation, the ductility demand is lower for structures designed according to Eurocode 8, because the ultimate rotation of the most engaged plastic hinge (i.e. the first activated hinge) is achieved for a roof displacement lower than 1.0 m. In addition, all results in terms of strength and ductility parameters are summarized in Table 5. Through the pushover both u and 1 multipliers are also monitored. The multiplier u is a measure of the overall overstrength of the structure. Conversely, 1 can be considered as an overdesign factor related to aspects of the design procedure, such as differences between actual and nominal material strength, member oversizing due to choices of commercial cross-section and design governed by deformation and/or non-seismic loading [36–38]. In addition, the ratio u/ 1 is a measure of redundancy. This value depends on the structural configuration, formation of the collapse mechanism, redistribution capacity and gravity loading [22]. These parameters are reported in Table 5. The pushover curves obtained under uniform load distribution give the lower values with a mean value of u/ 1 within the range of 1.35–2.13, thus slightly larger than 1.30 recommended by EN1998-1 [21].

Uniform load distribution provides, as expected, on average, higher values. As concerns the overdesign factor 1, it is observed that structures designed according to Eurocode 8 procedure FD-A show the highest overdesign factor with values sometimes reaching the half part of the behaviour factor q used in the design phase (q = 6.5). Conversely, structures designed by TPMC shows the lowest overdesign factor ranging from 1.01 to 1.28. The structures designed according to FD-B approach exhibit pushover response curves ranging between those provided by the structures compliant with TPMC and FD-A approaches. Indeed, the need to satisfy the code drift requirements and prescription on second-order effects compels to oversize the structural members to provide adequate lateral stiffness. Finally, it can be appreciated that the highest overall overstrength is given by structures designed according to FD-A code compliant approach while the lower overall overstrength is shown, on average, by TPMC structures thus exploiting the ductility resources provided by friction connections. Indeed, TPMC structures are not affected by the over-dimensioning influence of parameters accounting for second-order effects in code compliant procedures because they are directly accounted for by the collapse mechanism curve in the framework of a second order rigid plastic analysis. The overall ductility factor (μ) is computed for all structures in order to evaluate the plastic displacement capacity that MRFs can provide until the achievement of an interstorey drift ratio equal to 4%, that is assumed as the limit of performance at CP limit state. The μ factor is defined as:

µ=

max 1

where 151

max

(10) is the roof displacement when an interstorey drift ratio

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Fig. 11. Interstorey Drift Ratio (IDR) for MRFs designed according to FD-B approach.

equal to 4% is achieved into the structure and 1 is the roof displacement associated to the formation of the first plastic hinge (Fig. 7). Table 5 shows the overall ductility factors obtained from both 1st mode and uniform pattern pushovers. As it can be noted the structures exhibit a large range of values of µ .

seismicity level. In particular, for the sake of brevity, in Fig. 9 the matching of the average spectrum and the design one is reported only for the H spectrum, i.e. for a PGA equal to 0.35 g, for soil type C and 2% of damping. The basic data of the selected ground motions are reported in Table 6. The non-linear dynamic analyses are carried out using the same structural model adopted for pushover analyses with the additional assumption related to the viscous damping that was modelled with 2% tangent Rayleigh damping to the first and second modes of vibration, which are reported in Table 7 for the examined structures. The monitored performance indicators for all limit states are the peak and the residual interstorey drift ratios. The results are presented hereinafter with reference to the TPMC, FD-A and FD-B structures. Figs. 10–12 depict the average values of the transient interstorey drift ratio (IDR) demand along the building height for the three limit states. As a general remark, the examined design parameters do not highlight appreciable influence on the IDR demand. However, it is interesting to note that the numerical results show an almost uniform distribution of IDR along the building height, except for the first and last storey. The IDR demand at each limit state is fairly below the performance limits assumed equal to 0.04 rad. It is interesting to note that although the seismic design of the examined structures is influenced by drift limitation (limit assumed was 1.0%), the median values of IDR at DL state are ranging about the limit of 0.75%. At DL state all structures behave elastically, being the yield IDR larger than 1% in most of the cases. Thus, consistently with the results from pushover analyses, a limited inelastic demand can be observed at both SD and CP limit states. In particular, the median IDR for the SD is in the range of

5.2. Non-linear dynamic analyses results Non-linear Dynamic Analyses are also performed to investigate the structural performance for the 3 limit states defined in EN1998-3 [39], namely damage limitation (DL), significant damage (SD) and collapse prevention (CP). EN1998-3 [39] associates a seismic intensity with each limit states and establishes performance limits related to global and local damage. According to EN 1998, the seismic hazard is expressed in terms of the value of the reference peak ground acceleration agR on bedrock (namely ground type A as defined in the code). For each seismic zone agR corresponds to the reference probability of exceedance in 50 years of the seismic action for the no collapse requirement. To this reference ground motion an importance factor γI = 1.0 is assigned and the design ground acceleration agd is expressed as agd = γI agR for ground of type A. The value of the importance factor γI multiplying the reference seismic action to achieve the same probability of exceedance in TL years as in the TLR years for which the reference seismic action allows scaling the peak ground acceleration to get the relevant value for each limit state. In line with that, the factor γI was set equal to 0.59, 1.0 and 1.73 for DL, SD and CP limit state, respectively. A set of 14 natural records selected from RESORCE database [40] and properly scaled to match the design spectrum for the given 152

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Fig. 12. Interstorey Drift Ratio (IDR) for MRFs designed according to TPMC approach.

the cantilever-dominated behaviour of the structure, mainly due to the need to comply with the hierarchy of resistances that impose columns stronger and stiffer than the connected dissipative parts. As a general remark, it can be also observed that the floor accelerations are quite large, exceeding is several cases the acceleration of gravity. This outcome reveals that severe damage can be expected in acceleration-sensitive non-structural components, even though the corresponding structural demand is quite limited without yielding in the primary members.

1–1.5%, thus significantly lower than the limit of 2.5%. The cause for the obtained results lays in the most severe requirements between the drift limitations and stability criteria, as also shown by [20,22–25,38]. The residual interstorey drift ratios (RIDR) were monitored at each limit state because they provide useful data on the damage distribution and on the post-quake reparability of the structures. They were numerically obtained by lengthening the recorded accelerograms of 10 s with values of input acceleration equal to zero. It could be noted that at DL state all structures (Figs. 13–15 ) behave elastically. Hence, the RIDRs are close to zero at DL. The structures designed following the TPMC have smaller RIDRs compared to the FD-B structures for the SD and CP limit states, as depicted in Fig. 13 and Fig. 15. Anyway, the extent of the residual drifts is relatively small, thus allowing easily the repair after the earthquake. The lower values of residual interstorey drift are exhibited by the FD-A set of structures (Fig. 14), which can be easily explained by the larger overdesign of these frames. As it can be also recognized, the larger residual drifts occurred where the larger rotation demand in the friction connections is recognized. In the cases of TPMC and FD-B, this type of performance occurred at the upper levels owing to the cantilever-dominated behaviour of the structure. Peak floor accelerations (PSAs) are generally associated to nonstructural damage. Therefore, PSAs were also monitored to investigate in which terms the examined design procedures can influence the magnification of horizontal accelerations along the building height. Figs. 16–18 show the distribution of the average values of PSA normalized against the acceleration of gravity (g) along the building height per limit state. It is interesting to note that the average PSAs are similar for TPMC and FD-B at DL, SD and CP respectively. In addition, the higher PSA values occur at the top floor. This outcome is ascribable to

6. Conclusions A parametric study based on both nonlinear static and dynamic analyses is presented to investigate the seismic performance of momentresisting frames (MRFs) equipped with friction beam-to-column connections. These structures were designed according to two Eurocode compliant approaches [21], namely FD-A and FD-B and by an alternative approach that is the Theory of Plastic Mechanism Control [27]. The seismic performance-based evaluation was carried out considering three limit states according to EN1998-3 [39], namely damage limitation (DL), significant damage (SD) and collapse prevention (CP). Based on the obtained results the following remarks can be made:

• The obtained results highlight that it is feasible to design MRF • • 153

equipped with friction joints in order to decouple the overall strength and stiffness. In addition, the results show that TPMC procedure allows to design more efficient structures than the examined EC8 procedures, mainly because of the different way the P-Delta effects are accounted for. The FD-A set of structures has the larger sections for the columns as

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Fig. 13. Residual interstorey drift for TPMC 6-3-6 structures.

Fig. 14. Residual interstorey drift for FD-A 6-3-6 structures. 154

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Fig. 15. Residual interstorey drift for FD-B 6-3-6 structures.

Fig. 16. Average peak floor acceleration for TPMC 6-3-6 structures.

•

respect to FD-B frames that use the same profiles of the beams. On the contrary, similar profiles were obtained for the FD-B Eurocode compliant and TPMC design approaches with slightly larger beams for the former and columns for the latter. The slight differences are mainly caused by the serviceability and global stability limitations, which are more restrictive for the Eurocode compliant approach. These results confirm the need for improvements on the way to account for the P-Δ effects in the design based on the EC8. The FD-B, with respect to the TPMC approach, led to structures that possess larger overstrength, especially for the lower seismic hazard

• 155

levels, due to the more significant impact of the deformability and stability checks on the design. Nevertheless, the differences are less pronounced compared to the MRF designed following the FD-A approach that has the larger overstrength, very close to that of conventional MRF designed according to EC8. Therefore, structures equipped with friction devices exhibit satisfactory response with reduction of material consumptions due to the reduction of size of the members. The nonlinear dynamic analyses of the structures enforced the observations previously made. Indeed, the transient interstorey drifts

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Fig. 17. Average peak floor acceleration for FD-A 6-3-6 structures.

Fig. 18. Average peak floor acceleration for FD-B 6-3-6 structures.

• •

for the FD-B and TPCM sets of structures do not exceed the performance limits, with latter exhibiting the lower demand. The RIDR are quite small for all examined structures, with the lower values for the FD-A structures due to the stiffer structures obtained from design. The profiles of peak floor accelerations show that severe damage of the acceleration-sensitive non-structural components is expected for this type of structures.

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