1 Introduction

The seismic behaviour of dry-assembled precast frame structures has been thoroughly investigated in the last two decades, identifying those technological issues which deserve special detailing to achieve satisfactory seismic performance. The value of the behaviour factor to be used in a force-based design of precast concrete frames has been validated in Biondini and Toniolo (2009) on the basis of probabilistic analyses and experimental tests. Capacity design criteria for multi-storey precast frames have been proposed in Biondini et al. (2010). More recently, alternative displacement-based design procedures have been developed in Belleri (2017) and Dal Lago and Molina (2018). The large deformability and ductility capacities of precast structures having correct connection and member details have been confirmed by the results of several experimental tests conducted on full-scale structural prototypes (Priestley et al. 1999; Fischinger et al. 2008; Biondini and Toniolo 2009; Biondini et al. 2012; Negro et al. 2013; Brunesi et al. 2015; Dal Lago et al. 2017a, c, 2018d; Negro and Lamperti Tornaghi 2017; Toniolo and Dal Lago 2017). The structural behaviour of the main mechanical connections has been also studied by means of tests on individual devices or structural sub-assemblies. Column-foundation mechanical connections have been tested by Saisi and Toniolo (1999), Metelli et al. (2011a), Dal Lago et al. (2016), Orlando and Piscitelli (2018), and Tullini and Minghini (2016). Beam-column connections have been tested by Vintzeleou and Tassios (1987), Tsoukantas and Tassios (1989), Dei Poli et al. (1992), Psycharis and Mouzakis (2012a, b), Magliulo et al. (2015), Zoubek et al. (2015), Yuksel et al. (2015), and Muciaccia et al. (2017). Roof-to-beam connections have been tested by Belleri et al. (2014) and Dal Lago et al. (2017d). Panel connections have been tested by Metelli et al. (2011b), Belleri et al. (2016), Zoubek et al. (2016, 2018), Dal Lago et al. (2017a, b, 2018a, b), Yuksel et al. (2017), Dal Lago and Lamperti Tornaghi (2018), and Psycharis et al. (2018).

The field observations after recent earthquakes reported by Toniolo and Colombo (2012), Bournas et al. (2013b), Magliulo et al. (2014b), Belleri et al. (2015a), and Savoia et al. (2017) underline the problem of displacement compatibility between precast frames and cladding panels, whose seismic interaction has been investigated by Biondini et al. (2013a), Magliulo et al. (2014a), Scotta et al. (2015) and Belleri et al. (2018). Retrofit solutions have been proposed by Valente (2013), Belleri et al. (2015b, 2017), Magliulo et al. (2017), Sorace and Terenzi (2017), Dal Lago et al. (2018a), and Pollini et al. (2018). The seismic fragility of precast structures, addressed in literature by Kramar et al. (2010), Titi and Biondini (2014), Casotto et al. (2015), Belleri et al. (2015b), Babič and Dolšek (2016), Buratti et al. (2017), Demartino et al. (2017), Palanci et al. (2017), Titi et al. (2018), and Ercolino et al. (2018), may be strongly influenced by the connection system of the cladding panels. Moreover, a cladding connection system which involves in-plane interaction of the panels with the structure leads to highly non-uniform distribution of stiffness among the various frames of the buildings, acting in parallel, with the external cladded frames being much stiffer than the internal frames. In this way, the horizontal actions tend to redistribute towards the cladding panels, loading the diaphragm with higher stresses.

The diaphragm behaviour of precast roofing systems with structural concrete topping has been addressed in literature by Fleischman and Farrow (2001, 2003) and Fleischman et al. (2005a, b), among others. The diaphragm behaviour of dry-assembled precast decks, which cannot rely on a structural topping to stiffen the diaphragm, has been investigated by Ferrara and Toniolo (2008), Biondini et al. (2013b), Belletti et al. (2015), and Dal Lago and Ferrara (2016) with reference to specific dry-assembled structural arrangements. Experimental results on the diaphragm behaviour of full-scale dry-assembled precast prototypes subjected to seismic excitation have been reported by Biondini and Toniolo (2009), Schoettler et al. (2009), and Bournas et al. (2013a), showing that also dry-assembled diaphragms can provide relevant stiffness and strength, mainly relying on the mechanical connections of the deck elements.

The present paper investigates the seismic behaviour of precast buildings having various layouts of the diaphragm and of the cladding panel connection system through linear and non-linear dynamic analyses. In particular, three different types of connection are investigated: (1) roof-to-beam, (2) floor-to-floor, and (3) panel-to-panel connections. Different stiffness conditions of the deck are investigated by changing the connection types (1) and (2) from low stiffness with flexible roof-to-beam connections on unconnected floor elements to high stiffness with roof-to-beam conditions on mutually connected roof elements. Different stiffness distributions are investigated by changing the connections type (3), from uniform distribution without mutual panel-to-panel connections to highly non-uniform distribution with stiff panel-to-panel connections.

The effectiveness of dissipative panel and/or deck connections in improving the seismic behaviour of the overall structure by reducing its drift under controlled forces is also assessed by means of non-linear dynamic analysis.

2 Case study

A precast structure with layout and dimensions typical of Southern European industrial buildings is considered as a case study. It is a single-storey two-bay precast frame, made of three lines of columns spaced by 15 m. The columns are 7 m tall with a square section 0.6 × 0.6 m. The beams have rectangular section 0.6 × 0.8 m and span of 10 m. The roof elements are 15 m long and have TT section 0.6 m deep and 2.5 m wide. The distributed mass of structural and non-structural dead load is 320 kg/m2. The peripheral vertical cladding panels have dimensions 2.50 × 8.75 m with effective thickness of 0.12 m leading to a mass of 300 kg/m2. The cladding panels are placed along the two long sides of the building and parallel to the beams. All elements are made of concrete C45/55 (fck = 45 MPa). Figure 1 shows the geometry of the building and the scheme of the connections. Three roof-to-roof connections are located at the quarters of span of the elements. Three panel-to-panel connections are placed at the quarters of the distance between bottom and top hinges of each panel. The internal frame is identified by the alignment B, while the external frames are identified by the alignments A and C.

Fig. 1
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Case study building (dimensions in mm)

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Figure 2 shows a view of the 3D structural model of the building developed using the code Straus 7 (G + D Computing 2010). Columns and beams are modelled with beam elements. The columns are clamped to the foundation. Each beam end is connected to a column with a couple of dowels aligned in the direction orthogonal to the beam element. This connection is idealised with a hinge in the main bending plane of the beam and a monolithic joint in the other planes. The top of the columns and the centroid of the beams are connected by translational coupling links (Fig. 3). Roof elements and cladding panels are modelled with shell elements. Each roof-to-beam connection is modelled with a translational spring with very high translational stiffness in both the vertical (axis z in Fig. 3a) and horizontal direction orthogonal to roof elements (axis y in Fig. 3a). The stiffness associated with the direction parallel to the roof elements (axis x in Fig. 3a), which is among the investigated connections, is varied through the analyses. The distance between the centroid of the beam and the corner node of the rib plate element is covered by a translational coupling link (Fig. 3). The cladding panels are connected to the foundation beams at the bottom and to the peripheral beams at the top with hinged connections. Thus, the central nodes at the base of the panels are restrained, while the top connection is modelled with a spring with high stiffness restraining the relative displacements between the beam and the panel nodes. The mass is distributed according to the material density of the structural elements (2500 kg/m3). The additional mass associated with waterproofing and finishes on top of the roof elements is considered negligible.

Fig. 2
figure 2

3D view of the structural model

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Fig. 3
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Structural model: a scheme of elements and connections; b 3D solid view

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3 Natural frequencies and vibration modes

The natural frequencies and the associated vibration modes of the case study building are investigated by combining different stiffness values of the considered connections. These values have been chosen considering the order of magnitude of the elastic stiffness of mechanical connections tested within the European research projects SAFECAST (Dal Lago et al. 2016, 2017c, d, 2018d) and SAFECLADDING (Biondini et al. 2013a; Dal Lago et al. 2017a, b, 2018a, b, c; Toniolo and Dal Lago 2017). The following values of elastic stiffness are considered for beam-roof connections kb−r (kN/m):

  • kb−r = 103, order of magnitude for elastic stiffness of thin angle connections after activation (see Dal Lago et al. 2017d);

  • kb−r = 104, order of magnitude for elastic stiffness of thick angle connections after activation (see Dal Lago et al. 2017d) or for dowel connections with small diameter;

  • kb−r = 105, order of magnitude for elastic stiffness for dowel connections with large diameter (see Psycharis and Mouzakis 2012b);

  • kb−r = 1010, order of magnitude for rigid connections, such as welded connections.

The following values are considered for both roof-to-roof connections kr−r and panel-to-panel connections kp−p (kN/m):

  • kr−r = kp−p = 0, no connections;

  • kr−r = kp−p = 104, order of magnitude of the elastic stiffness of bolted Multiple Slit Devices (MSDs—see Dal Lago et al. 2018b);

  • kr−r = kp−p = 105, order of magnitude of the elastic stiffness of friction-based devices (FBDs—see Dal Lago et al. 2017a);

  • kr−r = kp−p = 106, order of magnitude for elastic stiffness of welded rectangular metallic plates (Schultz et al. 1994);

  • kr−r = kp−p = 1010, order of magnitude for rigid connections, such as welded bar connections.

Combining the elastic stiffness of the three orders of connections, 4 × 5 × 5 = 100 analyses have been performed to identify natural frequencies and vibration modes. Following Eurocode 8 (EN 1998-1:2004), half of the cross-sectional elastic stiffness is attributed to the column elements to account for cracking. Figure 4 shows the trends of natural frequencies and corresponding participation factors for different values of roof-to-beams connection stiffness kr−b. The diagrams are shown for increasing values of panel-to-panel stiffness kp−p and for different values of the roof-to-roof stiffness kr−r. Figures 5, 6 and 7 show the deformed shape associated with the main vibration modes of the structure.

Fig. 4
figure 4

Natural frequency and participation factor of the first vibration mode of the buildings versus the roof-to-roof connection stiffness kr−r for different values of the panel connection stiffness kp−p = 0, 104, 105, 106, 1010 and different values of the roof-to-beam stiffness kr−b: a, bkr−b = 103; c, dkr−b = 104; e, fkr−b = 105; g, hkr−b = 1010 (kN/m)

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Fig. 5
figure 5

First vibration mode of the building: akp−p = 0, kr−r = 0, kr−b = 104; bkp−p = 104, kr−r = 105, kr−b = 104 (kN/m)

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Fig. 6
figure 6

Building with stiffness of the connections kp−p = 104, kr−r = 0, and kr−b = 104 (kN/m): a first vibration mode; b second vibration mode

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Fig. 7
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Building with stiffness of the connections kp−p = 104, kr−r = 1010, and kr−b = 103 kN/m: a first vibration mode; b second vibration mode

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The condition kp−p = 0 is associated with a natural frequency of about 0.96 Hz, regardless the values of kr−b and kr−r (Fig. 4a, c, e, g). In this case, the structure is quite flexible and characterised by a good diaphragm action even with low stiffness of the deck connections. The corresponding vibration mode shows the in-phase displacement of internal and external frames without in-plane distortions (see Fig. 5a). This effect is due to the uniform distribution of mass and stiffness among frames. Moreover, a constant participation factor of about 90% is achieved for the first vibration mode (Fig. 4b, d, f, h).

For increasing values of kp−p, progressive stiffening of external frames occurs. The diaphragm becomes more stressed as the stiffness uniformity among the frames decreases. For low values of kr−b (Fig. 4a), the increase of stiffness for other connections modifies the natural frequency, which grows from 0.96 to 1.8 Hz for values of kr−r up to 105 kN/m, remaining constant for higher values. Figure 5b shows that the deformed shape of the building associated with the first vibration mode does not change from the case of no panel-to-panel and roof-to-roof connections to the case of panel-to-panel connections with rigid roof-to-roof connections, indicating a good diaphragm behaviour. Figure 6 shows the two most significant vibration modes of the structure without roof-to-roof connections, with the first mode associated with the deformation of the central frame, and the second mode related to phase opposition deformations of the external and central frames. In both cases, an important floor distortion occurs.

The diaphragm effect is limited when using flexible roof-to-beam connections, also in case of very stiff roof-to-roof connections. Figure 7 shows the main vibration modes related to this configuration. The deck is subjected to local torsional rotations in each building span and, consequently, an important distortion occurs despite the global base torsional moment is null. The difference between the deformed shapes associated with the two main vibration modes consists in the activation of the relative vertical sliding of the panels. The peculiar deformed configuration depicted in Fig. 7 is not desirable, since the rigid rotation of portions of the deck involves the concentration of displacement demand in the edge roof-to-beam connections, which could lead to loss of support and out-of-plane relative movements of the panels.

The values of the participation factor of the first natural vibration mode for low kr−b gradually decrease with the increase of kp−p. The participating mass progressively increases for the stiffer vibration modes associated with the external frames, which indicates an inadequate diaphragm action. For higher values of kr−b, the stiffening effect of the external frames is more effectively transmitted to the internal frame, with a dynamic behaviour associated primarily with the first mode. For the stiffer combinations of connections, the frequency associated with the first vibration mode attains a maximum value of 13.8 Hz (Fig. 4g).

For increasing values of kr−b and kr−r, a gradual increase of the participation factor of the first vibration mode occurs. This indicates a better collaboration between the frames and a good diaphragm effect. In general, as shown in Fig. 4b, d, f, h, the trend associated with natural frequency for increasing values of kr−r is characterised by three branches: an almost constant trend for both low and high stiffness values, and an almost linear branch for intermediate values. The limits of the pseudo-linear transition phase depend on the uniformity of stiffness among frames (kp−p) and on the effectiveness of the roof-to-beam connections.

4 Non-linear dynamic analysis

A set of non-linear dynamic analyses has been performed to investigate the structural response of the building under seismic action, considering three different types of roof-to-roof connections (none, MSD, and rigid), three types of roof-to-beam connections (angle, dowel, and rigid) and three types of panel-to-panel connections (none, FBD and rigid), for a total of 3 × 3 × 3 = 27 analyses.

The non-linear behaviour of both columns and selected connections is taken into account into the numerical model. Each column is reinforced considering a geometric reinforcement ratio ρ = 1%, with 12 Φ20 mm steel bars made of steel grade B450C (fyk = 450 MPa) placed as shown in Fig. 8, with a concrete cover of 30 mm. The steel bars and the concrete core are considered effectively confined by closed stirrups. Sargin model (Sargin and Handa 1969) is used for unconfined concrete. For the confined core, this model is properly modified after peak with a stress plateau up to the ultimate strain evaluated according to the Model Code 2010 (Fib 2010) in order to take into account the confining effects of the transversal reinforcement. A linear-parabolic stress–strain relationship is assumed for the steel reinforcement. A smeared plasticity model based on the cross-sectional non-linear moment–curvature relationship is used for the beam elements based on a Takeda hysteretic behaviour considering an unloading stiffness parameter equal to 0.4 (Takeda et al. 1970). The non-linear moment–curvature diagrams of the column cross-section are determined on the base of geometry, mechanical properties and acting axial load in seismic combination (Fig. 9).

Fig. 8
figure 8

Column cross-section (dimensions in mm)

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Fig. 9
figure 9

Non-linear moment–curvature diagrams of columns

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The monotonic load–displacement relationships of the connections (FBDs, MSDs, dowels and angles) are shown in Fig. 10. These load–displacement diagrams are calibrated based on the test results collected in Dal Lago et al. (2017a, 2018b), Psycharis and Mouzakis (2012b) and Dal Lago et al. (2017c), respectively. An elastic-plateau monotonic curve is used for both FBDs and dowels. An elastic-hardening monotonic stress–strain relationship is used for both MSDs and angles. A classic kinematic hardening hysteretic behaviour is assumed for FBDs and MSDs. A Takeda hysteretic behaviour is assumed for dowels and angles considering an unloading stiffness parameter equal to 0.4 (Takeda et al. 1970).

Fig. 10
figure 10

Non-linear load–displacement diagrams of connections

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The analyses have been performed under the accelerogram shown in Fig. 11. This accelerogram is achieved by analytically enriching in frequency the original signal recorded in Tolmezzo (Italy) during the 1976 earthquake to make it compatible with the elastic response spectrum of Eurocode 8 for soil type B (EN 1998-1:2004). The accelerogram has been scaled to a peak ground acceleration PGA = 0.32 g. This PGA value has been selected to make the results comparable with the ones obtained in a previous numerical investigation performed on a similar precast building, in which the diaphragm has been considered as perfectly rigid (Biondini et al. 2013a).

Fig. 11
figure 11

Modified Tolmezzo accelerogram: a accelerogram (PGA = 0.32 g); b elastic response spectrum compared with the model of Eurocode 8 for soil type B

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Table 1 resumes the main seismic performance indicators of the structure for all cases studied. The structure without panel-to-panel connections is characterised by uniform distributions of mass and stiffness among the frames and flexible behaviour with maximum displacements of about 190 mm and similar actions on the columns. Relative displacements between internal and external frames are small also in the configuration without roof-to-roof connections. The effectiveness of the diaphragm increases if angle connections are replaced by stiffer connections.

Table 1 Summary of results of the non-linear dynamic analyses: frame system
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If rigid or dissipative panel-to-panel connections are placed and there are no roof-to-roof connections, the structural drift can be reduced by means of rigid roof-to-beam connections. The structural drift can be significantly reduced by adding floor-to-floor MSDs, whose effectiveness is reduced if used in combination with angle roof-to-beam connections.

The base shear of the external frame, including also the contribution transmitted by the cladding panels through foundations, is much higher if panel-to-panel connections are considered. However, it is limited by the shear threshold when dissipative panel-to-panel connections are used.

Table 2 provides the main seismic performance indicators of the connections. If panel-to-panel connections are not used, all the combinations of connections lead to limited actions and good diaphragm behaviour. Elsewise, the diaphragm connections are considerably stressed. In particular, without roof-to-roof connections and with dowels between roof and beam, the actions in the dowels lead to yielding and involve sliding of some centimetres of the roof elements, which can cause problems of displacement compatibility.

Table 2 Summary of results of the non-linear dynamic analyses: connections
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The introduction of roof-to-roof connections significantly improves the diaphragm effect, reducing the relative displacements with respect to the previous case to about 30%. MSDs activate within the plastic range when angle of dowel roof-to-beam connections are used, thresholding the stress pattern of the deck. The loads increase up to three times if rigid floor-to-floor connections (e.g. welded) are used.

It is worth noting that replacing rigid connections with FBDs allows a reduction of the acting load to 40%. Dissipative connections activate in all cases considered. Angle roof-to-beam connections also activate in all cases.

Figure 12 shows the top displacement time histories of the building without panel-to-panel connections. Central and external frames have different responses in case of flexible connections, even if the vibrations are in phase and the differences are limited. It can also be observed that the introduction of MSD roof-to-roof connections leads to a good diaphragm effect also in case of flexible angle roof-to-beam connections.

Fig. 12
figure 12

Top displacement time histories of the building with no panel-to-panel connections: a angle roof-to-beam and no roof-to-roof connections; b dowel roof-to-beam and no roof-to-roof connections; c rigid roof-to-beam and no roof-to-roof connections; d angle roof-to-beam and roof-to-roof MSD connections

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The base shear versus top displacement diagram, including the contribution of the horizontal action at the base of the cladding panels, is very similar for both cases of effective and deformable diaphragm, as shown in Fig. 13. The base shear of the external frames shows peaks related to the vibration of the stiff panels.

Fig. 13
figure 13

Base shear versus top displacement hysteretic diagrams of the building with no panel-to-panel and no roof-to-roof connections: a angle roof-to-beam connections; b rigid roof-to-beam connections

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Figure 14 shows the top displacement time histories of the building with FBDs interposed between panels and without roof-to-roof connections. If angle roof-to-beam connections are used, the external frames do not influence the vibration of the central frame (no diaphragm effect). In this configuration, the introduction of dissipative devices between the panels does not avoid the structure to damage.

Fig. 14
figure 14

Top displacement time histories of the building with FBD panel-to-panel and no roof-to-roof connections: a angle roof-to-beam connections; b dowel roof-to-beam connections; c rigid roof-to-beam connections

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Dowel connections improve the collaboration among the frames. In this case, the maximum displacement is reduced to about 50%. This allows to avoid yielding at the column bases, even if a significant distortion of the deck occurs.

The top displacement time histories of both external and central frames are in phase and close, even if with non-negligible differences, only when rigid connections are used.

Figure 15 compares the base shear versus top displacement diagrams for the cases of angle and rigid roof-to-beam connections. It is noted that the excellent damping potential of the FBDs is exploited only if rigid deck connections are used. In this case, the relative displacement of the frames is strongly reduced.

Fig. 15
figure 15

Shear versus top displacement diagrams of the building with FBD panel-to-panel and no roof-to-roof connections: a angle roof-to-beam connections; b rigid roof-to-beam connections

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As shown in Fig. 16, the use of MSDs in between the roof elements significantly reduces the maximum top displacement of the structure also if angle roof-to-beam connections are used. Moreover, stiffer connections improve more significantly the seismic performance of the overall building.

Fig. 16
figure 16

Top displacement time histories of the building with FBD panel-to-panel and MSD roof-to-roof connections: a angle roof-to-beam connections; b dowel roof-to-beam connections; c rigid roof-to-beam connections

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The maximum top displacement attained with MSDs is limited to less than 14 mm for all the studied cases (Table 2). These values are consistent with the characteristics of this kind of device and are associated with the maximum exploitation of its dissipative capacity.

The maximum displacements of the central frame are further reduced with the use of rigid roof-to-roof connections, such as welds. In this case, as shown in Fig. 17, the diaphragm effect is satisfactory not only if using rigid roof-to-beam connections, but also if using dowels. It is worth noting that welded roof-to-beam connections are difficult to be made and unfrequently used in practice, since they could alter the simply supported static scheme of roof elements under gravity loads by creating a clamped roof-to-beam joint which draws high moments into connections and columns.

Fig. 17
figure 17

Top displacement time histories of the building with stiff roof-to-roof connections: a FBD panel-to-panel and angle roof-to-beam connections; b FBD panel-to-panel and dowel roof-to-beam connections; c FBD panel-to-panel and stiff roof-to-beam connections; d stiff panel-to-panel and stiff roof-to-beam connections

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5 Conclusions

The problem of the effectiveness of the diaphragm action in single-storey precast concrete frame structures has been investigated. The role of both deck connections (roof-to-roof and roof-to-beam) and cladding panel connections (panel-to-panel) on the seismic response of this type of structures has been investigated by means of both linear and non-linear dynamic analyses.

The results show that both deck and cladding panel connections play a fundamental role on the seismic performance of dry-assembled precast frame structures. Based on these results, the following conclusions can be drawn:

  • Uniform distribution of mass and stiffness in precast frame structures can be achieved through the adoption of a statically determined cladding panel connection system;

  • Statically undetermined cladding connection systems (dissipative or integrated) lead to relevant differences in terms of stiffness between external and internal frames;

  • Uniform distribution of mass and stiffness among the different frames leads to a uniform flexible seismic response of the structure, with both flexible and stiff diaphragm;

  • With flexible diaphragm, non-uniform distributions of mass and stiffness cause relevant deck distortion and out-of-phase response of the single frames, without relevant reduction of the seismic drift;

  • With stiff diaphragm, non-uniform distributions of mass and stiffness lead to large actions on the elements and connections of both deck and cladding panels;

  • Stiff diaphragms may be obtained with stiff roof-to-beam connections, or with flexible roof-to-beam and stiff roof-to-roof connections;

  • The forces in the connections can be limited with dissipative cladding connection systems without jeopardising the substantial improvement of the seismic performance of the structure, with relevant limitation of the drift;

  • The efficiency of dissipative cladding connection systems is reduced in structures with flexible diaphragm.

Furthermore, the use of low cost dissipative devices between the cladding panels and between the roof elements can remarkably improve the seismic performance of the structure with relevant reduction of drift under forces that are limited by the yield or slip threshold of the devices. The use of MSDs in the deck as floor-to-floor dissipative connections allows to fully exploit the benefits of the installation of panel-to-panel FBDs, protecting the roof elements from excessive rise of forces. This technological solution may allow precast frame structures to be fully operating even after the occurrence of earthquakes with seismic intensity associated with the ultimate limit state design.

The results presented in this paper have been obtained considering a single accelerogram and a given panel aspect ratio. Further studies are necessary to investigate the influence of the panel geometry and the role of uncertainties associated with both the seismic action and structural response by means of a probabilistic analysis.