2nd International Engineering Mechanics and Materials Specialty Conference le 2

è Congrès international de mécanique et des matériaux

Ottawa, Ontario

June 14-17, 2011 / 14 au 17 juin 2011

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Behaviour of a Low-Rise Concentrically Braced Frame Building with and without Dissipative Pin Connections

L. Tirca, C. Caprarelli and N. Danila Department of Building, Civil and Environmental Engineering, Concordia University, Montreal, Canada Abstract: This paper presents the concept of elastic response of braced frame members equipped with dissipative brace-to-column connections. In this study the single-pin connection was chosen to transfer the axial force of the brace to the column. The computer simulation of this single-pin connection, incorporated in a one-storey X-braced frame, was carried out using the OpenSees software and the analytical results were validated against the experimental test results. In addition to the European loading protocol, ECCS, considered in the experimental test, the AISC protocol used in the North American practice was employed. A comparative study of a seismic response of one-storey concentrically braced frame structure with and without dissipative connections was investigated through computer modeling. The system was subjected to quasi-static loading only.

1. Introduction

Concentrically braced steel frame (CBF) buildings are widely used in Canada to withstand earthquake loads. The current design philosophy consists of sizing braces to dissipate energy through yielding and/or buckling, while all other braced frame members behave elastically. In this case, when failure or damage occurs in the system, the replacement of braces becomes time consuming and labour costs can be fairly high. In order to devise a more efficient system, the concept of elastic response of braced frame members equipped with dissipative brace-to-column connections is studied. Although this concept is not new, it has not yet been promoted in seismic design. In addition, researchers have identified several brace failure cases due to inadequate connection details. Thus, damages observed from seismic events indicate the need to develop innovative structural systems with high stiffness, ductility and feasibility of repair. The Canadian Design of Steel Structures standard (CAS/S16, 2009) states that for primary framing members forming the seismic-force-resisting system of conventional constructions, the connections can be “designed and detailed such that the governing failure mode is ductile when the member gross section strength does not control the connection design loads”. Accordingly, the European seismic code (Eurocode 8, 2004) states that for concentrically braced frames “the overstrength condition for connections need not apply if the connections are designed to contribute significantly to the energy dissipation capability” of the system. However the statement is not followed by specific design requirements. Thus, the approach of dissipative connections was identified. This paper describes the behaviour of a CBF with single-pin dissipative connections and the rationale behind choosing it to transfer the axial force of the brace to the column member. More specifically, this connection was developed and experimentally tested during the joint European research project, named

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the “Innovations for Earthquake Resistant Design” (INERD), (Plumier et al., 2005; Plumier and Doneux, 2006). It consists of two outer-plates welded or bolted to the flanges of the column member, two inner-plates welded to the brace, and a pin running through the four plates. Under lateral loads, the pin exhibits inelastic deformation and dissipates energy through bending. In this study, the computer modelling of the single-pin connection incorporated in a one-storey X-braced frame, is carried out in the OpenSees software environment and is validated against experimental tests results, obtained from the INERD project. To analyse the behaviour of braced frames equipped with dissipative connections, the OpenSees model was subjected to two quasi-static cyclic loading protocols: the ECCS displacement loading protocol as developed by the aforementioned researchers and the AISC displacement protocol (AISC, 2005). Therefore, in this paper, the OpenSees model of a one-storey concentrically braced frame (CBF) with an X-bracing configuration is developed, the computer model is validated against experimental results, and a comparative study for the same CBF with and without dissipative connections is conducted. 2. Experimental Test Results In the frame of the INERD project, it was concluded that the pin’s length, its cross-sectional shape, the distance between the outer-plates, and the distance between inner-plates strongly influence the connection behaviour, more specifically, its capacity to dissipate energy. A three-dimensional view of a single-pin connection is illustrated in Figure 1. During the experimental program, different types of pin cross-sections, such as round, rectangular and rectangular with rounded corners, have been investigated. As per previous studies (Plumier et al., 2005; Vayas and Thanopoulos, 2005) and in agreement with the experimental results, the behaviour of the pin is similar to the behaviour of a four-point loaded beam. When considering the geometry of the connection as showed In Figure 2: two outer-plates welded or bolted to the column, two inner-plates connected to the brace member and a pin running through the four plates, it is seen that the pin is subjected to constant bending moment and dissipates energy in flexure. From the experimental tests, it was concluded that a rectangular pin shape is able to dissipate a larger amount of energy under small amplitude cycles than a rounded pin which performs better at larger amplitude cycles.

Figure 1: 3-D view of the brace-to-column connection Figure 2: Detail of the single-pin connection

On the other hand, a rounded pin can resist larger forces due to reduced effects of torsion, while a rectangular pin poses a larger moment of inertia. These results guided our decision to select the rectangular cross-section with rounded corners for further investigation. Regarding the distance between the inner-plates, it was concluded that the maximum energy is dissipated when a larger distance between these plates is provided. However, this configuration depends on the size and depth of the column’s cross-section which practically controls the length of the pin; therefore placing the inner-plates at the

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maximum allowable distance will optimize the functionality of the connection. The distance between the inner-plates and the outer-plates, as considered in the selected experiment test, are shown in Fig. 2. The behaviour of braces equipped with single-pin connections in an x-braced configuration is investigated by studying the experimental test results of a full scale braced frame, tested at Politecnico di Milano in Italy (Plumier et al., 2005) shown in Figure 3. As illustrated, the span and height of the frame is 3.4m and 3.0m respectively. The column cross-section is HE 240B and the beam cross-section is HE 200B. For these cross-sections the geometrical properties were obtained from the ARBED property tables. The beam is pin-connected to the column and both braces, made up of HE 160B profiles, are equipped with dissipative single-pin connections at both ends. The pin’s length is 240mm, the distance between the inner-plates is 50mm and the cross-sectional dimensions of the pin are 40 x 60mm. In addition, the thickness of the inner plates is 15mm and the thickness of the outer-plates is 25mm. Experimental test results demonstrated that the single-pin connection is able to dissipate energy under both quasi-static and seismic loads, while maintaining braces in elastic range.

Figure 3: Test set up (according to Plumier et al., 2005)

Thus, in consequence to the introduction of dissipative connections in a braced frame allows braces to behave elastically and avoids the asymmetrical braced frame response. As long as the buckling of braces is prevented, the braced frame behaves symmetrical and in this stage, equal axial forces are developed in both braces while it acts in tension or compression. The input energy focused in the brace-to-column single-pin connections causes the pin to yield first. To maintain the elastic behaviour in the braces it is recommended to design these members to develop 130% of their connection capacity in compression. Braces are allowed to behave only in elastic range and the braced frame deformation is provided by the bending deflection of the pin. Thus, when the brace acts in tension both pins deflect toward the brace and when the brace acts in compression both pins deflect toward the columns. 3. Modelling and Design of Single-Pin Connections The behaviour of the pin member, stated to behave as a four-point loaded beam, is studied using OpenSees, under monotonic and cyclic displacement loading at large inelastic deformations. Experimental test results showed that at the initial stage of loading the pin behaves as a simply supported beam. Then, any increase in loads forced the pin to experience all stages of flexural stresses from the initial yielding of the extreme cross-sectional fibers to the entire plastification of all fibers. During this transitory stage, clamping forces are developed at the pin supports, which in practice is the pin-hole of the outer-plate. Further, at subsequent loading steps, the pin behaves in the plastic range as a beam with fixed supports. In order to validate the design approach of the pin, two methods are employed in

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research. First, the pin is designed as a beam using the OpenSees software, for which the scheme is shown in Figure 4, and second the results are verified with a proposed static method known as the simple beam model given in references (Plumier et al., 2005 and 2006; Vayas and Thanopoulos, 2005). 3.1 The OpenSees beam model The OpenSees beam model, as shown in Figure 4, consists of eight nonlinear beam-column elements and four integration points per element. The section used to describe the beam is made up of 60 fibers, 12 along the depth of the cross-section and 5 along the width of the cross section. The length of the beam is the clear span between the outer-plates, therefore 240mm in the studied case. The material assigned to the beam model is Steel02 labelled Giuffré-Menegotta-Pinto material with the same steel properties as per the experimental test: Fy= 396MPa and Fu=558MPa. In the OpenSees beam model a very small strain hardening value of 0.0005 was considered. In order to represent the behaviour of the pin, the 25 mm thickness outer-plates acting as supports are modeled as rigid links. A calibrated Pinching4 material, explained further on, is used to simulate the deformation of the pin in the outer-plates support. To allow rotation between the beam member and the support (rigid link), a rotational spring formed of Pinching4 material is added at each beam end. If the axial force developed in the brace is P, then this value is equally transferred through the two inner plates (P/2) to the pin.

Figure 4: OpenSees beam model

During the experimental test, the studied pin member was able to deflect 20mm before failure was initiated. To validate the developed OpenSees beam model, the structure shown in Figure 4 was subjected to an incremented displacement loading until the ultimate capacity of the pin was reached. The two symmetrical loading points are marked in the aforementioned figure with P/2. The OpenSees output is discussed in terms of force-displacement and force-bending moment curve shown in Figure 5, respectively Figure 6. In addition the strain history distributed over the cross-sectional depth recorded at the mid-length of the pin is illustrated in Figure 7. It is noted that the yielding strain value is εy = Fy/E = 0.002 and E, the modulus of elasticity, as provided by the experimental test is equal to 206GPa. Thus, from Figure 7, the magnitude of the internal force which yields the extreme fibers of the pin is Py/2 = 108kN and its corresponding displacement and bending moment is δy = 0.35mm (Figure 5) respectively My = 9.5kNm (Figure 6). These values match the theoretical relationship My = WyFy where Wy is the elastic section modulus and the value of static deflection δy. When the whole cross-section was plastified under the applied displacement loading, the strain in the extreme fibers reached 10εy. The magnitude of the internal force applied to create the aforementioned strain shown in Figure 7 is Pp/2 = 163kN and its corresponding displacement is 4mm. From Figure 6, the bending moment developed under the Pp/2 force is Mp = 14.25kNm. Theoretically, this value corresponds to Mp = WpFy, where Wp is the plastic section modulus. Thus, the corresponded applied force at yield, Py, as well as the plastic force value, Pp was identified. Once the internal force is greater than 163kN, the whole pin cross-section exhibits plastic behaviour. The bending moment formed under the loading points is steadily increasing until the plastic moment is reached, while negative bending moment starts to develop in the fixed pin-hole supports. At this stage, as the applied force increases, the pin loses stiffness and the moment is transferred to the support causing the formation of a new hinge before the complete failure of the connection occurs. As a consequence, the moment at the point of application of the loads decreases and a moment at the support

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increases, causing the pin to behave as though it is clamped at its ends. As is shown in Figure 5, the OpenSees beam model is able to identify the phenomenon of clamping after yielding is initiated in the pin. Before failure was initiated, the displacement magnitude reached 20mm (Figure 5) and it matches the experimental results.

Figure 5: OpenSees output; Force - Displacement; Figure 6: OpenSees output; Force – Moment

Figure 7: Strains distribution at the mid-length of the pin

3.2 Simple beam model From both experimental tests and the OpenSees model, the same behavioural pattern was observed and for the preliminary design purpose a theoretical method was devised. In this light, the pin can be represented as a simply supported beam with a span equal to the distance between the outer-plates as shown in Figure 8. The axial tension/compression force developed in the brace is transferred to the pin through two-point loads located at the intersection of the inner-plates and the pin. As previously mentioned, the maximum value of the force Py corresponding to the yielding moment My is Py = 2My/a or Py/2 = My/a, where a = 87.5mm and is the distance between the outer-plate and the centroid of the inner-plate. For the simply supported beam, the static deflection when yielding is experienced by the extreme cross-sectional fibers is given by the following equation: δy = (My/6EI)aL(3 – 4a/L) where EI is the elastic stiffness of the pin. Therefore, for the same rectangular pin 40x60 [mm

2], My = 9.5kNm; Py/2 = 108kN and

δy = 0.35mm. From the mechanism of the simple beam model as shown in Figure 8 and by considering

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the small deflection theory, the deflection at strain hardening is δsh = δI = θa, where θ is the plastic rotation and is given by the following equation: θ = κshlp. The value of curvature corresponding to the strain hardening point κsh = 2εsh/h and the length of the plastic hinge, lp, can be approximated with the height of the pin cross-section. In general, the average strain hardening value, εsh is considered εsh = 10εy which is in agreement with Figure 7. By computing εy = 0.002 it results εsh = 0.02 and δsh = δI = θa = 2 x 0.02 x 87.5mm = 3.5mm ~ 4mm. This value is also correlated with the OpenSees beam model results shown in Figure 5. The values of Pp = PI = 163kN and the afferent approximate displacement value δI = 4mm correspond to the first segment of a tri-linear curve as shown in Figure 9.

Figure 8: Simple beam model and its plastic mechanism

In agreement with the plastic mechanism of the simple beam model, the ultimate load of the beam can be derived from the bending moment diagram shown in Figure 8. According to the plastic beam mechanism (Figure 8), by equating the work of the internal moments and the external forces we obtain (M1 + M2)θ = Puδu/2 or Pu/2 = (M1 +M2)/a. From this last equation and the OpenSees beam model we can express the value of Pu/2 as being approximately equal to the product of plastic modulus Wp and the ultimate strength of steel: Pu/2 = Wpζu/a. It means that the plastic moment of the pin, based on the ultimate stress, is Mu = Wpζu = 20kNm and Pu/2 = 230kN. This value also corresponds to the ultimate load obtained from the OpenSees beam model as is shown in Figure 5.

Figure: 9 Tri-linear curve of the pin response

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The ultimate strain εu corresponding to the ultimate force PII = Pu/2 and deflection δII = δu, is about εu = 0.1, and at this stage the calculation involves the tangent modulus of elasticity, Et. For a strain of 0.1 the corresponding plastic rotation is θ = 0.2 radians and the estimated ultimate plastic deflection is δu = δII = 1.15(0.2a) = 20mm which corresponds to the value given in the OpenSees beam model. Therefore, the second segment characterised by the tangent modulus of elasticity, Et represents the behaviour of the pin in its plastic range. Once the pin begins to exhibit plastic deformations, some clamping occurs at its ends. The plastic mechanism of the pin consists of the formation of two plastic hinges under the point loads and two at its supports. 3.3 Lateral drift In a braced frame structure, the ultimate pin connection deformation influences the development of the interstorey drift of the structure. In conformity with NBCC 2005 and for the ultimate limit state, this value is limited to 2.5%hs where hs is the storey height. Therefore, the pin should be calibrated for the following design criteria: i) strength: the compression capacity of the brace should be equal or larger than 130% the capacity of the pin connection and ii) deformation: the distance between the outer and inner-plates influences the deformation of the pin in bending and as a consequence the lateral deformation of the frame. If we consider a brace equipped with dissipative pin connections at both ends, the diagonal line will elongate with two times the inelastic transverse pin deformation, estimated at 2δII = 2[1.15(0.2a)] = 40mm. The horizontal projection of the deformation of the diagonal line with two pin connections is Δ = 2δII/ cosφ ~ 60mm for φ =41

0 (see Fig. 3). To ensure that the lateral drift is less than 2.5%hs, in this case

(h = 3m, a = 87.5mm), it is recommended that the connection deformation be less than 34.5mm and that “a” be larger than 75mm [a > 34.5/(1.15x0.4); a > 75mm]. 4. OpenSees Modelling of Braced Frames with and without Dissipative Connections A one-storey braced frame with X-bracing configuration equipped with pin connections at each brace’s end, as shown in Figure 3, was tested at Politecnico di Milano (Plumier et al., 2005) under the ECCS displacement protocol and historical ground motions. To emulate the braced frame behaviour with single-pin connections, the OpenSees model was developed and validated with the European experimental test results. The beams and columns were modeled using one beam-with-hinge element per member and the length of the plastic hinge was set to be equal to the depth of the member. Each column cross-section was defined as fiber section with 5 fibers along the flange width and 6 fibers along the depth of the web. The columns were hinged at their base and pinned at the beam column connection. The beam section was also defined as a fiber cross-section with again 5 fibers in the flange and 6 fibers in the web. The beam was connected to the column with a zero-length rotational spring, C1. The x and y displacements of the beam end nodes were slaved to those of the column end nodes. The spring in between the two nodes, was set to work in rotation and exhibited almost no stiffness. This allowed modelling the conventional shear connections found in concentrically braced frames. Each of the four brace segments were modeled with 8 nonlinear beam-columns elements and 4 integration points per element. For the modeling of the X-bracing configuration as shown in Figure 10, the tension brace was defined to work as one element using 16 sub-elements and the compression brace was designed as two half braces connected to the tension brace by very stiff rotational springs, C4. The purpose of choosing the non-linear beam-column element for braces was to ensure spreading of plasticity along the brace length when buckling occurred. The initial camber set to each brace element was Lbrace/800. The cross-section of each brace was defined with 5 fibers along the flange width and 6 fibers along the depth of the web. A section aggregator was used to assign a torsional stiffness to each braces sub-element’s cross-section. In order to connect the braces to the columns, four rigid links were used. These rigid links were defined as elastic beam-columns. The rigid links experience no deformations and therefore no plasticity is formed in them and the linear beam-column element sufficed as an element choice. These rigid links represent the part of the brace, or brace connectors (outer-plates) that are rigidly fastened to the column. The end node of the brace was connected to the end node of its respective rigid link. A zero-length spring was

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inserted between the two nodes. The propertied of these springs C2 and C3 were set for two different situations, one was to model a gusset plate and the other was to model the single-pin connection. In the case of a gusset plate, stiffer properties were set in order to imitate its rigid behaviour. All of the aforementioned members were modelled with the Steel02 Giuffré-Menegotta-Pinto material. This material is represented by a force-deformation relationship and it exhibits some isotropic strain hardening in both tension and compression. The pin connection, represented by zero-length elements deforming in x and y translations, was defined using the Pinching4 material. This material represents a pinched force-deformation response. The pinching that is exhibited is the loss of resistance during unloading of the pin in tension and compression right before reloading begins. In order to calibrate the material, the experimental results described in the reference: Plumier et al., 2005, were used. As shown below in Figure 11, a skeleton curve was built to encompass the total force deformation shape of the experimental testing. The three points defined in the skeleton curve represent the tri-linear curve of the pin stiffness. The first slope would define the elastic stiffness of the pin while the second slope defines the plastic stiffness and the third represents some overstrength of material. The fourth point, which forms a fourth slope, is used to represent the returning or unloading stiffness of the pin connection. The next step would be to define the pinched shape of the curve. This is done by specifying three floating point values in tension and three floating point values in compression. The first floating point value, both in tension and compression is defined by the ratio of the deformation at the point of reloading to the total hysteretic deformation demand. The second floating point value, again in both tension and compression, is the ratio of the force at the point of reloading to the force corresponding to the total hysteretic deformation demand. The third floating point value is a ratio of the strength developed upon unloading to the maximum strength developed in the monotonic loading stage.

Figure 10: OpenSees braced frame model Figure 11: Pinching material calibration The braced frame response was investigated under two displacement loading protocols: ECCS and AISC as shown in Figure 12. The protocols consist of applying 30 incremental amplitude displacement cycles in several steps with a maximum displacement of 2% storey height (60mm) to simulate the experimental test results. However, the distribution of these cycles is different for each of the two considered loading protocols. For example, following AISC protocol, the first 6 displacement cycles have an amplitude equal to yielding displacement of the beam. Then, the displacement amplitudes of each group of 4 identical cycles is: 2.25δy; 3.5δy; 4.75δy; 6.0δy; 7.25δy; 8.5δy and 1 cycle 10.0δy. Related to the ECCS protocol, the 3

rd cycle is 1.0δy and it follows in groups of 3 identical cycles incremented with 1.0δy from 2.0δy to 9.0δy,

and the last cycle is 10.0δy. A comparative response in terms of energy dissipation between experimental (ECCS only) and the OpenSees braced frame model with dissipative connections, loaded with both displacement protocols is shown in Figure 13. As illustrated, the total cumulative dissipated energy computed with the OpenSees

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model (31 cycles) under both loading protocols equates the energy dissipated during the experimental test and, in this respect, the OpenSees model of braced frame with single-pin connections is validated.

Figure 12: Loading protocols Figure 13: Cumulative dissipated energy

In addition, the force – displacement hysteresis loops (Figures 14 and 15) shows a maximum displacement of 60mm and a corresponding force of 800kN. A very good match was obtained between the experimental results (Plumier et al., 2005) and those simulated in OpenSees (Figure 14). Figure 15 shows the difference in behaviour between both loading protocols. The efficiency in terms of energy dissipation of ductile braced frames with dissipative connections versus ductile braced frames with shear connections (CBF) is shown in Figure 16. This result was obtained under a quasi-static analysis when the ECCS loading protocol was considered. In addition, the fundamental period of the CBF is 0.1s, while the period of the CBF with dissipative connection is 0.25s. However, further analytical research is required to emphasize the performance of a CBF with dissipative pin connections.

Figure 14: Force – displacement hysteresis loops: Figure 15: Force – displacement hysteresis loops: OpenSees model versus experimental (ECCS) OpenSees model (AISC) versus experimental (ECCS)

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Figure 16: Comparative response of CBF with and without pin connections: Cumulative energy

5. Conclusions The braced frame system with dissipative connections is an efficient earthquake resistant structure. Its efficiency consists of a reduced structural cost and feasibility of pin replacement after seismic events. The single-pin brace-to-column connections are able to behave in a ductile manner under larger loads and are capable of protecting braces from buckling. These connections are able to dissipate almost the same energy when the brace behaves in tension or compression. The simulated OpenSees model of the braced frame with dissipative single-pin brace-to-column connections was validated against experimental test results. Further research is required to assess the seismic performance of this innovative structural system that can be selected for either a new design or for seismic upgrade. 6. Acknowledgements This research was supported by the Natural Sciences and Engineering Research Council of Canada. The authors acknowledge researchers A. Plumier, C. Castiglioni, I. Vayas & L. Calado for providing test data. 7. References AISC. 2005a. ANSI/AISC 341-05, Seismic Provisions for Structural Steel Buildings. American Institute of

Steel Construction, Chicago, Illinois, USA. CSA. 2009, Design of Steel Structures, CSA-S16-09, Canadian Standards Association, Toronto, Canada. Eurocode 8. 2004, Design of structures for Earthquake Resistance, CEN, EU Standartization Committee, European Convention for Constructional Steelwork (ECCS), 1986. Recommended Testing Procedure for Assessing Behavior of Struct. Steel Elements under Cyclic Loads, ECCS Publ. no.45, Rotterdam, Plumier, A., Castiglioni, C., Vayas, I., Calado, L., 2005, Behaviour of seismic resistant braced frames with innovative dissipative (INERD) connections, EUROSteel Conference, Maastricht 5.2-25 – 5.2-32. Plumier, A., Doneux, C. 2006, Two Innovations for Earthquake Resistant Design, The INERD Project,

Université de Liège, Liège, Belgium. Vayas, I., Thanopoulos, P., 2005, Innovative Dissipative (INERD) Pin Connections for Seismic Resistant

Braced Frames, International Journal of Steel Structures, Vol. 5, pp.453–464.