Seismic Response Reduction of Steel MRF Using SMA Equipped Innovated Low-damage Column Foundation Connection

Connections in MRFs are the most important members and seismic behaviour is affected by function of beam column connections as well as column foundation connections. If the connections are able to provide the required ductility and efficiency against the seismic excitation, the seismic capacity of the MRF performed by these connections will be affected. SMAs have recently been used as a tool to dissipate energy in structures. So far, using of them for column foundation connections has been applied much less. In this paper, SMAs have been introduced and an innovated column foundation connection equipped with SMA has been suggested. Micro and macro behaviour of the connection has been studied and it was applied in sample MRF. Seismic response of the MRF under different earthquakes by equipping the connection with steels/SMAs bars have been studied and compared. Finally, results indicated that MRF with this connection showed proper seismic performance.


Introduction
One of the resistant structures against lateral loads is moment resistant frame (MRF) in which the beams and columns form a moment frame through a fixed support in connections.Connections are the most important members in MRFs.Because of this importance, recently many researchers focused their investigation on beam to column connection and behaviour of MRFs.Experimental results of three Reduced Beam Section Tubular TW-RBS connections under cyclic loading have been conducted [1].The load transfer mechanism and load-bearing capacity of cast steel joints for H-shaped beam to square tube column connection based on the deformation compatibility theory are studied [2].The optimum design of planar frames with semi-rigid connections by standard sections from (AISC) table has been Studied [3].Steel bolted connection and bolts satiation on connection plate for high strength steel connections built up with high strength bolts have been investigated [4].
The performance and ductility capacity of the connections in bending structures are the most crucial factors governing the seismic capacity of these structures.In addition to beam-column connections, the method of connecting the columns to foundations is of great importance in tolerating lateral loads by the MRFs.Different ways of connecting column to foundation brings about different performance of MRFs.Since the connecting method of column to foundation was decided by the designer, one can decide on frame performance selection.This issue can be the basis for offering a controlled connection method, the schematic of which has been shown in Figure 1.If the above mentioned connection has an unlimited rotational stiffness, it will function like a restraining connection; if it lacks a rotational stiffness, it will perform like a hinged connection and in the aforementioned scope, it will show appropriate performance under rotational and seismic loadings if it applies appropriate materials.The dynamic performance of the controlled connection requires high elasticity, great strains toleration, energy dissipation, resilience.Having applied the required plans in the connection, one can improve the stiffness, lateral ductility of steel moment frames (energy dissipation capability arising from seismic stimulations), and quake removing elements (kinds, stiffness, mortality).Thus, dynamic controlled performance of these connections calls for using special materials which are referred to as SMAs.

Introducing the Shape Memory Alloy (SMA) and Its Behavior
Shape memory alloys (SMAs) are exotic materials with magical properties under visible permanent deformations by up to 10% or more.In addition, they entail metallic properties such as strength, stiffness, high expenditure, cast ability and so on [5].In recent decades, a great deal of research in civil engineering and structural engineering have been focused on using intelligent systems in civil development projects with an emphasis on structural response control against vibration and seismic waves.Many innovative tools and systems have been proposed mainly using shape memory alloys based on Nitinol and copper so as to absorb some of the energy loss caused by earthquakes and dampen the earthquake forces aimed at structural retrofitting.Shape memory alloys have two outstanding features including a shape memory and superelastic behavior.The shape memory alloys are capable of bouncing back to a preset shape when heating up over the characteristic temperature of austenite transformation (Af).They are also capable of high strain recovery (about 8%).

Superelastic and Shape memory Effect of SMAs
The stress-strain hysteresis due to mechanical loading-unloading under isothermal conditions is known as superelastic effect.Figure 2. illustrates the conventional shape memory effect on path (1 to 6) and the superelastic effect on path (7 to 13) on temperature-stress-strain diagram [6].In response to superelastic shape memory alloys, the phase transformations lead to nonlinear hysteresis reaction.This has given such materials superior properties in energy dissipation as an excellent option for damper materials.

Austenite and Martensite Phase of SMAs
Because of different crystal structures of austenite and martensite, the SMAs lead to different superelastic responses in various parts, being sensitive to operating temperature.Figure 3. displays the performance of a superelastic wire sample at different temperatures.The classic Nitinol superelastic wires and rods are among SMA applicable in structural connections as adopted in the current paper.Many innovative tools and systems have been proposed mainly using SMAs based on Nitinol and copper so as to absorb some of the energy dissipation caused by earthquakes and damping the earthquake forces aimed at structural retrofitting.The variable stiffness in superelastic behavior can be used to control the force and displacement in three different strain scenarios.At strains lower than 1%, the austenite modulus of elasticity can be employed to limit the strains.In the middle strain levels more than 1% and less than 6%, the reduced modulus can be used to limit the force transferred to the structure, even if there is a large displacement.In large strains more than 6%, the increased modulus in stress induced martensitic phase can be used to control displacement under earthquake induced stress conditions.By the load removal, the low-stress path in reverse transfer leads to the hysteresis energy loss, which is a desirable feature control the vibrations exerted on structures.Furthermore, the superelastic behavior provides the use of austenite elements to self-centering property of SMAs.In fact, they obtain the original shape after deformation caused by stress or temperature.
Shape memory effect (Path 1-6) and superelastic effect (Path 7-13) can be seen.This reversibility effect is a manifestation of solid-phase transformations between a stable austenitic phase, high-temperature phase and low-temperature martensitic phase.

Review of Related Literature on SMAs Application in Steel Structures Connections
The application of SMAs in structure has been long highlighted.Application of SMA in tuned mass dampers to reduce the reaction of wide span steel frames has been studied [7].General applications of SMA in structures have been introduced [8].Generally speaking, after the 1994 Northridge earthquake numerous studies have been done on reinforcing the connections against the earthquake.Quite a few researchers have suggested using systems of SMAs due to their potential in creating a simple ductile self-centering mechanism as well as their unique capability in strain self-centering up to %8 to control the frequency reaction of connections under high earthquake vibrations especially in steel structures.Experimental testing on beam column connections in real scale with/without using Nitinol tendons have been reported [9].The shape memory effect has been tested in steel beam column connection using a Nitinol SMA under semi static loading.This connection includes four NiTi SMA rods which connected the upper and lower beam flanges to column flange and functioned as a primary torque conveyance mechanism [10].Some studies on connection sample with a primary strain using four 3 mm copper-aluminum-beryllium SMA rods have been done.The suggested structure with end plate connection between a structural hollow beam and wide flange steel column.SMA rods in austenite phase were used to reinforce the end plate on the column flange.Experimental testing indicated that beam column connection did not bring about a considerable a superelastic performance, balanced energy dissipation level, and strength drawdown after being exposed to numerous rotations up to %3 of relative displacement [11].Some comparative studies on internal beam column connections, Figure 4. have been studied.In which steel tendons , Nitinol martensite SMAs and superelastic Nitinol SMAs and aluminum, used.Superelastic SMA connections can recover %85 of their original shape after the relative displacement of %5 which made it possible to concentrate all the non-elastic displacement on the tendons while other parts of the connection were in an elastic state [12].The beam column connections in steel frames with two elements containing SMA rod with large diameters, Figure 5. using superelastic SMA elements with the capability of being self-centering and elements of martensite SMA with the capability of high energy dissipation ,encounter with seismic vibrations has been evaluated.For this purpose two large steel structures (3 & 9 stories) were applied and capabilities of optimized connections with SMAs tested.Various testing showed that connections equipped with energy dissipation SMAs turned out to be more effective on the maximum displacement, while superelastic SMAs performed better in controlling residual displacement of structure [13].The seismic performance of a variety of steel structure with various stories with SMA connections with focusing on rotational behavior of connections has been studied [14].Hysteresis performance of T-shaped plate connection and bolts containing SMAs have been tested and found out that they had proper capabilities of selfcentering and energy dissipation [15].The innovative connection containing end plates and bolts of SMAs, continuity plates, flange stiffeners, and web stiffeners has been studied.This connection turned out to have appropriate seismic performance, since its need for energy loss and ductility is provided with the transformation of shape memory bolts and thus the internal plastic hinge is formed, while structural parts mainly remain fixed within the elastic scope [16].This issue was studied in detail.Studying on rotational performance of the end plate connections that are connected using bolts of high strength steel and SMAs. Figure 6.indicates that the SMAs connections showed great selfcentering capability and applicative energy dissipation capacity with vibration absorption of up to %17.5.The common end plate Connection with high strength bolts showed that it offered an appropriate capacity for energy dissipation and ductility, but its rotational displacement was permanent.Moreover, in the SMA bolted connection, all the end plates function as a thick plate and no non-elastic displacement was observed in the plate.When the length and diameter of connection bolt was studied, thin bolts (long bolts with small diameter) showed higher ductility and better hysteresis stability [17].

The Sensitivity of MRF to Column Foundation Connections
The one span and one bay MRF and its geometry and dimensions, shown in Figure 7. was studied.Connection of column foundation is a torsion spring with the rotational stiffness of .The changes in the stiffness of torsional spring from to resulted in hinged and restraining connections respectively.With the fixed concentrated mass the changes in the period of the structure were measured according to the rotational stiffness of the springs, and response of base shear affected by Tabas and Elcentro earthquakes, measured and the results were shown in Figure 7.With respect to the changes of period as a function of connection stiffness (the presence of considerable changes in the period of 0.3 to 0.8 second, changes equal to nearly three times as the former) as well as the shear base spectrum (shown in Figure 10.) and its changes based on connection stiffness from 25 KN to 70 KN (nearly three times) for the earthquake with the damping of %7, the sensitivity of MRF to the column foundation connection method was quite obvious.

The Innovated Column Foundation Connection and Its Micro/Macro Behavior
The schematic view of fixed column foundation connection in Figure 8. is considered.It is assumed that the axial strain and stress caused by axial force in the column is tolerated by the base plate and foundation, where the column can rotate as the moment on the column at the support zone which is tolerated by the couple in the tie rod shown on the Figure 8. Assuming an IPB profile for the column and use of different materials for columns and rods as well as plastic entire cross section of the column, the equivalent diameter of rods can be calculated for replacement with the column to handle the incoming moment according to Equation 2. = Thickness of profiles flanges (IPB).= Thickness of profile web (IPB).
The for a few profiles can be obtained from Table 1.based on IPB and in terms of number of rods needed for different types of steel according to Equation 2, diameters of equivalent rods.

Control of Column Buckling
The free length of the rod before buckling can be calculated in terms of diameter and materials according Euler differential Equation 4. and behavior of compressive and tensile performance of rods can be changed in moment direction.  .By using the Equation 1. and measuring the diameter of the bars 3 , and the modeling of the connection both as micro and macro using OpenSees software (for macro model) and ABAQUS (for micro model) according to Figure 9. and conducting pushover analysis, the comparing of analysis findings for the base shear and the axial force of the bars (as indicated in Figure 10.) showed a similar behavior of both.

Verification of Connection Bars Performance
For verifying the performance of superelastic bars, used the experimental testing results obtained by Desroches, McCormick and Delemont, on the superelastic capability of Nitinol SMA wires and bars [18].The samples tested specifications and the loading protocol and the test results were shown in Figure 12.For modeling, OpenSees was applied and the tested bar and results obtained from OpenSees and experimental test results were compared, and the results of which were shown in Figure 13.

Performing the Test and Numerical Study of the Sample MRF
To performing the test as well as numerical study of steel MRF, one story and one bay steel frame were studied.First MRF was designed and then connection with steel bars designed and finally connection equipped with SMA bars was designed and finally performance of MRF with/without SMA bars was investigated.

Design of MRF Based on Iranian Codes (NIBC and 2800)
The live and dead loads as well as the combination of the loads were determined based on the sixth section of National Iranian Building Code(NIBC) , and its designing was conducted according to Iranian Earthquake Code 2800 (fourth edition, 2015).The geometric specifications, loading considerations, and factors of Code 2800 are shown in figure 14, and the result of frame design was shown in Figure 15.

Modeling of Frame and Connection in OpenSees and Considerations
The general model of the MRF with innovated connection were coded in OpenSees and for conducting the comparison of responses, the acceleration record scale factor ,as shown in Table 2. was measured according to Code 2800.The MRF was analyzed by using of Tabas, Elcentro, Luma , Kobe and Northridge earthquake records Figure 16. in two states: once under the scaled records; and the next time unde non scaled record of earthquakes Luma and Northridge, for comparing the performance.The effect of P-Δ was considered in the analysis and % was determined.Each time the structure was analyzed in two states of column foundation connection: once it included the innovated connection with steel bars; and the second time it was equipped with SMA bars (with the supposed specifications of the bars as shown in Figure 15.and with the selection of diameter and length in trial and error method, and buckling control according to Figure 9.).

Response Results of MRF with/without SMA Bars Connection
The responses obtained are shown in the analysis state under the scaled records in Figures 17 and 18  By analyzing the MRF through direct application of record to structure (non-scaled acceleration record) the records of Loma and Northridge earthquakes, the findings of the frame response were shown in Figure 19.The total result of responses are indicated in Table 3.

Conclusion
 The suggested model for connecting the steel column to foundation enjoyed a real-life performance and offered acceptable results in both micro/macro analyses.
 With respect to the conformity of macro model with the conducted mode, the innovated connection is easily capable of being conducted, and the model in macro state can be used and conducted in the structure.The SMA equipped connection is easily macro modeled in software capable of analyzing SMA elements especially the bars.
 By studying the performance of SMA equipped connection, the self-centering capability arising from SMA elements is quite obvious, so that in none of the effective records on the structure and hysteresis diagrams residuary displacements are observed in the connection at the end of the analysis.This indicates the proper and effective performance of SMA equipped connection in self-centripetal performance.
 With respect to the performance of the connection as well as connection bars (when severe seismic excitations occur only the connection bars are likely to be damaged) and the possibility of fixing or replacing them, one can consider the aforementioned connection as one of the low-damage connections.
 The analysis findings of the frame containing connection equipped with shape memory alloys under scaled record indicate that although it keeps maximum displacement extent for most of the earthquakes used at an authorized scope, it reduces the base shear to a considerable extent.
 In studying analysis findings of the frame under the non-scaled record, although roof level displacement increased in all earthquakes, the effective base shear on the structure reduced considerably in all earthquakes.Moreover, although the increase in response of the lateral displacement and floor drift can apparently be a weak point of the connection, the findings obtained indicate that in comparing the displacement and residuary drifts in roof level, the residuary drifts in the structure containing connection equipped with SMA (in the last cycle and the completion of the free vibration in the structure) enjoyed a lower and (at times) authorized connection and this is due to its selfcentering capability.
 The findings of the present study were considered for a particular bar with the supposed specifications.Since the connection is greatly dependent on the mechanical specifications (tensions in different phases, elasticity module, reversible strain) and engineering specifications (cross section and length), it is expected that better results to be achieved for the frame and connection performance by selecting appropriate mechanical specifications and optimizing the length and cross section for SMA bars.

Figure 1 .
Figure 1.Schematic of different kinds of column foundation connections and its application scope

Figure 3 .
Figure 3. Response of SMA wire under different temperature regimes

Figure 6 .
Figure 6.The connection model containing SMA bolts offered by [17]

Figure 7 .
Figure 7.The general model of frame with spring connection (torsional) and rotational stiffness of K θ and the changes in periods according to the rotational stiffness of K θ and comparing the shear base spectrum for changing of rotational stiff of K θ , under the earthquake records of Tabas and Elcentro

Figure 8 .=
Figure 8.The schematic model of the connection (with 1 and 2 connection bars on both sides of the column) and parameters of connecting , connection bars and column profile drawing Equation 4. (L/D & σ cr ) and taking yield stress limit into account and the elastic modulus , the ratio L/D was obtained according to Figure 9 (a) for different types of steel with different σ y and diameter depending on length, according to Figure 9. (b).

Figure 9 .
(a) ratio for steel , , (b) D and L of steel rods with different        column profile being IPB200, and supposing the usage of two bars on two sides of the connection,

Figure 10 .
Figure 10.The comparison of pushover analysis in both micro and macro5.3.Equipping the Connection with SMAThe steel bars were removed from the connection and superelastic Nitinol SMA bars were used instead.For this purpose the behavior of the superelastic SMA, Figure11.was compared with similar performance in elasticity and compression.

Figure14.Figure 15 .
Figure14.The geometric specifications, loading considerations, and Factors of Code 2800 in the studied MRF

Figure 17 .Figure 18 .
Figure 17.Responses Results of studied MRF contained an innovative connection with/without SMA under the scaled record of earthquake of Loma

Figure 19 .
Figure 19.Responses Results of studied frame contained an innovative connection with/without SMA under un-scaled earthquakes of Luma and Northridge