Location of Semi-Rigid Connection Effect On The Seismic Performance of Steel Frame Structures

In design steel frames, combining semi-rigid and rigid connections can result in better structural performance, particularly in seismic locations. In this study, the effects of semi-rigid beam-to-column connections located on the seismic performance of steel frame structures are investigated. The analysis uses six and twelve-story moment resisting steel frames (MRSF) with rigid, semi-rigid, and dual beam-column connections. These frames are designed according to the Egyptian design codes. Drain-2Dx computer program and seven earthquake ground motions are used in the non-linear dynamic analysis. The rotational stiffness of beam-to-column connections is indicated through the end xity factors with a value equal to 0.6. The performances of these frames are evaluated through the roof drift ratio (RDR), the maximum story drift ratios (SDR), and the maximum column axial compression force (MACF). The results indicated that the quantities of fundamental periods, roof drift ratio, the story drift ratio, and the column axial compression force are related to stiffness, rigidity, and the number of semi-rigid connections in steel frames.


Introduction
Computational mechanical and nonlinear analysis developments are provided structural engineers with general and systematic approaches for modeling and analyzing complex structures. Under both static and dynamic loads, a certain structure may be studied using a numerical simulation model that involves the effect of geometric and material nonlinearities. Computational process and nonlinear analysis developments have provided structural engineers with broad and systematic approaches for modeling and analyzing complex structures. In dynamic loadings, almost any complex model may be investigated using a numerical simulation framework that includes into consideration material and geometric nonlinearities. Despite advances in the analysis, the design procedure has remained unchanged. Most of today's designs are based on conventional trial-and-error methods, from which a structure is designed, examined, and evaluated for agreement with design requirements. If the structure's performance fails to satisfy the speci ed design requirements, the structure is redesigned. The design, analysis, and veri cation process continue until the design has been completed. In general, the nal design isn't optimal in any way. The trial-and-error process is especially ine cient for sophisticated designs that go beyond the designer's intuition and experience.
The rotational stiffness of the beam-to-column connection plays a signi cant effect in the optimal design and response of the structure. The design elements and connections of structures take into account some improvements in the steel frame system. Most design responsibilities in structural engineering are based on the connections in the steel frame being fully rigid. Therefore, the level of exibility of the connection in MRSF is ignored. Consequently, the predictions of structural response are inaccurate. Several kinds of research show that the real beam-to-column connections have some stiffness, in between the cases of fully rigid and ideal pinned cases. The semi-rigid effect on many parameters of the structure such as the frame drift, the moment distribution alongside the beams and columns, and the cost of the design frame structure (Kim and Chen 1996; Barsan and Chiorean 1999). Modern design codes such as Eurocode 3 (EC3) and the AISC-LRFD Speci cation license semi-rigid connection should be considered in the analysis to provide a correct stiffness of the structure and give more accurate results.
The behaviors of semi-rigid connections are investigated by several researchers in recent years. Akbas and Shen (2003) investigated the seismic behavior of steel buildings with combined rigid and semi-rigid frames. 5-and 10-stories SMRF designed according to the LRFD (1995) code. DRAIN-2DX program is used for nonlinear dynamic time history analysis of the two-dimensional models of the frames. The results indicated that in high seismicity regions might be used bolted semi-rigid steel frames with rigid steel MRFs. To simulate the semi-rigid response of the connections, the mathematical representation through the end-xity factor and the modi ed stiffness matrix was used to merge such behavior into structural analysis packages. To con rm the written program, a computer-based analysis was conducted using PROKON software and comparing analysis results with that obtained from the excel spreadsheet. It demonstrates that Excel's results were perfectly exact. Consequently, the procedure of establishing spreadsheets as nite element analysis software for a certain form of frames demonstrates its validity. Kartal et al. (2010) investigated the effects of semi-rigid connection on the steel braced RC frame, steel truss, and prefabricated structural system responses. SEMIFEM program was used in the numerical analysis. The semi-rigid connections were de ned by the rotational spring stiffness-connection ratio of structural members connected. The results indicated that semi-rigid connection degrees are an important factor in structural systems and their effect differ from structure to others. Ghassemieh et al. (2015) investigated how the exibility of the extended end-plate connections in uences the 4-, 8-, and 16-story steel moment frames. ABAQUS program was used for the frame models' nonlinear static pushover and incremental dynamic analyses. The results indicated that by increasing the connection exibility, the strength and stiffness of the frame are reduced. So, the natural period is increased. Feizi et al. (2015) investigated steel frames with three, eight, and fteen stories with rigid, semi-rigid, and dual beam-column connections under seismic force. Drain-2Dx computer program and ve earthquake ground motions are used in the non-linear dynamic analysis. The results indicated that in general, the seismic performances of dual-frame models are better than that of the rigid frame. Bayat and Zahrai (2017) investigated the seismic performance of steel frames with rigid and semi-rigid connections under ve earthquake records. 10, 15, and 20-story steel frames are modeled, designed, and nonlinear analyzing by ETABS software. The analysis results showed that by using semi-rigid connections, the base shear decreases, and smaller sections for beams and columns can use and leading to reduced cost. Nandeesha and Kashinath (2017) investigated the effect of end xity factors of joints on multi-story steel space frames under static loads. The results indicated that the structural behaviors of the frame are depending on the type of connections. Also, the end xity factors from 0.60 to 0.70 are the best range for beam design. Van  computer program is used non-linear static and incremental dynamic analysis. The results indicated that the lateral stiffness and strength will be calculated to be lower with the more accurate rigidity modeled of the structural frame.
Most studies are based on semi-rigid connections in the design and analysis of the frame structures. Although the semi-rigid connections are the source of the structure ductility level but increased the story drifts. Some research started to use the combined rigid and semi-rigid connection (dual frame) to take advantage of the two types of connections and to reduce the cost of structure design (Dubina et al. 2000). This paper focuses on a study the effects of semi-rigid beam-to-column connections location on the performance of steel frame structures under nonlinear dynamic analysis. The analysis uses six and twelve-story moment resisting steel frames with rigid, semi-rigid, and combined con gurations. These frames are designed according to the ECP-201 and ECP-205. The rotational stiffness of beam-to-column connections is indicated through the end xity factors with a factor equal to 0.6. The performances of the MRSF's with strong columns and weak beams are evaluated with different locations of semi-rigid connections. Drain -2Dx software is used in the nonlinear dynamic analysis of all frame cases (Parkash et al. 1993). The performance for these frames is incident through the roof drift ratio (RDR), the maximum story drift ratios (SDR), and maximum axial compression forces (MACF).

Connections Classi cation
Fully and partly restrained steel construction types are described by the American Institute of steel construction and load and resistance factor design speci cation ((AISC 2002, LRFD). This speci cation requires that the connections of the partly restrained type constructions be considered exible (semi-rigid) and, this exibility be evaluated by a reasonable analysis or experimental works. On the other hand, three types of connection: rigid; semi-rigid, and normally pinned are proposed in Eurocode 3 (EN 1993-1-1). Hence, there is not any information about semi-rigid connections in Egyptian steel design speci cations (ECP-205). Nader and Astaneh (1992) indicated that rigid connections are capable of developing a moment at the beam end equal to or greater than 90% of the xed end moment, while pinned connections can only develop a moment at the beam end less than 20% of the xed end beam. Chen et al. (1996) indicated that the end-xity factor is the conventional characteristic to calculate the end restraints beam. This factor de nes the rotation of the beam end divided by the joint rotation of the beam and the connection due to a unit end-moment. The equation to calculate the end-xity factor, "r" is de ned as: Where "R" is spring stiffness connection and "EI/L" is exure stiffness of the xed elements. This factor, r, is equal to 0 and 1 for pinned and xed connections, respectively. Therefore, the end-xity factor lies between 0 and 1 for a semi-rigid connection. The end-xity factor value of 0.6 is used in this study.

Structure Modeling
Six and twelve-story moment resisting steel frames are designed according to the ECP-201 and ECP-205.
These frames can be considered demonstrative of the low and medium-rise moment-resisting steel frames. The two frames have the same symmetrical square oor plan of 3 by 3 bays shows that in Fig. 1. Each bay is 8.00 m wide. Also, Fig. 1  The design internal forces are calculated by considering the critical combination of gravity and seismic or wind loading. The frame is designed with a reduction factor of 7. The modulus of elasticity of steel is considered 200 GPa and the strain hardening ratio is 0.01. The frames were designed to make sure that the columns are stronger than the beams. The frames required for design purposes are analyzed using the SAP-2000 computer program. Wide ange sections were used in the design of columns and beams elements. Detailed descriptions of the column and beam cross-sections are summarized in Table 1 for the six and twelve-story frames.
A mathematical model of the structure is introduced as a two-dimensional (2D) assemblage of non-linear elements. The model structures with semi-rigid connections are applied in the Drain-2dx computer program with considering the P-Δ effect (Prakash and Powell 1992). The Drain-2dx computer program is a general-purpose computer program for static and dynamic analysis of inelastic plane structures. The mass of the structure model is taken at the end nodes of element structures. The ber beam-column element type (15) is used to model the beam-column elements. The ber element model is based on dividing the element into segments and bers to capture the inelasticity alongside of the member. The connection behavior is represented by a rotational spring element type (4) that is introduced at the beamcolumn interface. The inelastic stiffness of the connections is depending on the connection end-xity factor. The partial end-xity factor is the relationship between the moment and the rotation at the connection, or the equivalent rotational spring constant. The effects of the rigid, semi-rigid, and combined con gurations under dynamic analysis have been studied on the overall behavior of the steel structures. In Table 2, seven earthquake ground motions from the PEER network with different frequency contents and motion measurement are used in the analysis. 3.0% viscous damping ratio for the rst and second natural modes of the frame structures was used in the analysis.

The fundamental period
The fundamental periods calculated by the Drain-2dx computer software to all MRSFs cases are shown in Table 3. It is seen that for all of the frame cases, as the stiffness of the beam-column connections decreases, the fundamental period increases, which, can be inferred as a decrease in the overall stiffness of the structures. The frame with a fully rigid connection (F1) has the lowest fundamental period and the frame with all semi-rigid connections (F2) has the greatest period in both 6-and 12-story MRSFs. By increasing the number of semi-rigid connections, the fundamental periods of frames are increased. In both 6-and 12-story MRSFs, the periods of dual frames (F3 and F5) cases are similar. Also, the periods of dual frames (F4 and F6) cases are similar. From the Table 3, by increasing the heights of the frame, the fundamental periods increased. So, the frame height, position, and a number of the semi-rigid connections are affected on the fundamental periods. These results are per those obtained by Feizi, et al. (2015).  Table 4. It is observed that as the number of semirigid connections increases, the RDR of the frame increase. Therefore, on average, the 6F2 frame case is the greatest RDR value in all frame cases. Moreover, the results in a Table 4 indicate that, on average, the RDR of the fully rigid frame (6F1) is close to the value in the hybrid frames (6F4, and 6F6) cases. Additionally, a little difference among the predictions of the RDR in the other two hybrid frames (6F3, and 6F5) cases. The Values of RDR for the 12-story MRSFs of all frame cases are summarized in Table 5. It is observed that as the number of semi-rigid connections increases, the RDR of the frame increase. Therefore, on average, the 12F2 frame case is the greatest RDR value in all frame cases. Moreover, the results in a Table 5 indicate that, on average, the RDR of the fully rigid frame (12F1) is close to the value in the hybrid frames (12F4, 12F5, and 12F6) cases.
The results presented in Tables 4-5 show that the RDR in the rigid frame is close to the hybrid frames (F4 and F6) cases. Moreover, the RDR of the frame increased as the number of semi-rigid connections and the frame height increased.

Maximum story drift ratio
The maximum story drift ratio (SDR) is a signi cant seismic demand measure that may be extracted from a load of information obtained from incremental dynamic analysis results to estimate the potential damage to structural elements (Gupta and Krawinkler 1999). The use of semi-rigid connections in steel frames increases the story drift ratio, especially in the higher stories (Dubina et al. 2000). Fig. 4 shows the variations of the mean of maximum SDRs along with the height of the 6-story frame for all frame cases.
Furthermore, the maximum SDRs of the earthquake loading cases occur in the third story of all frame cases. The maximum SDRs that occur in the frame with all connections are semi-rigid (6F2) compared to all frame cases. Moreover, the results in Fig. 4 indicate that a little difference among the predictions of the SDR in a fully rigid frame (6F1) with hybrid frames (6F4, and 6F6) cases. Additionally, a little difference among the predictions of the SDR in the other two hybrid frames (6F3, and 6F5) cases. The results presented in Figs. [4][5] show that by increasing the number of semi-rigid connections in steel frames, the story drifts ratio is increased. These results are per those obtained by Feizi, et al. (2015).
Column Maximum Axial-Compression-Forces Fig. 6 shows the variations mean MACFs in columns along with the height of the 6-story frame for all frame cases. The results shown in the gure indicate that the mean column MACFs occur in the rst story of all frame cases under the earthquake loading cases. Moreover, the mean column MACFs of hybrid frames cases are greater than that in a fully rigid frame (6F1). Additionally, a little difference among the predictions of the MACFs in the two-hybrid frames (6F3 and 6F4) cases.

Conclusions
In this study, six and twelve-story moment resisting steel frames with rigid, semi-rigid, and dual beamcolumn connections were designed according to the Egyptian design codes. Drain-2Dx computer program and seven earthquake ground motions are used in the non-linear dynamic analysis. The rotational stiffness of beam-to-column connections is indicated through the end xity factors with a value equal to 0.6. The following conclusions based on the results obtained are drawn.
The fundamental periods of the frame structures are increased by increasing the frame height and increasing the number of semi-rigid connections.
The roof drift ratio in the rigid frame is close to the frames with combined rigid and semi-rigid connections frame (F4 and F6) cases.
Moreover, the roof drift ratio of the frame increased as the number of semi-rigid connections and the frame height increased.
The by increasing the number of semi-rigid connections in steel frames, the story drifts ratio and the maximum column MACFs are increased.
In design steel frames, combining semi-rigid and rigid connections can result in better structural performance, particularly in seismic locations.