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March 5, 2018 | Author: Muhammad Sultan | Category: Column, Concrete, Light Rail, Stress (Mechanics), Strength Of Materials
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Case Study

Design and Construction of Steel–Concrete Hybrid Piers for a Light Rail Transit System in Palembang, Indonesia

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Wiryanto Dewobroto1; Iswandi Imran2; Effendi Johan3; and Sri Yanto4 Abstract: The light rail transit (LRT) project located in Palembang, Indonesia, is being built to address traffic congestion and support the success of the 2018 Asian Games, a multinational sports event. The project consists of constructing a railroad network along with several stations located at an elevation aboveground, supported by reinforced concrete (RC) piers. A problem arises when it is not possible to cast concrete for the cantilevers on some piers located on the roads with a high frequency of traffic congestion. One solution to this problem is to replace the RC piers with hybrid piers. The hybrid piers are modifications of the RC piers in which steel frames replace the concrete for the cantilevers. The use of these hybrid piers opens up the possibility of offsite fabrication of the steel cantilevers so that the erection can still take place during offpeak hours and take less time. The use of these hybrid piers is relatively new for construction projects in Indonesia; the Palembang LRT project is the first project to have used this method. For this reason, it is important to understand this method’s design principles and effects on the construction process, especially about the connections between the steel and concrete structures. The hybrid piers are better than the RC piers, because the hybrid piers eliminate the need for concrete casting, a process that often causes obstructions to traffic flow. This method has the potential to be an alternative to pier construction for regions with high traffic volumes and high risk of traffic congestion. DOI: 10.1061/ (ASCE)SC.1943-5576.0000318. © 2017 American Society of Civil Engineers. Author keywords: Steel-reinforced concrete; Connection system; Hybrid piers; RC piers; Alternative method of construction.

Introduction Infrastructure projects in Indonesia often use the reinforced concrete (RC) construction method. This situation is understandable, because materials for concrete construction are available more abundantly than are materials for steel construction, which are often import commodities. RC construction also happens to be the chosen method for the Palembang light rail transit (LRT) project, which is a project to build a mass transportation system that is taking place in Palembang, a city in the province of South Sumatra, Indonesia. The LRT will connect the Sultan Mahmud Badarudin II International Airport and Jakabaring Sports City. The LRT system was selected because it is considered to be a solution for traffic congestion in the city, which is predicted to become worse if not anticipated in advance, not to mention when the Asian Games, a multinational sports event, will be held there in 2018. The LRT project is expected to be an alternative transportation system that will reduce the frequency of traffic congestion in Palembang. For this reason, the LRT route will be parallel in the design to the current main traffic flows. To preserve the current road 1 Senior Lecturer, Dept. of Civil Engineering, Univ. Pelita Harapan, M. H. Thamrin 1100 Blvd., Lippo Karawaci, Tangerang 15811, Indonesia (corresponding author). ORCID: http://orcid.org/0000-0002-9773-0581. E-mail: [email protected] 2 Professor and Principal Engineer, Pusat Rekayasa Industri ITB, X-PAU Building, 3rd Floor, ITB, Ganesha 10, Bandung 40132, Indonesia. 3 Vice Director, PT. Perentjana Djaja Consultancy Services, Wisma Pede, 3–4th Floor, M. T. Haryono Kav 17, Jakarta 12810, Indonesia. 4 Vice Director, PT. Megah Bangun Baja Semesta, Jagad Building 2nd Floor, RP Soeroso 42A, Jakarta 10350, Indonesia. Note. This manuscript was submitted on November 2, 2016; approved on November 30, 2016; published online on February 14, 2017. Discussion period open until July 14, 2017; separate discussions must be submitted for individual papers. This paper is part of the Practice Periodical on Structural Design and Construction, © ASCE, ISSN 1084-0680.

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capacity, the railroad network and the stations will be built at an elevation aboveground supported by RC piers. This condition means that the RC pier structures will be the main structural system determining the bearing capacity of the whole LRT construction (Fig. 1).

Structural Piers to Support the LRT System The railroad network and stations (Fig. 1) consist of a simple beam system resting on RC piers built along the LRT route. A problem arises when it is not possible to cast concrete for the cantilevers on some piers located on roads that have a high frequency of traffic congestion. Using this method would cause an almost total blockage of traffic flow. One solution to this problem is to replace the RC piers [Fig. 2(a)] with hybrid piers [Fig. 2(b)]. The hybrid pier is a pier structure in which a steel structure and a RC structure are combined. This system is a good option, because it promises a final structure that is justified economically with an efficient construction process (Morino 1998; Roeder 1998). In the LRT project, the hybrid pier design is a modification of previous RC piers, that is, the RC part of the cantilever [Fig. 2(a)] is substituted with a steel frame [Fig. 2(b)]. The current RC pier design will still be used for the columns and foundations. It is apparent that a reconfiguration of the reinforcement of the columns used for the hybrid piers is needed to accommodate the steel frames. By using this hybrid pier system, the steel frames can be fabricated offsite, and the installation process can take place during off-peak hours and take less time.

Effects of the Hybrid System on the Pier Failure Mode The railroad network and the stations will be built at an elevation aboveground simply supported by pier structures or bridge columns. Depending on site conditions, some RC pier structures will still be built, and the hybrid pier structures (Fig. 2) will be constructed on the roads that have a high frequency of traffic

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congestion. The pier structures will be the main LRT system structures against vertical (gravitational) and lateral (seismic) loads. The horizontal structural system (beam configuration that supports the gravity load of the railroad and stations) is considered to not contribute to the strength of the lateral structural system or no effect in resisting the seismic load. All lateral load (seismic) will affect the pier structure, which works as a cantilever system with the foundation as the fixed support. In this condition, the pier structure’s failure mode is similar to that of ordinary bridge columns. The bottom part of the pier will experience inelasticity, whereas the rest of the pier will still be elastic (Priestley et al. 2007; Qinghua et al. 2008). The failure mode pattern on the bottom part of the pier (Priestley et al. 2007; Qinghua et al. 2008) will also apply to both the RC piers and the hybrid piers. The critical part, the part of the pier that will

Fig. 1. Typical view of a Palembang LRT station (courtesy of PT. Perentjana Djaja Consultancy Services)

experience inelasticity, is the bottom part near the foundation (cantilever support). The critical part is far from the steel frame, which is the additional part of the system. What this means is that the modification of RC piers to become hybrid piers does not affect the ability of those piers to resist seismic loads. The part that will experience inelasticity stays the same on both the RC piers and the hybrid piers and is not modified at all. This condition also results in only the gravitational or dead loads influencing the designs of the hybrid pier structures. Thus, the designs for these hybrid piers will not need any special analysis on seismic loads. Therefore, the effects of seismic loads on the structure should be anticipated from the beginning at the time when designing the RC pier structures.

Design of Steel Construction for the Hybrid Piers With the hybrid piers, a steel cantilever [Fig. 2(b)] replaces the concrete cantilever that is on the RC piers [Fig. 2(a)]. For design purposes, the steel frames are modeled separately and considered to be isolated structures. The supports are at Point A (pinned support) and Point B (roller support) for horizontal support. Then, there will be two gravitational load cases, full-side loading and half-side loading (Fig. 3). The load that will cause maximum force on the steel frames is full-side loading. Using analysis and design according to the latest Indonesian design regulation, Standar Nasional Indonesia (SNI) 1729:2015 (Standar Nasional Indonesia 2015; Dewobroto 2016), in which the AISC (2010) regulation was adopted, it is possible to calculate the dimensional profile for the steel frames (Fig. 4). For purposes of the construction process, there are three different segments of the steel frames. The joints fabricated in the workshop make use of the welded joints, which have the same design strength as that assigned for the steel profile. The erection process in the field makes use of heavy hex bolts based on the slip-critical capacity,

Fig. 2. Structural piers for LRT system support: (a) RC pier; (b) hybrid pier

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Fig. 3. Model of the hybrid pier steel cantilever with design loads

Fig. 4. Hybrid pier steel cantilever: (a) top view; (b) elevation

which also have the same design strength as that assigned for the steel profile.

Mechanism for Distribution of Force from Steel to Concrete Division of the Steel Frame into Segments and the Erection Process The steel frames with continuous main elements (Fig. 3) are in the hybrid pier columns [Fig. 5(c)]. The best way to join the steel to the concrete is by using the embedded system. For construction purposes, there are three different segments for the steel frames [Fig. 5(b)]. The embedding process of the middle segments happens during the concrete-placement process [Fig. 5(a)]. Erection of the two other segments takes place after the concrete has enough strength [Fig. 5(b)]. More important is that the erection process will take place during off-peak hours. Internal Design Distributions of Force from Steel to Concrete To determine whether the joint with the steel-embedded system can work well, it is necessary to predict and evaluate the mechanisms of internal force reaction transfer. Accordingly, it was necessary to © ASCE

initially discuss performance of the concrete columns where the joints were embedded. The hybrid pier system is basically a modification of the RC pier system, which was designed well in advance. Therefore, the details of the RC pier structure must have fulfilled all design criteria for both permanent (gravitational) and temporary (seismic) load conditions. The RC pier structure system was designed to support the floor-beam system, which is generally made of RC. It certainly leads to a greater load condition than the hybrid pier system, the structural system of which consists mainly of steel. Because of the magnitude of the column load, which is directly proportional to the borne load of the floor, the design loads of the hybrid pier system will certainly be smaller than the design loads of the RC pier system. Therefore, if the hybrid pier columns retain the details of the previous RC piers, their bearing capacity would certainly be sufficient. In relation to the joint-placement-to-column performance against earthquakes, under seismic load conditions, column performance can be considered a single-column system, which is fixed at the bottom part or as a cantilevered structure system. Therefore, a critical part of the column with an inelastic (plastic hinge) condition at the time of an earthquake is at the bottom part of the column, near its support (Priestley et al. 2007; Qinghua et al. 2008). Because the joint location is placed in the midpoint of the column height, which is far from the predicted critical part, to encounter an inelastic condition, the joint placement is not considered to deteriorate the performance of an existing column. By taking into account the two points just

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Fig. 5. Hybrid pier construction stages in the Palembang LRT project: (a) concrete placement; (b) steel erection; (c) final configuration

Fig. 6. Distributions of design forces from the steel to the concrete: (a) full-side loading; (b) half-side loading

discussed, joint evaluation is carried out only for permanent or gravity load conditions, which is an evaluation of the magnitude of the ongoing stress concentration. Case 1: Full-Side Loading Applying this design load will cause a maximum internal force on the cantilever element and will determine what steel profile to use (Fig. 3). Although this design load will cause a maximum internal force due to the symmetrical configuration of the structure, the internal forces will balance each other out. Because of this condition, the reaction force that transfers to the concrete will be of only a simple bearing stress type. A free-body diagram of the support due to the full-side loading is provided as Fig. 6(a). This case is the most basic mechanism for force distribution from the steel structure to the concrete structure. The determining factors are surface area and compressive strength of the concrete. Case 2: Half-Side Loading This case is a scenario in which the loading is on only one side of the cantilever, a loading scenario that rarely happens (Fig. 3). This © ASCE

scenario is an assumption that is necessary for anticipating some incidental scenarios. Because this is a public infrastructure, there has to be a better, more guaranteed safety factor. This scenario might happen when only one side of the cantilever is functioning and the other side is considered a failure (e.g., in the case of severe damage as a result of bomb blasts by terrorists). In this condition, all reaction forces on the cantilever will be distributed to the column/pier, and they become a vertical compression force and simple couple forces in the horizontal direction. A free-body diagram of the support due to the half-side loading is provided as Fig. 6(b). Distribution Mechanism of Dead Load (Full-Side Loading) Fig. 6(a) shows the distributions of the forces on the steel frames due to the maximum design loads (full-side loading) around the supports. The distribution of the forces from the steel to the concrete takes place near the support plate on the bottom, a square surface that has the same size as the width dimension of the horizontal and vertical steel sections in the middle. Both of the steel sections use

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the same HB 350 profile, so the area of the square is A1 = 350  350 mm (Fig. 7). The concrete that fills the steel profile acts as the stiffener so that there will not be any danger of local buckling. Evaluations of the force distribution from the steel to the concrete are assumed to be on a concrete pedestal surface with an area of A2 beneath the steel base-plate surface (A1). The surface dimension follows J8 of AISC (2010) or 10.14 of ACI (2011). According to the regulation, the force distribution will cover an area of the base side of a truncated square pyramid (A2) with the base-plate surface (A1) as the top side and the horizontal/vertical ratio of the sides as 2:1. A2 is also defined by the support placement configuration. This condition is necessary for calculating the overlapping effect. The dimensions of the areas A1 and A2 for determining the mechanism of force distribution from the steel to the concrete are available in Figs. 7(a and b), respectively. The concrete bearing capacity follows the formula f cPp, where f c = 0.65, the steel base-plate surface is A1 = 350  350 = 122,500 mm2, and the concrete pedestal evaluation surface is A2 = 650  650 = 422,500 mm2. According to AISC (2010), confinement can be taken to aid the bearing capacity because A2 > A1. For a concrete compressive strength of fc = 30 MPa rffiffiffiffiffi A2 0 Pp ¼ 0:85fc A1 (1)  1:7fc0 A1 A1 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffi A2 422;500 ¼ 1:579 ! Pp ¼ 1:579fc0 A1 0:85 ¼ 0:85 122;500 A1 Pp ¼ 1:579  30  122;500 

1 ’ 5;803 kN; then f c Pn 1;000

¼ 3;772 kN The frame reaction force from Fig. 6(a) is Pu = 1,797 kN. Thus, the bearing capacity ratio is R ¼ ðPu = f c Pn Þ ¼ ð1;797= 3;772Þ ¼ 0:476 n 1 ! okay.

Under a maximum loading condition (full-side loading), the steel cantilever system can withstand the load without interacting with or affecting the concrete pier. The tensile and compressive forces on the steel cantilever will balance each other out and not affect the concrete. For this reason, there is no need to worry about the additional deformation caused by the creep that often happens on a RC cantilever in the long term. Distribution Mechanism of the Incidental Load (Half-Side Loading) The steel cantilever construction for the Palembang LRT station pier structures is vital, because it will provide services to the public. As a consequence, safety is the highest priority for this project. One way to guarantee safety is to ensure that if any local failure occurs, it should not trigger failure of the whole system structure. Previous evaluations of the structures were against the internal force distributions, as shown in Fig. 6(a), for the purpose of anticipating maximum load scenarios. The evaluations were necessary to determine whether the force distributions from the steel to the concrete would cause any overstress. Although it was a maximum load scenario, the load configuration and the geometry of the structure were those of an ideal condition. Interactions between the steel and the concrete were not much, except for the vertical compressive reaction (Fig. 7). The evaluation result was quite satisfactory. Aside from the ideal (full-side loading) condition, it is also necessary to evaluate the structure against incidental conditions. In this case, an unbalanced situation would occur because only one of the cantilever arms is functioning. The causes can vary and are unexpected (e.g., a bomb explosion). Consideration of this condition is necessary, because a number of incidents that were previously considered impossible have happened. For modeling purposes, the design loads make use of half-side loading configurations (Fig. 3). The incidental (half-side loading) condition did not affect the design of the steel frames. The biggest effect it has is on the forcedistribution mechanism between the steel and the concrete, where

Fig. 7. Steel base-plate (A1) and concrete pedestal evaluation (A2) surfaces: (a) plan; (b) section a-a

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there are couple forces causing a moment on the concrete column. The reaction forces a distribution caused by the incidental loading [Fig. 6(b)]. The transferred vertical reaction force has a smaller value compared to that in the full-side loading condition. In that case, it will not cause a problem. In transferring the unbalanced forces in the steel to the concrete pier, it is necessary to add some stud anchors or shear studs with a diameter of 16 mm and a minimum tensile strength (Fu) of 450 MPa. The nominal shear strength of one shear stud on the concrete according to AISC (2010) is as follows: qffiffiffiffiffiffiffiffi Qn ¼ 0:5Asa fc0 Ec  Rg Rp Asa Fu (2) where Rg = 1.00; Rp = 0.75; and using concrete with compressive strength fc0 = 30 MPa, the minimum shear strength is Qn ¼ Qmin ¼ 67:8 kN. With the reaction force distribution shown in Fig. 6(b), the number of shear studs needed for each steel pier is n ¼ Tu =Qn ¼ 2; 101=67:8  31. However, some engineers in the project still have some doubts about this number. The reasons for those doubts are that the engineers do not have enough experiences in the hybrid pier system, the frame structure is that of a cantilever beam, which is considered a determinate structure (no moment redistribution under ultimate conditions), and the engineers consider the joint to be the weakest link. For assurance, the joint (between the steel and the concrete) will have the same design strength as the steel profile. For an HB 350 steel profile with yield strength Fy of 250 MPa, the maximum tensile strength is 4,376 kN. The number of shear studs necessary for said tensile strength would be approximately 65 studs, or twice the previously calculated number. The installation configuration of the shear studs is shown in Fig. 8.

[Figs. 4 and 5(b)]. The ASTM A325 (ASTM 2014) heavy hex bolt joint method is used to combine the segments, designated as slipcritical joints with the same design strengths as those of the steel profile. The joints are designated slip-critical to anticipate the occurrence of dynamic loads that result from LRT train movements. Improper welding can cause a distortion as a result of uncontrolled heat. The middle part uses a whole horizontal steel profile in the early stages to avoid this problem [Fig. 9(a)]. After all the welding on the middle part, the process continues by cutting the profile into three segments and installing a previously prepared bolt joint. This method ensures that the rest of the segment-installation process takes place exactly on the bolt joints to avoid any problems with the erection process. The work is continued to finish the segments as planned. The results are shown in Fig. 9(b). Dividing the steel frames into three segments also makes the hot-dip galvanizing process easier. This protection against rust acts as the minimal routine maintenance for the future. The process is reasonable in cost for the long term. It is necessary because those in charge of projects often consider routine maintenance to not be important or even ignore it, and there is little (not enough) or almost no budget allocation for the process. Column Concrete Placement The hybrid pier’s concrete-placement schedule has to be coordinated with the steel-frame fabrication schedule, because it is important to embed one of the steel segments in the concrete (Fig. 10). The to-be-embedded steel segment does not have any support during the concrete-placement process. For this reason, it is

Construction Method Fabrication at the Workshop Welding was the chosen method because of its simplicity and efficiency. For quality control, full construction of the steel structures took place at PT. Megah Bangun Baja Semesta workshop in Tangerang, Indonesia. The workshop is far from the project site (not even on the same island). The welding is intended to result in the same design strength as that of the steel profile, mostly using butt welding or full-penetration welding. For transportation to and erection at the site, there are three segments of the steel frames

Fig. 8. Shear studs as the mechanical method for transferring forces from steel to concrete

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Fig. 9. Steel frame fabrication at the workshop: (a) early stage, in which the middle part was whole during welding; (b) division of the profile into segments

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Fig. 10. Concrete placement over the steel frames (courtesy of PT. Perentjana Djaja Consultancy Services): (a) placement of the steel frames; (b) concrete-placement process; (c) after the removal of formwork

necessary to prepare some temporary support so that the frame does not move during the process. This support rests on the dried concrete column beneath it. To avoid uncontrolled lateral movements, the tremie method is applied during concrete placement. The tremie concrete-placement method refers to any placement by gravity feed from a hopper through a vertical pipe, starting from the bottom surface in the midpoint of the pier and then moving to the upper surface. For this method, a skilled and experienced field operator is required.

certain limits, the use of the hybrid pier is more costly than the original plan. The erection process for the steel cantilevers takes place in the nighttime when the traffic volume is low. The process finishes before the daytime. The process itself is quick; thus, the erection of the hybrid piers can be completed quickly. The site conditions, with high traffic volume under the hybrid piers that are under construction, are shown in Fig. 12. It is obvious that the RC system, which requires formwork, is not possible without causing traffic congestion.

Erection Stage of the Steel Cantilever Frames The main reason for using hybrid piers is that they are needed for the erection of the steel cantilever frames. The duration is short, and it can take place during off-peak hours. For this reason, the hybrid piers are suitable only for construction on a road with high traffic volumes. Off-peak hours in this LRT project is during the nighttime. One mobile crane with a capacity of 45 t is enough to erect the steel cantilever frames (Fig. 11). Hybrid Piers of the Palembang LRT The change of the pier system, from RC to hybrid, was triggered by the onset of potential traffic problems at the project site, which cannot be tolerated by the local authority. It was agreed that the hybrid pier system, as proposed later by the contractor, would not cause any potential problems. Because the change was made when the project was up and running, it was necessary to redesign and obtain a new tender to select a new subcontractor because there was some unplanned steel-structure work. Therefore, in the decision-making process, the cost differences between the two systems were not a major consideration on condition that the overall cost would still be within the range of the existing budget plan. As expected, within © ASCE

Conclusion For the RC pier built in the middle of the road with high traffic volumes, the implementation of the concrete placement in its cantilever part will cause intolerable traffic disruptions. As a consequence, the RC pier system, specifically intended for that location will not be applicable. It is necessary to replace the RC piers with the hybrid piers, a construction with both steel and concrete. With hybrid piers, the cantilever makes use of steel frames that can be fabricated offsite and quickly constructed when the traffic volumes are low, or during the night time. The parts of the RC piers that become the hybrid piers are not parts of the critical parts that will experience inelasticity during earthquakes. For this reason, gravitational loading governs the design of the hybrid piers. Evaluations of the structures against seismic loads are not necessary, because the critical parts are still the same as those in the previous evaluations of the RC piers. The steel-frame cantilever configurations of the hybrid piers that are symmetrical and continuous are the ideal structural conditions under which to join the concrete parts. As a result, the embedded system is enough to join the steel parts to the concrete parts. On the basis of this system, it is necessary to evaluate the force-distribution

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Fig. 11. Steel frame erection at night (courtesy of PT. Perentjana Djaja Consultancy Services): (a) lifting; (b) joining process; (c) finishing off the other side

Fig. 12. Site conditions for hybrid pier construction in Palembang, Indonesia (courtesy of PT. Perentjana Djaja Consultancy Services)

mechanism against the two extreme loading conditions. One condition will be to anticipate maximum loading (full-side loading), and the other one will be to anticipate incidental loading (half-side loading). In the full-side loading case, the condition under which maximum dead loads take place, the pier’s bearing capacity is more than enough. In the half-side loading case, for the incidental loading condition, the analyses of the force distribution from the steel to the concrete show that shear connectors or shear studs are necessary. The hybrid pier’s concrete-placement schedule has to be in coordination with the steel-frame fabrication schedule, because it is important to embed one of the steel segments in the concrete for the embedded system to work. At the time of writing, there have been several hybrid pier systems installed successfully. The traffic conditions, which are very congested underneath during the day, do not get disrupted often during construction process. It could happen because the installations of the steel-frame cantilever systems are conducted on the night when traffic is relatively settled down. It also means that the hybrid pier system successfully anticipates problems caused by use of the © ASCE

conventional RC pier system. Thus, the hybrid pier system is an effective alternative to the construction of a pier structure at locations with high traffic volumes, such as the ones commonly found in Palembang.

Acknowledgments The authors thank Totok Andi Prasetyo for assistance with the special data that have greatly improved this paper. Also, the authors extend their gratitude to Edi Prayitno, who prepared the calculation reports and structural drawings.

References ACI (American Concrete Institute). (2011). “Building code requirements for reinforced concrete and commentary.” ACI 318-11/ACI 318R-11, Farmington Hills, MI. AISC. (2010). “Specification for structural steel buildings.” ANSI/AISC 360-10, Chicago.

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Qinghua, A., Dongsheng, W. A. N. G., Hongnan, L. I., and Zhiguo, S. U. N. (2008). “Evaluation of the seismic performance of reinforced concrete bridge columns based on plastic hinge model.” Proc., 14th World Conf. on Earthquake Engineering, China Earthquake Administration Ministry of Housing and Urban-Rural Development, Beijing. Roeder, C. W. (1998). “Overview of hybrid systems united for seismic states.” Eng. Struct., 20(4–6), 355–363. Standar Nasional Indonesia (SNI). (2015). “Spesifikasi untuk bangunan gedung baja structural.” Standar Nasional Indonesia 1729:2015, Badan Standardisasi Nasional, Jakarta, Indonesia.

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ASTM. (2014). “Standard specification for structural bolts, steel, heat treated, 120/105 ksi minimum tensile strength (withdrawn 2016).” A325-14, West Conshohocken, PA. Dewobroto, W. (2016). “Steel structure—Behavior, analysis & design.” AISC 2010, 2nd Ed., Jurusan Teknik Sipil UPH Press, Tangerang, Indonesia (in Bahasa Indonesia). Morino, S. (1998). “Recent developments in hybrid structures in Japan: Research, design and construction.” Eng. Struct., 20(4–6), 336–346. Priestley, M. J. N., Calvi, G. M., and Kowalsky, M. J. (2007). Displacement based seismic design of structures, IUSS Press, Pavia, Italy.

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