Progressive Collapse Resistance of a New Staggered Story Isolated System ()
1. Introduction
A novel isolated structure known as the staggered story isolated system was created based on the mid-story isolated system (see Figure 1). While the isolation story of the traditional mid-story isolated system is located in a specific story of the structure, the isolation story of the new staggered story isolated system is divided into two parts, with the isolation story of the frame part located in the middle of the structure, forming a similar mid-story isolated system. The core-tube’s isolation story exists at the bottom of the tube, producing a base isolated system similar to that. Assuring the integrity of the core-tube is a benefit of the new staggered story isolated system. One of the emblematic structures of the new staggered story isolated system, Baotou’s Huafa Xintiandi Project [1] , is located in Inner Mongolia, China. Additionally, the Second Phase of Haikou Meilan Airport [2] and the North Terminal of Urumqi International Airport [3] both use the new staggered story isolation system. Using a finite element model, Zhang Yafei et al. [4] studied the reaction of a super-tall staggered story isolated system to three different types of ground motions and performed a zonal comparison with the response of the mid-story isolated system. In order to study the nonlinear dynamic time-history response under rare earthquakes, Liu Dewen et al. [5] constructed a new staggered tale isolated system taking soil-structure interaction into consideration. A nonlinear finite element model of a new staggered story isolated system was created by Zhang Yafei et al. [6] and compared to the mid-story isolated system, the base isolation system, and the aseismic structure.
Progressive collapse resistance is a chain reaction failure that occurs in a relatively small part of the structure but results from a large scale collapse failure that is disproportionate to the initial local failure. In the Code for the Design of Collapse Resistance of Building Structures (T/CECS392: 2021) [7] , progressive collapse is defined as damage that begins in a relatively small portion of the structure, which then extends from member to member, and eventually leads to the collapse of a part of the structure or the collapse of the whole structure. The engineering community realized the danger of progressive collapse when the Ronan Point flats in London, UK fell [8] . Using SAP2000 finite element analysis software, Shalva Maijanshvili et al. [9] examined the progressive collapse resistance of a nine-story steel frame building. Zhu Mingcheng et al. [10] conducted a preliminary qualitative examination of the transverse and longitudinal joint
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Figure 1. (a) Base isolated structure; (b) Mid-story isolated structure; (c) The new story staggered isolated system.
progressive collapse in north China of a five-story brick and concrete structure caused by a gas explosion. On the basis of the test results and phenomena, Yi Weijian et al., [11] conducted research on the resistance to progressive collapse of reinforced concrete frame buildings, examined the test model frame, and explored the mechanical mechanism of the building. In a finite element simulation investigation of extremely long complex isolated structures, Du Yongfeng et al. [12] independently took into account the impact of floor action on the structure’s resistance to progressive collapse. Du Yongfeng et al. [13] examined a concrete frame isolated structure using LS-DYNA finite element analysis software. The structure’s resistance to progressive collapse was assessed by applying explosive loads at various locations in the basement. Zhang Youjia et al. [14] established a structural model with finite element software ABAQUS, and analyzed the anti-progressive collapse capability of RC space beam-plate structure under unequal span arrangement by Pushdown method. The research object used by Yu Xiaohui et al. [15] was an 8-story, 4-span concrete frame structure, and they compared the pushdown curve under various vertical loading regimes. To determine the collapse resistance mechanism of the structure, Meng Bao et al. [16] performed collapse resistance test analysis on frame columns with various joint connection modes.
The previous analyses suggest a scarcity of research on traditional seismic structures, with fewer studies on new staggered-story seismic isolation structures and their ability to withstand continuous collapse. This paper addresses this gap by using SAP2000 to establish an 18-story model of a new staggered-story seismic isolation structure. The study analyses the damage effects of continuous collapse on key components, such as corner and side columns, using the method of removing components. Non-linear dynamic analysis is employed to investigate the continuous collapse resistance, internal forces, and plastic hinge distributions of the remaining members. A comparison is made between the structure’s internal forces and plastic hinge distributions before and after the removal of key members to analyze the damage effects of the structure.
2. The Finite Element Model
2.1. Project Overview
A new 18-story staggered story isolated system uses a frame-core tube structure. The building is located in a high-intensity earthquake zone. According to the Chinese code for Seismic Design of Buildings, the site category is Class I, and the seismic fortification intensity is 8 degrees. The basic seismic acceleration is 0.20 g. The construction is a 32 m × 32 m square. The bottom story height is 4.5 m, and the standard story height is 3.6 m. The ninth story’s top and the bottom of the core-tube contain the isolation story. The dead load on each story is 3.0 kN/m2, whereas the live load on each story is 2.0 kN/m2. The frame beam is meant to have a C30 concrete strength grade, the bottom plate is designed to be 200 mm thick, and the frame column and core-tube are designed to have a C40 concrete strength grade. The frame’s beam, column and core tube, have concrete strengths of C40, 50 mm for protection, HRB400 for the beam and column’s reinforcement, and HPB300 for the stirrup. Design calculations were performed on the structure. Table 1 displays the frame beam and column information. They are designed following the Chinese design code and the Code for Design of Concrete Structures and the Code for Seismic Design of Buildings, as shown in Figure 2.
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Figure 2. New staggered story isolated structure. (a) Plan; (b) Elevation; (c) 3D.
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Table 1. Dimension of frame section.
2.2. Model Parameters
The 18 story structure model was created using the finite element program SAP2000. The isolation story is located in the ninth story’s top and the bottom of the core tube. The support and column are joined by a solid junction. The structure has 68 isolation supports overall, of which 48 are installed in the frame isolation story and 20 are installed at the base of the core-tube. In each case, LRB600 lead rubber bearings are employed, and important bearing relevant parameters are listed in Table 2. The multi-layer shell is used to imitate the reinforced area at the bottom of the core-tube, while the elastic thin shell is used to simulate the non-reinforced area. Table 3 displays the facts on the shear wall. Takeda hysteresis type was assigned to C40 concrete non-linear materials, whereas Kinematic hysteresis type was assigned to HRB400 steel and HPB300 steel. Frame column adopts PMM plastic hinge and frame beam adopts M3 plastic hinge.
3. Progressive Collapse Resistance Methods
The tie force method, local strengthening, linear static dismantling, linear static alternate path, and nonlinear dynamic alternate path are the basic progressive collapse resistance methods. Among these, the nonlinear dynamic alternate path method is a popular and accurate design method for progressive collapse resistance at the moment [17] . As a result, the nonlinear dynamic alternate path method is employed to evaluate the structure’s resistance to collapse.
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Table 2. Parameters of isolated bearings.
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Table 3. Dimension of frame section.
The nonlinear dynamic method simulates the behavior of a structure under dynamic loading by solving the differential equations of motion of the structure and integrating them directly in a stepwise manner. This method can calculate the internal forces and deformations of the members by solving the differential equations of motion. This method considers the deformation of the structure in both the elastic and plastic ranges, making it more appropriate for structures with nonlinear behavior.
Since the structure in this paper is a new staggered story isolated system, frame columns and isolation of typical parts are selected from the bottom, frame isolation story and core-tube bottom isolation story, and the core-tube shear wall is dismantled component analysis. In accordance with DoD2010 [18] code, when doing a nonlinear dynamic analysis, the structure should first reach a stable state under gravity conditions, and then the target member should be removed sudden until the structure becomes stable or collapses.
The DoD2010 guidelines for collapse say that a structure will enter the state of collapse if the vertical displacement of the removed member’s vertex exceeds 20% of the smallest span of the connecting beams. Alternately, use the maximum permissible plastic hinge angle as the criteria for failure. Figure 3 in the SAP2000 finite element analysis program depicts the five-pointed skeleton curve of the member’s plastic hinges. Point A denotes the initial loading, Point B the member yield point, Point C the maximum bearing capacity of the hinges, Point D the remaining strength of the hinges, and Point E the total failure of the hinges. Points IO, LS, and CP, which stand for immediate occupancy, life safety, and collapse prevention, respectively, are acceptable standards for hinge among them. In structural analysis, the member is deemed broken when the plastic hinge of a beam or column structure reaches the CP stage.
The corner column, side column, and inner column, respectively, are the ground floor removal members. From the isolation story of the frame, the corner isolation support, side isolation support, and inner isolation support are each removed in turn. In turn, the Q1 wall, Q2 wall, and Q3 wall support for the core-tube’s bottom are removed. According to DoD2010, when removing core-tube shear walls, two times the height of H may be removed for any wall
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Figure 3. Skeleton curve of plastic hinges.
that is longer than 2H; if the wall is shorter than 2H, the full length may be removed. The walls Q1, Q2, and Q3 were therefore removed for the analysis of progressive collapse resistance. Figure 4 depict the numbers of removed members and columns at the bottom floor as well as the number of removed members and structural supports at the frame’s isolation story. The shear wall of the core-tube and the support under the wall are removed, as shown in Figure 5. Remove each member as a working condition, each working condition is shown in Table 4.
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Figure 5. Remove the shear wall of core-tube.
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Table 4. Remove the member under different working conditions.
4. Nonlinear Dynamic Analysis of Peripheral Frame Failure
4.1. Analysis of Vertex Displacement-Time History Curve of Remove the Member under Different Working Conditions
The ground floor’s vertical displacement-time history responses curve is depicted in Figure 6, and the member of the frame’s isolation story’s vertical displacement-time history responses curve is depicted in Figure 7. The vertical displacement-time history responses curve demonstrates that after the member is removed, the displacement increases quickly, oscillates up and down over a period of time, and then tends to stabilize. When the side column is removed, the maximum vertex displacement is 22.07 mm, which is 1.83 times greater than the maximum vertex displacement when the ground floor corner column and 1.72 times greater than the maximum vertex displacement when the ground floor inner column are removed. When the isolation support of the frame isolation story is removed, the vertex displacement reaches the maximum when the side support is removed. When the side column is removed, the maximum displacement is 20.48 mm, which is 1.51 times greater than the maximum displacement of the corner support’s vertex and 1.52 times greater than the displacement of the interior support’s vertex. The maximum vertex displacement is much less than the critical amount for progressive collapse, according to the DoD2010 Code for collapse. When a separate member is removed from the same floor, the corner member’s vertex displacement is smaller than that of the inner member and smaller than that of the edge span member. The vertex displacement of the ground floor member is greater than the vertex displacement of the isolation support in the isolation story for the removal of a member at the same position in a different story. The ground floor corner column’s, side column’s, and inner
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Figure 6. Remove the shear wall of core-tube Vertical displacement of the joint at the top of the removed column on ground floor.
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Figure 7. Vertical displacement of the joint at the top of the removed column on frame the top of the removed column on frame.
column’s maximum displacements are, respectively, 1.1 times, 1.03 times, and 1.01 times that of the isolation story’s equivalent support vertex. After the isolation support of the isolation story is removed, it can be inferred that the remaining structure can sustain more weight.
4.2. Internal Force Analysis of Adjacent Beams under Different Working Conditions
Figure 8 displays the bending moment-time history curves of adjacent frame beams following the removal of members in various working conditions. The moment of the beam end grows quickly in each working conditions when the frame beams are next to each other in the X and Y directions, then oscillates up and down for a period of time before tending to stabilize. The bending moment oscillation interval is larger and the bending moment is less after stability in the first and fourth working conditions. The bending moment oscillation interval is minimal, but the bending moment after stability is significant, in the second and fifth working conditions. The distribution diagram of the structural plastic hinge is shown in Figure 9. In each working conditions, the plastic hinge of the frame beam is quickly formed and developed. The most plastic hinges are made in working condition two, and the plastic hinges of neighboring frame beams are generated quickly and rise quickly. The two span frame beams in the center of the frame quickly transition into the plastic stage and form plastic hinges. The moment of the beam end carries the structural resistance, and the structure is in the plastic stage. The frame columns supporting the frame beams in the X and Y directions limit the frame beams’ ability to bend once the structure enters the plastic stage, preventing the structure from moving into the suspension cable stage.
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Figure 9. Structure plastic hinge distribution after removal of under each working conditions. (a) Structure plastic hinge distribution after removal of corner column; (b) Structure plastic hinge distribution after removal of side column; (c) Structure plastic hinge distribution after removal of inner column; (d) Structure plastic hinge distribution after removal of corner support; (e) Structure plastic hinge distribution after removal of side support; (f) Structure plastic hinge distribution after removal of inner support.
4.3. Internal Force Analysis of Adjacent Frame Columns under Different Working Conditions
The axial force-time history curves of adjacent columns under working conditions 1, 2, 3, 4, 5, and 6 are displayed in Figure 10 after the members have been removed. The axial force of column No. 2 next to the corner column increases most noticeably in the first working condition when compared to the gravity working condition. The remaining columns’ axle forces rise by less than 15% when the front axle force is removed. The axial force of No. 5 column grew by 29%, that of No. 11 column next to the middle column of the side span increased by 36%, and that of the other supports increased by less than 15% in the second operating condition. In the third working mode, the axial force of the No.2 column adjacent to the dismantled column increases by 30%, 27%, 22%, 17%, 16% and 6% respectively, compared with that before the removal of the No. 10 column, No. 1 column, and No. 3, 7 and 11 columns. The axial force growth of the other supports is less than 10% in the fourth operating mode, but it grows by 50% for No. 2 support next to the angular support and by 14% for No. 9 support as compared to prior removal. The axial force of nearby bearing 11 grows by 46% under operating condition five, that of supporting 5 by 31%, and that of other supports is less than 15%. The axial force of nearby supporting 16 increases by 31% under operating condition six mode, that of bearing 2 increases by 29%, and that of other supports is less than 15%.
The findings indicate that the neighboring member is primarily responsible for bearing the axial force of the dismantled member, whereas the other members are only partially responsible. The axial force increase of the neighboring frame column and support is the biggest, which will become the high incidence area of later failure. The force transfer mechanism after the removal of the member gradually weakens as it is far away from the member the impact of an accidental load on a failure member decreases with the distance of the column or frame from the failure member.
5. Nonlinear Dynamic Analysis of Core-Tube Failure
Figure 11 depicts the stress nephogram of the core-tube under various working conditions after the bottom support of the core-tube has been removed. The shear wall’s maximum stress in the seventh working condition is 8.1 - 9 Mpa. The shear wall’s maximum stress in the ninth working state ranges from 6.3 to 7.2 Mpa. The shear wall is under a maximum stress of 7.65 to 8.5 Mpa in working condition 9. The shear wall’s maximum stress in the tenth working state is 15.3 - 17 Mpa. The shear wall’s stress exceeds the norm for its strength under maximum stress, and no shear wall is harmed.
After the removal of the shear walls, Figure 12 depicts the stress nephogram of the core-tube. When a wall is removed, the load on the remaining shear walls does not achieve the expected level of strength, resulting in damage to every shear wall. There is barely any structural distortion. The ninth working condition’s maximum vertex movement is less than 7 mm. The analysis’s findings
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Figure 11. The stress nephogram of the core-tube under various working conditions of the support is removed (Units: Mpa). (a) Remove the stress nephogram of support under Q1 and Q2 shear walls; (b) Remove the stress nephogram of support under Q3 shear walls; (c) Remove the stress nephogram of support under Q1, Q2, Q3 and Q4 shear walls; (d) Remove the stress nephogram of support under Q1, Q4 and Q5 shear walls.
indicate that under any working condition, the residual shear wall can disperse the uneven gravity force and further prevent the progressive collapse of the shear wall In conclusion, the structural deflection is greatly reduced and the vertex displacement is much smaller after the removal of shear walls than it is after the removal of the outer frame columns. Shear walls are strong enough to withstand a building’s progressive collapse.
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Figure 12. Stress nephogram of core-tube under different wall removal working conditions (Units: Mpa). (a) Remove the stress nephogram of Q1 and Q2 shear walls; (b) Remove the stress nephogram of Q3 shear walls; (c) Remove the stress nephogram of Q1, Q2, and Q4 shear walls; (d) Remove the stress nephogram of Q1, Q4 and Q5 shear walls.
6. Conclusions
A new staggered story isolated system’s finite element model is established in this work. The nonlinear dynamic AP method is used to analyze the structure’s progressive collapse, and the findings are as follows:
1) No progressive collapse happens under any working condition due to the new staggered story isolated system’s strong resistance to it. The progressive collapse of the structure is the least after the removal of the ground floor corner column and the most after the removal of the ground floor side span column.
2) The failure of the shear wall of the core-tube has little influence on the structure, and the existence of the core-tube can improve the progressive collapse resistance of the structure.
3) The collapse resistance of the remaining structure after the removal of the ground floor members is smaller than that of the remaining structure after the isolation story members.
4) When a member is removed, the neighboring member mostly bears the demolished member’s axial force. The axial force decreases with increasing distance from the member, following the trend of “greater near and smaller far”. There will be a significant risk of further damage to nearby locations.
Acknowledgements
The writers gratefully acknowledge the financial support of National Natural Science Fund of China (No.52168072 & No.51808467), High-level Talent Support Project of Yunnan Province, China (2020).