Progressive collapse test of assembled monolithic concrete frame spatial substructures with different anchorage methods in the beam

Abstract

In this study, three two-third-scale assembled monolithic concrete spatial frame substructures with three beams and four columns were tested to evaluate progressive collapse resistance. The test parameters are anchorage methods, such as 90° hooked bar, lap splice in U-shaped assembled monolithic concrete beam, and headed bar using welded anchor plate. Force–displacement-controlled pseudo-static loading was applied to the mid-column. On the basis of structural performance, including load-carrying capacity, deformation capacity, crack distribution, rebar strain, and failure mode, the progressive collapse resistance mechanism of the specimens was analyzed. Test results showed that three types of cracks were developed: initial flexural cracks in beam–column joints, diagonal cracks due to compressive arch action, and tension cracks due to catenary action. The specimen using the headed bar exhibited the best progressive collapse performance, whereas the specimen using the lap splice connection showed the worst structural performance. Regardless of anchorage methods, bond failure did not occur during progressive collapse. The progressive collapse performance of the specimen was assessed based on Chinese and American codes.

Keywords

assembled monolithic concrete frame structure headed bar hooked bar lap splice progressive collapse spatial substructure

Introduction

Progressive collapse damage of the Ronan Point public in the United Kingdom caused the world to think and respond to the questions of thousand structures (Pearson and Delatte, 2003). Progressive collapse of building structures is affected by the initial damage of a structural component under accidental load, which in turn causes the structure to collapse partially or collectively. However, the ultimate progressive collapse damage is not proportional to the initial damage level. On the basis of initial research on progressive collapse of structures, theoretical systems have been proposed, experiments and simulations have been performed, and various research results have been applied to relevant design codes. Progressive collapse of reinforced concrete (RC) structures has been studied since 10 years ago. Although the special anti-progressive collapse specification has been specified in RC structures, studies on assembled monolithic concrete (AMC) and precast concrete (PC) for practical application are relatively limited as various connection types are still being developed.

Prefabricated members originated in the United Kingdom in 1875 (Morris, 1978). Since then, the construction method using prefabricated parts has been developed for over 140 years. Given the vulnerability of structural integrity, the structural performance of prefabricated structures is substantially affected by connection methods. Birkeland and Birkeland (1996) studied various connection methods of prefabricated concrete structures. Studies on the progressive collapse behavior of AMC and PC buildings are more relevant than those of RC buildings. Considering that the collapse of AMC and PC buildings is often caused by the failure of joints, Nimse et al. (2014) conducted an experimental study on the progressive collapse performance of three one-third-scale PC beam–column substructures and a cast-in-place substructure with different forms of joints. Kang and Tan (2015a, 2017) and Kang et al. (2015b) compared the progressive collapse resistance of PC beam–column substructures using hook and lap splice connection methods with that of RC beam–column substructures. Rashidian et al. (2016a, 2016b) performed a progressive collapse test and numerical analysis in three-tenth-scale RC moment substructures under static load to investigate the effect of cross-beams. Qian and Li (2013, 2019a, 2019b) and Qian et al. (2018, 2019c) performed a series of pioneer tests on PC spatial frames to resist progressive collapse. Feng et al. (2018, 2019) completed some interesting numerical simulation and analysis on the progressive collapse of RC structures. Su et al. (2009) studied the influence of longitudinal reinforcement ratio, ratio of beam width to beam height, and loading rate on the load resistance of 12 double-span RC beam specimens in the process of progressive collapse. Choi and Kim (2011) conducted a progressive collapse resistance test on RC beam–column substructures designed using seismic and nonseismic details, and the test results were compared with the recommendations of FEMA 356 (2000) and GSA2003 (2003). Lim et al. (2017) studied the effects of rotational capacity and horizontal constraints on catenary action (CA) in five RC frame structures under static load. Li et al. (2011) proposed an improved tie-force method and compared it with the numerical design model. Yu (2012), Yu and Tan (2010, 2013a, 2013b, 2014, 2017), and Yu et al. (2018) tested 12 RC plane frame substructures to evaluate the effects of joint anchorage, top and bottom reinforcement ratio at the middle joint, and span height ratio on progressive collapse performance. On the basis of the technical specification JGJ1-2014 (2014), 90° hooked bars or welded joint should be used in beam–column joints to satisfy structural integrity. However, vulnerability of the structural integrity at the connection between PC members is critical to the progressive collapse performance of building structures. The majority of existing studies focus on the progressive collapse resistance of steel and RC structures. Furthermore, planar substructures (i.e. neglecting cross-beams) and spatial substructures (i.e. with cross-beams) of RC have been considered, whereas research on spatial substructures (i.e. with cross-beams) of AMC and PC with different anchorage methods in the beam–column joint, which describes actual situations, is limited. Therefore, further studies on the progressive collapse performance of AMC structures are required to solve the current issue and improve the design method for the anti-progressive collapse of AMC building structures.

According to the existing research results, the deformability of AMC or PC member in compressive arch action (CAA) and CA is not as high as that of the cast-in-situ RC one. The main focus of this article is on the behavioral differences of the AMC specimen with different anchorage methods in the beam–column joint. In this study, three two-third-scale AMC spatial beam–column substructures were tested to evaluate progressive collapse performance. Three connection methods, such as 90° hooked bar, lap splice, and headed bar using welded anchor plate, were considered. Structural performances, including load-carrying capacity, deformation capacity, crack distribution, and failure mode, were evaluated.

Test plan

Test specimens

The Technical Specification for Prefabricated Concrete Structures (JGJ1-2014, 2014) states that an AMC structure can be analyzed in the same way as RC structures. Thus, a five-story RC moment frame structure was used to design the test specimens. Figure 1 shows the structural plane and elevation dimensions. Three and four spans were used in the x- and y-directions, respectively. Each span was 6.0 m long. The height of the first floor was 4.2 m, and the height of the other floors was 3.0 m. According to Abrams (1987), a scale factor for test specimens should not be less than 1/4. Considering the laboratory conditions, a two-third scale was determined in the beam–column test specimens.

Figure 1.

Dimensions and details of the prototype structure (unit: mm): (a) plan view and (b) elevation view.

It can be seen from Figure 2 that as a middle column at the long edge of the structure is removed, the residual structure of the prototype produces deformations and internal forces. The residual part of the removed column rotates and the connecting beam generates a certain moment of torsion, as shown in Figure 2(d). To consider the spatial bearing behaviors of the residual structure, especially the influence of the torsion moment, the experimental specimen of the frame substructure is designed, as shown in Figure 3. The columns in the specimen are enhanced to realize the constraints of frame columns on frame beams of the specimen.

Figure 2.

Calculation model and results of the prototype of the frame structure: (a) calculation model, (b) deformed shape, (c) distribution of moment, and (d) distribution of torsion.

Figure 3.

Calculation model and results of the specimen of the frame substructure: (a) calculation model, (b) deformed shape, (c) distribution of moment, and (d) distribution of torsion.

Figure 4 and Table 1 show the details of the beam–column substructures for the progressive collapse test. Due to symmetry of test specimens, Figure 4 presents only a one-third part of the test specimens. The test specimen consists of three half AMC beams and four RC columns. The length of each AMC beam was 3600 mm, and the height of each RC column was 1870 mm. The cross-sectional area of the beam was 200 mm × 420 mm, which consisted of PC (200 mm × 300 mm of shaded area in Figure 4) and RC parts. The cross-sectional area of the mid-column measured 350 mm × 350 mm. To provide reliable anchorage resistance for the beam end and structural rigidity to the entire structure, the cross-sectional area of the exterior columns was increased to 400 mm × 400 mm, based on the analysis shown Figures 2 and 3. Three HRB 400-C16 bars (diameter = 16 mm and cross-sectional area = 201.1 mm²) and two HRB 400-C16 bars were used for the top and bottom longitudinal bars in the beam end section, respectively. HPB300-A8 bars (diameter = 8 mm and cross-sectional area = 50.3 mm²) were utilized for transverse reinforcement. HRB 400-C20 and C25 bars were used for longitudinal bars of columns. The tensile test of reinforcing bars and the cubic compressive test of concrete were carried out. Table 2 shows the material properties of reinforcing bars and concrete. Three prefabricated beams were cured first for 28 days. Beam stirrups were opened on the upper side of the prefabricated beam to facilitate the placement of the top bars. After beam top bars were installed, upper stirrups were arranged in the cast-in-place part of the beams. The prefabricated beams and the column part were assembled, and concrete was simultaneously poured in the beams, columns, and beam–column joints.

Figure 4.

Dimensions and details of test specimens (unit: mm): (a) PC-H, (b) PC-L, and (c) PC-A.

Table 1.

Test parameters.

Specimen	Anchorage type	Development length of bottom bars (mm)	Beam end section		Beam middle section
Specimen	Anchorage type	Development length of bottom bars (mm)	Top bar	Bottom bar	Top bar	Bottom bar
PC-H	90° hooked bar	320	3C16	2C16	2C16	2C16
PC-L	Lap splice	1040	3C16	2C18	2C16	2C16
PC-A	Headed bar	320	3C16	2C16	2C16	2C16

Concrete covers of the beam and column are 20 and 30 mm, respectively.

Table 2.

Material properties.

Specimen	Material	Property	Prefabricated part		Cast-in-situ part
Specimen	Material	Property	A8	C16	A8	C16	C18	C20	C25
PC-H	Reinforcing bars	Yield strength (MPa)	455	517	389	492	–	466	464
		Tensile strength (MPa)	575	628	573	618	–	584	601
		Elongation (%)	32.5	21.7	37.5	22.5	–	25.7	26.2
	Concrete	Cubic compressive strength (MPa)	48.44		48.34
PC-L	Reinforcing bars	Yield strength (MPa)	382	552	382	518	502	467	466
		Tensile strength (MPa)	564	659	564	628	621	580	591
		Elongation (%)	35.8	21.3	35.8	21.7	21.1	26.0	24.4
	Concrete	Cubic compressive strength (MPa)	42.33		48.48
PC-A	Reinforcing bars	Yield strength (MPa)	358	499	358	619	–	523	516
		Tensile strength (MPa)	550	625	550	786	–	652	647
		Elongation (%)	38.3	22.5	38.3	23.3	–	21.3	21.0
	Concrete	Cubic compressive strength (MPa)	41.66		43.60

For the structural integrity of AMC beam–RC column joints, specimens PC-H, PC-L, and PC-A used 90° hooked bar, lap splice, and headed bar using welded plate in the beam–column joints, respectively. On the basis of JGJ1-2014 (2014) and 15G310-1-2 (2015), 90° hook was used for longitudinal bars of AMC beams in specimen PC-H. The development length of 90° hooked bars was 320 mm, which satisfied the design code requirement. In specimen PC-L, a U-shaped AMC beam with a length of 720 mm at both ends was used for lap splice, and 90° hooked bars at the beam end were installed above the bottom bars of the U-shaped AMC beam, which decreased the effective beam depth. Considering the equivalent principle of the flexural moment, two HRB 400-C18 bars (diameter = 18 mm and cross-sectional area = 254.5 mm²) were used at the beam end section.

Loading device

Figure 5 shows the test setup. After the specimen was manufactured, a mechanical jack and a force sensor were installed under the mid-column to support the column in the frame so that the beam remains in its original state before loading. Vertical loading was applied using a hydraulic jack to the mid-column, which exemplifies the column loss scenario. To remove the mechanical jack under the mid-column, the hydraulic jack was unloaded at 5-kN step. Force-controlled loading was applied to the peak strength at 10-kN step, and then displacement-controlled loading was applied at 20-mm step until the end of the test. Three exterior column foundations were completely fixed using the anchored steel beams on the strong floor.

Figure 5.

Test setup: (a) boundary conditions and (b) loading device.

Test scheme

Figure 6 shows the layout of linear displacement transducers and strain gauges. A total of 10 electronic displacement transducers and 12 dial gauges were used to measure the deflection of beams and displacement of columns and footings, respectively. A total of 78 strain gauges were installed in the beam end section, beam middle section, and column. In Figure 4, notations L, M, R, T, B, and C indicate the left end, middle location, right end, upper part, lower part, and column, respectively. All specimens have the same location of the strain gauges, but the strain of C18 spliced bars at the beam bottom was additionally measured in specimen PC-L. The load cells with capacities of 10 and 30 t were used to measure the loads of screw and hydraulic jacks, respectively.

Figure 6.

Layout of measurement devices: (a) displacement gauges and (b) strain gauges.

Test results and discussion

Failure mode

Figures 7 and 8 show the crack distributions of beam–column joints of in- and out-of-plane frames, respectively. Three specimens exhibited similar crack distribution at each load mechanism. Figure 7 presents three observed types of cracks in two exterior columns of the in-plane frame: ① flexural cracking in the beam–column joint, ② diagonal cracking due to CAA, ③ and flexural cracking due to CA. As specimen PC-A used the headed bars for the beam longitudinal bars, additional diagonal cracks occurred by head bearing force in the beam–column joint. At the initial loading stage, cracks simultaneously occurred at the top of the beam near the exterior columns and the beam bottom near the mid-column. Under CAA, concrete crushing occurred in the compression zone of the beam section, thereby increasing crack length and width. Ultimately, tension cracks developed in the entire beam section under CA. It can be observed from Figure 8 that the side columns of the out-of-plane frame showed only flexural cracks due to the asymmetric behavior. The tensile force of beam rebars in CA caused the cantilever action of the side column, which developed transverse tensile cracks on the outer side of the side column.

Figure 7.

Crack distribution in the beam–column joint of the in-plane frame: (a) PC-H, (b) PC-L, and (c) PC-A.

Figure 8.

Crack distribution in the beam–column joint of the out-of-plane frame: (a) PC-H, (b) PC-L, and (c) PC-A.

On the basis of the loading program, three stages were considered in test specimens under progressive collapse. Table 3 shows the damage development of the specimens.

Table 3.

Record of the test phenomenon.

Stage	Test phenomenon	PC-H	PC-L	PC-A
Second	Flexural cracks in the beam	13.7 (48)	6.5 (62)	4.3 (52)
	Flexural cracks in the exterior beam–column joint ①	24.9 (108)	15.4 (112)	13.4 (102)
	Flexural cracks in the side beam–column joint ①	–	–	28.5 (167)
	Concrete crushing in the beam	65.9 (202)	41.6 (187)	34.3 (182)
	Diagonal cracks at the bottom of the exterior columns ②	65.9 (202)	81.6 (197)	49.7 (197)
	Peak strength	86.0 (202)	81.6 (197)	69.9 (204)
Third	Concrete crushing in the cross-beam	86.0 (202)	221.8 (159)	110.0 (202)
	Rebar fracture in the beam near the mid-column	186.0 (188)	300.5 (135)	285.7 (163)
	Flexural cracks at the bottom of the exterior columns ③	490.4 (104)	513.0 (94)	452.4 (103)
	Rebar fracture in the beam near the left exterior column	559.3 (95)	526.8 (97)	–

Values indicate the vertical displacement (mm) of the mid-column, values inside parentheses indicate the corresponding vertical load (kN), and “–” indicates that relevant cracks did not occur.

In the first stage of self-weight unloading, the hydraulic jack of the mid-column was not in contact with the ball hinge, and the mechanical jack below the mid-column was completely unloaded. In all specimens, vertical displacement was extremely small and cracks did not occur.

In the second stage, vertical load was applied to the first peak strength. The specimens showed the behavior, including initial stiffness and cracks, due to CAA at the same load or displacement. The peak point of CAA and the post-extrapolation crack of the column appeared simultaneously.

In the third stage, loading was applied until specimen failure. In specimen PC-A, no fracture occurred in the longitudinal bar at the top of the beam when the test was terminated at the displacement of 675 mm due to the limitation of the stroke of the hydraulic jack and vacant space under the mid-column. Compared with specimens PC-L and PC-A, early fracture of the beam bottom bars near the mid-column occurred in specimen PC-H, showing low corresponding strength. CA in specimen PC-H occurred later than that of specimen PC-A, indicating that the performance of specimen PC-H to resist the CA was worse than that of specimens PC-L and PC-A.

Overall crack distribution

Figure 9 shows the crack distribution of the front and back sides in specimens at the end of the tests. No evident torsional cracks occurred on the front and back sides of the beam with the bottom longitudinal bar fractured at the end of the beam near the mid-column in the three specimens, and the cracks overlap because the beam has relieved the torsion. Unlike existing test results of plane frames (i.e. without a cross-beam), cracks on both sides of the longitudinal bar at the bottom of the beam near the mid-column end without fractures in the PC-L and PC-A specimens are torsional. This phenomenon occurred because the large deflection of the cross-beam generates out-of-plane deformation of the mid-column, which causes torsion of the beam in the in-plane frame. Given the small loading displacement of specimen PC-H, cracks of the double-span beam in plane were not penetrated and torsional cracks were not substantial.

Figure 9.

Overall crack distribution.

Load–deflection relationship

Figure 10 shows the load–deflection relationship of the mid-column in test specimens. Table 4 presents the load-carrying capacity, mid-column deflection, and resistance ratio of the CA to CAA. Given the stroke limitation of the loading device, specimen PC-A was loaded to 675 mm, without fracture in the beam top bars. Under failure of the mid-column, the load resistance mechanism of the substructure can be divided into beam flexural behavior, CAA, and CA in accordance with the loading condition (Zhang and Cao, 2017). In the evaluation of the composite force mechanism in actual structures, the evident boundary between the beam flexural behavior and CAA is neglected. Furthermore, the definition of CA is unclear. Yi et al. (2008) defined the beginning of CA as a transition point where the compression bar stress changes from compression to tension. Yu and Tan (2010) considered the second load increase point in the load–deflection relationship. In this study, the strain of the top bars at the beam end near the exterior column was considered to determine the starting point of the CA following the definition of Yi et al. (2008) (Figure 9). In general, the load-carrying capacity of CAA was greater than that of the CA, showing a ratio of 0.49–0.68.

Figure 10.

Load–deflection relationship of test specimens.

Table 4.

Summary of test results.

Specimen	Load (kN)					Mid-column deflection (mm)					F _ca /F _caa
	F _y	F _caa	F _1st	F _cas	F _ca	Δ_y	Δ_caa	Δ_1st	Δ_cas	Δ_ca
PC-H	69.892	202.236	187.915	102.604	106.413	18.1	86.0	186.0	469.9	550.7	0.53
PC-L	187.435	196.980	135.091	84.31	97.192	41.6	81.6	300.5	330.5	526.8	0.49
PC-A	136.931	201.680	163.000	167.087	137.087	20.6	90.2	285.7	270.1	675.0	0.68

F _y and Δ_y indicate the yield load and deflection corresponding to the rebar yielding of the beam end, respectively; F_caa and Δ_caa indicate the peak strength and deflection of the compressive arch action, respectively; F_1st and Δ_1st indicate the load and deflection corresponding to the bottom bar fracture, respectively; F_cas and Δ_cas indicate the load and deflection at initial catenary action, respectively; F_ca and Δ_ca indicate the load and deflection corresponding to top bar fracture in catenary action, respectively.

Three specimens exhibited similar load–deflection relationships. At the beginning of the CAA, the test specimens showed elastic behavior. As the mid-column deflection increased, CAA developed in the continuous beam of the in-plane frame, which increased the peak strength that is greater than that of beam moments without consideration of compression force. After the peak strength, the load-carrying capacity decreased slowly due to concrete crushing in the compression zone of the continuous beam and the beam bottom bar fracture near the mid-column. Ultimately, the test specimens failed by fracture of the beam top bars near the exterior columns. Specimens PC-A and PC-H showed the same progressive collapse behavior in the CAA and CA. However, early fracture of the beam bottom bars occurred in specimen PC-H. Specimen PC-L using lap splice exhibited progressive collapse behavior less than that of specimens PC-A and PC-H. Both the beam in plane and the beam out of plane play a role in the stage of CAA, while only the beam in plane makes a contribution in the stage of CA. Under these circumstances, the CA in the spatial substructure is not as obvious as that in the plane substructure.

On the basis of the finite element analysis results of Rashidian et al. (2016b), early rebar fracture is affected by a large beam height. Given the large beam height of test specimens, early rebar fracture occurred in this study.

Lateral displacement of columns

Figure 11 shows the lateral displacement variance of exterior columns at the height corresponding to the center of the beam section in accordance with the mid-column deflection. A positive value of the lateral displacement indicates outward movement from the mid-column, whereas a negative value indicates inward movement in the direction of the mid-column. As the mid-column deflection increased, the lateral displacement of the left and right columns increased in the CAA and then decreased in the CA. By contrast, the side column that connects to the cross-beam was pulled inward, and the cross-beam was in tension because of insufficient constraint of the mid-column. A larger lateral displacement of the exterior columns was measured in specimen PC-H than specimens PC-L and PC-A, showing early fracture of the beam bottom bars.

Figure 11.

Lateral displacement of columns.

Beam deflection

Figure 12 shows the deflection distribution of the continuous beam and cross-beam. Under small mid-column deflection, the beam deflection at the yield load F_y was close to that corresponding to CAA. At the initial CA, the beam deflection increased in the following order: PC-A < PC-L < PC-H. Specimen PC-A showed the largest deflection at the end of the CA (i.e. PC-L < PC-H < PC-A). In specimens PC-H and PC-L, the bottom bars were fractured at the left beam near the mid-column, which caused a larger defection of the left beam than the right beam (Figure 12(a)). In specimen PC-A, an opposite behavior occurred.

Figure 12.

Deflection distribution of test specimens: (a) continuous beam of the in-plane frame and (b) cross-beam of the out-of-plane frame.

Rebar strain

Figure 13(a) and (b) shows the strain variation of the longitudinal bars of the left beam near the exterior column and mid-column in PC-H. Rebar yield strain was measured as 0.0025 from the material test, and the ultimate strain was set at 0.01 on the basis of Section 6.2.1 of GB50010-2010 (2010). All rebars were yielded, and the strain was larger than the ultimate strain. The beam top bars close to the exterior column and the beam bottom bars close to the mid-column showed tensile behavior during the test. The beam bottom bars near the exterior column and the top bars near the mid-column were affected by compression force. As CAA changed to CA, the compressive strain of reinforcing bars decreased due to increased tensile behavior of beams.

Figure 13.

Rebar strains: (a) left beam near the exterior column in PC-H, (b) left beam near the mid-column in PC-H, and (c) average strain of beam bars.

Figure 13(c) shows the average strain of beam rebars based on the mid-column deflection. In the left beam, right beam, and cross-beam, four strain values of the top and bottom bars at the beam section of the mid-span were used (i.e. ε_m = (ε_MT1 + ε_MT2 +ε_MB1 + ε_MB2)/4; Figure 6). In the left and right beams, compression force was first applied and converted into tension force at the CA. The cross-beam was in a state of tension. In specimens PC-L and PC-A, the average rebar strain of the cross-beam was maintained at a certain value of tension force.

Effect of anchorage types

Lap splice in U-shaped prefabricated beams of specimen PC-L decreased the bond strength when cracks occurred. Although the headed bar using a welded anchor plate in specimen PC-A decreased the requirement of bar development length, stress concentration occurred in concrete near the anchor plate. Regardless of anchorage types, bond failure did not occur in all specimens. Three specimens exhibited a similar behavior in the initial flexural step. According to Kang and Tan (2015a) and Kang et al. (2015b), the load-carrying capacity of the specimen using 90° hooked bars under CAA is greater than that using lap splice due to the reduced flexural moment. However, in CAA, the load-carrying capacity of specimen PC-L using lap splice was only 2.6% and 2.3% less than those of PC-H and PC-A, respectively. Given that C16 bars were replaced with C18 bars for bar splices in PC-L, the load-carrying capacity of CAA was similar to those of the other specimens.

Specimens PC-A and PC-H showed a similar progressive collapse behavior in CA, but the deformation capacity of PC-A was 22.6% greater than that of PC-H. This result indicates that PC-A exhibits improved structural capacity in CA. By contrast, the load-carrying capacity of specimen PC-L was 17.8% and 49.5% less than those of PC-H and PC-A in the CA, respectively. Furthermore, early failure occurred in PC-L. Thus, progressive collapse performance is evaluated in the following order: PC-A > PC-H > PC-L.

Performance assessment of collapse prevention

Transformation of the load–deflection relationship

In the prototype structure, the floor of the corresponding area of the test specimen substructure is a two-way slab, shown in Figure 14(a). The load (dead load and live load) on the prototype transferred from the floor to the beam exhibits triangular distribution, and the maximum load on the out-of-plane beam is twice the load on the in-plane beam, as shown in Figure 14(b). During the test, the load on the specimen model is concentrated force, as shown in Figure 14(c). Of course, the weight of the beam is uniformly distributed and exists in both the model and the prototype. In the performance assessment, it is necessary to solve the transformation of load and deflection.

Figure 14.

Load transfer and load and deflection in the prototype and the model: (a) load transferring on the floor, (b) prototype of the substructure, and (c) model of the substructure.

The performance evaluation is mainly based on two indexes of bearing capacity and deformation. Based on the condition that the vertical mid-column deflection and structural energy in the model and prototype are equal, the concentrated load in the test is transformed into the uniform force in the prototype structure. The equations are as follows

Δ = δ

(1)

P Δ = ql δ

(2)

where Δ and δ are the mid-column deflections in the model and the prototype structure, respectively, P is the concentrated force on the test model, q is the maximum of the distributed force on the in-plane beam in the prototype structure, and l is the span of beams.

Substituting equation (1) into equation (2), the following relationship of P and q can be obtained and used in force transformation

q = \frac{P}{l}

(3)

Performance assessment

CECS392:2014 (2014) gives the acceptance criteria for the design of preventing progressive collapse in this way. Once a column fails or is removed, the original structure becomes a residual structure. When the linear static procedure (LSP) is adopted, the bearing capacity of the residual structural members shall meet equation (4). While the nonlinear static procedure (NSP) or nonlinear dynamic procedure is used, the plastic rotation angle of the horizontal members of the residual structure should be satisfied (equation (5))

S_{d} \leq R_{d}

(4)

θ_{p, e} \leq [θ_{p, e}]

(5)

where S_d is the design value of the load combination effect of the residual structure, R_d is the design value of the bearing capacity of the residual structure, θ_p,e is the design value of the plastic angle of the residual structure horizontal member, and [θ_p,e] is the limit value of the plastic rotation angle of horizontal members of the residual structure; for the RC aseismic designed beam, [θ_p,e] = 0.04.

Corresponding to the substructure of the present test, S_d is the effect value at 2.0(DL + 0.5LL). At this point, the peak value of distributed load on the beam is

q_{d} = 2.0 (DL + 0.5 LL) \frac{l}{2} = 28.0 kN / m

(6)

where q_d is the design peak value of the distributed load on the beam; DL and LL are the standard values of dead load and live load determined by design, respectively; here DL = 6.0 kN/m² and LL = 2.0 kN/m².

From load–deflection curves of the substructure measured by test, as shown in Figure 10, the measured peak value P_R, that is, the bearing capacity of the residual structure in the stage of the beam mechanism, can be obtained. Based on equation (3), the concentrated force P_R = F_caa can be transformed into distribution force q_R, which is shown in Table 5.

Table 5.

Performance assessment of specimens by CECS392:2014 (2014).

Specimen	Bearing capacity in LSP				Plastic rotation angle in NSP
	F _caa (kN)	q _R (kN/m)	q _d (kN/m)	Acceptance criteria: q_R ≥ q_d	Δ_caa (mm)	θ _p,e (rad)	[θ_p,e] (rad)	Acceptance criteria: θ_p,e ≤ [θ_p,e]
PC-H	202.236	50.559	28.0	Acceptable	86.0	0.022	0.04	Acceptable
PC-L	196.980	49.245	28.0	Acceptable	81.6	0.020	0.04	Acceptable
PC-A	201.680	50.420	28.0	Acceptable	90.2	0.023	0.04	Acceptable

LSP: linear static procedure; NSP: nonlinear static procedure.

At the same time, from Figure 10, the corresponding deflection Δ = Δ_caa can be obtained. Based on equation (7) derived from the geometric relationship, the tested plastic rotation angle can be obtained, as shown in Table 5

θ_{p, e} = \frac{Δ}{l}

(7)

From the test results shown in Table 5, the performance of the specimens in LSP or NSP can meet the requirement of CECS392:2014 (2014).

According to ASCE 41-13 (2013), GSA2016 (2016) defines force-controlled action and deformation-controlled action, and gives the discrimination and classification conditions at the same time. In the present test, the load–deflection curves of the three specimens (Figure 10) are regarded as deformation controlled, including primary and secondary component actions. GSA2016 (2016) uses demand–capacity ratio (DCR) and plastic rotation angle as the discriminant indexes of LSP and NSP, respectively.

For deformation-controlled actions in all primary and secondary components in LSP (GSA2016, 2016), it is checked whether the following condition is satisfied

DCR = \frac{Q_{UD}}{Q_{CE}} < ϕ m

(8)

where Q_UD is the resulting actions (internal forces and moments), Q_CE is the expected strength of the component or element, m is the component or element demand modifier (m-factor, for which the value is 16), ϕ is the strength reduction factor from the appropriate material specific code (ϕ = 1.0).

In the present test, the load case linear static analysis (LSA) for deformation actions is

Q_{UD} = \frac{G_{LD} l^{2}}{2}

(9)

G_{LD} = Ω_{LD} (1.2 DL + 0.5 LL)

(10)

Ω_{LD} = 1.2 m_{LIF} + 0.8

(11)

where m_LIF is the smallest m of any primary beam (m = 16); G_LD is the increased gravity loads for deformation-controlled actions for LSA, and Ω_LD is the load increase factor for calculating deformation-controlled actions for LSP.

Components and elements analyzed using NSP shall satisfy the requirements of ductility or deformation capacity under the increased gravity loads for nonlinear static analysis (NSA). The acceptance criteria of beams is

θ_{p, N} \leq [θ_{p, N}]

(12)

where θ_p,N is the design value of the plastic rotation angle of the horizontal member in the residual structure under LSA and [θ_p,N] is the limit value of the plastic rotation angle of the horizontal member in the residual structure under LSA; for the RC aseismic designed beam, [θ_p,N] = 0.1.

In the present test, the load case NSA for deformation actions is

Q_{N} = \frac{G_{N} l^{2}}{2}

(13)

G_{N} = Ω_{N} (1.2 DL + 0.5 LL)

(14)

Ω_{N} = \frac{1.04 + 0.45}{(θ_{pra} / θ_{y}) + 0.48}

(15)

where θ_pra is the plastic rotation angle, θ_y is the yield rotation angle, G_N is the increased gravity loads for NSA, and Ω_N is the dynamic increase factor for calculating deformation- and force-controlled actions for NSA.

The performance of the specimens in LSP can meet the requirement of GSA2016 (2016), while that in NSP can not, as shown in Table 6.

Table 6.

Performance assessment of specimens by GSA2016 (2016).

Specimen	DCR in LSP				Plastic rotations angle in NSP
	Q _CE = F_caa (kN)	DCR	ϕm	Acceptance criteria:DCR ≤ϕm	Δ_ca (mm)	θ _p,N (rad)	[θ_p,N] (rad)	Acceptance criteria: θ_p,N ≤ [θ_p,N]
PC-H	202.236	6.49	16.0	Acceptable	550.7	0.14	0.1	Unacceptable
PC-L	196.980	6.66	16.0	Acceptable	526.8	0.13	0.1	Unacceptable
PC-A	201.680	6.50	16.0	Acceptable	675.0	0.17	0.1	Unacceptable

DCR: demand–capacity ratio; LSP: linear static procedure; NSP: nonlinear static procedure.

Conclusion

In this study, three two-third-scale spatial sub-frames with three AMC beams and four RC columns were tested to evaluate progressive collapse performance. Force–displacement-controlled pseudo-static loading was applied to the mid-column. For the structural integrity of AMC beams, 90° hooked bars, lap splice in U-shaped AMC beam, and headed bars using welded anchor plate were used in the beam–column joint. The effect of anchorage types on the progressive collapse resistance of the spatial sub-frame was investigated on the basis of the test results. The main test results are summarized as follows:

Three types of cracks, namely, flexural, diagonal (due to CAA), and tension (due to CA), occurred in the test specimens. In CAA, diagonal cracks developed in the exterior beam–column joints of the in-plane frame. In CA, the tension force of beams generated tensile cracks on the outer side of the exterior columns, which exhibited cantilever behavior.

The progressive collapse resistance of test specimens using various connection details was evaluated in the following order: headed bars > 90° hooked bars > lap splice in U-shaped AMC beam. In all specimens, bond failure did not occur regardless of connection details. However, the specimen using headed bars showed many cracks in the beam–column joint, whereas the specimen using 90° hooked bars showed the least cracks.

Although there are some differences in the bearing behavior of the substructure with different anchorage methods in the beam–column joint, the progressive collapse performance of test specimens can meet the requirement of CECS392:2014 (2014) in LSP or NSP and GSA2016 (2016) in LSP, not that of GSA2016 (2016) in NSP.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was supported by the National Natural Science Foundation of China (Grant No. 51578228) and the National Key Research and Development Program of China (Grant No. 2016YFC0701400), which is gratefully acknowledged.

ORCID iD

Wang-Xi Zhang

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Progressive collapse test of assembled monolithic concrete frame spatial substructures with different anchorage methods in the beam–column joint

Abstract

Keywords

Introduction

Test plan

Test specimens

Loading device

Test scheme

Test results and discussion

Failure mode

Overall crack distribution

Load–deflection relationship

Lateral displacement of columns

Beam deflection

Rebar strain

Effect of anchorage types

Performance assessment of collapse prevention

Transformation of the load–deflection relationship

Performance assessment

Conclusion

Footnotes

Declaration of Conflicting Interests

Funding

ORCID iD

References