Collapse resistance of composite beam-column assemblies with unequal spans under an internal column-removal scenario

Engineering Structures 206 (2020) 110143

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Collapse resistance of composite beam-column assemblies with unequal spans under an internal column-removal scenario

T

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Wei-hui Zhonga,b, Zheng Tana, Li-min Tiana, , Bao Menga, Xiao-yan Songa, Yu-hui Zhenga a b

School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China Key Lab of Structural Engineering and Earthquake Resistance, Ministry of Education, Xi’an University of Architecture and Technology, Xi’an 710055, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Composite beam-column assembly Cover plate reinforced connection Composite beam Unequal span Progressive collapse

To investigate the collapse performance of composite beam-column assemblies consisting of three columns and two beams with unequal spans under an internal column removal scenario, static loading tests with either unequal spans (1.4:1 or 0.6:1) or an equal span (1:1) were conducted. Experimental results, including the loaddisplacement responses, failure modes, internal force development and resistance mechanism, are discussed in detail. Besides, the contributions of different resistance mechanisms to the total resistance of the two-bay beams are quantitatively separated, which include the flexural resistance and catenary resistance of two-bay beams. In addition, finite element models of three specimens are validated based on the test results. Furthermore, the numerical models are used to illustrate the effect of the composite effect and unequal height-span ratio of twobay beams on the collapse-resistant performance of the assembly. The results showed that the concrete slabs contributed to an increased collapse resistance of the composite beam-column assemblies. Decreasing the beam span resulted in a larger resistance under both mechanisms, whereas increasing the beam height increased the resistance under the flexural mechanism but contributed little to that under the catenary mechanism.

1. Introduction Studying the progressive collapse of building structures is important for understanding the relevant controlling mechanism and for avoiding disasters such as the collapse of the 22-story Ronan Point apartment building in London that occurred in 1968. A building suffers progressive collapse when its structure is partially damaged by accidental loads, such as those induced by natural disasters (e.g., earthquakes and typhoons) or human factors (e.g., explosions, fires, and impact), which results in a chain reaction that eventually leads to the collapse of the entire building [1]. Over the last few decades, numerous tests on steel structures and composite structures, including the beam-column substructure, planeframe structure, and space-frame structure have been conducted under an internal column-removal scenario. Kozlowski et al. [2] experimentally investigated the behavior of full-steel and composite beam-column assemblies with respect to progressive collapse, and showed that the plastic rotation of the composite beam-column substructure was smaller than that of the steel beam-column substructure. Zhong et al. [3] conducted a static loading test with different stiffness connections, including a welded flange-bolted web connection, a top-seat angle with double web angle connection and a double web angle connection under

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an internal column-removal scenario. The rotational capacity and failure modes of joints under different connection modes were analyzed, the results showed that different stiffness connections affected the catenary mechanism. Yang and Tan [4] carried out a series of experiments using double half-span composite beam assemblies under middle-column and side-column loss. The results showed that the resistant mechanism of the composite beam-column substructure was different under the two different column-loss conditions. The floor had a large influence on the joint performance and catenary mechanism and could significantly improve the collapse resistance of the structure. Through a series of tests performed using composite joints, the same authors [5] observed that the double half-span assemblies do not account for the change in the bending point position during failure; therefore, it cannot accurately reflect subsequent changes in the transmission path caused by local failure of the substructure. However, they showed that a substructure comprising three columns and two beams can effectively avoid this problem. The failure mode and resistant mechanism of composite beam-column assemblies under middle-column loss have been thoroughly explored experimentally, and the irrationality of the simplified double half-span beam-column assemblies has been analyzed in detail. Guo et al. [6] analyzed the collapse resistance of a one-storey four-bays composite frame and found

Corresponding author. E-mail address: [email protected] (L.-m. Tian).

https://doi.org/10.1016/j.engstruct.2019.110143 Received 28 July 2019; Received in revised form 24 December 2019; Accepted 24 December 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.

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2. Experimental program

that the structure mainly relies on the plastic hinge mechanism and catenary mechanism to resist progressive collapse. Shan et al. [7] worked on a two-storeys four-bays RC frame with infill walls after a column failure, the results showed that the infill walls may change the failure mode of the frame. Fu et al. [8] conducted a progressive collapse test on a one-third-scale steel-frame-composite floor structure, calculated the bearing capacity and deformation capacity of the three-dimensional composite frame, and discussed its failure. Dinu et al. [9] investigated the collapse resistance of a structure under middle-column removal using a two-bay steel frame test and analyzed the specific load transfer path in the large deformation stage. Several studies have recently investigated the collapse-resistant performance of concrete structures. For example, Ren et al. [10] tested seven one-third-scale concrete beam-column assemblies (including five beam-slab specimens and two continuous beam specimens without a floor slab) and studied the influence of parameters such as the beam height, slab width, and slab thickness on the collapse resistance of the assemblies. Yi et al. [11] carried out static loading tests on slab-column structures with concealed beams under collapse conditions and showed that the floor loads were mainly transmitted via slab deflection and membrane action, where the membrane effect successfully delayed collapse. Qian and Li [12,13] dynamically tested a series of reinforced concrete beam-column substructures and quarter-scale specimens formed by a 2-bay slab, where the dynamic load redistribution performance of the specimens through dynamic tests was studied. These previous studies can be divided into the following three categories based on the different types of structure studied [14]: steel structures, composite structures and concrete structures. In addition, the studies can be classified based on the specimen type studied: beamcolumn substructure, plane-frame structure, and space-frame structure. The planar-frame structure is responsible for the Vierendeel effect of the structure, while the space-frame structure accounts for the spatial effect, where the most realistic simulation structure is subjected to a force under the collapse conditions. However, owing to the high cost of the aforementioned tests, it is not feasible to conduct a large number of experimental studies. Therefore, it is necessary to examine the specimens as beam-column assemblies. Composite beam-column assemblies can be used to investigate the load transfer of the entire structure, which is similar to what happens in a prototype structure. Hence, the failure mode and mechanism of members and composite joints under collapse conditions can be analyzed, and systematic test data for analysis of structural collapse can be extracted. Until recently, studies of the collapse-resistant mechanism of frame structures have mainly focused on slab effect, joint behavior, boundary conditions and infilled wall of structures with equal span ratios, but no systematic studies of composite beam-column assemblies with unequal spans under progressive collapse exist. However, composite structures with unequal spans are common in engineering applications; thus, there is a gap in the knowledge regarding their resistance to collapse. In this study, the influence of unequal spans on the collapse performance of composite beam-column assemblies (two beams and three columns) are investigated using the alternate load path method [15] to address the above-mentioned gap in the knowledge. The comprehensive performance of the composite beam-column assemblies under column-loss failure are evaluated considering the failure modes, bearing capacity, deformation capacity, and internal force development. In addition, the resistant mechanism is investigated for specimens with different span ratios. Contribution coefficients of resistance are introduced to quantitatively analyze the contributions of different resistant mechanisms to the total resistance of two-bay beams. In addition, a finite element simulation is performed to further study the performance of the substructure in resisting progressive collapse. Based on a full-scale model, the influence of the composite effect and unequal height-span ratio of two-bay composite beams on the collapse-resistant performance of the assembly are analyzed.

2.1. Substructure selection In this study, a composite beam-column assembly was built based on the alternate load path method without considering the failure process or the cause of middle-column loss and only considering the influence of the residual substructure on the collapse resistance of the structures under external load. Referring to the Chinese design standards [16,17], three specimens were designed and fabricated in a 1/3scale assembly consisting of two side columns, an internal failure column, and composite beams with unequal spans ratios (L1/L2 = 1.4, 1.0, 0.6). The substructure loses its vertical bearing capacity after the removal of the internal column, it was assumed that a vertically concentrated load acts on the failure column [3]. In addition, the inflection points of the bending moment of the two side columns were assumed to be located approximately at the midpoint of the upper and lower columns. It should be noted that in order to consider the effect of the indirect influence area on the collapse-resistant performance of a composite beam-column substructure, the inflection point was simplified as a hinge joint along with the position of the inflection point and the 1/4 L2 of the outreach beam as the boundary. Thus, the composite beam-column assembly model was obtained as shown in Fig. 1. 2.2. Specimen design The span ratios of the three specimens labeled WUFG-1.4, WUFG1.0, and WUFG-0.6 are 1.4, 1.0, and 0.6, respectively, while the span (L2) of the east composite beam is 1500 mm for the standard span, and the spans (L1) of the west composite beam are 2100 mm, 1500 mm, and 900 mm, respectively. The length of the side column is 1100 mm for all three specimens. The steel beams and columns are made of grade Q235B steel, with cross-sections of H150 × 100 × 6 × 9 (mm) and H150 × 150 × 8 × 10 (mm) [H-overall depth (d) × flange width (bf) × web thickness (tw) × flange thickness (tf)], respectively. The detailed engineering drawing of specimen WUFG-1.4 is shown in Fig. 2 as a representative example. The thickness of the floor slab is 55 mm according to the scale ratio (1/3) and the arrangement of the steel bar and shear studs. The thickness of the protective layer is 10 mm, and the effective width of the slab is 600 mm. Fig. 3 shows the distribution of

Direct influence area

Indirect influence area

Concrete slab

Indirect influence area

Failure column

R0 0.5Lc 0.5Lc

R0

Upper East

West Lower

1/4L2

L1

L2

1/4L2

Fig. 1. Composite beam-column substructure with three columns and two beams. 2

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Fig. 2. Detailed dimensions of the composite beam-column substructure. All values are in mm.

The two side columns were subjected to a constant compressive force by the 30-T hydraulic jacks to consider the influence of the side column compressive force. Four vertical beams were connected to the gantry mounting, thereby forming a self-balanced stability system. The loading setup was designed to address many of the inconveniences presented by testing specimens with unequal spans. During testing, the controlled vertical load under displacement exerted by the 100-T hydraulic actuator was applied on the internal column at a rate of 5 mm/min until the specimen reached failure.

the reinforcement and details of the connections. The longitudinal reinforcing bars were placed on the top and bottom of the concrete slab. HPB300 hot-rolled steel bar was used for the reinforcing bar, Ф10@125 for the longitudinal reinforcing bar, Ф6@125 for the steel bar in the orthogonal direction, and the end of the longitudinal reinforcement was welded to the beam-end baffle to consider the actual anchorage. The upper longitudinal reinforcement and the distribution reinforcement formed a reinforcing bar net. The reinforcement ratio is 0.95%, which satisfies the design requirements [16]. Shear studs with a diameter of 13 mm and length of 45 mm were welded to the steel beams. Based on the full shear connection of the composite beams, the studs were arranged in a double row with a spacing of 125 mm. An open-type YX28200-600 profiled decking sheet with a thickness of 0.6 mm was used. In accordance with the recommended standard of the Federal Emergency Management Agency [18], the CPS joint was used as the beam-column connection, where the cover plate and flange of the beam were connected with a fillet weld. In addition, full penetration welding was used to connect the beam welding and column flange. Because of the strengthening of the flange at the end of the beam, the plastic hinge moves away from column flange, which provides high joint ductility.

2.4. Instrumentation The instrumentation layout for all specimens was similar. For brevity, only the layout of specimen WUFG-1.4 is described herein in detail (see Fig. 5). The main parameters monitored during testing are the displacement of the specimens, strain in the key section, strain in the concrete slab and the steel bar, rotation of the beam-to-column joint, and the horizontal reaction force of the side column. The measurement of displacement included the vertical displacement of the composite beam and the horizontal displacement at the middle of the side columns were to determine the horizontal stiffness of the test setup. Strain gauges were attached to eight critical sections (B1-B6 and C1C2). During testing, the strains on the B1 (B6) and B3 (B4) sections were mainly used to obtain the strain distribution at the beam-to-column interface; the strains on the B2 (B5) and C1 (C2) sections were mainly used to calculate the axial force across the steel beam and the horizontal reaction at the bottom of the side columns. Six inclinometers (I1-I6) were attached to the beam end to measure its rotation. Four 100 kN tension-compression load cells were installed at the upper and middle sections of the side columns to obtain the horizontal reaction; two load cells were arranged at the top of the side column to monitor the influence of the compressive forces on the column. Fig. 5(b) shows the concrete surface strains, profile decking strains, and strains in the reinforcement.

2.3. Test setup The test loading setup for specimen WUFG-1.4 (as a representative example) is shown in Fig. 4. The top loading plate of the failure column was connected to a 100 T hydraulic actuator using four screws. A vertical load was applied to simulate the load on the failure column under progressive collapse during testing. Lateral restraint columns were installed on the north and south sides of the ground beam to prevent out-of-plane flexural buckling of the specimens. The upper and middle ends of side columns Z1 and Z3 were connected to horizontal hinged components (fixed on the reaction beam) to attain the horizontal hinge constraint and the lower ends of side columns Z1 and Z3 were connected to the ground beam to simulate the hinge constraint.

Fig. 3. Beam-to-column connections. (a) Distribution of reinforcement, (b) 1–1, and (c) 2–2. All values are in mm. 3

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Fig. 4. Loading test setup. 1-Gantry mounting; 2Hydraulic actuator; 3-Vertical beam; 4-Jack beam; 5-Reaction beam; 6-Load cell; 7-Jack; 8Lateral and vertical sliding restraint; 9-Pulley; 10-Ground beam; 11-Hinged connection; 12West beam (L1 = 2100 mm, 1500 mm, 900 mm); 13-East beam (L2 = 1500 mm for the standard span).

2.5. Material properties

Table 1 Material properties of the specimens.

To determine the properties of the steel material, three samples were cut from each structural steel member and reinforcement. The average values of the material properties are shown in Table 1. The concrete slab is made of concrete with a strength grade of C20. Three standard 150 × 150 × 150 mm concrete cubes and three 150 × 150 × 300 mm concrete cylinders were tested. The average compressive strength of the concrete cube is 17.9 MPa, the average axial compressive strength is 13.1 MPa, and the Young’s modulus is 2.41 × 104 MPa. It should be noted that, owing to the small spacing between steel bars and studs in the concrete slab, small-aggregate mix chippings were used to prepare the concrete, which resulted in relatively low concrete strength.

Components

Yield strength fy /MPa

Tensile strength fu /MPa

Elastic modulus E × 105/MPa

Elongation percentageΔ/%

Column flange Column web Beam flange Beam web Shear tab Cover plate Φ10 reinforcement Profile decking Bolt

263 399 283 308 296 290 503 346 940

425 533 428 467 454 457 597 387 1130

2.10 1.98 1.90 1.95 2.12 1.95 2.01 2.01 2.10

34 28 33 29 29 32 15 20 –

Fig. 5. Instrumentation layout where all values are in mm. 4

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500

C1

450

C2

Vertical load(kN)

B2

A1

400 350

gradually moved toward the beam web, accompanied by an arc-like crack pattern. Owing to the internal force redistribution of the two-bay composite beams, the vertical load gradually increased above the peak from the previous period and reached a maximum peak load (corresponding to point B2 (233 mm, 396 kN) in Fig. 6). The crack penetrated the bolt hole on the upper row of the beam web until the web completely fractured, as shown in Fig. 8(b). Finally, specimen WUFG-1.0 was destroyed and the test was terminated. Fig. 8(c) depicts severe concrete crushing at the middle beam-to-column joint. The load-displacement behavior of WUFG-0.6 was similar to the other specimens in early stages of loading without any apparent change. When the displacement of specimen WUFG-0.6 increased to 177 mm, the load reached 430 kN. At this time, the joint J3 fractured between the cover plate and the failure column flange, as shown in Fig. 9(a), and the load suddenly dropped to 342 kN. As the loading displacement continued to increase to 228 mm, the load reached a new peak (corresponding to point C2 in Fig. 6); then, the tensile flange of the east steel beam fractured, as shown in Fig. 9(b), the vertical load dropped sharply, and the experiment was terminated. Fig. 9 depicts the failure modes of specimen WUFG-0.6. As seen in Fig. 6, at the initial stage of the loading, the peak loads of the three specimens increased with a decrease in the span ratio, which in turn reduced the initial fracture displacement. The test results showed that the failure modes of specimen WUFG-0.6 were different from those of specimens WUFG-1.0 and WUFG-1.4; this is because the fracture occurred at the beam end and the plastic hinge did not move away from the connection. The reason for this is that the strength of the weld between the cover plate at joint J4 and the failure column flange was insufficient, resulting in advanced failure of the weld connection. For WUFG-1.0, when the tensile flange of the steel beam fractured, the existence of a greater synergistic effect between the two-bay composite beams resulted in the vertical load of the structure reaching its maximum value. However, for the unequal-span specimens, the different linear stiffness and plastic rotation behavior on either side of the composite beam were not conducive to synergistic interplay between the two-bay beams, thereby resulting in a decrease in the ultimate resistance.

A2

B1

300 250 200 150

WUFG-1.4 WUFG-1.0 WUFG-0.6

100 50 0

0

50

100

150

200

250

300

350

Failure column displacement(mm)

400

Fig. 6. Vertical load-displacement curves of specimens.

3. Experimental results and discussion 3.1. Test curve and failure mode The load-displacement curves of the three specimens with different spans are shown in Fig. 6. During loading, two peak load points are observed for each specimen, where the associated failure modes are shown in the photographs in Figs. 7–9. The initial behavior of WUFG-1.4 was continuous until the displacement reached 266 mm, at which point the tensile flange (close to the cover plate) of the short beam near the failure column fractured, as shown in Fig. 7(a). At this point, the load dropped from 359 kN to 240 kN instantly (corresponding to point A1 in Fig. 6). Owing to the fracture of the tensile flange, the centroid of the section started to shift toward the compression flange, and part of the internal force of the section was transferred by the reinforcement web. As the load increased, the crack continued to develop toward the bolt hole in the upper row until the vertical load reached a new peak (corresponding to point A2 in Fig. 6). Fig. 7(b) shows the fractured beam web, which caused a sharp reduction in the load. During the second load increase, the sound of several internal reinforcements fracturing in the concrete slab was clearly heard, but the load continued to increase. No obvious damage occurred to the long-span steel beam until the test ended. The upper flange of the steel beam near the removed column and the lower flange of the steel beam near the side column started to buckle. Fig. 7(c) shows that the concrete at the top of the removed column was crushed, and the profile decking near the side column fractured. Fig. 8 shows the failure mode of specimen WUFG-1.0. Although nonlinearity was observed in the load-displacement response at a displacement of 25 mm, cracks were observed in the concrete slabs around the side column. As the displacement increased to 205 mm, the tensile flange (close to the cover plate) of the west beam near the failure column fractured (corresponding to point B1 in Fig. 6), as shown in Fig. 8(a). As the displacement increased, the crack in the tensile flange

(a) Fractured beam flange (J4)

3.2. Analysis of cracks The final cracks in the concrete slabs of three specimens after testing are shown in Fig. 10. The main cracks were located near the beam-tocolumn connection. Diagonal tensile cracks at ~45° were observed on both sides of the concrete slabs. A longitudinal crack formed along the longitudinal direction of the composite beam in all three specimens; under a vertical load, the side beam-to-column joint was subjected to a negative bending moment, which resulted in a crack in the concrete on the top surface of the slab. In contrast, the internal beam-to-column joint was subjected to a positive bending moment, causing the concrete at the top surface of the slabs to be crushed. According to the experimental observations, as shown in Fig. 10, the concrete slab cracks near the side column flanges appeared almost simultaneously, and the

(b) Fractured beam web (J4) (c) Crushed concrete at the top of the failure column

Fig. 7. Photographs of the failure modes of specimen WUFG-1.4. 5

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(a) Fractured beam flange (J3)

(b) Fractured beam web (J3)

(c) Fractured profile decking flange (J2/J5)

Fig. 8. Photographs of the failure modes of specimen WUFG-1.0.

during the low-deformation stage. When the horizontal displacement returned to zero, the arch action failed. For unequal-span specimens, as the displacement increased, the shorter beam resisted a greater axial force, resulting in a greater bending deformation of side column Z1 than Z3. In the case of WUFG-1.0, the deformation development of side columns Z1 and Z3 was very similar and showed a linear relationship before the tensile flange fractured. As the displacement continued to increase, the slopes of the curves (undamaged composite beam) began to increase, corresponding to a rapid increase in the horizontal displacement of the side column.

distribution of cracks in the two-span slabs was similar for all cases. However, for specimens with unequal spans, tensile cracks at the initial stage of the loading first appeared in the short-span slab and then in the long-span slab. Comparing the final crack distributions of the three specimens, it is observed that the crack densities of the slabs increased continuously as the span ratio decreased, indicating that unequal spans in one slab significantly affect crack development in the slab. 3.3. Deflection shapes of the composite beams The deflection shape of the test specimens as a function of increasing displacement of the removed column are shown in Fig. 11. It can be seen that the vertical displacement development of the two-bay beams was similar. At the initial stage of loading, the deformation morphology of the composite beam-column substructure exhibited a typical flexural pattern (approximately quadratic curve). With increasing displacement, the vertical displacement profiles of the beams exhibited a two-bar tensile characteristic (approximately linear curve), indicating that the structural resistant mechanism is constantly changing from flexural to catenary mechanism as the load increases. It should be mentioned that the fracture of the flange and the web affects the deformation process of the assemblies. Fig. 11(a) depicts the ultimate deformation of the three specimens. It is observed that the profile of the two-bay beams turns into one that resembles two straight lines. Comparing Fig. 11(a) with Fig. 11(b), it can be seen that the displacement development of the two-bay composite beams was similar to the point before the steel beam was destroyed for specimen WUFG-1.0, and the short beams of the asymmetric specimens had a larger vertical displacement and a faster development.

4. Analysis of resistant mechanism 4.1. Development of internal forces Fig. 13 shows the development curves of the bending moment (B1/ B3/B4/B6 section) and the axial force (B2/B5 section) of the three specimens with different spans under different loading displacements. It is observed that the development of axial force in the three specimens was similar. At the initial stage of loading, the axial force in a composite beam was compressive due to the arch action effect. For specimen WUFG-1.4, arch action was the most significant at a displacement of 0.21 h (h is steel beam height, corresponding to an axial force of −30 kN) and ended at 0.40 h. For specimen WUFG-1.0, arch action was the most significant at 0.24 h (corresponding to an axial force −35 kN) and ended at ~0.33 h. For specimen WUFG-0.6, arch action was the most significant at 0.21 h (corresponding to an axial force −33 kN) and ended at approximately 0.43 h. By comparison, the unequal spans had little effect on the compression arch action. Moreover, arch action was beneficial to the bearing capacity of the three specimens. As shown in Fig. 13(a), (b), in the initial stage of loading, the bending moment developed rapidly, and the axial force was small. The resistance of the assemblies was mainly offered by the flexural mechanism. When key sections of the composite beams form a plastic hinge, the bending moment is maintained at this level. Meanwhile, the axial force of the specimens changes from compression to tension and develops rapidly, resulting in the catenary mechanism. When the displacement reached the first peak load in the load-displacement curves,

3.4. Horizontal displacement development of the side columns Fig. 12 shows the relationship between the displacement of the failure column and the horizontal displacement of the side column. Negative values represent the outward deformation of the side column, while positive values represent inward deformation of the side column. From Fig. 12, it can be seen that the initial displacements of the three specimens were negative, indicating that the arch action occurred

(a) Fractured weld (J4)

(b) Fractured beam flange (J4)

(c) Fractured profile decking(J2/J5)

Fig. 9. Photographs of the failure modes of specimen WUFG-0.6. 6

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WUFG-1.4

Diagonal tensile crack

Cracked concrete

Longitudinal through-crack

(a) WUFG-1.4 WUFG-1.0

Cracked concrete

Diagonal tensile crack

Longitudinal through-crack

(b) WUFG-1.0 WUFG-0.6

Cracked concrete

Diagonal tensile crack

Longitudinal through-crack

(c) WUFG-0.6 Fig. 10. Illustrations of the final crack patterns of the specimens.

v=25mm v=50mm v=100mm v=150mm v=200mm v=250mm v=300mm v=350mm v=396mm

400

WUFG-1.4 D0 D5 D4

D6

D3

D7 -1500 -1000 -500

0

500

Locations(mm)

1000 1500

350

WUFG-1.0

v=25mm v=50mm v=100mm v=150mm v=200mm v=250mm v=300mm v=339mm

D0

D4

D5

300 250 D3

200

D6

150 100 50

D7

D2

0 -1500

-1000

-500

0

500

Locations(mm)

1000

1500

(b) Development of the deflections of the beams Fig. 11. Deflection shapes of the specimens. 7

300 250

Deflection(mm)

550 500 450 400 350 300 250 200 150 100 D2 50 0 -2100

Deflection(mm)

Deflection(mm)

(a) Deformation shapes after testing WUFG-0.6

200

D5

D4

150

v=25mm v=50mm v=100mm v=150mm v=200mm v=228mm

D0

D6

D3

100 50

D2

D7

0 -900 -600 -300

0

300

600

Locations(mm)

900 1200 1500

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At middle of side column Z1 At middle of side column Z3

20 15 10

v=23mm v=31mm

5 0 0

50

100

150

200

250

300

350

Failure column displacement(mm)

400

30

At middle of side column Z1 At middle of side column Z3

25 20 15 10

v=18mm v=20mm

5 0 0

50

100

150

200

250

300

350

Failure column displacement(mm)

(a) WUFG-1.4:1

Horizontal displacement(mm)

25

Horizontal displacement(mm)

Horizontal displacement(mm)

W.-h. Zhong, et al.

At middle of side column Z1 At middle of side column Z3

20 15 10

v=25mm

5

v=30mm

0 0

50

100

150

200

250

Failure column displacement(mm)

(b) WUFG-1.0:1

(c) WUFG-0.6:1

Fig. 12. Horizontal displacement development of the specimens.

the corresponding fracture of the steel beam occurred, and the bending moment of the weakest section decreased instantaneously. The corresponding axial force also decreased slightly before the axial force began to increase steadily again. Finally, for WUFG-1.0, the axial force of the two-bay composite beams was different due to the asymmetric fracture of the beam-to-column joints. For specimens with unequal spans, the axial force of the composite beams with shorter spans was greater than that of the longer spans owing to a higher linear stiffness.

4.2. Resistant mechanism Fig. 14. Analysis diagram of composite beam-column assembly.

The simplified analysis model for the composite beam-column assembly is shown in Fig. 14. The total resistance (P) is the sum of the resistance of the east composite beam (PE) and the resistance of the west composite beam (PW ) , and each resistance can be divided in the flexural mechanism resistance (PF ) and catenary resistance (PC) . The flexural resistant mechanism (PFW , PFE) is composed of the vertical components of the shear force (V2, V3) , while the catenary mechanism resistance is composed of the vertical components of the axial force (N2, N3) . In addition, PFW (PCW ) and PFE (PCE) are the flexural mechanism resistance (catenary mechanism resistance) values of the west composite beam

300 WUFG-1.4

200 100

PC = PCW + PCE = NW sin θ2 + NE sin θ3

(2)

The axial force of the west composite beam The axial force of the east composite beam

600

Axial force(kN)

Axial force(kN)

400

(1)

600

700

The axial force of the west composite beam The axial force of the east composite beam

500

NW = N1 = N2, NE = N3 = N4

500 400

WUFG-1.0

300 200 100

Zero axial force

0 0

50

Zero axial force

0

100 150 200 250 300 350 400

0

Failure column displacement(mm)

50

100

150

200

The axial force of the west composite beam The axial force of the east composite beam

500

Axial force(kN)

600

and east composite beam, respectively. According to the simplified analysis model, it is easy to calculate the resistances of the two-bay beams using Eqs. (1)–(4), where NW and NE are the axial forces of the west and east composite beams, respectively, and θ1 − θ4 are the beamend rotations of the west and east composite beams.

250

300

400 300

WUFG-0.6

200 100 Zero axial force

0 0

350

50

100

150

200

250

Failure column displacement(mm)

Failure column displacement(mm)

(a) Axial force

40 20

Side connection -B1 Middle connection -B3 Middle connection -B4 Side connection of -B6

0 -20 -40 -60 -80

0

50

100

150

200

250

300

350

Failure column displacement(mm)

400

WUFG-1.0

60

Bending moment(kN·m)

60

80

80

WUFG-1.4

Bending moment(kN·m)

Bending moment(kN·m)

80

40 20

Side connection -B1 Middle connection -B3 Middle connection -B4 Side connection of -B6

0 -20 -40 -60 -80

0

50

100

150

200

250

300

350

Failure column displacement(mm)

(b) Bending moment Fig. 13. Internal force development of the specimens. 8

WUFG-0.6

60 40 20

Side connection -B1 Middle connection -B3 Middle connection -B4 Side connection of -B6

0 -20 -40 -60 -80

0

50

100

150

200

250

Failure column displacement(mm)

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that of the axial force of section B2/B5. Compared with the curve of catenary mechanism resistance and the axial force development curve, the axial force developed significantly in the initial stage of loading (displacement less than 100 mm), while the resistance offered by the catenary action was relatively small, indicating that the development of the catenary action always lags with respect to the axial force. This is because the resistance offered by the catenary mechanism of the composite beam is determined by the axial force and the beam-end rotation. Therefore, it is necessary to ensure effective pull-up between the beamto-column members and the strong rotation ability of connections. Moreover, as can be inferred from the contribution coefficient of the resistant mechanism shown in Table 2, the flexural contribution coefficients of specimens WUFG-1.4 and WUFG-1.0 were ~70%, while that of the contribution of the catenary mechanism resistance was ~30%. Specimen WUFG-0.6 was prematurely completed owing to the insufficient strength of the weld connection between the cover plate and the failure column flange, resulting in an underdeveloped catenary action, which contributed only 13%.

Table 2 Contribution coefficients of the two-bay beams. Specimens

αF

βC

αFW

αFE

βCW

βCE

γ

ε

WUFG-1.4 WUFG-1.0 WUFG-0.6

0.71 0.72 0.87

0.29 0.28 0.13

0.30 0.31 0.59

0.41 0.41 0.28

0.13 0.13 0.09

0.16 0.15 0.04

0.43 0.44 0.68

0.57 0.56 0.32

PF = PV − PC = PFW + PFE = VW cos θ2 + VE cos θ3

(3)

PV = PW + PE = (PCW + PFW ) + (PCE + PFE)

(4)

Based on the principle of energy balance, the internal energy of the structure is composed of the internal energies from different mechanisms of the two-bay beams. To quantitatively analyze the contributions of different resistant mechanisms of two-bay beams to the total resistance, the corresponding contribution coefficients can be calculated using Eqs. (5)–(8). The results are shown in Table 2. v

v

αF = ∫0 PFdi dv / ∫0 Pdi dv = αFW + αFE v

v

v

= ∫0 PFWdi dv / ∫0 Pdi dv + ∫0 PFEdi dv / ∫0 Pdi dv v

4.2.2. Flexural resistance of two-bay beams The resistance provided by the flexural mechanism of the composite beam-column substructure is offered by the two-bay beams. From Eq. (3), the resistance offered by the west and east composite beams of the specimens are obtained, as shown in Fig. 16. The results showed that the ratios (αFW / αFE) of the contribution coefficients of the flexural resistance were approximately equal to the span ratios of the two-bay beams before the first fracture occurred. As the steel beam on one side of the specimens underwent fracture, the bending capacity of the damaged composite beam was greatly reduced. Furthermore, the resistance offered by the corresponding flexural mechanism decreased instantaneously, while the flexural resistance of the undamaged composite beam continued to play an important role during the large deformation stage.

(5)

v

βC = ∫0 PCdi dv / ∫0 Pdi dv = αCW + αCE v

v

v

v

= ∫0 PCWdi dv / ∫0 Pdi dv + ∫0 PCEdi dv / ∫0 Pdi dv

(6)

γ = αFW + βCW

(7)

ε = αFE + βCE

(8)

where αF and βC are the contribution coefficients of the flexural and catenary mechanisms, respectively; αFW and αFE are the flexural-mechanism contribution coefficients of the west and east composite beams, respectively; βCW and βCE are the catenary-mechanism contribution coefficients of the west and east composite beams, respectively; γ and ε are the contribution coefficients of the west and east composite beams, respectively.

4.2.3. Catenary mechanism resistance of two-bay beams The PC value contains two components, PCW and PCE , which are shown for all three specimens in Fig. 17. The contributions of the catenary mechanism resistance for the two-bay beams in the whole loading process are shown in Table 2. For specimen WUFG-1.4, the shorter beam bore more load and failed before the longer beam owing to larger beam-end rotation and a higher linear stiffness, causing underutilization of the catenary action of the long beam. For specimen WUFG-1.0, the resistance offered by the two-bay beams was similar to that before specimen fracture. When the tensile flange of the west beam broke, the resistance offered by the west beam dropped below that offered by the east beam. For specimen WUFG-0.6, owing to the insufficient strength of the weld between the long beam and failure column flange, the damage occurred earlier than in the short beam, causing underutilization of the catenary action of the long beam. Comparing the trends in Figs. 16 and 17, the two-bay beams of the

4.2.1. Flexural and catenary resistances Fig. 15 shows the development curves of the flexural and catenary resistance of the specimens, along with the vertical displacement of the failure column determined based on the simplified analysis model. It can be seen that in the initial stage of loading, the total resistance of the three specimens was almost entirely offered by PF . When a local fracture first appears in the specimens, the effective section of the beam end suddenly decreases, resulting in a rapid decline in PF , while PC increases rapidly at this time. This process describes a transition from the flexural to catenary mechanism, i.e., a transition stage. As the displacement of the failure column increases, PC gradually exceeds PF and plays a major role in offering resistance to the load. The development characteristics of the flexural mechanism curve were similar to that of the bending moment development curve of section B3/B4. However, the development characteristics of the catenary mechanism were different from Total load -PV

Total load -PV

400

By flexural action-PF By catenary action-PC

By catenary action-PC

300

300

200

200

100

100 Zero vertical load

0

WUFG-1.4 0

50

100 150 200 250 300 350 400

Failure column displacement(mm)

(a) Specimen WUFG-1.4

Zero vertical load

0

WUFG-1.0 0

50

100

150

200

250

300

350

Failure column displacement(mm)

(b) Specimen WUFG-1.0 Fig. 15. Resistant mechanism development of the specimens. 9

Total load -PV

500

By flexural action-PF

Vertical load(kN)

Vertical load(kN)

400

Vertical load(kN)

v

By flexural action-PF By catenary action-PC

400 300 200 100

Zero vertical load

0

WUFG-0.6 0

50

100

150

200

250

Failure column displacement(mm)

(c) Specimen WUFG-0.6

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200 150 100 50 0

By flexure action-PC

By flexure action of west composite beam(2100mm) -PFW

-50

-100 -150

Zero vertical load

By flexure action of east composite beam(1500mm) -PFE

0

50

WUFG-1.4

100 150 200 250 300 350 400 450

Failure column displacement(mm)

(a) Specimen WUFG-1.4

300 250 200 150 100 50

By flexure action-PC By flexure action of west composite beam(1500mm) -PFW Zero vertical load

0 -50

-100

By flexure action of east composite beam(1500mm) -PFE

0

50

100

150

200

250

WUFG-1.0 300

Failure column displacement(mm)

350

(b) Specimen WUFG-1.0

Vertical load by flexure action(kN)

250

Vertical load by flexure action(kN)

Vertical load by flexure action(kN)

W.-h. Zhong, et al. 450 400 350 300 250 200 150 100 50 0 -50 -100 -150

By flexure action-PC By flexure action of west composite Zero vertical load beam(900mm) -PFW By flexure action of east composite beam(1500mm) -PFE WUFG-0.6

0

50

100

150

200

250

Failure column displacement(mm)

(c) Specimen WUFG-0.6

Fig. 16. Flexural resistance development of the specimens.

three specimens provided flexural resistance mainly during the small deformation stage. When fracture of the beam bottom flange occurred near the failure column, the bending moment of the corresponding beam end decreased sharply, resulting in a significant decrease in the bending resistance. In such a scenario, the resistance of the catenary mechanism plays a major role and exceeds that of the flexural mechanism. There was no obvious reduction in the bending resistance of undamaged beams, and the external load was mainly resisted by the flexural and catenary mechanisms, which indicates asynchronism of the resistant mechanism of the two-bay beams.

are represented by truss elements (T3D2), the profiled decking is described by shell elements (S4R), and the other components are represented by the C3D8R elements with eight nodes and reduced integration. A dense fine mesh with a size of ~5 mm was used in the concentration zone. The actual stress-strain constitutive relationships of the steel components and reinforcing bars are defined according to the material properties shown in Table 1. The concrete damage plasticity model from ABAQUS is suggested for simulating the constitutive relationship of concrete. The tensile and compressive strengths in concrete material tests and stress-strain relationships are derived from the Chinese Code for Design of Concrete Structures Appendix C [19]. Integrated ductile metal damage criterion and the element delete method in ABAQUS are used to simulate the fracture of steel. The criterion defines the fracture strain, triaxial stress, and strain rate of the material required to cause fracture after reaching the fracture strain value [20,21]. It should be noted that the middle restraint of the side column needs to be connected to the fixed connection plate using an axial connection element in order to simulate the influence of peripheral members on the collapse resistance. The axial restraint stiffness provided by gantry mounting can be calculated according to the horizontal load displacement curve of the side-column middle-restraint point. Loading displacement was applied on the failure column at a slow rate and the boundary conditions of specimens are shown in Fig. 19.

4.2.4. Resistant mechanism of two-bay beams PW and PE values for the specimens calculated using Eq. (4) are shown in Fig. 18. The resistance contributions of the two-bay beams to the whole loading process are shown in Table 2. The results show that the long beam of specimen WUFG-1.4 did not fully exert a catenary action; however, as the long beam was not damaged, the flexural mechanism resistance of the long beam strongly contributed to the total resistance; the contribution of the longer beam was 43% and that of the shorter beam was 57%. The development of resistance in specimen WUFG-1.0 was similar to that in WUFG-1.4, and hence, will not be discussed further. The long beam of specimen WUFG-0.6 was damaged before the short beam. Thus, the flexural and catenary mechanisms of the long beam were not equal. The resistance contribution of the long beam was only 32%, which was around half of that in the short beam (68%).

5.2. Model validation A comparison of the results of the numerical model and the experimental tests for specimens with unequal spans is shown in Fig. 20. For specimens WUFG-1.4 and WUFG-1.0, the load-displacement curves obtained by numerical modeling were very close to the experimental results. In particular, the trends of sharp decreases and subsequent increases in the load are very similar. Owing to insufficient weld strength between the east beam and the failure column wall of specimen WUFG0.6, differences between the numerical simulation and experimental results are observed in the large-deformation stage. However, overall,

5. Numerical analysis 5.1. Finite element analysis model FEA models with unequal spans are developed using ABAQUS. For composite beam-column assemblies, the main components include steel beams, steel columns, a concrete slab, reinforcing bars, bolts, profiled decking, shear tabs, and cover plates. The reinforcing bars in the slab

Fig. 17. Catenary mechanism development of the specimens. 10

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Total load -PV The load by west composite Zero vertical load beam(2100mm) -PW The load by west composite beam(1500mm) -PE

0

50

WUFG-1.4

100 150 200 250 300 350 400 450

Failure column displacement(mm)

500 450 400 350 300 250 200 150 100 50 0 -50

Total load -PV The load by west composite beam(1500mm) -PW The load by west composite beam(1500mm) -PE

Zero vertical load

0

50

100

150

200

500 450 400 350 300 250 200 150 100 50 0 -50 -100 -150

Vertical load(kN)

Vertiacl load(kN)

400 350 300 250 200 150 100 50 0 -50 -100 -150

Vertical load(kN)

W.-h. Zhong, et al.

250

WUFG-1.0 300 350

Failure column displacement(mm)

Total load -PV The load by west composite Zero vertical load beam(900mm) -PW The load by west composite beam(1500mm) -PE

0

50

100

150

WUFG-0.6 200

Failure column displacement(mm)

250

Fig. 18. Resistance development of two-bay beams.

Fig. 19. Finite element analysis model.

Fig. 20. Comparison of load-displacement curves predicted by the FEA model and the actual curves experimentally.

column web through a high strength bolt of grade 10.9 M22 and a shear plate (L110 × 12 mm). The beam and column steel materials are Q235, with a nominal yield strength and tensile strength of 235 and 353 MPa, respectively; the strength-to-yield ratio is ~1.5. In addition, HPB300 hot-rolled steel bar with a nominal yield strength of 300 MPa was used as reinforcement. The concrete strength grade is C25, and the depth and width of the RC slab are 100 mm and 1500 mm, respectively, with a protective layer thickness of 20 mm. The slab was reinforced by two layers of 14-mm-diameter deformed bars along the longitudinal direction with 150 mm spacing and an upper layer of 8-mm-diameter deformed bars in the transverse direction with 200 mm spacing. Shear studs with a length of 19 mm were welded along the beam length with a spacing of 210 mm to transfer shear forces between the steel beams and concrete slab. The studs were arranged in a double row with a spacing of 150 mm, which achieved a full shear connection. The same FEA method as the one described in Section 5.1 was used.

the numerical results agree well with the experimental results. Fig. 21 shows simulated images of local fracture in the connection for comparison with the corresponding experimental results presented in Figs. 7–9. It can be seen that the failure processes predicted by the FEA model were similar to those observed experimentally, except for WUFG-0.6. Therefore, the numerical model can accurately simulate the fracture location and fracture development path of specimens, validating this modeling method. Thus, it is deemed reliable for predicting other behaviors of the assembly, as discussed in the following section. 6. Parametric studies 6.1. Full-scale model In order to investigate the composite effect and unequal height-span ratio affecting the behavior of the composite beam-column assemblies after column loss, a full-scale model of the substructure was designed with a 4500 × 7500 × 3300 mm structure. The cross-sections of steel beams and columns are H450 × 300 × 11 × 18 (mm) and HW400 × 400 × 13 × 21 (mm). The steel beam was connected to the

6.2. Composite effect Fig. 22 shows the influence of the concrete slab on the load11

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(a) Specimen WUFG-1.4

(b) Specimen WUFG-1.0

(c) Specimen WUFG-0.6 Fig. 21. Failure mode of specimens predicted by the FEA simulation. 2100

v=1137mm

v=447mm

1500

C1(478mm,1656kN)

1200

S2(1137mm,1118kN)

900 S1(447mm,1170kN) 600

WUFG WUFG-CS

300 0

0

200

400

600

800

900

939kN

600

231kN

300

69kN

0

Total load -PV

-300

By flexural action-PF

1200

0

1400

200

400

600

800

WUFG

(a) Vertical load-displacement curves

1218kN

900 600

438kN

300 -34kN

0

Total load -PV

1000

1200

By flexural action-PF By catenary action-PC

-600 1400

Failure column displacement(mm)

Failure column displacement(mm)

1200

-300

By catenary action-PC

-600

1000

Vertical load(kN)

1500

v=1220mm 1553kN

1500

1049kN

1200

C2(1220mm,1519kN)

Vertical load(kN)

Vertical load(kN)

1800

v=478mm

1800

0

(b) Resistance development of model WUFG

200

400

600

800

WUFG-CS 1000

1200

1400

Failure column displacement(mm)

(c) Resistance development of model WUFG-CS

Fig. 22. Influence of the composite effect on load-displacement behavior. Table 3 Comparison of the load at fracture points. Models

WUFG WUFG-CS Difference

Load at first fracture point (kN)

Load at second fracture point (kN)

P

PF

PC

P

PF

PC

1170 1656 41.5%

939 1218 23.8%

231 438 17.7%

1118 1519 35.9%

69 −34 −9.2%

1049 1553 45.1%

12

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Fig. 23. Influence of unequal spans on the load-displacement curves.

capacity of the first fracture was mainly due to differences in the flexural and catenary mechanisms. When the second fracture occurred, the flexural and catenary mechanism resistances of model WUFG were 69 kN and 1049 kN, while the corresponding values for model WUFG-CS were −34 kN and 1553 kN. As the axial force of the reinforcement contributes greatly to the total axial force under large deformation, the difference in the bearing capacity of the two models was mainly due to the catenary mechanism resistance. Therefore, the composite effect plays a key role in improving the bearing capacity over the whole loading process.

displacement curves of the substructure. It can be seen that the existence of the concrete slab effectively increased the initial stiffness and the bearing capacity over the entire loading process. The failure modes of the two models (WUFG-CS (with concrete slab) and WUFG (without concrete slab)) were as follows: the flange beam near the failure column fractured first, and then the tensile flange beam near the side column fractured. The load of the fracture points over the whole loading process of the two models are shown in Table 3. The first peak load of model WUFG-CS increased by 41.5% compared with WUFG, while the second peak load was increased by 35.9%. The resistance curves of the two models are shown in Fig. 22(b), (c). The flexural resistance and catenary resistance of model WUFG were 939 kN and 231 kN, respectively, while the corresponding values for model WUFG-CS were 1218 kN and 438 kN, when the beam bottom flange fractured. This is because the initial bending stiffness of model WUFG-CS was larger than that of WUFG, which resulted in a higher flexural mechanism resistance for WUFG-CS. In addition, the axial force of the reinforcement in the slab was relatively high when the tensile flange near the failure column fractured, resulting in the catenary resistance of the model WUFG-CS being higher than that of model WUFG. The difference in the bearing

6.3. Unequal height-span ratio of two bay-beams 6.3.1. Equal height with unequal spans of two-bay beams In the case of two-bay beams having unequal span and height-span ratios but equal height, the east composite beam is taken as a standard beam (span of 4500 mm, steel height of 450 mm). Furthermore, the span of the west composite beam (2700, 3600, 4500, 5400, and 6300 mm) was changed using a suitable range of height-span ratios. The load-displacement curves of these five models are shown in 13

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W.-h. Zhong, et al.

Fig. 24. Influence of unequal beam height on the load-displacement curves.

Fig. 23(a). Before the first fracture of the specimens, the initial stiffness and peak resistance of the flexural mechanism stage decreased as the span of the west beam increased. The resistances of the two-bay beams are shown in Fig. 23(b)-(i). As seen in Fig. 23(b), (c), it can be seen that the resistance provided by the catenary and flexural mechanisms increased continuously with decreasing span, except for WUFG-S1. The axial force of model WUFG-S1 did not develop owing to the excessive span ratio of the west beam, which resulted in the resistance provided by the catenary mechanism of the standard composite beam being much smaller than that of other specimens, as shown in Fig. 23(g). However, the flexural and catenary mechanism resistance of the west beam increased with decreasing height-span ratio, as shown in Fig. 23(d), (f). Therefore, decreasing the span of the composite beam can effectively increase the progressive collapse resistance under the flexural and catenary mechanisms, while an excessively short span is not conducive to displacement development of structures.

taken as the standard beam (span of 4500 mm, steel height of 450 mm). Various west composite beam heights of 290, 370, 450, 530, and 610 mm were used with a suitable range of height-span ratios. The load-displacement curves of these five models are shown in Fig. 24(a). Before the first fracture of the specimens, as the height of the west beam increased, the initial stiffness and peak resistance of the flexural mechanism stage increased. The resistances of the two-bay beams are shown in Fig. 24(b)-(i). Fig. 24(b), (c) show that the flexural resistance increased continuously with increasing west beam height, although there was little difference in the catenary resistance for each model. The difference in flexural resistance of each model was mainly reflected in the west composite beam, as shown in Fig. 24(d), (e), while there was little difference in the catenary resistance of the two-bay beam, as shown in Fig. 24(f), (g). Therefore, increasing the beam height effectively improved the progressive collapse resistance under the flexural mechanism, but had limited impact compared to that under the catenary mechanism.

6.3.2. Equal span with unequal height of two-bay beams Where the steel beam height and height-span ratio of two-bay beams are not equal but the span is equal, the east composite beam is 14

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7. Conclusions

Declaration of Competing Interest

In this paper, three specimens with unequal spans were tested until failure and the effect of the composite slab and height-span ratios under an internal column-removal scenario are systematically analyzed. The collapse mechanism and resistance of two-bay beams are investigated using full-scale FEA models. The following conclusions are made from analysis of the results:

We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled “Collapse resistance of composite beam-column assemblies with unequal spans under an internal column-removal scenario”.

(1) Three specimens exhibited similar deformation patterns when the fracture of the beam bottom flange occurred near the failure column, the bending moment of the corresponding beam end decreased sharply, resulting in a significant decrease in flexural resistance. In such a scenario, the resistance provided by the catenary mechanism played a major role and exceeded the contribution of the flexural mechanism. The reduction in flexural resistance of beams without damage was not obvious, i.e., the external load was mainly resisted by both the flexural and catenary mechanisms, which revealed the asynchronism of the resistant mechanism of two-bay beams. (2) In the low-deformation stage, as the span ratio decreased, the bearing capacity of the three specimens in the plastic stage increased, which in turn decreased the initial fracture displacement. This shows that increasing the span ratio significantly increased the bearing capacity of beams in the plastic stage of the structure but was not conducive to the development of structural displacement. (3) The contributing coefficients of resistance presented in this paper can be used to quantitatively assess the contribution of different resistant mechanisms to the total resistance of the two-bay beams with unequal spans. Compared with specimens of unequal spans, specimen WUFG-1.0 offered a much higher resistance in the largedeformation stage than in the flexural mechanism phase because of the synergistic effect between the two-bay beams. This shows that a structure with equal spans has a greater collapse-resistant bearing capacity in the large-deformation stage than one with unequal spans. (4) Specimens WUFG-1.4 and WUFG-1.0 showed contributions of ~70% and ~30% from flexural and catenary resistance, respectively, during the entire loading process. For specimens with equal spans, the catenary resistance for the shorter beam was larger than that for the longer beam, which indicated that the catenary action of the long-span beam was not significant. Therefore, the key design metric for the prevention of progressive collapse should focus on maximizing the catenary action of the longer beam. (5) The existence of slabs can significantly enhance the progressive collapse resistance over the entire process. The resistance of the composite beam-column assembly increased by 41.5% during the low-deformation stage and by 35.9% during the large-deformation stage compared to the assembly without a slab. The decrease of the span length effectively improved the progressive collapse resistance via the flexural and catenary mechanisms, although very short spans were not conducive to displacement development of the structures. Increasing the beam height effectively improved the progressive collapse resistance under the flexural mechanism but had a limited effect on the catenary mechanism.

Acknowledgements The authors gratefully acknowledge financial support from the National Natural Science Foundation of China (grant no. 51678476, 51608433) and Development Project of Shaanxi Province (grant no. 2018ZDXM-SF-097). Any opinions, findings, conclusions, and recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the sponsors. References [1] UFC 4-023-03. Design of buildings to resist progressive collapse. Washington DC: Department of Defense; 2013. [2] Kozlowski A, Gizejowski M, Sleczka L, Pisarek Z, Saleh B. Experimental investigations of the joint behavior-Robustness assessment of steel and steel-concrete composite frames. Proceedings of eurosteel conference, Budapest, Hungary. 2011. [3] Zhong WH, Meng B, Hao JP. Performance of different stiffness connections against progressive collapse. J Constr Steel Res 2018;135:162–75. [4] Yang B, Tan KH. Behavior of composite beam-column joints in a middle-columnremoval scenario: Experimental tests. J Struct Eng 2014;140(2):1–20. [5] Yang B, Tan KH, Xiong G, Nie SD. Experimental study about composite frames under an internal column-removal scenario. J Constr Steel Res 2016;121:341–51. [6] Guo LH, Gao S, Fu F, Wang Y. Experimental study and numerical analysis of progressive collapse resistance of composite frames. J Constr Steel Res 2013;89:236–51. [7] Shan S, Li S, Xu S, Xie L. Experimental study on the progressive collapse performance of RC frames with infill walls. Eng Struct 2016;111:80–92. [8] Fu QN, Tan KH, Zhou XH, Yang B. Load-resisting mechanisms of 3D composite floor systems under internal column-removal scenario. Eng Struct 2017;148:357–72. [9] Dinu F, Marginean I, Dubina D, Petran I. Experimental testing and numerical analysis of 3D steel frame system under column loss. Eng Struct 2016;113:59–70. [10] Ren PQ, Li Y, Lu XZ, Zhou YL. Experimental investigation of progressive collapse resistance of one-way reinforced concrete beam-slab substructures under a middlecolumn-removal scenario. Eng Struct 2016;118:28–40. [11] Yi WJ, Zhang FZ, Kunnath SK. Progressive collapse performance of RC flat plate frame structures. J Struct Eng 2014;140(9):04014048. [12] Qian K, Li B. Dynamic performance of RC beam-column substructures under the scenario of the loss of a corner column-Experimental results. Eng Struct 2012;42:154–67. [13] Qian K, Li B. Dynamic and residual behavior of reinforced concrete floors following instantaneous removal of a column. Eng Struct 2017;148:175–84. [14] Wei JP, Tian LM, Hao JP, Li W, Zhang CB, Li TJ. Novel principle for improving performance of steel frame structures in column-loss scenario. J Constr Steel Res 2019;163:105768. [15] GSA. Progressive collapse analysis and design guidelines for new federal office buildings and major modernization projects. Washington DC: United States General Services Administration; 2013. [16] GB50017-2017. Standard for design of steel structures. Beijing: Ministry of Housing and Urban-Rural Development, China; 2017. [17] JGJ 138-2016. Code for design of composite structures. Beijing: Ministry of Housing and Urban Rural Development, China; 2016. [18] FEMA-351. Recommended seismic evaluation and upgrade criteria for existing welded steel moment-frame buildings. California: Federal Emergency Management Agency; 2000. [19] GB50010-2010. Code for design of concrete structures. Beijing: Ministry of Housing and Urban Rural Development, China; 2010. [20] Yu HL, Jeong DY. Application of a stress triaxiality dependent fracture criterion in the finite element analysis of unnotched Charpy specimens. Theory Appl Fract Mec 2010;54(1):54–62. [21] Tian LM, Wei JP, Hao JP. Optimisation of long-span single-layer spatial grid structures to resist progressive collapse. Eng Struct 2019;188:394–405.

8. Author statement This manuscript has not been published or presented elsewhere in part or in entirety and is not under consideration by another journal. We have read and understood your journal’s policies, and we believe that neither the manuscript nor the study violates any of these. There are no conflicts of interest to declare.

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