Structure behavior of reinforced concrete beam-slab assemblies subjected to perimeter middle column removal scenario

Engineering Structures 208 (2020) 110336

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Structure behavior of reinforced concrete beam-slab assemblies subjected to perimeter middle column removal scenario

T

⁎

Jun Yua,b, , Li-zhong Luoa,b, Qin Fangc a

Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing 210098, China College of Civil and Transportation Engineering, Hohai University, Nanjing 210098, China c Army Engineering University of PLA, Nanjing 210007, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Progressive collapse Reinforced concrete Beam-slab assembly Column removal scenario Tensile membrane action Catenary action

The perimeter columns of framed structures are more vulnerable to terrorist attacks due to accessibility. The beams and slabs above the damaged columns are the primary structural members to redistribute gravity load to avoid progressive collapse. Therefore, to investigate the structural behavior of reinforced concrete (RC) beamslab assemblies against progressive collapse introduced by a perimeter middle column removal scenario, an experimental program and numerical analyses were carried out in this paper. Three 3/10 scaled specimens, each of which consisted of two square slab panels and seven beams, were tested with equivalent uniformly distributed loading (UDL) achieved by a 12-loading apparatus. High-fidelity finite element models were used to conduct parametric studies after the validation, recheck the validity of the loading apparatus and highlight the effect of loading positions. The concerned parameters include the geometric parameters of beams caused by different seismic design intensity, the slab thickness and reinforcement ratio, and the type of reinforcing bars (i.e. deformed and plain). The results indicate that progressive collapse is resisted by compressive arch action and flexural action of the beams and slabs connecting the stub above the removed column at small deformation stage, whereas catenary action of longitudinal beams and tensile membrane action of slabs are more prevailing at large deformation stage. Moreover, higher seismic design intensity results in a larger resistance at small deformation stage, and plain bars cause larger deformation capacity. Finally, loading positions approaching the stub above the removed column tends to show smaller structural resistance.

1. Introduction With the increasing threats from terrorist attacks and the growing interest in robustness of structures, progressive collapse performance of structures becomes the concern of government agencies and structural engineers. As it is difficult to quantify the threats or accidents, threatindependent approaches through single column removal scenarios (CRS) to conduct progressive collapse analysis are preferred and adopted by design guidelines [1–3]. Out of a framed structure, beam-column substructures directly above the removed column are regarded as the most critical structural elements to redistribute the gravity load. As a result, a great many researches have been dedicated to structural behavior of reinforced concrete (RC) beam-column assemblies and frames under CRS, including single-story two-bay beams [4–7], single-story frames [8–12], and multi-story frames [13–16]. The results demonstrated that if adequate laterally restraints are provided at the beam ends, RC beams have

⁎

large potential resistance on top of conventional flexural capacity corresponding to plastic hinge mechanisms. Moreover, although progressive collapse is a dynamic response in nature, it inherently correlates with quasi-static behavior of structures, and thus nonlinear structural resistance can be converted to dynamic resistance of structures through energy method [17], dynamic load amplification factor [18,19] or single degree of freedom method [20] etc. In recent years, it is realized that ignoring slabs could significantly underestimate the progressive collapse resistance of structures. Consequently, more researches have been conducted on structural behavior of RC beam-slab assemblies under different CRS [10,21–28], which results in different boundary conditions and involved slab panels to the concerned beam-slab assembles. Among various CRS, perimeter columns are more vulnerable due to their accessibility. The most famous case is the progressive collapse of Murrah Federal Building in Oklahoma City after a truck explosion blew away the perimeter middle (PM) columns. Lu et al. [27] conducted an experimental program on RC

Corresponding author at: Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing 210098, China. E-mail address: [email protected] (J. Yu).

https://doi.org/10.1016/j.engstruct.2020.110336 Received 17 July 2019; Received in revised form 17 January 2020; Accepted 1 February 2020 0141-0296/ © 2020 Elsevier Ltd. All rights reserved.

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J. Yu, et al.

beam-slab assemblies and corresponding beam specimens under a PM CRS with concentrated loading and fixed boundary conditions. Lim et al. [10] tested a beam-slab substructure and a corresponding 3D bare frame with concentrated loading. The columns of the substructure and the frame were restrained. The RC beam-slab assemblies in the above two reports failed with severe damage near the middle column stub, and the results indicate that the presence of slabs significantly improved structural resistance and the primary load transfer mechanism is beam action and catenary action at small and large deformation stage, respectively. Yu and Luo [28] tested an RC beam-slab assembly under a PM CRS with uniformly distributed loading (UDL). The specimen was supported by pin connected steel columns with three sides restrained by steel beams and a series of inclined rods. The results show that the specimen failure was governed by the severe damage at the longitudinal beam ends near a supporting column. However, the slab edges were quite flexible in rotation, and further improvement of test-up is required. It should be pointed out that as beam-slab assembles are typically scaled in testing, and the plain bars are used as longitudinal bars [10,27], whereas in the current engineering practice in China, deformed bars are prevailingly used in slabs. The effect of bar type on the progressive collapse resistance of beam-slab assemblies is not clear. Up to now, there is no standard loading approach to test static progressive collapse resistance of structures. Take a beam-slab assembly of a regular framed structure for example. Before a column removal, a UDL exists on slabs and supporting columns are in axial compression accordingly. When a column is suddenly removed, the corresponding support force is immediately diminished and the axial force of all the columns above the removed column is diminished within the scale of milliseconds [29]. For the concerned beam-slab assemblies, this process can be represented by suddenly applying a downward concentrated load at the column stub to counterbalance the original net support force, i.e. the difference of the axial force of the removed column and the upper story column. Following the column removal, the eventual loading pattern for the beam-slab assembly is the original UDL. In summary, the loading for the concerned beam-slab assembly is service load (including UDL and net upward supporting force) plus a sudden downward concentrated load and immediately becomes UDL. The dynamic response is induced by the concentrated load, and meanwhile the beam-slab assembly should be able to redistribute the corresponding UDL. Moreover, the sudden downward load is equal to the net upward supporting force, which is the product of the UDL multiplied by the corresponding tributary area. According to the above-mentioned loading variation, three loading approaches are used in testing progressive collapse behavior of beamslab assemblies. The most realistic approach is simulating the entire procedure of loading variations. This is achieved by initially putting weights uniformly onto the top surface of the assemblies and replacing the removed column with a jack to support the stub. After the system is in equilibrium, the reaction of the jack is gradually decreased to zero and the ultimate displacement of the corresponding column stub is recorded. Through repeating the above procedure, it is able to construct a structural resistance curve. For example, Yi et al. [22] experimentally investigated the progressive collapse resistance of RC flat plate specimens with such a loading approach. Under an interior CRS, they applied UDL through placing sand bags for six rounds from 10.25 kN/m2 to 20.5 kN/m2, but the specimen showed no failure and they eventually used concentrated loading to achieve the specimen failure. It seems that this loading approach is too expensive for quasi-static tests, but it is very suitable for dynamic tests because the latter requires just one loading cycle. For instance, Xiao et al. [24] uniformly placed load weights on all the slabs of a two-story 1/2 scaled three-dimensional RC framed structure and then obtained the dynamic response of the structure under specified CRS. The second approach is focusing on how beam-slab assemblies rebalance UDL after a column removal and thus using a loading-tree apparatus (typically 12 loading points) to achieve an equivalent UDL

6000

6000

6000

6000

6000

6000

6000

6000

6000

6000

Removed perimeter column

Region to be tested

Fig. 1. Plan view of the prototype frame (unit: mm).

[21,23,26,28]. Through the loading tree, a point load is transferred into multiple points, and it is much easier to keep loading to obtain structural resistance. However, the determination of loading point locations is not illustrated, and the effectiveness of the loading apparatus at large deformation stage is not quantified as well. The last approach is achieved by applying a concentrated load at the stub above of the removed column [10,25,27], which is only concerned with the effect of sudden applied load but ignoring the existence of service load. In fact, the former is proportional to the total load of the latter. Under PM CRS, the failure modes of beam-slab assemblies under a UDL [28] is quite different from those under a concentrated load [10,27]. Yu et al. [30] numerically compared the above-mentioned three loading approaches, and pointed out that structural resistance with the first and second loading approach is similar and the concentrated loading approach underestimates the structural resistance. Therefore, applying equivalent UDL is the best solution to seek realistic loading, structural resistance, failure modes and testing cost of beam-slab assemblies against progressive collapse. As specimens in progressive collapse tests are typically limited, numerical analysis with finite element (FE) method is often employed for investigating the resistance of substructures. Macro-based FE models with beam elements are computationally-efficient in calculating the resistance and the internal forces of beam-column assemblies and frames as well as global responses of entire structures [31–35]. On the other hand, high-fidelity FE models with solid elements are more capable of demonstrating the failure modes and load transfer mechanisms in details besides the resistance, which is more suitable for two-dimensional structural elements such as infill walls [36] and slabs [30,37]. Therefore, high-fidelity FE models are used in this paper. To more feasibly and realistically demonstrate the structural behavior of RC beam-slab assemblies under a PM CRS, an experimental program was carried out with an improved static-determinate test setup. Three 3/10 scaled RC beam-slab assemblies were fabricated and quasi-statically tested with approximate UDL achieved by 12-loading apparatus. The concerned parameters included seismic design intensity and bar types (i.e. deformed or plain). The experimental results are presented in terms of overall structural resistance, crack patterns, failure modes, the distribution of reaction forces and strains of beam and slab reinforcement to provide a more deep understanding toward the load transfer mechanisms of the beam-slab assemblies in a PM CRS. Thereafter, high-fidelity finite element models are built, validated with experimental results, and then further used to investigate the effects of geometric parameters of the specimens and loading positions on the structural behavior of RC beam-slab assemblies. In particular, the validity of the 12-loading apparatus is rechecked and the effect of loading 2

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Table 1 Geometric parameters of prototype and scaled specimens. Parameters

Prototype 1

Scaled specimen 1

Prototype 2

Scaled specimen 2

Seismic design intensity Beam section (mm × mm) Column section (mm × mm) Slab thickness (mm) Beam span (mm) Slab cover thickness (mm) Beam cover thickness (mm)

6 deg (PGA = 0.05 g) 500 × 300 550 × 550 180 6000 20 25

150 × 90 180 × 180 54 1800 6 10

8 deg (PGA = 0.2 g) 600 × 300 600 × 600 180 6000 20 25

180 × 90 180 × 180 54 1800 6 10

4600

470

50

500

Beam KL2

Slab flange h=100mm T(R)6@160 Top Reinf.

Slab flange h=100mm

Column2

500

1800

1800

500

500

Beam KL2

Column3

Column4

Y

T(R)6@160

T(R)6@160

Top Reinf.

Top Reinf.

Column1

2300 1800

Slab h=54mm

500

470

500 T(R)6@160 Top Reinf.

Column5

Beam KL1

X

Beam KL3

Beam KL3

Bottom Reinf.

Slab h=54mm

Bottom Reinf.

500

50

T(R)6@160

Beam KL3

Hole

T(R)6@160

Removed edge column

Beam KL1

Fig. 2. Layout of beam-slab specimen (unit: mm).

2300

A

A

500

R4@160 480 1800

A A

B C B

C

Beam KL1

90

3T(R)8

2T(R)8

A-A

2T(R)8

R4@160 480 1800

B C

C

R4@80 560

Beam KL2 R6@70

500 R6

nut

8T12(M12 threaded bolt) R6@70 180

150

96 54

150

96 54

2T(R)8

B

A

R4@80 560

R4@80 560

1130

A

D

90

180

B-B

C-C

57 70 70

A

295

A

R4@80 560

2300

630

D

D-D

Fig. 3. Reinforcement detailing in the beams of S1(3) (unit: mm).

slab assemblies, three specimens were designed in accordance with Chinese code for concrete structures [38] and seismic design of buildings [39]. The prototypes of the specimens are located in a ten-story RC framed structure with 6 spans and 4 bays at each plan. The story height is 3.3 m and 3.0 m for the first story and the rest stories, respectively. The span length at the two orthogonal directions is 6 m. The dead load and the live load used for structure design are 5.0 kN/m2 and 2.0 kN/

positions is highlighted 2. Experimental program 2.1. Specimen design To investigate the progressive collapse performance of RC beam3

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35

Table 2 Reinforcement detailing of specimens. Beam KL1 Ends Top

Bottom

30

Beam KL2 and 3 Mid-span

Ends

Top

Top

Bottom

Mid-span Bottom

Top

25

Stress (MPa)

Specimen

Concrete cylinder-1 Concrete cylinder-2 Model- default parameters Model- Calibrated parameters

Bottom

S1

2T8 2T8 R4@80

2T8 2T8 R4@160

3T8 2T8 R4@80

2T8 2T8 R4@160

S2

3T10 2T10 R4@50

2T10 2T10 R4@100

3T10 3T10 R4@50

2T10 3T10 R4@100

20 15 10 5

m2, respectively. The seismic intensity of 6 deg and 8 deg corresponding to the peak ground acceleration (i.e. PGA) of 0.05 g and 0.2 g is considered, respectively. After a PM column at the ground story is removed, the directly affected region is the one enclosed by the red box, as indicated in Fig. 1. As the affected floors are identical in terms of structure and loading, a single story floor system is quite representative [17]. Due to the space limit in the laboratory, the specimens were scaled down from the prototype with a factor of 3/10 and the same reinforcement ratios. Accordingly, the geometric parameters of primary structural members in the prototypes and the specimens are listed in Table 1. As the columns of the beam-slab assemblies were made as a stub and connected to steel supporting columns, for simplicity they were all taken 180 mm by 180 mm for the three specimens. The three specimens are denoted as S1, S2 and S3, respectively. S1 and S2 were scaled down from prototype 1 and 2 designed with seismic intensity of 6 deg and 8 deg, respectively. Therefore, the comparison of S2 and S1 is able to demonstrate the effect of seismic design intensity on structural behavior against progressive collapse. Both S1 and S3 were scaled down from prototype 1, but the deformed and plain reinforcing bars were used in S1 and S3, respectively, of which the comparison is able to show the effect the bond behavior of reinforcement. All the three specimens shared the same plan dimensions and slab reinforcement detailing, as shown in Fig. 2. Each specimen consisted of two slab panels, two longitudinal beams KL1 and two KL2 in X-direction, and three transverse beams KL3 in Y-direction, as well as the slab flanges along the three boundaries that were used to represent the continuity of slabs across the boundary beams. The single span in each direction was 1800 mm, and the thickness of the slab panel was 54 mm. To improve the anti-torsional capacity of the slab flanges which were used to represent the rotational restraints from the adjacent panels, the corresponding slab thickness was increased to 100 mm and the cantilever length was taken as 500 mm. The reinforcing bars with diameter of 6 mm were orthogonally placed at the bottom of the entire slab panels with a center-to-center spacing of 160 mm. The distance from the inner side of the beams to the adjacent slab bar was 55 mm. The top slab reinforcing bars were placed across and perpendicular to the beam axis with a spacing of 160 mm as well. Moreover, the top bars were extended into and anchored in the slab flanges. For specimen S1 an S2, the slab reinforcement was ribbed bars (denoted by letter “T”), whereas for specimen S3 the slab reinforcement was pain bars (denoted by “R”).

0 0.0000

0.0025

0.0050

0.0075

0.0100

0.0125

0.0150

Strain (H) Fig. 4. Uniaxial compressive stress-strain relationship of concrete based on standard cylinder tests.

In addition, at each mid-span which was 50 mm away from the free edge, a hole with the diameter of 22 mm was cast to hang weights during the test, representing the effect of the gravity load applied at the adjacent slab panels on the rotational restraints to the slab panels above the removed column. Fig. 3 demonstrates the reinforcement detailing of beams and columns in specimen S1. There were 8 T12 bars in each column with stirrups of R6@70 mm. All the beams had the same cross-sectional dimensions (150 mm × 90 mm) and the arrangement of stirrups. The closed hoops R4 were placed at the beam ends with spacing of 80 mm to increase confinement to concrete and the corresponding ductility, and 160 mm at the mid-span. For the perimeter beam KL1, the reinforcing bars with 2 T8 were throughout both the entire top and the bottom layer. For the other beams, the bottom bars were 2 T8, and the top bars were 3 T8 at the joint region with the middle bar curtailed at 630 mm from the adjacent column axis. Note that specimen S3 had the same detailing as S1, except the bar types. In comparison, all the beams in S2 was 180 mm in depth and 90 mm in width. The reinforcement detailing at critical sections of S1 and S2 is listed in Table 2. 2.2. Material properties Table 3 listed the material properties of reinforcing bars. The uniaxial compressive strength of concrete was 31.08 MPa in accordance with the tests on the standard cylinders (150 mm in diameter and 300 mm in height). Moreover, Fig. 4 shows the experimental compressive strain-stress relationships of concrete. 2.3. Test set-up Fig. 5 demonstrates the test set-up of RC beam-slab assemblies under PM CRS. Similar to previous work [28], the UDL was achieved by

Table 3 Mechanical properties of reinforcing bars. Type

Diameter (mm)

Elastic modulus (MPa)

Yield strength (MPa)

Yield strain (με)

Tensile strength (MPa)

Elongation ratio*

Deformed bar

10 8 6

183,499 183,161 192,215

481 488 511

2623 2664 2658

648 623 607

28.60% 28.22% 26.64%

Plain bar

8 6 4

219,857 231,794 172,637

364 493 591

1655 2127 3008

536 690 649

33.82% 33.33% 13.40%

* The elongation ratio is determined based on the original gage length 5 times bar diameter. 4

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Fig. 5. Test set-up.

Fig. 6. Positions of loading system (unit: mm).

beams through steel bolts. Each end of the secondary distribution beam was seated onto the centroid of a triangular steel plate through a balland-socket connection. Three vertices of each triangular plate were placed onto the specified position of the slab surface with hex bolts, steel loading plates and rubber mats. To prevent the hard contact between the hex bolts and the concrete, which was very likely to punch the RC slab, the square loading plates and rubber mats with the

a 12-loading-point apparatus, consisting of a reaction frame, a hydraulic jack, a primary and two secondary distribution beams, four triangular steel plates and additional connections. During the test, the two ends of the hydraulic jack was connected to a reaction beam of the portal frame and the primary distribution beam through one-way pin connections, respectively. The ends of the primary distribution beam were connected to the middle span of the two secondary distribution 5

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320

S1

280

S3

Punching of slab

240

Load (kN)

S2

200 160 120 Rebar rupture Crushing of concrete at beam ends First peak resistance- Fp Ultimate load-Fu

80 40 0 0

Fig. 7. Details of steel column support and inclined restraint.

50

100

150

200

300

350

400

450

Fig. 9. Load displacement curve of RC beam-slab assemblies.

perimeter of 280 mm were inserted between the hex nuts and the concrete surface. Each loading point coincided with the centroid of 1/ 12 area of the slab surface, as illustrated in Fig. 6. Similar to Qian’s work [40], the restraints from the adjacent spans to the beam-slab assembly were equivalently achieved by connecting the assembly to the fixed steel columns. As a result, each assembly was supported by five steel columns with the height of 500 mm and the circular hollow sections, of which the outer diameter was 140 mm and the thickness was 14 mm, as shown in Fig. 7. The top end of the supporting column was connected to a beam-column stub and the bottom end was connected to the ground beams which were anchored onto the strong floor. These steel columns were able to provide reaction forces in terms of axial forces, lateral shear forces and bending moments. The labels of the supporting columns were shown in Fig. 8, in which C1 and C5 indicate the columns at the ends of the longitudinal perimeter beams, and C3 the column at one end of the transverse beam. Specimen S2 was the first one for test, and during the test, the mobilization of catenary action of perimeter beams and tensile membrane action of slabs caused the yielding and weld damage of the supporting columns C1 and C5, resulting in the resistance of S2 unable to further increase. Therefore, in the following test an inclined restraint, namely, IC1 and IC2, was respectively connected to C1 and C5 to improve lateral restraint stiffness. IC1 and IC2 were made of two segments of steel hollow tubes connected to a tension/compression load cell at

Table 4 Critical structural resistance and corresponding displacement. Specimen

S1 S2 S3

First peak resistance

Minimum value of softening state

Ultimate load

Fp (kN)

Dp (mm)

Fm (kN)

Dm (mm)

Fu (kN)

Du (mm)

213 289 187

59 77 60

158 – 153

173 – 192

253 – 253

348 – 425

Fu/Fp

1.188 – 1.353

the center. Moreover, one end of the inclined restraint was pinned to the steel column and the other end was pinned to the ground beam, as shown in Fig. 7. Both the continuity of the slabs from the directly affected region to the adjacent bays and the gravity applied at the adjacent bays could help to restrain the boundary rotation of the beam-slab specimens. As a result, the former was achieved by increasing the thickness of slab flanges to improve torsional stiffness, and the latter was achieved by hanging weights of 3.1 kN at the middle span of each slab flange.

C3

C2

C1

C4

C5

BL

250

Vertical displacement of middle column stub (mm)

BL BL B BL B B B BL VV LV LV VV LV LV 002 -004 -006 -008 009 -007 -005 -003 001

V-

Fig. 8. Scheme of intrumentation. 6

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The vertical displacement is 10mm

The vertical displacement is 60mm

The vertical displacement is 180mm

(a)

(b) Fig. 10. Cracking patterns and failure mode of the perimeter beams of S1: (a) Cracking patterns; (b) Failure mode.

The vertical displacement is 12mm

The vertical displacement is 72mm

(a)

The vertical displacement is 240mm

(b) Fig. 11. Cracking patterns and failure mode of the perimeter beams of S2: (a) Cracking patterns; (b) Failure mode.

2.4. Instrumentation

3. Experimental results

Besides the applied load, the vertical reaction forces, the beam deflections, and the strains of reinforcement in beams and slabs were measured as well to illustrate the load transfer mechanisms of beamslab assemblies under a PM CRS. To obtain the vertical reaction force of each supporting column, a series of strain gages were attached at the mid-height section of the steel column to work as a load cell. Displacement transducers (namely, BLV-001 ~ 009 as shown in Fig. 8) were installed to record the vertical deflection of the two perimeter beams. The critical beam sections, at which the strains of steel reinforcement were measured, are denoted from A to I as shown in Fig. 8.

3.1. Load-displacement curves Fig. 9 demonstrates the load-displacement curves of the three specimens, in which the displacement was taken from the measurement of BLV-001, i.e., the vertical displacement of the middle column stub or middle joint displacement (MJD). Basically, all the three specimens developed resistance to the first peak, followed by a softening resistance, and then a re-ascending resistance. The softening resistance of specimen S1 and S3 was caused by the concrete crushing at the longitudinal and transverse beam ends near the supporting columns C1, C3 and C5. However, the softening resistance of S2 was ascribed to the 7

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The vertical displacement is 10mm

The vertical displacement is 60mm

(a)

The vertical displacement is 195mm

(b) Fig. 12. Cracking patterns and failure mode of specimen S3: (a) Cracking patterns; (b) Failure mode.

Vertical displacement (mm)

0

100

200

300

400 -1800

Intial stage Yield of top rebar at beam ends (155kN) First peak resistance (187kN) Minimum resistance in softening state(153kN) Ultimate resistance (253kN)

-1500

-1200

-900

-600

-300

0

300

600

900

1200

1500

1800

Relative postion to the middle column stub center (mm) Fig. 13. Deflection profiles of the perimeter beams of S3.

ultimate load was around 253kN. However, the corresponding ultimate displacement of S1 and S3 was 343 mm and 434 mm, respectively. The test on S1 was terminated due to bar fracture, whereas the test on S3 was finished due to the middle column stub nearly contacting the ground beams. This means the ultimate deformation capacity of S3 could be even larger than the current test result. The larger deformation capacity of S3 was attributed to the facts that (1) the plain bars have larger elongation ratio than the deformed bars, and (2) the plain bars are more easily slipped due to weaker bond strength.

concrete crushing and the supporting column failure. Therefore, the post-peak resistance of S2 is not used for further analysis. The load and the corresponding MJD at the critical points are listed in Table 4. The ultimate load of the re-ascending structural resistance of S1 and S3 due to catenary action (CTA) of longitudinal beams and tensile membrane action (TMA) of slabs significantly exceeds the first peak resistance. The comparison of pre-peak load-displacement curves of S1 and S2 shows that the peak resistance of S2 (289kN) was 35.68% greater than the one of S1 (213kN), suggesting that the design with higher seismic intensity is beneficial to increase progressive collapse resistance at small deformation stage. This is because higher seismic intensity results in larger beam sections, more beam reinforcement and greater flexural stiffness of beams. For a given span, increasing beam depth reduces beam span-to-depth ratio, which is very positive to develop compressive arch action (CAA) of RC beams [41]. Specimen S3 and S1 shared the same geometric properties except the type of reinforcing bars. The peak resistance of S1 (213kN) with deformed bars is 1.139 times that of S3 (187kN) with plain bars. This is mainly because the yield strength of plain bars was lower than that of deformed bars, as seen in Table 3. After the softening, both S1 and S3 could develop structural resistance beyond the first peak, and the

3.2. Cracking pattern and failure modes The cracking patterns and failure modes of the longitudinal perimeter beams of S1 ~ 3 were demonstrated in Fig. 10, Fig. 11 and Fig. 12, respectively. For each specimen, the crack patterns at the four vertical displacements are presented, corresponding to 1/15 section depth, around Dp, Dm and Du, respectively, in which the definition of Dp, Dm and Du are shown in Table 4. It is observed that the cracks initially occurred near the beamcolumn interfaces, i.e. section A, C, D and F. Near section C and D, the cracks initiated from the beam bottom to the top, indicating the 8

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Fig. 14. Failure modes of transverse beams: (a) Specimen S1; (b) Specimen S2; (c) Specimen S3.

Plastic hinge

Plastic hinge

Loading plate

Y

(a)

Y

(b)

X

Plastic hinge

Plastic hinge

Loading plate

Y

Y

(a)

X

(b)

X

X

Fig. 15. Cracking pattern of the slabs of S1 and S3 at failure stage: (a) Top surface of slabs in S1; (b) Bottom surface of slabs in S1: (c) Top surface of slabs in S3; (d) Bottom surface of slabs in S3.

9

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X

C5

300

C1 C2 Load-displacement curve C3 C4 C5

100 80

240

75

180

50

120

25

60

300

IC1 IC2

Load-displacement curve

240

60

180

40

120

20

60

0

0

-20

-60 Catenary mechanism

CAA mechanism

0 0

(a)

50

100

150

250

300

350

0 400

-40

100

Y

C1

X

C4

C5

80

200 150

40

100

20

50

100

150

(b)

0

80

160

240

320

400

250

300

350

Load-displacement curve

240

60

180

40

120

20

60

0

0

-20

0 480

-60 Catenary mechanism

-40

(b)

Vertical displacement of middle column stub (mm)

-120 400

300 IC1 IC2

CAA mechanism

0

200

Vertical displacement of middle column stub (mm)

80

250

60

50

100

300

C1 Load-displacement curve C2 C3 C4 C5

Axial reaction (kN)

C3

Load (kN)

C2

0

(a)

Vertical displacement of middle column stub (mm)

120

Axial force (kN)

200

Load (kN)

Y

C1

C4

Load (kN)

Axial force(kN)

100

C3

Axial reaction (kN)

C2

Load(kN)

125

0

80

160

240

320

400

-120 480

Vertical displacement of middle column stub (mm)

Fig. 16. Vertical reactions of supporting columns: (a) Specimen S1; (b) Specimen S3.

Fig. 17. Axial reactions of inclined restraints: (a) Specimen S1; (b) Specimen S3.

mobilization of sagging moment. When the displacement reached Dp, the inclined cracks developed from the beam top to the bottom near section A and F, reflecting the development of hogging moment and shear force at the beam ends, and moreover, the concrete at the bottom of beam ends started to crush and spall. With further increasing MJD, the number of cracks gradually increased, the existing cracks became wider near section A and F, and the concrete at the bottom of beam ends severely crushed. As a result, the beam ends formed plastic hinges and contributed large rotations. Meanwhile, in the beam segments near section A, B, E and F, a great many cracks went through the entire beam sections from the bottom, suggesting the mobilization of axial tension in the beams and the development of CTA. At the ultimate state, the failure modes demonstrate that the distribution of cracks at the both sides of the middle column stub is very symmetric. Except the beam ends near section A and F, the cracks in the rest beam segments were all initiated from the beam bottom, and became inclined when reached the beam top. This is because the vertical movement of the middle column stub was restrained by the transverse beam and torsion was motivated in the longitudinal beams. The beam ends near section A and F sustained combined action of hogging moment, shear force and torsion. Consequently, the concrete severely cracked and spalled, making the longitudinal bars and stirrups exposed. As the beam depth of S2 was the largest, the cracks were the most severe to accommodate the required deformation. Although S3 deformed more than S1, less cracks occurred in the perimeter beams of S3 due to weak bond. For simplicity, only the deflection curves of specimen S3 at different critical instants are demonstrated in Fig. 13. It is seen that S3 deformed

in a very symmetric manner at both sides of the middle column stub. Moreover, the slopes of the deflections at the beam ends are much larger than those near the middle column stub, indicating much larger local rotations at the beam ends. Accordingly, the local failure at the beam ends near the supporting column were more severe than that near the middle column stub. Fig. 14 shows the failure modes of the transverse beam of the three specimens. A plastic hinge with severe concrete spalling and crushing together with compression reinforcement buckling was formed at the beam end near section I, which was supported by column C3. The transverse beam rotated around the plastic hinge, and the middle column stub was pulled in Y-direction, further introducing torsion to the longitudinal perimeter beams. Except beam end near section I, the cracks in the rest beam segments basically started from the beam bottom to the top, suggesting the development of sagging moment. Due to weak bond of plain bars, the number of cracks in the transverse beam of S3 was less than those of S1. Fig. 15 demonstrates that the crack patterns of the slabs of S1 and S3 were similar at the end of the test. Generally, the distribution of cracks was very symmetric. As shown in Fig. 15(a) and (c), the cracks at the top slab surface were distributed along the inner side of the boundary beams, indicating the development of hogging moment. Moreover, the cracks at the top surface were intensively distributed in the area between the outer six loading plates and the neighboring transverse boundary beams. However, the cracks near the middle column stub were very rare. As illustrated in Fig. 15(b) and (d), the cracks were extensively distributed at the entire bottom surface of the slab panels. In particular, 10

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hinge near section I. This suggests that the transverse beam and the corresponding slab regions were able to transfer a very large proportion of load through the flexural action. However, with further increasing displacement, the axial forces in column C1 and C5 became the largest, indicating the predominance of CTA of the perimeter beams and TMA of the slabs. Fig. 17 elucidates the development of the axial reaction of IC1 and IC2, in which the positive and negative values denote axial tension and compression, respectively. Prior to the displacement of 125 mm and 142 mm for S1 and S3, respectively, inclined restraints sustained axial compression, indicating the development of CAA of the perimeter beams. With further increasing vertical displacement, the axial tension of inclined restraints kept increasing, suggesting the development of CTA and TMA in the longitudinal direction. The presence of slabs makes beams evolve into CTA at the displacement around 20% less than one beam depth. However, the mobilization of CTA was unable to immediately improve structural resistance, because at that moment the softening of structural resistance due to concrete crushing at the beam ends of the transverse beam was more dominant. Fig. 18(a) and (b) demonstrate the proportion of reaction forces to the total reaction force for specimen S1 and S3, respectively. For the two specimens, C2 and C4 totally contributed around 15%~20% reaction forces. Prior to the displacement of 50 mm, the contribution of column C3 and the sum of C1 and C5 were quite comparable. Thereafter, with increasing the vertical displacement, the contribution of the sum of C1 and C5 kept increasing from around 45% to 55%, whereas the reaction provided by column C3 kept decreasing from around 40% to 30%. This indicates that at small deformation stage (prior to displacement of 50 mm), the applied vertical load were mainly transferred to the supporting columns through longitudinal beams and the transverse beam as well as corresponding slabs, whereas at the large deformation, the longitudinal perimeter beams and the corresponding slabs are the primary load transfer path and the transverse beam still contributed a considerable proportion of resistance.

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Vertical displacement of middle column stub (mm) For simplicity, specimen S3 was used to demonstrate the readings of strain gages of steel reinforcement inside the slabs and at critical beam sections. Fig. 19 shows the strain distribution along the perimeter beams at different vertical displacement of middle column stub (MJD). As the bar strains at section E was not monitored, it is assumed the bar strains at section E is the same as those at section B due to symmetry. Prior to the first peak resistance, the strain distribution is demonstrated every 1/10 beam depth, and thereafter it is shown every beam depth until the ultimate stage. Note that at large deformation stage, some strain gages lost functions due to fracture of wires, in particular at the regions with plastic deformations. Fig. 19(a) and (b) demonstrate the strain distribution of top and bottom reinforcement of the perimeter beams, respectively. It is seen that the strains at section A, F, C, and D near the beam-column interfaces increased much more quickly than those at mid-span section B and E. At section A and F, the top reinforcement was always in tension and yielded from MJD of 30 mm, and the available data indicate bottom reinforcement in compression even beyond yield strain from MJD of 45 mm. This indicates hogging moment was very dominant at the beam ends. At section C and D, the bottom reinforcement was always in tension and yielded after MJD of 15 mm, whereas the top reinforcement changed from compression to tension at MJD of 15 mm. When MJD was less than 60 mm, the strains of reinforcement at mid-span section B and E were quite minimal, as section B and E coincided with the counterflexure points of the perimeter beams. However, after MJD of 150 mm, all the reinforcement at those sections came into tension, suggesting axial tension of the beam gradually extended from the middle column stub to the mid-pan and eventually to the far ends near section A and F. In summary, the perimeter beam developed bending moments at small

Fig. 18. Contribution of each support at the column stub: (a) Specimen S1; (b) Specimen S3.

the cracks along the diagonal of each slab panel originated from the middle column stub were quite prevalent, indicating the development of the sagging moment. In addition, the cracks along the inner side of boundary beams have penetrated from the top surface to the bottom of the slab. As the concrete cover was 6 mm for the slabs, the tremendous tension in the slab reinforcement resulted in the splitting and cracking of concrete. Consequently, the grid cracks were visible, in particular in the area close to the perimeter beams and in the longitudinal direction. This reflects the large mobilization of TMA in the longitudinal direction. 3.3. Reactions of supporting columns and inclined restraints The measurement of vertical reactions (i.e. axial forces) of supporting columns is able to illustrate the load redistribution of applied vertical load. Fig. 16(a) and (b) show that the development of axial forces in column C1 and C5, which supported the perimeter beams, as well as the ones in C2 and C4 supporting the two corners was quite symmetric for specimen S1 and S3, indicating the validity of the test set-up. At the range of displacement prior to 200 mm and 258 mm for specimen S1 and S3, respectively, column C3 which supported the transverse beam sustained the largest axial force, column C2 and C4 took the least, and column C1 and C5 were in-between. Moreover, the softening of structural resistance correlated to the decreasing of the reaction force provided by column C3 due to the formation of plastic 11

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Fig. 19. Strains of reinforcement in the perimeter beam of specimen S3: (a) Top reinforcement; (b) Bottom reinforcement.

4. Numerical investigation program

deformation stage, and CTA at large deformation stage. Fig. 20 demonstrated the strain distribution of reinforcing bars in the transverse beam. At section G near the middle column stub, only bottom reinforcement was in tension. At section I near the supporting column, the top and bottom reinforcement is always in tension and compression, respectively, suggesting the development of predominant hogging moment, and the bar yielded from MJD of 45 mm. At mid-span section H, the strain of top reinforcement shifted from almost zero to tension after MJD of 60 mm, but the bottom reinforcement is always in tension, corresponding to the sagging moment at the middle span of the transverse beam and slight axial tension due to section G restrained by the longitudinal beams. This illustrates that the transverse beam mainly worked as a beam with section I fixed and section G vertically supported and yet with weak rotational restraint provided by the torsional stiffness of the longitudinal beams. The strain distributions of the slab reinforcement of specimen S3 at MJD of 60 mm and 300 mm are shown in Fig. 21 to illustrate the load transfer mechanisms throughout the slabs at different deformation stages. The strain readings with the grey and white background respectively indicate the value smaller and greater than the yield strain. The bottom slab reinforcement along the diagonal of each panel, as indicated by the dash line in Fig. 21(a) and (c), was more easily to develop large strains. This observation complies with the failure modes shown in Fig. 15(d), in which the cracking were initiated from the removed column and went along the diagonal of the panel. The top slab reinforcement near the boundary beams developed strains much faster than the rest, corresponding to the development of the negative yield lines of the slab. Fig. 21(c) and (d) demonstrate that at the large deformation, both the top and bottom reinforcing bars are in tension, because all slab reinforcing bars worked as flanges of the beams under flexure and developed TMA. In addition, strain gages spoiled at the large post-yield tension and failed to further provide readings.

As the structural behavior of the RC beam-slab assemblies against progressive collapse involves a great many geometric and material parameters, it is necessary to identify the pertinent parameters. Therefore, in this section, high-fidelity numerical models are built, validated and then extended to conduct parametric studies.

4.1. Introduction of numerical models The numerical models of the RC beam-slab assemblies are built with Ls-Dyna, as shown in Fig. 22, namely, M1 and M3 for specimen S1 and S3, respectively. During the modeling, the distribution beams and the triangular plates are simplified and represented by rigid beam elements. In addition, the connections in the loading system are all modeled as pin connections. The contact between loading plates and rubber mats are all set as automatic surface-to-surface contact with the definition of friction coefficients at the surfaces. The weight of distribution beams and triangular steel plates is around 751.8 kg and applied to the RC beam-slab assembly. Concrete is modeled using 8-node solid elements with reducing integration scheme. In accordance with mesh sensitivity analysis, the element size of 11 mm is used in the region one beam depth away from the beam end, as highlighted in the inset of Fig. 22, and the elements with maximum dimensions of 20 mm are used in the rest regions. Reinforcing bars are modeled using 2-node Hughes-Liu beam elements with 2 × 2 Gauss quadrature integration at the cross-section, and connected to surrounding concrete using keyword *CONSTRAINED_BEAM_IN_SOLID. Considering the strong bond between the deformed bars and concrete, perfect bond is assumed for model M1, whereas the bond-slip behavior is considered for model M3 due to weak bond of plain bars, in which the bond-slip relationship is determined in accordance with Model Code 2010 [42]. 12

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with rigid material.

150mm 300mm 425mm

4.1.3. Loading procedures The self-weight of the loading apparatus and the specimen itself is applied first. After reaching the equilibrium, the push down loading scheme is achieved by defining a velocity-time curve for the loading point, which is at the center of the primary distribution beam, as indicated in Fig. 22. The velocity gradually increases from zero to 0.33 mm/ms within 100 ms and remains constant thereafter.

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Fig. 23(a) shows that the numerical resistance of the two specimens agree very well with the experimental results at the initial ascending and softening stage. However, at the re-ascending stage, the numerically predicted structural resistance is always greater than the experimental one. Fig. 23(b) demonstrates that the numerical reaction forces of columns C1, C2 and C3 agree well the experimental ones, but predicted reactions of C2 and C3 are greater than the measured values after the displacement of around 160 mm and the predicted reaction of C1 is smaller than the experimental one after the displacement of around 280 mm. The main reason is that the connection between the primary and the secondary distribution beam in testing was semi-rigid using a single bolt, whereas in numerical modeling the connection is pin. Fig. 24 illustrates that at large deformation stage of the experiment, due to the rotation of pin connection, the jack and the distribution beams are all slanting. As the exterior side of the specimen (i.e. the part near the perimeter beams) deforms more than the interior side, the distance l2 exceeds l1, resulting in the load distributed to the exterior side larger than that to the interior side. This non-uniform load distribution can also be confirmed by the observation that the local punching of the RC slab was more easily to occur during the testing. In comparison, at the ultimate capacity of numerical model M1 (i.e. at MJD of 298 mm), the reaction forces at the four pin connections that support the two secondary distribution beams are 75.3 kN, 73.9 kN, 79.8 kN and 79.5 kN, suggesting that the load distribution is basically uniform. Fig. 25 demonstrates the failure modes of the top and the bottom surface of the slabs in model M1 at MJD of 300 mm. Material model CSCM is unable to track the concrete cracking, but the large cracking corresponds to large plastic strains. Therefore, the effective plastic strain contours are usually used to show the crack patterns. It is seen that at the slab top, the severe cracks are mainly concentrated at the inner side of the boundary beams and then extended from the beam ends to the central region of the slabs. This is very similar to the crack patterns demonstrated in Fig. 15(a). At the bottom surface of the slab, the extensive cracks covers almost the entire slab panel with dominance in panel diagonal, which is identical to the crack patterns shown in Fig. 15(b). Due to symmetry, Fig. 26 shows the stress contour of slab reinforcement of one panel in model M3 at the MJD of 300 mm. Fig. 26(a) demonstrates that the majority of the bottom slab reinforcement is in post-yield tension, in particular along the longitudinal and diagonal directions, suggesting the mobilization of TMA and reflecting the effect of positive yield line. Fig. 26(b) elucidates that the top slab reinforcement is in tension as well but the reinforcement at the inner side of boundary beams is mainly in post-yield tension due to the formation of negative yield lines, in particular in the longitudinal direction. The stress contour is quite similar to the pattern of strain contour of slab reinforcement shown in Fig. 21(c) and (d). In summary, the numerical results reasonably agree with the experimental results in terms of failure modes and strain distribution of reinforcement. Moreover, the numerically predicted structural resistance agrees well with the experimental one in ascending and softening but becomes larger than the experimental one mainly due to the non-uniform loading at large deformation stage in the test. Consequently, the numerical model is able to help demonstrate the

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Fig. 20. Strains of reinforcement in the transverse beam of specimen S3: (a) Top reinforcement; (b) Bottom reinforcement.

4.1.1. Material models Continuous surface cap model (CSCM) has been successfully used for concrete in the simulation of RC structures subject to CRS [30,36,43], and thus the full version of CSCM is used with the corresponding material parameters calibrated by material tests. The comparison of experimental and numerical results of a concrete cylinder under uniaxial compression is shown in Fig. 4. Moreover, to eliminate the over-twisted elements and further the numerical computation, the maximum principal strain of 0.1 and the minimum principal strain of −0.05 are both used for failure criteria. A bilinear elastic plastic-hardening model with keyword *MAT_PLASTIC_KINEMATIC is used for all steel reinforcement, of which the material properties are listed in Table 3. In addition, elastic model is used for rub mats with elastic modulus of 20 MPa and Poisson’s ratio of 0.47. 4.1.2. Boundary conditions Five supporting columns are modeled using beam elements with hollow circular sections. The elastic material models are used for the columns with elastic modulus of 200 GPa and Poisson’s ratio of 0.3. The bottom end of each column is fixed. During the tests, inclined restraints were connected to the top of the columns C1 and C5 to improve lateral stiffness. Moreover, the reaction force provided by the inclined restraints and their end movement are both measured so that the corresponding horizontal stiffness can be evaluated. In numerical study, the contribution of the inclined restraints are considered using horizontal springs, which are modeled with discrete beam elements. The axial stiffness of each spring is 6.858 kN/mm. The hanging weights of 3.1 kN at the middle span of each slab flange are represented by a steel plate 13

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Fig. 21. Strains of reinforcement in slabs of specimen S3: (a) Slab bottom at MJD of 60 mm; (b) Slab top at MJD of 60 mm; (c) Slab bottom at MJD of 300 mm; (d) Slab top at MJD of 300 mm.

The validated numerical models are used to investigate the parameters of beam depth, slab depth, reinforcement ratio and loading positions on the progressive collapse resistance of RC beam-slab assemblies. By default, the parameters are varied on top of the model M1, and in each analysis case only one parameter is changed.

beams and TMA of slabs. This is because these actions are more determined by the amount of reinforcement. The tension reinforcement ratio (ρb) of the perimeter beam is 0.84%. During increasing ρb of the perimeter beam, all the top and bottom beam reinforcement ratios are increased proportionally. Fig. 27(b) shows that solely increasing ρb slightly improves the first peak resistance, but evidently enhances the ultimate structural resistance due to CTA of beams and TMA of slabs. For instance, increasing ρb from 0.84% by 40% (i.e., ρb = 1.18%) increases the first peak resistance by around 12% and the ultimate capacity by around 25%, respectively.

4.3.1. Effect of beams The structural design with higher seismic intensity typically results in a larger beam depth and reinforcement ratio. Fig. 27(a) shows that with increasing beam depth from 150 mm by 16% and 32%, the first peak resistance increases from 217 kN to 258 kN and 302 kN, respectively. This is because the increase of beam depth enhances the flexural stiffness and reduces beam span-to-depth ratio, further improving the development of CAA of beams. Moreover, a larger beam depth makes beam rotate at the expense of more concrete crushing, resulting in more severe softening of structural resistance. However, the beam depth has nearly no effect on re-ascending structural resistance due to CTA of

4.3.2. Slab thickness and slab reinforcement Fig. 28(a) illustrates that increasing slab depth could improve structural resistance at small and large deformation stage. For example, increasing slab thickness from 54 mm to 78 mm (i.e. by 44%), the first peak resistance and the ultimate capacity is increased by 16.59% and 10.78%, respectively. Slab reinforcement ratio is adjusted by changing the spacing of bars both at the top and bottom. The default tension reinforcement ratio (ρsb) of the slab is 0.38%. Fig. 28(b) indicates that increasing ρsb improves the first peak resistance but more effectively the structural resistance at large deformation stage. For example, increasing ρsb by 60% (i.e., ρsb = 0.61%) results in the first peak resistance, the

structural resistance with uniform loading at large deformation, and is then used for parametric studies. 4.3. Parametric studies

14

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Fig. 22. Numerical model of RC beam-slab assembly. 350 300 250

Load (kN)

ultimate resistance and the deformation capacity increasing by 16.3%, 37.4% and 18.3%, respectively. This is because at small deformation stage, the slab reinforcement could contribute the flexural resistance either at the yield lines or T-shaped and L-shaped composite beam sections, and the development of TMA of slabs also depends on the amount of slab reinforcement. To verify which bars are really effective to improve the structural resistance of beam-slab assemblies at large deformation stage, a strengthening scheme of placing three additional R6 bars near the perimeter beam is adopted, as illustrated in the inset of Fig. 28(b). The results show that this strengthening scheme is quite comparable to increase ρsb by 23.7% (i.e. ρsb = 0.47%), in which the latter requires much more reinforcement than the former. This comparison suggests that only the continuous slab reinforcement near the perimeter beam is effectively contributed to improve structural resistance by developing TMA. Therefore, it is suggested to put more continuous slab reinforcement in the slab strip beside the beams if it is necessary to strengthen progressive collapse resistance of structures.

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Experimental result of C1 Experimental result of C2 Experimental result of C3 Numerical result of C1 Numerical result of C2 Numerical result of C3

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Fig. 23. Comparison of numerical and experimental results: (a) structural resistance; (b) reaction forces. 15

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Fig. 24. Load distribution of loading apparatus at large deformation stage.

Fig. 25. Failure mode of slabs in model M1 at MJD of 300 mm: (a) Top surface of the slab; (b) Bottom surface of the slab.

5. Conclusions

thoroughly investigated through experiments and numerical simulations. Three 3/10 scaled specimens were tested with equivalent uniformly distributed loading (UDL) and careful instrumentation. Highfidelity finite element models are used to conduct parametric studies after the validation of numerical models. The main findings and

In this paper, the progressive collapse resistance and the load transfer mechanisms of reinforced concrete (RC) beam-slab assemblies under a perimeter middle (PM) column removal scenario (CRS) are 16

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Fig. 27. Effect of geometric properties of beam on structural resistance: (a) Beam depth hb; (b) Beam reinforcement ratio ρb.

conclusions are shown as follows:

large deformation stages, respectively. The plain bars increase deformation capacity of beam-slab assemblies due to larger elongation ratios, which is more beneficial to develop larger structural resistance without bar fracture. Increasing slab thickness is able to improve structural resistance through the entire deformation history, and increasing slab reinforcement ratio more evidently improves structural resistance at large deformation stage. However, only the continuous bottom slab reinforcing bars near the perimeter beams are effective. (5) The 12-point loading scheme in the current experimental program is able to represent UDL at the MJD smaller than 175 mm (i.e. around one beam depth), but thereafter is prone to make the load distributed to the points near the perimeter beam larger than the rest points. Moreover, the closer to the middle column stub the load is applied, the smaller the structural resistance is. In comparison, numerical models are able to achieve a true UDL in investigating the structural behavior of beam-slab assemblies.

(1) The load transfer mechanisms of RC beam-slab assemblies under a PM CRS are the compressive arch action of the longitudinal beams and flexural action of the transverse beam and slabs connecting the middle column stub at small deformation stage (approximately prior to one beam depth of 150 mm). Catenary action (CTA) of longitudinal beams, tensile membrane action (TMA) of slabs and flexural action of transverse beam are the load transfer mechanisms against progressive collapse at large deformation stage. (2) The development of axial tension in the perimeter beams initiated from the section near the middle column stub and gradually extended to the mid-span and eventually to the beam ends near the supporting columns. Even at the large deformation stage, the beam ends still sustained hogging moment, which requires the future investigation on rotation capacities of RC beams under combined axial tension and bending. (3) With increasing the deformation of the RC beam-slab assemblies, the load transferred along the longitudinal direction to the supporting columns increased from 45% to 55%, whereas the load transferred along the transverse direction to the supporting column decreased from 40% to 30%. The two corner supporting columns resisted around 15% to 20% of the total load applied to slab surface. (4) Seismic design with higher intensity typically results in larger beam depth and greater beam reinforcement ratio, in which the former and the latter are able to improve structural resistance at small and

CRediT authorship contribution statement Jun Yu: Conceptualization, Methodology, Writing - original draft, Funding acquisition. Li-zhong Luo: Investigation, Formal analysis, Writing - original draft. Qin Fang: Supervision, Validation, Writing review & editing. 17

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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

[18]

Acknowledgement

[21]

The authors would like to acknowledge the financial support by the National Natural Science Foundation of China, China (No. 51408189); Natural Science Foundation of Jiangsu Province, China (No. BK20180073); the Fundamental Research Funds for the Central Universities, China (No. 2019B12814) and Qinglan Project of Jiang Su Province, China.

[22]

[19] [20]

[23] [24] [25]

[26]

References

[27] [1] Department of Defense (DOD). UFC 4-023-03, design of buildings to resist progressive collapse. Including change 2 – 1 June 2013; 2013. http://dod.wbdg.org/. [2] European Committee for Standardization. EN 1991-1-7: Eurocode 1 – actions on structures – Part 1–7: General actions – accidental actions. Brussels: CEN; 2006. [3] General Services Administration (GSA). Progressive collapse analysis and design guidelines for new federal office buildings and major modernization projects; 2003. [4] FarhangVesali N, Valipour H, Samali B, Foster S. Development of arching action in longitudinally-restrained reinforced concrete beams. Constr Build Mater 2013;47:7–19. [5] Yu J, Tan KH. Structural behavior of reinforced concrete beam-column subassemblages under a middle column removal scenario. J Struct Eng 2013;139:233–50. [6] Yu J, Tan KH. Experimental and numerical investigation on progressive collapse resistance of reinforced concrete beam column sub-assemblages. Eng Struct 2013;55:90–106. [7] Kang S-B, Tan KH. Behaviour of precast concrete beam–column sub-assemblages subject to column removal. Eng Struct 2015;93:85–96. [8] Lew HS, Bao Y, Sadek F, Main JA, Pujol S, Sozen MA. An experimental and computational study of reinforced concrete assemblies under a column removal scenario. NIST Technical Note 1720: National Institute of Standards and Technology, U.S. Department of Commerce; 2011. p. 106. [9] Yu J, Tan KH. Special detailing techniques to improve structural resistance against progressive collapse. J Struct Eng 2014;140. 04013077-(1-15). [10] Lim NS, Tan KH, Lee CK. Experimental studies of 3D RC substructures under exterior and corner column removal scenarios. Eng Struct 2017;150:409–27. [11] Pham AT, Tan KH. Experimental study on dynamic responses of reinforced concrete frames under sudden column removal applying concentrated loading. Eng Struct 2017;139:31–45. [12] Yu J, Tan KH. Structural behavior of reinforced concrete frames subjected to progressive collapse. ACI Struct J 2017;114:63–74. [13] Yi WJ, He QF, Xiao Y, Kunnath SK. Experimental study on progressive collapseresistant behavior of reinforced concrete frame structures. ACI Struct J 2008;105:433–9. [14] Li S, Shan S, Zhai C, Xie L. Experimental and numerical study on progressive collapse process of RC frames with full-height infill walls. Eng Fail Anal 2016;59:57–68. [15] Kai Q, Yang Y, Wang Y-M, Bing L. The effects of bracing on the behavior of RC multi-story frames to resist progressive collapse. In: Structures congress 2017. Denver: ASCE; 2017. p. 180–6. [16] Qian K, Li B. Effects of masonry infill wall on the performance of RC frames to resist progressive collapse. J Struct Eng 2017;143:04017118. [17] Izzuddin BA, Vlassis AG, Elghazouli AY, Nethercot DA. Progressive collapse of

[28]

[29] [30]

[31] [32] [33] [34] [35]

[36]

[37]

[38]

[39]

[40] [41] [42] [43]

19

multi-storey buildings due to sudden column loss – Part I: Simplified assessment framework. Eng Struct 2008;30:1308–18. Mashhadi J, Saffari H. Modification of dynamic increase factor to assess progressive collapse potential of structures. J Constr Steel Res 2017;138:72–8. Amiri S, Saffari H, Mashhadi J. Assessment of dynamic increase factor for progressive collapse analysis of RC structures. Eng Fail Anal 2018;84:300–10. Yu J, Yin C, Guo Y. Nonlinear SDOF model for progressive collapse responses of structures with consideration of viscous damping. J Eng Mech 2017;143:04017108. Pham XD, Tan KH. Experimental study of beam–slab substructures subjected to a penultimate-internal column loss. Eng Struct 2013;55:2–15. Yi W-J, Zhang F-Z, Kunnath S. Progressive collapse performance of RC flat plate frame structures. J Struct Eng 2014;140:04014048. Dat PX, Tan KH. Experimental response of beam-slab substructures subject to penultimate-external column removal. J Struct Eng 2015;141:04014170. Xiao Y, Kunnath S, Li FW, Zhao YB, Lew HS, Bao Y. Collapse test of three-story halfscale reinforced concrete frame building. ACI Struct J 2015;112:429–38. Hou J, Song L. Progressive collapse resistance of RC frames under a side column removal scenario: the mechanism explained. Int J Concr Struct Mater 2016;10:237–47. Qian K, Li B, Zhang Z. Influence of Multicolumn removal on the behavior of RC floors. J Struct Eng 2016;142:04016006. Lu X, Lin K, Li Y, Guan H, Ren P, Zhou Y. Experimental investigation of RC beamslab substructures against progressive collapse subject to an edge-column-removal scenario. Eng Struct 2017;149:91–103. Yu J, Luo L. Experimental investigation on structural behaviour of RC beam-slab assemblies against progressive collapse. In: 6th international conference on design and analysis of protective structures (DAPS 2017). Melbourne, Australia; 2017. p. Paper#84. Sasani M, Bazan M, Sagiroglu S. Experimental and analytical progressive collapse evaluation of actual reinforced concrete structure. ACI Struct J 2007;104:731–9. Yu J, Luo L, Li Y. Numerical study of progressive collapse resistance of RC beamslab substructures under perimeter column removal scenarios. Eng Struct 2018;159:14–27. Houcine ME, Said M, Adnan I. A controlled destruction and progressive collapse of 2D reinforced concrete frames. Coupled Syst Mech 2018;7:111–39. Yu J, Tan KH. Numerical analysis with joint model on RC assemblages subjected to progressive collapse. Mag Concr Res 2014;66:1201–18. Kunnath SK, Bao Y, El-Tawil S. Advances in computational simulation of gravityinduced disproportionate collapse of RC frame buildings. J Struct Eng 2018;144. Feng DC, Wang Z, Wu G. Progressive collapse performance analysis of precast reinforced concrete structures. Struct Design Tall Specl Build 2019;28. Feng D-C, Xie S-C, Ning C-L, Liang S-X. Investigation of modeling strategies for progressive collapse analysis of RC frame structures. J Perform Constr Facil 2019;33. Yu J, Gan Y-P, Wu J, Wu H. Effect of concrete masonry infill walls on progressive collapse performance of reinforced concrete infilled frames. Eng Struct 2019;191:179–93. Pham AT, Lim NS, Tan KH. Investigations of tensile membrane action in beam-slab systems under progressive collapse subject to different loading configurations and boundary conditions. Eng Struct 2017;150:520–36. Ministry of Housing and Urban-Rural Development of the People's Republic of China (MOHURD). Code for design of concrete structures. GB50010-2010. Beijing, China; 2010. Ministry of Housing and Urban-Rural Development of the People's Republic of China (MOHURD). Code for seismic design of buildings, GB50011-2010. Beijing, China; 2010. Qian K, Li B, Ma JX. Load-carrying mechanism to resist progressive collapse of RC buildings. J Struct Eng 2015;141:04014107. Yu J, Tan KH. Analytical model for the capacity of compressive arch action of reinforced concrete sub-assemblages. Mag Concr Res 2014;66:109–26. Fib. fib Model Code for Concrete Structures 2010. Ernst & Sohn; 2013. Pham AT, Tan KH, Yu J. Numerical investigations on static and dynamic responses of reinforced concrete sub-assemblages under progressive collapse. Eng Struct 2017;149:2–20.