Progressive collapse of steel moment-resisting frame subjected to loss of interior column: Experimental tests

Engineering Structures 150 (2017) 203–220

Contents lists available at ScienceDirect

Engineering Structures journal homepage: www.elsevier.com/locate/engstruct

Progressive collapse of steel moment-resisting frame subjected to loss of interior column: Experimental tests Honghao Li a,b,c, Xianghui Cai d, Lei Zhang a,b,c, Boyi Zhang a,b,c, Wei Wang a,b,c,⇑ a

Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, Harbin Institute of Technology, Harbin 150090, China Key Lab of Smart Prevention and Mitigation of Civil Engineering Disasters of the Ministry of Industry and Information Technology, Harbin Institute of Technology, Harbin 150090, China c School of Civil Engineering, Harbin Institute of Technology, 150090, China d Architectural Design and Research Institute of HIT, Harbin Institute of Technology, Harbin 150090, China b

a r t i c l e

i n f o

Article history: Received 30 May 2016 Revised 6 January 2017 Accepted 17 July 2017

Keywords: Progressive collapse Static push-down analysis Steel moment-resisting frame Catenary action Flexural action Dynamic peak displacement

a b s t r a c t A static push-down analysis is conducted experimentally using a 1/3 scale one-story bare steel moment frame substructure in this study. The objectives of this test include: (1) investigating the behavior of bare steel moment frame under column loss scenario; (2) validating the computational models developed for the purpose of investigating progressive collapse of steel frame structures. The contributions of collapse resisting mechanisms including flexural action and catenary action to the robustness of the system as the increase of the vertical displacement of the center column are quantified. The test results reveal that flexural action plays an important role in resisting progressive collapse along the entire loading process. However, the catenary action becomes the primary collapse resisting mechanism in the final stage of loading. Dynamic responses of the test specimen are estimated using energy-based method. It is shown the test specimen behaves elastically subjected to sudden loss of the center column and therefore progressive collapse will not occur. The dynamic increase factor is also estimated on the basis of the testing results. The analysis results suggest that catenary action has a great impact on the value of the dynamic increase factor under large deformation conditions. Ó 2017 Published by Elsevier Ltd.

1. Introduction The mechanism of progressive collapse is extremely complicated since it is a highly nonlinear dynamic event involving a full structural system. It is difficult, if not impossible, to accurately investigate the process using hand calculations or simple analysis methods. Considering the expense, difficulty and risk of experimental tests on progressive building collapse and fast development of computer technology, computational models has become the primary tools to investigate progressive collapse. However, to improve the accuracy and reliability of the computational models, more high quality experimental results which can be used for model validation are needed. Before 2013, the number of examples of experimental studies on progressive building collapse was less than 15 [4], which was quite rare comparing to computational research. In recent years (2013–2016), more research efforts were dedicated to the investi-

⇑ Corresponding author at: School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China. E-mail address: [email protected] (W. Wang). http://dx.doi.org/10.1016/j.engstruct.2017.07.051 0141-0296/Ó 2017 Published by Elsevier Ltd.

gation of progressive building collapse experimentally. Experimental collapse testing on steel structures can be divided into three categories: (1) subassemblage testing; (2) full structural system testing; and (3) one-story substructure testing. Most of the experimental research falls into the first category. This type of testing mainly focuses on the planar behavior of beam-to-column connections under column loss scenarios. Sadek et al. [18] presented experimental studies on steel moment connections under column loss scenarios. Guo et al. [5], Guo et al. [7] investigated the collapse resistance of two 1/3 scaled composite frames experimentally, with special emphasis on the behavior of rigid and semi-rigid composite joints subjected to loss of midcolumn. Yang and Tan [24], Yang and Tan [25] investigated the responses of different types of semi-rigid and simple bolted connections and composite joints under column loss scenarios. Li et al. [10], Li et al. [11], and Wang et al. [22] conducted experimental tests on the behaviors of beam-to-column subassemblages with different moment connection configurations after loss of an interior column. Liu et al. [12], Liu et al. [13], Liu et al. [14] investigated the dynamic performances of bolted connections subjected to sudden column losses in order to figure out the impact of dynamic

204

H. Li et al. / Engineering Structures 150 (2017) 203–220

effects on the responses of these connections. Haremza et al. [2] presented the behavior of steel-concrete composite joints subjected to column loss due to fire. Other examples of subassemblage testing that focused on steel structures include Guo et al. [6], Weigland and Berman [23], and Oosterhof and Driver [17]. Subassemblage tests allow the collapse resistance mechanisms to be studied in detail. However, the gravity loads are redistributed in a planar manner and 3-D effects are neglected in such testing schemes. In the second category, the response of an entire building after loss of one or several columns is investigated. The behavior of a full structural system can be captured by such tests and the vulnerability of the structural system to progressive collapse can be evaluated accurately. However, full system tests are typically difficult to be densely instrumented and it is difficult to investigate isolated collapse resistance mechanisms since complex interacting processes are usually incorporated in this category of testing, whose effects are difficult to discern [4]. On the other hand, the costs of such tests are high and their size also makes it difficult to be conducted in the structural laboratories. Therefore, such tests are rare. Examples of full system testing on steel structures can be found in Chen et al. [3], Song and Sezen [19], Zandonini et al. [27], and Song et al. [20]. Considering the pros and cons of the first two categories of testing, one-story substructure tests should be a reasonable compromise. Firstly, it is practical to densely instrument and the individual effects of collapse mechanisms can be discerned; secondly, 3-D effects with respect to load redistribution and boundary conditions can be fully considered under such test schemes; last but not least, they can be conducted in the structural slab without occupying significantly large space. The only two examples of such tests on steel structures in the literature are Astaneh-Asl [1] and Johnson et al. [9]. However, these two studies did not thoroughly investigated the collapse resistance mechanisms developed in the collapse process quantitatively. In order to fill these gaps, a one-story substructure testing, which is a static push-down test of a 1/3 scale two bay by two bay bare moment resisting steel frame is conducted and the behavior of the structure subjected to loss of an interior column is investigated. This study sheds light on the evaluation and quantification of the formation and development of collapse resistance mechanisms, including flexural action and catenary action, in the collapse process with respect to different structural component orientations, which have not been addressed by the other category 3 tests in the literatures. Three dimensional effects and the load redistribution pattern in two-way manner, which have not been adequately studied in the past, are also explored herein.

2. Experimental program 2.1. Test specimen A prototype steel framed building which was designed for northeastern part of China was selected to investigate its behavior under column loss scenarios. The L-shaped building is a six-story shopping mall and is designed on the basis of National Standard of the People’s Republic of China: Code for Design of Steel Structures (GB 50017-2003) [16]. As shown in Fig. 1, the longer wing of the building has a dimension of 10 m
60 m (2 bay by 16 bay) and the dimension of the shorter wing is 26 m
12 m (5 bay by 2 bay). Moment-resisting frames are utilized to resist lateral loads. The building is designed for the lowest seismic risk with seismic precautionary intensity 6 according to National Standard of the People’s Republic of China: Code for Seismic Design of Buildings (GB 50011-2010) [15]. When this criterion for seismic precaution of buildings is considered, the gravity loads control the design

of the structural system and thus the seismic effects are neglected. However, basic seismic detailing is still required. This configuration was chosen because they represent typical steel framed buildings in northeastern China. On the other hand, there is a notion in the structural engineering community that stringent seismic detailing leads to an increasing collapse resistance and thus the prototype structure should be quite vulnerable to progressive collapse under column loss scenarios. Therefore, it is of great importance to gain insights into the robustness of such structures, on the basis of which strategies for the improvement of the collapse resistance of these buildings can be developed. As shown in Fig. 1(b), the highlighted two bay by two bay substructure from the shorter wing of the building is considered in the experimental test reported herein. The test specimen is a two bay by two bay, bare steel moment resisting frame structure. Due to the space limitation in the structural laboratory, the specimen was designed and fabricated with a length scale factor (SL ) of 1/3. As shown in Fig. 2, the span length in both directions is 2 m and the story height is 1 m. Although there were structural components in both first and second floor as shown in Fig. 2(a) and (b), the only role of the 2nd floor structural members is to provide necessary boundary conditions and the center stub column was not extended and connected to any structural components in the second floor. Therefore, the test herein should be labeled as a category 3 testing, i.e. a one-story substructure test. All of the beam-to-column connections of the test specimen were welded moment connections. The details of the moment connections in the direction of strong axis and weak axis of the columns are shown in Fig. 3(a) and (b), respectively. Along column lines A, B, and C, which is also the direction of the strong axis of the columns, the ends of the moment beams were directly welded to the column flanges, as shown in Fig. 3(a). As shown in Fig. 3(b), in the vicinity of the beam-to-column connections along column lines 1, 2, and 3, which is also the weak axis direction of the columns, the tapered beam ends were welded into the column inner profile by all around welding. Thus, the beam flanges at the beam ends act as the continuity plates. The three-dimensional view of the connection region of the stub column was shown in Fig. 3(c). The shear connections used in the prototype structure were composed of single-plate, shear tab connections that were filet welded to the girders and bolted using three M18 bolts to 12 mm shear tabs. Therefore, three M6 bolts and 4 mm thick shear tab were used in the shear connections of the test specimen, as shown in Fig. 3 (d) and (e). The center column was a 400 mm long unsupported stub column to simulate the column loss scenario. The eight columns on the perimeter were intact with their feet anchored to the strong floor to represent the boundary condition induced by the foundation/lower stories. As is shown in Fig. 2(b), there was a 400 mm by 400 mm square opening comprised of four short steel H-shaped beams in the center of the 2nd floor, which was connected to the exterior structural components using three Hshaped beams in parallel. The connections in the second floor were all fully welded connections. Such structural layouts ensured that the translations and the rotations of the column ends were all constrained to simulate the boundary conditions of the 2nd floor column ends because when upper floors existed, these deformations of the column ends were also constrained. There were no infill beams in the 2nd floor. The loading equipment and other instruments can be installed through the opening and seated right on the top of the stub column in the 1st floor. The cross sections of the structural members are listed in Table 1. To facilitate the following discussions, first floor beams, columns are designated as E-P-X. In this notion, E is the structural element type, where ‘‘C” represents columns, ‘‘B” represents moment beams, ‘‘I” represents infill beams, ‘‘MC” represents moment connections and ‘‘SC” represents shear connections. P is the position

H. Li et al. / Engineering Structures 150 (2017) 203–220

205

(a) Axis 1 to 11

(b) Axis 11 to 19 Fig. 1. Plan view of the prototype structure.

of the structural member described by the closest column lines in Fig. 2 and X, when designated, is orientation (East, West, North, South) as indicate in Fig. 2. For example, C-B3 represents the column at the junction of column lines B and 3. B-B12 represents the moment beam in bay 12 at column line B. Designation

I-AB12-N represents the north infill beam in the panel bounded by column lines A, B, 1 and 2. MC-B12-W means the moment joint at the west end of beam B-B12. SC- BC23-SE means the shear connection located in the vicinity of southeastern portion of the panel bounded by column lines B, C, 2, and 3, i.e. the shear connection at

206

H. Li et al. / Engineering Structures 150 (2017) 203–220

(a) Plan view of the first floor

(b) Plan view of the second floor Fig. 2. Test specimen.

the east end of infill beam I-BC23-S. For simplicity, it referred to the four exterior penultimate columns, C-A2, C-C2, C-B1 and CB3 when mentioning ‘‘exterior columns” and the term ‘‘moment beams” represented the four beams connecting to the stub column, i.e. B-B12, B-B23, B-AB2, and B-BC2. The material properties of the structural steel used to fabricate the specimen, including the yield stress and strain, ultimate stress and strain, and failure strain, were obtained through tensile coupon tests of the beam flange and web, column flange and web, and the shear tab. The test results are shown in Table 2. All the values given in Table 2 are averages from three tests. The yielding strength and tensile strength of the bolts are 640 MPa and 800 MPa respectively according to GB 50017-2003. Since it was observed during the test that the failure mode of the shear connections was the shear failure of the bolts, single shear test was conducted to evaluate the shear strength of the bolts and investigate the behavior of the bolts under shear until failure occurred. On the other hand, the single shear test results can be implemented to calibrate the computational models for the shear connections in an easy and convenient manner. The test specimen used in the single shear test was shown in Fig. 4(a) and (b). The loaddeformation relationship based on averaging the results of three tests were shown in Fig. 4(c).

2.2. Test setup The test setup is shown in Fig. 5. A static push-down loading scheme was implemented in this test. A concentrated load was applied to the top of the stub column which was unsupported until failure occurred. In order to do so, a 1000 kN hydraulic jack with a maximum stroke of 500 mm was installed on the top of the stub column and the load applied to the test specimen was recorded using a load cell. The reaction force was transferred to a large scale double H shaped loading beam which was supported by two H frames. A special loading system was designed as shown in Fig. 6 to avoid the rotations of the stub column so that the concentrated load could be applied vertically. Two lateral restraint systems were installed at the mid-point of B-B12 and B-B23 to avoid lateral movement of these two beams, as shown in Fig. 5(b). No such systems were needed by the moment beams in the other direction

since their lateral movement could be restrained by the infill beams. The loads were applied in load-control upon the estimated elastic range and in displacement-control in plastic range. 2.3. Instrumentation As shown in Fig. 7, the vertical displacement of the stub column was measured using four string potentiometers (SP1 to SP4) which were placed at the corners of the stub column. The deforming profiles of the each moment beams were measured by 2 linear variable differential transformers (LVDTs), which were placed at a distance of 1/3 and 2/3 of the span length from the stub column respectively along the beam length. The lateral deformation at the beam-to-column connections was measured by 4 LVDTs. Fig. 8 shows the locations of 112 strain gauges which were attached to beam surfaces to measure the strain distributions along the height of the cross sections at four different locations on each beam. Each section was designated as S-X-N, in which X is the beam locator, and N is the section number, among which S-X-1 and S-X-4 represents the cross sections in the vicinity of the ends of beam X and S-X-2 and S-X-3 locates at the points of trisection of the beam. The strain gauges along S-X-1 and S-X-4 provide information about the connection behavior under column loss scenario. The cross section S-X-4 of each beam is the most critical cross section where fracture may occur. According to the computational simulation before the test, the beam section between S-X-2 and S-X-3 remain elastic and therefore the readings of the strain gauges at these two cross sections could be used to calculate the variation history of internal forces as well as the load redistributions throughout the entire loading process. 3. Experimental results 3.1. Observed behavior and failure modes Fig. 9 illustrates the behavior of the test specimen after the test. It was obvious that the specimen experienced large deflections and rotations prior to failure. The maximum vertical displacement of stub column reached 420 mm before fracture of the bottom flange of B-AB2 near the connection MC-AB2-S. The displacement

207

H. Li et al. / Engineering Structures 150 (2017) 203–220

Moment column Moment beam

Continuity plate

Moment column

Moment beam

(a) Details of moment connections in strong axis direction: side view

(b) Details of moment connection in weak axis direction: top view

Moment beam

Infill beam

(c) Moment connections at the stub column: 3D view

(d) Details of shear connections

(e) Shear connections: 3-D view Fig. 3. Details of the connections.

Table 1 Cross sections of structural members.

a

Structural components

Cross sectiona

1st floor moment beams 2nd floor moment beams and opening Strengthening beams Infill beams Columns

H150
75
5
7 H200
100
5.5
7 H200
100
5.5
7 H100
50
5
7 H100
100
6
8

H-depth (mm)
width (mm)
web thickness (mm)
flange thickness.

measurement was based on the average value of the deformation measured by SP1 through SP4 in Fig. 7. The corresponding chord rotation h, which is equal to the vertical displacement of the stub column divided by the span length, was 0.21 rad. The rotation is greater than 0.20 rad required by UFC 4-023-03 [21], indicating

that the moment beams are capable of carrying the tie forces which allow the test specimen to be mechanically tied together. The failure modes of the test specimen was carefully documented during the test and can be summarized as follows: (1) Local buckling occurred at top flanges of moment beams in the vicinity of the connections region of the stub column when the vertical displacement, D, reached around 40 mm and the corresponding chord rotation h was 0.02. Fig. 10(a) illustrates the local buckling of the beam flanges after the test. (2) The bottom bolt of the shear connection SC-BC12-NW fractured in shear when D ¼ 200 mm and h ¼ 0:10. Similar failures occurred at the other shear connections as the displacement increased. As shown in Fig. 10(b), at the end of

208

H. Li et al. / Engineering Structures 150 (2017) 203–220

Table 2 Material properties of the structural steel used to fabricate the specimen.

c d

Yield stress (MPa)

Beam flange Beam web Column flange Column web Shear tab

381 362 344 351 241

Strain Stress Strain Strain

Yield straina

Ultimate stress (MPa)b

Ultimate straina,c

0.0021 567 0.166 0.0021 503 0.148 0.0025 536 0.168 0.0021 549 0.161 0.0013 384 0.153 pffiffiffiffiffi values corresponding to a gauge length of 5.65 S0 , where S0 is the original cross section area of the coupons. corresponding to the ultimate tensile strength of the tested structural steel. corresponding to the ultimate stress/ultimate tensile strength of the tested structural steel. when fracture occurs.

(b) Vertical view of the specimen

(a) Plan view of the specimen 14.0 12.0 10.0

Load (kN)

a b

Component

8.0 6.0 4.0 2.0 0.0 0.0

2.0

4.0

6.0

8.0

10.0

12.0

Displacement (mm)

(c) Test results Fig. 4. Single shear test.

(a) Overview

(b) Perspective view Fig. 5. Test setup.

Fracture straina,d 0.321 0.259 0.323 0.240 0.226

H. Li et al. / Engineering Structures 150 (2017) 203–220

(a) Loading system setup

209

(b) Components of the loading system

Fig. 6. Close-up at the loading system.

(a) B-B12

(b) B-B23

( a ) B – BC2

( b ) B - A B2

Fig. 7. Locations of LVDTs and string potentiometers (SP).

the test, it was found that the bottom and center bolts of the shear connections SC-BC23-NE, SC-AB12-SW, and SCAB23-SE fractured in shear and the top bolt at these connections did not fail due to the binding effect between the flange of the infill beams and the flange of moment beams. (3) As shown in Fig. 10(c), lateral torsional buckling occurred to all the moment beams, which was initiated when D ¼ 300.

(4) The bottom flange of the moment beam B-AB2 near the stub column fractured when D reached approximately 421 mm, and the fracture propagated to the web immediately, as shown in Fig. 10(e). The test was terminated considering safety issue. It was also observed that due to catenary forces which were developed in the moment beams, which will be discussed in the

210

H. Li et al. / Engineering Structures 150 (2017) 203–220

(a) B-B12

(b) B-B23

(c) B-BC2

(d) B-AB2 Fig. 8. Locations of the strain gauges.

H. Li et al. / Engineering Structures 150 (2017) 203–220

(a) Overall view

(b) Close-up in the vicinity of the stub column

Fig. 9. Behavior of the test specimen after the test.

(a) Local buckling of the flanges of the moment beams near the removed column

(b) Failure of shear connections: bolts fractures in shear

(c) Lateral torsional buckling of the moment beams

(d) Inclination of column C-A2 and local bucking of the column flange

(e) Fracture of the bottom flange of B-BC2 Fig. 10. Failure modes of the test specimen after loading.

211

0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 -3.0 0

100

200

300

400

DIfference in percentage (%)

H. Li et al. / Engineering Structures 150 (2017) 203–220

DIfference in percentage (%)

212

3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 0

100

Displacement: average value (mm)

1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 -3.0 -3.5 -4.0 100

300

400

(b) SP2 DIfference in percentage (%)

DIfference in percentage (%)

(a) SP1

0

200

Displacement: average value (mm)

200

300

400

Displacement: average value (mm)

(c) SP3

4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 0

100

200

300

400

Displacement: average value (mm)

(b) SP4

Fig. 11. Difference between the displacement measured by each string potentiometer and the average displacement.

400

ingful to compare the behavior of the test specimen, which is a three-dimensional bare steel frame without considering the floor slabs to the behavior of the 3D steel frame with floor slabs under the same column loss scenario to investigate the impact of the slabs on the robustness of the system and the development of collapse resistance mechanisms in the collapse process. The latter experiment is currently being conducted at Harbin Institute of Technology.

D

C 350

B

300

Load (kN)

250

A 200 150

3.2. Load and displacement measurements

100 50 0

0

100

200

300

400

500

Displacement (mm) Fig. 12. The relationship between the load applied to the top of the stub column vs. the vertical displacement of the stub column.

following sections, the moment connections MC-AB2-N, MC-BC2-S, MC-B12-E, and MC-B23-W, were pulled inward and local buckling occurred at the flanges of the column near these connections, as shown in Fig. 10(d). Although the lateral restraint system as well as the loading restraint device were installed to prevent the occurrence of the lateral torsional buckling of the moment beams and they provided some torsional strength for the stub column, lateral torsional buckling still occurred because of the narrow flanges of the moment beams. Failures such as lateral torsional buckling and local buckling may not occur under the presence of the floor slabs as shown in the beam-to-column subassemblage tests conducted by Yang et al. [26] on the robustness of composite joints. Thus, it is mean-

Fig. 11 shows the difference between the string potentiometer readings and their average value. It can be seen that the maximum difference was around 4%, which means no rotation occurred around the column lines as shown in Fig. 2 and the stub column moved downward vertically throughout the loading process. However, the stub column twisted as a result of the lateral torsional buckling of the four moment beams. The relationship between the concentrated load applied to the top of the stub column and vertical displacement of the stub column is shown in Fig. 12. The displacement value was obtained from averaging the measurements of the four string potentiometers as shown in Fig. 7. The occurrence of the failures descried in the last section was marked as A, B, C, and D, in sequence. It can be seen from Fig. 12 that the load increased with the displacement linearly until D ¼ 24 mm and the applied load F ¼ 120 kN and the initial stiffness of the system was 5000 kN/m. Then the curve entered ‘‘elastic-plastic” stage when the deformation was between 24 mm to 40 mm. Nonlinearity occurred at this stage and the structure stiffness started to decrease. When the vertical displacement D reaches 40 mm, the load F equals to 160 kN. After that, as the displacement increased, the system behaved plastically although the relationship between load and displacement appeared closed to a straight line. Thus, the load-displacement curve could be approximated by a bilinear model with initial

213

H. Li et al. / Engineering Structures 150 (2017) 203–220

Lateral deformation of the joint (mm)

Vertical displacement (mm)

300 250 200 150 100 50 0 -2000

5 0 -5 0

50

100

150

200

250

300

350

400

-10 -15 -20 -25

MC-B12-E

-30

MC-B23-W

-35

MC-AB2-N

-40

MC-BC2-S

-45 -50

Vertical displacement of the removal column (mm) -1500

-1000

-500

0

500

1000

1500

2000

Span-wise distance (mm) Fig. 13. Deflection profile of the double-span beam lies in column axis 2.

stiffness of 5000 kN/m and the deterioration stiffness in the plastic range was around 620 kN/m, which was 12% of the initial stiffness in the elastic range. The peak value of the collapse resistance of the test specimen was 385 kN when D ¼ 421 mm. Similar observations were made in the subassemblage tests conducted by Sadek et al. [18] on the behavior of moment connections including welded unreinforced flange-bolted web (WUF-B) connections and reduced beam section (RBS) connections under column removal scenarios. The vertical displacement profiles of the moment beams in column axis 2 under various loading conditions was shown in Fig. 13. The figure demonstrated that when the vertical deformation of the stub column was small (D < 40 mm), the moment beams were deformed in a flexural pattern. The displacement profile of each beam could be approximated as a straight line as the vertical displacement increased. Similar observations were made with respect to the deformation profiles of the moment beams in column axis B. Fig. 14 illustrates the relationships between the lateral displacements of the four edge beam-to-column connections and the vertical displacement. Negative value means a displacement towards the stub column, i.e. the connection was pulled inward. It was illustrated that an initial outward displacement was observed at the moment connection MC-B12-W and MC-B23-E, which were in column line B, following by inward displacements as remarkable amount of tensile forces were developed in these beams, indicating the load carrying mechanism of the moment beams was transferred from flexural behavior to catenary behavior. The other two beams maintained an inward displacement throughout the entire loading process. However, the value was small initially. The inward displacements of all connections began to increase in a faster pace after the vertical displacement D reached 60 mm, indicating that catenary action was triggered in these beams. These four curves were closed to each other and the maximum value of the lateral deformation of the 4 connections were all around 50 mm, which was 2.5% of the span length.

3.3. Strain measurements Fig. 15(a) illustrates the strain distributions along S-B23-1 when the vertical displacement of the stub column is equal to 10 mm, 30 mm, 50 mm, 70 mm and 90 mm, respectively. It could be seen that when the vertical displacement reached 90 mm, the strain values at the top and bottom flange of the beam exceeded the yield strain of the structural steel, which is approximately 2000 le. Otherwise the cross section behave elastically. Plots of the readings of the strain gauges at section S-B23-2 and S-B23-3 corresponding to vertical displacement of 50 mm, 100 mm,

Fig. 14. Lateral deformation of the exterior beam-to-column joints.

150 mm, 200 mm, 300 mm, and 400 mm were illustrated in Fig. 15(b) and (c). The values of the strains were all below the yield strain of the structural steel, which implied that these two sections behave elastically during the entire loading process. The strain distributions along the section S-B23-4, which was the most critical cross section of beam B-B23, at various deformation conditions were presented in Fig. 15(d). The corresponding vertical displacement of the stub column was 10 mm, 20 mm, 30 mm, 40 mm, and 50 mm, respectively. When the vertical displacement reached 40 mm, the strains of the entire cross section went beyond the yield strain, which indicated the formation of the plastic hinge. According to Fig. 15(b) and (c), the strain distributions along these cross sections were linear and basically symmetric with respect to the centroid line of the cross section when the vertical displacement of the stub column was smaller than 100 mm, indicating that at this stage of loading, small amount of axial force was developed in the beams and the predominant mechanism to resist progressive collapse was the flexural action. As the increase of the vertical displacement, the tensile strains exceeded the compressive strains and the difference between them became larger and larger, which suggested that catenary action was mobilized in beam B-B23 and became more and more influential. However, the compressive strains still existed, which implied the flexural action still played a role in resisting progressive collapse. Therefore, it can be summarized that the main collapse resistance mechanisms of the test specimen were flexural action and catenary action. Fig. 16 shows the readings of the strain gauges attached to beam B-BC2 and similar trend was observed. The strain gauge readings from the other two moment beams were not listed since similar phenomenon were observed.

4. Discussions of experimental results 4.1. Calculation of internal forces in the moment beams The internal forces in the moment beams can be calculated on the basis of strain gauge readings at cross sections S-X-2 and S-X-3 of each moment beam and thus the contributions of flexural action and catenary action to the collapse resistance of the system could be quantified. Fig. 17(a) illustrates the idealized computational model for the internal forces in moment beams and Fig. 17(b) is the free body diagram of the beam portion between section S-X-2 and S-X-3. The internal forces at the cross sections S-X-2 and S-X-3 are V X2 , N X2 , M X2 , and V X3 , N X3 , M X3 , respectively. The subscript X represents the moment beam under consideration. N X1 and N X2 represent the catenary force developed in the beams and they can be calculated as follows,

H. Li et al. / Engineering Structures 150 (2017) 203–220

150

150

135

135

120 D=10

105

D=30

90

D=50 D=70

75

D=90

60 45 30 15 0 -2500-2000-1500-1000 -500

0

Distance to the bottom flange (mm)

Distance to the bottom flange (mm)

214

D=150

90 75

D=200 D=300 D=400

60 45 30 15 0 -2000 -1500 -1000

-500

0

500

Strain ( )

Strain ( )

(a) S –B23- 1

( b ) S– B 2 3- 2

1000

1500

2000

150

135 120 D=50

105

D=100

90

D=150

75

D=200

60

D=300 D=400

45 30 15 -900

-600

-300

0

300

600

900

Distance to the bottom flange (mm)

Distance to the bottom flange (mm)

D=100

105

500 1000 1500 2000 2500 3000

150

0 -1200

D=50

120

135 120 D=10 105

D=20

90

D=30

75

D=40 D=50

60 45 30 15

0 -13000-10000 -7000 -4000 -1000 2000 5000 8000 11000 14000

1200

Strain ( )

Strain (

( c ) S– B 2 3 - 3

)

(d) S-B23-4

Fig. 15. Strain distributions along the various cross-sections of B-B23.

NX2 ¼

EAðSX23 þ SX24 þ SX25 Þ 3

ð1Þ

where SX23 , SX24 , and SX25 are the readings of the strain gauges attached on the beam web along S-X-2. According to Fig. 13, the deflection profile of the beam between the cross section S-X-2 and S-X-3 can be approximated as a straight line. From the equilibrium condition, the shear force V X2 can be calculated as followed,

V X2 ¼

M X2  M X3 3ðM X2  M X3 Þ ¼ L 1=3L

ð2Þ

M X2 and MX3 can also be calculated from the strain gauge measurements as well. The curvature of the cross-section S-X-i, where i is 2 or 3, can be expressed as:

1

q

¼

SXi3  SXi5 2ðSXi3  SXi5 Þ MXi ¼ ¼ h  2t f ðh  2t f Þ=2 EI

ð3Þ

Thus, the bending moment at cross section S-X-i can be calculated as follows:

M Xi ¼

2ðSXi3  SXi5 ÞEI h  2tf

ð4Þ

Therefore, the contribution of one moment beam (B-X) to the total collapse resistance of the system can be expressed as:

F X ¼ V X2 cos hX þ N X2 sin hX

ð5Þ

And the concentrated force F applied to the stub column can be calculated as follows:

F¼

X X FX ¼ ðV X2 cos hX þ NX2 sin hX Þ

ð6Þ

where hX is the rotation at S-X-2 and F X is the contribution of one moment beam to the collapse resistance. In Eq. (5), V X2 cos hX is the vertical component of the shear force at cross section S-X-2 and N X2 sin hX is the vertical component of axial force at the same cross section. In the other words, V X2 cos hX and N X2 sin hX represent the contributions of the flexural action and catenary action in a moment beam to the collapse resistance of the system, respectively. hX can be calculated on the basis of the vertical displacement measured by the LVDTs placed at S-X-2 and S-X-3. 4.2. Development of collapse resistance mechanics and load redistribution The contributions of the flexural action and catenary action to the collapse resistance are demonstrated in Figs. 18 and 19 illustrates the proportion of flexural action and catenary action in the total collapse resistance, respectively. An important trend which

215

150

150 135 120 D=10

105

D=30

90

D=50 D=70

75

D=90

60 45 30 15 0 -1300 -1000 -700 -400 -100 200

Distance to the bottom flange (mm)

Distance to the bottom flange (mm)

H. Li et al. / Engineering Structures 150 (2017) 203–220

135 120 105 90 D=50

75

D=100

60

D=150

45

D=200 D=300

30

D=400

15 0

500

-800

800 1100 1400 1700

-500

-200

Distance to the bottom flange (mm)

150 135 D=50

120

D=100

105

D=150

90

D=200 D=300

75

D=400

60 45 30 15 0

0

400 800 1200 1600 2000

Distance to the bottom flange (mm)

( a ) S- B C 2- 1

-2000-1600-1200 -800 -400

100

400

700

1000

1300

Strain ( ) ( b) S- BC 2 - 2

Strain ( )

150 135 120 D=10 105

D=20

90

D=30

75

D=40 D=50

60 45 30 15 0 -5000

-2000

1000

4000

7000

Strain ( )

Strain ( )

( c ) S- B C 2- 3

( d) S- BC 2 - 4

10000

Fig. 16. Strain distributions along the various cross-sections of B-BC2.

S-X-2 S-X-3

Stub column (a) Idealized computational model

(b) Internal forces at cross sections S-X-2 and S-X-3

Fig. 17. Idealized computational model and internal forces at cross sections S-X-2 and S-X-3 of a moment beam (B-X).

13000

216

H. Li et al. / Engineering Structures 150 (2017) 203–220

400 Resistance from catenary action

390

Axial force in B-BC2

340

Axial force in B-B23

Resistance from flexural action

250 200 150

0.58

290

0.48

240

0.38

190

0.28

140 0.18

90

100

40

50

-10

0 0

0.68

N/Np

300

440

Axial forces (kN)

Collapse resistance (kN)

350

0.78 Total resistance

0.08 0

50

100

150

200

250

300

350

400

-0.02

Vertical displacement (mm) 50

100

150

200

250

300

350

400 Fig. 20. Axial forces in B-B23 and B-BC2.

Vertical displacement (mm)

Portion occupied by each mechanism (

)

Fig. 18. Contributions of flexural action and catenary action to the collapse resistance of the system.

100

80

60

Flexural action Catenary action

40

20

0 0

50

100

150

200

250

300

350

400

Vertical displacement (mm) Fig. 19. Proportion occupied by flexural action and catenary action in total resistance of progressive collapse.

can be observed in Fig. 18 is that the proportion of flexural action decreased as the increase of the displacement and the percentage taken up by the catenary action increased. According to these two figures, it can be seen that when the vertical displacement of the stub column is smaller than 40 mm, the collapse resistance of the system came from the flexural action alone. Then small amount of catenary action was developed in the moment beams, taking up 5% of the total collapse resistance at the vertical displacement of 120 mm, corresponding to the chord rotation of 0.06 rad. The number increased to 17% at the vertical displacement of 240 mm. Although the catenary action started to play a more significant role in resisting progressive collapse and made up larger and larger portion of the total collapse resistance, the amount of collapse resistance provided by flexural action continued increasing until the displacement reached 240 mm. Therefore, in early loading stage, flexural action was the primary mechanism to resist progressive collapse and the contributions of the catenary action to the total collapse resistance was limited. After that, the amount of collapse resistance provided by flexural action dropped and the portion in the total collapse resistance that the catenary action accounted for grew in a much faster pace. At the vertical displacement of 370 mm, the catenary action accounted for slightly larger than 50% of the total collapse resistance and became the predominant mechanism to resist progressive collapse. The number kept increasing and reached the maximum value of nearly 60% before failure occurred at the vertical displacement of 421 mm. Therefore,

under large deformation condition, catenary action was crucial for the collapse resistance of the test specimen. Although the flexural action was not as influential, the contributions of the flexural action was still substantial. This phenomenon is quite different with what was observed in the experimental tests conducted by Yang and Tan [24,25] on the behaviors of bolted simple and semi-rigid connections under column loss scenarios, in which the flexural action disappeared or even played a negative role in resisting progressive collapse and all the collapse resistance was provided by the catenary action in the final stage of collapse. Therefore, the typology of the beam-to-column connections has great impact on determining the development of flexural action as well as catenary action. The comparison between the axial forces developed in B-B23 and B-BC2 is shown in Fig. 20. Considering the symmetry of the test specimen, the given plots were representative and therefore the axial forces developed in the other two moment beams that were connected to the stub column were not presented herein. It was evident that the axial force developed in B-BC2 was much larger than B-B23. The largest tensile force developed in B-BC2 was about 470 kN, corresponding to 0.78N P , where N P is the tensile capacity of the moment beams used in the test, which is 596.85 kN. The largest tensile force developed in B-B23 was around 70 kN, corresponding to 0.12N P which is 1/7 of B-BC2. The deviation between the amounts of the catenary action developed in these two beams was due to the difference of the stiffness of the exterior beam-to-column connections. B-B23 lay in the direction of strong axis of the columns and B-BC2 was in the weak axis direction. The flexural stiffness in strong axis of the columns was about 12 times larger than the flexural stiffness in weak axis. Thus, more catenary action could be developed in B-BC2 under the same vertical displacement because more constraints were provided. Therefore, it can be conferred that the lateral restraint of the beam plays a significant role in the development of catenary action. Fig. 21 demonstrates the collapse resistance provided by the flexural action in the moment beams B-B23 and B-BC2. It can be seen that the two curves were closed to each other, indicating that similar amounts of flexural action were developed in these two beams. It can be seen from Figs. 18–22, the trends of the development of flexural action and catenary action were not significantly influenced by the lateral torsional buckling of the moment beams. 4.3. Load redistribution pattern Besides the development of collapse resistance mechanisms, the load redistribution pattern of the test specimen subjected to loss of center column could also be determined by the internal forces in the moment beams. The vertical load F X dis , which is

217

Vertical component of shear force(kN)

H. Li et al. / Engineering Structures 150 (2017) 203–220

In Eq. (7), F X dis also represents the contributions of the moment beam B-X to the collapse resistance of the structural system. Thus, as shown in Fig. 22, the moment beams in strong axis direction (BB23) and weak axis direction (B-BC2) contributed to the total collapse resistance of the structure almost equally when flexural action was the predominant collapse resisting mechanism. As the vertical displacement of the stub column increased, the difference between these two became larger and larger after catenary action started to play a significant role in resisting progressive collapse. Therefore, the contributions of the moment beams in different directions varied throughout the entire loading process.

60 50 40 30 B-B23 B-BC2

20 10 0

0

50

100

150

200

250

300

350

4.4. Estimation of dynamic peak displacement and dynamic increase factor

400

Vertical displacement (mm) Fig. 21. Collapse resistance provided by flexural action in B-B23 and B-BC2.

140

i_dis

(kN)

120

B-B23 B-BC2

100 80 60 40

W ext ¼ F C DD

20 0

0

50

100

150

200

250

300

350

400

Vertical displacement (mm) Fig. 22. The load distributed from B-B23 and B-BC2 to exterior columns C-B3 and C-C2.

transferred from a moment beam B-X to the exterior edge column which it was connected to can be determined as:

FX

dis

Although the test conducted in this study was a static pushdown analysis, the test results could be used to estimate the dynamic responses of the structure by using the energy based method proposed by Izzuddin et al. [8]. The method was on the basis of the law of energy conservation, i.e. W ext ¼ W int . In this section, when estimating the dynamic response of the test specimen, the center column is assumed to be intact initially and then be removed instantaneously. Thus, for the one-story substructure considered herein, after sudden loss of the center column, the external work done by the system when peak dynamic displacement (PDD) of the center column DD is reached can be expressed as:

¼ V X2 cos hX þ NX1 sin hX

ð7Þ

Fig. 22 illustrates the comparison between the vertical loads distributed from beam B-B23 to column C-B3 and from beam BBC2 to column C-C2 with the increase of the vertical displacement of the stub column, respectively. The amounts of vertical loads transferred from both beams to the exterior columns were closed to each other until the vertical displacement reached around 250 mm. After that, the difference between these two became larger and larger with the increase of the vertical displacement. The amount of the loads transferred to column C-B3 kept increasing whereas the amount of the loads transferred to column C-C2 started to decrease with a slow pace. This is because the amount of catenary action developed in beam B-B23 was much larger than in B-BC2, as is shown in Fig. 20 under large deformation condition. Before fracture occurred, the amount of vertical load transferred to C-B3 was about two times of C-C2. Similar trend was observed in C-B1 and C-A2. In summary, for the given structure, the amount of loads redistributed to the exterior columns in East-West direction and NorthSouth direction was closed to each other in early stage of loading. However, after catenary action was mobilized in the moment beams, more loads were redistributed to the strong axis columns C-B1 and C-B3, comparing with the weak axis columns C-A2 and C-C2 and the difference between them was larger and larger as the vertical displacement increased. Therefore, the catenary action does not only have a significant impact on the collapse resistance of the system under large deformation condition, but also plays a significant role in redistributing loads under column loss scenarios.

ð8Þ

where F C is the gravity load previously carried by the center column. The internal (strain) energy stored in the system at this moment can be expressed as

Z W int ¼

DD

f ðDÞdD

ð9Þ

0

f ðDÞ represents the load-deformation relationship obtained from the static push-down testing conducted herein. Thus, by equating the right part of the above two equations, the PDD after sudden loss of the center column can be calculated as,

Z

DD ¼

DD

f ðDÞdD

ð10Þ

0

FC

The PDD of the test specimen as well as the prototype structure can be estimated by applying the energy-based method. For the test specimen, f ðDÞ is shown in Fig. 12. The gravity load F cm , which is carried by the center column of the test specimen, can be calculated on the basis of F cp , which is the gravity loads carried by the column at the same location in the prototype structure by using the similitude theory. It is known that the geometric scale factor used in this test SL ¼ 3. The materials that are used for the structural members and connections in the test specimen and the prototype structure are identical, which means the stress scale factor Sr ¼ 1. Therefore, the force scale factor can be expressed as:

SF ¼

F cp ¼ Sr  S2L ¼ 9 F cm

ð11Þ

F cp is calculated on the basis of the load combination given by UFC 4-023-03, which is 120% dead load plus 50% of the live load and it F

turned out F cp ¼ 234 kN. Therefore, F cm ¼ 9cp ¼ 26 kN. Thus, the value of F cm was substituted in Eq. (10) and a trial-and-error process was conducted. The calculation results revealed that the PDD of the test specimen DD was 8.7 mm. The displacement is so small that the test specimen still behaves elastically according to Fig. 12 and thus

218

H. Li et al. / Engineering Structures 150 (2017) 203–220

0.10

0.15

0.20

d

/

y

2.00

)

0.25

0.30

Dynamic increase factor

0.05

0.35

1.8 1.6 1.4 1.2 0

50

100

150 d

200

0

1.20

f ðDÞdD D0

F st f ð D0 Þ D0 ¼Z D 0 Fd f ðDÞdD

2

4

6

8

10

12

14

16

18

20

Fig. 24. Comparison between the DIF estimated on the basis of test results using energy-based method and the equation given by UFC-023-03 [21].

ð12Þ

ð13Þ

0

It is worthwhile to mention that F d can also be considered as the designed gravity load which is previously carried by the removed column. Fig. 23 shows the relationship between the value of DIF and F d which is applied to the center column as a concentrated force. The DIF is also shown as a function of the normalized load F d =F y , where F y ¼ ry Ac . ry is the yielding strength of the structural steel used in the center column and Ac is the area of the cross section of the center column. It can be seen from Fig. 23 that the value of the DIF lies between 1.3 and 2.0. The value of DIF decreased with the increase of F d when F d was smaller than 150 kN. The DIF then increased as the F d became larger, when catenary action started to ramp up to resist progressive collapse. In UFC 4-023-03 [21], the equation for calculating the value of DIF is expressed as:

0:76 XN ¼ 1:08 þ hpra =hy þ 0:83

0

(kN)

Thus, the DIF can be defined as

XN ¼

1.40

Normalized rotation ( p/ y)

no collapse will occur. The PDD of the prototype structure DDP ¼ SL  DD = 3
8.7 = 26.1 mm. Since the test specimen will not collapse subjected to sudden loss of the interior column, it can be concluded that the prototype structure will survive progressive collapse, too. Considering dynamic nature of progressive collapse, the loads applied to the floor areas above the removed column have to be multiplied by the dynamic increase factor (DIF) XN when nonlinear static procedure is used to estimate the deformation demand of the considered structure under column loss scenario (UFC 4-023-03). The DIF can be defined as the ratio of the loads applied statically and dynamically when the structure is subjected to the same deformation demand D0 and it is used to amplify the gravity loads which are applied to the structure when nonlinear static analysis is used to estimate the dynamic peak displacement. When D0 is known, the static load F st could be expressed as F st ¼ f ðD0 Þ. The dynamic load F d can be expressed:

Fd ¼

UFC-023-03 (2013) 1.60

250

Fig. 23. Dynamic increase factor vs. the gravity loads.

R D0

Energy based method 1.80

1.00 1.0

ð14Þ

where hpra is the allowable plastic rotation and hy is the yield rotation of the cross section. The comparison between the DIF calculated according to Eq. (14) and the DIF estimated on the basis of the test results using energy-based method with respect to the normalized rotation (hpra =hy ) is presented in Fig. 24. It can be seen that the DIF estimated on the basis of the test results were 10–16% larger than

the DIF calculated according to Eq. (14) when the normalized rotation ranged between 0.4 and 6. After that, the former increased but the latter decreased as the increase of the normalized rotation. As a result, the difference between them became larger and larger. Before fracture occurred (hpra =hy ¼ 20), the DIF estimated on the basis of the test results using energy-based method was 35% larger than the DIF calculated on the basis of UFC 4-023-03. Thus, the DIF given by UFC 4-023-03 was unconservative for the test specimen in this study, especially under large deformation condition, when large amount of catenary action was developed in the moment beams. The curves shown in Figs. 23 and 24 can be used in the nonlinear static analysis of a structure under column loss scenarios in different design conditions. If the design requirements of structure acceptance criteria, as discussed in UFC 4-023-03, is known by the designers, the curve shown in Fig. 24, which represented the relationship between the value of DIF and the level of plastic deformation should be implemented. Then the nonlinear static should be performed and the PDD of the structure and internal forces of the structure should be evaluated to determine whether the deformation capacities and the strength of the structural components satisfy the design requirements. In comparison, the implement of the curve shown in Fig. 23 might be more straightforward. Once the loads carried by the column of interest is known, the DIF can be obtained on the basis of Fig. 23. Thus, the PDD and internal forces of the structural system subjected to sudden loss of the column can be determined. If the deformation and load demand do not exceed the capacity of the structure, the structure should be robust enough to resist progressive collapse. The relationship between the PDD and the concentrated load applied to the stub column is shown in Fig. 25. It can be seen that the maximum load which could be previously carried by the center column of the test specimen subjected to sudden loss of the column was around 260 kN before fracture occurred. The curve is also

400 350 300

Load (kN)

Dynamic increase factor

Normalized load ( 0.00 2.0

250 200 150 load vs. PDD

100 50 0

static load-deflection curve 0

100

200

300

400

Vertical displacement (mm) Fig. 25. Comparison between the static load-deflection curve and the curve representing load vs. dynamic peak displacement.

H. Li et al. / Engineering Structures 150 (2017) 203–220

an estimation of the load-displacement curve obtained from dynamic push-down analysis, which is more rigorous to evaluate the collapse resistance of a certain structure under column loss scenarios.

5. Summary and conclusions In this study, an experimental test was conducted to investigate the robustness of a 1/3 scale, one-story bare steel moment frame substructure with appropriate boundary conditions. A static push-down analysis was performed experimentally to evaluate the behavior of the test specimen subjected loss of the center column. The development of the collapse resistance mechanisms, including the flexural action and catenary action was quantified. The test results were also used to discuss the dynamic behavior of the structure subjected to sudden loss of the center column. The following conclusions are drawn:  The test specimen exhibits remarkable collapse resistance and ductility under column loss scenario. The test specimen is able to bridge over a load of 385 kN, which is applied to the top of the stub column. The maximum vertical displacement is as large as 421 mm, corresponding to the chord rotation of 0.21 rad.  In the early stage of loading, the flexural action is the primary mechanism to resist progressive collapse, which accounts for more than 80% of the total collapse resistance before the vertical displacement of the stub column reaches 240 mm. Then as the increase of the vertical displacement, the amount of collapse resistance provided by the flexural action drops and catenary action developed in the moment beams grows in a fast pace. The proportion made up by the catenary action developed in the moment beams is around 60% of the total collapse resistance in the final stage of loading. The amount of the catenary force developed in the moment beams in the strong axis of the columns is much larger than in the weak axis of the columns, which means the stiffness of the exterior connections has great impact on the development of catenary action. By comparing with the experimental results in other studies, it can be concluded that the development of flexural action and catenary action is substantially influenced by the types of the beam-to-column connections.  The amounts of loads redistributed to the strong axis exterior columns and weak axis exterior columns, which are also the contributions of the moment beams to the collapse resistance of the structural system, are closed to each other in early stage of loading, when flexural action is the predominant collapse resisting mechanism. However, the loads transferred to the strong axis columns become larger and larger comparing with the loads transferred to the weak axis columns as the enlargement of the vertical displacement, indicating the stiffness of the exterior connections can also influence the load redistribution pattern.  The peak dynamic displacement of the test specimen subjected to sudden loss of the center column is 8.7 mm, which is 1.94 times of the static displacement under the same loading condition. The test specimen still behaves elastically under such deformation and thus no progressive collapse will occur after sudden loss of the center column. The value of dynamic impact factor lies between 1.3 and 2.0. Comparison between the curves presenting the value of dynamic increase factor estimated using energy based method on the basis of the test results and the DIF calculated according to UFC 4-023-03 with respect to normalized rotation shows that it might be unsafe to use the latter curve under large deformation, when large amount of catenary action is developed in the moment beams.

219

 The catenary action is crucial for the collapse behavior of the tested structure, especially under large deformation conditions. It provides substantially large amount of collapse resistance, determines the load redistribution pattern, and needs to be considered when determining the dynamic impact factor in nonlinear static analysis under large deformation condition.

Acknowledgement The presented work was supported by grants from the National Natural Science Foundation of China under Grant No. 51408152, the Fundamental Research Funds for the Central Universities through grant HIT.NSRIF.2015098, China Postdoctoral Science Foundation through grant 2014M550194, and China Postdoctoral Science Foundation through grant 2015T80353. 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] Astaneh-Asl A, Jones B, Zhao Y, Hwa R. Progressive collapse resistance of steel building floors. Report number UCB/CEE-Steel-2001, 3; 2001. [2] Haremza C, Santiago A, Simões da Silva L. Experimental behaviour of heated composite steel-concrete joints subject to variable bending moments and axial forces. Eng Struct 2013;51:150–65. [3] Chen J, Huang X, Ma R, He M. Experimental study on the progressive collapse resistance of a two-story steel moment frame. J Perform Constr Facil 2012;26 (5):567–75. [4] El-Tawil S, Li H, Kunnath S. Computational simulation of gravity-induced progressive collapse of steel-frame buildings: current trends and future research needs. J Struct Eng 2014;140(8). A2513001. [5] Guo L, 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. [6] Guo L, Gao S, Wang Y, Zhang S. Tests of rigid composite joints subjected to bending moment combined with tension. J Constr Steel Res 2014;94:76–83. [7] Guo L, Gao S, Fu F. Structural performance of semi-rigid composite frame under column loss. Eng Struct 2015;95:112–26. [8] Izzuddin BA, Vlassis AG, Elghazouli AY, Nethercot DA. Progressive collapse of multi-storey buildings due to sudden column loss. Part I: simplified assessment framework. Eng Struct 2008;30(5):1308–18. [9] Johnson ES, Meissner JE, Fahnestock L. Experimental behavior of a half-scale steel concrete composite floor system subjected to column removal scenarios. J Struct Eng 2015. 04015133. [10] Li L, Wang W, Chen Y, Lu Y. Experimental investigation of beam-to-tubular column moment connections under column removal scenario. J Constr Steel Res 2013;88:244–55. [11] Li L, Wang W, Chen Y, Lu Y. Effect of beam web bolt arrangement on catenary behaviour of moment connections. J Constr Steel Res 2015;104:22–36. [12] Liu C, Tan KH, Fung TC. Dynamic behavior of web cleat connections subjected to sudden column removal scenario. J Constr Steel Res 2013;86:92–106. [13] Liu C, Tan KH, Fung TC. Investigations of nonlinear dynamic performance of top-and-seat with web angle connections subjected to sudden column removal. Eng Struct 2015;99:449–61. [14] Liu C, Fung TC, Tan KH. Dynamic performance of flush end-plate beam-column connections and design applications in progressive collapse. J Struct Eng 2016;142(1). 04015074. [15] Ministry of Construction China. GB 50011-2010: code for seismic design of buildings. Beijing (China): Architecture and Building Press; 2010 [in Chinese]. [16] Ministry of Construction of China. GB50017-2003: code for design of steel structure. Beijing (China): China Planning Press; 2013 [in Chinese]. [17] Oosterhof S, Driver RG. Behavior of steel shear connections under columnremoval demands. J Struct Eng 2015;141(4). 04014126. [18] Sadek F, Main JA, Lew HS, Robert SD, Chiarito VP, El-Tawil S. An experimental and computational study of steel moment connections under a column removal scenario. NIST technical note 1669. Gaithersburg (MD): National Institute of Standard and Technology; 2010. [19] Song BI, Sezen H. Experimental and analytical progressive collapse assessment of a steel frame building. Eng Struct 2013;56:664–72. [20] Song BI, Giriunas KA, Sezen H. Progressive collapse testing and analysis of a steel frame building. J Constr Steel Res 2014;94:76–83. [21] UFC. UFC 4-023-03: design of buildings to resist progressive collapse. Washington, D.C.: Department of Defense; 2013. [22] Wang W, Fang C, Qin X, Chen Y, Li L. Performance of practical beam-to-SHS column connections against progressive collapse. Eng Struct 2016;106:332–47. [23] Weigland JM, Berman JW. Integrity of bolted angle connections subjected to simulated column removal. J Struct Eng 2015. 04015165.

220

H. Li et al. / Engineering Structures 150 (2017) 203–220

[24] Yang B, Tan KH. Behavior of composite beam-column joints in a middlecolumn-removal scenario: experimental tests. J Struct Eng 2013;140(2). 04013045. [25] Yang B, Tan KH. Experimental tests of different types of bolted steel beamcolumn joints under a center-column-removal scenario. Eng Struct 2013;54:112–30.

[26] 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 (6):341–51. [27] Zandonini R, Baldassino N, Freddi F. Robustness of steel-concrete flooring systems – an experimental assessment. Stahlbau 2014;83(9):608–13.