Influence of masonry infill walls on fire-induced collapse mechanisms of steel frames

Journal of Constructional Steel Research 155 (2019) 426–437

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Journal of Constructional Steel Research

Influence of masonry infill walls on fire-induced collapse mechanisms of steel frames Sidi Shan a,b,d, Shuang Li b,c, Shuhong Wang a,⁎, Halil Sezen d, Mehmet M. Kose d,e a

School of Resources and Civil Engineering, Northeastern University, Shenyang 110819, China Key Lab of Structures Dynamic Behavior, 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 d Department of Civil, Environmental and Geodetic Engineering, The Ohio State University, Columbus, OH 43210, USA e Department of Civil Engineering, Kahramanmaras Sutcu Imam University, Kahramanmaras 46050-9, Turkey b c

a r t i c l e

i n f o

Article history: Received 14 September 2018 Received in revised form 18 December 2018 Accepted 5 January 2019 Available online xxxx Keywords: Fire-induced collapse Infill walls Steel frames Fire scenarios Load redistribution

a b s t r a c t This paper numerically investigates the influence of masonry infill walls on collapse mechanisms of steel frames under fire scenarios. Three six-story by five-bay steel frames were designed in this study. One of these frames had no infill walls, another one had horizontal infill walls, and the last one had vertical infill walls. Load redistribution and fire resistance were investigated under edge bay fire scenario and central bay fire scenario. The numerical results indicated that masonry infill walls provide alternate load paths in fire conditions, causing significantly large variations of axial forces in surrounding columns. Furthermore, the lateral resistance of the infilled frames is provided by the integral loading resisting system under edge bay fire scenario. The infill walls decrease the buckling temperature and increase the collapse temperature of the heated columns. A series of parametric analyses were performed to investigate the factors influencing the fire resistance of the steel frames. Finally, a preliminary design method was proposed with an aim to prevent the collapse of steel frames with infill walls under fire scenarios. © 2019 Elsevier Ltd. All rights reserved.

1. Introduction The fire-induced collapse of a structure refers to the phenomenon when damage of local members caused by fire leads to a sequence of failures in surrounding members, eventually resulting in a partial or complete collapse of the structure disproportionate to the initial damage. Usually, the fire-induced collapse may lead to catastrophic human and property losses, such as the collapse of World Trade Center towers caused by uncontrolled fire on September 11, 2001. At present, multistory structures are usually built on a steel skeleton system because of their high construction efficiency and low labor costs. However, the steel structures may be vulnerable to collapse since the material properties of steel decrease sharply at elevated temperature. Hence many experimental [1], numerical [2–9] and analytical [10] studies have been performed in recent years, in order to better understand the collapse mechanisms of steel structures under fire scenarios and to propose reasonable fire resistance design approaches. Nonetheless, very few of them considered the interaction between steel frame members and masonry infill walls under fire scenarios, even though masonry infill walls are widely used in frame structures for building envelopes and interior partitions. ⁎ Corresponding author. E-mail address: [email protected] (S. Wang).

https://doi.org/10.1016/j.jcsr.2019.01.004 0143-974X/© 2019 Elsevier Ltd. All rights reserved.

Masonry infill walls have been shown to have significant influence on the progressive collapse performance of frame structures under column removal scenario [11]. Sasani and Sagiroglu [12] suddenly removed two adjacent columns in the first story of Hotel San Diego, an actual RC frame structure with masonry infill walls, and showed that the masonry infill walls could help to reduce the overall deformation. Li et al. [13] and Shan et al. [14] conducted deformation controlled quasi-static tests to investigate the influence of full-height infill walls and partial infill walls on progressive collapse behavior of RC frames under central column removal scenarios, respectively. They showed that the masonry infill walls provide alternate load paths and significantly increase the resistance, however, reduce ductility, change load carrying pattern and damage mode as well. A series of quasi-static tests were conducted by Brodsky and Yankelevsky [15] to study the progressive collapse mechanisms of infilled RC frames under external column removal scenarios. Three types of failure modes were observed in their tests due to the influence of masonry infill walls. Qian and Li [16] experimentally studied the progressive collapse performance of three-story-by-two-bay infilled RC frames under column removal scenarios, and indicated that the critical sections of beams in second and third stories are different due to the interaction between masonry infill walls and frame members. It is worth noting that although several researchers investigated the progressive collapse behavior of infilled RC frames under column

S. Shan et al. / Journal of Constructional Steel Research 155 (2019) 426–437

427

2. Frame details and fire scenarios

is designed to resist wind and earthquake loading [19]. The dead load (DL) is assumed to be 6.125 kN/m2 for the roof and 4.125 kN/m2 for other stories, while the live load (LL) is assumed to be 2 kN/m2 for the roof and 3.5 kN/m2 for other stories. All beam sections are adopted as HN298×149×5.5×8, in which the first, second, third and fourth number indicate the height of section, flange width, web thickness and flange thickness (unit: mm), respectively. The external column section is adopted as HW250×250×9×14. The internal column section is adopted as HW350×350×12×19 for the first and second stories, HW300×300×10×15 for the third and fourth stories, and HW250× 250×9×14 for the fifth and sixth stories. Bending orientation of all frame members is parallel to the plane of the frame, i.e., all sections are bending about their strong axis. Steel material, with Young's modulus of 2.06 × 105 MPa and yield strength of 235 MPa at ambient temperature, is used for the frame members. The prototype steel frame building had no masonry infill wall (bare frame), had horizontal masonry infill walls (infilled frame 1), and had vertical masonry infill walls (infilled frame 2). The masonry infill walls were made of concrete bricks with dimensions of 390 mm×190 mm×190 mm and 190 mm×190 mm×190 mm, and have a thickness of 190 mm. The compressive strengths is 7.5 MPa for the brick and 5 MPa for the mortar, respectively. The concrete masonry prism compressive strength is calculated as follows [20]:

2.1. Frame details

f m ¼ 0:46  f 1 ð1 þ 0:07f 2 Þ

The purpose of this study is to investigate the influence of masonry infill walls on the collapse mechanisms of steel frames under compartment fire. Since the collapse mechanism of the 3D structures with masonry infill walls against fire is mainly related to the collapse of the 2D frames with infill walls, 2D moment resisting frame (MRF) is used to investigate the influence of the masonry infill walls [14], and is adopted in this study. A prototype steel frame building was designed [17,18], as shown in Fig. 1. The building has five-bay by six-bay with 6 m span, and has six stories with 3.3 m story height. One plane frame marked by the dash line on the plan view in Fig. 1(a) is analyzed in this study. The building

where f1 and f2 are the bricks and the mortar compressive strength respectively. The compressive strength of the concrete masonry infill walls, fm, calculated from Eq. 1, is equal to 3.8 MPa.

removal scenarios, none of them studied the influence of masonry infill walls on collapse performance of steel frames against fire. In a fire condition, many frame members may be heated and elongated simultaneously, then buckled subsequently at elevated temperature due to the restraints by the surrounding elements. Therefore, the load redistribution pattern and collapse process of frames under fire situation are different. Furthermore, the fire resistance of a structure (defined as the time or the elevated temperature when a structure collapses) cannot be clearly evaluated by simply removing one potentially damaged column, as in the progressive collapse studies. In this study, explicit nonlinear dynamic analyses are performed with an aim to investigate the influence of masonry infill walls on the fire-induced collapse behaviors of steel frames. The modeling approaches of the frame members and masonry infill walls were first validated against fire tests of two steel frames and a lateral quasi-static test of infilled steel frame, respectively. The load redistribution and fire resistance of the infilled steel frames were studied. A series of parametric analyses were performed and the influence of load ratios, strength and quantity of infill walls was investigated. Finally, in this study, a preliminary design approach was proposed to prevent the fire-induced collapse of infilled steel frames.

0:9

2.2. Fire scenarios The fire scenario discussed in this study involves only one compartment in the first story to be heated since their load ratios were the largest, in comparison with columns in the upper stories. Two fire scenarios are considered, namely edge bay fire (Fire 1), and central bay fire (Fire 2), respectively. The two columns on each side of the heated bay

C1 Bay A

(a) Plan view

Fire 2

ð1Þ

BB6

BD6

BB5

BD5

BB4

BD4

BB3

BD3

BB2

BD2

BB1

BD1

C2

C3 Fire 2 C4

Bay B

Bay C

C5 Fire 1 C6

Bay D

Bay E

(b) Bare frame

Fire 1

(c) Infilled frame 1

Fire 2

(d) Infilled frame 2 Fig. 1. The prototype steel frame building.

Fire 1

428

S. Shan et al. / Journal of Constructional Steel Research 155 (2019) 426–437

are assumed to be heated uniformly across its cross-section under EN 1991-1-2:2002 standard temperature-time curve [21], and the rest of the frame members are assumed to be maintained at ambient temperature (20°C).

code [27], The Young's modulus of concrete masonry infill walls is calculated as follows:

3. Modeling and analysis method

where fm is the compressive strength of masonry infill walls. Based on the experimental results in Refs. [13, 14], the residual compressive strength is 10% of the maximum strength, the strain at maximum strength is 0.0022, and the ultimate strain is 0.0055. The tensile stressstrain envelop curve of infill walls contains two linear branches: the ascending branch before tensile strength, then the descending branch till ultimate strain. The tensile strength of infill walls (ft) is adopted to be 10% of the compressive strength [28]. The strain at the tensile

250

20°C 100°C

200°C 300°C

Stress (MPa)

200 150 100 50 0 0.00

0.05

0.10 0.15 Strain

(a) Steel

0.20

400°C 500°C 600°C 700°C 800°C 900°C 1000°C 1100°C 1200°C

0.25

ð2Þ

strength (εcr) is calculated by (Efmt ), and the ultimate strain is 6εcr [29]. The stress-strain relationship curve of the infill walls in this study is shown in Fig. 2(b). The variations in infill wall properties at elevated temperature are specified in accordance with EN 1992-1-2 [30]. 4. Verification 4.1. Masonry infilled frame at ambient temperature In order to validate the modeling approach for masonry infill walls proposed in this study, the masonry infilled frame tested by Tasnimi and Mohebkhah [31] are simulated. The details of the masonry infilled frames are shown in Fig. 3, and the top story beam is loaded cyclically under displacement control in test. Calculated and measured response of the frame compare reasonably well, as shown in Fig. 4. 4.2. Fire response of steel frames Test results of two groups of steel frames (EHR3 and ZSR1) in Ref. [32] were used to validate the modeling method in this study. The details of the steel frames are shown in Fig. 5. All frame members of EHR3 were uniformly heated, while the frame members in the left bay of ZSR1 were heated. The numerical simulation results of the displacements against the temperature are compared with test data in Fig. 6. It can be observed that the numerical results compare reasonably well with the fire behavior of the frames. 4.3. Masonry infill wall in fire Due to the scarcity of experimental data on in-plane performance of masonry wall, the out-of-plane behavior of numerical modeling of masonry infill wall at elevated temperature was validated using data from a masonry wall fire test by Nguyen and Meftah [33]. The length and height of the 100 mm thick masonry wall was equal and 3 m. The masonry wall was installed in a support frame and was heated on one face following standard fire curve in Eurocode 1 [21]. The temperature

0

1 0

Stress (MPa)

The MRF finite element models are created and explicit nonlinear dynamic analyses are conducted by using ABAQUS program [22]. The frame members are modeled by using a series of 2-node Timoshenko beams (B31) elements. An initial mid height imperfection of 1/1000 of the column length is applied to all columns. The columns in the first story are assumed to be fixed at the ground level, and the connections between columns and beams are assumed to be rigid. Therefore, the fracture and failure of the connections are not taken into account during the analysis. The masonry infill walls are simulated by using three dimensional 4-node shell elements with reduced integration (S4R). The interface between the frame members and masonry infill walls is modeled by using tie constraints, assuming no relative motion between them. The damping ratio ζ = 0.05 is used for the entire bare steel frame model. The explicit dynamic analysis is employed in this study to get a better numerical convergence under large deformation. A timescale method is used to scale the fire duration from hours to several minutes, in order to save the computing cost. The time scale ratio of 1 min to 1 s is adopted for the heating duration. This timescale not only accurately represented the behavior of steel frames at elevated temperature, but also significantly save the computing time. A similar approach was performed by Jiang and Li [6,8]. The analysis is conducted over two steps. In the first step, the gravity load combination of 1.2DL + 0.5LL recommended by GSA [23] is applied to the steel frame before dynamic analysis. The gravity load is increased slowly within 5 s to reach the final values, and then it remained constant for 2 s to eliminate any dynamic effects. In the second step, the gravity load is kept unchanged while the temperature of the heated column is increased from ambient temperature to 1000°C with standard temperature-time curve given by Eurocode 1 [21]. The steel properties for ambient temperature are assumed with Young's modulus of 2.06 × 105 MPa. The yield strength of steel at ambient temperature is 235 MPa. The Poisson's ratio is assumed to be 0.3. The steel properties for elevated temperatures are temperature dependent recommended by EN 1993-1-2 [24], with thermal expansion of 1.4 × 105/°C [24]. The limiting strain for yield strength is 0.15 and the ultimate strain is 0.2 [24]. The stress-strain relationship of the steel materials in the frame models is shown in Fig. 2(a). The Concrete Damaged Plasticity model in Abaqus program [24] is used to represent the masonry infill walls material, in which the skeleton curve is represented by the Kent-Scott-Park material model [25,26]. According to MSJC

Em ¼ 900f m

0

-1 -2 -3 -4 -0.008 -0.006 -0.004 -0.002 0.000 0.002 Strain

(b) Masonry infill walls

Fig. 2. Constitutive relationship adopted for steel and masonry infill walls.

S. Shan et al. / Journal of Constructional Steel Research 155 (2019) 426–437

gradient across the thickness of the masonry wall is assumed to be 9T °C/m according to the test results [33], in which T is the temperature at mid-section of the masonry wall. As seen in Fig. 7, the calculated 2.26m

429

out-of-plane displacement at the central part of masonry wall was compared with the response measured during the fire test. The response predicted by the numerical model agree well with the test results. Therefore, it can be speculated that the in-plane behavior of the masonry infill walls against fire can also be reasonably predicted.

Cyclic loading (-)

(+)

5. Results and discussion 1.80m

=315MPa Section: IPE140 =7.63MPa Infill thickness: 0.11m

In order to examine the influence of the masonry infill walls under fire scenarios, numerical analyses of the bare frame, the frame with horizontal masonry infill walls (infilled frame 1), and the frame with vertical infill walls (infilled frame 2) are conducted for the two fire scenarios as shown in Fig. 1.

300

0

Lateral load (kN)

200 100 0 -100 -200

0 Test Numerical

-300 -60 -40 -20 0 20 40 60 Lateral displacement (mm)

80

Fig. 4. Comparison of numerical and tested lateral load-displacement for masonry infilled frame specimens [31].

Out-of-plane displacement (mm)

Fig. 3. Details of the masonry infilled frame against cyclic loading [31].

100 80 60 40 Test Numerical

20 0

0

50

100 150 Time (min)

200

250

Fig. 7. Comparison of out-of-plane displacement at the center of masonry wall against fire between test and numerical results [33].

Fig. 5. Details of the tested steel frames against fire [32].

Fig. 6. Comparison of numerical and tested results of steel frames against fire [32].

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S. Shan et al. / Journal of Constructional Steel Research 155 (2019) 426–437

5.1. Edge bay fire (Fire 1) The variation of axial force in columns in the first story in the bare frame against Fire 1 is illustrated in Fig. 8(a). As the temperature increases, the heated columns C5 and C6 elongated in the early heating stage. Additional axial compressive forces are developed in the heated column C5 caused by the restraints provided by the surrounding members. Since more restraints are provided by the surrounding members on column C5 than column C6, higher axial force is developed within column C5 than that within C6 at elevated temperature in the early heating stage until the buckling of C5 occurs. It is worth noting that the axial compressive forces in columns C4 and C6 decrease, as the axial compressive force in C5 increases until C5 reaches its buckling load at a temperature of 647.5 °C with an axial force of −514.0 kN. It indicates that the gravity load previously carried by C4 and C6 is transferred to column C5 in the early heating stage. It is worth noting that the column C6 elongates under Fire 1 whereas no thermal expansion occurs in C4, thus more gravity load transfer from C4 to C5 than from C6 to C5 as column C5 elongates at elevated temperatures. Therefore, the reduction of compressive force in C4 is 100.1 kN whereas that in C6 is only 20.8 kN, when buckling of column C5 occurs. Beyond this point, the axial load previously carried by column C5 is gradually redistributed back to the adjacent columns (C4 and C6), resulting in an increase of axial force in columns C4 and C6. The column C6 starts to buckle as the axial

Axial Force (kN)

0

-200

C1 C2 C3 C4 C5 C6

-400

-600

0

200

400 600 800 Temperature ( C)

1000

(a) Bare frame

Axial Force (kN)

0 -200

C1 C2 C3 C4 C5 C6

-400 -600 -800

0

200

400 600 800 Temperature ( C)

1000

(b) Frame with horizontal infill walls (Infilled frame 1) C1 C2 C3

Axial Force (kN)

1000 500

C4 C5 C6

0

0

-500 -1000 -1500

0

compressive force reaches its buckling load at a temperature of 794.8 C with an axial force of −211.8 kN. It should be noted from Fig. 8 (a) that in bare frame while axial forces change significantly in columns C4 and C5, there are small variations in axial forces in columns C1, C2 and C3. It can be seen in Fig. 8(b) that in the case of the infilled frame 1 (frame with horizontal infill walls), buckling (sudden drop in axial force) occurs in column C5 at a temperature of 521.5 °C with an axial force of −705.4 kN, and buckling occurs in column C6 at a temperature of 757.2 °C with an axial force of −227.0 kN. As shown in Fig. 8(c), the corresponding temperature for column C5 in infilled frame 2 (frame with vertical infill walls) is 521.5 °C with an axial force of −1483.3 kN, whereas column C6 buckles at a temperature of 728.3 °C with an axial force of −241.9 kN. The buckling temperatures of C5 and C6 in infilled frames are lower than those in the bare frame. As displayed in Fig. 8 (b) and (c), in infilled frames 1 and 2, the axial compressive forces in C4 and C6 decrease with axial compressive force in C5 and keep increasing until buckling load is reached. Thereafter, gravity loads carried by C5 are gradually transferred to the neighboring columns C4 and C6, until C6 buckles and the frame collapses. The redistribution process of gravity loads among columns in infilled frame 1 and 2 is similar to that in bare frame. However, because of more restraints provided by infill walls to the frames, higher axial compressive forces are generated in column C5 in infilled frame 1 and 2 in the early heating stage, resulted in a reduction of buckling temperature. It should be noted that the axial force in column C5 in infilled frame 2 is significantly larger than that in infilled frame 1 before buckling of column C5 occurs. This phenomenon can be attributed to the fact that the infill walls on the second story provided additional restraints on the top beam-column joint of column C5 in infilled frame 2. The deformed shapes of three frames when the buckling of C5 occurs are displayed in Fig. 9 with a magnification factor of 50. The Mises stress contours of masonry infill walls are also shown in Fig. 9. It can be seen that in bare frame, the beams in bay D (edge bay) are deformed in double curvature, indicating the development of frame action in these beams [11]. Shear resistances are provided by these beams to transfer the loads from the fire compartment to other parts at elevated temperature. In infilled frame 1, the bending position in surrounding beams changed from the beam ends to the mid-span, and high Mises stress is developed in the diagonal region of the infill wall at the top story in bay D. It can be inferred that a portion of load is redistributed from the fire compartment (edge bay) to the other parts of the frame through diagonal region of the infill wall, rather than through shear or flexural resistance of the surrounding beams. In the case of infilled frame 2, it can be seen that high Mises stresses are developed in the diagonal region of infill walls in each story. Due to the vertically continuous layout of masonry infill walls in five stories, the frame in bay D is stiffened and strengthened, and behaves as an integral load resisting system and exhibits an integral rotation at elevated temperature. Table 1 shows the axial force in columns when C5 starts to buckle during Fire 1 scenario. The ratio of axial compressive force in each column in the first story and the original axial compressive force is also shown as percentage. As indicated, when C5 buckles, axial compressive forces in column C4 and C6 decrease approximately 24.5% and 10.2% in bare frame compared with initial axial forces, whereas the corresponding changes are approximately 69.3% and 36.1% in infilled frame 1. In infilled frame 2, significantly large tensile force is developed in column C4 (672.9 kN) when column C5 buckles, whereas the variation of axial compressive force within C6 is small (only 9.9% decrease). Infill walls are installed in five stories in bay D (between columns C4 and C5) in infilled frame 2 whereas no infill wall is installed in bay E (between columns C5 and C6). This resulted in much larger stiffness in bay D than that of bay E. Therefore, the reaction force transferred to C4 is significantly larger than the force redistributed to C6. This also caused significantly large variation in internal force in column C4, but small changes in internal force in C6. It is worth noting that the significantly large °

200

400 600 800 Temperature ( C)

1000

(c) Frame with vertical infill walls (Infilled frame 2) Fig. 8. Axial forces at the columns C1, C2, C3, C4, C5 and C6 under Fire 1.

S. Shan et al. / Journal of Constructional Steel Research 155 (2019) 426–437

Fig. 9. Deflected shapes of three frames under Fire 1 (with a magnification factor of 50).

axial force variations occurred in columns C2 and C3 in infilled frame 2, compared to those in the bare frame and infilled frame 1. As shown in Table 1, axial compressive forces in columns C2 and C3 in the bare frame change approximately −0.1% and 1.2%, respectively. The corresponding values in the infilled frame 1 are 7.8% and 2.1%, respectively, which are larger than those of the bare frame. As in infilled frame 2, the increase in axial compressive force in column C2 is approximately 228.3%, which is significantly larger than the bare frame and infilled frame 1 Furthermore, a maximum tensile force of 523.0 kN was developed in column C3 in infilled frame 2.

431

As mentioned above, with column C5 and C6 elongating at elevated temperatures, there is no thermal expansion occurs in C4, resulted in a lateral deflection of the frames due to the compatibility requirement. As shown in Fig. 10(a), the lateral resistance of the bare frame is primarily provided by shear and flexural resistance of frame members in each story. However, in the infilled frames, due to the contribution of masonry infill walls to the integrity of the resisting system, the lateral resistance is predominantly provided by the integral resistance of the overall frame, rather than shear and flexural resistance of frame members. As shown in Fig. 10(b), most portion of lateral load transferred through diagonal region of infill walls to adjacent frame members in the form of axial compressive force, resulting in vertical force within surrounding columns. Therefore, significantly larger variations of axial forces are developed in C2 and C3 in infilled frame 2. On the other hand, since no infill wall participates in resisting lateral load in bay A (between column C1 and C2) and bay E, small changes in the axial force are observed in columns C1 and C6. In the case of infilled frame 1, infill walls are installed only in the top story, thus the variations of axial forces in C2 and C3 in infilled frame 1 are larger than those in bare frame but smaller than those in infilled frame 2. Fig. 11 compares the final failure patterns for the three frames under Fire 1 only. Fig. 12 presents the comparison of the vertical displacements at the top of column C6. The upward displacements are attributed to the expansion of the heated columns, and the downward displacements are caused by the buckling of column C5 and C6. The collapse of bare frame, infilled frame 1 and infilled frame 2 occurs at a temperature of 802.2°C, 836.9°C, and 831.3°C, respectively. Beyond these points, the top end of Column 6 move downward rapidly. Logically, infill walls significantly increase the stiffness and strength of the frame. Therefore, they increase the time to collapse with increasing temperature. The infill walls, however, also increase axial compressive force in column C5, resulting in an earlier start for the collapse sequence. After the buckling of C5 occurs, the alternate load redistribution paths provided by infill walls increase the robustness of the entire frame and hence raise the collapse temperature. In infilled frame 1, the collapse in bay E is induced by the failure of infill walls and beams in bay D. It should be noted that the top end of column C6 in infilled frame 2 reaches a re-stabilization at a temperature of 832.2 °C, even though column C6 completely lost its capacity before this point. In infilled frame 2, due to presence of vertical infill walls in five stories, significantly larger stiffness and strength increase is observed compared with the case of infilled frame 1. Therefore, bay D in infilled frame 2 stands after buckling of column C5 occurs, as shown in Fig. 11(c). From the other viewpoint, adequate layout of infill walls in bay D prevents the propagation of collapse in bay E toward other parts of the frame. Furthermore, since approximately half gravity load in bay E is resisted by the infill walls in bay D in infilled frame 2 in this situation, the bay E of infilled frame 2 could re-stabilize with cantilever beam mechanisms [6]. 5.2. Central bay fire (Fire 2) Fig. 13 shows the axial force distribution in the columns in the first story under Fire 2 scenario. It is observed that the axial force variations within the columns in three frames are quite similar with those against Fire 1. Due to the vertical restraint by the frame members, the axial compressive force in column C3 increases in the early heating stage. As a

Table 1 Axial force in columns when C5 starts to buckle during Fire 1.

Bare frame Infilled frame 1 Infilled frame 2

C1

C2

C3

C4

C5

C6

−220.4 (8.0%) −30.3 (11.4%) −239.3 (16.6%)

−413.7 (−0.1%) −437.3 (7.8%) −1339.9 (228.3%)

−413.5 (1.2%) −423.0 (2.1%) 523.0 (−)

−308.7 (−24.5%) −127.0 (−69.3%) 672.9 (−)

−514.0 (24.2%) −705.4 (73.9%) −1483.3 (263.6%)

−183.2 (−10.2%) −132.1 (−36.1%) −184.9 (−9.9%)

Note: (−) indicates large tensile force develops in the column.

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Vertical component force Horizontal component force Horizontal displacement

Displacement

Diagonal region Compression force C2 Shear

C3 Shear

(a) Bare steel frame

C2 Compression

C3 Tension

(b) Infilled steel frame

Fig. 10. Comparison of deformation patterns of bare steel frame and infilled steel frame under lateral displacement action in Fire 1.

direct result, the compressive force in column C2 decreases in bare frame as shown in Fig. 13(a). Furthermore, due to the additional restraint provided by the infill walls, the infilled frame 2 has the largest

vertical stiffness and strength among the three frames under Fire 2 scenario. Therefore, the axial forces in C2 and C3 increase rapidly and drastically in infilled frame 2 compared with those in bare frame and infilled frame 1. Consequently the buckling temperature of C3 in infilled frame 2 is the lowest. In the bare frame, buckling of column C3 occurs at a temperature of 660.0 °C with an axial force of 504.5 kN. In the case of the infilled frame 1, column C3 reaches its buckling load at a temperature of 615.5 °C with an axial force of 668.1 kN. The corresponding temperature for column C3 in infilled frame 2 is 484.9 °C with an axial force of 1698.6 kN. Since bay C is restrained on both sides, rather than restrained only on one side at the edge bays, the buckling temperatures of the heated columns in three frames under Fire 2 are lower compared with those counterparts under Fire 1 shown in Fig. 8. Table 2 shows the axial force in columns C1, C2 and C3 in three frames when C3 buckles under Fire 2 scenario. The ratio of axial compressive force and the original axial compressive force in each column in the first story is also shown as percentage. The axial compressive force within column C1 increases up to 31.3% in infilled frame 1, whereas the variations of axial force within C1 are 2.2% for bare frame and −1.1% for infilled frame 2. The reason is quite similar to the case of Fire 1. The largest variation in infilled frame 1 is due to the vertical component force caused by the infill walls in bay A, as illustrated in Fig. 10 (b). The small variations in the bare frame and the infilled frame 2, however, are due to the fact that no infill wall participates in lateral load resistance in bay A at elevated temperature. As shown in Fig. 13, after the buckling of column C3 occurs, the axial compressive force in column C3 is reduced, and the axial compressive force in column C2 starts to increase, indicating that the gravity load previously carried by column C3 is redistributed to column C2. The deflected shapes of three frames when column C5 buckles are shown in Fig. 14 with a magnification factor of 50. The overall lateral displacements under Fire 2 scenario are not as obvious as those under Fire 1 scenario, due to the vertical axis of symmetry and constraints by beams in bay C. Similar to the case of Fire 1, load from the fire

Fig. 11. Failure mode of the three frames under Fire 1.

Fig. 12. Vertical displacement of the top of column C6 during Fire 1.

S. Shan et al. / Journal of Constructional Steel Research 155 (2019) 426–437

Fig. 13. Axial forces in columns C1, C2 and C3 under Fire 2.

compartment (bay C) in bare frame is transferred through frames in bay B and D to adjacent bays. Load from the top story in bay B in infilled frame 1 is transferred through diagonal region of infill wall in bay A in the form of axial compressive force, which further explains the largest variations of axial force within column C1 in infilled frame 1 at elevated temperature. In infilled frame 2, however, a portion of load in the fire compartment is redistributed to the other parts of the frame through diagonal region in infill walls in bay B and D. The final failure modes for three frames under Fire 2 are shown in Fig. 15, and the vertical displacements at the top of column C3 are

Table 2 Axial forces in columns when C5 starts to buckle during Fire 2.

Bare frame Infilled frame 1 Infilled frame 2

C1

C2

C3

−208.5 (2.2%) −271.3 (31.3%) −203.0 (−1.1%)

−313.8 (−24.2%) −89.8 (−77.9%) 875.0 (−)

−504.5 (23.4%) −668.1 (61.2%) −1698.6 (311.0%)

Note: (−) indicates large tensile force develops in the column.

433

Fig. 14. Deflection shapes of three frames under Fire 2 (with a magnification factor of 50).

compared in Fig. 16. The collapse of bare frame and infilled frame 1 during Fire 2 occurs at a temperature 823.6°C, 902.6°C, respectively. Since the fire compartment is restrained on both sides under Fire 2, bare frame and infilled frame 1 collapse at higher temperatures compared with the case against Fire 1. The collapse of the bare frame and infilled frame 1 can be attributed to the failure of the beams and infill walls in adjacent bays (bay B and D). Since more infill walls exist in adjacent bays (bay B and D), the infilled frame 2 has much larger stiffness and strength compared with infilled frame 1, thus withstand collapse longer under Fire 2 scenario. It should be mentioned that significant axial tensile forces are developed in the beams surrounding the infill walls in infilled frame 1 and infilled frame 2 under Fire 1 and Fire 2 scenarios. The tensile forces in surrounding beams are mainly caused by horizontal component forces in infill walls, as illustrated in Fig. 10(b). It is worth noting that the tensile forces in surrounding beams start to decrease as the damage in the diagonal region of the infill wall occurs. Due to the length limitation, this phenomenon is not discussed in detail here.

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Fig. 16. Vertical displacement of the top of column C3 during Fire 2.

6.2. Influence of strength of infill walls In order to study the influence of strength of infill walls on the fire resistance of steel frames, the strength of infill walls was varied in a series of analyses, ranging from 3.8 MPa to 20 MPa. The vertical displacements of infilled frame 1 against edge bay and central bay fire scenarios were compared in Fig. 18, respectively. It can be seen that increasing the strength of infill walls increases the fire resistance of steel frames but not significantly. The infilled frame 1 against edge bay fire reaches a re-stabilization by increasing the strength of infill walls to 20 MPa, and the collapse during central bay fire was prevented when the strength of infill walls was increased to 8 MPa. 6.3. Influence of number of infill walls

Fig. 15. Final shapes of three frames under Fire 2.

From the analysis results mentioned above, it is apparent that masonry infill walls play a key role in resisting collapse of steel frames during fire. With and aim to investigate the influence of number of infill walls, the horizontal infill walls were installed in one story (top story), two stories (fourth and top stories) and three stories (second, fourth and top stories) in this study, respectively. Fig. 19 presents the variations of axial displacements of heated columns against edge bay fire and central bay fire, respectively. It can be seen that more infill walls could increase the collapse temperature of the steel frames. Furthermore, installation of infill walls in three stories could prevent collapse of steel frame during edge bay fire, and installation of infill walls in two stories could prevent collapse of steel frame against central bay fire. It is suggested to design or retrofit steel frames with appropriate number of infill walls, in order to prevent collapse against fire.

6. Parametric analysis

7. Prevention of collapse of infilled steel frames during fire

In this section, the influence of load ratios, strength, and quantity of infill walls on fire resistance of steel frames are investigated. The frame details, fire scenarios, modeling and analysis method described above are adopted in this parametric study.

The finite element model proposed in this study can predict the fireinduced collapse response of the infilled frames with good accuracy. However, the modeling techniques may be a bit sophisticated for engineers and the finite element analysis under fire scenario is too much time consuming. In order to prevent the fire-induced collapse resistance of infilled steel frames for practical purposes, a preliminary design approach for masonry infill walls was proposed in this section. In this approach, the masonry infill wall is substituted by an equivalent diagonal compressive strut representing the infill wall [34,35]. The design approach was applied to the six-story steel frame and was verified by finite element analysis. The design objective is to determine the required design parameters of masonry infill walls, such as number, strength, and thickness, to resist collapse when buckling of columns occurs under fire scenarios. This implies that the infilled steel frame is retrofitted by using masonry infill walls to resist the imposed gravity load of 1.2DL + 0.5LL specified in GSA [23]. Fig. 11 shows the resisting mechanisms of the infilled steel frames subjected to the buckling of columns caused by adjacent bay fire. The vertical resistance provided by

6.1. Influence of load ratios The gravity load on the frames taken in the analyses above was determined according to GSA [23] by using a load combination of 1.2DL + 0.5LL, which led to a load ratio of 0.27 for the internal columns in the first story. In this section, the load ratio was increased to 0.5 and 0.75, respectively, and the numerical analyses against edge bay fire and central bay fire were conducted. Fig. 17 shows the vertical displacements of heated columns for different load ratios under Fire 1 and Fire 2 scenarios, respectively. It can be observed that the buckling and collapse temperatures of three frames decrease with increasing load ratios. In order to improve collapse performance against fire, it suggested designing the frames with lower load ratios.

S. Shan et al. / Journal of Constructional Steel Research 155 (2019) 426–437

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Fig. 17. Influence of load ratios on vertical displacement of frames at heated bays.

Fig. 18. Influence of strength of infill walls on vertical displacements of frames at heated bays.

the diagonal compressive struts can be calculated by using the following equations: Rvertical ¼ Raxial sinα α ¼ arctan Hinf =Linf

ð3Þ


Raxial ¼ f m t inf winf

ð4Þ ð5Þ

where Rvertical is the vertical resistance provided by the diagonal compressive strut, Raxial is the resistance of the diagonal compressive strut, Hinf is the height of the masonry infill wall, Linf is the length of the infill wall, tinf is the thickness of the infill wall, and winf is the width of the equivalent diagonal compressive strut. According to FEMA356 [35], winf can be determined from Eq. 6. −0:4

winf ¼ 0:175ðλlb Þ

r inf

ð6Þ

λ¼

 1 Em t inf sin2α 4 4Efe Icol H inf

ð7Þ

where lb is the length of beam between centerlines of columns, rinf is the length of the diagonal region of masonry infill wall, Efe is the modulus of elasticity of frame material, and Icol is the moment of inertia of columns. As shown in Fig. 20, plastic hinges are usually formed at the ends of beams as the bending moment resistance of cross section reaches its maximum moment capacity Mp. The vertical resistance provided by each plastic hinge can be calculated from Eq. 8. Rhinge ¼ Mp =L

ð8Þ

where L is the span of beam. To resist fire-induced collapse, it is required that the vertical resistance provided by the equivalent diagonal compressive struts and

Fig. 19. Influence of number of infill walls on vertical displacements of frames at elevated bays.

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4.

5.

6. Fig. 20. Resisting mechanism of masonry infilled frame against fire scenarios.

beams with plastic hinges is larger than the load applied on them: Rmasonry þ Rframe ≥1:2DL þ 0:5LL

ð9Þ

Rmasonry ¼ nm Rvertical

ð10Þ

Rframe ¼ ns Rhinge

ð11Þ

where Rmasonry is the vertical resistance provided by masonry infill walls, Rframe is the vertical resistance provided by the steel frame, nm is the number of masonry infill walls in the bays resisting collapse of the steel frame under fire scenario, and ns is the number of plastic hinges on the beams resisting collapse. After determining the required parameters, such as strength and thickness of masonry infill walls, the required number of masonry infill walls to prevent fire-induced collapse is computed from Eq. 12: nm ≥

1:2DL þ 0:5LL−Rframe f m t inf winf sinα

ð12Þ

The above approach for design of masonry infill walls was applied to the six-story steel frames as shown in Fig. 1. According to the nonlinear dynamic analysis results as shown in Figs. 11 and 15, the bare frame is vulnerable to collapse when edge bay or central bay heated. In order to resist collapse under fire scenarios, the required number of masonry infill walls was calculated as three both for Fire 1 and Fire 2 according to Eq. 12. The calculated required number of the masonry infill walls compares well with the results of finite element models as indicated in Fig. 19. In the numerical analyses, the steel frame withstood collapse against edge bay fire when masonry infill walls horizontally installed in three stories, and withstood collapse against central bay fire when installed in two stories. 8. Conclusions In this research, the influence of masonry infill walls on collapse of steel frames is investigated under fire scenarios. Nonlinear dynamic analyses were conducted using six-story by five-bay steel bare frame, a frame with horizontal infill walls and a frame with vertical infill walls in Abaqus program. Main conclusions of this research can be drawn as follows: 1. Infill walls provide alternate load paths to redistribute the load from the fire compartment. Compressive forces are developed in the diagonal region of infill walls, causing large variation of axial forces in columns at elevated temperature. 2. Lateral deflections are developed in frames as heated columns elongated in external bay fire to meet the compatibility requirement. The lateral deformations under central bay fire scenario, however, are not obvious due to the vertical axis of symmetry and constraints provided by beams on each side of central bay. 3. It is seen that under edge bay fire scenario, the lateral resistance of the bare frame is primarily provided by shear resistance of frame members. However, the infilled frames deform in an integral rotation

7.

at edge bay fire scenario, and the lateral resistance is primarily provided by the integral loading resisting system. Presence of infill walls decreases the buckling temperature of the heated columns, but makes the frame resist collapse longer and larger temperatures. Infill walls above the heated column provided additional restraints at the beam-column joints, which resulte in a larger buckling load for frame with vertical infill walls than that for the frame with horizontal infill walls under edge bay fire scenario. A series of parametric analyses has been conducted to investigate the influence of load ratios, strength and quantity of infill walls. The results show that the larger load ratio can result in lower buckling and collapse temperature. The strength and quantity of infill walls can be determined to effectively prevent collapse under fire scenarios. A preliminary design approach for design of masonry infill walls was proposed in this study. The approach turned out to be effective in evaluating the rational design of masonry infill walls required to prevent collapse of steel frames against fire.

Acknowledgment This research is jointly supported by the China Postdoctoral Science Foundation (No. 2018M631807), National Natural Science Foundation of China (Grant Nos. 51474050, U1602232, 51578202), Fundamental Research Funds for the Central Universities, China (Nos. N160103002, N170108029), National Natural Science Foundation of Liaoning, China (Nos. 201702281). The research funds above are greatly appreciated by the authors. Part of this research was conducted during the visits of the first and fifth authors to The Ohio State University (OSU). The first author acknowledges the financial support provided by the China Scholarship Council (File No. 201306120170) for his 18-month visit to OSU. The fifth author's one-year visit to The Ohio State University was funded by the Scientific and Technological Research Council of Turkey. This study was also partially supported by the Ohio Supercomputer Center through an allocation of computing time. References [1] B. Jiang, G.-Q. Li, L. Li, B.A. Izzuddin, Experimental studies on progressive collapse resistance of steel moment frames under localized furnace loading, J. Struct. Eng. 144 (2) (2018) (04017190-1-04017190-10). [2] R. Sun, Z. Huang, I.W. Burgess, Progressive collapse analysis of steel structures under fire conditions, Eng. Struct. 34 (2012) 400–413. [3] R. Sun, Z. Huang, I.W. Burgess, The collapse behavior of braced steel frames exposed to fire, J. Constr. Steel Res. 72 (2012) 130–142. [4] E. Talebi, M.M. Tahir, F. Zahmatkesh, A.B.H. Kueh, Comparative study on the behavior of buckling restrained braced frames at fire, J. Constr. Steel Res. 102 (2014) 1–12. [5] A. Agarwal, A.H. Varma, Fire induced progressive collapse of steel building structures: the role of interior gravity columns, Eng. Struct. 58 (2014) 129–140. [6] B. Jiang, G.-Q. Li, A. Usmani, Progressive collapse mechanisms investigation of planar steel moment frames under localized fire, J. Constr. Steel Res. 115 (2015) 160–168. [7] R. Sun, I.W. Burgess, Z. Huang, G. Dong, Progressive failure modeling and ductility demand of steel beam-to-column connections in fire, Eng. Struct. 89 (2015) 66–78. [8] J. Jiang, G.-Q. Li, Progressive collapse analysis of 3D steel frames with concrete slabs exposed to localized fire, Eng. Struct. 149 (2017) 21–34. [9] B. Jiang, G.-Q. Li, L. Li, B.A. Izzuddin, Simulations on progressive collapse resistance of steel moment frames under localized fire, J. Constr. Steel Res. 138 (2017) 380–388. [10] D. Lange, C. Röben, A. Usmani, Tall building collapse mechanisms initiated by fire: Mechanisms and design methodology, Eng. Struct. 36 (2012) 90–103. [11] E. Akah, C. Wood, K. Li, H. Sezen, Experimental investigation of collapse performance of a steel frame building for disproportionate collapse, Eng. J. AISC. 55 (3) (2018) 143–159. [12] M. Sasani, S. Sagiroglu, Progressive collapse resistance of hotel San Diego, J. Struct. Eng. 134 (3) (2008) 478–488. [13] S. Li, S. Shan, C. Zhai, L. Xie, Experimental and numerical study on progressive collapse process of RC frames with full-height infill walls, Eng. Fail. Anal. 59 (2016) 57–68. [14] S. Shan, S. Li, S. Xu, L. Xie, Experimental study on the progressive collapse performance of RC frames with infill walls, Eng. Struct. 111 (2016) 80–92. [15] A. Brodsky, D.Z. Yankelevsky, Resistance of reinforced concrete frames with masonry infill walls to in-plane gravity loading due to loss of a supporting column, Eng. Struct. 140 (2017) 134–150.

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