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Collapse of steel-concrete composite frame under edge-column loss—Experiment and its analysis
Engineering Structures xxx (xxxx) xxxx
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Collapse of steel-concrete composite frame under edge-column loss—Experiment and its analysis ⁎
Jing-Zhou Zhanga, Guo-Qiang Lia,b, , Jian Jiangc a
College of Civil Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, China State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, China c School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Composite-framed structure Flat concrete floor system Experimental investigation Finite element method Membrane action Catenary action Resistance-displacement curve
Previous studies on steel frames cannot consider the effect of concrete slabs on the collapse behavior of structures, while recent experimental studies on steel-concrete composite frames fail to fully mobilize the tensile membrane action in slabs and catenary action in beams which have great influence on the failure mode of the frame. Large-scale experiments are conducted in this study on steel frames with flat concrete slabs to investigate the resistance mechanisms and typical failure modes of the structure. An edge-column removal scenario is used to consider a worse condition than an internal-column removal case. The resistance-vertical displacement relationship at the column-removal location, horizontal displacements at the structural edges and final failure patterns of main structural components are reported. Parametric studies are conducted using a validated numerical model to further quantify the effect of concrete slab thicknesses, reinforcement diameters, and beam section dimensions on the collapse resistance of composite structures. A simplified calculation method is also proposed to predict the resistance-displacement curve of composite framed structures under an edge-column loss scenario. The experimental results show that even without external horizontal restraints, tensile catenary action and membrane action can significantly develop in the steel beams and concrete slabs, respectively, at large deflections of structures under an edge-column loss scenario. Positive yield lines are found to distribute diagonally in the slab extending from the column-removal location to the two corners of the slab, while negative yield lines elliptically distribute along the edges of the slab. The numerical results highlight that the contribution of tensile membrane action in concrete slabs to the collapse resistance is less significant than that of catenary action in steel beams. Moreover, increasing the section height of beams guarantees a greater plastic bearing capacity of composite structures, but it fails to always provide a larger ultimate bearing capacity due to a poorer ductility.
1. Introduction A structure is prone to progressively collapse when it fails to bridge over the loads sustained by damaged structural components due to blast or impact. In practical safety design, sufficient robustness of structures should be guaranteed to prevent the potential casualties and treasure losses in the event of collapse. The Alternate Path Method is recommended by the DoD (Department of Defense) in USA [1] to evaluate the robustness of structures against collapse, wherein the response of the remaining structure is explicitly investigated for adequate column loss scenarios. The GSA (General Services Administration) in USA [2] suggests that the scenarios of corner and edge column loss should be especially considered in the Alternate Path Method due to the relatively greater likelihood of inducing progressive collapse. ⁎
Steel framed structures with concrete slabs are now commonly used in industrial and residential buildings. The resistance of such a composite structure against progressive collapse is usually assessed by removing a column at specified locations. Experimental tests, as the most reliable and explicit way, have been launched on two-dimensional (2D) steel frames [3–5], column-beam connections [6–8] and three-dimensional (3-D) steel frames [9,10] to investigate the collapse mechanism of structures. However, among these studies, the contribution of concrete slab systems to the global performance of structures is usually simplified or ignored. The applicability of the conclusions drawn based on steel frames to real composite framed-structures remains to be confirmed [11]. Recently, experimental studies on steel framed-structures with concrete slabs due to column losses have been carried out [12–15].
Corresponding author at: College of Civil Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, China. E-mail address: [email protected] (G.-Q. Li).
https://doi.org/10.1016/j.engstruct.2019.109951 Received 15 March 2019; Received in revised form 13 November 2019; Accepted 15 November 2019 0141-0296/ © 2019 Published by Elsevier Ltd.
Please cite this article as: Jing-Zhou Zhang, Guo-Qiang Li and Jian Jiang, Engineering Structures, https://doi.org/10.1016/j.engstruct.2019.109951
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Table 1 Section dimensions of steel beams and columns. Component
Section Dimension (Total Height × Flange Width × Web Thickness × Flange Thickness)
Steel Grade
Beam Column
H100 × 67 × 4.5 × 6 H200 × 200 × 6 × 8
Q235 Q235
Note: Dimensions in mm. Table 2 Material properties of the test specimen.
Fig. 1. Schematic of the tested frame.
Material
E (105 MPa)
fy (MPa)
fu (MPa)
εu
Beam Web Beam Flange Column Web Column Flange Reinforcement Stud Concrete
1.95 2.06 1.91 1.96 1.85 – 0.254
286 300 320 300 420 – –
382 392 479 440 640 450 22.9 (axial compression) 28.1 (cubic compression)
0.22 0.185 0.18 0.20 0.11 – –
Fig. 2. Plan view of the tested frame. (Dimensions in mm.)
Song and Sezen [12] tested an existing steel framed building, named Ohio Union building, by instantaneously removing four columns at the first story. The building remained stable after the removal of all the columns. Hadjioannou et al. [13] conducted large-scale tests on two composite framed-structures due to the loss of interior and exterior columns. Suffering from the service loads, both structures survived the column-removal stage. In the tests by Fu et al. [15], the effect of slab aspect ratios, slab boundary conditions and composite action degrees on the collapse resistance of structures was studied. The resistancedisplacement curves of four scaled composite structures under interior column loss scenarios were compared. It was concluded that the composite action degree and slab boundary condition had limited effects on the collapse resistance at the limit state, while a smaller aspect ratio guaranteed a larger ultimate bearing capacity of structures. However, the potential tensile membrane action in slabs and catenary action in
Fig. 4. Layout of cross section of the beam B. (Dimensions in mm.)
beams were not fully mobilized in these experiments, due to the failure of some structural components such as failure of bolts at column-beam connections and shear damage of studs between the concrete slab and steel beam. Thus, the resistance-displacement curves for these structures failed to significantly re-ascend at large deflections. Moreover, scenarios of interior column losses are always considered in previous experimental studies on composite framed-structures, but research on edge-column loss scenarios is rare in the literature. In this paper, a large-scale experiment was conducted on a
Fig. 3. Elevation view of the tested frame. (Dimensions in mm.) 2
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the slab, of which each has a cover thickness of 10 mm. The cross section dimensions of steel columns and beams are shown in Table 1. To achieve rigid column-to-beam connections, all steel beams were connected to the columns by gas metal arc welding (GMAW) with filler metal E50-6. The nominal ultimate strength of the filler metal is greater than that for the steel beams and columns. The slab was connected to steel beams by shear studs, and a full shear connection between them was assumed based on the Code for Design of Steel Structures (GB50017-2017) [16]. The shear studs have a diameter of 19 mm and a central distance of 110 mm. The elastic modulus, yield strength, tensile strength and ultimate strain for the steel and concrete are listed in Table 2. The yield strength of steel beams and columns is about 300 MPa. The material properties were obtained from tensile coupon tests where an average value of three coupons was used. The details of the cross section of the beam B are shown in Fig. 4. A fully restrained boundary condition between the five steel columns and ground base was used, as shown in Fig. 5. The bottom of the column was connected to the foundation by eight bolts along the four edges, and eight stiffeners were welded to the flange at the column bottom to prevent local buckling of the column components. No other external restraint was imposed to the frame, except the rigid restraints on the columns.
Fig. 5. Foundation of the steel column.
composite-framed structure subject to an edge-column loss. The collapse resistance and failure mode of the composite frame were investigated. A simplified calculation method was then proposed to predict the collapse resistance of composite-framed structures due to an edge-column loss. The accuracy of the calculation method was validated against experimental results. Moreover, numerical models were created and validated against experimental results to further investigate the effect of slab thickness, reinforcement diameter and steel beam section height on the collapse resistance of structures.
2.2. Test setup and loading procedure Fig. 6 shows the experimental setup. The actuator was connected to the frame at the column-removal location by a steel conversion component, as shown in Fig. 7. During the loading process, the reaction forces from the actuator were sustained by the strong concrete reaction floor system with a thickness of 900 mm. The loading and movement range of the actuator are 1000 kN and 1000 mm, respectively. To ensure that the actuator only moves vertically, the actuator was laterally supported by several diagonal steel braces to prevent its potential horizontal movements. During the statically loading procedure, the force-controlled loading rule was initially adopted with a 10 kN increment at each step. When the load exceeded 80 kN, it was switched to a displacement-controlled rule, wherein the displacement at the column-removal location was increased by 5 mm per step until it reached 300 mm. Finally, the displacement-controlled rule was adjusted to augment by 10 mm at each step until the failure of the frame.
2. Experimental program 2.1. Test specimen A test was conducted on a single-storey, two bay-by-one bay steel frame with reinforced concrete slabs, as shown in Fig. 1. The height of the frame is 1.3 m. A rectangular plan dimension of 3 m × 4.8 m was designed. The longitudinal and transverse spans of the concrete slab are 2.4 m and 1.8 m, respectively, as illustrated in Fig. 2. To account for the realistic restraints provided by the surrounding substructures, a 0.6-m cantilever span of slab was fabricated. The details of the frame along the axis B are shown in Fig. 3. The thickness of the reinforced concrete slab is 60 mm. Both the longitudinal and transverse reinforcement have a diameter of 6 mm and a spacing of 200 mm. There are two identical reinforcement layers in
Fig. 6. Test setup. 3
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Fig. 7. Connection between the actuator and the specimen.
Fig. 10. Resistance-displacement curve in Ref. [17].
3. Experimental results and discussions Fig. 8. Arrangements of the LVDTs.
3.1. Resistance-vertical displacement The resistance-vertical displacement curve at the column-removal location (V2) is shown in Fig. 9. The ultimate bearing capacity and failure displacement of the specimen were 227 kN and 606 mm, respectively. The ultimate rotation capacity of the fully welded beamcolumn connection was 0.33 rad. Three stages (Stage I, II and III) were defined to represent the elastic-plastic, transition, and membrane/catenary action stage of the resistance-displacement curve, respectively. The resistance corresponding to the end of elastic-plastic stage I can be determined based on the yield-line theory. The resistance mechanism of the structure gradually transited from flexural action to tensile action during the stage II. It can be seen that the ultimate bearing capacity of the structure was about 2.8 times greater than the plastic bearing capacity. When the displacement reached 606 mm, the fracture initially occurring at the bottom flange of steel beams near the column-removal location rapidly penetrated the whole cross section, leading to the dramatic decrease of the resistance-displacement curve of the structure. Compared with that reported by Fu et al. [17] on a composite framed-structure under an internal column loss (presented in Fig. 10), the resistance-displacement curve herein for an edge column loss ascended more notably at large deflections even without external lateral restraints imposed on the structure. This is because the specimen in the test by Fu et al. [17] involves many other structural components and connections, such as steel bolts, end plates, angles and decks. The occurrence of some failures, including fracture of bolts and angles at column-beam connections, shear damage of studs between concrete slabs and steel beams, and local fracture of steel decks, resulted in that the potential tensile membrane action in slabs and catenary action in beams were not fully mobilized.
Fig. 9. Resistance-vertical displacement curve of the tested frame.
2.3. Test measurements The arrangements of linear variable displacement transducers (LVDTs) are presented in Fig. 8. The transducers V1, V3 and V4 were used for measuring the vertical displacements at the mid-span position of the beams A, C and B, respectively. The transducer V2 recorded the vertical displacement at the column-removal location. The transducers V5 ~ V7 measured the horizontal displacement at the corresponding beam ends.
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Fig. 11. Horizontal displacement-vertical displacement curves of the tested frame.
(a) Front view
(b) Right view
Fig. 12. Final deformation shape of the slab.
Fig. 13. Negative yield lines at the slab bottom.
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displacements at V5 and V7 became inward when the vertical displacement at V2 reached 120 mm, indicating that tensile catenary action in beams A, B and C started to develop. However, the catenary action in the beams A and C was found to be more significant than that in the beam B considering that the final lateral displacement at V5 was 4 times greater than that at V7. This is because the beam B performed as a cantilever for this column-removal scenario, of which the axial restraints were much weaker than those provided to the beams A and C. This phenomenon is not likely to occur for an internal column loss scenario, wherein catenary action can significantly develop in both longitudinal and transverse beams. Fig. 14. Fracture of the steel beam.
3.3. Failure pattern The final deformation shapes of the slab, steel beam and column are shown in Figs. 12–15, respectively. As presented in Fig. 12, a main crack in concrete was found on the slab top, which was in an elliptical shape along the edges of the specimen. Many diagonal cracks were also found, extending from the columns A and E to the column C. There was obvious spalling of concrete along the diagonals of the structure from the column-removal location to the columns B and D, which are known as the positive yield lines of the slab. Fig. 13 shows the damage pattern of concrete at the bottom of the slab. Numerous diagonal cracks formed and stretched from the column-removal location. The concrete was spalled along the edge regions of the structure. These elliptical regions are known as the negative yield lines of the slab. The frame failed to sustain more loads due to a fracture at the bottom flange of steel beam near the column-removal location, as shown in Fig. 14. This fracture resulted in a dramatic decrease of the resistance-displacement curve of the frame when the vertical displacement reached 606 mm. The final deformation shape of the column E is shown in Fig. 15. Severe local buckling can be observed at the left flange near the column bottom. This horizontal displacement further validated the significant development of tensile catenary action in the steel beams A and C.
Fig. 15. Inward lateral displacement of the column.
4. Simplified calculation method 3.2. Horizontal displacement-vertical displacement The collapse resistance of composite framed-structures in the event of a side or middle column loss has been previously investigated [11,18]. The response of structures was represented by the corresponding substructure with simplified boundary conditions. The simplifications for the middle and side column loss scenarios are shown in Fig. 16 and Fig. 17, respectively. However, this idealized fixed boundary condition is no longer reasonable for the tested substructure in this study without sufficient external restraints. To analytically determine the resistance-displacement curve for the frame in the experiment, a tri-linearized relationship proposed in Ref. [11] was used, wherein the main mechanism characteristics of the structure at column-removal stage were guaranteed to be captured. As
Fig. 11 shows the relationships between horizontal displacements at V5 ~ V7 and vertical displacement at the column-removal location (V2). A negative value represents that the horizontal displacement is away from the column-removal location and vice versa. The column D was found to barely have lateral displacements. This is because the tensile force in the peripheral beams connecting to column D was quite small and this column hardly deformed even at large deflections. It is therefore concluded that in the event of a column loss, the contributions of the columns diagonally adjacent to the column-removal location to redistributing the vertical loads are limited. The direction for lateral
Fig. 16. Simplification of the structure for middle column loss scenario [18]. 6
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Fig. 17. Simplification of the structure for side column loss scenario [11].
considering that tensile catenary action dominated the resistance mechanism in steel beams at large deflections [19]. The plastic bearing capacity of the structure was calculated by virtual work principle, wherein the internal virtual work was equal to that by external forces. The plastic bearing capacity is given by:
Fy = (Mx + Mx′ )
4l L 4 1 + (My + My′ ) + (MxN + MxP ) + MyN L l L l
(1)
wherein Mx and My are the positive bending moment of slab section about Y- and X- direction (per unit width), respectively; M′x and M′y are the negative bending moment of slab section about Y- and X- direction (per unit width), respectively; MxP is the positive plastic moment of X direction beam; MxN and MyN are the negative plastic moment of beams in X-and Y- direction, respectively. In Ref. [11], the ultimate bearing capacity of the structure was analytically determined by an energy-based method, wherein the following three contributions to internal energy dissipations at large deflections were considered: (1) elongation of reinforcement and steel beams Win1; (2) tensile force-induced additional bending moment due to geometric nonlinearity Win2, wherein the tensile forces include the tensile membrane forces along yield lines of the slab and tensile catenary forces in steel beams; (3) the bending moment along yield lines of the slab Win3. For the substructure tested in this study, however, the internal energy dissipation due to the elongations of reinforcement and steel beams Win1 was ignored considering that no effective lateral restraint was provided to the structure. The analytical method herein was amended only to account for the contributions from Win2 andWin3. The ultimate bearing capacity of structure in the experiment is directly given by:
Fig. 18. Tri-linearized resistance-displacement relationship.
shown in Fig. 18, the parameters vA and vB are the displacements at the column-removal location corresponding to the end of elastic-plastic and transition stages, respectively. The parameter vC is the failure displacement, and Fu and Fy are the ultimate and plastic bearing capacity of the structure, respectively. The details for determining vA and vB are given in Ref. [11]. To determine the plastic and ultimate bearing capacity, the yieldline and failure patterns of the structure were defined based on experimental observations, as shown in Fig. 19 and Fig. 20, respectively. The red dashed curves represent the elliptical negative yield lines at the bottom of the slab, while the blue lines denote the diagonally distributed positive yield lines at the top of the slab. In the failure pattern, negative and positive moment hinges at beam ends were excluded
Fig. 19. Yield-line pattern of structure in the experiment. 7
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Fig. 20. Failure pattern of structure in the experiment.
Fu = Ca bv (
Ty L l
+4
Tx l v L 4l ) + 4Fux + (Cm My + My′ ) + (Cm Mx + Mx′ ) L L l L (2)
where
Ca =
3k + 2 k3 − 2 6(1 + k ) 6(1 + k )2
Cm = 1 + χ1
χ b2 k−1 b − 2 (k 2 − k + 1) 2 3 (3)
wherein Ca accounts for the contribution from the membrane forcesinduced bending moment; Cm considers the interaction between the axial force and bending moment in slab sections; b and k are parameters quantifying the distributions of membrane forces in the slab; Ty and Tx are the yield forces of reinforcement in slab section in Y- and X- direction (per unit width), respectively; Fux is the yield force of steel beam section in X direction. The detailed expressions of these parameters are given in Ref. [11]. The comparison of the resistance-displacement curves from the experiment and simplified calculation method is shown in Fig. 21. A reasonable agreement was achieved since the predicted ultimate bearing capacity was found to be only 6.7% greater than the measured value.
Fig. 21. Comparison of the resistance-displacement curves from the experiment and simplified calculation method. Table 3 Material properties for steel in the numerical model. Material
E (105 MPa)
fy (MPa)
E p(103 MPa)
εf
v
Beam Web Beam Flange Column Web Column Flange Reinforcement
1.95 2.06 1.91 1.96 1.85
286 300 320 300 420
0.912 0.987 1.496 1.261 3.057
0.20 0.17 0.17 0.18 0.10
0.3 0.3 0.3 0.3 0.3
5. Numerical modelling 5.1. Numerical model
Note: Ep, εf and v are the post-yield modulus, fracture strain and Poisson’s ratio of steel, respectively.
A numerical model was created in finite element software ABAQUS [20], and its reliability was validated against experimental results in Section 3. The steel columns and beams were simulated by four-node shell elements (S4R). The reinforcement was modeled by two-node truss element (T3D2). The eight-node solid element (C3D8R) was used
Fig. 22. Material properties of concrete. 8
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Table 4 Material properties for concrete in the numerical model. E (105 MPa)
fu (MPa)
v
Dilation Angle
Eccentricity
fb0/fc0
KC
Viscosity
0.254
22.9 (Compression) 2.29 (Tension)
0.2
30°
0.1
1.16
0.667
0.001
true strain and stress used in the numerical model were converted from the nominal values based on Eq. (4):
εt = ln(1 + εn ) σt = σn (1 + εn )
(4)
whereεt and εn are the true and nominal strain, respectively; σt and σn are the true and nominal stress, respectively. The Mises yield surface is adopted to account for yielding, wherein the relationship of the uniaxial yield stress and equivalent plastic strain of steel material is defined. The isotropic hardening rule is employed to consider the hardening behavior of the material. The yield surface changes size uniformly in all directions when the yield stress varies as plastic strain occurs. The ductile damage model was used to account for the failure of steel [21]. The fracture strain was taken as the ultimate strain in the coupon test. The damage evolution was based on the displacement of the element, wherein the failure displacement was taken as 6.7 mm. It was determined by ensuring that the numerical resistancedisplacement curve of the structure sharply decreased at the same displacement as measured in the experiment. The material properties of steel used in the numerical model are summarized in Table 3. The concrete damaged plasticity model was used to consider the failure of concrete [22]. This model was also employed by researchers to analyze the punching shear of concrete slabs [23,24], wherein some key parameters were calibrated based on the experimental load-displacement relationship for an interior slab-column connection and this model was further proved to be reliable for interior and edge slab-column connections with more complicated loading conditions. As shown in Fig. 22, the compressive stress-inelastic strain relationship and tensile stress-cracking strain relationship were defined to account for the compressive and tensile behavior of concrete, respectively. The damage-inelastic/cracking strain relationships were specified to consider the deterioration of concrete. The damage factor was determined based on the Codes for Design of Concrete Structures (GB50010-2010) [25]. The material properties of concrete in the numerical model are shown in Table 4. All steel members in the numerical model (the beams, columns and stiffeners) were merged as a new assembly considering that all the beam-column connections are fully welded. In the experimental tests, no shear stud fractured, and thus negligible relative slip between the steel beam and concrete slab was assumed. The steel beams were therefore connected to concrete slab by “Tie” command. The reinforcement was “Embedded” into the concrete slab. The bottom surfaces of columns were assumed to be fully restrained. The details of the finite element model are shown Fig. 23. A displacement-controlled loading process at the predefined column-removal location was used in the numerical model. To account for the effect of geometrical nonlinearities on the structural behavior of the frame model at large deflections, the NLGEOM option was selected.
Fig. 23. Details of the finite element model.
Fig. 24. Comparison of resistance-vertical displacement relationship.
5.2. Validation of the numerical approach Fig. 25. Comparison of horizontal-vertical displacement relationship.
To validate the numerical model, the resistance-vertical displacement relationship, horizontal-vertical displacement relationship and failure mode of the structure from the numerical approach were compared with those from the experiment in Section 3. Fig. 24 shows the comparison of the resistance-vertical displacement relationship of the tested frame. The numerical model slightly overestimated the collapse resistance of the structure at large deflections. In the experiment, the
to simulate the concrete slab. The mesh size of concrete slab is 50 mm (longitudinal direction) × 50 mm (transverse direction) × 15 mm (thickness). The global mesh size of steel columns and beams are 25 mm. A 50 mm global size was designated for the reinforcement in the slab. A bi-linear stress–strain relationship of steel was assumed. The
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Fig. 26. Comparison of the failure mode of the slab.
Fig. 27. Comparison of the failure mode of the steel beam.
Fig. 28. Stress extraction locations in the numerical model.
Fig. 30. Stress evolutions in the reinforcing bar.
Fig. 29. Stress evolutions in the steel beam.
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Table 5 Details of numerical model. No.
Variable
Slab Thickness
Reinforcement
Beam Section
N1 N2 N3 N4
Control specimen Slab thickness
60 70 80 90
Φ6@200 Φ6@200 Φ6@200 Φ6@200
100 100 100 100
N5 N6 N7
Reinforcement diameter
60 60 60
Φ7@200 Φ8@200 Φ9@200
100 × 67 × 4.5 × 6 100 × 67 × 4.5 × 6 100 × 67 × 4.5 × 6
+16.7% (36.1%)* +33.3%(77.8%)* +50%(125%)*
N8 N9 N10
Beam height
60 60 60
Φ6@200 Φ6@200 Φ6@200
120 × 67 × 4.5 × 6 140 × 67 × 4.5 × 6 160 × 67 × 4.5 × 6
+20% +40% +60%
× × × ×
67 67 67 67
× × × ×
Deviation Percentage 4.5 4.5 4.5 4.5
× × × ×
6 6 6 6
– +16.7% +33.3% +50%
Note: *indicates the change percentage of the reinforcement area. Dimensions in mm.
Fig. 31. Comparison of the resistance-displacement curves for models N1 ~ N10.
sections (locations 2, 3 and 4) of the reinforcing bar were selected. For the location 1, the stress along the axis of the beam (S11) at the top and bottom flanges was presented. For the locations 2, 3 and 4 of the reinforcing bar, the stress along the X-direction was presented. As shown in Fig. 29, the initial tensile stress at the bottom flange was greater than that at the top flange, suggesting that this section suffered from a sagging moment at the beginning. When the vertical displacement at the column-removal location reached about 150 mm, the tensile stresses at both the bottom and top flanges started to steadily increase. Finally, the tensile stresses at the bottom and top flanges reached about 300 MPa, indicating the sufficient development of catenary action in steel beam C. As shown in Fig. 30, the tensile stresses in reinforcing bar at these locations increased at large deflections. Moreover, the closer the location to the edge was, the greater the tensile stress was. The stress evolution in the reinforcing bar further demonstrated the diagonally distributed positive yield lines at the bottom of the slab.
lateral displacement for the column E (Fig. 3) was somewhat greater than that for the column A at large deflections due to some unexpected systematic errors, which resulted in that the tensile catenary action in the steel beam C was less significant than that in the steel beam A. Therefore, the numerical resistance-displacement curve re-ascended more apparently than that of the experiment. The comparison of the horizontal displacement at V5 is shown in Fig. 25. It can be seen that the predicted horizontal displacements from numerical analysis agreed well with the experimental results when the vertical displacement was less than 400 mm. After reaching 400 mm, the numerical analysis tended to underestimate the horizontal displacement at V5. Fig. 26 and Fig. 27 show the comparisons between the numerical and experimental results of the final failure mode of the slab and steel beam, respectively. These further validated the reliability of the numerical approach. To further study the development of catenary action in the steel beam and tensile membrane action in the slab, the evolution of the stress state at some key locations (shown in Fig. 28) of the frame in the numerical model was presented in Fig. 29 and Fig. 30. The middle span section of steel beam C (location 1) and three diagonally distributed 11
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• The positive yield lines of the slab diagonally distributed, stretching
5.3. Parametric study The validated numerical model was used to investigate the effect of concrete slab thickness, reinforcement diameter and steel beam dimensions on the structural behavior of composite framed-structures. The details of the parameters are shown in Table 5, wherein N1 is the basic model and its parameters are taken as those measured in the experiment. The deviation percentages of parameters in models N2 ~ N10 were calculated as the ratio of the difference of the corresponding quantity to that of the model N1. Note that the effect of reinforcement is mainly due to the cross section area, rather than the diameter. The reinforcement areas were increased by 36.1%, 77.8% and 125% for N5 ~ N7, respectively. The effect of aforementioned structural parameters on the resistance-displacement curves of structures is shown in Fig. 31. The failure of these structures was all due to the fracture at the bottom flange of the steel beam near the column-removal location, as shown in Fig. 27(b). The findings are summarized as follows:
• •
Declaration of Competing Interest We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work and we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.
• The plastic bearing capacity of the structure was mainly affected by •
•
slab thickness and steel beam height. A larger slab thickness and beam height ensured a greater plastic bearing capacity. Increasing the slab thickness and reinforcement diameter enhanced the ultimate bearing capacity, while a larger beam section height failed to provide a greater ultimate bearing capacity. For N8 ~ N10, the ultimate bearing capacity was 6.4%, 7.8% and 8.1% less than that for N1, respectively. This is because the failure displacement at the column-removal location decreased when the beam section height increased, resulting in less development of tensile catenary action in steel beams. It is therefore concluded that in practical safety design of structures against progressive collapse, increasing the section height of beams is not always conservative. The effect of reinforcement diameter on the resistance-displacement curve of the structure was less significant than those of slab thickness and steel beam height. For N5 ~ N7, the reinforcement areas increased by 36.1%, 77.8% and 125%, respectively, while the ultimate bearing capacity was found to be only 2.6%, 4.4% and 5.6% larger than that for structure N1, respectively. This phenomenon suggests that the contribution of tensile membrane action in reinforcement to the collapse resistance is less significant than that of catenary action in steel beams.
Acknowledgements The work presented in this paper was supported by the ThirteenFive Science and Technology Support Program with grant 2016YFC0701203. References [1] DoD. Design of buildings to resist progressive collapse. UFC 4-023-03: Washington, DC: Department of Defense; 2013. [2] GSA. Progressive collapse analysis and design guidelines for new federal office buildings and major modernization projects. Washington, DC: General Services Administration; 2013. [3] Jiang B, Li G, Li L, Izzuddin BA. Experimental studies on progressive collapse resistance of steel moment frames under localized furnace loading. J Struct Eng 2018;144(2):04017190. [4] Li G, Li L, Jiang B, Lu Y. Experimental study on progressive collapse resistance of steel frames under a sudden column removal scenario. J Constr Steel Res 2018;147:1–15. [5] Guo LH, Gao S, Fu F, Wang YY. Experimental study and numerical analysis of progressive collapse resistance of composite frames. J Constr Steel Res 2013;89:236–51. [6] Yang B, Tan KH. Experimental tests of different types of bolted steel beam–column joints under a central-column-removal scenario. Eng Struct 2013;54:112–30. [7] Lew HS, Main JA, Robert SD, Sadek F, Chiarito VP. Performance of steel moment connections under a column removal scenario I: experiments. J Struct Eng ASCE 2013;139(1):98–107. [8] Khandelwal K, El-Tawil S. Collapse behavior of steel special moment resisting frame connections. J Struct Eng 2007;133(5):646–55. [9] Dinu F, Marginean I, Dubina D, Petran I. Experimental testing and numerical analysis of 3D steel frame system under column loss. Eng Struct 2016;113:59–70. [10] Li H, Cai X, Zhang L, Zhang B, Wang W. Progressive collapse of steel momentresisting frame subjected to loss of interior column: Experimental tests. Eng Struct 2017;150:203–20. [11] Li G, Zhang J, Jiang J. Analytical modeling on collapse resistance of steel beamconcrete slab composite substructures subjected to side column loss. Eng Struct 2018;169:238–55. [12] Song BI, Sezen H. Experimental and analytical progressive collapse assessment of a steel frame building. Eng Struct 2013;56:664–72. [13] Hadjioannou M, Donahue S, Williamson EB, Engelhardt MD. Large-scale experimental tests of composite steel floor systems subjected to column loss scenarios. J Struct Eng 2018;144(040171842). [14] Johnson ES, Meissner JE, Fahnestock LA. Experimental behavior of a half-scale steel concrete composite floor system subjected to column removal scenarios. J Struct Eng 2016;142(2):04015133. [15] Fu QN, Tan KH, Zhou XH, Yang B. Three-dimensional composite floor systems under column-removal scenarios. J Struct Eng 2018:144. [16] Ministry of Construction of China. Code for Design of Steel Structures (500172017): Beijing; 2017. [17] Fu QN, Tan KH, Zhou XH, Yang B. Load-resisting mechanisms of 3Dcomposite floor systems under internal column-removal scenario. Eng Struct 2017;148:357–72. [18] Zhang JZ, Li GQ. Collapse resistance of steel beam-concrete slab composite substructures subjected to middle column loss. J Constr Steel Res 2018;145:471–88. [19] Izzuddin BA. A simplified model for axially restrained beams subject to extreme loading. Int J Steel Struct 2005;5(5):421–9. [20] ABAQUS Analysis User's Manual Version 6.7. ABAQUS Inc.; 2007.
6. Conclusion This paper presented an experimental investigation on structural responses of composite framed-structures due to an edge-column loss. The progressive collapse resistance of the frame significantly re-ascended at large deflections. Typical failure modes of the frame due to edge column loss were obtained. The effect of concrete slab thickness, reinforcement diameter and steel beam dimensions on collapse resistance of structures was numerically investigated. To facilitate the development of safety design of structures against collapse, a simplified analytical method for predicting the collapse resistance of the frame due to an edge-column loss was also proposed. The following conclusions can be drawn:
• The experimental results showed that for an edge-column loss sce-
•
from the column-removal location to the two corners of the slab. The negative yield lines elliptically formed along the edges of the slab. Increasing the beam height guaranteed a greater plastic bearing capacity of the structure, but it may fail to provide a larger ultimate bearing capacity due to a poorer ductility. The simplified calculation method was capable of capturing the main mechanical features of the resistance-displacement curves of the frame due to an edge-column loss. The predicted ultimate bearing capacity of the frame was found to be only 6.7% greater than the experimental value.
nario, both tensile catenary action in steel beams and membrane action in concrete slabs can significantly develop at large deflections of steel-concrete composite frames without external horizontal restraints. The frame failed due to the fracture at the bottom flange of the steel beam near the column-removal location. The catenary action in the double-span beam after column loss was more notable than that in the beam perpendicular to it. Moreover, the contributions of the columns diagonally adjacent to the columnremoval location to redistributing the vertical loads were limited. 12
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element analysis of punching shear. Comput Struct 2015;151:73–85. [24] Genikomsou AS, Polak MA. Finite element analysis of punching shear of concrete slabs using damaged plasticity model in ABAQUS. Eng Struct 2015;98:38–48. [25] Ministry of Construction of China. Code for Design of Concrete Structures (500102010): Beijing; 2010.
[21] Hillerborg A, Modeer M, Petersson PE. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem Concr Res 1976;6:773–82. [22] Lee J, Fenves GL. Plastic-damage model for cyclic loading of concrete structures. J Eng Mech 1998;124(8):892–900. [23] Wosatko A, Pamin J, Polak MA. Application of damage–plasticity models in finite
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Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Collapse of steel-concrete composite frame under edge-column loss—Experiment and its analysis ⁎
Jing-Zhou Zhanga, Guo-Qiang Lia,b, , Jian Jiangc a
College of Civil Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, China State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, China c School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Composite-framed structure Flat concrete floor system Experimental investigation Finite element method Membrane action Catenary action Resistance-displacement curve
Previous studies on steel frames cannot consider the effect of concrete slabs on the collapse behavior of structures, while recent experimental studies on steel-concrete composite frames fail to fully mobilize the tensile membrane action in slabs and catenary action in beams which have great influence on the failure mode of the frame. Large-scale experiments are conducted in this study on steel frames with flat concrete slabs to investigate the resistance mechanisms and typical failure modes of the structure. An edge-column removal scenario is used to consider a worse condition than an internal-column removal case. The resistance-vertical displacement relationship at the column-removal location, horizontal displacements at the structural edges and final failure patterns of main structural components are reported. Parametric studies are conducted using a validated numerical model to further quantify the effect of concrete slab thicknesses, reinforcement diameters, and beam section dimensions on the collapse resistance of composite structures. A simplified calculation method is also proposed to predict the resistance-displacement curve of composite framed structures under an edge-column loss scenario. The experimental results show that even without external horizontal restraints, tensile catenary action and membrane action can significantly develop in the steel beams and concrete slabs, respectively, at large deflections of structures under an edge-column loss scenario. Positive yield lines are found to distribute diagonally in the slab extending from the column-removal location to the two corners of the slab, while negative yield lines elliptically distribute along the edges of the slab. The numerical results highlight that the contribution of tensile membrane action in concrete slabs to the collapse resistance is less significant than that of catenary action in steel beams. Moreover, increasing the section height of beams guarantees a greater plastic bearing capacity of composite structures, but it fails to always provide a larger ultimate bearing capacity due to a poorer ductility.
1. Introduction A structure is prone to progressively collapse when it fails to bridge over the loads sustained by damaged structural components due to blast or impact. In practical safety design, sufficient robustness of structures should be guaranteed to prevent the potential casualties and treasure losses in the event of collapse. The Alternate Path Method is recommended by the DoD (Department of Defense) in USA [1] to evaluate the robustness of structures against collapse, wherein the response of the remaining structure is explicitly investigated for adequate column loss scenarios. The GSA (General Services Administration) in USA [2] suggests that the scenarios of corner and edge column loss should be especially considered in the Alternate Path Method due to the relatively greater likelihood of inducing progressive collapse. ⁎
Steel framed structures with concrete slabs are now commonly used in industrial and residential buildings. The resistance of such a composite structure against progressive collapse is usually assessed by removing a column at specified locations. Experimental tests, as the most reliable and explicit way, have been launched on two-dimensional (2D) steel frames [3–5], column-beam connections [6–8] and three-dimensional (3-D) steel frames [9,10] to investigate the collapse mechanism of structures. However, among these studies, the contribution of concrete slab systems to the global performance of structures is usually simplified or ignored. The applicability of the conclusions drawn based on steel frames to real composite framed-structures remains to be confirmed [11]. Recently, experimental studies on steel framed-structures with concrete slabs due to column losses have been carried out [12–15].
Corresponding author at: College of Civil Engineering, Tongji University, 1239 Siping Road, Shanghai 200092, China. E-mail address: [email protected] (G.-Q. Li).
https://doi.org/10.1016/j.engstruct.2019.109951 Received 15 March 2019; Received in revised form 13 November 2019; Accepted 15 November 2019 0141-0296/ © 2019 Published by Elsevier Ltd.
Please cite this article as: Jing-Zhou Zhang, Guo-Qiang Li and Jian Jiang, Engineering Structures, https://doi.org/10.1016/j.engstruct.2019.109951
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Table 1 Section dimensions of steel beams and columns. Component
Section Dimension (Total Height × Flange Width × Web Thickness × Flange Thickness)
Steel Grade
Beam Column
H100 × 67 × 4.5 × 6 H200 × 200 × 6 × 8
Q235 Q235
Note: Dimensions in mm. Table 2 Material properties of the test specimen.
Fig. 1. Schematic of the tested frame.
Material
E (105 MPa)
fy (MPa)
fu (MPa)
εu
Beam Web Beam Flange Column Web Column Flange Reinforcement Stud Concrete
1.95 2.06 1.91 1.96 1.85 – 0.254
286 300 320 300 420 – –
382 392 479 440 640 450 22.9 (axial compression) 28.1 (cubic compression)
0.22 0.185 0.18 0.20 0.11 – –
Fig. 2. Plan view of the tested frame. (Dimensions in mm.)
Song and Sezen [12] tested an existing steel framed building, named Ohio Union building, by instantaneously removing four columns at the first story. The building remained stable after the removal of all the columns. Hadjioannou et al. [13] conducted large-scale tests on two composite framed-structures due to the loss of interior and exterior columns. Suffering from the service loads, both structures survived the column-removal stage. In the tests by Fu et al. [15], the effect of slab aspect ratios, slab boundary conditions and composite action degrees on the collapse resistance of structures was studied. The resistancedisplacement curves of four scaled composite structures under interior column loss scenarios were compared. It was concluded that the composite action degree and slab boundary condition had limited effects on the collapse resistance at the limit state, while a smaller aspect ratio guaranteed a larger ultimate bearing capacity of structures. However, the potential tensile membrane action in slabs and catenary action in
Fig. 4. Layout of cross section of the beam B. (Dimensions in mm.)
beams were not fully mobilized in these experiments, due to the failure of some structural components such as failure of bolts at column-beam connections and shear damage of studs between the concrete slab and steel beam. Thus, the resistance-displacement curves for these structures failed to significantly re-ascend at large deflections. Moreover, scenarios of interior column losses are always considered in previous experimental studies on composite framed-structures, but research on edge-column loss scenarios is rare in the literature. In this paper, a large-scale experiment was conducted on a
Fig. 3. Elevation view of the tested frame. (Dimensions in mm.) 2
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the slab, of which each has a cover thickness of 10 mm. The cross section dimensions of steel columns and beams are shown in Table 1. To achieve rigid column-to-beam connections, all steel beams were connected to the columns by gas metal arc welding (GMAW) with filler metal E50-6. The nominal ultimate strength of the filler metal is greater than that for the steel beams and columns. The slab was connected to steel beams by shear studs, and a full shear connection between them was assumed based on the Code for Design of Steel Structures (GB50017-2017) [16]. The shear studs have a diameter of 19 mm and a central distance of 110 mm. The elastic modulus, yield strength, tensile strength and ultimate strain for the steel and concrete are listed in Table 2. The yield strength of steel beams and columns is about 300 MPa. The material properties were obtained from tensile coupon tests where an average value of three coupons was used. The details of the cross section of the beam B are shown in Fig. 4. A fully restrained boundary condition between the five steel columns and ground base was used, as shown in Fig. 5. The bottom of the column was connected to the foundation by eight bolts along the four edges, and eight stiffeners were welded to the flange at the column bottom to prevent local buckling of the column components. No other external restraint was imposed to the frame, except the rigid restraints on the columns.
Fig. 5. Foundation of the steel column.
composite-framed structure subject to an edge-column loss. The collapse resistance and failure mode of the composite frame were investigated. A simplified calculation method was then proposed to predict the collapse resistance of composite-framed structures due to an edge-column loss. The accuracy of the calculation method was validated against experimental results. Moreover, numerical models were created and validated against experimental results to further investigate the effect of slab thickness, reinforcement diameter and steel beam section height on the collapse resistance of structures.
2.2. Test setup and loading procedure Fig. 6 shows the experimental setup. The actuator was connected to the frame at the column-removal location by a steel conversion component, as shown in Fig. 7. During the loading process, the reaction forces from the actuator were sustained by the strong concrete reaction floor system with a thickness of 900 mm. The loading and movement range of the actuator are 1000 kN and 1000 mm, respectively. To ensure that the actuator only moves vertically, the actuator was laterally supported by several diagonal steel braces to prevent its potential horizontal movements. During the statically loading procedure, the force-controlled loading rule was initially adopted with a 10 kN increment at each step. When the load exceeded 80 kN, it was switched to a displacement-controlled rule, wherein the displacement at the column-removal location was increased by 5 mm per step until it reached 300 mm. Finally, the displacement-controlled rule was adjusted to augment by 10 mm at each step until the failure of the frame.
2. Experimental program 2.1. Test specimen A test was conducted on a single-storey, two bay-by-one bay steel frame with reinforced concrete slabs, as shown in Fig. 1. The height of the frame is 1.3 m. A rectangular plan dimension of 3 m × 4.8 m was designed. The longitudinal and transverse spans of the concrete slab are 2.4 m and 1.8 m, respectively, as illustrated in Fig. 2. To account for the realistic restraints provided by the surrounding substructures, a 0.6-m cantilever span of slab was fabricated. The details of the frame along the axis B are shown in Fig. 3. The thickness of the reinforced concrete slab is 60 mm. Both the longitudinal and transverse reinforcement have a diameter of 6 mm and a spacing of 200 mm. There are two identical reinforcement layers in
Fig. 6. Test setup. 3
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Fig. 7. Connection between the actuator and the specimen.
Fig. 10. Resistance-displacement curve in Ref. [17].
3. Experimental results and discussions Fig. 8. Arrangements of the LVDTs.
3.1. Resistance-vertical displacement The resistance-vertical displacement curve at the column-removal location (V2) is shown in Fig. 9. The ultimate bearing capacity and failure displacement of the specimen were 227 kN and 606 mm, respectively. The ultimate rotation capacity of the fully welded beamcolumn connection was 0.33 rad. Three stages (Stage I, II and III) were defined to represent the elastic-plastic, transition, and membrane/catenary action stage of the resistance-displacement curve, respectively. The resistance corresponding to the end of elastic-plastic stage I can be determined based on the yield-line theory. The resistance mechanism of the structure gradually transited from flexural action to tensile action during the stage II. It can be seen that the ultimate bearing capacity of the structure was about 2.8 times greater than the plastic bearing capacity. When the displacement reached 606 mm, the fracture initially occurring at the bottom flange of steel beams near the column-removal location rapidly penetrated the whole cross section, leading to the dramatic decrease of the resistance-displacement curve of the structure. Compared with that reported by Fu et al. [17] on a composite framed-structure under an internal column loss (presented in Fig. 10), the resistance-displacement curve herein for an edge column loss ascended more notably at large deflections even without external lateral restraints imposed on the structure. This is because the specimen in the test by Fu et al. [17] involves many other structural components and connections, such as steel bolts, end plates, angles and decks. The occurrence of some failures, including fracture of bolts and angles at column-beam connections, shear damage of studs between concrete slabs and steel beams, and local fracture of steel decks, resulted in that the potential tensile membrane action in slabs and catenary action in beams were not fully mobilized.
Fig. 9. Resistance-vertical displacement curve of the tested frame.
2.3. Test measurements The arrangements of linear variable displacement transducers (LVDTs) are presented in Fig. 8. The transducers V1, V3 and V4 were used for measuring the vertical displacements at the mid-span position of the beams A, C and B, respectively. The transducer V2 recorded the vertical displacement at the column-removal location. The transducers V5 ~ V7 measured the horizontal displacement at the corresponding beam ends.
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Fig. 11. Horizontal displacement-vertical displacement curves of the tested frame.
(a) Front view
(b) Right view
Fig. 12. Final deformation shape of the slab.
Fig. 13. Negative yield lines at the slab bottom.
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displacements at V5 and V7 became inward when the vertical displacement at V2 reached 120 mm, indicating that tensile catenary action in beams A, B and C started to develop. However, the catenary action in the beams A and C was found to be more significant than that in the beam B considering that the final lateral displacement at V5 was 4 times greater than that at V7. This is because the beam B performed as a cantilever for this column-removal scenario, of which the axial restraints were much weaker than those provided to the beams A and C. This phenomenon is not likely to occur for an internal column loss scenario, wherein catenary action can significantly develop in both longitudinal and transverse beams. Fig. 14. Fracture of the steel beam.
3.3. Failure pattern The final deformation shapes of the slab, steel beam and column are shown in Figs. 12–15, respectively. As presented in Fig. 12, a main crack in concrete was found on the slab top, which was in an elliptical shape along the edges of the specimen. Many diagonal cracks were also found, extending from the columns A and E to the column C. There was obvious spalling of concrete along the diagonals of the structure from the column-removal location to the columns B and D, which are known as the positive yield lines of the slab. Fig. 13 shows the damage pattern of concrete at the bottom of the slab. Numerous diagonal cracks formed and stretched from the column-removal location. The concrete was spalled along the edge regions of the structure. These elliptical regions are known as the negative yield lines of the slab. The frame failed to sustain more loads due to a fracture at the bottom flange of steel beam near the column-removal location, as shown in Fig. 14. This fracture resulted in a dramatic decrease of the resistance-displacement curve of the frame when the vertical displacement reached 606 mm. The final deformation shape of the column E is shown in Fig. 15. Severe local buckling can be observed at the left flange near the column bottom. This horizontal displacement further validated the significant development of tensile catenary action in the steel beams A and C.
Fig. 15. Inward lateral displacement of the column.
4. Simplified calculation method 3.2. Horizontal displacement-vertical displacement The collapse resistance of composite framed-structures in the event of a side or middle column loss has been previously investigated [11,18]. The response of structures was represented by the corresponding substructure with simplified boundary conditions. The simplifications for the middle and side column loss scenarios are shown in Fig. 16 and Fig. 17, respectively. However, this idealized fixed boundary condition is no longer reasonable for the tested substructure in this study without sufficient external restraints. To analytically determine the resistance-displacement curve for the frame in the experiment, a tri-linearized relationship proposed in Ref. [11] was used, wherein the main mechanism characteristics of the structure at column-removal stage were guaranteed to be captured. As
Fig. 11 shows the relationships between horizontal displacements at V5 ~ V7 and vertical displacement at the column-removal location (V2). A negative value represents that the horizontal displacement is away from the column-removal location and vice versa. The column D was found to barely have lateral displacements. This is because the tensile force in the peripheral beams connecting to column D was quite small and this column hardly deformed even at large deflections. It is therefore concluded that in the event of a column loss, the contributions of the columns diagonally adjacent to the column-removal location to redistributing the vertical loads are limited. The direction for lateral
Fig. 16. Simplification of the structure for middle column loss scenario [18]. 6
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Fig. 17. Simplification of the structure for side column loss scenario [11].
considering that tensile catenary action dominated the resistance mechanism in steel beams at large deflections [19]. The plastic bearing capacity of the structure was calculated by virtual work principle, wherein the internal virtual work was equal to that by external forces. The plastic bearing capacity is given by:
Fy = (Mx + Mx′ )
4l L 4 1 + (My + My′ ) + (MxN + MxP ) + MyN L l L l
(1)
wherein Mx and My are the positive bending moment of slab section about Y- and X- direction (per unit width), respectively; M′x and M′y are the negative bending moment of slab section about Y- and X- direction (per unit width), respectively; MxP is the positive plastic moment of X direction beam; MxN and MyN are the negative plastic moment of beams in X-and Y- direction, respectively. In Ref. [11], the ultimate bearing capacity of the structure was analytically determined by an energy-based method, wherein the following three contributions to internal energy dissipations at large deflections were considered: (1) elongation of reinforcement and steel beams Win1; (2) tensile force-induced additional bending moment due to geometric nonlinearity Win2, wherein the tensile forces include the tensile membrane forces along yield lines of the slab and tensile catenary forces in steel beams; (3) the bending moment along yield lines of the slab Win3. For the substructure tested in this study, however, the internal energy dissipation due to the elongations of reinforcement and steel beams Win1 was ignored considering that no effective lateral restraint was provided to the structure. The analytical method herein was amended only to account for the contributions from Win2 andWin3. The ultimate bearing capacity of structure in the experiment is directly given by:
Fig. 18. Tri-linearized resistance-displacement relationship.
shown in Fig. 18, the parameters vA and vB are the displacements at the column-removal location corresponding to the end of elastic-plastic and transition stages, respectively. The parameter vC is the failure displacement, and Fu and Fy are the ultimate and plastic bearing capacity of the structure, respectively. The details for determining vA and vB are given in Ref. [11]. To determine the plastic and ultimate bearing capacity, the yieldline and failure patterns of the structure were defined based on experimental observations, as shown in Fig. 19 and Fig. 20, respectively. The red dashed curves represent the elliptical negative yield lines at the bottom of the slab, while the blue lines denote the diagonally distributed positive yield lines at the top of the slab. In the failure pattern, negative and positive moment hinges at beam ends were excluded
Fig. 19. Yield-line pattern of structure in the experiment. 7
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Fig. 20. Failure pattern of structure in the experiment.
Fu = Ca bv (
Ty L l
+4
Tx l v L 4l ) + 4Fux + (Cm My + My′ ) + (Cm Mx + Mx′ ) L L l L (2)
where
Ca =
3k + 2 k3 − 2 6(1 + k ) 6(1 + k )2
Cm = 1 + χ1
χ b2 k−1 b − 2 (k 2 − k + 1) 2 3 (3)
wherein Ca accounts for the contribution from the membrane forcesinduced bending moment; Cm considers the interaction between the axial force and bending moment in slab sections; b and k are parameters quantifying the distributions of membrane forces in the slab; Ty and Tx are the yield forces of reinforcement in slab section in Y- and X- direction (per unit width), respectively; Fux is the yield force of steel beam section in X direction. The detailed expressions of these parameters are given in Ref. [11]. The comparison of the resistance-displacement curves from the experiment and simplified calculation method is shown in Fig. 21. A reasonable agreement was achieved since the predicted ultimate bearing capacity was found to be only 6.7% greater than the measured value.
Fig. 21. Comparison of the resistance-displacement curves from the experiment and simplified calculation method. Table 3 Material properties for steel in the numerical model. Material
E (105 MPa)
fy (MPa)
E p(103 MPa)
εf
v
Beam Web Beam Flange Column Web Column Flange Reinforcement
1.95 2.06 1.91 1.96 1.85
286 300 320 300 420
0.912 0.987 1.496 1.261 3.057
0.20 0.17 0.17 0.18 0.10
0.3 0.3 0.3 0.3 0.3
5. Numerical modelling 5.1. Numerical model
Note: Ep, εf and v are the post-yield modulus, fracture strain and Poisson’s ratio of steel, respectively.
A numerical model was created in finite element software ABAQUS [20], and its reliability was validated against experimental results in Section 3. The steel columns and beams were simulated by four-node shell elements (S4R). The reinforcement was modeled by two-node truss element (T3D2). The eight-node solid element (C3D8R) was used
Fig. 22. Material properties of concrete. 8
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Table 4 Material properties for concrete in the numerical model. E (105 MPa)
fu (MPa)
v
Dilation Angle
Eccentricity
fb0/fc0
KC
Viscosity
0.254
22.9 (Compression) 2.29 (Tension)
0.2
30°
0.1
1.16
0.667
0.001
true strain and stress used in the numerical model were converted from the nominal values based on Eq. (4):
εt = ln(1 + εn ) σt = σn (1 + εn )
(4)
whereεt and εn are the true and nominal strain, respectively; σt and σn are the true and nominal stress, respectively. The Mises yield surface is adopted to account for yielding, wherein the relationship of the uniaxial yield stress and equivalent plastic strain of steel material is defined. The isotropic hardening rule is employed to consider the hardening behavior of the material. The yield surface changes size uniformly in all directions when the yield stress varies as plastic strain occurs. The ductile damage model was used to account for the failure of steel [21]. The fracture strain was taken as the ultimate strain in the coupon test. The damage evolution was based on the displacement of the element, wherein the failure displacement was taken as 6.7 mm. It was determined by ensuring that the numerical resistancedisplacement curve of the structure sharply decreased at the same displacement as measured in the experiment. The material properties of steel used in the numerical model are summarized in Table 3. The concrete damaged plasticity model was used to consider the failure of concrete [22]. This model was also employed by researchers to analyze the punching shear of concrete slabs [23,24], wherein some key parameters were calibrated based on the experimental load-displacement relationship for an interior slab-column connection and this model was further proved to be reliable for interior and edge slab-column connections with more complicated loading conditions. As shown in Fig. 22, the compressive stress-inelastic strain relationship and tensile stress-cracking strain relationship were defined to account for the compressive and tensile behavior of concrete, respectively. The damage-inelastic/cracking strain relationships were specified to consider the deterioration of concrete. The damage factor was determined based on the Codes for Design of Concrete Structures (GB50010-2010) [25]. The material properties of concrete in the numerical model are shown in Table 4. All steel members in the numerical model (the beams, columns and stiffeners) were merged as a new assembly considering that all the beam-column connections are fully welded. In the experimental tests, no shear stud fractured, and thus negligible relative slip between the steel beam and concrete slab was assumed. The steel beams were therefore connected to concrete slab by “Tie” command. The reinforcement was “Embedded” into the concrete slab. The bottom surfaces of columns were assumed to be fully restrained. The details of the finite element model are shown Fig. 23. A displacement-controlled loading process at the predefined column-removal location was used in the numerical model. To account for the effect of geometrical nonlinearities on the structural behavior of the frame model at large deflections, the NLGEOM option was selected.
Fig. 23. Details of the finite element model.
Fig. 24. Comparison of resistance-vertical displacement relationship.
5.2. Validation of the numerical approach Fig. 25. Comparison of horizontal-vertical displacement relationship.
To validate the numerical model, the resistance-vertical displacement relationship, horizontal-vertical displacement relationship and failure mode of the structure from the numerical approach were compared with those from the experiment in Section 3. Fig. 24 shows the comparison of the resistance-vertical displacement relationship of the tested frame. The numerical model slightly overestimated the collapse resistance of the structure at large deflections. In the experiment, the
to simulate the concrete slab. The mesh size of concrete slab is 50 mm (longitudinal direction) × 50 mm (transverse direction) × 15 mm (thickness). The global mesh size of steel columns and beams are 25 mm. A 50 mm global size was designated for the reinforcement in the slab. A bi-linear stress–strain relationship of steel was assumed. The
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Fig. 26. Comparison of the failure mode of the slab.
Fig. 27. Comparison of the failure mode of the steel beam.
Fig. 28. Stress extraction locations in the numerical model.
Fig. 30. Stress evolutions in the reinforcing bar.
Fig. 29. Stress evolutions in the steel beam.
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Table 5 Details of numerical model. No.
Variable
Slab Thickness
Reinforcement
Beam Section
N1 N2 N3 N4
Control specimen Slab thickness
60 70 80 90
Φ6@200 Φ6@200 Φ6@200 Φ6@200
100 100 100 100
N5 N6 N7
Reinforcement diameter
60 60 60
Φ7@200 Φ8@200 Φ9@200
100 × 67 × 4.5 × 6 100 × 67 × 4.5 × 6 100 × 67 × 4.5 × 6
+16.7% (36.1%)* +33.3%(77.8%)* +50%(125%)*
N8 N9 N10
Beam height
60 60 60
Φ6@200 Φ6@200 Φ6@200
120 × 67 × 4.5 × 6 140 × 67 × 4.5 × 6 160 × 67 × 4.5 × 6
+20% +40% +60%
× × × ×
67 67 67 67
× × × ×
Deviation Percentage 4.5 4.5 4.5 4.5
× × × ×
6 6 6 6
– +16.7% +33.3% +50%
Note: *indicates the change percentage of the reinforcement area. Dimensions in mm.
Fig. 31. Comparison of the resistance-displacement curves for models N1 ~ N10.
sections (locations 2, 3 and 4) of the reinforcing bar were selected. For the location 1, the stress along the axis of the beam (S11) at the top and bottom flanges was presented. For the locations 2, 3 and 4 of the reinforcing bar, the stress along the X-direction was presented. As shown in Fig. 29, the initial tensile stress at the bottom flange was greater than that at the top flange, suggesting that this section suffered from a sagging moment at the beginning. When the vertical displacement at the column-removal location reached about 150 mm, the tensile stresses at both the bottom and top flanges started to steadily increase. Finally, the tensile stresses at the bottom and top flanges reached about 300 MPa, indicating the sufficient development of catenary action in steel beam C. As shown in Fig. 30, the tensile stresses in reinforcing bar at these locations increased at large deflections. Moreover, the closer the location to the edge was, the greater the tensile stress was. The stress evolution in the reinforcing bar further demonstrated the diagonally distributed positive yield lines at the bottom of the slab.
lateral displacement for the column E (Fig. 3) was somewhat greater than that for the column A at large deflections due to some unexpected systematic errors, which resulted in that the tensile catenary action in the steel beam C was less significant than that in the steel beam A. Therefore, the numerical resistance-displacement curve re-ascended more apparently than that of the experiment. The comparison of the horizontal displacement at V5 is shown in Fig. 25. It can be seen that the predicted horizontal displacements from numerical analysis agreed well with the experimental results when the vertical displacement was less than 400 mm. After reaching 400 mm, the numerical analysis tended to underestimate the horizontal displacement at V5. Fig. 26 and Fig. 27 show the comparisons between the numerical and experimental results of the final failure mode of the slab and steel beam, respectively. These further validated the reliability of the numerical approach. To further study the development of catenary action in the steel beam and tensile membrane action in the slab, the evolution of the stress state at some key locations (shown in Fig. 28) of the frame in the numerical model was presented in Fig. 29 and Fig. 30. The middle span section of steel beam C (location 1) and three diagonally distributed 11
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• The positive yield lines of the slab diagonally distributed, stretching
5.3. Parametric study The validated numerical model was used to investigate the effect of concrete slab thickness, reinforcement diameter and steel beam dimensions on the structural behavior of composite framed-structures. The details of the parameters are shown in Table 5, wherein N1 is the basic model and its parameters are taken as those measured in the experiment. The deviation percentages of parameters in models N2 ~ N10 were calculated as the ratio of the difference of the corresponding quantity to that of the model N1. Note that the effect of reinforcement is mainly due to the cross section area, rather than the diameter. The reinforcement areas were increased by 36.1%, 77.8% and 125% for N5 ~ N7, respectively. The effect of aforementioned structural parameters on the resistance-displacement curves of structures is shown in Fig. 31. The failure of these structures was all due to the fracture at the bottom flange of the steel beam near the column-removal location, as shown in Fig. 27(b). The findings are summarized as follows:
• •
Declaration of Competing Interest We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work and we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.
• The plastic bearing capacity of the structure was mainly affected by •
•
slab thickness and steel beam height. A larger slab thickness and beam height ensured a greater plastic bearing capacity. Increasing the slab thickness and reinforcement diameter enhanced the ultimate bearing capacity, while a larger beam section height failed to provide a greater ultimate bearing capacity. For N8 ~ N10, the ultimate bearing capacity was 6.4%, 7.8% and 8.1% less than that for N1, respectively. This is because the failure displacement at the column-removal location decreased when the beam section height increased, resulting in less development of tensile catenary action in steel beams. It is therefore concluded that in practical safety design of structures against progressive collapse, increasing the section height of beams is not always conservative. The effect of reinforcement diameter on the resistance-displacement curve of the structure was less significant than those of slab thickness and steel beam height. For N5 ~ N7, the reinforcement areas increased by 36.1%, 77.8% and 125%, respectively, while the ultimate bearing capacity was found to be only 2.6%, 4.4% and 5.6% larger than that for structure N1, respectively. This phenomenon suggests that the contribution of tensile membrane action in reinforcement to the collapse resistance is less significant than that of catenary action in steel beams.
Acknowledgements The work presented in this paper was supported by the ThirteenFive Science and Technology Support Program with grant 2016YFC0701203. References [1] DoD. Design of buildings to resist progressive collapse. UFC 4-023-03: Washington, DC: Department of Defense; 2013. [2] GSA. Progressive collapse analysis and design guidelines for new federal office buildings and major modernization projects. Washington, DC: General Services Administration; 2013. [3] Jiang B, Li G, Li L, Izzuddin BA. Experimental studies on progressive collapse resistance of steel moment frames under localized furnace loading. J Struct Eng 2018;144(2):04017190. [4] Li G, Li L, Jiang B, Lu Y. Experimental study on progressive collapse resistance of steel frames under a sudden column removal scenario. J Constr Steel Res 2018;147:1–15. [5] Guo LH, Gao S, Fu F, Wang YY. Experimental study and numerical analysis of progressive collapse resistance of composite frames. J Constr Steel Res 2013;89:236–51. [6] Yang B, Tan KH. Experimental tests of different types of bolted steel beam–column joints under a central-column-removal scenario. Eng Struct 2013;54:112–30. [7] Lew HS, Main JA, Robert SD, Sadek F, Chiarito VP. Performance of steel moment connections under a column removal scenario I: experiments. J Struct Eng ASCE 2013;139(1):98–107. [8] Khandelwal K, El-Tawil S. Collapse behavior of steel special moment resisting frame connections. J Struct Eng 2007;133(5):646–55. [9] Dinu F, Marginean I, Dubina D, Petran I. Experimental testing and numerical analysis of 3D steel frame system under column loss. Eng Struct 2016;113:59–70. [10] Li H, Cai X, Zhang L, Zhang B, Wang W. Progressive collapse of steel momentresisting frame subjected to loss of interior column: Experimental tests. Eng Struct 2017;150:203–20. [11] Li G, Zhang J, Jiang J. Analytical modeling on collapse resistance of steel beamconcrete slab composite substructures subjected to side column loss. Eng Struct 2018;169:238–55. [12] Song BI, Sezen H. Experimental and analytical progressive collapse assessment of a steel frame building. Eng Struct 2013;56:664–72. [13] Hadjioannou M, Donahue S, Williamson EB, Engelhardt MD. Large-scale experimental tests of composite steel floor systems subjected to column loss scenarios. J Struct Eng 2018;144(040171842). [14] Johnson ES, Meissner JE, Fahnestock LA. Experimental behavior of a half-scale steel concrete composite floor system subjected to column removal scenarios. J Struct Eng 2016;142(2):04015133. [15] Fu QN, Tan KH, Zhou XH, Yang B. Three-dimensional composite floor systems under column-removal scenarios. J Struct Eng 2018:144. [16] Ministry of Construction of China. Code for Design of Steel Structures (500172017): Beijing; 2017. [17] Fu QN, Tan KH, Zhou XH, Yang B. Load-resisting mechanisms of 3Dcomposite floor systems under internal column-removal scenario. Eng Struct 2017;148:357–72. [18] Zhang JZ, Li GQ. Collapse resistance of steel beam-concrete slab composite substructures subjected to middle column loss. J Constr Steel Res 2018;145:471–88. [19] Izzuddin BA. A simplified model for axially restrained beams subject to extreme loading. Int J Steel Struct 2005;5(5):421–9. [20] ABAQUS Analysis User's Manual Version 6.7. ABAQUS Inc.; 2007.
6. Conclusion This paper presented an experimental investigation on structural responses of composite framed-structures due to an edge-column loss. The progressive collapse resistance of the frame significantly re-ascended at large deflections. Typical failure modes of the frame due to edge column loss were obtained. The effect of concrete slab thickness, reinforcement diameter and steel beam dimensions on collapse resistance of structures was numerically investigated. To facilitate the development of safety design of structures against collapse, a simplified analytical method for predicting the collapse resistance of the frame due to an edge-column loss was also proposed. The following conclusions can be drawn:
• The experimental results showed that for an edge-column loss sce-
•
from the column-removal location to the two corners of the slab. The negative yield lines elliptically formed along the edges of the slab. Increasing the beam height guaranteed a greater plastic bearing capacity of the structure, but it may fail to provide a larger ultimate bearing capacity due to a poorer ductility. The simplified calculation method was capable of capturing the main mechanical features of the resistance-displacement curves of the frame due to an edge-column loss. The predicted ultimate bearing capacity of the frame was found to be only 6.7% greater than the experimental value.
nario, both tensile catenary action in steel beams and membrane action in concrete slabs can significantly develop at large deflections of steel-concrete composite frames without external horizontal restraints. The frame failed due to the fracture at the bottom flange of the steel beam near the column-removal location. The catenary action in the double-span beam after column loss was more notable than that in the beam perpendicular to it. Moreover, the contributions of the columns diagonally adjacent to the columnremoval location to redistributing the vertical loads were limited. 12
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element analysis of punching shear. Comput Struct 2015;151:73–85. [24] Genikomsou AS, Polak MA. Finite element analysis of punching shear of concrete slabs using damaged plasticity model in ABAQUS. Eng Struct 2015;98:38–48. [25] Ministry of Construction of China. Code for Design of Concrete Structures (500102010): Beijing; 2010.
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