To investigate the progressive collapse behavior of Steel Reinforced Concrete (SRC) column-steel beam hybrid frame after the failure of key structural elements, a PQ-Fiber model for an 8-storey structure is established in ABAQUS program. Nonlinear dynamic and static pushdown analysis are carried out after the failure and removal of the bottom-middle and bottom-corner columns. Numerical results of both methods agree well with each other. Results show that SRC column-steel frame has good resistance to progressive collapse under dynamic instantaneous load. After sudden removal of a bottom middle column, the development of structural collapse exhibits two mechanisms, the beam mechanism and the catenary mechanism. When the structure is within small deformation range, the collapse resistance of the residual frame is provided by the beam bending moment capacity, which is beam mechanism. For large deformation situation, the collapse resistance is mainly provided by the beam tensile strength, which is catenary mechanism. However, with the removal of a bottom corner column, the residual structure only undergoes the beam mechanism even for large deformations. For future practical applications, the influence of the steel ratio, steel section size, and the vertical position of the removed key components are investigated through a detailed parametric study.
After the progressive collapse of the Ronan Point apartment due to gas explosion in London in 1968 [
Many experimental and theoretical studies on the progressive collapse behavior of reinforced concrete frame and steel frame have been reported, including structural collapse mode and dynamic increasing factor. Tsai and Lin [
From the above literature, it can be seen that the current theory or experiment studies on progressive collapse are mostly about reinforced concrete structures (RC) and steel structures. In practical engineering, other than just steel structure or RC structures, more and more hybrid structures are developed to meet higher requirement of structure durability, performance, and economic and other aspects. A type of hybrid frame which consists of Steel Reinforced Concrete (SRC) column and structural steel beam is one of the widely used hybrid structures. It was proved to have good seismic performance and economic advantages compared with just structure steel frame or RC frame structure. However, there is little research on the progressive collapse ability of this SRC column-steel beam hybrid frame structure. It is most likely to occur under occasional impact loads such as explosion.
This paper addresses the progressive collapse behavior of SRC column-steel beam hybrid frame. An 8-storey hybrid frame structure was designed according to the current Seismic Code of China, and the pushdown analysis was carried out by using alternate path method under the occasional load. Based on the analysis results, the progressive collapse ability and collapse mechanism of the hybrid frame were studied, and the influence of the parameters such as the steel ratio of SRC column, steel section size, and the vertical position of removing key components were also investigated.
In this study, ABAQUS program was employed for structure analysis. The hybrid frame components are all modeled by the two-dimensional plane element. This type of unit allows shear deformation, and takes into account the limited axial strain. The finite element model of a hybrid frame is shown in Figure
Finite element model of a hybrid frame.
Discretization of the steel in the SRC column.
The concrete 03 in PQ-Fiber was used for the concrete constitutive model. This model is based on the concrete skeleton curve in current Chinese Code [
Stress-strain curve of concrete.
The stress-strain curves of concrete under uniaxial compression (Figure
USTEEL02 model of PQ-FIBER is used for the constitutive model of steel and rebar. Figure
In order to verify the applicability of the modeling in ABAQUS program of the SRC column-steel beam hybrid frame, the seismic behavior of the hybrid frame experiment conducted by Li and Zhao [
The good agreement between the FEM method and the experimental results shows that it is feasible to carry out the elastoplastic simulation analysis to the SRC column-steel beam hybrid frame in the ABAQUS with PQ-FIBER.
The straightforward progressive collapse capacity analysis of a frame is dynamic analysis on the remaining structure under the instantaneous load from the force redistribution due to sudden collapse or failure of one column (Khandelwal and El-Tawil, 2011 [
For the model considered in this paper, the material nonlinearity of steel and concrete needs to be considered in the analysis due to the large deformation estimated. In addition, due to the large number of elements involved in this model, the displacement-controlled nonlinear static method will be employed to improve the efficiency and accuracy of analysis. The structure dynamic effect will be considered and the dynamic increasing factor will be investigated.
In accordance with DOD2010 [
According to US specification GSA2003 [
Specifically in the ABAQUS program, the failure component is firstly removed by using life and death unit method, which can be achieved by the command of
As a verification pushdown method is used to simulate a 1/3 reinforced concrete frame experiment, which is designed according to the reinforced concrete design specification [
Stress-strain curve of steel.
Load-displacement curve of SRC hybrid frame.
Load-displacement curves of pushdown analysis and test results.
Assuming the relationship between applied load
In order to make the analysis result more clear, this paper adopts the concept of the load resistance coefficient proposed by Khandelwal and El-Tawil [
Considering (
According to DOD2010 [
As for the removal of key components in progressive collapse analysis, GSA2003 [
In this paper, pushdown analysis will be carried out by removing the bottom corner column and the middle column. Their effect on structure progressive collapse behavior was analyzed and parameters analysis was investigated.
The calculation model is 8-storey SRC column-steel beam hybrid frame structure. The plan drawing is shown in Figure
The planar arrangement of the hybrid frame structure.
Dead loads on both floor and roof are 5.0 kN/m2, live loads on floor and roof are 2.0 kN/m2 and 0.5 kN/m2, respectively. The combination of load effects in this paper is calculated according to the
Cross section of SRC column.
SRC column | Section size (mm) | Steel size (mm) (height × width × web × flange) | Longitudinal reinforcement |
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5–8 storey |
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As shown in Figure
Elevation drawing of the hybrid frame structure.
The middle column B4 is removed from the frame and the column top is used as control node. Both dynamic analysis and pseudostatic pushdown analysis were carried out using ABAQUS program.
The dynamic displacement of the middle column upper node and the bending moment of the connecting beam are shown in Figures
The displacement of middle column upper node versus time in dynamic model.
The bending moment of connecting beam to middle column upper node versus time in dynamic model.
The deformation of frame after collapse of column B4 is shown in Figure
Deformation cloud diagram of the hybrid frame after the failure of the bottom middle column.
Vertical displacement-resistance coefficient curve of the hybrid structure after the failure of the bottom middle column.
Static displacement-resistance coefficient curve
Dynamic displacement-resistance coefficient curve
Figure
Bending moment-resistance coefficient curve of the steel beam connected with the removed middle column.
Figure
Axial force-resistance coefficient curve of the steel beam connected with the removed middle column.
The corner column B1 is removed from the frame and the column top is used as control node. Both dynamic analysis and pseudostatic pushdown analysis were carried out using ABAQUS program. From the pseudostatic pushdown analysis the deformation of overall structure is analyzed and shown in Figure
Deformation of the hybrid frame after the failure of the bottom corner column.
Figure
Vertical displacement-resistance coefficient curve of the hybrid structure after the failure of the bottom corner column.
Static displacement-resistance coefficient curve
Dynamic displacement-resistance coefficient curve
The relationships of the beam bending moment versus resistance coefficient of the structure after bottom corner column removed are given in Figure
Bending moment-resistance coefficient curve of the steel beam connected with the removed corner column.
The relationship of the axial force versus resistance coefficient of the structure after bottom corner column is removed is given in Figure
Axial force-resistance coefficient curve of the steel beam connected with the removed corner column.
From the above discussion, it can be seen that there are two stages in the progressive collapse process of SRC column-steel beam hybrid frame: “beam mechanism” and “catenary mechanism,” which is similar to the failure process of RC frame and steel frame [
SRC column is the basic vertical load-bearing component in a hybrid frame. According to the design rules of steel composite structure [
Different SRC column-steel ratio parameters for models (
Model | Steel size in 1–4 storeys (mm) (height × width × web × flange) | Steel size in 5–8 storeys (mm) (height × width × web × flange) | Steel ratio in 1–4 storeys (%) | Steel ratio in 5–8 storeys (%) |
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The SRC column-steel beam hybrid frame analysis model was established according to the three different column-steel ratio parameters in Table
Figure
It can be seen from Figure
Displacement-resistance curve of the three models with different steel ratio after the bottom middle column was removed.
Figure
Displacement-resistance curve of the three models with different steel ratio after the bottom corner column was removed.
As can be seen from the figure, with the increase of steel ratio in the SRC columns, the resistance coefficient growth rate is very small. This is a similar conclusion as the removal of middle column. Increasing the steel ratio of the SRC column has a slight effect on the anticollapse ability of hybrid frame structure.
The beam mechanism stage is the first stage of the progressive collapse process of the SRC column-steel beam hybrid frame. In that stage the anticollapse ability of the structure is mainly provided by the bearing capacity of the beam. Therefore the cross-sectional size of the beam has a direct effect on the progressive collapse of the structure. In addition, changing the beam cross-sectional dimensions, the beam-to-column linear stiffness ratio of the frame will also change. Also the beam-to-column linear stiffness ratio is an important factor in determining the integrity of the structure, which will affect the structure ductility, internal force distribution and energy consumption, and other properties. Therefore, this paper presents a parametric analysis for the hybrid frame with different beam cross-sectional dimensions and corresponding beam-to-column linear stiffness ratios, which is shown in Table
Beam dimension and corresponding beam-to-column linear stiffness ratios (models (
Model | Beam dimension (mm) (height × width × web × flange) | Beam-to-column linear stiffness ratios in storeys 1–4 ( |
Beam-to-column linear stiffness ratios in storeys 5–8 ( |
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The curves of the vertical displacement versus resistance coefficient of the hybrid frame with different beam parameters (Table
Vertical displacement-resistance coefficient relationship of models with different beam parameters after removing the bottom middle column.
It can be seen from Figure
The curves of the vertical displacement versus resistance coefficient of the hybrid structure from the three models (Table
The vertical displacement-resistance coefficient relationship of models with different beam parameters after removing the bottom corner column.
The effects of the removal of the middle column and the corner column on the progressive collapse behavior and the corresponding collapse mechanism are studied in the previous section; however, both analyses are about removal of the bottom storey column elements. To investigate more the effect of the vertical position of the removal column on the progressive collapse behavior, further pushdown analysis was conducted on the first, fourth, and seventh storey columns to represent the lower, middle, and upper parts of the structure.
Figures
Vertical displacement-resistance coefficient curves obtained by removing the middle column in different floors.
Vertical displacement-resistance coefficient curves obtained by removing the corner column in different storeys.
In this paper, the ABAQUS program is used to establish the SRC column-steel beam hybrid frame model, of which the progressive collapse behavior is studied by both dynamic analysis and the pseudostatic pushdown method. The results of both methods agree well with each other. Some conclusions can be drawn from this investigation.
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The authors declare that there are no conflicts of interest regarding the publication of this paper.
The first author would like to express gratitude to the National Natural Science Foundation of China for the financial support (Grant no. 51408556).