Progressive Collapse of Exterior Reinforced Concrete Beam–Column Subassemblages: Considering the Effects of a Transverse Frame
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Abstract
Many experimental studies have evaluated the inplane behavior of reinforced concrete frames in order to understand mechanisms that resist progressive collapse. The effects of transverse beams, frames and slabs often are neglected due to their probable complexities. In the present study, an experimental and numerical assessment is performed to investigate the effects of transverse beams on the collapse behavior of reinforced concrete frames. Tests were undertaken on a 3/10scale reinforced concrete subassemblage, consisting of a doublespan beam and two end columns within the frame plane connected to a transverse frame at the middle joint. The specimen was placed under a monotonic vertical load to simulate the progressive collapse of the frame. Alternative load paths, mechanism of formation and development of cracks and major resistance mechanisms were compared with a twodimensional scaled specimen without a transverse beam. The results demonstrate a general enhancement in resistance mechanisms with a considerable emphasis on the flexural capacity of the transverse beam. Additionally, the role of the transverse beam in restraining the rotation of the middle joint was evident, which in turn leads to more ductile behavior. A macromodel was also developed to further investigate progressive collapse in three dimensions. Along with the validated numerical model, a parametric study was undertaken to investigate the effects of the removed column location and beam section details on the progressive collapse behavior.
Keywords
progressive collapse reinforced concrete beams experiment alternative load path finite element analysis1 Introduction
The progressive collapse of structures due to natural and manmade disasters has been the main focus of many recent studies. For example, Sasani et al. (2007, 2008a, b, 2011a, b) made great efforts to investigate the collapse behavior of fullscale reinforced concrete (RC) structures. In all of these cases, compressive arch action in beams, Vierendeel action in beams and columns, and also catenary action in longitudinal reinforcements were identified as the main resistance mechanisms against progressive collapse. Yi et al. (2008) performed laboratory tests on an RC planar frame in which the static responses were examined under progressive collapse.
In many studies, in scenarios in which the middle column was removed, the structural responses of RC subassemblages, including double beams and triple columns, were considered as a basis for estimating the resistance of real structures. Su et al. (2009) evaluated the loadcarrying capacity of RC subassemblages against progressive collapse. They tested 12 reducedscale specimens where the beams were restrained longitudinally against axial deformation. The results indicated that compressive arch actions due to longitudinal restraint can significantly enhance the loadcarrying capacity of the beams. Sasani and Kropelnicki (2008) studied the behavior of a 3/8scaled model of a continuous perimeter beam in a reinforced concrete frame structure following the removal of a supporting column. An experiment by Lew et al. (2011) examined the behavior of two fullscale RC subassemblages subjected to static loading under a middle column removal scenario. As with previous research, the resistance of subassemblages was based on arching and catenary actions. Yu and Tan (2011, 2013a, b) performed an experimental test on eight halfscale RC subassemblages under a middle column removal scenario.
Yu and Tan (2014) also proposed special detailing techniques for RC subassemblages to improve structural resistance under the column removal scenario. Tsai and Huang (2015) tested the collapse resistance of six reinforced concrete subassemblages designed with different spantodepth ratios and varied stirrup spacings under gravitational loading. Farhang Vesali et al. (2013), Choi and Kim (2011) and Kim and Choi (2015) presented other notable studies that focused on the collapse behavior of RC subassemblages. Qian et al. (2014) investigated the contribution of secondary loadcarrying mechanism, including transverse beams and membrane action of the slabs in RC assemblies. Qian et al. (2015) studied the threedimensional (3D) effects on the progressive collapse behavior of RC frames. In addition to middle beam–column assemblies, extensive research by Qian and Li (2012a, b, 2015) investigated the behavior of RC frames under the loss of a corner column and quantified slab effects on the dynamic performance of RC frame subjected to the loss of column scenario.
In addition to experimental studies, other research has focused on analytical evaluations of RC subassemblages. Bao et al. (2014) performed a computational investigation of the middle beam–column assemblies and developed two types of models: detailed and reduced models. Bao et al. (2008) and Bao and Kunnath (2010) developed macromodel approaches to study the progressive collapse behavior of RC assemblies. Sasani et al. (2011b) introduced detailed models for modeling the bar fractures in RC frames under progressive collapse.
In most of the experimental and truescale studies, little attention has been paid to the effects of transverse beams, and in particular, the additional resistance due to transverse members is not discussed. Hence, a 3D beam–column subassemblage is assessed experimentally in the present study. Investigating the roles of transverse beams in providing alternative load paths under the column removal scenario was the main purpose of the performed evaluation. In addition to the experiment, a finite macro element model is also developed using the open source platform, OPENSEES (2007), to provide comprehensive insight into the experimental observations.
2 Test Program
To investigate the role of transverse beams, a 3D subassemblage including three columns, three beams and a middle column stub is tested in the present study. Due to the probable complexities, a 3/10scaled specimen is used here. The 3D specimen is an extension of a planar (2D) subassemblage that was tested separately by Ahmadi et al. (2016) and the results will be used to provide a better understanding of the effects of the transverse beam. The 2D specimen includes two end columns, a middle column stub and two beams. To make a 3D specimen, a transverse frame consisting of a beam and an end column is added at the middle joint. The specimens were fastened to a displacement control point loaded above the column; the test continued until complete failure of the specimen. During testing, corresponding displacements and strains at predefined points and sections were measured and the formation of resistance mechanisms and failure modes were recorded.
2.1 Specimen Design

Dead load of superimposed roof: 0.48 kN/m^{2}

Dead load of superimposed floor: 1.44 kN/m^{2}

Roof live load: 1.20 kN/m^{2}

Floor live load: 4.79 kN/m^{2}

SDS: 0.291 g

SD1: 0.182 g
As shown in Fig. 2, the upper and lower longitudinal beam reinforcements are anchored mechanically into exterior columns to simulate continuity in external beam–column joints. Given the short length of the specimens, there was no need to use splices in the beam reinforcements. Longitudinal column reinforcements are anchored by 90° hooks inside the foundations. To prevent structural slippage, each foundation is attached to the strong laboratory floor using four threaded rods. The tops of the columns were mechanically anchored to the main frame to restrict displacements at these points. Downward displacement and rotation of the tops of the columns remained unrestrained.
Geometric properties of prototype and scaled specimens.
Prototype and scaled specimen  Beam net span (mm)  Transverse beam net span (mm)  Beam size (mm)  column size (mm)  Reinforcement ratio at the columns  Reinforcement ratio at the joint  Reinforcement ratio at the beam mid span  

Depth  Width  Depth  Width  Top  Bottom  Top  Bottom  
Prototype  5385  –  500  700  700  700  1.7 % (12#9)  0.65 % (4#8)  0.41 % (2#9)  0.32 % (2#8)  0.41 % (2#9) 
2D scaled specimen  1500  –  140  200  200  200  1.7 % (12T8)  0.62 % (3T8)  0.41 % (2T8)  0.41 % (2T8)  0.41 % (2T8) 
3D scaled specimen  1500  1400  140  200  200  200  1.7 % (12T8)  0.62 % (3T8)  0.41 % (2T8)  0.41 % (2T8)  0.41 % (2T8) 
With regard to the scaling of the specimens, the maximum size of the aggregate for the concrete mix design was less than 10 mm. In the technical literature, it is assumed that the ratio of the maximum prototype to the model concrete aggregate is equal to the scale factor of the specimen. Nonetheless, the use of an aggregate with the maximum possible size is always recommended, such that the high relative tensile strength of the model concrete is minimized (Harris and Sabins 1999).
The average compressive and tensile strengths of the concrete were 26 and 1.5 MPa, respectively. The yield and ultimate strengths of the beam and longitudinal column reinforcements were 530 and 650 MPa, respectively. The rupture strain of the reinforcement was 0.19, according to the reinforcement tensile tests.
2.2 Instrumentation
2.3 Test Setup and Loading
3 Test Results
The present study focuses on the effects of transverse beams; therefore, the results of the 3D specimen are discussed in detail and only the differences with the planar subassemblage are highlighted. The specimens were exposed to monotonic downward vertical displacement at the middle column stub until fractures occurred in the lower and upper bars of the beam. Maximum displacement of the middle column at the end of the test was 340 mm and the chord rotation of the beam was 0.2 radians (11.46°). The failure of the specimen had the following characteristics: (1) flexural cracks developed at the joints interfaces; (2) the compressive concrete was crushed at the joint interfaces due to the extension of cracks within the upper part of the beams; and (3) fractures occurred in both the beam bottom bars next to the middle column stub and the beam top bars in the exterior beam column joints, in transverse and inplane beams, respectively.
3.1 Crack Patterns
3.2 Load–Displacement Curve
Increasing displacement up to 276 mm increased the vertical load, resulting in the first fracture in the lower longitudinal bar in the beam with a vertical load of 53 kN. The first rebar fracture occurred at the location of the main crack in the south beam at the interface with the middle column stub. The second fracture in the beam’s lower rebar occurred at the same place with a displacement and load of 297 mm and 51 kN, respectively.
Comparison of Force and displacement at critical points of 2D and 3D specimen.
Specimen  Flexural action  Compressive arch action  beginning of catenary action  Catenary action  

P (FA) (kN)  Y (FA) (mm)  P (CCA) (kN)  Y (CCA) (mm)  P0 (CA) (kN)  Y (CA) (mm)  P (CA) (kN)  Y (CA) (mm)  
2D specimen  20.7  18.5  28.1  50  21  135  35.6  306 
3D specimen  23–(32)  16.9–(30)  38.18  67  33.2  151.2  53  340 
Difference %  11.1–(55)  9.5–(62)  36  35  58  12  49  11 
The first peak in the load–displacement curve corresponds to the CAA capacity of the subassemblage. In comparison to the flexural capacity, arching action enhances the structural resistance by up to 19 percent. Comparison of 2D and 3D results demonstrated that CAA for a 2D frame enhances the structural resistance by about 36 percent over flexural capacity but in a 3D frame this increase is 19 percent. As mentioned above, the development of compressive forces enhances CAA capacity and the transverse beam in the 3D specimen does not have enough restriction at its ends for the development of an axial force and arching action. Indeed, the CAA capacity for both specimens had the same resistance elements and mechanisms.
Large deflections and crack development at the depth of the beams led to the gradual elimination of compressive axial forces and the consequent reduction in the load carrying capacity of the specimen. The load capacity of the specimen up to a displacement of 151 mm and loading force of 33 kN decreased. Beyond this point, the vertical load increased because of the development of tensile forces in the beams.
Force and displacement at critical points of load–deflection curves.
Flexural action  CAA action  Second part of load increasing  1st rebar fracture  2st rebar fracture  Top rebar fracture  Catenary action  

Calculated  Experimental  Experimental  Calculated  experimental  
Displacement (mm)  –  16.9  67  151  276  297  340  320  340 
Force (KN)  19.4 (25.7)^{*}  23  38  33  53  51  53  59.9  53 
As presented in Table 3, there was little difference between the calculated values and the results obtained from the CA capacity tests for a 3D specimen. Fracture of the upper beam bars occurred at a value between yield and ultimate strength in response to the stress concentration at the middle and end joint interfaces and the effect of shear force on rebar under tension.
The load–displacement curves were identical for the 2D and 3D specimens up to a vertical displacement of 18 mm. Because the flexural and arching actions of the inplane beams are dominant during this stage, this similarity is obvious. Numerical analyses in the next section demonstrate that within this stage, small axial forces were developed in the transverse beam. Generally, owing to the lack of axial restraint in the transverse beam, arching actions could not develop. Hence, flexural action is the dominant mechanism in the transverse frame. The flexural capacity of a transverse frame leads to higher resistance for 3D specimen events – in the post peak phase of the load–displacement curve (Fig. 11). The area under the load–displacement curve for the 3D specimen is 1.9 times larger than the corresponding value for the 2D assembly.
3.3 Deflection Profile
3.4 Strain Measurements
The reinforcement strains in the top and bottom rebars at section B11 at the transverse beam (Fig. 16b) show that the strains in the reinforcement in this section remained in the elastic range. In addition, tensile strain in the top and bottom rebars indicates the development of axial tension during the second half of the loading procedure.
The experimental results in the present study demonstrate the significant role of transverse frames in the redistribution of unbalanced loads resulting from a column removal scenario. With RC moment frames, a consideration of the redistribution of unbalanced loads in all directions leads to more economical and precise design.
4 Numerical Analysis
Numerical evaluation is performed to provide a more comprehensive insight into the collapse behaviors of the tested subassemblages. Large deformations in structural members under column removal scenarios increase the complexity of the analysis using finite element methods. Analyses of geometric and material nonlinearity, which structures experience during progressive collapse, are far beyond the typical conditions considered in the development of finite element platforms or conventional design codes. Also severe cracking and bar fractures are not easily applicable in finite element simulations. The behavior of beam–column joints is neglected in typical software applications using beam and column elements. Nonelastic behavior in conventional analyses was limited to the flexural yielding of beams and columns, whereas experimental and analytical studies revealed the effects of connections in the general behavior of structural systems, especially during earthquakes or the progressive collapse of structures as investigated by Bao et al. (2014), Lew et al. (2014) and Lowes and Altoontash (2003). In the present study, the OPENSEES opensource platform is used to analyze the subassemblages affected by column removal scenarios.
4.1 Modeling Approach
To consider rotations of the joint interfaces due to bond slip and yielding of steel bars, a zerolength section element was used to attach the beams and columns to the joint block. Barslip formulation in the configuration of the bilinear steel material is used for zero length section elements to consider bar slip in joint interfaces. The bar fracture is considered by using maximum and minimum strain in reinforcing steel materials. Shear behavior of the beam–joint interface is modeled by zero length elements with the elastic material at the joint interface of beams. A uniaxial constitutive model with linear tension softening (concrete02) was used to model the concrete material. Reinforcement was modeled as reinforcing steel material from the software library by applying maximum and minimum strains for modeling the rebar fracture. The tests performed in the present study, along with the experimental tests in literature, were used to calibrate the numerical model.
4.2 Calibration of Modeling
No similar tests for calibrating a numerical model have been presented in the wide range of literature on the experimental study of progressive collapse that has been reviewed. Because of this deficiency, the tests performed in the present study, as well as the 2D fullscale laboratory tests by Lew et al. (2011), have been used to calibrate the numerical models. Two specimens representative of Intermediate Moment Frames (IMF) and Special Moment Frames (SMF) were designed and tested under monotonic downward loading by Lew et al. (2011). The IMF model specimen N1 is used for a parametric study in Sect. 4.4. The 2D and 3D specimens are the subject of the experimental work in this study. These specimens were identical in dimensions and detailing, but the 3D specimen had an additional transverse frame. The characteristics of these two specimens were identical and reported in the specimen detail in Sect. 2.
4.3 Investigation of Numerical Model Results
Numerical results in Fig. 23b confirm that the amount of axial force in the transverse beam is significantly small during loading. The compressive axial forces of the transverse beam increase during the initial stages of the loading process, up to a vertical displacement of 32 mm. At greater displacements, the axial compressive forces start to decrease, and at a vertical displacement of 52 mm, the forces change from compression to tension. These tension forces continue to increase up to the end of the test. However, in spite of the same trends in the development of axial forces in both the main and transverse beams, the dominant mechanisms are different. The main resistance mechanism in the transverse beam is flexural action, whereas resistance in the main beams is based on different mechanisms, such as flexural, arching and catenary actions during the different steps of analysis.
Generally, the simulation results indicate that the introduced analytical model, along with the joint model and zero length elements, provide a reliable prediction of the structural behaviors of RC subassemblages under a column removal scenario. The introduced framework can be used to analyze RC frames with different geometric and boundary conditions and can also be used for 3D frames.
4.4 Parametric Study
Details of models for parametric study.
Prototype and specimen  Beam size (mm)  column size (mm)  Reinforcement ratio at the joint  Reinforcement ratio at the beam mid span  Reinforcement ratio at the beam mid height  Analysis model  

Width  Depth  Width  Depth  Top  Bottom  Top  Bottom  Mid height  
N1  700  500  700  700  0.67 % (4#8)  0.43 % (2#9)  0.33 % (2#8)  0.43 % (2#9)  –  
N2  700  500  700  700  0.67 % (4#8)  0.43 % (2#9)  0.33 % (2#8)  0.43 % (2#9)  –  
N3  700  500  700  700  0.67 % (4#8)  0.43 % (2#9)  0.33 % (2#8)  0.43 % (2#9)  –  
N4  700  500  700  700  0.67 % (4#8)  0.43 % (2#9)  0.33 % (2#8)  0.43 % (2#9)  0.33 % (2#8) (inplane beam)  
N5  700  700  700  700  0.46 % (4#8)  0.35 % (3#8)  0.35 % (3#8)  0.35 % (3#8)  –  
N6  700  600  700  700  0.55 % (4#8)  0.35 % (2#9)  0.41 % (3#8)  0.35 % (2#9)  – 
Progressive collapse strength and proportions to gravity loads of the removed column.
Model  CAA strength (kN)  CA strength (kN)  Gravity load (G_{N}) (kN)  CAA/G_{N}  CA/G_{N} 

N2  393  747  254  1.54  2.94 
N3  490  924  507  0.97  1.82 
Two optional methods for increasing progressive collapse resistance are: increasing the beam heights and adding longitudinal reinforcement to the exterior beams. In this study two models, N5 and N6, with 700 and 600 mm beam heights, respectively, were analyzed. The details of these models were identical to those of the IMF specimen (N1), which had a transverse beam; however, there were differences in the beam heights and modifying longitudinal reinforcement for satisfying minimum reinforcement percentages in the ACI code.
Based on the investigation performed by Yu and Tan (2014), half of minimum reinforcements in the N4 model, which were defined by ACI 318, were added to the midheights of the exterior beams. In Fig. 25b, the load displacement response of N2, N4, N5 and N6 were plotted. Increasing the beam height significantly increases the flexural and arch action resistance of the beams. However, the deeper beams lead to the fracture of longitudinal bars in the early stages of loading and consequently decrease the catenary action of the subassemblage. However, adding longitudinal reinforcement in the mid heights of the beam section also has little effect on flexural and arching actions. Instead, it improves the tensile resistance of the beam and thereupon increases catenary action of the substructure.
5 Conclusions

Experimental observations demonstrate that the arching and catenary actions could not develop in a transverse beam due to insufficient axial restraint. In contrast, the flexural capacity of the subassemblage is enhanced because of the additional flexural resistance of the third beam. In addition, comparison of the 3D and planar specimens demonstrated that the transverse beam helps to achieve a more symmetric and ductile behavior within the main beams.

The results also show that the enhancement of structural resistance due to the arching action, in comparison to flexural action, is about 19 %. In addition, ultimate arching action is achieved at a vertical displacement equal to half the beam depth. The change in the axial forces from compression to tension starts at a displacement equal to the beam depth at the middle joint. The enhancement due to catenary capacity in the end of the test is about 1.4 times the arching capacity. Similar conclusions have been reported in previous research, but with some differences in ratios.

A numerical study of the subassemblages indicated that the proposed macrobased model could provide a reliable foundation for the analysis of progressive collapse in RC frames. Different resistance mechanisms in RC assemblies under the column removal scenario could be simulated using the proposed framework.

Increases in beam heights significantly increase the beam action mechanisms of the substructures. However, an increase in beam heights leads to fracturing of longitudinal bars at early stages of loading and consequently decreases the catenary action of the subassemblage.

Adding longitudinal reinforcement to the midheight sections of the beam increases the catenary action of the substructure considerably without a change in model behavior at other stages.
Although an extensive study has been performed to understand the collapse behavior of RC assemblies, some aspects need further evaluation. The role of slabs in structural behavior and a consideration of the effects of an initial incident that triggers the progressive collapse are the main areas that should be addressed in the near future.
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