- Open Access

# Progressive Collapse Resistance of RC Frames under a Side Column Removal Scenario: The Mechanism Explained

- Jian Hou
^{1}and - Li Song
^{2}Email author

**10**:134

https://doi.org/10.1007/s40069-016-0134-y

© The Author(s) 2016

**Received:**7 December 2015**Accepted:**25 February 2016**Published:**11 March 2016

## Abstract

Progressive collapse resistance of RC buildings can be analyzed by considering column loss scenarios. Using finite element analysis and a static test, the progressive collapse process of a RC frame under monotonic vertical displacement of a side column was investigated, simulating a column removal scenario. A single-story 1/3 scale RC frame that comprises two spans and two bays was tested and computed, and downward displacement of a side column was placed until failure. Our study offers insight into the failure modes and progressive collapse behavior of a RC frame. It has been noted that the damage of structural members (beams and slabs) occurs only in the bay where the removal side column is located. Greater catenary action and tensile membrane action are mobilized in the frame beams and slabs, respectively, at large deformations, but they mainly happen in the direction where the frame beams and slabs are laterally restrained. Based on the experimental and computational results, the mechanism of progressive collapse resistance of RC frames at different stages was discussed further. With large deformations, a simplified calculation method for catenary action and tensile membrane action is proposed.

## Keywords

- progressive collapse
- RC frame structures
- catenary action
- tensile membrane action

## 1 Introduction

The situation in which there is local failure of a primary structural component that leads to the collapse of adjoining members is called progressive collapse, and this, in turn, leads to total collapse or the collapse of a disproportionately large part of the affected structure (ASCE 2010). Various buildings throughout the world have gone through partial or total progressive collapse throughout the past several decades. These collapses have resulted from gas explosion, terror attack, and other factors. These progressive collapse accidents resulted in significant property loss and casualties. The engineering community has therefore paid greater attention to the situations of buildings subjected to damage from abnormal events. New codes and standards for development have been considered by public regulatory agencies. Implicit resistance to progressive collapse is achieved by maintaining the integrity and ductility of the structure and explicit resistance is achieved by providing alternate load paths so that local damage is absorbed by the structure to avert major collapse (GSA 2013; DoD 2009).

Design codes and guidelines currently in place are not considered to completely satisfy the requirements for progressive collapse design. Also, to obtain a better understanding of the mechanisms of progressive collapse resistance of structures, further research is necessary. Seeking the establishment of rational methods to assess structural robustness under extreme accidental events is the ultimate goal. Many efforts have been made recently to carry out research on the behavior of building structures with the loss of a column. Much attention has been given to the behavior of beams that bridge over removed column areas, which are under amplified gravity loads in beam-column substructures or planar frames (Sadek et al. 2011; Mehrdad et al. 2011; Choi and Kim 2011; Su et al. 2009; Yi et al. 2008; Hou and Yang 2014; Kim and Choi 2015; Kang et al. 2015). It was concluded that a generous reserve capacity of the catenary action in beams that carry the gravity loads in a tension mode is necessary for mitigating progressive collapse. For different seismic fortification intensities, it was noted that the load versus displacement curves exhibited similar characteristics, and the more stringent seismic design and detailing increased the failure displacement and the ultimate load. There have been reports of studies that have analyzed progressive collapse behavior of RC frames or beam-slab substructures by experiments or numerical analyses (Mehrdad et al. 2007; Pham and Tan 2013a, b; Pachenari and Keramati 2014; Qian et al. 2015). It was found that tensile membrane actions in slabs that inevitably develop in large deformation stage play a key role in its collapse resistance. In order to reduce the computational costs of the conventional finite element methods, some researchers (Brunesi and Nascimbene 2014) have presented an open access procedure using a fiber-based model for large scale nonlinear transient dynamic analysis of three-dimensional frames. Málaga-Chuquitaype et al. (2016) have examined the contribution of secondary frames to the mitigation of collapse in steel buildings, which provides the reference for RC buildings. Based on Monte Carlo simulation, Brunesi et al. (2015) have developed a framework for progressive collapse fragility analysis of RC frames, in which the random properties of materials, geometrical parameters et al. can be considered. However, experimental and computational study on the progressive collapse of space RC frames is currently inadequate, and no reasonable or simplified mechanism and calculation method for the progressive collapse resistance of space RC frame structures has yet been developed.

Here we report the results from a computational and experimental study that investigated the static responses of a RC frame that had side column loss. We also evaluated the effect of both tensile membrane action in the frame slabs and catenary action in the frame beams to assess the progressive collapse resistance of structures. A one-third scale structure was designed, built and tested. To get more detailed structural information during the progressive collapse, a non-linear numerical analysis was conducted using the LS-DYNA finite element software (Hallquist 2007). Based on experimental and computational results, the mechanism of progressive collapse resistance of RC frames at different stages is discussed further. With large deformations, a simplified calculation method for catenary action and tensile membrane action are proposed.

## 2 Experimental Program and Finite Element Modeling

### 2.1 Experimental Program

Details of prototype frame.

Items | Floor height | Bay span | Depth span | Beam size | Column size | |||
---|---|---|---|---|---|---|---|---|

Depth | Width | Depth | Width | |||||

3300 mm | 3900 mm | 5400 mm | Bay direction | Depth direction | ||||

350 mm | 450 mm | 200 mm | 400 mm | 400 mm | ||||

Items | Floor loads | Seismic fortification intensity | Materials | |||||

Live (other/roof) | Constant (other/roof) | 7 | Concrete | Longitudinal steel bars | Stirrups | |||

2.5/0.5 kN/m | 6.0/7.5 kN/m | C30 | HRB335 | HPB300 |

Yi et al. (2008) constructed a middle column of a planar frame by stacking two mechanical jacks and a load cell, and investigated the structural response before and after the middle column was removed. In the initial stage of the experiment, we applied a constant vertical load to the top of the removed column area and the model load was achieved by the unloading of the mechanical jacks. In our experiment, no constant load was placed on the top of the area where the column was removed at the beginning of the experiment. The step-by-step loading process was initiated by a MTS servo actuator on the top of the removed side column. In fact, the results of the two kinds of loading mode are almost equivalent, but the latter is less complicated. Therefore, the second loading mode was adopted in the literature (Sadek et al. 2011) and our experiment. Actually, a static experimental progressive collapse evaluation is presented in the paper. However, a typical building structure exhibits a highly nonlinear dynamic response under a sudden column loss scenario. Based on the energy conservation principle, Izzuddin et al. (2008) proposed a simplified method by which the simplified dynamic response and progressive collapse resistance can be derived from the static progressive collapse response.

### 2.2 Finite Element Modeling

Properties of steel bars and concrete.

Material | Diameter measurement, mm | Young’s modulus, MPa | Yield strength, MPa | Ultimate strength, MPa | Rupture strain, | ||
---|---|---|---|---|---|---|---|

Necking zone | Outside necking zone | ||||||

Steel bars |
| 8.0 | 2.0 × 10 | 347.0 | 488.6 | 25.3 % | 16.1 % |

| 6.4 | 2.0 × 10 | 283.2 | 443.8 | 31.0 % | 20.6 % | |

| 3.5 | / | 331.0 | 387.6 | / | / | |

Young’s modulus, MPa | Compression strength of concrete prism, MPa | ||||||

Concrete | 3.05 × 10 | 36.8 |

Defining a one-dimensional contact interface (Contact_1d in LS-DYNA) was used to model bond-slip behavior between the solid elements that represented concrete as well as the beam elements that represented reinforcing bars. Two sets of nodes were required to define the contact, with the concrete nodes specified as master nodes and the reinforcement nodes specified as slave nodes. The parameters of the bond-slip model were selected with reference (Shi and Li 2009). Bond slip was not considered for column longitudinal and transverse reinforcement. The beam elements that represented the reinforcing bars were constrained to be within the solid elements with the CONSTRAINED_LAGRANCE_IN_SOLID card.

## 3 Analysis of Progressive Collapse Process

### 3.1 Elastic Stage

As show in Fig. 5, Section OA can be considered as the elastic stage with cracking of frame beams observed at State A, and the displacement of the removed column was less than 5 mm in this stage. It can be seen from Fig. 7 that the bottom reinforcement was in tension and the stress was almost linearly increased with increases in the vertical displacement of the removed column in the longitudinal and transverse beams at this stage. However, the values of the stress were lower than the corresponding yield values. The top reinforcement was in compression and the stress was very small in the longitudinal and transverse beams at this stage. As shown in Fig. 8, the stress of the slab bottom reinforcement was very small at this stage. The above analysis indicated that the frame beams and slabs were almost in the elastic state.

### 3.2 Elastoplastic Stage

In Fig. 5, Section AB is the elastoplastic stage, and the displacement of the removed column was about 28 mm at State B. In this stage, the vertical load no longer increased linearly with increasing vertical displacement of the removed column. As shown in Fig. 7, the bottom reinforcement had entered the yield state in this stage. From the stress of the slab bottom reinforcement, it was found that the stress of a part of the reinforcement near the removed column obviously increased with increases in the vertical displacement of the removed column, but the stress of the others far from the removed column was still very small at this stage. Based on the experimental observation, it was found that the concrete of frame slabs had obviously cracked, and plastic hinges in the frame beam ends near the removed column had formed in this stage.

### 3.3 Plastic Stage

In Fig. 5, Section BC is the plastic stage, and the displacement of the removed column was about 68 mm at State C. displacement of the column that was removed was approximately 68 mm in State C. The increasing rate of the vertical load in this stage with increasing vertical displacement of the removed column decreased significantly, and the deformations were dominated by plastic rotations of the frame beams. From the longitudinal reinforcement stress at the frame beam ends near the removed column, it was observed that the top reinforcement changed to tension from compression in the longitudinal beams in this stage. However, due to the lack of lateral support or constraint, the top reinforcement in the transverse beam was still under the compression state at this stage. As shown in Fig. 8, the stress of a part of the reinforcement near the removed column significantly increased with increases in the vertical displacement of the removed column, and the maximum of the stress had exceeded 200 MPa. However, the greater the distance from the removed column, the smaller the stress became.

### 3.4 Composite Stage of Catenary and Tensile Membrane

## 4 Progressive Collapse Resistance Mechanism

### 4.1 Catenary Mechanism of Beams

Figure 6 shows the failure pattern of the frame model. Due to the entire failure of the transverse frame beam and the transverse direction of the frame slabs in the failure zone, the effect of the transverse beam and the transverse direction of the slabs can be ignored, while calculating the progressive collapse resistance of the whole structure at a collapse limit state.

*A*

_{th}is the area of steel bars through whole span, and \( f_{y} \) is the yield stress of the steel bars in frame beams. The model was originally proposed by Li et al. (2011), and the reliability was verified by Hou and Yang (2014).

### 4.2 Tensile Membrane of Slabs

### 4.3 Validation

Based on analysis and experimental results, it is noted that the limit vertical displacement of the frame structure is controlled by frame beams on the A-axis. Based on the literature (Hou and Yang 2014), the calculated value of the limit vertical displacement of the removed column (\( v_{u} \)) is 356.7 mm. Substituting the value of \( v_{u} \), the geometric dimensions and the properties of steel bars of the frame beams on the A-axis into Eq. (1), the progressive collapse resistance of frame beams (\( P_{\text{ub}} \)) can be calculated 41.5 kN.

Based on the deformation compatibility condition of the frame beams and slabs, the limit vertical displacement of Point K (\( v \)) is equal to the limit vertical displacement of the removed column (\( v_{u} \)). Therefore, the value of \( v \) should be 356.7 mm. Substituting the value of \( v \), the geometric dimensions and the properties of steel bars of the frame slabs into Eqs. (2), (3) and (4), the progressive collapse resistance of frame slabs is 14.9 kN.

By using the principle of superposition, the progressive collapse resistance of the whole frame structure is 56.4 kN. The calculated value is 7.1 % smaller than the experimental result. Portions of the steel bars have entered the hardening stage in the collapse limit state, but steel hardening is not considered in the model. Thus, the progressive collapse resistance obtained from the model is somewhat conservative. Moreover, it can be found that the progressive collapse resistance of frame slabs is 26.4 % of the progressive collapse resistance of the whole frame structure.

## 5 Conclusion

A static test and finite element analysis to assess the progressive collapse resistance of an RC frame mechanism after a side column loss are described. The progressive collapse process of the structure can be sectioned into four stages, based on the experimental and computational results, which are the elastic stage, the elastoplastic stage, the plastic stage and the composite stage of catenary action and tensile membrane action.

The progressive collapse of the structure occurs only in the bay where the removal side column is located. Also, due to the lack of lateral support or constraint, the transverse frame beam and the transverse direction of the frame slabs in the collapse area almost entirely failed in the collapse limit state. Greater catenary action and tensile membrane action are respectively mobilized in the longitudinal frame beams and the longitudinal direction of the frame slabs.

Based on the computational and experimental results, a simplified model of the progressive collapse resistance of a RC frame after a side column is removed was proposed in which frame beams and slabs are taken as the catenary mechanism and tensile membrane mechanism, respectively. In the catenary mechanism, the axes of the longitudinal frame beams can be taken as straight. For the tensile membrane mechanism, the internal area of the frame slabs surrounded by the negative moment yield lines can be viewed as an analysis object, and its two areas of progressive collapse resistance were still in two different planes at the collapse limit state.

## Declarations

### Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 51208421 and 51378506).

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

## References

- American Society of Civil Engineers (ASCE). (2010).
*Minimum design loads for buildings and other structures. SEI/ASCE 7-10*. Reston, VA: American Society of Civil Engineers.Google Scholar - Brunesi, E., & Nascimbene, R. (2014). Extreme response of reinforced concrete buildings through fiber force-based finite element analysis.
*Engineering Structures,**69*, 206–215.View ArticleGoogle Scholar - Brunesi, E., Nascimbene, R., Parisi, F., & Augenti, N. (2015). Progressive collapse fragility of reinforced concrete framed structures through incremental dynamic analysis.
*Engineering Structures,**104*, 65–79.View ArticleGoogle Scholar - Choi, H., & Kim, J. (2011). Progressive collapse-resisting capacity of reinforced concrete beam-column subassemblage.
*Magazine of Concrete Research,**63*(4), 297–310.View ArticleGoogle Scholar - Department of Defense (DoD). (2009).
*Unified facilities criteria, design of buildings to resist progressive collapse*. Washington DC: Department of Defense.Google Scholar - GB50010-2010. (2010).
*Code for design of concrete structures*. Beijing, China: National Standard of the People’s Republic of China.Google Scholar - GB50011-2010. (2010).
*Code for seismic design of buildings*. Beijing, China: National Standard of the People’s Republic of China.Google Scholar - General Services Administration (GSA). (2013).
*Alternate path analysis and design guidelines for progressive collapse resistance*. Washington DC: General Services Administration.Google Scholar - Hallquist, J. (2007).
*LS-DYNA keyword user’s manual*. Livermore: Livermore Software Technology Corporation. Version 971.Google Scholar - Hou, J., & Yang, Z. (2014). Simplified models of progressive collapse response and progressive collapse-resisting capacity curve of RC beam-column sub-structures.
*Journal of Performance of Constructed Facilities,**28*, 04014008. doi:10.1061/(ASCE)CF.1943-5509.0000492.View ArticleGoogle Scholar - Izzuddin, B. A., Vlassis, A. G., Elghazouli, A. Y., & Nethercot, D. A. (2008). Progressive collapse of multi-storey buildings due to sudden column loss—part I: Simplified assessment framework.
*Engineering Structures,**30*, 1308–1318.View ArticleGoogle Scholar - Kang, S. B., Tan, K. H., & Yang, E. H. (2015). Progressive collapse resistance of precast beam-column sub-assemblages with engineered cementitious composites.
*Engineering Structures,**98*(1), 186–200.View ArticleGoogle Scholar - Kim, J., & Choi, H. (2015). Monotonic loading tests of RC beam-column subassemblage strengthened to prevent progressive collapse.
*International Journal of Concrete Structures and Materials,**9*(4), 401–413.View ArticleGoogle Scholar - Li, Y., Lu, X. Z., Guan, H., & Ye, L. P. (2011). An improved tie force method for progressive collapse resistance design of reinforced concrete frame structures.
*Engineering Structures,**33*, 2931–2942.View ArticleGoogle Scholar - Málaga-Chuquitaype, C., Elghazouli, A. Y., & Enache, R. (2016). Contribution of secondary frames to the mitigation of collapse in steel buildings subjected to extreme loads.
*Structure and Infrastructure Engineering,**12*(1), 45–60.View ArticleGoogle Scholar - Mehrdad, S., Andre, W., & Ali, K. (2011). Bar fracture modeling in progressive collapse analysis of reinforced concrete structures.
*Engineering Structures,**33*, 401–409.View ArticleGoogle Scholar - Mehrdad, S., Marlon, B., & Serkan, S. (2007). Experimental and analytical progressive collapse evaluation of actual reinforced concrete structure.
*ACI Structural Journal,**104*(6), 731–739.Google Scholar - Pachenari, A., & Keramati, A. (2014). Progressive collapsed zone extent estimation in two-way slab floors by yield line analysis.
*Magazine of Concrete Research,**66*(13), 685–696.View ArticleGoogle Scholar - Pham, X. D., & Tan, K. H. (2013a). Experimental study of beam-slab substructures subjected to a penultimate-internal column loss.
*Engineering Structures,**55*, 2–15.View ArticleGoogle Scholar - Pham, X. D., & Tan, K. H. (2013b). Membrane actions of RC slabs in mitigating progressive collapse of building structures.
*Engineering Structures,**55*, 107–115.View ArticleGoogle Scholar - Qian, K., Li, B., & Ma, J. X. (2015). Load carrying mechanism to resist progressive collapse of RC buildings.
*ASCE Journal of Structural Engineering,**141*(2), 04014107.View ArticleGoogle Scholar - Sadek, F., Main, J. A., Lew, H. S., & Bao, Y. H. (2011). Testing and analysis of steel and concrete beam-column assemblies under a column removal scenario.
*ASCE Journal of Structural Engineering,**137*(9), 881–892.View ArticleGoogle Scholar - Shi, Y. C., & Li, Z. X. (2009). Bond slip modelling and its effect on numerical analysis of blast-induced responses of RC columns.
*Structural Engineering and Mechanics,**32*(2), 251–267.View ArticleGoogle Scholar - Su, Y. P., Tian, Y., & Song, X. S. (2009). Progressive collapse resistance of axially-restrained frame beams.
*ACI Structural Journal,**106*(5), 600–607.Google Scholar - Yi, W. J., He, Q. F., Xiao, Y., & Kunnath, S. K. (2008). Experimental study on progressive collapse-resistant behavior of reinforced concrete frame structures.
*ACI Structural Journal,**105*(4), 433–439.Google Scholar