An experimental test was carried out on a 3/10 scale subassemblage in order to investigate the progressive collapse behavior of reinforced concrete (RC) structures. Investigation of alternative load paths and resistance mechanisms in scaled subassemblage and differences between the results of full-scale and scaled specimens are the main goals of this research. Main characteristics of specimen response including load-displacement curve, mechanism of formation and development of cracks, and failure mode of the scaled specimen had good agreement with the full-scale specimen. In order to provide a reliable numerical model for progressive collapse analysis of RC beam-column subassemblages, a macromodel was also developed. First, numerical model was validated with experimental tests in the literature. Then, experimental results in this study were compared with validated numerical results. It is shown that the proposed macromodel can provide a precise estimation of collapse behavior of RC subassemblages under the middle column removal scenario. In addition, for further evaluation, using the validated numerical model, parametric study of new subassemblages with different details, geometric and boundary conditions, was also done.
Evaluating the ability of structures to resist progressive collapse has been the focus of researchers and government agencies for years. Design codes use direct and indirect design methods for protection against progressive collapse. The indirect design method prevents progressive collapse by providing a minimum level of strength, continuity, and ductility of the structure. The direct design method explicitly considers resistance to progressive collapse during the design process. ASCE7-05 [
SLR requires that the building, or parts of the building, provide sufficient strength to resist load. In this method, the strength and ductility of critical elements can be determined during the design process (DOD, 2010) [
Previous studies by Bao et al. [
In conventional methods of design, only the flexural mechanism is considered as an ALP, and CAA and CA are beyond the scope of the design codes. CAA is a mechanism of resistance to vertical loads through the development of axial compressive force in beams. Development of this axial force requires the restriction of longitudinal deflection of beams by other members of the frame. CA is resistant to vertical loads through the development of tensile force in the horizontal members. Development of tensile force in beams requires a large deformation in the beam and the ability to create longitudinal restriction to balance this force.
This paper presents two procedures for evaluation of RC subassemblages under column removal scenario: First, it investigates the mechanisms of ALP by testing one scaled RC subassemblage and the results are compared with a full-scale model. Technical and economical constraints limit the use of full-scale specimens to study progressive collapse. This makes the possible use of scaled models of great importance. Understanding the behavior of scaled RC subassemblages under large deformations caused by column removal scenario, capability of scaled model in assessing progressive collapse, and comparison of scaled results with full-scale specimen are the objectives of this empirical research. Then, a numerical study is also utilized in order to provide a better assessment of macromodels in progressive collapse analysis of RC subassemblages. The macromodel is first evaluated using experimental results in the literature; and next, the results of the scaled specimen are compared with validated numerical model. In addition, for further evaluation of capability in numerical model, six new subassemblages with different reinforcement and geometry are analyzed.
This experimental study was performed as part of a research program to evaluate progressive collapse of structures at the Iran University of Science and Technology (IUST). The specimen included two single-bay beams, one middle joint, and two end columns with foundations. The full-scale test was performed by Lew et al. [
The details of the full-scale specimen have been provided in Lew et al. [
Plan layout of prototype building.
The selected subassemblage was a part of the exterior frame in axis 1 between axes
Details of the scaled specimen.
Table
Geometric properties of prototype frames and specimens.
Specimen | Beam |
Beam size (mm) | Column size (mm) | Reinforcement |
Reinforcement |
Reinforcement | ||||
---|---|---|---|---|---|---|---|---|---|---|
Depth | Width | Depth | Width | Top | Bottom | Top | Bottom | |||
Full-scale specimen (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) |
Scaled specimen | 1500 | 140 | 200 | 200 | 200 | 1.7% ( |
0.62% (3T8) | 0.41% (2T8) | 0.41% (2T8) | 0.41% (2T8) |
The ratios of the top beam reinforcement at joints and at the beam mid span were considered to be 0.62% (3T8) and 0.41% (2T8), respectively. The ratio of the bottom beam reinforcement for the whole span was considered to be 0.41% (2T8). All stirrups had nominal diameter of 6 mm with two 135° hooks. The stirrups were distributed with a center-to-center spacing of 130 mm and 75 mm at mid span of the beams and at the beam ends, respectively. According to the expected ductile behavior of the specimen and the dominance of CAA, flexural action, and CA instead of shear behavior, the effect of size dependence on shear behavior could be neglected, Yu and Tan [
Figure
Layout of displacement measurements.
Figure
Layout of strain gauges reinforcement.
Figure
Setup of the test specimen.
Four steel channels (UPN 80) with section dimensions of 45 × 8 mm (flanges) and 80 × 6 mm (web) were attached to the loading frame and the laboratory floor to prevent out-of-plane displacement. To reduce friction between the specimen and channels, the surfaces of the channels and specimen were lubricated at probable contact sites.
The specimen was placed under monotonic downward vertical displacement at the middle column until fracture occurred at the top reinforcement of the beam end. Concrete crushed at the top of the beam in the middle connection and flexural cracks developed throughout the depth of the beam-column interface. The test was terminated after the fracture of the beam top bar at vertical displacement of 306 mm. Figure
Fracture of bars. (a) Middle joint. (b) End joint.
Middle joint
End joint
Applying vertical displacement to the middle column caused flexural cracking along the beam. The main flexural cracks developed in the connection of beam to column. In vertical displacement of 25 mm equal to vertical load of 23 kN, inclined cracks developed at the beam-column joints in the end columns. As vertical displacement increased to 40 mm, corresponding to vertical loading of 27 kN, more flexural cracks formed in the beams and shear cracks started to develop in the bottom of the columns.
As vertical displacement of the center column increased to 110 mm with a vertical load of about 21 kN, concrete crushing occurred in the areas of the beams subjected to high compression near the middle column and the bottom of the beams at both ends. By the end of this stage, the main flexural cracks became deeper at the ends of the beams and were up to 90% of the total height of the beams.
The bottom bar of south beam adjacent to the middle column fractured after vertical displacement of 170 mm. When vertical displacement increased to 230 mm, the other bottom bar at this place fractured. With further displacement of middle column, the top bar at the south end of the beam fractured and test was halted. Full-depth cracks in the beam-column interface and in the middle of the beams were visible at this time. Figure
Crack pattern in south end of the specimen.
Figures
Comparison of crack pattern in full-scale and scaled specimens at vertical displacements of middle joint equal to 1.2 times the beam height.
Comparison of crack pattern in full-scale and scaled specimens at the end of tests.
A comparison of crack pattern for the full-scale and scaled specimens shows that the crack patterns and location of the main cracks are similar. Despite this overall similarity, the number of cracks in the columns and connection were much fewer in the scaled specimen than in the full-scale specimen. In the full-scale specimen, more cracks were distributed along the beams, but considerably fewer cracks were observed in the scaled specimen. Based on experimental studies reported in Harris and Sabins [
Fracture of the rebar at the south face of middle joint caused main cracks in this region to develop. As cracks were developed more in one side of the joint, middle connection started to rotate. The rotation of middle connection in the scaled specimen is more severe in comparison to the full-scale specimen, which can be seen in Figure
Figure
Comparison of results from scaled specimen and scaled results from prototype.
As plotted, the specimen developed three stages of alternative load path including flexural action (FA), Compression Arch Action (CAA), and catenary action (CA), despite bar fracture at early stage of CA. At a vertical displacement of 50 mm, the load reached an initial peak of 28.1 kN which corresponded to CAA capacity of subassemblage. As displacement increased, the vertical load decreased and started to increase again at a displacement of 135 mm, which corresponded to a vertical load of 20.9 kN. Applying more displacement caused the fracture of the first rebar at the middle joint at displacements of 170 mm which caused a sudden drop in the load from 22.4 kN to 12.9 kN. With increasing the displacement, the load started to increase again until the fracture of second bottom bar occurred at displacement of 230 mm and load value of 25.7 kN. Applying load was stopped with the fracture of one of the beam top bars at the south beam-column connection at displacement of 306 mm and load value of 38.2 kN, which attained a maximum for CA capacity.
Comparison of scaled and full-scale specimens shows that, despite bar fracture at scaled specimen in the early stage of CA, general behaviors are similar. In the first stage of loading curve, both curves are almost identical until they reached their CAA capacity. Approximately linear behavior of material and less and small cracks in concrete in this stage can be a justification for this similarity in this region of load-displacement curves. Beyond vertical displacement of 38 mm, the load in scaled-down curve from full-scale specimen started to decrease whereas in test specimen of this research, the load continued to increase up to displacement of 50 mm. Generally, from displacement of 38 mm to 170 mm, the graph of the scaled specimen is above the scaled-down results of the full-scale specimen. As mentioned earlier, because of relatively high strain gradient in addition to larger yielding strength of reinforcing steel in scaled specimen, the flexural strength of scaled specimen is higher than the predicted value from scaling. Also less cracks in scaled specimen lead to relatively high stiffness of the specimen against vertical load. It should be noted that, for the full-scale specimen, the failure criterion was the fracture of bottom bar in middle connection. Hence, the bottom bar participated in the CA capacity up to collapse of the specimen. In scaled specimen, because of bottom bar fraction, only top bars strength participates in CA capacity of the subassemblage beyond vertical displacement of 230 mm.
Table
Comparison of force and displacement at critical points of scaled specimen and scale-down results of prototype.
Specimen | Flexural action | Compressive arch action | Beginning of catenary action | Catenary action | ||||
---|---|---|---|---|---|---|---|---|
|
|
|
|
|
|
|
|
|
Scaled specimen | 20.7 | 18.5 | 28.1 | 50 | 21 | 135 | 35.6 | 306 |
Scaled-down results from prototype | Not reported | Not reported | 26.6 | 38.1 | 17.64 | 122 | 49.2 | 339 |
Difference% | — | — | 5.6 | 31.2 | 19 | 10.7 | 38.2 | 10.8 |
Table
Force and displacement at critical points of load-deflection curves.
Flexural action | CAA action | Second part of load increasing | 1st rebar fracture | 2nd rebar fracture | Top rebar fracture | Catenary action | ||||
---|---|---|---|---|---|---|---|---|---|---|
Calculated | Experimental | Calculated | Experimental | Calculated | Experimental | |||||
Displacement (mm) | 21.4 | 18.5 | — | 50 | 135 | 170 | 230 | 306 | 300 | 306 |
Force (KN) | 17.7 | 20.7 | — | 28.1 | 21 | 22.4 | 25.7 | 35.6 | 39 | 35.6 |
Fracture of the bottom rebars in beam eliminated flexural resistance in the middle joint. The tensile force acted as the only resisting mechanism in the specimen. The onset of CA occurred simultaneously with fracture of the second beam bottom reinforcement at a vertical displacement of 230 mm, which corresponds to 1.53 times the beam height. Maximum CA capacity was achieved only through the top beam reinforcements. CA enhanced structural resistance by about 80% compared to flexural action.
Table
Force equilibrium diagram in CA stage [
In the technical literature
The deflection profile of the specimen at the different steps of loading is shown in Figure
Deflection profiles of specimen corresponding to indicated loads.
Figure
Strain in bars at beam mid span versus vertical displacement of middle joint.
Experimental and analytical studies by Bao et al. [
In this paper, Opensees software [
For nonlinear behavior of elements, a displacement-based fiber element that exists in the software library was used. Analytical and experimental studies have shown that the shear behavior of frame elements in progressive collapse is not the dominant overall behavior of the structures. Hence, in spite of some shear cracks in the experiment of this research, it was ignored and displacement-based fiber elements were selected for modeling of RC beam-column subassemblages.
The joint element introduced by Altoontash [
Configuration of the joint element [
Investigation of several experimental studies shows that, because of noncyclic nature of loading in a progressive collapse, shear panels also remain intact and bar fractures at the middle joints are the main failure mode of the structures. In addition to some specimens bar-slip affected the responses of the substructures. In this research, to calculate the material properties for the rotational springs of the joint model, the behavior of shear panel and joints interface are considered. The membrane 2000 program based on MCFT theory was used to calculate properties of shear panel springs [
Spring properties of joint element for the scaled specimen.
Shear panel spring
Interface spring
The properties of the spring in the middle joint are attained by putting bar-slip formulation in the configuration of bilinear steel material for moment curvature analysis of beam and column sections at joints. The results of the analysis in sections are used to define trilinear uniaxial materials in order to represent the member end rotation spring properties.
Figure
Numerical model of subassemblage.
Full-scale laboratory tests by Lew et al. [
Numerical and experimental load-deflection results for IMF and SMF specimens.
By validation of numerical model, the load-displacement curves from experimental test and the numerical model for scaled specimen are shown in Figure
Numerical and experimental load-deflection results of the scaled specimen.
Figure
Comparison of beam axial force in numerical model with and without fixed ends.
Horizontal displacements of end columns at the beam mid heights are plotted in Figure
Horizontal displacement of end columns versus vertical displacement of center column.
Stress results at mid span for top and bottom bars are shown in Figures
Strain in top reinforcing bar at mid span of beams.
Strain in bottom reinforcing bar at mid span of beams.
To evaluate the effect of reinforcement percentage and geometry on the load-displacement curve, a parametric study was also conducted in this study. Six new models with similar characteristics of IMF specimen (full-scale) but with different reinforcement in beam or geometry were analyzed. The objective of this study is to show the capability of numerical model in order to attain response of structure with different details of reinforcement and geometry.
Details of reinforcement in beams are presented in Table
Details of beams reinforcement for specimens M1 to M5.
Prototype and specimen | Beam net span (mm) | Beam size (mm) | Column size (mm) | Reinforcement |
Reinforcement |
Reinforcement |
Reinforcement |
Changes in | ||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Depth | Width | Depth | Width | Top | Bottom | Top | Bottom | Mid height | ||||
Prototype M1 | 5385 | 700 | 500 | 700 | 700 | 1.7% (12#9) | 0.67% (4#8) | 0.43% (2#9) | 0.33% (2#8) | 0.43% (2#9) | — | — |
M2 | 5385 | 700 | 500 | 700 | 700 | 1.7% (12#9) | 1.01% (6#8) | 0.64% (3#9) | 0.51% (3#8) | 0.64% (3#9) | — | 50% top & bot |
M3 | 5385 | 700 | 500 | 700 | 700 | 1.7% (12#9) | 0.67% (4#8) | 0.64% (3#9) | 0.32% (2#8) | 0.64% (3#9) | — | 50% bot |
M4 | 5385 | 700 | 500 | 700 | 700 | 1.7% (12#9) | 1.01% (6#8) | 0.43% (2#9) | 0.51% (3#8) | 0.43% (2#9) | — | 50% top |
M5 | 5385 | 700 | 500 | 700 | 700 | 1.7% (12#9) | 0.67% (4#8) | 0.43% (2#9) | 0.33% (2#8) | 0.43% (2#9) | 0.33% (2#8) | 50% top at mid height |
Effect of reinforcement on load-displacement curve.
As represented in Figure
To investigate the effect of beam geometry on the progressive collapse behavior, two models with different beam height were also analyzed. The details of models are identical with IMF specimen (M1 model), but with 600 and 700 mm beam height for M6 and M7, respectively. For each model, minimum reinforcement of flexural members as specified in ACI 318 was considered. The load-displacement curves of M6 and M7 are plotted in Figure
Effect of beam geometry on load-displacement curve with same reinforcement.
In general, the results showed that the proposed numerical model with connection, which has five spring joint elements, predicted the behavior of RC subassemblages under the column removal scenario with good accuracy. This macromodel can be used to analyze frames with different geometric and boundary conditions and 3D frames because of the proposed characteristics of the joint element.
A scaled RC beam-column subassemblage was quasi-statically tested under removal of the middle column scenario to investigate the structural behavior of the subassemblage and development of ALP mechanisms during progressive collapse. In addition, a macromodel with five spring joint elements was used to evaluate the different subassemblages under the column removal scenario. The results of this study are listed as follows: Similar to the full-scale specimen, scaled specimen accurately predicted structural behavior in progressive collapse. Despite similarity in general structural behavior, the number of cracks in full-scale specimen was more than scaled specimen. Moreover, cracks were distributed along the full-scale specimen which results in more ductile behavior in comparison with scaled specimen. Comparison of load-displacement results of middle joint for scaled and full-scale specimens showed good agreements, and the capability of scaled specimen in order to estimate the behavior of subassemblage under progressive collapse scenario was evaluated. The most significant characteristics of scaled specimen failure were spalling and crushing of the concrete at the top of the beam near the middle connection, development of flexural cracks at the beam-column joint interfaces, and fracture of the reinforcement rebar at the openings of the main flexural cracks. The mechanisms for the ALPs of flexural action, CAA, and CA developed in the subassemblage. Compared to flexural action, CAA increased structural resistance by up to 30%. Displacement of the compressive arch was about 40% of the beam height. In vertical displacement of about 1.3 times the beam height, CA developed and produced a maximum capacity in displacement of about twice the height of the beam. Because of the asymmetry in the profile of deformation in the subassemblage and the concentration of flexural cracking on one side of the middle joint, CA increased by just 20% of the structural capacity compared to flexural action. The flexural behavior of the beam and column elements, shear behavior of the joint panel, and beam-to-column connection interface behavior, including rebar bond-slip, were considered during the numerical modeling. The results showed that the numerical model can effectively simulate the structural behavior of the subassemblages under the column removal scenario. This numerical model can also be used to examine structures with different geometries and boundary conditions.
The authors declare that there is no conflict of interests regarding the publication of this paper.