This paper presents the numerical assessment of the progressive collapse resistance of a

seismic-resistant steel building with post-tensioned beam-column connections. The

numerical simulations are carried out in 3D under a loss of column scenario. The 3D model

considers the effect of the composite slab, where composite beams and their shear

connectors are modeled with a combination of shell, beam and nonlinear connector

elements. All the beam-column and beam-to-beam connections are modeled using

nonlinear connector elements with appropriate failure criteria. Moreover, the steel frame

for which a column is removed is modelled in full detail with the aid of 3D solid elements

to accurately capture its local and global nonlinear behavior. Nonlinear static analyses are

carried out to identify the failure modes of the building under a sudden loss of column

scenario and investigate the effect of the floor slab on the overall progressive collapse

resistance

Dimopoulos, Christoforos

Freddi, Fabio

Karavasilis, Theodore

Vasdravellis, George

English

Dimopoulos, C

Freddi, F

Karavasilis, TL

Vasdravellis, G

UCL Discovery

     3D NUMERICAL ASSESSMENT OF THE PROGRESSIVE COLLAPSE RESISTANCE OF A SEISMIC-RESISTANT STEEL BUILDING WITH POST-TENSIONED BEAM-COLUMN CONNECTIONS  Christoforos A. Dimopoulos Marie Skłodowska Curie Research Fellow School of Engineering, University of Warwick Coventry CV4 7AL, UK E-mail: dchristoforos@hotmail.com  Fabio Freddi Marie Skłodowska Curie Research Fellow School of Engineering, University of Warwick Coventry CV4 7AL, UK E-mail: freddi.fabio82@gmail.com  Theodore L. Karavasilis Professor of Structures and Structural Mechanics Faculty of Engineering and the Environment, University of Southampton Southampton SO17 1BJ, UK E-mail: T.Karavasilis@soton.ac.uk  George Vasdravellis Assistant Professor of Structural Engineering Institute for Infrastructure and Environment, Heriot-Watt University Edinburgh EH14 4AS, UK E-mail: G.Vasdravellis@hw.ac.uk     1. ABSTRACT  This paper presents the numerical assessment of the progressive collapse resistance of a seismic-resistant steel building with post-tensioned beam-column connections. The numerical simulations are carried out in 3D under a loss of column scenario. The 3D model considers the effect of the composite slab, where composite beams and their shear connectors are modeled with a combination of shell, beam and nonlinear connector elements. All the beam-column and beam-to-beam connections are modeled using nonlinear connector elements with appropriate failure criteria. Moreover, the steel frame for which a column is removed is modelled in full detail with the aid of 3D solid elements to accurately capture its local and global nonlinear behavior. Nonlinear static analyses are carried out to identify the failure modes of the building under a sudden loss of column scenario and investigate the effect of the floor slab on the overall progressive collapse resistance.    2. INTRODUCTION  Conventional seismic-resistant structures, such as steel moment-resisting frames (MRFs), are designed to experience significant inelastic deformations under strong earthquakes [1]. Inelastic deformations result in damage of structural members and residual interstory drifts, which lead to high repair costs and disruption of the building use or occupation. The aforementioned socio-economic risks highlight the need for widespread implementation of minimal-damage structures, which can reduce both repair costs and downtime. Amongst others, steel frames equipped with self-centering beam–column connections with post-tensioned high strength bars ([2], [3]) demonstrated their superior seismic performance, i.e. in minimizing the damage in the main structural components and in providing self-centering capability even under strong earthquakes. However, specialization of the structure in order to improve the seismic performances should not affect their capability to resists other types of hazard and multi-hazard considerations are required ([4]).  Amongst others, man-made hazards deriving from events such as fire, explosions or impact gained the attention of many researchers in the last decades because of the possibility of progressive collapse [5]. Progressive collapse of a structure occurs when the failure of a structural component, leads to the collapse of the surrounding members, promoting additional or even global collapse.  Despite the relatively large body of research on the seismic behavior of self-centering moment resisting frames (SC-MRFs), their robustness under a column loss scenario is not thoroughly studied. SC-MRFs are placed at the perimeter of a building as lateral force resisting system and, hence, they are prone to accidental events that could produce the loss of one or more columns. Previous research on robustness of steel concrete composite frames focused on their 2D behavior or on the isolated behavior of their slab by itself. The present paper focuses on the robustness of SC-MRFs under a column removal scenario accounting also for the contribution of the 3D membrane effects of the slab based on 3D finite element models developed in ABAQUS.    3. CASE STUDYING BUILDING  A 5-story SC-MRF using post-tensioned (PT) connections with web hourglass shape steel pins (WHPs) [3] is used as the prototype building. The plan view and elevation are shown in Fig. 1. The frame uses perimeter SC-MRFs to resist seismic loads, while the interior frames are designed for gravity loads only. Two high strength steel bars located at the mid depth of the beam, one at each side of the beam web, pass through holes drilled on the column flanges. The bars are post-tensioned and anchored to the exterior columns. WHPs are inserted in aligned holes on the beam web and on supporting plates welded to the column flanges. Energy is dissipated through inelastic bending of the WHPs while the self-centering capabilities are ensured by the gap opening mechanism and the presence of the PT bars. More details on the case study building are reported in [3] and [6].   4. VALIDATION OF THE NUMERICAL MODELS   Numerical models are built in ABAQUS [8] to simulate the behavior of the basic structural components (Fig. 2) i.e. fin plate connections, steel-concrete composite beams, and the SC-MRFs and are validate against experimental results.  4.1 Validation of the steel-concrete composite beam  For the validation of the numerical model of the composite beam, an experimental investigation by Vasdravellis et al. ([7], [9]) of simply supported beams under a single point load is considered. Full geometrical and material properties are given in that reference. The steel material of the beam is simulated by using the elasto-plastic stress-strain law with hardening. An elastic perfectly-plastic model was used to simulate the material response of the reinforcement. The concrete is modeled by using the concrete damage plasticity model in ABAQUS. The concrete stress-strain curve in compression follows a modified Hognestad stress-strain relationship [10] while the modulus of elasticity of the  concrete Ec is taken according to EC2 [11]. For the validation of the numerical model, the experimentally determined tensile strength is considered. For the progressive collapse investigation, the mean tensile strength fctm is taken according to EC2 [11]. An idealized behavior in tension is assumed for the concrete with a linear softening and a residual tension strength of 0.1fctm starting at strain equal to 0.05.   ABDC1 2 3 4 5 6SC-MRFSC-MRFBracedFrameBracedFrameG10 G11 G12G7 G8 G9G4 G5 G6G1 G2 G3 G13 G14 G15IPE2208.0 m5.0 mIPE4004m4@ 3.2mSC-MRFFig. 1: a) Plan view and b) elevation view of the prototype building  Composite Beam Fin Plate Connection  Centerline of beamMiddle surface ofconcrete slabConnectors representingshear studs    Fig. 2: (a) Composite beam & fin-plate connection of a beam; and mechanical idealization of (b) composite beam and (c) fin plate connections  Connector elements (of Cartesian and Align type) connecting the middle surface of the concrete slab to the middle surface of the beam elements are used to model the shear studs. An elastic-perfectly plastic behavior is assumed for the shear connectors. Experimental strengths are used for the validation of the numerical models of the composite beams. Nominal strengths according to EC4 [15] are used in the progressive collapse simulations. Maximum slips obtained from push-out tests are used in the numerical analyses to consider fracture of the studs. Fig. 3 shows a comparison between numerical and experimental results for the case of sagging and hogging moment, respectively. The simplified numerical model can capture the sagging and hogging behavior of the composite beam. The larger force capacities exhibited in the hogging moment can be contributed to the idealized behavior that was adopted for the concrete in tension. Spring elementRigid Element GAP Element 4.2 Validation of the fin-plate connections  The experimental results from Thompson [12], described in detail in [13], have been used to validate the simplified numerical model for the fin plate connection. The fin plate connection is modelled using the component method where at each bolt level a spring is considered having stiffness and strength that described best the combined behaviour of the fin plate, the beam web and the bolt. The stiffness and strength of these springs are estimated according to EC3-1.6 [14] while the ultimate deformations according to [15]. Gap-like springs are attached at the beam flange levels to account to contact phenomenon at large displacements. Fig. 4 shows the numerical results of a four-bolt fin plate connection accompanied with the corresponding experimental results. A good agreement can be observed for the two cases.  0 0.05 0.1 0.15 0.2050100150200250Displacement (m)Force (kN)  Experiment (Sagging)ABAQUS (Sagging)Experiments (Hogging)ABAQUS (Hogging) Fig. 3: Comparison of numerical and experimental results for the composite beam  0 0.1 0.2 0.3 0.4020406080100Displacement (m)Force (kN)  Experiment 1Experiment 2Experiment 3ABAQUS Fig. 4: Comparison of numerical and experimental results for the fin-plate connection   4.3 Validation of the PT connection  The model of the PT connection with WHPs used in the SC-MRF of the case study  building, has been validate elsewhere [16] and found capable in capturing the cyclic behaviour and the local and global failure modes up to excessive imposed deformations.  5. FINITE ELEMENT MODEL OF THE BUILDING  The ABAQUS finite element model of the first floor of the prototype building provides insights in the progressive collapse resistance of SC-MRFs (Fig. 5). Only one of the two SC-MRFs, which exhibits column failure, is modelled using eight-node linear brick element (C3D8R) while the PT bars are modelled with truss elements. All the rest of the structural members (beams, columns, braces) are modelled with beam-column elements (B31). The concrete slab is modelled with shell elements (S4R). Fin plates and shear studs are modelled using connector elements as explained in the previous sections. Appropriate contact interactions are considered for the SC-MRF and the contact of the slab to the main beams. A 120 mm-thick slab reinforced with a N12/150 mm top and bottom rebar mesh is considered. A ‘bolt load’ is used to model the initial post-tensioning force in the PT bars. A nonlinear static analysis is first performed to apply the initial force in the PT bars. The upper ends of columns are modelled as pinned representing inflection point in steel column [17]. Both gravity columns with pinned supports and SC-MRF columns with fixed support extend up the half-height of the second floor. In a subsequent nonlinear static analysis, the support of the column that is failed is removed and a vertical downwards displacement is applied to the top of the column. The standard ‘Full Newton’ solution technique is adopted together with an automatic incrementation scheme for the application of the loading.  Fig. 6 shows the deformed shape of the building when the failed column reaches a displacement equal to 1.60 m. Fig. 7 shows the force versus vertical displacement at the removed column resulting from the nonlinear static analysis for three structural configurations: (i) the SC-MRF is modelled on its own; (ii) the first floor is modelled but no slab is included; and (iii) the first floor is modelled including the concrete slab and its composite action with the steel sections. The horizontal axis represents the vertical displacement of the removed column and the vertical axis the associated reaction load. It can be seen that the effect of the beams and the fin plate connections is negligible. The strength of the second structural configuration is the same as the first configuration. The effect of the composite action of the concrete action and the secondary beams, however, significant since its contribution increases the overall resistance of the system by 30%.    Fig. 5: Finite element model of the building   Fig. 6: Deformation state of the building after the column removal (1.60m displacement)  0 0.5 1 1.5 20500100015002000Pushdown Displacement (m)Force (kN)  Only SC-MRFFirst floor (No Slab)First floor (Slab) Fig. 7: (a) Load-displacement curves from nonlinear static analyses  6. CONCLUSIONS  This paper studied the progressive collapse resistance of a steel building with SC-MRFs. Simplified numerical models were built and validated against experimental results for the composite slab and the fin plate connection. Static nonlinear analyses were performed to study the robustness of the building against a sudden column removal of the SC-MRF. It was found that the contribution of the steel beams alone is negligible, however the effect of the composite slab is significant and could overcome the 30% of the overall progressive collapse resistance of the building.   7. REFERENCES  [1] Eurocode 8, “Design of structures for earthquake resistance. Part 1: General rules, seismic action and rules for buildings”, European Committee for Standardization (CEN), Brussels, Belgium, 2005. [2] Garlock M, Sause R and Ricles J, “Behavior and design of posttensioned steel frame systems”, Journal of Structural Engineering, Vol.133, No.3, 2007, pp.389–399.  [3] Tzimas AS, Dimopoulos AI and Karavasilis TL, “EC8-based seismic design and assessment of self-centering post-tensioned steel frames with viscous dampers”, Journal of Constructional Steel Research, Vol. 105, 2015, pp. 60–73. [4] Li Y, Ahuja A, Padgett JE, “Review of methods to assess, design for, and mitigate multiple hazards”, Journal of Performance of Constructed Facilities, Vol. 26, No. 1, 2012, pp. 104-117. [5] El-Tawil S, Li H and Kunnath S, “Computational Simulation of Gravity-Induced Progressive Collapse of Steel-Frame Buildings: Current Trends and Future Research Needs”, Journal of Structural Engineering, Vol. 140, No. 8, 2014, pp. 1 - 12. [6] George Vasdravellis, Marco Baiguera and Dina Al-Sammaraie, "Numerical simulation of the progressive collapse behaviour of steel self-centering moment resisting frames", Eighth International Conference on STEEL AND ALUMINIUM STRUCTURES, Hong Kong, China, December 7 – 9, 2016 [7] Vasdravellis G, Uy B, Tan EL and Kirkland B, “The effects of axial tension on the sagging-moment regions of composite beams”, Journal of Constructional Steel Research, Vol. 72, 2012, pp. 240-253. [8] ABAQUS/Standard and ABAQUS/Explicit – Version 6.13.1. “ABAQUS Theory Manual”, Dassault Systems, 2016. [9] Vasdravellis G, Uy B, Tan EL and Kirkland B, “The effects of axial tension on the hogging-moment regions of composite beams”, Journal of Constructional Steel Research, Vol. 68, 2012, pp. 20-33. [10] Hognestad E, ‘A study of combined bending and axial load in reinforced concrete members’, Bull. Ser. No. 399, University of Illinois at Urbana-Campaign, College of Engineering, Engineering Experiment Station, Urbana, IL. [11] Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings, European Committee for Standardization, 2004. [12] Thompson SL, “Axial, shear and moment interaction of single plate ‘shear tab’ connections”, MS thesis, Milwaukee School of Engineering, Milwaukee, 2009. [13] Main JA and Sadek F, “Modeling and Analysis of Single-Plate Shear Connections under Column Loss”, Journal of Structural Engineering, Vol. 140 (3), 2014. [14] Eurocode 3: “Design of steel structures - Part 1-8: Design of joints”, European Committee for Standardization, 2003. [15] Eurocode 4: “Design of composite steel and concrete structures - Part 1-1: General rules and rules for buildings”, European Committee for Standardization, 2004. [16] Vasdravellis G, Karavasilis TL, and Uy B, “Finite element models and cyclic behavior of self-centering steel post-tensioned connections with web hourglass pins,” Eng. Struct., vol. 52, pp. 1–16, 2013. [17] Ding Y, Song X and Zhu HT, “Probabilistic progressive collapse analysis of steel-concrete composite floor systems”, Journal of Constructional Steel Research, Vol. 129, 2017, pp. 129–140.                3D NUMERICAL ASSESSMENT OF THE PROGRESSIVE COLLAPSE RESISTANCE OF A SEISMIC-RESISTANT STEEL BUILDING WITH POST-TENSIONED BEAM-COLUMN CONNECTIONS  Christoforos A. Dimopoulos Marie Skłodowska Curie Research Fellow School of Engineering, University of Warwick Coventry CV4 7AL, UK E-mail: dchristoforos@hotmail.com  Fabio Freddi Marie Skłodowska Curie Research Fellow School of Engineering, University of Warwick Coventry CV4 7AL, UK E-mail: freddi.fabio82@gmail.com  Theodore L. Karavasilis Professor of Structures and Structural Mechanics Faculty of Engineering and the Environment, University of Southampton Southampton SO17 1BJ, UK E-mail: T.Karavasilis@soton.ac.uk  George Vasdravellis Assistant Professor of Structural Engineering Institute for Infrastructure and Environment, Heriot-Watt University Edinburgh EH14 4AS, UK E-mail: G.Vasdravellis@hw.ac.uk   ΠΕΡΙΛΗΨΗ  Σε αυτό το άρθρο παρουσιάζεται μια αριθμητική διερεύνηση της αντοχής έναντι κατάρρευσης ενός μεταλλικού κτιρίου με συνδέσεις δοκού υποστυλώματος αυτο-επαναφερόμενης συμπεριφοράς. Η ανάλυση λαμβάνει υπόψη το τρισδιάστατο φορέα του πρώτου ορόφου του κτιρίου. Το τρισδιάστατο μοντέλο λαμβάνει υπόψη την επίδραση της σύμμικτης πλάκας, η οποία προσομοιώνεται με ένα συνδυασμό στοιχείων κελύφους, δοκού, και μη γραμμικών ελατηρίων. Πέρα από τις συνδέσεις δοκού υποστυλώματος αυτό-επαναφερόμενης συμπεριφοράς, όλες οι υπόλοιπες συνδέσεις δοκού-δοκού και δοκού-υποστυλώματος είναι συνδέσεις διάτμησης και προσομοιώνονται χρησιμοποιώντας μη γραμμικά ελατήρια με κατάλληλες συνθήκες αστοχίας. Επιπλέον, το μεταλλικό πλαίσιο το οποίο υφίσταται την απώλεια υποστυλώματος προσομοιώνεται με τρισδιάστατα στοιχεία ελαστικότητας. Για τον προσδιορισμό των μορφών αστοχίας του κτιρίου και τη διερεύνηση της επίδρασης της σύμμικτης πλάκας στην αντοχή του κτιρίου έναντι σταδιακής κατάρρευσης πραγματοποιούνται μη γραμμικές στατικές αναλύσεις. Η επίδραση της σύμμικτης πλάκας είναι αρκετά σημαντική με συνεισφορά η οποία μπορεί να ξεπερνά και το 30% της ολικής αντοχής.   

3D numerical assessment of the progressive collapse resistance of a seismic resistant steel building with post-tensioned beam-column connections

This paper presents the numerical assessment of the progressive collapse resistance of aseismic-resistant steel building with post-tensioned beam-column connections. Thenumerical simulations are carried out in 3D under a loss of column scenario. The 3D modelconsiders the effect of the composite slab, where composite beams and their shearconnectors are modeled with a combination of shell, beam and nonlinear connectorelements. All the beam-column and beam-to-beam connections are modeled usingnonlinear connector elements with appropriate failure criteria. Moreover, the steel framefor which a column is removed is modelled in full detail with the aid of 3D solid elementsto accurately capture its local and global nonlinear behavior. Nonlinear static analyses arecarried out to identify the failure modes of the building under a sudden loss of columnscenario and investigate the effect of the floor slab on the overall progressive collapseresistance

Teeside University's Research Repository

3D numerical assessment of the progressive collapse resistance of a seismic-resistant steel building with post-tensioned beam-column connections

Teesside University Research

  
 
 
 
3D NUMERICAL ASSESSMENT OF THE PROGRESSIVE COLLAPSE 
RESISTANCE OF A SEISMIC-RESISTANT STEEL BUILDING WITH POST-
TENSIONED BEAM-COLUMN CONNECTIONS 
 
Christoforos A. Dimopoulos 
Marie Skłodowska Curie Research Fellow 
School of Engineering, University of Warwick 
Coventry CV4 7AL, UK 
E-mail: dchristoforos@hotmail.com 
 
Fabio Freddi 
Marie Skłodowska Curie Research Fellow 
School of Engineering, University of Warwick 
Coventry CV4 7AL, UK 
E-mail: freddi.fabio82@gmail.com 
 
Theodore L. Karavasilis 
Professor of Structures and Structural Mechanics 
Faculty of Engineering and the Environment, University of Southampton 
Southampton SO17 1BJ, UK 
E-mail: T.Karavasilis@soton.ac.uk 
 
George Vasdravellis 
Assistant Professor of Structural Engineering 
Institute for Infrastructure and Environment, Heriot-Watt University 
Edinburgh EH14 4AS, UK 
E-mail: G.Vasdravellis@hw.ac.uk 
 
 
 
 
1. ABSTRACT 
 
This paper presents the numerical assessment of the progressive collapse resistance of a 
seismic-resistant steel building with post-tensioned beam-column connections. The 
numerical simulations are carried out in 3D under a loss of column scenario. The 3D model 
considers the effect of the composite slab, where composite beams and their shear 
connectors are modeled with a combination of shell, beam and nonlinear connector 
elements. All the beam-column and beam-to-beam connections are modeled using 
nonlinear connector elements with appropriate failure criteria. Moreover, the steel frame 
for which a column is removed is modelled in full detail with the aid of 3D solid elements 
to accurately capture its local and global nonlinear behavior. Nonlinear static analyses are 
carried out to identify the failure modes of the building under a sudden loss of column 
scenario and investigate the effect of the floor slab on the overall progressive collapse 
resistance.  
 
 2. INTRODUCTION 
 
Conventional seismic-resistant structures, such as steel moment-resisting frames (MRFs), 
are designed to experience significant inelastic deformations under strong earthquakes [1]. 
Inelastic deformations result in damage of structural members and residual interstory drifts, 
which lead to high repair costs and disruption of the building use or occupation. The 
aforementioned socio-economic risks highlight the need for widespread implementation of 
minimal-damage structures, which can reduce both repair costs and downtime. Amongst 
others, steel frames equipped with self-centering beam–column connections with post-
tensioned high strength bars ([2], [3]) demonstrated their superior seismic performance, i.e. 
in minimizing the damage in the main structural components and in providing self-
centering capability even under strong earthquakes. 
However, specialization of the structure in order to improve the seismic performances 
should not affect their capability to resists other types of hazard and multi-hazard 
considerations are required ([4]).  
Amongst others, man-made hazards deriving from events such as fire, explosions or impact 
gained the attention of many researchers in the last decades because of the possibility of 
progressive collapse [5]. Progressive collapse of a structure occurs when the failure of a 
structural component, leads to the collapse of the surrounding members, promoting 
additional or even global collapse.  
Despite the relatively large body of research on the seismic behavior of self-centering 
moment resisting frames (SC-MRFs), their robustness under a column loss scenario is not 
thoroughly studied. SC-MRFs are placed at the perimeter of a building as lateral force 
resisting system and, hence, they are prone to accidental events that could produce the loss 
of one or more columns. Previous research on robustness of steel concrete composite 
frames focused on their 2D behavior or on the isolated behavior of their slab by itself. The 
present paper focuses on the robustness of SC-MRFs under a column removal scenario 
accounting also for the contribution of the 3D membrane effects of the slab based on 3D 
finite element models developed in ABAQUS.  
 
 
3. CASE STUDYING BUILDING 
 
A 5-story SC-MRF using post-tensioned (PT) connections with web hourglass shape steel 
pins (WHPs) [3] is used as the prototype building. The plan view and elevation are shown 
in Fig. 1. The frame uses perimeter SC-MRFs to resist seismic loads, while the interior 
frames are designed for gravity loads only. Two high strength steel bars located at the mid 
depth of the beam, one at each side of the beam web, pass through holes drilled on the 
column flanges. The bars are post-tensioned and anchored to the exterior columns. WHPs 
are inserted in aligned holes on the beam web and on supporting plates welded to the 
column flanges. Energy is dissipated through inelastic bending of the WHPs while the self-
centering capabilities are ensured by the gap opening mechanism and the presence of the 
PT bars. More details on the case study building are reported in [3] and [6]. 
 
 
4. VALIDATION OF THE NUMERICAL MODELS  
 
Numerical models are built in ABAQUS [8] to simulate the behavior of the basic structural 
components (Fig. 2) i.e. fin plate connections, steel-concrete composite beams, and the 
SC-MRFs and are validate against experimental results. 
 4.1 Validation of the steel-concrete composite beam 
 
For the validation of the numerical model of the composite beam, an experimental 
investigation by Vasdravellis et al. ([7], [9]) of simply supported beams under a single 
point load is considered. Full geometrical and material properties are given in that 
reference. The steel material of the beam is simulated by using the elasto-plastic stress-
strain law with hardening. An elastic perfectly-plastic model was used to simulate the 
material response of the reinforcement. The concrete is modeled by using the concrete 
damage plasticity model in ABAQUS. The concrete stress-strain curve in compression 
follows a modified Hognestad stress-strain relationship [10] while the modulus of elasticity 
of the  concrete Ec is taken according to EC2 [11]. For the validation of the numerical 
model, the experimentally determined tensile strength is considered. For the progressive 
collapse investigation, the mean tensile strength fctm is taken according to EC2 [11]. An 
idealized behavior in tension is assumed for the concrete with a linear softening and a 
residual tension strength of 0.1fctm starting at strain equal to 0.05.  
 
A
B
D
C
1 2 3 4 5 6
SC-MRF
SC-MRF
Braced
Frame
Braced
Frame
G10 G11 G12G7 G8 G9G4 G5 G6G1 G2 G3 G13 G14 G15
IP
E2
20
8.0 m
5.
0 
m
IP
E4
00
4m
4@
 3
.2
m
SC-MRF
Fig. 1: a) Plan view and b) elevation view of the prototype building 
 
Composite Beam Fin Plate Connection  
Centerline of beam
Middle surface of
concrete slab
Connectors representing
shear studs
 
   
Fig. 2: (a) Composite beam & fin-plate connection of a beam; and mechanical idealization of (b) composite 
beam and (c) fin plate connections 
 
Connector elements (of Cartesian and Align type) connecting the middle surface of the 
concrete slab to the middle surface of the beam elements are used to model the shear studs. 
An elastic-perfectly plastic behavior is assumed for the shear connectors. Experimental 
strengths are used for the validation of the numerical models of the composite beams. 
Nominal strengths according to EC4 [15] are used in the progressive collapse simulations. 
Maximum slips obtained from push-out tests are used in the numerical analyses to consider 
fracture of the studs. 
Fig. 3 shows a comparison between numerical and experimental results for the case of 
sagging and hogging moment, respectively. The simplified numerical model can capture 
the sagging and hogging behavior of the composite beam. The larger force capacities 
exhibited in the hogging moment can be contributed to the idealized behavior that was 
adopted for the concrete in tension. 
Spring 
element
Rigid 
Element 
GAP 
Elemen
t
 4.2 Validation of the fin-plate connections 
 
The experimental results from Thompson [12], described in detail in [13], have been used 
to validate the simplified numerical model for the fin plate connection. The fin plate 
connection is modelled using the component method where at each bolt level a spring is 
considered having stiffness and strength that described best the combined behaviour of the 
fin plate, the beam web and the bolt. The stiffness and strength of these springs are 
estimated according to EC3-1.6 [14] while the ultimate deformations according to [15]. 
Gap-like springs are attached at the beam flange levels to account to contact phenomenon 
at large displacements. Fig. 4 shows the numerical results of a four-bolt fin plate 
connection accompanied with the corresponding experimental results. A good agreement 
can be observed for the two cases. 
 
0 0.05 0.1 0.15 0.2
0
50
100
150
200
250
Displacement (m)
Fo
rc
e 
(k
N
)
 
 
Experiment (Sagging)
ABAQUS (Sagging)
Experiments (Hogging)
ABAQUS (Hogging)
 
Fig. 3: Comparison of numerical and experimental results for the composite beam 
 
0 0.1 0.2 0.3 0.4
0
20
40
60
80
100
Displacement (m)
Fo
rc
e 
(k
N
)
 
 
Experiment 1
Experiment 2
Experiment 3
ABAQUS
 
Fig. 4: Comparison of numerical and experimental results for the fin-plate connection 
 
 
4.3 Validation of the PT connection 
 
The model of the PT connection with WHPs used in the SC-MRF of the case study 
 building, has been validate elsewhere [16] and found capable in capturing the cyclic 
behaviour and the local and global failure modes up to excessive imposed deformations. 
 
5. FINITE ELEMENT MODEL OF THE BUILDING 
 
The ABAQUS finite element model of the first floor of the prototype building provides 
insights in the progressive collapse resistance of SC-MRFs (Fig. 5). Only one of the two 
SC-MRFs, which exhibits column failure, is modelled using eight-node linear brick 
element (C3D8R) while the PT bars are modelled with truss elements. All the rest of the 
structural members (beams, columns, braces) are modelled with beam-column elements 
(B31). The concrete slab is modelled with shell elements (S4R). Fin plates and shear studs 
are modelled using connector elements as explained in the previous sections. Appropriate 
contact interactions are considered for the SC-MRF and the contact of the slab to the main 
beams. A 120 mm-thick slab reinforced with a N12/150 mm top and bottom rebar mesh is 
considered. A ‘bolt load’ is used to model the initial post-tensioning force in the PT bars. A 
nonlinear static analysis is first performed to apply the initial force in the PT bars. The 
upper ends of columns are modelled as pinned representing inflection point in steel column 
[17]. Both gravity columns with pinned supports and SC-MRF columns with fixed support 
extend up the half-height of the second floor. In a subsequent nonlinear static analysis, the 
support of the column that is failed is removed and a vertical downwards displacement is 
applied to the top of the column. The standard ‘Full Newton’ solution technique is adopted 
together with an automatic incrementation scheme for the application of the loading.  
Fig. 6 shows the deformed shape of the building when the failed column reaches a 
displacement equal to 1.60 m. Fig. 7 shows the force versus vertical displacement at the 
removed column resulting from the nonlinear static analysis for three structural 
configurations: (i) the SC-MRF is modelled on its own; (ii) the first floor is modelled but 
no slab is included; and (iii) the first floor is modelled including the concrete slab and its 
composite action with the steel sections. The horizontal axis represents the vertical 
displacement of the removed column and the vertical axis the associated reaction load. It 
can be seen that the effect of the beams and the fin plate connections is negligible. The 
strength of the second structural configuration is the same as the first configuration. The 
effect of the composite action of the concrete action and the secondary beams, however, 
significant since its contribution increases the overall resistance of the system by 30%.  
 
 
Fig. 5: Finite element model of the building 
  
Fig. 6: Deformation state of the building after the column removal (1.60m displacement) 
 
0 0.5 1 1.5 2
0
500
1000
1500
2000
Pushdown Displacement (m)
Fo
rc
e 
(k
N
)
 
 
Only SC-MRF
First floor (No Slab)
First floor (Slab)
 
Fig. 7: (a) Load-displacement curves from nonlinear static analyses 
 
6. CONCLUSIONS 
 
This paper studied the progressive collapse resistance of a steel building with SC-MRFs. 
Simplified numerical models were built and validated against experimental results for the 
composite slab and the fin plate connection. Static nonlinear analyses were performed to 
study the robustness of the building against a sudden column removal of the SC-MRF. It 
was found that the contribution of the steel beams alone is negligible, however the effect of 
the composite slab is significant and could overcome the 30% of the overall progressive 
collapse resistance of the building. 
 
 
7. REFERENCES 
 
[1] Eurocode 8, “Design of structures for earthquake resistance. Part 1: General rules, 
seismic action and rules for buildings”, European Committee for Standardization 
(CEN), Brussels, Belgium, 2005. 
[2] Garlock M, Sause R and Ricles J, “Behavior and design of posttensioned steel frame 
systems”, Journal of Structural Engineering, Vol.133, No.3, 2007, pp.389–399. 
 [3] Tzimas AS, Dimopoulos AI and Karavasilis TL, “EC8-based seismic design and 
assessment of self-centering post-tensioned steel frames with viscous dampers”, 
Journal of Constructional Steel Research, Vol. 105, 2015, pp. 60–73. 
[4] Li Y, Ahuja A, Padgett JE, “Review of methods to assess, design for, and mitigate 
multiple hazards”, Journal of Performance of Constructed Facilities, Vol. 26, No. 1, 
2012, pp. 104-117. 
[5] El-Tawil S, Li H and Kunnath S, “Computational Simulation of Gravity-Induced 
Progressive Collapse of Steel-Frame Buildings: Current Trends and Future Research 
Needs”, Journal of Structural Engineering, Vol. 140, No. 8, 2014, pp. 1 - 12. 
[6] George Vasdravellis, Marco Baiguera and Dina Al-Sammaraie, "Numerical 
simulation of the progressive collapse behaviour of steel self-centering moment 
resisting frames", Eighth International Conference on STEEL AND ALUMINIUM 
STRUCTURES, Hong Kong, China, December 7 – 9, 2016 
[7] Vasdravellis G, Uy B, Tan EL and Kirkland B, “The effects of axial tension on the 
sagging-moment regions of composite beams”, Journal of Constructional Steel 
Research, Vol. 72, 2012, pp. 240-253. 
[8] ABAQUS/Standard and ABAQUS/Explicit – Version 6.13.1. “ABAQUS Theory 
Manual”, Dassault Systems, 2016. 
[9] Vasdravellis G, Uy B, Tan EL and Kirkland B, “The effects of axial tension on the 
hogging-moment regions of composite beams”, Journal of Constructional Steel 
Research, Vol. 68, 2012, pp. 20-33. 
[10] Hognestad E, ‘A study of combined bending and axial load in reinforced concrete 
members’, Bull. Ser. No. 399, University of Illinois at Urbana-Campaign, College of 
Engineering, Engineering Experiment Station, Urbana, IL. 
[11] Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for 
buildings, European Committee for Standardization, 2004. 
[12] Thompson SL, “Axial, shear and moment interaction of single plate ‘shear tab’ 
connections”, MS thesis, Milwaukee School of Engineering, Milwaukee, 2009. 
[13] Main JA and Sadek F, “Modeling and Analysis of Single-Plate Shear Connections 
under Column Loss”, Journal of Structural Engineering, Vol. 140 (3), 2014. 
[14] Eurocode 3: “Design of steel structures - Part 1-8: Design of joints”, European 
Committee for Standardization, 2003. 
[15] Eurocode 4: “Design of composite steel and concrete structures - Part 1-1: General 
rules and rules for buildings”, European Committee for Standardization, 2004. 
[16] Vasdravellis G, Karavasilis TL, and Uy B, “Finite element models and cyclic 
behavior of self-centering steel post-tensioned connections with web hourglass pins,” 
Eng. Struct., vol. 52, pp. 1–16, 2013. 
[17] Ding Y, Song X and Zhu HT, “Probabilistic progressive collapse analysis of steel-
concrete composite floor systems”, Journal of Constructional Steel Research, Vol. 
129, 2017, pp. 129–140. 
 
 
 
 
 
 
 
 
 
 
  
 
 
 
3D NUMERICAL ASSESSMENT OF THE PROGRESSIVE COLLAPSE 
RESISTANCE OF A SEISMIC-RESISTANT STEEL BUILDING WITH POST-
TENSIONED BEAM-COLUMN CONNECTIONS 
 
Christoforos A. Dimopoulos 
Marie Skłodowska Curie Research Fellow 
School of Engineering, University of Warwick 
Coventry CV4 7AL, UK 
E-mail: dchristoforos@hotmail.com 
 
Fabio Freddi 
Marie Skłodowska Curie Research Fellow 
School of Engineering, University of Warwick 
Coventry CV4 7AL, UK 
E-mail: freddi.fabio82@gmail.com 
 
Theodore L. Karavasilis 
Professor of Structures and Structural Mechanics 
Faculty of Engineering and the Environment, University of Southampton 
Southampton SO17 1BJ, UK 
E-mail: T.Karavasilis@soton.ac.uk 
 
George Vasdravellis 
Assistant Professor of Structural Engineering 
Institute for Infrastructure and Environment, Heriot-Watt University 
Edinburgh EH14 4AS, UK 
E-mail: G.Vasdravellis@hw.ac.uk 
 
 
ΠΕΡΙΛΗΨΗ 
 
Σε αυτό το άρθρο παρουσιάζεται μια αριθμητική διερεύνηση της αντοχής έναντι 
κατάρρευσης ενός μεταλλικού κτιρίου με συνδέσεις δοκού υποστυλώματος αυτο-
επαναφερόμενης συμπεριφοράς. Η ανάλυση λαμβάνει υπόψη το τρισδιάστατο φορέα του 
πρώτου ορόφου του κτιρίου. Το τρισδιάστατο μοντέλο λαμβάνει υπόψη την επίδραση της 
σύμμικτης πλάκας, η οποία προσομοιώνεται με ένα συνδυασμό στοιχείων κελύφους, 
δοκού, και μη γραμμικών ελατηρίων. Πέρα από τις συνδέσεις δοκού υποστυλώματος αυτό-
επαναφερόμενης συμπεριφοράς, όλες οι υπόλοιπες συνδέσεις δοκού-δοκού και δοκού-
υποστυλώματος είναι συνδέσεις διάτμησης και προσομοιώνονται χρησιμοποιώντας μη 
γραμμικά ελατήρια με κατάλληλες συνθήκες αστοχίας. Επιπλέον, το μεταλλικό πλαίσιο το 
οποίο υφίσταται την απώλεια υποστυλώματος προσομοιώνεται με τρισδιάστατα στοιχεία 
ελαστικότητας. Για τον προσδιορισμό των μορφών αστοχίας του κτιρίου και τη 
διερεύνηση της επίδρασης της σύμμικτης πλάκας στην αντοχή του κτιρίου έναντι 
σταδιακής κατάρρευσης πραγματοποιούνται μη γραμμικές στατικές αναλύσεις. Η 
επίδραση της σύμμικτης πλάκας είναι αρκετά σημαντική με συνεισφορά η οποία μπορεί να 
ξεπερνά και το 30% της ολικής αντοχής.   


http://discovery.ucl.ac.uk/1575844/1/Freddi_Dimopoulos%20et%20al.%202017_HCSS_3D%20num%20asses.%20of%20progressive%20collapse%20of%20seismic-res%20steel%20building%20with%20PT%20connections%20-%20Submitted.pdf

3D numerical assessment of the progressive collapse resistance of a seismic-resistant steel building with post-tensioned beam-column connections

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