Keywords—non-linear analysis, transient coupled temperature-displacement, wide pre-stressed reinforced concrete beams

Abstract—When using wide pre-stressed reinforced concrete

beams for realization of prefabricated concrete slabs beside their mechanical disadvantages with respect to the regular ones, their increased risk of brittle failure and other uncertainty in their behavior have to be considered. Since in structural design structural height might be imposed, wide beams with all their disadvantages become the right solution. But how the mechanical behavior of the prefabricated floor system can be influenced in case of fire? The paper presents numerical modeling for prefabricated floor system using wide reinforced concrete beams considered together with the corresponding double floor with precast slab and concrete topping, subjected to fire in different fire scenarios, establishing the scenario with the highest risk on the structural stability.

I. INTRODUCTION N practice of precast concrete structures several structural solutions are widely spread. Double floor systems are

assuring the necessary speed in structure realization as well as the structural flexibility, which, in combination with use of wide pre-stressed reinforced concrete beams, presents countless benefits, but at the same time raises questions with respect to their mechanical behavior when subjected to loadings. Provisions of existing design codes are not clearly covering all the possible load situations according to [1], neither use of wide pre-stressed reinforced concrete since either code provisions are not covering or the structural system used [1] has no or limited references in codes and practice. From fire resistance point of view the degree of fire resistance is established according to [3], which is establishing the necessary fire resistance of each structural element. According to provisions of [2] fire resistance is assured by foreseeing specific concrete cover of reinforcement. Use of pre-stressed

This work was realized as consequence of the research concerns of the

Technical University of Cluj-Napoca, Faculty of Civil Engineering. A. Puskás is now with the Department of Structures, Faculty of Civil

Engineering, Technical University of Cluj-Napoca, G. Baritiu street no. 25, 400027, Cluj-Napoca, Romania (phone:+40-264-401545, e-mail: attila.puskas@dst.utcluj.ro).

A. Chira is working at the Department of Structural Mechanics, Faculty of Civil Engineering, Technical University of Cluj-Napoca, G. Baritiu street no. 25, 400027, Cluj-Napoca, Romania. He is now postdoctoral researcher of the Department of Building Structures, Faculty of Civil Engineering, Department of Building Structures, Thákurova 7, 166 29 Praha 6, Czech Republic (e-mail: alexandru.chira@ fsv.cvut.cz).

slab elements can avoid excessive deformations and postpone the appearance of cracks [4], and as consequence the excessive exposure of reinforcement to fire. Due to the decreased structural height of wide beam floor systems their sensibility to fire is crucial. Studies on wide reinforced concrete beams subjected to fire shows that in numerical analysis the beam supposed to different fire scenarios has an adequate behavior for the imposed fire resistance degree [5], but their behavior as part of the floor system needs further investigations.

II. PROBLEM FORMULATION For studying the behavior of the wide pre-stressed reinforced concrete beam subjected to different fire scenarios a floor system using this type of beam is considered [6], as presented in Fig. 1.

Fig. 1 floor system layout

For the modeling the floor system effective width of the beam has been considered (Fig. 2) according to the clause 5.3.2.1 of [1], taking into consideration the used concrete and reinforcement quantity, quality and disposal.

Flanged wide reinforced concrete beam subjected to fire - numerical investigations

A. Puskás and A. Chira

I

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ISBN: 978-1-61804-240-8 132

Fig. 2 effective width of the beam

The total double floor thickness is 17 cm, build up by a 8 cm precast floor of C40/50 class concrete and a 8 cm topping of C25/30. The main wide beam reinforcement is presented on Fig. 3. Its total length is 7.86 a, while the cross-section is 25x120 cm. The concrete quality used is C30/37, with longitudinal and transversal reinforcements PC52 type and active reinforcements of St1660 type having 12.9 mm diameter. For the analysis Abaqus FEM code [7] has been used, with different material law for both concrete and steel, for every change of temperature. For concrete it has been used the C3D8T solid elements: an 8-node thermally coupled brick, tri-linear displacement and temperature and for the reinforcements the T3D2T elements: a 2-node 3-D thermally coupled truss. The analysis was done in three steps: in the first one the pre-tensioning was done and in the second one the gravity loads were applied for both a static general analysis being used. In the third step a transient coupled temperature-displacement analysis have been used [8][9][10][11][12].

Fig. 3: main wide beam reinforcement

For the analysis of the beam taking into account the effective width of the beam three different fire scenarios have been used [5],considering two hours from the curve presented in figure 4.

Fig. 4: ISO 834 standard fire curve [2]

III. MODELING OF THE BEAM ON FIRE In order to investigate the flanged wide reinforced concrete

beam subjected to fire analyses have been performed using Abaqus finite element analysis. Results for the three scenarios are presented in the followings:

A. Scenario I The first scenario of fire takes into consideration acting of

the fire along the whole length and aside the whole width of the flanged beam (Fig. 5).

Fig. 5: Scenario I of fire action

Fig. 6: Displacement after two hours of fire, d=10.96 cm

Fig. 7: Concrete plastic equivalent strain from compression,

PEEQ=7.61E-3

Fig. 8: Concrete plastic equivalent strain from tension,

PEEQT=9.59 E-3

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ISBN: 978-1-61804-240-8 133

Fig. 9: Steel plastic equivalent strain, PEEQ=9.50E-3

Fig. 10: Temperature distribution on concrete after two hours of fire,

Tmax=1052ºC

Fig. 11: Temperature distribution on steel after two hours of fire,

Tmax=981.6 ºC

Fig. 12: Time versus maximum temperature curve on concrete

Fig. 13: Displacement – maximum temperature diagram

B. Scenario II The second scenario of fire considers the fire acting in the

middle of the opening on a strip of 0.50 m wide, aside the whole width of the flanged beam (Fig. 14).

Fig. 14: Scenario II of fire action

Fig. 15: Displacement after two hours of fire, d=1.087 cm

Fig. 16: Concrete plastic equivalent strain from compression,

PEEQ=1.90E-3

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ISBN: 978-1-61804-240-8 134

Fig. 17: Concrete plastic equivalent strain from tension,

PEEQT=3.71E-3

Fig. 18: Steel plastic equivalent strain, PEEQ=4.08E-3

Fig. 19: Temperature distribution on concrete after two hours of fire,

Tmax=978.7ºC

Fig. 20: Temperature distribution on steel after two hours of fire,

Tmax=913.9 ºC

Fig. 21: Time versus maximum temperature curve on concrete

Fig. 22: Displacement – maximum temperature diagram

C. Scenario III In the third scenario of fire it have been considered acting

on a strip of 0.50 m wide near the support, aside the whole width of the flanged beam (Fig. 23).

Fig. 23: Scenario III of fire action

Fig. 24: Displacement after two hours of fire, d=0.072 cm

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ISBN: 978-1-61804-240-8 135

Fig. 25: Concrete plastic equivalent strain from compression,

PEEQ=4.39E-3

Fig. 26: Concrete plastic equivalent strain from tension,

PEEQT=5.14E-3

Fig. 27: Steel plastic equivalent strain, PEEQ=6.78E-3

Fig. 28: Temperature distribution on concrete after two hours of fire,

Tmax=969.4ºC

Fig. 29: Temperature distribution on steel after two hours of fire,

Tmax=908.4 ºC

Fig. 30: Time versus maximum temperature curve on concrete

Fig. 31: Displacement – maximum temperature diagram

IV. DISCUSSION The three scenarios taken into consideration in the investigation presents possible situation of fire acting on the beam. When comparing results obtained for flanged wide reinforced concrete beam with respect to the independent wide reinforced concrete beam [5] one can remark similar behavior of the beams under the same external load, but deflection of the beam, internal stresses in concrete and reinforcements as well as internal temperature are of more reduced values.

Comparison of the results for the three scenarios is unnecessary since the load given by the fire in the first scenario is incomparable with the other two scenarios. Even so we can remark the increased risk for the stability of the element for scenario I since after one hour it reaches excessive deformation (beyond l/100), where the concrete cover of the tensioned reinforcements is already inexistent. For scenarios II and III the deformation occurred is almost negligible under the external and fire loads.

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ISBN: 978-1-61804-240-8 136

V. CONCLUSION The behavior of the flanged wide reinforced concrete beam

subjected to fire according to the presented numerical investigation can be considered highly satisfying, taking in consideration the designed concrete cover and the imposed fire resistance of the element of 15 minutes. Fire resistance of the beam is improved when joint with the flanges is considered and pre-stressing for the beam is applied, avoiding excessive deflection even after one hour of fire load. Temperature in the reinforcements reaches dangerous values after one hour of fire load.

The displacements after two hours of fire are less for the wide beam interacting with the precast slab then the results only on the wide beam alone [5], 3 times less for the first and second scenario and almost 8 times less for the third scenario.

Modeling the interaction of the precast slab with the prestressed wide beam gives a more accurate representation on the behavior of the beam subjected to gravity and fire loads. For a better understanding of the mechanical behavior the authors will have to do some experimental investigations in order to see if the numerical model is close to reality.

REFERENCES [1] *** SR EN 1992-1-1-2004, Eurocode 2, Design of concrete structures.

Part 1-1: General rules and rules for buildings, 2004. [2] *** SR EN 1992-1-2-2004, Eurocode 2, Design of concrete structures.

Part 1-2: General rules – structural fire design, 2004. [3] ***. (1999). P118-99: Normativ de siguranță la foc a construcțiilor [4] A. Puskas, Z. Kiss, “Testing of a wide reinforced concrete beam”, The

7th Central European Congress on Concrete Engineering, Balatonfüred, Hungary, 22-23 September 2011, pp. 315-318

[5] A. Puskas, A. Chira, “Numerical Investigations on a Wide Reinforced Concrete Beam Subjected to Fire”, Proceedings of the 4th International Conference on Mathematical Models for Engineering Science - MMES '13, Brasov, Romania, June 1-3, 2013, pp. 169-174, ISBN: 978-1-61804-194-4

[6] Z. Kiss, K. Bálint, A. Puskás, “Steel or concrete structure – prefabricated or cast in situ? The design of a multistory building in Bucharest for Kika”, III, Medunarodna Savetovanke, Subotica, 8-9. Octobar 2009, p. 79-93.

[7] Abaqus. Abaqus Analysis User's Manual. [8] I. Moga, L. Moga, “Heat flow simulation through the window together

with the wall in which is fitted in”, IASTED conference “Applied Simulation and Modeling” Palma de Mallorca, Spain, 29 – 31 August, 2007, ISBN: 978-0-88986-687-4

[9] A. Faris, A. Nadjai, S. Choi, “Numerical and experimental investigations of the behavior of high strength concrete columns in fire”, Elsevier, Engineering structures, 2010.

[10] K. Venkatesh, R. Nikhil, “A simplified approach for predicting fire resistance of reinforced concrete columns under biaxial bending”, Elsevier, Engineering structures, 2012.

[11] Qing-Hua Tan,Lin-HaiHan n, Hong-XiaYu, Fire performance of concrete filled steel tubular (CFST) column to RC beam joint, Fire Safety Journal, 2012

[12] Anil Agarwal , Lisa Choe , Amit H. Varma ,,Fire design of steel columns: Effects of thermal gradients’’ Elsevier, Journal of Constructional Steel Research, 2014.

A. Puskás is Assistant Professor at Faculty of Civil Engineering of Technical University of Cluj-Napoca, Romania, since 2007. He received the B.S. and Ph.D. degrees in civil engineering in 1995 and 2012, respectively, from Technical University of Cluj-Napoca, Romania, and M.S. degree in Business Administration from Faculty of Business of Babes-Bolyai University, Cluj-Napoca, Romania, in 2005. In 2013 he graduated a Postgraduate Course in

Sustainable Urbanization at Technical University of Cluj-Napoca, Romania and participated in a short course in Sustainability: Principles and Practice at Massachusetts Institute of Technology, Cambridge, United States.

He joined Technical University of Cluj-Napoca, Romania in 2003 as Teaching Assistant. From 2000 he have also worked as Structural Designer, leading or participating in design of several steel, concrete, masonry or wooden structured industrial and public buildings. Since 2005 he is also Technical Director of a privately owned construction company, with extensive activity in industrial and public building design and realization. He has authored more than 30 Journal and Conference papers. His current interests include pre-stressed concrete design, sustainable structural solutions, sustainability of structures and their environmental impact as well as waste recycling in construction industry.

Dr. Puskás is member of The International Federation for Structural Concrete, The American Concrete Institute, Association of Environmental Engineering and Science Professors, Romanian Green Building Council and Association of Structural Designer Civil Engineers. A. Chira is Assistant Professor at Faculty of Civil Engineering of Technical University of Cluj-Napoca, Romania, since 2014. He received the B.S. and Ph.D. degrees in civil engineering in 2008 and 2011, respectively, from Technical University of Cluj-Napoca, Romania,

He joined Technical University of Cluj-Napoca, Romania in 2010 as Teaching Assistant. In 2007 he started to work as Structural Designer, being involved in the design of concrete, steel or masonry both industrial and public buildings.

Dr. Chira is member of research team ,,Computational Modeling and Advanced Simulation in Structural and Geotechnical Engineering’’.

Advances in Applied and Pure Mathematics

ISBN: 978-1-61804-240-8 137