Materials and structures

Vilnius Gediminas Technical University Lithuanian Academy of Sciences Journal of Civil Engineering and Management 2004, Vol X, Supplement 1 Vilnius Technika 2004 ISSN 1392-3730 EDITORIAL BOARD Editor-in-Chief Prof Edmundas K. ZAVADSKAS, Lithuanian Academy of Sciences, Vilnius Gediminas Technical University, Saulởtekio al. 11, LT-10223 Vilnius-40, Lithuania Editors Managing editor Assoc Prof Darius BAẩINSKAS, Vilnius Gediminas Technical University, Saulởtekio al. 11, LT-10223 Vilnius-40, Lithuania Dr Rogerio BAIRRAO, Portuguese National Laboratory for Civil Engineering, Av. Brasil, 101, 1700-066 Lisboa, Portugal Prof Gyửrgy L. BALZS, Budapest University of Technology and Economics, Mỷegyetem rkp.3, H-1111 Budapest, Hun- gary Assoc Prof Erik BEJDER, Aalborg University, Fibigerstraede 16, 9220 Aalborg, Denmark Prof Adam BORKOWSKI, Institute of Fundamental Techno- logical Research, Swiổtokrzyska 21, 00-049 Warsaw, Poland Prof Michaự BOLTRYK, Biaựystok Technical University, Wiejska 45A, 15-351 Biaựystok, Poland Prof Patrick J. DOWLING, Felow Royal Society, University of Surrey, Guildford GU25XH, UK Prof Aleksandr A. GUSAKOV, Moscow State University of Civil Engineering, Dorogomilevskaja, 5/114, 121059 Moscow, Russia Prof Boris V. GUSEV, International and Russian Engineering Academies, Tverskaja 11, 103905 Moscow, Russia Assoc Prof Edward J. JASELSKIS, Iowa State University, Ames, IA 50011, USA Prof Oleg KAPLIẹSKI, Poznan University of Technology, Piotrovo 5, 60-965 Poznan, Poland Prof Herbert A. MANG, Austrian Academy of Sciences, Vienna University of Technology, Karlsplatz 13, A-1040 Vienna, Austria Prof Antanas ALIKONIS, Vilnius Gediminas Technical Uni- versity, Saulởtekio al. 11, LT-10223 Vilnius-40, Lithuania Prof Juozas ATKOẩINAS, Vilnius Gediminas Technical University, Saulởtekio al. 11, LT-10223 Vilnius-40, Lithuania Prof Algirdas E. ẩIịAS, Vilnius Gediminas Technical Uni- versity, Saulởtekio al. 11, LT-10223 Vilnius-40, Lithuania Assoc Prof Juozas DELTUVA, Kaunas University of Tech- nology, Studentứ g. 48, LT-3028 Kaunas, Lithuania Prof Romualdas GINEVIẩIUS, Vilnius Gediminas Technical University, Saulởtekio al. 11, LT-10223 Vilnius-40, Lithuania Prof Arvydas JUODIS, Kaunas University of Technology, Studentứ g. 48, LT-3028 Kaunas, Lithuania Prof Prancikus JUéKEVIẩIUS, Vilnius Gediminas Techni- cal University, Saulởtekio al. 11, LT-10223 Vilnius-40, Lithuania Prof Rimantas KAẩIANAUSKAS, Lithuanian Academy of Sci- ences, Vilnius Gediminas Technical University, Saulởtekio al. 11, LT-10223 Vilnius-40, Lithuania Prof Gintaris KAKLAUSKAS, Vilnius Gediminas Technical University, Saulởtekio al. 11, LT-10223 Vilnius-40, Lithuania International Editorial Board Prof Rene MAQUOI, University of Liege, Building B52/3, Chemin des Chevreuils 1, B 4000 Liege, Belgium Prof Yoshihiko OHAMA, Nihon University, Koriyama, Fukushima-Ken, 963-8642, Japan Prof Friedel PELDSCHUS, Leipzig University of Applied Science, 132 Karl Liebknecht St, 04227 Leipzig, Germany Prof Karlis ROCENS, Latvian Academy of Sciences, Riga Technical University, zenes str. 16, Riga, LV-1048 Latvia Prof Les RUDDOCK, University of Salford, Salford, Greater Manchester M5 4WT, UK Prof Miroslaw J. SKIBNIEWSKI, Purdue University, West Lafayette, Indiana 47907-1294, USA Prof Martin SKITMORE, Queensland University of Techno- logy, Brisbane QLD 4001, Australia Prof Zenon WASZCZYSZYN, Cracow University of Techno- logy, Warszawska 24, 31-155 Krakow, Poland Prof Frank WERNER, Bauhaus University, Marienstrasse 5, 99423, Weimar, Germany Prof Nils-Erik WIBERG, Chalmers University of Technology, SE - 412 96 Gửteborg, Sweden Prof Jiứớ WITZANY, Czech Technical University, Prague, Thỏkurova 7, CZ 166 29 Praha 6, Czech Republic Local Editorial Board Prof Stanislovas KALANTA, Vilnius Gediminas Technical University, Saulởtekio al. 11, LT-10223 Vilnius-40, Lithuania Prof Ipolitas Z. KAMAITIS, Lithuanian Academy of Sciences, Vilnius Gediminas Technical University, Saulởtekio al. 11, LT-10223 Vilnius-40, Lithuania Prof Romualdas MAẩIULAITIS, Vilnius Gediminas Techni- cal University, Saulởtekio al. 11, LT-10223 Vilnius-40, Lithuania Prof Gediminas J. MARẩIUKAITIS, Vilnius Gediminas Tech- nical University, Saulởtekio al. 11, LT-10223 Vilnius-40, Lithuania Prof Josifas PARASONIS, Vilnius Gediminas Technical Uni- versity, Saulởtekio al. 11, LT-10223 Vilnius-40, Lithuania Prof Vytautas STANKEVIẩIUS, Lithuanian Academy of Sciences, Lithuanian Institute of Architecture and Building Construction, Tunelio g. 60, LT-3035 Kaunas, Lithuania Prof Vytautas J. STAUSKIS, Vilnius Gediminas Technical University, Saulởtekio al. 11, LT-10223 Vilnius-40, Lithuania dnaslairetaMgnidliuB serutcurtS ,scisyhPdnascinahceMlarutcurtS seigolonhceTnoitamrofnI dnaygolonhceTnoitcurtsnoC tnemeganaM forP .KsinorduASARADEVK, ,ytisrevinUlacinhceTsanimideGsuinliV ,11.laoiketởluaS ainauhtiL,04-suinliV32201-TL forP sadlaumoRSYéUAB , ,ytisrevinUlacinhceTsanimideGsuinliV ,11.laoiketởluaS ainauhtiL,04-suinliV32201-TL forP KsarỷtrASAKSUALKA, ,ytisrevinUlacinhceTsanimideGsuinliV ,11.laoiketởluaS ainauhtiL,04-suinliV32201-TL 3 3 2004, Vol X, Suppl 1, 39 JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT http:/www.vtu.lt/english/editions ISSN 13923730 RESISTANCE OF MASONRY WALL PANELS TO IN-PLANE SHEAR AND COMPRESSION Piotr Aliawdin 1 , Valery Simbirkin 2 , Vassili Toropov 3 1 University of Zielona Góra, Poland. E-mail: P.Aliawdin@ib.uz.zgora.pl 2 Belarussian Research Institute for Construction (BelNIIS), Minsk, Belarus. E-mail: simbirkin@hotmail.com 3 Altair Engineering, Coventry, UK. E-mail: toropov@altair.com Received 30 Apr 2004; accepted 7 June 2004 Abstract. The paper presents results of large-scale tests carried out on masonry wall panels made of perforated bricks. The specimens were subjected to in-plane: lateral loading combined with different levels of axial compression; concentrated compressive load applied to the wall top at different distances from the wall edge. Relationships between shear strength and deformability of masonry and compressive stresses perpendicular to the shear plane have been found. An evaluation of strength of masonry under local compression is given depending on the position of the concentrated load relative to the wall edge. Analysis of test results and comparison of calculation techniques adopted in different design codes is performed. Behaviour of the test specimens is modelled using the finite element method. Keywords: masonry structures, full-scale tests, shear, compression, strength, deformations. 1. Introduction By the present time, an extensive theoretical and experimental research has been carried out on the behaviour of masonry structures made of solid clay bricks, for instance [15]. However, there are a few test results for masonry structures made of perforated bricks that are widely used in practice and have a number of advantages. This study presents an experimental and analytical research into the behaviour of masonry wall panels made of perforated clay bricks. The test specimens were subjected to in-plane 1) local compressive force, and 2) rack- ing shear force combined with vertical compression. For each loading type, two test series have been devised. In the local compression tests, position of the applied force was changed. In the shear tests, lateral force was combined with different levels of axial compression. In the first case, vertical kinematic restraints were installed on the wall top to prevent in-plane rotation of the walls. The vertical pressure arising in this case varied during the loading process and had the minimum value. In the second case, the lateral load was combined with the given vertical compression. The loading of the specimens was increased mono- tonically up to the total failure of the specimens. The resistance of the masonry walls to the predominant action was evaluated with reference to the strength and deformability. 2. Properties of masonry and masonry materials The following materials were used for producing the test specimens: • Clay bricks (length 250 mm, width 120 mm, height 88 mm) with vertical holes. Each brick had 21 holes whose cross-sections were square-shaped, 20x20 cm (volume of holes is 28 % of the gross volume). Brick grade M150. • Dry pre-packed mortar mix, grade M100: Portland cement of grade 500ÄÎ  180 kg/t, lime  50 kg/t, sand  770 kg/t, water-retaining agent Valotsel 45000  0,3 κg/t. The strength properties of the brick and mortar were determined experimentally. Their mean values are presented in Table 1. Table 1. Brick and mortar strengths aPM,htgnertskcirB hsitirByb(evisserpmoC ,]6[1293SBdradnatS )Dxidneppa skcirbgnitsetyb(elisneT )gnidnebrof 6,133,2 aPM,htgnertsratroM gnitsetyb(evisserpmoC )mm7,07edisfosebuc yrnosamagnitsetyb(raehS )skcirbeerhtfotnemgarf 7,219,932,0 4 4 P. Aliawdin, et al / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT  2004, Vol X, Suppl 1, 39 Strength and deformative properties of the masonry under short-term compression were determined by tests of five prismatic specimens having dimensions lxhxt = 380×490×250 mm. On all four vertical sides of each specimen, displacement transducers were installed over a gauge length of 200 mm. They measured longitudinal (vertical) and lateral (horizontal) deformations of the masonry. The strains measured in this way were used to calculate the deformation modulus and the Poissons ratio of the masonry. While testing the specimens, the mortar compressive strength was checked. Its mean value was 9,9 MPa. The tests showed that the masonry compressive strength ranged between 8,4 and 11,1 MPa, and its value averaged over strengths obtained for five specimens was equal to σ ult = 9,3 MPa. Averaged curves for strains, secant deformation modulus, and Poissons ratio of the masonry are presented in Fig 1. à) 0 0,2 0,4 0,6 0,8 1  50  25 0 25 50 75 100 125 ε ×10 5 s/s ult longitudinal strain lateral strain elongation shortening b) 0 0,1 0,2 0,3 0,4 0,5 0,6 7500 10000 12500 15000 17500 E sec , MPa s/s ult c) 0 0,1 0,2 0,3 0,4 0,5 0,6 0,00 0,05 0,10 0,15 0,20 0,25 Poisson's ratio s/s ult Fig 1. Dependences of strains ∑∑ ∑∑ ∑, secant deformation modulus E sec , and Poissons ratio upon stress level for masonry under axial short-term compression The initial modulus of elasticity of the masonry is computed according to [7] using the following logarith- mic stress-strain relation proposed by L. I. Onistchik:         −−= ult ult E µσ σ µσ ε 1ln 0 , (1) where: σ is the mean compressive stress in the test specimens; ∑ is the mean experimental value of strains obtained under stress σ; µ is the plasticity coefficient depending on the masonry type. The value of the masonry initial modulus of elasticity computed in this way is equal to 11 290 MPa. 3. Response to shear Shear tests were performed on six wall panels that were produced of the masonry with the chain bond. The overall dimensions of the specimens were as follows: length 1500 mm, height 1500 mm, thickness 120 mm, with the thickness of mortar joints of 10 to 12 mm. Af- ter manufacture the specimens were stored under poly- ethylene until the mortar has hardened (not less than 3 days). The tests were carried out at an age of the specimens 19 to 25 days (after the mortar achieved the compressive strength of 10 MPa). The test specimens were divided into two series (Fig 2). The specimens of the first series (series 1A) were tested for incremental lateral load P, applied to the top of the panel in its plane, combined with minimal vertical pressure that was necessary to prevent in-plane rotation of the wall. The vertical pressure was produced by spring kinematic restraints on the wall top and varied during loading so that detachment of the wall bottom from the floor was not greater than 5 cm. Displacement transducers (LVDTs) were installed along the wall height to measure lateral deflections during loading (Fig 2). In addition, displacement transducers were used to measure translation of the horizontal support and detachment caused by a compliantly re- strained rotation of the wall in its plane. Their readings were taken into account for calculation of the clear lateral deflections by correcting the values obtained by LVDTs Th1Th5. Unlike the first type specimens, specimens of the series 1B were loaded, in addition to the lateral load P, with a vertical uniformly distributed load q equal to 0,2F k = 225 kN/m, where F k is the ultimate failure load in the pure compression case. This load did not vary during the testing. The load P was applied to four top rows of bricks, and displacements were measured only at one level (at a height of 1450 mm from the wall bottom). The test showed that specimens of the series 1A collapsed immediately after a zigzag crack has appeared 5 5 P. Aliawdin, et al / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT  2004, Vol X, Suppl 1, 39 a) Test series 1A (three specimens) b) Test series 1B (three specimens) Fig 2. Shear test setup along the wall diagonal connecting the lateral loading point and the horizontal support (Fig 3, a). The failure lateral load was equal to: 120,0 kN for the first specimen, 113,8 kN for the second specimen, and 80,0 kN for the third one. Therefore, the failure lateral load averaged over three these values was P ult = 104,6 kN. At the ultimate stage, average total value of the compressive load q was equal to 118 kN. Experimental graphs showing the deforming process of the series 1A specimens are presented in Fig 4. The walls of the series 1B having been tested for combined shear and compression failed also with an in- clined crack connecting the lateral loading point and the horizontal support. However, in this case some vertical a) Series 1A (P ult =104,6 kN) b) Series 1B (P ult =192,6 kN) Fig 3. Crack patterns after testing (general views and local failure at horizontal support) cracks were observed, and a local failure at the horizontal support was clearer (Fig 3, b). The ultimate failure lateral load was equal to: 200,0 kN for the first specimen, 207,7 kN for the second specimen, and 170,0 kN for the third one. The failure lateral load averaged over three the values was P ult = 192,6 kN.  LVDTs 6 6 a) 0 50 100 150 0 5 10 15 20 25 Lateral displacement, mm Wall height, cm P/Pult=0,10 P/Pult=0,29 P/Pult=0,48 P/Pult=0,67 b) Fig 4. Lateral deflections for the series 1A specimens: a) distribution of displacements along the wall height; b) loaddisplacement relationships The lateral load-displacement relationship averaged over results of three tests of the series 1B is shown in Fig 5. 0 0,2 0,4 0,6 0,8 1 0 0,5 1 1,5 2 2,5 Lateral displacement, mm (h=1450 mm) P/P ult Fig 5. Lateral deflections for the series 1B specimens Comparing the graphs presented in Figs 4 and 5 we can notice that in-plane shear behaviour of the series 1B specimens was more plastic than the behaviour of the series 1A specimens which deformed almost elastically up to the failure (excepting a displacement leap observed at the second loading stage) and collapsed in a brittle mode. Indeed, in the series 1A specimens the cracks were not observed up to the failure, but cracks in the series 1B specimens appeared under the lateral load equal to 0,3 to 0,4 of the ultimate load. However, the specimens of the series 1A had a much lower rigidity than those of the other test series. Their failure occurred at lateral deflections that were an order of magnitude higher than ultimate deflections of the series 1B specimens. More- 0 0,2 0,4 0,6 0,8 0 5 10 15 20 25 Lateral displacement, mm P/ P ult h=850 mm h=1150 mm h=1450 mm over, the compressive action on the masonry walls re- sulted in 84 % increase of the load-carrying capacity of the walls under lateral loading. Therefore, the effect of vertical compression leads to a higher resistance of the masonry walls to shear loads, making their rigidity and load-carrying capacity higher. Behaviour of the test specimens is modelled on the finite element basis using Software Stark_Es of the MicroFE family. The wall panels are modelled with highly accurate hybrid plane stress elements (mesh 30x30) derived using a Reissner functional [8]. Second order geometrical effects and unilateral elastic supports are taken into account. As an example, Fig 6 shows some analysis results for the specimens of series 1A. a) Deformed scheme b) Distribution of vertical normal stresses σ z along the wall length at a level of a half of the wall height Wall length, m Fig 6. Finite element analysis results for wall panels of series 1A (under P = 104,6 kN) The test results presented above enable to draw an experimental relationship between the shear strength and compressive stress rate in masonry. This relationship is presented in Fig 7. As we can see in Fig 6, the masonry shear strength depends almost linearly upon the compressive stress level. ó z , MPa 0 -0,40 -0,80 -1,20 -1,60 -2,00 -2,40 -2,80 -3,20 -3,60 -4,00 0,00 0,15 0,30 0,45 0,60 0,75 0,90 1,05 1,20 1,35 1,50 P. Aliawdin, et al / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT  2004, Vol X, Suppl 1, 39 7 7 0 0,2 0,4 0,6 0,8 1 1,2 1,4 0 0,5 1 1,5 2 2,5 3 Compressive stress, MPa Shear strength, MPa test EC6, eq. 3.3a EC6, eq. 3.3c Ðÿä4 mortar strength masonry strength Fig 7. Relationships between masonry shear strength and compressive stress level Hence we can propose the following empirical formula for approximate evaluation of the shear strength of masonry in a plane stress state for different levels of the compressive stresses: zultult σττ 28,0 0, += , (2) where: ult τ is the masonry shear strength; z σ is the mean compressive stress perpendicular to the shear plane; 0,ult τ is the initial masonry shear strength, under zero compressive stress. In equation (2), all magnitudes are in MPa. Equation (2) is valid for only the cases where the compressive stress ⌠ does not exceed 0,2 of the ultimate compressive strength. A similar relationship is given in Eurocode 6 [9] to compute the masonry shear strength depending on the compressive stress value. In our case, this strength should be determined using equation 3.3a [9] but its value must be not higher than a value computed by equation 3.3c [9]. A graphical representation of the values calculated by these equations for our cases is given in Fig 7. As can be seen, equation 3.3a overestimates the shear strength of masonry, but equation 3.3c provides a rather high safety margin for the masonry shear strength. 4. Response to local compression For local compression tests of masonry walls, six specimens were produced and stored analogously as de- scribed in the previous section. The test specimens were tested to collapse for concentrated vertical load P applied incrementally at a distance 650 mm (series 2A) and 350 mm (series 2B) from the wall edge, as shown in Fig 8. The bearing area was 10×12 = 120 cm 2 . Along the loading line on both sides of the specimens, displacement transducers (Tv, Fig 8) were installed at the middle height over a gauge length of 800 mm to measure mean vertical strains. The tests showed that the specimens of both series had the same failure mode  the failure was practically brittle with formation of a local failure zone under the bearing and a vertical crack along the loading line (Fig 9). a) Test series 2A (three specimens) b) Test series 2B (three specimens) Fig 8. Local compression test setup Fig 9. Failure pattern P. Aliawdin, et al / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT  2004, Vol X, Suppl 1, 39 8 8 Until the load reached the value P = 150 kN, the mean vertical strains increased with loading almost iden- tically for specimens of both series and had a slightly non-linear kind (Fig 10). However, further loading caused a deviation of the load-strain curve for series 2B from the direct line and from the curve shown by the series 2A specimens. After that, under the load 188 to 200 kN the failure of the series 2B specimens occurred. The mean value of the failure load for these specimens was 192,7 kN. The series 2A specimens showed a higher load- bearing capacity equal to 220 to 256 kN with the mean value of 234,7 kN. 0 50 100 150 200 0 5 10 15 20 25 30 ε x10 5 2 , kN series 2A series 2B Fig 10. Experimental load-strain curves At the failure moment, the mean value of the mid height vertical strain was 5 1050 ⋅ and 5 1035 ⋅ for specimens of the series 2A and 2B respectively. As can be seen from Fig 1a, such strains correspond to compressive stresses not exceeding a half of the ultimate strength of masonry in pure axial compression. Thus the failure of the specimens was local below the loaded area. The results presented enable to evaluate the effect of increase of the masonry resistance to concentrated compressive loads as compared with overall axial compression case. Table 2 presents values of the enhancement factor for concentrated loads obtained experimentally and calculated according to different building codes. Table 2. Local compression effect Enhancement factor for concentrated compressive loads Test series test SNiP [10] EC6 [9], PN [11] 2A 2,1 1,5 1,45 2B 1,7 1,5 1,35 As we can see from Table 2, all design codes pro- vide a rather high safety margin for the compressive strength of masonry subjected to concentrated loads. In addition, Russian code [10] defines the same enhancement factor for both the test series and, in contrast to Eurocode 6 [9] and Polish code [11], does not take into account changes of the masonry local compressive strength depending on the wall height. The ultimate stage of the wall behaviour is modelled on the basis of the finite element method using Software Stark_Es. Results of the analysis are given in Fig 11. The analysis shows that for specimens of the different series under the ultimate failure load the maximum compressive stresses below the loaded area (ó z ) have the same ratio as the loads applied. However, calculated tensile stresses in the orthogonal direction (ó x ), which have caused the vertical crack formation in the test specimens, in the series 2B specimens are 1,25 times greater than in the series 2A specimens even under a smaller load. This indicates that in the series 2B specimens local compression (casing-type) effect is not so significant than in the other series specimens. This fact is affirmed by the kind of deformation distribution in the vicinity of the loaded area  in the series 2A specimens the effective area is greater than in the other specimens. From the deformed shape presented in Fig 11 we can assume that the effec- Fig 11. Results of finite element analysis (displacement scale 200:1) b) Series 2B a) Series 2A P. Aliawdin, et al / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT  2004, Vol X, Suppl 1, 39 9 9 tive area includes wall parts of 250 mm length for the series 2A specimens and 200 mm for the series 2B specimens to both sides from the loaded area (but not 120 mm as adopted in code [10] for both our cases). In this case, the enhancement factor calculated by Eq (19) given in [10] would be equal to 1,82 and 1,71 for specimens of the first and the second series respectively. These values are much closer to the experimental ones than those calculated according to [10]. Therefore, the masonry resistance to concentrated compressive loads can be evaluated sufficiently accurate by the finite element analysis. 5. Conclusions 1. Large-scale tests carried out on masonry wall panels subjected to in-plane lateral (shear) loading combined with different levels of axial compression show that: • Behaviour of masonry wall panels subjected to pure shear is almost perfectly elastic, the failure occurs in a brittle mode. Compressive load affects the shear behaviour of the masonry making it plastic. • Shear capacity of masonry walls increases by about 80 % due to the action of axial compressive load equal to 20 % of the ultimate compressive strength; the lateral rigidity of such walls can be of an order of magnitude higher as compared with the walls under pure shear. 2. Local compression tests of masonry walls show that resistance of masonry to concentrated compressive load depends significantly on the distance from the wall edge to the load position even if this distance 2,5 times greater than the wall thickness. This fact is not taken into account in SNiP II-22-81 [10]. A finite element analysis can be used for strength evaluation for masonry subjected to concentrated loads. Acknowledgement. The authors are pleased to acknowl- edge the support of INTAS under international project 00-0600. References 1. Bull, J. W. Computational modelling of masonry, brick- work and blockwork structures. Saxee-Coburg Publications, 2001. 346 p. 2. Hendry, A. W. Structural masonry. London: Mac-Millan Education Ltd, 1990. 284 p. 3. Majewski, S.; Szojda, L. Numerical analysis of a masonry structure. Engineering and construction, 2002, No 10, p. 578581 (in Polish). 4. Orùowicz, R.; Maùyszko, L. Masonry structures. Cracks and their elimination. Olsztyn: Wydawnictwo Uniwersytetu Warmiñsko-Mazurskiego, 2000. 152 p. (in Polish). 5. Kubica, J.; Drobiec, Ù.; Jasiñski, R. Study of secant deformation modulus of masonry. In: Proceedings of XLV Scientific Conference KILiW PAN i KN PZITB. Wrocùaw- Krynica, 1999, p. 133140 (in Polish). 6. BRITISH STANDARD BS 3921: Specifications for clay bricks. London: British Standards Institution, 2001. 22 p. 7. Sementsov, S. A. On the method of selection of logarith- mic stress-strain relation using test data. In: Strength and stability of large-panel structures, Vol 15. Moscow: Gosstroyizdat, 1962, p. 303309 (in Russian). 8. Semenov, V. A.; Semenov, P. J. Highly accurate finite elements and their use in software MicroFE. Residential Construction, 1998, No 8, p. 1822 (in Russian). 9. prEN 1996-1-1: Redraft 9A. Eurocode 6: Design of masonry structures  Part 1-1: Common rules for reinforced and unreinforced masonry structures.  European Commit- tee for Standardization, 2001. 123 p. 10. SNiP II-22-81. Masonry and reinforced masonry structures. Design Code. (ÑÍèÏ II-22-81. Moscow: Gosstroi USSR, 1983. 39 p. (in Russian). 11. PN-B-03002:1999. Masonry structures. Design and analysis. PKN, 1999. 67 p. (in Polish). P. Aliawdin, et al / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT  2004, Vol X, Suppl 1, 39 11 11 2004, Vol X, Suppl 1, 1118 JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT http:/www.vtu.lt/english/editions ISSN 13923730 FE SOFTWARE ATENA APPLICATIONS TO NON-LINEAR ANALYSIS OF RC BEAMS SUBJECTED TO HIGH TEMPERATURES Darius Bacinskas 1 , Gintaris Kaklauskas 2 , Edgaras Geda 3 Dept of Bridges and Special Structures, Vilnius Gediminas Technical University, Saulëtekio al 11, LT-10233 Vilnius-40, Lithuania. E-mail: 1 Darius.Bacinskas@st.vtu.lt, 2 Gintaris.Kaklauskas@st.vtu.lt, 3 egeda@salmija.lt Received 15 Apr 2004; accepted 23 Feb 2004 Abstract. Reinforced concrete structures subjected to fire will generally experience complex behaviour. This paper presents a strategy of numerical simulation of reinforced concrete members exposed to high temperatures and subjected to external loading. Finite element modelling of full load  deflection behaviour of experimental reinforced concrete beams reported in the literature has been carried out by the FE software ATENA. A constitutive model based on Eurocode 2 specifications has been used in the analysis. Comparison of numerical simulation and test results have shown reason- able accuracy. Keywords: reinforced concrete fire design, non-linear finite element analysis, fire tests, fire resistance, constitutive models of concrete and steel. 1. Introduction There are many buildings and civil engineering structures (tunnels, high-rise buildings, bridges and viaducts, containment shells, offshore platforms, airport runways etc.) under construction which are at risk of fire. A few dramatic accidents in recent years have prompted inves- tigations in the field of safety of reinforced concrete structures subjected to fire. Fires in railway Channel Tunnel (autumn 1996), in the road tunnels of Mont Blanc (France/Italy 1999), in the television tower of Ostankino (Moscow, 2000), in the Twin Towers (New York, 2001) should be mentioned [1]. In all cases, the load-bearing capacity of structure in the actual fire conditions is of primary importance for evacuation of persons and things, as well as for safety of rescue teams. The analysis of the behaviour of load-bearing members under high temperature conditions is very compli- cated [2, 3]. Various factors influencing the behaviour of members need to be taken into account, including: variation of member temperature with time, variation of temperature over the cross-section and along the member, temperature effects on material properties (expan- sion, creep, reduction in strength and stiffness, spalling, etc), material non-linearity, external restrains, section shape, etc. A parametric study of the influence of different factors on the behaviour of RC beams and frames is presented in [4]. Because of the no-linear nature of the problem, closed-form solutions usually cannot be found and an iterative approach is required [5]. The non-linear behaviour of a member under elevated temperature conditions can be simulated using the finite element method [6, 7]. Because of increasing interest in the field of structural fire protection, the number of existing software capable to analysing the thermal response of materials under transient heating conditions is quite large [8, 9]. The majority of these programmes was developed in professional software houses, such as DIANA [10], ATENA [11], ABAQUS, MSC.MARC, etc. Such programmes have many advantages including documentation, sophisticated non-linear material models, pre/post- processing facilities, etc. This paper presents a strategy of numerical simulation of reinforced concrete members exposed to high temperatures and subjected to external loading. Finite element modelling of full load  deflection behaviour of experimental reinforced concrete beams reported in [12] has been carried out by the FE software ATENA. A constitutive model based on Eurocode 2 specifications for fire design [13] has been used in the analysis. Compari- son of numerical simulation and test results has been carried out. 2. Reported fire tests of RC beams employed in the numerical analysis The present analysis employs experimental data [12] of reinforced concrete beams subjected to external loading and elevated temperatures. A total of 13 specimens were cast and tested. Except for TSB2-1, the other specimens were heated on three surfaces (the bottom and two [...]... X.; Tan T.-H.; Tan, K.-H and Guo, Z Effect of Force Temperature Paths on Behaviour of Reinforced Concrete Flexural Members Journal of Structural Engineering, Vol 128, No 3, March 2002, p 365373 Khoury, G A.; Anderberg, Y.; Both, K.; Felinger, J.; Majorana, C E and Hoj, N P Fire Design of Concrete: Materials, Structures and Modelling In: Proc of the 1st fib Congress Concrete Structures in 21st Century,... truss (Figs3, 4): dial gauges In.1 and In.4 for tensile member 16; In.2 and In.5for tensile member 511; In.3 and In.6for compressive struts 17 and 510, respectively Fig6 Kinetics of strain in steel web members of SN-1-1 (Figs3, 4) Tension members: 16 (T-9, T-10) and 511 (T-15, T-16); compression members: 17 (T-11, T-12) and 510 (T-13, T-14); 1, 2 strain of compression and tension members, respectively... (In.1) (a) and M1 (In.3 and In.4) (b) of SN-1-4 truss after failure 26 R ẩechaviốius / JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 2004, Vol X, Suppl 1, 2329 mm limit (the total loading F reached 86,6kN and 103,3kN, and F2 for one DS was equal to 24,5kN and 29,3kN, respectively It is clearly shown in Fig 7: the joint M6 (In.1) slip strains were very similar to those of the joint M1 (In 3 and In 4)... neglected Thus, the duration of thermal exposure between the FT and TF paths can be considered to be the same The specimens were 1300 mm long, 100 mm wide, and 180 mm deep, with a 10 mm concrete cover all round the section The specimens were cast in two batches of normal Portland cement (Standard grade China cement), natural river sand and crushed limestone with 15 mm maximum size The mean compressive... Concrete Structures Part 1: General Rules and Rules for Buildings European Committee for Standartisation, Brussels, Oct 2001 230 p Mutoh, A and Yamazaki, N Non-linear Analysis of Reinforced Concrete Members under High Temperature In: Proc of Conf DIANA Computational Mechanics94 Kluwer Academic Publishers, 1994, p 4555 17 Karihaloo, B L Fracture Mechanics and Structural Concrete Longman Scientific and Technical,... bars 17 and 510 under the loading of 80 kN (c = 86,64 MPa) and in the members in tension 16 and 511 under the loading of 110 kN (c= 121,46 MPa) were close to those calculated theoretically according to the experimentally defined pipe compressive (Et) and tensioned bars elasticity models: E c =2,10ã10 5 MPa, and Et=2,12ã105 MPa But from F=8590kN loading the growth of strains of compressed pipes and from... solution core and the user interface The solution core has got capabilities for the 2D and 3D analysis of continuum structures It has libraries of finite elements, material models and solution methods ATENA User Graphic Interface for 2D analysis is a programme, which enables access to the ATENA solution core It is limited to 2D graphical modelling and covers the state of plane stress, plain strain and rational... acknowledged 10 de Witte, F C and Wijtze, P K DIANA Finite Element Analysis Users Manual Release 8.1 Analysis Procedures TNO Building and Construction Research, Delft, 2002 580 p References 1 2 11 Cervenka, V and Cervenka, J ATENA Program Documentation Part 2 ATENA 2D User Manual Prague, 2002 138 p Felicetti, R.; Gambarova, P G and Meda, A Expertise and Assesment of Structures after Fire In: Report... Kurstjens, P B J Creep and damage research on timber joints Part two Rapport 25.4-89-15 C HD-24, StevinLaboratorium, Delft University of Technology, Netherlands, 1989 3 Blass, J H.; Ehlbeck, J and Schlager, M Characteristic strength of toothed-plate connector joints Holz als Rohund Werkstoff, 51, 1993, p 395399 7 13 Standard of Germany DIN 1052, Part 2: Timber structures design and construction (Deutsche... variables are height and width of stiffeners bsw and ssw1; positions of stiffeners, sw1 and sw2, and the number of the stiffeners The numbers and the dimensions of stiffeners on the bottom flange may be different from those on the Fig 6 Dimensions of the bottom flange The constraints can be classified into three categories: the geometrical constraints, the strength constraints and the fabrication constraints . Khoury, G. A.; Anderberg, Y.; Both, K.; Felinger, J.; Majorana, C. E. and Hoj, N. P. Fire Design of Concrete: Materials, Structures and Modelling. In: Proc. of the 1st fib Congress Concrete Structures. masonry structures  Part 1-1: Common rules for reinforced and unreinforced masonry structures.  European Commit- tee for Standardization, 2001. 123 p. 10. SNiP II-22-81. Masonry and reinforced. round the section. The specimens were cast in two batches of normal Portland cement (Standard grade China cement), natural river sand and crushed limestone with 15 mm maximum size. The mean compressive

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