Uniaxial compressive stress strain model for clay brick masonry

Transcription

1 Uniaxial copressive stress strain odel for clay brick asonry Heant B. Kaushik, Durgesh C. Rai* and Sudhir K. Jain Departent of Civil Engineering, Indian Institute of Technology Kanpur, Kanpur , India Material stress strain properties are required in the nonlinear analyses of structures. Stress strain relationships for soe construction aterials such as concrete and steel are available in the literature and design codes. However, such relationships are not easily available for one of the ost widely used construction aterial, i.e. asonry. In the present coprehensive experiental study, copressive stress strain relationships for asonry are deterined by testing 84 asonry pris speciens constructed using bricks fro four different anufacturers and three ortar grades. By regression analysis of experiental data, analytical expressions are proposed to estiate the odulus of elasticity of asonry. An analytical odel is proposed to adequately plot the stress strain curves for asonry using six control points on the curves. A siplified analytical odel is also proposed that can be conveniently used in finite eleent analysis progras. Keywords: Brick asonry, copressive strength, ortar, stress strain relations. BRICK asonry is a coon construction aterial in India because of its abundance, low cost, good sound and heat insulation properties, and availability of skilled labour. Masonry is extensively used in India as infill walls in reinforced concrete buildings. Analysis and design of buildings with asonry require aterial properties of asonry; for exaple, odulus of elasticity of asonry is required in the case of linear static analysis. Stress strain curves of asonry are required in the case of ore detailed nonlinear analyses such as static pushover analysis, which is being used quite frequently nowadays. However, stress strain curves of asonry are not available easily because of insufficient controlled experiental studies and significant geographical variation in aterial properties. Only a few experiental studies worldwide have proposed analytical relationships to plot the stress strain curves of asonry; however, these relationships are not easy to use because of the requireent of large aount of input data. Liited experiental research has been carried out in India to deterine the stress strain curves of asonry typically constructed in the Indian industry 1,2. In the present study, extensive experiental testing of brick *For correspondence. (e-ail: dcrai@iitk.ac.in) asonry priss is perfored to obtain the nonlinear stress strain curves of brick asonry. Further, siple analytical equations are developed by regression analysis of the experiental data to estiate the odulus of elasticity and to plot the stress strain curves for asonry. Experiental study In the present experiental study, 84 speciens of brick asonry priss (cobination of bricks anufactured by four local kilns, and three ortar grades) were tested to obtain stress strain curves for typical asonry used in the Indian construction industry. Hand-oulded burnt clay solid bricks were used in constructing asonry priss. The bricks were anufactured by four different anufacturers (designated as M, B, S, and O), and had approxiate length, width and height as 230, 110 and 75 respectively. Different grades of ortar (ceent : lie : sand by volue) used in the study were: 1 : 0 : 6 (weak), 1 : 0 : 3 (strong), and 1 : ½ : 4½ (interediate). Copressive load was applied in displaceent control on five brick high asonry priss using MTS servo-hydraulic actuator. Approxiate height of five-brick high asonry pris with 10 thick ortar joints was about Epsilon extensoeters were used to record the displaceent response across three ortar joints as shown in Figure 1 a. Load and displaceent easureents were recorded in real tie using a coputer-based data acquisition syste. General test set-up and typical failure odes of asonry priss are shown in Figure 1. The copression testing was perfored according to ASTM specifications 3, which are quite siilar to those given in the Indian asonry code (IS: ) 4. Stress strain curves obtained fro the experiental testing are shown in Figure 2, and a suary of the test results, including pris strength ( f ), failure strain, and odulus of elasticity of asonry (E ) is presented in Table 1. Mean copressive strengths of four types of bricks ( f b ), and three grades of ortar ( f j ) used in the study are also given in Table 1. Mean values of f were found to be 4.1, 7.5 and 6.6 MPa for priss constructed with weak, strong, and interediate ortar respectively, and ean ultiate strains at failure were , and for the three cases respectively. The Indian asonry code 4 specifies soe ultiplying factors to be used in CURRENT SCIENCE, VOL. 92, NO. 4, 25 FEBRUARY

2 Table 1. Suary of test results on clay brick asonry Brick type a f b (MPa) f j (MPa) f (MPa) Failure strain E (MPa) Priss with weak ortar 1 : 0 : 6 (4 7 speciens) M 17.7 (0.23) b 3.1 (0.22) 4.0 (0.13) (0.53) 2239 (0.30) B 16.1 (0.08) 2.9 (0.17) (0.45) 1795 (0.17) O 28.9 (0.23) 5.1 (0.16) (0.15) 2630 (0.14) S 20.6 (0.17) 4.3 (0.17) (0.14) 2355 (0.19) Average 20.8 (0.33) 4.1 (0.24) (0.43) 2300 (0.24) Priss with strong ortar 1 : 0:3 (4 7 speciens) M 17.7 (0.23) 20.6 (0.08) 7.4 (0.10) (0.28) 3585 (0.18) B 16.1 (0.08) 6.5 (0.14) (0.39) 3592 (0.25) O 28.9 (0.23) 8.5 (0.21) (0.36) 5219 (0.50) S 20.6 (0.17) 7.6 (0.17) (0.55) 4250 (0.44) Average 20.8 (0.33) 7.5 (0.18) (0.41) 4200 (0.38) Priss with interediate ortar 1 : 0.5 : 4.5 (4 7 speciens) M 17.7 (0.23) 15.2 (0.06) 6.5 (0.19) (0.17) 3542 (0.27) B 16.1 (0.08) 5.9 (0.23) (0.40) 3509 (0.49) O 28.9 (0.23) 7.2 (0.24) (0.32) 4712 (0.33) S 20.6 (0.17) 6.8 (0.23) (0.31) 3325 (0.26) Average 20.8 (0.33) 6.6 (0.20) (0.34) 3800 (0.35) a M, B, O, S are initials of four different brick anufacturers. Average water absorption of brick speciens was found to be 12.3% with coefficient of variation = b Figures in parentheses indicate coefficient of variation. Figure 2. Copressive stress strain curves for asonry. Figure 1. a, Test set-up for copression testing of asonry pris. b, c, Typical failure odes showing vertical splitting of speciens. 498 correcting the pris strength of asonry for height-tothickness ratio of pris lower than 5.0. For the present set of tests, this correction factor coes out to be about Generally, five-brick high asonry priss are tested to obtain the pris strength of asonry, and the correction factors are then used to arrive at copressive strength of asonry (or design strength of asonry) fro asonry pris strength (ASTM 3 ). Therefore, this factor has not been used in the present study, and the results presented here represent the true values as obtained in the tests. Masonry with weak ortar was found to be less stiffer than that constructed with the other two grades of ortar. Modulus of elasticity is calculated fro stress strain curves by easuring the slope of secant between ordinates corresponding to 5 and 33% of the ultiate strength of the speciens. Experiental results show that E can be directly correlated with f, and it was found that E CURRENT SCIENCE, VOL. 92, NO. 4, 25 FEBRUARY 2007

3 varies between 250 and 1100 ties f for the present dataset (Figure 3). A relatively good coefficient of correlation (C r = 0.63) was found between the experientally observed E values and those estiated using the following equation: E 550 f. (1) Therefore, it is recoended that for brick asonry used in the Indian construction industry, E ay be estiated as an average value of 550 ties f. Perforance of asonry with interediate ortar, which has lie content, was uch better than that of asonry with the other two ortar grades (Figure 2). Pris strength of asonry with interediate ortar was only about 13% lesser than that with strong ortar, while failure strain was about 50% ore. A significant iproveent in ductility of asonry was observed because of the presence of lie in the ortar, without any considerable reduction in its copressive strength. This shows that using lie in the ortar offers distinct structural advantages. Control points on stress strain curves of asonry Based on the liit states proposed in the literature 5, stress strain curves of asonry obtained in the present study are idealized using six control points, which correspond to six significant events on stress strain curves (Figure 4). The control points identified based on the results of the present tests are: f : Maxiu dependable copressive strength of asonry (on descending curve) f : Maxiu residual copressive stress in asonry (on descending curve). Strain values corresponding to these control points are shown in Figure 4. Strain readings corresponding to the control points 5 and 6 could not be recorded in case of priss constructed with weak ortar, because of brick ortar bond failure in ost of the speciens, and thus abrupt and brittle failure of the speciens. These idealized stress strain curves can be conveniently used in the analysis and design of asonry structures constructed with bricks and ortar of siilar aterial and strength. Analytical odel for stress strain curves of asonry Estiation of pris strength of asonry It is not always feasible to conduct copression testing of asonry priss to obtain the actual pris strength, which is the basic structural property for design of asonry. On the other hand, copressive strengths of bricks ( f b ) and ortar ( f j ) can be easily evaluated by the tests. In such cases, the following relation can be conveniently used to estiate f using f b and f j : α β b j, f = Kf f (2) f : Point up to which the stress strain curves reain linear f : Vertical splitting cracks in bricks start developing at about this stress f : Vertical splitting cracks in bricks propagate excessively throughout asonry. 4. f : Ultiate stress level in asonry (pris strength). Strain in pris for ortar grades Stress in ters of f 1:0:6 1 : 0 : 3 1 : 0.5 : Figure 3. Variation of odulus of elasticity of asonry with corresponding copressive strengths. Figure 4. Control points on stress strain curves of asonry. CURRENT SCIENCE, VOL. 92, NO. 4, 25 FEBRUARY

4 where K, α and β are constants. In eq. (2), α ust be higher than β because f is found to depend ore upon the strength of bricks used in asonry. Based on the experiental results of the present study, K, α, and β are obtained as 0.63, 0.49 and 0.32 respectively, by unconstrained regression analysis of eq. (2) using least-square fit ethod. Therefore, the following equation is proposed for estiating f : b f = 0.63 f f j ; (3) Standard error of estiate 0.48 MPa. A siilar equation with different values of the constants K, α and β was proposed by Dayaratna 6 for Indian bricks: b j f = f f ; (4) Standard error of estiate 2.2 MPa. Errors in estiation of f would be uch higher when eq. (4) is used, because of equal weightage given to the copressive strengths of bricks and ortar. On the contrary, eq. (3), proposed in the present study, predicts realistically the strength that agrees quite well with the experiental observations (Table 2). Therefore, eq. (3) is proposed for estiating f, which is further used here for developing stress strain curves for asonry. Estiation of peak strain of asonry Stress strain curves obtained in the present study indicate that the ascending part of the curve can be represented by a parabola, which has also been reported earlier The parabolic variation can be expressed in non-diensional for in ters of stress ratio and strain ratio as: Table 2. Coparison of asonry pris strength obtained by different sources Experiental value Analytical f (MPa) using f ε ε = 2, f ε ε 2 where f and ε are copressive stress and strain in asonry respectively, and ε is the peak strain corresponding to f. Based on the present experiental results, the parabolic curve is further extended in the descending part till f drops to 90%, after which the curve is siplified as a straight line till the residual stress in asonry is reached (0.2f ). The following equation is proposed in the present study to estiate ε by regression analysis of the experiental data, which provides a good fit to the experiental data: 0.27 f ε = ; Standard error of estiate f j E Equations (3), (5), and (6) can be easily used to plot the ascending part of the stress strain curve of the asonry up to {ε, f }, and then the parabolic curve can be extended in the descending part up to 0.9f, as shown in Figure 5. A linear descending part follows the parabolic part till {2ε, 0.2f } for ortar without any lie content, and till {2.75ε, 0.2f } for ortar with lie content. A higher failure strain value is proposed for asonry constructed with lie ortar, because lie is found to introduce flexibility in the asonry. Siplified tri-linear stress strain odel Generally, siplified, piece-wise linear stress strain curves are sufficient as an input in ost of the finite eleent coputer analysis progras. Based on the present study, siplified stress strain curves for asonry consisting of three continuous piece-wise linear segents are proposed here (Figure 6), which can be conveniently (5) (6) f b (MPa) f j (MPa) f (MPa) Present study Dayaratna (8) 2.0 (96) (22) 1.9 (49) (8) 2.6 (96) (8) 2.2 (96) (9) 5.3 (41) (0) 5.0 (30) (1) 6.7 (27) (4) 5.7 (34) (6) 4.5 (44) (0) 4.3 (37) (9) 5.8 (25) (3) 4.9 (40) Figures in parentheses indicate per cent error between experiental values and those obtained fro other sources. 500 Figure 5. Analytical odel for stress strain curves of asonry. CURRENT SCIENCE, VOL. 92, NO. 4, 25 FEBRUARY 2007

5 Figure 6. Siplified tri-linear stress strain odel for asonry. specified in coputer progras and finite eleent software for structural analysis. The first segent ends at 0.75f, and although soe nonlinearity was observed in the experiental curves at this stress level, the corresponding strain is considered as , assuing the linear behaviour. The second segent ends at f, with corresponding strain as 0.003, followed by the last segent which is continued until the residual stress in asonry (0.2f ) is reached. Strain corresponding to 0.2f is taken as for asonry constructed with ortar containing lie, and for asonry constructed using ortar without any lie content. Conclusion Uniaxial copressive testing of 84 asonry priss was conducted using four different bricks and three ortar grades. Based on experiental observations, odulus of elasticity of asonry is found to vary between 250 and 1100 ties the pris strength of asonry. An average value of 550 ties the pris strength is proposed in the present study. The copressive strength of asonry was found to increase with the copressive strength of bricks and ortar. The trend was ore proinent in case of asonry constructed with weaker ortar. Therefore, using a ortar grade of higher strength than required ay not always produce high-strength asonry. Masonry with lie ortar was found to undergo about 50% ore copressive deforation than that constructed using ortar without lie, while the reduction in copressive strength was only about 13% when lie ortar was used. Therefore, adding lie to ortar is a recoended practice in asonry construction. An analytical odel is developed to adequately replicate the experientally obtained asonry stress strain curves using six control points. The odel is general and quite convenient to use because the only input paraeters required are the copressive strengths of the bricks and ortar. Further, a siplified tri-linear stress strain odel for asonry is proposed, which can be easily specified in coputer progras and software for analysis of structures with asonry eleents. The results discussed in the present study ay be valid only for the North Indian brick industry. However, the proposed odels are generalized and ay be ipleented for other regions with slight odifications in input paraeters. Further experiental verification ay be required for extension of these results for bricks found in other regions, and ortar of different grades. 1. Sarangapani, G., Venkataraa Reddy, B. V. and Jagadish, K. S., Structural characteristics of bricks, ortar and asonry. J. Struct. Eng. (India), 2002, 29, Naraine, K. and Sinha, S. N., Behaviour of brick asonry under cyclic copressive loading. J. Constr. Eng. Manage., 1989, 115, ASTM C a, Standard test ethod for copressive strength of asonry priss. In Masonry Test Methods and Specifications for the Building Industry, Aerican Society for Testing and Materials (ASTM), Pennsylvania, 2001, 4th edn. 4. IS: , Indian standard code of practice for structural use of unreinforced asonry. In Bureau of Indian Standards (reaffired 1998), New Delhi, 3rd revision, Ewing, B. D. and Kowalsky, M. J., Copressive behaviour of unconfined and confined clay brick asonry. J. Struct. Eng., 2004, 130, Dayaratna, P., Brick and Reinforced Brick Structures, Oxford and IBH, New Delhi, Paulay, T. and Priestley, M. J. N., Seisic Design of Reinforced Concrete and Masonry Buildings, Wiley-Interscience, New York, Priestley, M. J. N. and Elder, D. M., Stress strain curves for unconfined and confined concrete asonry. ACI J., 1983, 80, Sawko, F. and Rouf, M. A., On the stiffness properties of asonry. Technical Note 381. Proc. Inst. Civil Eng., 1984, Part 2, vol. 77, pp Kent, D. C. and Park, R., Flexural ebers with confined concrete. J. Struct. Div., ASCE, 1971, 97, ACKNOWLEDGEMENTS. We acknowledge help extended by Dr K. K. Bajpai, Mr Ua Mahesh Reddy and staff of Structural Engineering Laboratory, IIT Kanpur while conducting the experients. Financial assistance provided by the Ministry of Huan Resource Developent, Governent of India is also acknowledged. Received 20 February 2006; revised accepted 12 October 2006 CURRENT SCIENCE, VOL. 92, NO. 4, 25 FEBRUARY