Thesis presentation
- 1. THE FOUR-HINGE METHOD OF ANALYSIS OF MASONRY ARCHES STUDENT: PAVEL TROFIMOV D08118499 DT024/4
- 2. SUMMARY OF WORK CARRIED OUT I. Preliminary design Figure 3 Segmental masonry arch Figure 1 Force diagram Figure 2 Line of thrust Table 1 Stresses in the arch Due to self-weight fm.min = 0.035 (N/mm2 ) , Tension fm.max = 0.068 (N/mm2 ) , Compression Allowable ft.bond.MIN = 0.091 (N/mm2 ), Tension fm.k = 10.7 (N/mm2 ), Compression
- 3. SUMMARY OF WORK CARRIED OUT II. Theoretical analysis Results Model 1 (Unreinforced) P = 2.4 kN αB=64.97˚ βC=70.44˚ Model 2 (Reinforced) P = 68.4 kN αB=64.97˚ βC=57.39˚ Figure 6 Angles to hinges B&C Figure 5 Collapse load Model 2Figure 4 Collapse load Model 1
- 4. SUMMARY OF WORK CARRIED OUT III. Experimental Figure 7 Experimental setup Figure 8 Arch contruction Figure 9 Abutment model 2 Figure 11 Model 1 test setupFigure 10 Abutment model
- 5. PROJECT FINDINGS Figure 12 Failure mode, Model 1 Figure 13 Failure mode, Model 2 Table 2 Collapse load Name kN Model 1Exp. 9.58 Model 2Exp. 35.88 Model 1Theor. 2.36 Model 2Theor. 68.42 Figure 15 Tension zone Figure 16 Compression zoneFigure 14 Load vs. displacement
- 6. SUMMARY OF WORK CARRIED OUT IV. LUSAS Finite Element Analysis Applied actions: PMODEL 1 = 5.7 kN PMODEL 2 = 20.0 kN Figure 17 Isometric view, LUSAS model Figure 18 Maximum principal stresses (Model 2) Table 3 Stresses LUSAS vs. allowable, Compression ‘-‘, Tension ‘+’ Name N/mm2 ShearEpoxy ShearMasonry FlexureMasonry TensionSteel TensionEpoxy Model 1LUSAS 0.24 (B) 0.78 / -0.92 (B) Model 2LUSAS 2.91 (A-B) 0.84 (B) 2.70 / -3.50 (B) 8.99 (B) 0.01 (B) Allowable 2.03 1.82 0.091 / -10.7 154 0.12
- 7. PROJECT FINDINGS • The formation of four-hinge mechanism does not necessarily lead to ultimate collapse but rather to SLS failure in unreinforced masonry arches. • In masonry arches reinforced with the near surface reinforcement, as examined, it’s likely to get a failure via debonding of reinforcement. • Strengthening of the arch on the soffit with near surface reinforcement proves to provide a stiffer structure. It reduces deflections and, prevents crack formation and propogation. • This form of strenghtening of masonry arches proves to inefficient, as it difficult to utilize the tensile properties of reinforcement at the hinges where it expected to be in tension. • The four-hinge mechanism of failure is the mode of failure most likely to occur in the arch with a quarter-span point load, however, it has been shown in leterature that in 90% of the cases the presence of the fill responsible for the stability of the arch, thus it can result in a different mode of failure. • Based on the limited models tested, the method of analysis to predict the collapse load for masonry arches must be treated with caution as it heavily relies on the assumptions such as: abutments are rigid and the four-hinge mechanism of failure is the only mode of failure allowed to develop. Figure 19 Debonded reinforcement, tension zone. Figure 20 Debonded reinforcement, compression zone.
- 8. SUGGESTIONS FOR THE FUTURE RESEARCH • The assumptions that abutments are rigid must be strictly adhered to, this can be done by ensuring no rotation is allowed in the reaction frame e.g. by providing spikes welded to the reaction frame to prevent the rotation of concrete abutment inside the casing. • To investigate the behaviuor and the mode of failure of the arches further, presence of the fill must be considered. • Different method of reinforcing the arch may be concidered in aim to achieve a full composite action between steel and masonry. This can be done by cutting grooves in the masonry and embedding steel bars inside the grooves which can provide for a larger contact area between steel and brick. Also, mechanical ancors may be considered either insitu or drilled to hold the steel in place. • Provision of strain gauges on the reinforcing steel to record the stresses in the reinforcement during the testing. The attempt must be made to place the gauges where hinges are expected to form on the intrados. • Different finite element modelling techniques may by investigated to approximate the real structure. Finite element model to simulate the cracked section can give more accurate results on the behaviour of the arch under load. Figure 21 Abutment rotation.
- 9. THANK YOU
- 10. 772-1:2011, I. S. E. 2011. Methods of test for masonry units- Part 1: Determination of compressive strength. NSAI. 1015-11:2000, I. S. E. 2000. Methods of test for mortar for masonry-part 11: determination of flexural and compressive strength of hardened mortar. NSAI. 1992-1-1:2005, I. S. E. 2005. Eurocode 2: Design of concrete structures. NSAI. 1993-1-1:2005, B. E. 2005. Eurocode 3: Design of steel structures. BSI. 12390-3:2009, I. S. E. 2009. Testing hardened concrete-Part 3: Compressive strength of test specimens. NSAI. A.J., C. M. A. P. 1987. A mechanism program for computing the strength of masonry arch bridges. research report 124. Transport and road research laboratory. AMRHEIN, J. E. 1972. Masonry design manual, Masonry Industry Advancement Committee. BAKER, P. A. J. A. 1936. The Analysis of Engineering Structures. The voussoir Arch. Second Edition ed. London. BSI 2000. BSI Code of practice for the use of masonry-part2 : The structural use of reinforced and prestrerssed masonry. BS 5628-2:2000.2000. COLIN, C. 2011. Plastic Analysis. http://www.colincaprani.com/ CANCELLIERE, I., IMBIMBO, M. & SACCO, E. 2010. Experimental tests and numerical modelling of reinforced masonry arches. Engineering Structures, 32, 776-792. CHEN Y., A. A. F., GARRITTY S.W. 2006. Modified four-hinge mechanism method for masonry arches strengthened with near-surface reinforcement. Engineering Structures. COLIN, C. 2011. Virtual Work. http://www.colincaprani.com/ CURTIN, W. G., EASTERBROOK, D. & CURTINS CONSULTING ENGINEERS. 2006. Structural masonry designers' manual, Oxford ; Malden, MA, Blackwell Science. GERE, J. M. 2009. Mechanics of materials, London, Cengage Learning. HENDRY, A. W., SINHA, B. P. & DAVIES, S. R. Design of masonry structures, London, E. & F. N. Spoon. HEYMAN, J. 1995. The stone skeleton : structural engineering of masonry architecture, Cambridge, Cambridge University Press. HEYMAN, J. 1999. The science of structural engineering, London, Imperial College Press. HEYMAN, J. 2008. Basic structural theory, Cambridge ; New York, Cambridge University Press. KHARAB, A. & GUENTHER, R. B. 2006. An introduction to numerical methods : a MATLAB approach, Boca Raton, Fla. ; London, Chapman & Hall/CRC. LUSAS 2011a. 'Element Reference Manual'. LUSAS Version 14 ed. LUSAS 2011b. 'Introduction to LUSAS'. LUSAS Version 14 ed. LUSAS 2011c. 'Theory Manual'. LUSAS Version 14 ed. MELBOURNE, C. 1995. Arch bridges : proceedings of the First International Conference on Arch Bridges held at Bolton, UK on 3-6 September 1995, London, Thomas Telford. MOSS, R. 1995. Guidance for engineers conducting static load tests on building structures. BRE information paper. MOY, S. S. J. 1996. Plastic methods for steel and concrete structures, Basingstoke, Macmillan. PAGE, J. & TRANSPORT RESEARCH LABORATORY (GREAT BRITAIN) 1993. Masonry arch bridges, London, HMSO. TEYCHENNE, D. C., FRANKLIN, R. E., ERNTROY, H. C., MARSH, B. K. & BUILDING RESEARCH ESTABLISHMENT. 1997. Design of normal concrete mixes, Watford, Construction Research Communications. References