A mindlin shell finite element for stone masonry bridges with backfill
Keywords:masonry arches, no tension joints, thick shell elements, octave script
Stone masonry bridges are difficult to analyse with commercial finite element (FE) packages for their specific heterogeneous composition. The stone arch is best modelled as a thick shell where there are predestined directions of tension failure, normal to the bed joints. A dedicated, very simple, Mindlin shell finite element is developed with five translational degrees of freedom per node. It features compatibility with linear isoparametric or constant strain elements for the backfill. Most bridges can be analysed with a sufficient accuracy assuming plain strain conditions. The element then simplifies to a Timoshenko beam element with three translational degrees of freedom per node. An application of the latter one to the bridge at Poniklá is presented.
The Highways Agency, London, www.highways.gov.uk. Design manual for roads and bridges, vol. 3, Highway structures: inspection and maintenance, section 4, Assessment, Part 3, The assessment of highway bridges and structures, 2001.
Ministry of transport of the Czech Republic. Zatížitelnost zděných klenbových mostů - Load rating of masonry arch bridges, 2008.
T. E. Ford, C. E. Augarde, S. S. Tuxford. Modelling masonry arch bridges using commercial finite element software. In Proceeding of the 9th International Conference on Civil and Structural Engineering Computing. Civil-Comp Press, Stirling, 2001.
Mott-MacDonald, 20-26 Wellesley road, Croydon, CR9 2UL, UK. CTAP manual for the assessment of masonry arch bridges, 1990.
R. Bridle, T. Hughes. An energy method for arch bridge analysis. Proceedings of the Institution of Civil Engineers 89:375–385, 1990. https://doi.org/10.1680/iicep.1990.9397.
M. Gilbert. RING: a 2D rigid block analysis program for masonry arch bridges. In Proceedings of the 3rd International Arch Bridges Conference, pp. 459–464. 2001.
W. Harvey. Application of the mechanism analysis to masonry arches. Structural engineer 66:77–84, 1988.
P.-O. Persson, G. Strang. Simple mesh generator in MATLAB. SIAM Review 46(2):329–345. https://doi.org/10.1137/S0036144503429121.
R. D. Mindlin. Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. ASME Journal of Applied Mechanics 18(1):31–38, 1951. https://doi.org/10.1115/1.4010217.
A. Pipard, R. Ashby. An experimental study of a voussoir arch. Proceedings of the Institution of Civil Engineers 10:383, 1938.
A. J. S. Pippard. The civil engineer in war, vol. 1, chap. The Approximate Estimation of Safe Loads on Masonry Bridges., pp. 365–372. 1948. https://doi.org/10.1680/ciwv1.45170.0021.
G. Lindberg, M. D. Olson, G. R. Cowper. New developments in the finite element analysis of shells, 1969. https://apps.dtic.mil/sti/pdfs/AD0707780.pdf.
W. Flugge. Stresses in shells. Springer Verlag, 1962.
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