\r\nrepresent fundamental elements of buildings and bridges. Different

\r\nmethods are available for analysing the structural behaviour of

\r\nslabs. In the early ages of last century, the yield-line method has

\r\nbeen proposed to attempt to solve such problem. Simple geometry

\r\nproblems could easily be solved by using traditional hand analyses

\r\nwhich include plasticity theories. Nowadays, advanced finite element

\r\n(FE) analyses have mainly found their way into applications of

\r\nmany engineering fields due to the wide range of geometries to

\r\nwhich they can be applied. In such cases, the application of an

\r\nelastic or a plastic constitutive model would completely change the

\r\napproach of the analysis itself. Elastic methods are popular due to

\r\ntheir easy applicability to automated computations. However, elastic

\r\nanalyses are limited since they do not consider any aspect of the

\r\nmaterial behaviour beyond its yield limit, which turns to be an

\r\nessential aspect of RC structural performance. Furthermore, their

\r\napplicability to non-linear analysis for modeling plastic behaviour

\r\ngives very reliable results. Per contra, this type of analysis is

\r\ncomputationally quite expensive, i.e. not well suited for solving

\r\ndaily engineering problems. In the past years, many researchers have

\r\nworked on filling this gap between easy-to-implement elastic methods

\r\nand computationally complex plastic analyses. This paper aims at

\r\nproposing a numerical procedure, through which a pseudo-lower

\r\nbound solution, not violating the yield criterion, is achieved. The

\r\nadvantages of moment distribution are taken into account, hence the

\r\nincrease in strength provided by plastic behaviour is considered. The

\r\nlower bound solution is improved by detecting over-yielded moments,

\r\nwhich are used to artificially rule the moment distribution among

\r\nthe rest of the non-yielded elements. The proposed technique obeys

\r\nNielsen’s yield criterion. The outcome of this analysis provides a

\r\nsimple, yet accurate, and non-time-consuming tool of predicting the

\r\nlower-bound solution of the collapse load of RC slabs. By using

\r\nthis method, structural engineers can find the fracture patterns and

\r\nultimate load bearing capacity. The collapse triggering mechanism is

\r\nfound by detecting yield-lines. An application to the simple case of

\r\na square clamped slab is shown, and a good match was found with

\r\nthe exact values of collapse load.","references":"[1] Braestrup M.W., Yield-line theory and limit analysis of plates and slabs,\r\nMagazine of Concrete Research, 22, 99-106, 1970.\r\n[2] Code of Practice for Structural Use of Concrete, The Government of the\r\nHong Kong Special Administrative Region, 2013.\r\n[3] Calladine C.R. (2008), \u201dPlasticity for engineers\u201d, Hellis Horwood,\r\nChichister, UK.\r\n[4] Cook R.D., Malkus D.S., Plesha M.E., Witt R.J., Concepts and\r\napplications of Finite Element analysis, Wiley, fourth edition, 2002.\r\n[5] Gilbert M., He L., Pritchard T., \u201dThe yield-line method for concrete slabs:\r\nautomated at last\u201d, The Structural Engineer, 93, 44-48, 2015.\r\n[6] Ingerslev A. , \u201dThe strength of rectangular slabs\u201d, The Structural\r\nEngineer, 1, 3-14, 1923.\r\n[7] Jackson A.M., Middleton C.R., \u201dClosely correlating lower and upper\r\nbound plastic analysis of real slabs\u201d , The Structural Engineer, 91, 34-40,\r\n2013.\r\n[8] Johansen K.W., \u201dYield-line theory\u201d, London, UK: Cement and Concrete\r\nAssociation, 1962.\r\n[9] Mac Lane S., Birkhoff G. (1991) Algebra, American Mathematical\r\nSociety, p. 145, ISBN 0-8218-1646-2.\r\n[10] Mathworks, MATLAB R2012a, The MathWorks Inc., 2012.\r\n[11] Morley C.T., Yield criteria for elements of reinforced concrete slabs,\r\nIABSE, 1979.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 135, 2018"}