Finite element lower bound “yield line” analysis of isotropic slabs using rotation-free elements

Abstract

A new lower bound finite element method for slab analysis is presented as a practical substitute to full, non-linear, finite element methods that require expert knowledge and long running times. The method provides a general, safe and efficient lower bound solution for the analysis of reinforced concrete slabs up to failure. As it is finite element based, the method is more general than the yield line and strip methods currently in use. Furthermore, its lower bound nature makes it safer than the yield line method. The method uses a rotation-free, plate finite element modified to allow plastic "yield lines" to pass through at any direction. Yield lines are generated at the principal moment directions when the plastic moment capacity is attained. The material is assumed to be elastic perfectly-plastic. Following the general spirit of yield line analysis, the effects of a yield line are projected to the sides of the triangular element and then used to calculate the bending curvatures. The method's efficiency is achieved by using rotation-free plate elements with a single degree of freedom per node and by the incremental solution that does not require iterations. The method's accuracy and convergence are assessed by comparing standard cases with known results. In all cases, results were close to the theoretical values with difference of less than 1%. It is also used to solve a practical sized flat slab problem in order to demonstrate the method's efficiency, convergence, and speed.

Analytical solution on highway U-shape bridges using isotropic plate theory

“…For this purpose a parametric study on both overall and local structural components (e.g., side girders or deck) needs to be fully conducted first. However, the inconvenience or even incorrectness was also obvious if still using the improper beam theory or time-consuming finite-element modeling as stated earlier (Keller and Schollmayer, 2004;Al-Sabah and Falter, 2013;Kadkhodayan and Maarefdoust, 2014). Therefore, a proper analytical solution for U-shape bridges no matter for study or design is urgently needed.…”

Rotation-free finite element ‘yield line’ analysis of non-isotropic slabs

“…To date, attempts to automate the strip method have been successful only for small problems (Burgoyne and Smith 2008;O'Dwyer and O'Brien 1998). In addition, the accuracy of the results is reduced if the actual slab failure pattern is not parallel to the strips; for more details see Al-Sabah and Falter (2013).…”

“…These results can be used to trace the non-linear load deflection of any node and moment distribution in the slab up to failure. The convergence criteria currently used in the computer program developed by the authors is related to the deflection of a selected point; for more details see Al-Sabah and Falter (2013).…”

“…To date, a generic approach to automatic yield line analysis has yet to be developed. A detailed review of the automation of yield line analysis is provided by Al-Sabah and Falter (2013).…”

Donja I Gornja Granica Opterećenja Pravougaonih I Kružnih Ploča

“…Примена методе горње границе је најраспрострањенија и у литератури је позната под називом теорија линије лома (yield line theory). Теорија линија лома дефинише горњу границу оптерећења и примену налази, осим код армиранобетонских плоча, и код веза у челику, челичних плоча и армиранобетонских зидова [2]. Последње две методе одређују интервал граничног оптерећења.…”