Papers by Keyword: Limit Analysis

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Authors: Andrea Bacigalupo, Andrea Cavicchi, Luigi Gambarotta
Abstract: The influence of the bond pattern on the in-plane limit strength of masonry is analyzed through a simplified procedure based on the application of the safe theorem of limit analysis to the unit cell that generates the whole masonry by periodic repetition. The limit strength domains of running bond, English bond and herringbone bond masonry are obtained with different orientations of the mortar bed joints with respect to the principal directions of the average stress. The effects of different brick geometries are analyzed and comparisons between strength properties of different masonry patterns are made.
Authors: J.P. Hambleton, Scott William Sloan
Abstract: The kinematic (upper bound) method of limit analysis is a powerful technique for evaluating rigorous bounds on limit loads that are often very close to the true limit load. While generalized computational techniques for two-dimensional (e.g., plane strain) problems are well established, methods applicable to three-dimensional problems are relatively underdeveloped and underutilized, due in large part to the cumbersome nature of the calculations for analytical solutions and the large computation times required for numerical approaches. This paper proposes a simple formulation for three-dimensional limit analysis that considers material obeying the Mohr-Coulomb yield condition and collapse mechanisms consisting of sliding rigid blocks separated by planar velocity discontinuities. A key advantage of the approach is its reliance on a minimal number of unknowns, can dramatically reduce processing time. The paper focuses specifically on tetrahedral blocks, although extension to alternative geometries is straightforward. For an arbitrary but fixed arrangement of blocks, the procedure for computing the unknown block velocities that yield the least upper bound is expressed as a second-order cone programming problem that can be easily solved using widely available optimization codes. The paper concludes with a simple example and remarks regarding extensions of the work.
Authors: Santiago Huerta, Paula Fuentes
Abstract: The Franciscan church of La Peregrina in Sahagún (Spain) was founded in the 13th Century. It has undergone many transformations and additions throughout its history. The most important were carried out in the 17th Century when the church was converted to the Baroque style. The apse vaults were demolished and new timbrel vaults were built hiding the Mudéjar windows. In the nave, the transverse arches that supported the modern roof were also demolished, internal counterforts were built and new barrel timbrel vaults with lunettes, erected. Eventually, an oval dome was built on the transept. Recent restoration work will give the building a new use. The project aims to recover the Mudéjar apse with its windows providing natural light to the presbytery. This involves the demolition of the Baroque vaults above the presbytery (a barrel vault terminated with a semi-dome). The oval dome will lose some buttressing to the side of the apse and an expertise was required to assess the feasibility of the operation. In the present paper the structure of the church will be described and the analysis of the oval dome with and without the presbytery vaults will be explained.
Authors: S.B. Yu, J.P. Hambleton, Scott William Sloan
Abstract: Anchors are widely used in foundation systems for structures requiring uplift resistance. As demonstrated by numerous theoretical and experimental studies on the subject, uncertainty remains as to both the theoretical uplift capacity of anchors in idealised soils and the suitability of the various modelling assumptions in capturing the responses observed during tests. This study, which deals exclusively with the theoretical uplift capacity, presents newly obtained predictions of uplift capacities and the corresponding collapse mechanisms for inclined strip anchors in sand. The analysis is based on the upper bound (kinematic) method of limit analysis and the so-called block set mechanism, in which a collapse mechanism consisting of sliding rigid blocks is optimised with respect to interior angles and edges of the blocks. It is demonstrated that the method provides lower (better) estimates of uplift capacity in some cases compared to previous upper bound calculations. Also, variations in the predicted collapse mechanism with changes in embedment and inclination are assessed in detail.
Authors: Egidio Rizzi, Giuseppe Cocchetti, Giada Colasante, Fabio Rusconi
Abstract: In this paper, an analytical and numerical analysis on the collapse mode of circular masonry arches is presented. Specific reference is made to the so-called Couplet-Heyman problem of finding the minimum thickness necessary for equilibrium of a masonry arch subjected to its own weight (Heyman 1977). The note reports the results of an on-going research project at the University of Bergamo. First, analytical solutions are derived in the spirit of limit analysis, according to the classical three Heyman hypotheses and explicitly obtained in terms of the unknown angular position of the intrados hinge at the haunch, the minimum thickness to radius ratio and the non-dimensional horizontal thrust (Colasante 2007, Cocchetti et al. 2010). Results are then compared to Heyman solution. Though only the first of these three characteristics is perceptibly influenced in engineering terms, especially at increasing opening angle of the arch, the treatment settles an important conceptual difference on the use of the true line of thrust, along the line of Milankovitch work. Second, numerical simulations by the Discrete Element Method (DEM) in a Discontinuous Deformation Analysis (DDA) computational environment are provided, to further support the validity of the obtained solutions, with good overall matching of the obtained results (Rusconi 2008, Rizzi et al. 2010).
Authors: Hong Wei Song, Hai Tao Wang
Abstract: One of the most popular pre-reinforcement structures in the construction of tunnels through weak grounds would be the pipe roof reinforcement. This composite structure consists on installing, prior to the excavation of a length of tunnel, a series of pipes, either parallel to the tunnel axis or at a certain angle with it. By injecting grout through the pipes, the ground in between the pipes is stiffened and the pipes are connected, creating a kind of ‘umbrella’ above the area to be excavated. In this paper, by modifying the upper bound solution for tunnel face stability, the three-dimensional model for expressing the tunnel face stability with pipe roof reinforcement was established. For a typical example, the solutions computed by the proposed approach were compared with the results given by wedge model, trapezoid wedge model and centrifugal-model test to verify the reasonability of the method. It is shown that the calculation results of limit analysis are in close agreement with test results.
Authors: Mario Como, Simona Coccia, Fabio di Carlo
Abstract: The determination of the seismic strength of masonry building is strictly connected to the in-plane strength of masonry walls under the action of horizontal forces. Simplified criteria are currently available in literature, based on modelling of the structure as loaded by dead loads and by a gradually increasing distribution of horizontal forces, proportional to the mass of the building. According to this approach, called push-over method, the seismic strength of the building corresponds to the intensity of these gradually increasing horizontal loads, leading the building to the failure condition. This paper moves in the framework of the Limit Analysis, based on the Heyman’s masonry model (1966), rigid in compression with no tensile strength. The resistant model refers to a multi-storey wall with openings arranged in regular patterns, along both vertical and horizontal directions, reinforced at floor levels by steel ties. The in-plane failure of the regular multi-storey walls can occur with the development of various kinematically admissible mechanisms, characterized by the attainment of the yielding state in the steel ties. The proposed methodology consists in the definition of the mechanism along which the failure effectively occurs and in a subsequent check of the statical admissibility of the internal stress state at the limit load. Only in this case, the corresponding kinematical multiplier is the effective collapse multiplier. The presence of the panels situated above the openings strongly conditions the in-plane failure of the wall, acting as diagonal struts, causing different horizontal displacements between the piers at the floor levels and consequently engaging the horizontal ties in the mechanism. In order to ensure the development of the global failure, avoiding local brittle failures, steel strengths of the ties have thus to be suitably defined. Finally, a parametric investigation is carried out considering different geometries of masonry walls and varying the position of the piers self-weights and the horizontal forces distribution, constant or proportional to the height of the masses from the foundation level.
Authors: Bo Yu, Lu Feng Yang
Abstract: An efficient elastic modulus adjustment procedure to evaluate lower-bound ultimate bearing capacity of spatial frame structures was proposed based on the strain energy equilibrium principle. Four strategies to determine the elastic modulus adjustment factor were developed based on the fixed strain method (FSM), circular arc method (CAM), strain energy conservation law (SECL) and strain energy equilibrium principle (SEEP). The precisions and convergent properties of above four strategies were quantitatively investigated through two numerical examples. The results show that the efficiency and accuracy of the SEEP are of most acceptable.
Authors: Ireneusz Markiewicz
Abstract: The paper presents a selected example of investigations, carried out by the author, on complex thin-walled structures [3] that were designed based on the method of statically admissible discontinuous stress fields (the SADSF method, [1,2,4,5]) with the condition of equalized effort in the limit state. The SADSF method is substantiated based on the conclusions that follow on the lower bound theorem of limit analysis, and is an approximate method. The aim of the investigations was practical verification of solutions of the SADSF method in elasto-plastic and elastic range of stress, because these ranges are not taken into account in the method. The existing application software of the SADSF method allows one to design very complex thin-walled structures which are free of cardinal errors. Moreover, the method can be easily used by practically any engineer.
Authors: Xiao Ming Tu, Yu You Yang, Gui He Wang
Abstract: With the development and utilization of underground space, some new tunnel forms are emerging, such as the rectangular tunnel, double tunnels, treble tunnels and so on. The aim of this paper is to determine the collapse face pressure of a rectangular tunnel driven by a pressurized shield. The calculation is based on the upper-bound method of the limit analysis theory. A translational kinematically admissible failure mechanism consists a sequence of truncated rigid cones are considered for the calculation schemes. The numerical results obtained by the calculation are presented.
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