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Bearing capacity of shallow foundations
Published in Hsai-Yang Fang, John L. Daniels, Introductory Geotechnical Engineering, 2017
Hsai-Yang Fang, John L. Daniels
In the solution of a solid mechanics problem, three basic conditions must be satisfied, namely (a) the stress equilibrium equations, (b) the stress–strain relations, and (c) the compatibility equations. The stress–strain (constitutive) relations have been discussed in Chapter 10. In an elastic-plastic material (Fig. 10.1), however, there is as a rule a three-stage development in a solution when the applied loads are gradually increased from zero to some magnitude. The complete solution by this approach is cumbersome for all but the simplest problems, and methods are needed to furnish the load-carrying capacity in a more direct manner (Chen and Davidson, 1973). Limit analysis is a method that enables a definite statement to be made about the collapse load without carrying out the step-by-step elastic-plastic analysis.
Evaluation of face stability with the consideration of seepage forces in shallow tunnels
Published in Jian Zhao, J. Nicholas Shirlaw, Rajan Krishnan, Tunnels and Underground Structures, 2017
The purpose of limit analysis is to estimate the stability conditions for a mechanical system regardless of the behavior of the material it is made of. The stability conditions for this system are derived in terms of the loads that can be applied to the system without causing its failure. There are two theorems in the limit analysis: one is the upper bound theorem and the other is the lower bound theorem. In the upper bound theorem, the loads for the stability of the system can be estimated by a kinematically admissible failure mechanism when the power of the loads applied to the system is larger than the power that can be dissipated within the system during its movement. On the other hand, in the lower bound theorem, any set of loads that satisfies equilibrium and yield criterion of the material within a stress field can be found. Leca and Dormieux (1990) used the limit analysis concept to evaluate the stability of a tunnel face driven in frictional soil and compared these results with centrifuge tests. A reasonable agreement was found between the theoretical upper bound estimates and the face pressures measured at failure from the tests. Therefore, the upper bound theorem has been adopted in this study for evaluation of the stability of a tunnel face.
Some Elastic-Plastic Problems
Published in Abdel-Rahman Ragab, Salah Eldin Bayoumi, Engineering Solid Mechanics, 2018
Abdel-Rahman Ragab, Salah Eldin Bayoumi
Limitations, however, have to be set on the structure, such that reloading must keep the total stresses, the residual added to the current service stresses, well within the elastic range. To meet this objective, two basic theorems are involved, namely, limit analysis and shakedown. Limit analysis is concerned with the determination of ultimate loads at which the structure undergoes unrestricted plastic flow, i.e., behaves like a mechanism. These limit loads or, say, collapse loads, have been determined in this chapter for several components, e.g., bent bars and plates, twisted bars, pressurized tubes, and rotating disks.
Stability evaluations of three-layered soil slopes based on extreme learning neural network
Published in Journal of the Chinese Institute of Engineers, 2020
An-Jui Li, Kelvin Lim, Abdoulie Fatty
Limit analysis method which produces solutions in terms of limit load can be based on either the kinematically admissible velocity field (upper bound) or the statically admissible stress field (lower bound). Due to the fact of the difficulty in computing the stress field in a slope, most of the studies in the literature are based on the upper bound method. Lyamin and Sloan (2002a, b) and Krabbenhoft et al. (2005) have overcome this issue with the recently developed upper and lower bound finite element limit analysis software, OptumG2 (Krabbenhoft, Lyamin, and Krabbenhoft 2015). The new formulation has been used to solve various geotechnical problems (Sloan 2013). So far, a number of stability charts for various types of slopes (including fill slopes) have been developed using the finite element limit analysis methods (Kim, Salgado, and Yu 1999; Li, Merifield, and Lyamin 2009, 2010; Qian et al. 2014; Lim, Li, and Lyamin 2015).
Seismic Assessment of the Lima Cathedral Bell Towers via Kinematic and Nonlinear Static Pushover Analyses
Published in International Journal of Architectural Heritage, 2020
Edoardo Rossi, Filippo Grande, Marco Faggella, Nicola Tarque, Adriana Scaletti, Rosario Gigliotti
A kinematic limit analysis is an approach aimed at identifying all the possible mechanisms which a part of a structure can be subject to, when stressed by a particular kind of action (seismic in our case). Based on the virtual work principle, it consists in the evaluation of a coefficient, which multiplies the actions, related to the activation of a particular mechanism. Limit analysis can be carried out according to two approaches: static and kinematic. The former provides a set of equilibrated actions, which are statically compatible, and evaluates a lower bound for the actions a structure can support. The latter, on the other hand, starts from the definition of a possible collapse mechanism. Then, through the application of the virtual work principle, calculates the actions that activate such mechanism, setting an upper bound. For more detailed information please refer to Augusti and Sinopoli (1992), Block, Ciblac, and Ochsendorf (2006), Como (2015), Gilbert and Melbourne (1994), Heyman (1966), Kooharian (1952), Lagomarsino and Cattari (2015), Livesley (1967), Milani, Lourenço, and Tralli (2007), Podestá (2012), and Vinci (2012). Equation (1) describes the calculation of a generic multiplier , , and , respectively, represent a generic force trying to activate the mechanism and the distance of such force with respect to the overturning point, while and are the force and distance of stabilizing actions. The mechanism corresponding to the smallest multiplier is the one that will, most likely, take place
Seismic performance of historical vaulted adobe constructions: a numerical case study from Yazd, Iran
Published in International Journal of Architectural Heritage, 2018
Neda H. Sadeghi, Daniel V. Oliveira, Mariana Correia, Hamed Azizi-Bondarabadi, Agustín Orduña
The main assumptions of the classic limit analysis approach are masonry material has zero tensile strength and infinite compressive strength, while sliding mechanisms cannot happen (Heyman 1982). Although limit analysis is not able to provide deformability information (e.g., the behavior curve), it predicts the load carrying capacity and the associated failure mechanism, which are critical for engineers in charge of safety assessment of structures. For further details about the well-known limit analysis theory, the reader is referred to Heyman (1997) and Orduña (2003).