• Structural Engineering and Mechanics
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• v.33 no.2
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• pp.159-177
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• 2009

The aim of this paper is to give a rigorous framework for the interpretation of limit analysis results including large displacements. The presentation is oriented towards unidimensional media (beams) but two-dimensional (plates) or three-dimensional media are also concerned. A single-degree-of-freedom system is first considered: it shows the basic phenomena of large displacement limit analysis or second-order limit analysis. The results are compared to those of a continuous system and the differences between both systems are discussed. Theoretical results are obtained using the kinematical approach of limit analysis. An admissible load-displacement plane is then defined, according to the yield design theory. The methodology used is applied to frame structures. The presented results are nevertheless different from those already published in the literature, as the virtual displacement field can be distinguished from the displacement field at collapse. The simplicity of large displacement limit analysis makes it attractive for practical engineering applications. The load-displacement upper bound can be used for instance in the optimal design of steel frames in seismic areas.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.5
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• pp.524-531
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• 2004

To investigate relevance of the definition of the reference stress to estimate J and $C^{*}$ for surface crack problems, this paper compares FE J and $C^{*}$ results for surface cracked pipes with those estimated according to the reference stress approach using various definitions of the reference stress. Pipes with part circumferential inner surface crack and finite internal axial crack are considered, subject to internal pressure and global bending. The crack depth and aspect ratio are systematically varied. The reference stress is defined in four different ways using (i) the local limit load, (ii) the global limit load, (iii) the global limit load determined from the FE limit analysis, and (iv) the optimized reference load. It is found that the reference stress based on the local limit load gives overall excessively conservative estimates of J and $^{*}$. Use of the global limit load clearly reduces the conservatism, compared to that of the local limit load, although it can provide sometimes non-conservative estimates of J and $^{*}$. The use of the FE global limit load gives overall non-conservative estimates of J and $^{*}$. The reference stress based on the optimised reference load gives overall accurate estimates of J and $^{*}$, compared to other definitions of the reference stress. Based on the present finding, general guidance on the choice of the reference stress for surface crack problems is given.

• Structural Engineering and Mechanics
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• v.8 no.4
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• pp.421-438
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• 1999

In this paper a practical limit load estimating procedure is proposed for general pipe-elbow structures subjected to complex loading (in-plane and out-of-plane bending, internal pressure and axial force). The explicit calculating formulae are presented on the basis of theoretical analysis combined with numerical simulation. Von Mises' yield criterion is adopted in both analytical and numerical calculation. The finite element examination shows that the method provides a simple but satisfactory prediction of pipe structures in engineering plastic analysis.

• Computational Structural Engineering
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• v.8 no.1
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• pp.123-126
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• 1995

The purpose of the analysis is the numerical simulation of structures strained to the limit loads. The finite element calculations and experiments with cracked structures have been carried out yielding over limit strains between 10% and 15% by single peak load. Load versus displacement-diagrams and J-diagrams up to the limit load are calculated. By this way the influence of geometric parameters may be assessed in the post yield region. It is proposed to use such calculations to correlate experiments carried out with small specimens to experiments simulating the true dimensions of the design structure.

• Computers and Concrete
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• v.3 no.1
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• pp.1-15
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• 2006

The seismic safety of reinforced concrete containment building can be evaluated by probabilistic analysis considering randomness of earthquake, which is more rational than deterministic analysis. In the safety assessment of earthquake-resistant structures by the deterministic theory, it is not easy to consider the effects of random variables but the reliability theory and random vibration theory are useful to assess the seismic safety with considering random effects. The reliability assessment of reinforced concrete containment building subjected to earthquake load includes the structural analysis considering random variables such as load, resistance and analysis method, the definition of limit states and the reliability analysis. The reliability analysis procedure requires much time and labor and also needs to get the high confidence in results. In this study, random vibration analysis of containment building is performed with random variables as earthquake load, concrete compressive strength, modal damping ratio. The seismic responses of critical elements of structure are approximated at the most probable failure point by the response surface method. The response surface method helps to figure out the quantitative characteristics of structural response variability. And the limit state is defined as the failure surface of concrete under multi-axial stress, finally the limit state probability of failure can be obtained simply by first-order second moment method. The reliability analysis for the multiaxial strength limit state and the uniaxial strength limit state is performed and the results are compared with each other. This study concludes that the multiaxial failure criterion is a likely limit state to predict concrete failure strength under combined state of stresses and the reliability analysis results are compatible with the fact that the maximum compressive strength of concrete under biaxial compression state increases.

• Proceedings of the Korean Geotechical Society Conference
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• 2009.03a
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• pp.1113-1124
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• 2009

The limit equilibrium method and finite element method have been commonly used to assess the stability of anchored slope. However, the existing limit equilibrium methods do not consider the load transfer of anchor and, if the potential failure surface crosses the bonded zone of anchors, the anchor loads are not included in computing the factor of safety. In this paper, simplified bishop method, one among several methods based on the limit equilibrium is used to develope the Excel Sheet program and the working load of anchor along the failure surface is calculated by Flamant's formula, proposed by Morlier and Tenier(1982). Additionally, the finite element analysis of anchored slope considering the load transfer is performed in order to compare with the result from the limit equilibrium analysis and analyze the reinforced effect of anchor. From this study, new modelling method that limits the reinforcing range and considers the load transfer is proposed and Excel Sheet program is developed. The factor of safety for several cases between PC STABL and Excel Sheet program is also compared for verification of the program.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.12 s.243
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• pp.1605-1614
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• 2005

For the last four decades, tension test of notched bars has been performed to investigate the effect of stress triaxiality on ductile fracture. To quantify the effect of the notch radius on stress triaxiality, the Bridgman equation is typically used. However, recent works based on detailed finite element analysis have shown that the Bridgman equation is not correct, possibly due to his assumption that strain is constant in the necked ligament. Up to present, no systematic work has been performed on fully plastic stress fields for notched bars in tension. This paper presents fully plastic results for tension of notched bars and plates in plane strain, via finite element limit analysis. The notch radius is systematically varied, covering both un-cracked and cracked cases. Comparison of plastic limit loads with existing solutions shows that existing solutions are accurate for notched plates, but not for notched bars. Accordingly new limit load solutions are given for notched bars. Variations of stress triaxiality with the notch radius and depth are also given, which again indicates that the Bridgman solution for notched bars is not correct and inaccuracy depends on the notch radius and depth.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.5
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• pp.586-593
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• 2007

This paper proposes closed-form plastic limit load solutions for elbow with local wall thinning at extrados under internal pressure. This work was performed using 3-dimensional, small strain FE analyses based on elastic-perfectly plastic materials. The wide range of elbow and local wall thinning geometries are considered. For systematic analyses for effect of axial thinning extent on limit loads, two limiting cases are considered; a sufficiently long thinning, and the circumferential part-through surface crack. Then, the closed-form plastic limit load solutions for intermediate thinning are obtained by using result of two limiting cases. The effect of axial thinning extent for elbow on plastic limit load is highlighted by comparing with that for straight pipes. Although the proposed limit load solutions are developed for the case when local wall thinning exist in the center of elbow, it is also shown that they can be applied to the case when local wall thinning exists anywhere within elbow.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.9
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• pp.1469-1476
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• 2003

This paper provides plastic limit load solutions of cylinders with circumferential part-through surface cracks under combined axial tension, internal pressure and global bending. Such solutions are developed based on detailed three-dimensional (3-D) finite element (FE) limit analyses using elastic-perfectly-plastic material behaviour, together with analytical solutions based on equilibrium stress fields. For the crack location, both external and internal cracks are considered. Furthermore, in terms of the crack shape, both semi-elliptical and constant-depth surface cracks are considered. The resulting limit load solutions are given in a closed form, and thus can be easily used in practical situations. Being based on detailed 3-D FE limit analysis, the present solutions are believed to most reliable, and thus to be valuable information for integrity assessment of piping.

• Journal of the Korean Geotechnical Society
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• v.24 no.11
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• pp.55-60
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• 2008

This paper presents how the load transfer mechanism of the ground anchor affects on the stability analysis of anchored slope. The finite element analysis and the conventional limit equilibrium analysis on the anchored slope were performed and compared. The limit equilibrium analysis of the anchored slope is widely used in design practice due to the easiness of the analysis. However, the load transfer mechanism is not considered properly for the analysis. When the failure surface passes through the bonded length of an anchor, the anchor load is disregarded and the factor of safety for the anchored slope is smaller than it should be. In this study, the load transfer distribution was incorporated into the limit equilibrium stability analysis of the anchored slope and the results were compared with those of finite element analysis.