Limit Moment Research Articles

Numerical method for the primary torsional capacity of arbitrary steel cross sections considering nonlinear plastic behaviour

In structural design, plastic capacities of cross sections are of great importance for evaluating the capacity of steel members. Moreover, when it comes to problems of member stability, states of partial plasticisation are of interest as well. Depending on the cross section geometry and the material law to be considered, the determination can be challenging. This particularly applies to load conditions characterised by shear stress states, as for instance in the case of primary torsion (St. Venant's torsion). Simplifications are therefore often made with regard to the cross section geometry and engineering models are applied if the plastic limit moment of primary torsion Mpl,xp is to be determined. However, numerical methods allow a precise determination of properties and stress distributions of arbitrary cross section. In the present study, corresponding finite element formulations are combined with a plasticity algorithm for torsional analysis considering effects of nonlinear isotropic hardening. The approach approximates the nonlinear material law by a multilinear curve, which is stepwise evaluated based on linear hardening formulations. It allows determining states of partial cross section plasticisation for any strain or deformation state as well as the identification of the plastic limit capacity of the cross section. Results of the implemented algorithm are presented and verified for different common steel profiles showing excellent agreement to comparative studies.

Effect of Pad Thickness and Width Variations on Plastic Limit Moment in Cylindrical Pressure Vessels Due to Nozzle In-Plane Load

This study investigates how different pad thicknesses and diameters affect the maximum stress a cylindrical pressure vessel can handle without failing, particularly around the areas where nozzles are attached. Nozzles on these vessels often face directional stress from loads applied in a specific plane, and these stresses mustn’t push the nozzle material beyond its breaking point. The research used computer simulations to see how these vessels, with various pad sizes and a set shell and nozzle size, behave under increasing stress until they reach their breaking point. Findings indicate that making the pad thicker or wider increases the vessel’s resistance to breaking up to a certain point; beyond this optimal size, making the pad larger doesn’t provide any additional benefit. This information helps design better and safer pressure vessels by identifying the best pad size to prevent failure. The study contributes to understanding how to avoid design issues and optimize the construction of these vessels, adhering to specific industry standards.

Граничний стан армованих двошарнірних арок двотаврового перерізу

The method of determining the limit load for double-hinged arches is considered. The calculation is performed using the limit equilibrium method. The cross-section of the arch is taken in the form of a reinforced I-beam. The strain-deformed state of the I-beam material is described by the Prandtl diagram. But unlike the classical diagram, it has different yield points under tension and compression. The reinforcement material is described by the classic Prandtl diagram with the same yield strength in tension and compression.In most cases, the ultimate equilibrium of the cross-section is based on the use of one factor ˗ the plastic moment, upon reaching which the cross-section enters a plastic state with the possibility of unlimited deformation. But such an approach cannot be adopted for an arch, as significant longitudinal forces arise in its sections. Ignoring longitudinal forces leads to errors in determining the ultimate load. Therefore, for arches, when determining the limit state of the cross section, it is important to take into account both the bending moment and the longitudinal force. That is, for the transition of the section to the limit state, it is necessary to apply a limit moment to it, which corresponds to a certain longitudinal force. This leads to the concept of the region of cross-sectional strength, constructed in the coordinates of the bending moment - longitudinal force. The boundary of this region indicates the limit state of the cross-section and is described by the flow conditions, which can be obtained by considering the plastic equilibrium of the cross-section. Using the flow conditions, the equilibrium equation of the arch and some constraints, it is possible to formulate an optimization problem for finding the limit load. Limit load (objective function) is the smallest load that satisfies the arch equilibrium equation, yield conditions and constraints. The project variable is the coordinate of the cross-section that enters the plastic stage. The solution of this problem for arches of constant and variable stiffness was performed using electronic spreadsheets. Arch calculations were also performed in PC Lira-CAD. A comparison of the calculation results showed a satisfactory convergence.

Seismic combined bearing capacity of strip footings on partially saturated soils using lower bound theorem of finite element limit analysis and second-order cone programming

The seismic bearing capacity of strip footings resting on unsaturated soils subjected to combined loading is investigated in this study using a combination of lower bound limit analysis and finite element discretization. Second-order cone programming (SOCP) is used in this instance to simulate the nonlinear form of the universal perfectly-plastic Mohr-Coulomb yield criterion during the stress field optimization process. Under no-flow and steady-state infiltration/evaporation flow conditions, the significant influence of matric suction induced below the surface footing is accounted for using the suction stress concept. The load eccentricity and inclination applied to the footing and pseudo-static forces exerted simultaneously to the footing (superstructure) and underlying soil are all incorporated into the equilibrium equations, resulting in combinations of limit moment (M), and vertical (V), and shear (H) forces, under the influence of seismic loading. The results demonstrate that the matric suction induced within the porous structure of the underlying soil stratum increases the capacity of the surface footing to withstand various combinations of eccentric and inclined loadings under seismic excitation. Moreover, at a given hydraulic condition, the failure envelopes of obliquely/eccentrically loaded shallow foundations shrink significantly with the increase in the seismic intensity; the process which is more highlighted in sand (no-suction and all flow conditions). As the flow state in the unsaturated clay changes from infiltration to evaporation, the failure envelopes are observed to enlarge. In addition, as the load inclination angle reaches the soil-footing interface friction angle, the ultimate horizontal bearing capacity of the foundation resting on sand (no-suction) drops to zero; however, there still exists a residual shear resistance in the underlying clay layer or unsaturated sand, posing non-zero horizontal bearing capacity even at extremely high angles of inclination. Last but not least, the influence of earthquake horizontal loading on the bearing capacity envelopes of a shallow footing resting on a sand deposit was corroborated to be more pronounced than on a cohesive soil deposit. Indeed, the intrinsic (residual) cohesion, normally found in cohesive soils, was realized to contribute significantly to suppress the detrimental effect of earthquake horizontal loading.

Біодинаміка техніки поштовху штанги у важкоатлетів різної статі

The purpose of the study was to examine the biodynamics of the clean and jerk technique of the different gender athletes in weightlifting. Materials and methods. The following methods were used in the study: the study of scientific and methodological literature, Internet resources, pedagogical observations, video recordings of competitions, biomechanical analysis of the structure of the movement of the barbell, methods of mathematical statistics. More than 90 elite weightlifters participated in the research, in the conditions of competitive activity at the World, European and Ukrainian championships during the last ten years. Results and discussion. The analysis of the biodynamic characteristics of the barbell clean and jerk technique shows that the individual values of the force of interaction of athletes with the barbell in weightlifters of different genders and groups of weight categories have some differences: some of them increase with an increase in the body weight of athletes, others decrease, and some do not change, respectively. The biodynamic characteristics of the barbell clean and jerk in female weightlifters in terms of the force of interaction with the barbell have significant differences from the similar strength characteristics of male weightlifters. Tendencies were established to decrease simultaneously with the increase in weight categories of athletes in the magnitude of the force of interaction of athletes with the barbell at the limit moment between the phases of pre-acceleration and the transition phase, in the transition phase (in clean), in the phase of active braking and drive (in women in jerk). The level of force applied to the barbell in the phase of the catch in jerk does not change in all weight category groups of male athletes. A comparative analysis of the biodynamic components of the technique of performing the clean in the different gender weightlifters shows that they have significant differences in the level of manifestation of the force of interaction with the barbell. At the same time, female athletes have higher level of interaction with the barbell than male. Such a conclusion requires coaches to take into account these features during the development of biodynamic characteristics of the technique of performing competitive exercises by athletes of different genders and groups of weight categories, as well as during the process of improving the technique of motor actions. The analysis of the characteristics of the force of interaction with the barbell of different gender athletes in the jerk phases shows that female weightlifters in some phases of the movement apply a higher level of maximum force to the barbell than male athletes, and in others, its level of force is lower, despite of the fact that they lift a barbell of much less weight. Conclusion. Most of the biodynamic components of the technique of lifting the barbell in jerk are significantly higher in women than in men. The vast majority of biodynamic components of the jerk technique among athletes of groups 1-3 of weight categories have significant differences in the magnitude of the force of interaction with the barbell, including depending on the weightlifter’s gender

Joint convergence of sample cross-covariance matrices

Suppose $X$ and $Y$ are $p\times n$ matrices each with mean $0$, variance $1$ and where all moments of any order are uniformly bounded as $p,n \to \infty$. Moreover, the entries $(X_{ij}, Y_{ij})$ are independent across $i,j$ with a common correlation $\rho$. Let $C=n^{-1}XY^*$ be the sample cross-covariance matrix. We show that if $n, p\to \infty, p/n\to y\neq 0$, then $C$ converges in the algebraic sense and the limit moments depend only on $\rho$. Independent copies of such matrices with same $p$ but different $n$, say $\{n_l\}$, different correlations $\{\rho_l\}$, and different non-zero $y$'s, say $\{y_l\}$ also converge jointly and are asymptotically free. When $y=0$, the matrix $\sqrt{np^{-1}}(C-\rho I_p)$ converges to an elliptic variable with parameter $\rho^2$. In particular, this elliptic variable is circular when $\rho=0$ and is semi-circular when $\rho=1$. If we take independent $C_l$, then the matrices $\{\sqrt{n_lp^{-1}}(C_l-\rho_l I_p)\}$ converge jointly and are also asymptotically free. As a consequence, the limiting spectral distribution of any symmetric matrix polynomial exists and has compact support.

Limit state analysis of thin plates and slabs by a numerical pseudo-lower yield design approach

The prediction of failure load, collapse mechanism and moment distribution at limit state plays a crucial role in structural design. For plates and slabs, numerical lower bound solutions and associated limit moment distribution are rarely reported due to the difficulties in constructing moment-based plate elements used in the static formulation. In this paper, a novel numerical limit state analysis procedure, which uses pseudo-static theorem and conic programming, is developed. The total moment fields are decomposed into parts involving a fictitious elastic moment and a self-equilibrated residual moment. Equilibrium equations for the self-equilibrated residual moment field are satisfied in a weak sense by means of the displacement-based elements. Numerical solutions are obtained rapidly with the use of second-order cone programming. Various plates and slabs with arbitrary geometries and boundary conditions are examined, providing accurately estimated collapse load factors and the moment distribution at limit state.

When Time Is Out of Joint

I argue that the il y a is intrinsically connected to Levinas’s understanding of the tragic, and that Levinas offers an original reading of Shakespearean tragedy that goes beyond traditional aesthetic conceptions of artistic and tragic form and breaks with ancient tragedy. The il y a is implicated in the limit moment Levinas encountered while in captivity, suspended from the world, when time was out of joint. Focusing on Hamlet, who some have argued represents a failure of aesthetic form, I suggest rather that in construing Hamlet as the tragedy that constitutes a reflection on the meaning of the tragic il y a, Levinas identifies Shakespeare’s originality as a tragedian by pointing to the ungraspability of the formless. For Levinas, the tragic lies not in death but in having to be. Levinas’s incipient theory of Shakespearean tragedy provides insight into the complex role art plays for Levinas.

Micromechanical elastoplastic limit analysis of in-plane bending of Functionally Graded Pipe elbows

Pipe elbows, also known as pipe bends, are important components of a piping system. These curved elements are very flexible when compared to their straight counterparts, and are often responsible for reducing the reaction forces and moments within the piping system. However, due to large deformations, the elbows are more likely to exceed their stress limits. The effect of in-plane bending on plastic limit loads of Functionally Graded (FG) pipe bends is presented using three-dimensional non-linear finite element analysis and a micromechanical constitutive model. The effective properties of the material are estimated by the Mori–Tanaka homogenization scheme and the TTO plasticity model. The analysis was carried out for different loading cases, geometries and volume fraction distribution. The results showed that an FG elbow has a very distinct behavior comparatively to a similar homogeneous elbow made out of metal, specially in terms of limit moments and stress distribution. Finally, an analytical model to estimate the limit moment of FG elbows is presented.

수중 폭발에 의한 함체의 비탄성 휘핑 응답에 관한 연구

The primary effect of the far-field underwater explosion (UNDEX) is the whipping of the ship hull girder. This paper aims to verify why inelastic effects should be considered in the whipping response estimations from the UNDEX simulations. A navy ship was modeled using Timoshenko beam elements over the ship length uniformly keeping the constant midship section modulus. The transient UNDEX pressure was produced using two types of the Geers-Hunter doubly-asymptotic models: compressible and incompressible fluids. Because the UNDEX model based on incompressible fluid assumption provided more increased fluid volume acceleration in the bubble phase, the incompressible fluid-based UNDEX model was adopted for the inelastic whipping response analyses. The non-linear hull girder bending moment-curvature curve was used to embed inelastic effects in the UNDEX analyses where the Smith method was applied to derive the non-linear stiffness. We assumed two stand-off distances to see more apparent inelastic effects: 40.5 m and 35.5 m. In the case of the 35.5 m stand-off distance, there was a statistically significant inelastic effect in terms of the average of peak moments and the average exceeding proportional limit moments. For the conservative design of a naval ship under UNDEX, it is recommended to use incompressible fluid. In the viewpoint of cost-effective naval ship design, the inelastic effects should be taken into account.

Post-buckling optimization of bending-induced variable stiffness composite cylinders considering worst geometric imperfections

Variable stiffness (VS) composite cylinders have attracted much more attention in the aerospace industry, due to their significantly improved mechanical properties. Most of the existing studies on the optimization of VS composite cylinders are based on linear buckling analysis, without considering the imperfection sensitivity and ignoring the potential of the non-linear post-buckling bearing of cylindrical shells. Therefore, the imperfection sensitivity analysis of VS composite cylinders under bending load is performed in the non-linear post-buckling regime. It is illustrated that the optimized result based on the linear buckling analysis is not robust, if imperfections are taken into account. Moreover, an optimization framework considering imperfection sensitivity is established, wherein the Worst Multiple Perturbation Load Approach (WMPLA) is used to calculate the lower-bound limit moment of composite cylinders. The critical moment of the optimized result with the worst imperfections has an improvement of 13.81%, and the knockdown factor (KDF) is improved by 27.27%. It is demonstrated to be necessary to consider the imperfection sensitivity based on the non-linear post-buckling analysis during the optimization of VS composite cylinders, and the considerable performance with improved anti-imperfection ability can be realized by tailoring the fiber orientation of VS cylinders.

Remarks on the range and multiple range of a random walk up to the time of exit

We consider the scaling behavior of the range and p-multiple range, that is the number of points visited and the number of points visited exactly p≥1 times, of a simple random walk on ℤd, for dimensions d≥2, up to time of exit from a domain DN of the form DN=ND, where D⊂ℝd, as N↑∞. Recent papers have discussed connections of the range and related statistics with the Gaussian free field, identifying in particular that the distributional scaling limit for the range, in the case D is a cube in d≥3, is proportional to the exit time of Brownian motion. The purpose of this note is to give a concise, different argument that the scaled range and multiple range, in a general setting in d≥2, both weakly converge to proportional exit times of Brownian motion from D, and that the corresponding limit moments are “polyharmonic”, solving a hierarchy of Poisson equations.

A comparative study of shape imperfection and internal pressure effects on plastic, shakedown and elastic limit loads using large and small strain formulation of 90° pipe bends

The present work quantifies the effect of ovality and wall thinning on plastic, shakedown and elastic limit load of pipe bends under cyclic in-plane closing bending load and internal pressure. Three-dimensional finite element analyses with large strain (geometric nonlinear analysis) formulation was performed by considering the pipe bend material to be elastic-perfectly plastic. Plastic limit loads are determined from the plot of reaction moment versus angular rotation curve. Abdalla's simplified technique (ST) was used to calculate elastic and shakedown limit loads. The presence of ovality shows significant effect on plastic, shakedown and elastic limit loads and their boundaries for all the models. Thinning has minimal effect on plastic limit loads for large strain analysis while it has a remarkable effect on elastic and shakedown limit loads for ovality up to 5%. Experimental plastic limit moments in open literature was used to validate the present finite element (FE) plastic limit loads. Plastic, shakedown and elastic limit boundaries of large strain analysis or geometric non linear (GNL) analysis were compared with the respective boundaries of small strain analysis or Geometric linear (GL) analysis. Mathematical equations are formulated to express the generated limit moment boundaries for shape imperfect pipe bends.

Pure bending of pipe-in-pipe systems

Abstract Subsea pipelines and PIP systems experience large bending moments during installation and operation. However, unlike single-walled pipelines, the behaviour of PIPs under bending has been only marginally addressed. In the current study, the bending response of PIP systems with diameter-to-thickness ratio (D/t) of 15–40 is investigated. Linear bifurcation analyses (LBA) and geometrically nonlinear analyses (GNA) are conducted on PIPs of varying lengths. Analytical expressions are provided to predict the classical and nonlinear limit moments of PIPs, and are compared to existing expressions for single-walled pipelines. Ultimate bending moments of PIPs are obtained from physical four-point bending tests and are compared against geometrically and materially nonlinear analyses (GMNA). The finite element results show that in PIPs with centralizers, the limit moments (GNA) drop slightly, however, the ultimate moments (GMNA) remain unchanged. A parametric study of the effect of geometry and material properties of the inner and outer pipes on the ultimate moment of PIPs is presented. It is understood that the ultimate moments of PIPs with thick tubes are predominantly influenced by the material nonlinearities rather than ovalization of the tubes.

Determination of plastic, shakedown and elastic limit loads of 90°pressurized pipe bends with shape imperfections

This study determines the plastic, shakedown and elastic limit loads and the corresponding regimes of 90° pressurized pipe bends with shape imperfections subjected to cyclic in-plane closing bending moment. Three dimensional FE analyses with small strain formulation was performed. The induced shape imperfections are ovality and thinning, which were varied from 0% to 20% with a 5% increment at every step. Plastic limit load was determined from the moment rotation curve while shakedown and elastic limit loads were determined by using Abdalla's simplified technique (ST). The analysis indicates that the presence of ovality produces considerable effect on plastic limit loads. Thinning alters plastic limit loads only for long bend radius models with no ovality when normalised internal pressure ratio is unity and in other cases its effect is minimal. Presence of ovality and thinning has a remarkable effect on shakedown and elastic limit loads and their regimes though the thinning effect is insignificant at higher ovality (10%–20%). Bree diagram was constructed for the reference pipe bend models. It was observed that the failure of pipe bends is due to either reversed plasticity or ratcheting. Mathematical equations are proposed to express the generated plastic, shakedown and elastic limit moment boundaries for the analyzed pipe bend models.

Effect of wall thinning on the Shakedown Interaction Diagrams of 90-degree back-to-Back Bends Subjected to Simultaneous Steady Internal Pressures and Cyclic In Plane Bending Moments

This research studies the effect of wall thinning on generated shakedown (SD) interaction diagrams of pressurized low-carbon steel 90-degree (90-Deg) back-to-back (B2B) bends. More precisely, the SD limit moments are determined for various steady internal pressure spectra thus generating the targeted SD boundaries. The SD limit moments are computed utilizing a direct non-cyclic technique termed: SD-DNT short for Shakedown-Direct Noncyclic Technique. The bends analyzed are subjected to simultaneous steady internal pressure spectra and cyclic in-plane closing (IPC) and in-plane opening (IPO) bending moment modes discretely. The finite element (FE) method is utilized for solution and analyses. The wall thinning accounted for is solely due to service conditions. Different thinning locations are selected and analyzed along with different selected thinning percentages. The selected thinning locations within both bends include intrados, extrados, crowns, and both intrados and extrados once at a time. Thinning locations are analyzed for maximum selected thinning percentages of 30%, 50%, and 60%. Additionally, SD interaction diagrams of sound 90-Deg B2B bends are generated for comparisons. Outcomes of the SD-DNT are successfully validated against full elastic-plastic cyclic loading FE simulations. Outcomes of conducted analyses, generally, revealed that thinnings at crowns resulted in least combined cyclic moment-steady internal pressure capacities respectively followed by intrados, intrados and extrados, and finally extrados thinnings. Post-SD responses namely, alternating plasticity and ratcheting responses are accurately determined upon crossing the generated SD boundaries. Finally, an exemplary generated SD boundary is expressed in mathematical equation for selected analyzed thinned case.

Load carrying capacities of pressurized 90 degree miter and smooth bends subjected to monotonic in-plane and out-of-plane bending loadings

The present research focuses on generating interaction diagrams (i.e. limit moment boundaries vs steady internal pressure spectra) of pressurized 90o miter and smooth bends. One-, two-, three-, and four-weld miter bends are modelled and analyzed. Additionally, 90o smooth bends (SBs) bearing the miter bends’ same material and major geometric parameters are analyzed thus providing broader range of comparisons concerning structural responses to external applied loadings. All bends analyzed are subjected to steady internal pressure spectra and monotonic in-plane closing, in-plane opening, and out-of-plane bending moment modes discretely. The finite element (FE) method is utilized for solution and analyses. Limit load FE validation studies are initially conducted against experimental test outcomes of both miter and smooth bends subjected to different bending modes. Outcomes of conducted FE validation studies illustrated excellent correlation as compared to the experimental tests recordings. Interaction diagrams are successfully generated for pressurized miter and SBs possessing nominal pipe size (NPS) of 10 in. Schedule (SCH) 40 Standard (STD) and NPS 10 in. SCH 20 subjected to the three bending modes. The American Society of Mechanical Engineers (ASME) Twice-Elastic-Slope (TES) Method is adopted for computing limit moments. It is generally observed that the combined load carrying capabilities (moments-pressures) increase as the number of miter welds increases; however, SBs recorded considerably higher limit moments and broader internal pressure spectra. Finally, all generated limit moment boundaries are expressed in mathematical equations.

Asymptotic distributions of Wishart type products of random matrices

We study asymptotic distributions of large dimensional random matrices of the form $BB^{*}$, where $B$ is a product of $p$ rectangular random matrices, using free probability and combinatorics of colored labeled noncrossing partitions. These matrices are taken from the set of off-diagonal blocks of the family $\mathcal{Y}$ of independent Hermitian random matrices which are asymptotically free, asymptotically free against the family of deterministic diagonal matrices, and whose norms are uniformly bounded almost surely. This class includes unitarily invariant Hermitian random matrices with limit distributions given by compactly supported probability measures $\nu$ on the real line. We express the limit moments in terms of colored labeled noncrossing pair partitions, to which we assign weights depending on even free cumulants of $\nu$ and on asymptotic dimensions of blocks (Gaussianization). For products of $p$ independent blocks, we show that the limit moments are linear combinations of a new family of polynomials called generalized multivariate Fuss-Narayana polynomials. In turn, the product of two blocks of the same matrix leads to an example with rescaled Raney numbers.

Shakedown Limits for Hillside Nozzles in Cylindrical Vessels

This research paper is concerned with the mechanical behavior of the cylindrical vessels with hillside nozzles when subjected to both pressure and nozzle bending loads in cyclic forms. The influence of hillside angle on shakedown (SD) limits of the connection under cyclic pressure and combined steady pressure with cyclic nozzle bending is investigated. A shell finite element analysis model is built for the assembly using five different hillside angles ranging from 0 deg to 40 deg. Shakedown limits are determined by a direct technique known as the nonlinear superposition method (NSM). Bree diagrams for cyclic out of plane opening (OPO)/in plane (IP) nozzle moments combined with steady internal pressure are determined. The results show an increase in both OPO and IP shakedown moments as the hillside angle is increased. In addition, the OPO shakedown limit moments for all hillside angles were found to be insensitive to the level of internal pressure; this differs from the IP shakedown moment which starts to decrease with pressure for the high pressures.

O VOO DA SERPENTE E AS ASAS DA BORBOLETA: SOBRE DOIS POEMAS DE ROBERTO CORRÊA DOS SANTOS

Ao abordar dois poemas de Roberto Corrêa dos Santos, neste artigo, tenho como propósito analisá-los a partir dos conflitos ali refletidos e pautados por uma construção poética que, ao evocar o sagrado, adentra campos sociais e políticos, operando contra as forças coercitivas e elevando o canto à vida, mesmo vislumbrando momentos limites entre os afetos – que geram vida, que provocam morte.