The estimation of the critical load of a braced framework

1955 ◽  
Vol 231 (1184) ◽  
pp. 25-36 ◽  
Keyword(s):  
Critical Load ◽  
Critical Loads ◽  
The Other ◽  
Simple Criterion ◽  
Relaxation Methods ◽  
The Stability

With present methods of estimating the critical loads of triangulated frameworks by relaxation methods it is difficult to decide near the critical load whether the process is converging and the structure is stable, or whether the process is diverging and the structure unstable. This difficulty does not arise in the method presented here. Each triangle of the framework in turn is replaced by a hypothetical member until finally only one member of the truss remains, and this member has been modified in such a way as to take into account the stiffnesses of all the other members of the truss. A simple criterion for the stability of this final equivalent member is established and an example of the application of the method given.

CRITICAL LOADS OF SQUARE PLATES UNDER DIFFERENT INPLANE LOAD CONFIGURATIONS ON OPPOSITE EDGES

2001 ◽  
Vol 01 (02) ◽  
pp. 283-291 ◽  
Author(s):  
S. G. LEE ◽  
S. C. KIM ◽  
J. G. SONG
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stability Analysis ◽  
Critical Load ◽  
Critical Loads ◽  
Patch Load ◽  
Fixity Factor ◽  
The Stability ◽  
Opposite Tendency ◽  
Width Factor

The elastic critical load coefficients of square plates, under different inplane load configurations on opposite plate edges, are determined and the results compared. The stability analysis was performed by a finite element method that was developed by the authors. The parameters considered in the analysis are the Kinney's fixity factor, and the width factor of the patch load. It was found that the coefficients of the critical loads increase with increasing values of fixity and width factors. The opposite tendency is that a plate under a patch loaded towards the two corners of an edge is more stable than a plate loaded concentrically at the center of the edge.

Snapping of Low Pinned Arches on an Elastic Foundation

1973 ◽  
Vol 40 (3) ◽  
pp. 741-744 ◽  
Author(s):  
G. J. Simitses
Keyword(s):  
Critical Load ◽  
Elastic Foundation ◽  
Critical Loads ◽  
Entire Range ◽  
Buckling Load ◽  
Stability Studies ◽  
Deflection Curve ◽  
The Stability ◽  
Load Deflection Curve ◽  
Range Of Values

The problem of a low half-sine pinned arch under a quasi-statically applied half-sine load is considered. The low arch is resting on an elastic foundation. Critical loads are obtained by investigating the stability of the equilibrium positions by considering all possible modes of deformation. It is assumed that the behavior of the arch is linearly elastic up to the critical load. The entire range of values for the modulus of the foundation is considered. The results are presented graphically as either critical load (snap-through) or classical buckling load (stable bifurcation) versus the rise parameters for a large number of values of the modulus of foundations. This investigation presents an interesting model for stability studies, because, depending on the value of the rise parameter and the modulus of the foundation, the load-deflection curve exhibits the possibilities of the top-of-the-knee buckling, snap-through buckling through unstable bifurcation, and classical buckling (stable bifurcation).

Elastic Stability of Two-Span Continuous Beams under Moving Loads

2005 ◽  
Vol 8 (2) ◽  
pp. 157-172 ◽  
Author(s):  
Lei Zhang ◽  
Gengshu Tong
Keyword(s):  
Critical Load ◽  
Linear Approximation ◽  
Critical Loads ◽  
Elastic Stability ◽  
The Other ◽  
Moving Loads ◽  
Absolute Moment ◽  
Load Combination ◽  
Continuous Beams ◽  
Shear Centre

The elastic stability of two span continuous beams has been studied using FEA methods. Two formulae for estimating the critical loads are proposed, one is suitable for two-span beams with one span loaded, while the other is suitable for two-span beams with both spans equally loaded. Two identical concentrated loads symmetrically located about the mid-span of each loaded span were considered in the derivation of both formulae, and the effect of the height of loaded points for doubly symmetric beams was included. The formulae presented are also accurate enough in calculating the critical loads for two-span continuous beams with the mono-symmetric sections used in practice if the point of load application is at or above the shear centre. A linear approximation is suggested for the interaction of two spans when the two spans of the beam are not equally loaded. For a two-span continuous runway girder supporting moving cranes, the minimum critical load and the maximum absolute moment were investigated, some possible combination of wheel forces on beams considered, and approaches to calculating the critical load for each load combination are suggested when the girder has either one or two cranes moving along it.

scholarly journals Research on Voltage Stabilizing Control Strategy of Critical Load in Unplanned Island Based on Electric Spring

Electronics ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 80
Author(s):  
Hongjun Wang ◽  
Chunchao Song ◽  
Youjun Yue ◽  
Hui Zhao
Keyword(s):  
Critical Load ◽  
Control Strategy ◽  
Critical Loads ◽  
Control Mode ◽  
Experimental Simulation ◽  
Hybrid Microgrid ◽  
Stabilizing Control ◽  
Working Principle ◽  
Bus Voltage ◽  
The Stability

Aiming to solve the problem of voltage fluctuation of critical load caused by lack of control when an unplanned island occurs in a microgrid, a voltage stabilizing control strategy of critical load based on electric spring is proposed in this paper. When unplanned islanding occurs in a microgrid system, the system bus voltage fluctuates dramatically due to instantaneous power imbalance, compromising the power supply safety of important loads on the bus. In this paper, the electric spring control mode is integrated into the voltage stabilizing control strategy of critical loads in an unplanned island for the first time to realize the protection of critical loads. First of all, a model of an optical storage AC/DC hybrid microgrid is built, the overall system architecture is determined, and the microgrid is divided into four working states. Second, the working principle of electric spring is introduced, and a decoupling control strategy based on double closed loop is proposed. Finally, the experimental simulation of the proposed control strategy is experimentally simulated in Matlab/Simulink environment. The simulation findings show that when the bus voltage and current of microgrid change due to an unplanned island, the proposed control strategy based on electric spring may achieve the stability of voltage and current on critical loads.

The Approximate Elastic Critical Loads of Continuous Struts

1962 ◽  
Vol 66 (622) ◽  
pp. 652-654
Author(s):  
H. Waters
Keyword(s):  
Critical Load ◽  
Critical Loads ◽  
Axial Load ◽  
Simultaneous Equations ◽  
The Stability

The determination of the critical axial load of a strut having one or more intermediate supports and varying stiffness is made difficult by the highly transcendental nature of the simultaneous equations involved. It is therefore usual to make a test of the stability of the strut at some arbitrarily chosen load, as for example when applying the convergence technique. The behaviour of the strut then indicates whether the chosen load is too high or too low, and another load is selected and another test made. Although the true critical load is eventually reached, it is clear that if its value can be fairly closely approximated at the outset, then the labour of calculation will be greatly reduced.

Uniformity of Magnification from Different Electron Microscopes

1967 ◽  
Vol 25 ◽  
pp. 32-33
Author(s):  
Godfrey C. Hoskins ◽  
V. Williams ◽  
V. Allison
Keyword(s):  
Diffraction Grating ◽  
The Other ◽  
Carbon Replica ◽  
Electron Microscopes ◽  
The Stability

The method demonstrated is an adaptation of a proven procedure for accurately determining the magnification of light photomicrographs. Because of the stability of modern electrical lenses, the method is shown to be directly applicable for providing precise reproducibility of magnification in various models of electron microscopes.A readily recognizable area of a carbon replica of a crossed-line diffraction grating is used as a standard. The same area of the standard was photographed in Phillips EM 200, Hitachi HU-11B2, and RCA EMU 3F electron microscopes at taps representative of the range of magnification of each. Negatives from one microscope were selected as guides and printed at convenient magnifications; then negatives from each of the other microscopes were projected to register with these prints. By deferring measurement to the print rather than comparing negatives, correspondence of magnification of the specimen in the three microscopes could be brought to within 2%.

scholarly journals Black Hole Algorithm for Sustainable Design of Counterfort Retaining Walls

2020 ◽  
Vol 12 (7) ◽  
pp. 2767 ◽  
Author(s):  
Víctor Yepes ◽  
José V. Martí ◽  
José García
Keyword(s):  
Black Hole ◽  
Sustainable Design ◽  
Retaining Walls ◽  
The Other ◽  
Trade Off ◽  
Construction Company ◽  
Geometric Variables ◽  
The Stability ◽  
The Cost ◽  
Black Hole Algorithm

The optimization of the cost and CO 2 emissions in earth-retaining walls is of relevance, since these structures are often used in civil engineering. The optimization of costs is essential for the competitiveness of the construction company, and the optimization of emissions is relevant in the environmental impact of construction. To address the optimization, black hole metaheuristics were used, along with a discretization mechanism based on min–max normalization. The stability of the algorithm was evaluated with respect to the solutions obtained; the steel and concrete values obtained in both optimizations were analyzed. Additionally, the geometric variables of the structure were compared. Finally, the results obtained were compared with another algorithm that solved the problem. The results show that there is a trade-off between the use of steel and concrete. The solutions that minimize CO 2 emissions prefer the use of concrete instead of those that optimize the cost. On the other hand, when comparing the geometric variables, it is seen that most remain similar in both optimizations except for the distance between buttresses. When comparing with another algorithm, the results show a good performance in optimization using the black hole algorithm.

scholarly journals A Fractional SAIDR Model in the Frame of Atangana–Baleanu Derivative

2021 ◽  
Vol 5 (2) ◽  
pp. 32
Author(s):  
Esmehan Uçar ◽  
Sümeyra Uçar ◽  
Fırat Evirgen ◽  
Necati Özdemir
Keyword(s):  
Existence And Uniqueness ◽  
Laplace Transformation ◽  
Cell Phones ◽  
Mobile Network ◽  
The Other ◽  
Banach Fixed Point Theorem ◽  
Propagation Models ◽  
Computer Worms ◽  
Computer Viruses ◽  
The Stability

It is possible to produce mobile phone worms, which are computer viruses with the ability to command the running of cell phones by taking advantage of their flaws, to be transmitted from one device to the other with increasing numbers. In our day, one of the services to gain currency for circulating these malignant worms is SMS. The distinctions of computers from mobile devices render the existing propagation models of computer worms unable to start operating instantaneously in the mobile network, and this is particularly valid for the SMS framework. The susceptible–affected–infectious–suspended–recovered model with a classical derivative (abbreviated as SAIDR) was coined by Xiao et al., (2017) in order to correctly estimate the spread of worms by means of SMS. This study is the first to implement an Atangana–Baleanu (AB) derivative in association with the fractional SAIDR model, depending upon the SAIDR model. The existence and uniqueness of the drinking model solutions together with the stability analysis are shown through the Banach fixed point theorem. The special solution of the model is investigated using the Laplace transformation and then we present a set of numeric graphics by varying the fractional-order θ with the intention of showing the effectiveness of the fractional derivative.

scholarly journals Competing Conventions with Costly Information Acquisition

Games ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 53
Author(s):  
Roberto Rozzi
Keyword(s):  
Information Acquisition ◽  
Evolutionary Model ◽  
Equilibrium Selection ◽  
The Other ◽  
Group Interactions ◽  
Social Coordination ◽  
Long Run ◽  
Stochastic Stability Analysis ◽  
The Stability ◽  
The Cost

We consider an evolutionary model of social coordination in a 2 × 2 game where two groups of players prefer to coordinate on different actions. Players can pay a cost to learn their opponent’s group: if they pay it, they can condition their actions concerning the groups. We assess the stability of outcomes in the long run using stochastic stability analysis. We find that three elements matter for the equilibrium selection: the group size, the strength of preferences, and the information’s cost. If the cost is too high, players never learn the group of their opponents in the long run. If one group is stronger in preferences for its favorite action than the other, or its size is sufficiently large compared to the other group, every player plays that group’s favorite action. If both groups are strong enough in preferences, or if none of the groups’ sizes is large enough, players play their favorite actions and miscoordinate in inter-group interactions. Lower levels of the cost favor coordination. Indeed, when the cost is low, in inside-group interactions, players always coordinate on their favorite action, while in inter-group interactions, they coordinate on the favorite action of the group that is stronger in preferences or large enough.

A Biomechanical Evaluation of Three Forms of Internal Fixation Used in Ankle Arthrodesis

1994 ◽  
Vol 15 (6) ◽  
pp. 297-300 ◽  
Author(s):  
Michael P. Dohm ◽  
James B. Benjamin ◽  
Jeffrey Harrison ◽  
John A. Szivek
Keyword(s):  
Internal Fixation ◽  
Plate Fixation ◽  
Ankle Arthrodesis ◽  
Biomechanical Study ◽  
The Other ◽  
Fixation Failure ◽  
Plate Group ◽  
Biomechanical Evaluation ◽  
The Stability ◽  
Fibular Strut

A biomechanical study was undertaken to evaluate the relative stability of three types of internal fixation used for ankle arthrodesis. Crossed screw fixation, RAF fibular strut fixation, and T-plate fixation were tested in 30 cadaver ankles using an MTS machine. T-plate fixation consistantly provided the stiffest construct when compared with the other types of fixation. Failure occurred by distraction of bony surfaces, posterior to the plane of fixation, in the crossed screw and RAF groups. In contrast, failure in the T-plate group occurred through compression of bone anterior to the midcoronal plane of the tibia. Although the stability of fixation is only one factor in determining the success or failure of ankle arthrodesis, the results of this study would support T-plate fixation over the other forms tested.

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