The effect of finite deformations in the elastic stability of plane frames

1962 ◽  
Vol 266 (1324) ◽  
pp. 47-67 ◽  
Keyword(s):  
Critical Load ◽  
Failure Load ◽  
Elastic Stability ◽  
Load Level ◽  
Load Factor ◽  
Proportional Loading ◽  
Arbitrary Load ◽  
Plane Frames ◽  
The Difference ◽  
Rigid Joints

The circumstances are discussed under which orthogonal relations exist between the elastic critical modes of plane frames subjected to proportional loading. Orthogonal relations may be obtained provided the loading does not produce any components of deformation associated with any of the critical modes at arbitrary levels of the load factor, and provided no part of the structure remains statically indeterminate due to bar forces when all rigid joints are replaced by pin joints. When at arbitrary load factors, the structure deforms with components associated with any of the buckling modes, the elastic failure load is not identical with the lowest elastic critical load, although for many frames the two loads may be very close. A general expression is obtained which reveals the relation between the deformations at an arbitrary load level and the deflexions given by linear analysis. The difference between the elastic failure load and the elastic critical load is discussed, and an approximate treatment applicable to certain types of frame and associated loading is developed.

Elastic-plastic failure loads of plane frames

1963 ◽  
Vol 274 (1358) ◽  
pp. 343-364 ◽  
Keyword(s):  
Failure Load ◽  
Load Factor ◽  
Proportional Loading ◽  
Rigid Plastic ◽  
Plastic Failure ◽  
Elastic Plastic ◽  
Plane Frames ◽  
Plane Frame ◽  
Failure Loads ◽  
Close Estimate

When deformations become finite, the load factor required to produce rigid-plastic deformation of a plane frame under proportional loading differs from the load factor at collapse as given by simple plastic theory. The effect of all work terms involving the squares of member rotations is investigated and a simple formula derived. The effect of finite deformations on the load capacities of elastic-plastic frames is then studied. It is shown theoretically that, if certain approximations are made, the Rankin© load, based on the rigid-plastic failure load and the lowest critical load, give a close estimate of the actual failure load of such a structure. The nature of the approximations made to arrive at this result shows under what circumstances the Rankine load cannot be expected to provide a close estimate of failure. Experimental and theoretical results illustrating the degree of correlation are presented and discussed.

The Further Exploration of Applying Small-Strain and Large-Strain Formulations to SMA

2012 ◽  
Vol 529 ◽  
pp. 228-235
Author(s):  
Jie Yao ◽  
Yong Hong Zhu
Keyword(s):  
Phase Transformation ◽  
Constitutive Model ◽  
Uniaxial Tension ◽  
Driving Force ◽  
Research Team ◽  
Large Strain ◽  
Small Deformation ◽  
Small Strain ◽  
Proportional Loading ◽  
The Difference

Recently, our research team has been considering to applying shape memory alloys (SMA) constitutive model to analyze the large and small deformation about the SMA materials because of the thermo-dynamics and phase transformation driving force. Accordingly, our team use simulations method to illustrate the characteristics of the model in large strain deformation and small strain deformation when different loading, uniaxial tension, and shear conditions involve in the situations. Furthermore, the simulation result unveils that the difference is nuance concerning the two method based on the uniaxial tension case, while the large deformation and the small deformation results have huge difference based on shear deformation case. This research gives the way to the further research about the constitutive model of SMA, especially in the multitiaxial non-proportional loading aspects.

Tribological properties of beef tallow as lubricating grease

2017 ◽  
Vol 69 (5) ◽  
pp. 645-654 ◽  
Author(s):  
Juozas Padgurskas ◽  
Raimundas Rukuiža ◽  
Ihor Mandziuk ◽  
Arturas Kupcinskas ◽  
Katerina Prisyazhna ◽  
...  
Keyword(s):  
Critical Load ◽  
Tribological Properties ◽  
Beef Tallow ◽  
Friction And Wear ◽  
Load Level ◽  
Synthesis Process ◽  
Polymer Additives ◽  
Lubricating Grease ◽  
Content Type ◽  
Thermally Processed

Purpose The purpose of this paper is to report on the tribological properties of beef tallow grease and improvements therein through modification with special processing, polymeric compounds and additives. Design/methodology/approach Pure original beef tallow grease was used as a biological lubricating grease reference material for the tribological research. Beef tallow was modified and synthesized by adding special biological anti-oxidant additives, LZ anti-wear additives, waste polyethylene terephthalate (PET) polymer compounds and thermally processed graphite. Findings Rheometric measurements indicate that the beef tallow grease modification technology used in this study enables control of the synthesis process to produce lubricants with the required microstructure. Investigation results of the tribological properties of differently modified greases show that beef tallow synthesized with polymer additives efficiently operates together with anti-wear additives to reduce friction and wear. The grease compound with thermally processed graphite has good tribological properties at 300 N load levels. The critical load level of lubricating greases could be significantly increased through the use of anti-wear additives and thermally processed graphite. Originality/value Investigation results of the tribological properties of differently modified beef tallow greases show that beef tallow synthesized with polymer additives efficiently operates together with anti-wear additives to reduce friction and wear. The critical load level of lubricating beef tallow greases could be significantly increased using anti-wear additives and thermally processed graphite.

scholarly journals Application of ANN to evaluate effective parameters affecting failure load and displacement of RC buildings

2009 ◽  
Vol 9 (3) ◽  
pp. 967-977 ◽  
Author(s):  
M. Hakan Arslan
Keyword(s):  
Failure Load ◽  
Back Propagation ◽  
Load Level ◽  
Effective Parameters ◽  
Rc Buildings ◽  
Building Stock ◽  
Capacity Curves ◽  
Rc Building ◽  
Failure Loads ◽  
Turkish Earthquake Code

Abstract. This study investigated the efficiency of an artificial neural network (ANN) in predicting and determining failure load and failure displacement of multi story reinforced concrete (RC) buildings. The study modeled a RC building with four stories and three bays, with a load bearing system composed of columns and beams. Non-linear static pushover analysis of the key parameters in change defined in Turkish Earthquake Code (TEC-2007) for columns and beams was carried out and the capacity curves, failure loads and displacements were obtained. Totally 720 RC buildings were analyzed according to the change intervals of the parameters chosen. The input parameters were selected as longitudinal bar ratio (ρl) of columns, transverse reinforcement ratio (Asw/sc), axial load level (N/No), column and beam cross section, strength of concrete (fc) and the compression bar ratio (ρ'/ρ) on the beam supports. Data from the nonlinear analysis were assessed with ANN in terms of failure load and failure displacement. For all outputs, ANN was trained and tested using of 11 back-propagation methods. All of the ANN models were found to perform well for both failure loads and displacements. The analyses also indicated that a considerable portion of existing RC building stock in Turkey may not meet the safety standards of the Turkish Earthquake Code (TEC-2007).

scholarly journals Metamaterials with engineered failure load and stiffness

2019 ◽  
Vol 116 (48) ◽  
pp. 23960-23965 ◽  
Author(s):  
Sai Sharan Injeti ◽  
Chiara Daraio ◽  
Kaushik Bhattacharya
Keyword(s):  
Mechanical Properties ◽  
Sensitivity Analysis ◽  
Critical Load ◽  
Failure Load ◽  
Weight Ratio ◽  
Fracture Load ◽  
Specific Load ◽  
Load To Failure ◽  
Failure Location ◽  
Theoretical Results

Architected materials or metamaterials have proved to be a very effective way of making materials with unusual mechanical properties. For example, by designing the mesoscale geometry of architected materials, it is possible to obtain extremely high stiffness-to-weight ratio or unusual Poisson’s ratio. However, much of this work has focused on designing properties like stiffness and density, and much remains unknown about the critical load to failure. This is the focus of the current work. We show that the addition of local internal prestress in selected regions of architected materials enables the design of materials where the critical load to failure can be optimized independently from the density and/or quasistatic stiffness. We propose a method to optimize the specific load to failure and specific stiffness using sensitivity analysis and derive the maximum bounds on the attainable properties. We demonstrate the method in a 2D triangular lattice and a 3D octahedral truss, showing excellent agreement between experimental and theoretical results. The method can be used to design materials with predetermined fracture load, failure location, and fracture paths.

Research of the Deflections of Beams Reinforced with BFRP Armature and Hybrid Reinforcement Using Metal and BFRP Armature

2019 ◽  
Vol 968 ◽  
pp. 301-308 ◽  
Author(s):  
Olexander I. Valovoi ◽  
Olexander Yu. Eremenko ◽  
Maksym O. Valovoi ◽  
Serhii O. Volkov
Keyword(s):  
Static Loading ◽  
Statistical Error ◽  
Load Level ◽  
Fine Aggregate ◽  
River Sand ◽  
Metal Armature ◽  
The Difference ◽  
Hybrid Reinforcement ◽  
Free Beam

It is presented the study of the beam samples reinforced with metal armature, BFRP armature and beams with hybrid reinforcement using metal and BFRP armature. Half of the tested samples of beams were manufactured on concrete with river sand, as a fine aggregate. The others were made on concrete with fractionated fine wastes of Mining and Beneficiary complex (MBC) instead of the river sand. The tests were carried out by static loading of the scheme of a single-run free beam loaded in the thirds of gear. It was established that the beams reinforced with BFRP armature and the beams with hybrid reinforcement showed an increase of strength, about 40%, compared with the beams reinforced with metal reinforcement. The deflections of the beams reinforced with BFRP armature were 315% -331% higher than the deflections of the beams reinforced with metal reinforcement and 165% -205% higher than it is allowed by standards. The use of hybrid reinforcement allowed reducing their deflections in two times compared to the beams reinforced with BFRP armature. At a load level of 60% of the destructive, the deflections of beams with hybrid reinforcement BFRP and metal armature did not exceed the maximum permissible norm. When concrete samples manufactured, the substitution of the river sand with fine fractionated wastes from the Mining and Beneficiary complex (MBC) did not affect their durability and deformability (the difference between the values according to these indicators is within the statistical error).

Follower forces: Leipholz's early researches in elastic stability

1990 ◽  
Vol 17 (3) ◽  
pp. 277-286 ◽  
Author(s):  
G. M. L. Gladwell
Keyword(s):  
Critical Load ◽  
Key Words ◽  
Lower Bounds ◽  
Critical Loads ◽  
Elastic Stability ◽  
Follower Force ◽  
Historical Account ◽  
Nonconservative Systems ◽  
Flutter Instability ◽  
Force Systems

This paper provides an historical account of Leipholz's research into elastic stability. Emphasis is placed on divergence and flutter instability of follower force systems, the derivation of lower bounds for the critical load for divergence, and estimates for critical loads for flutter. Key words: elastic stability, divergence, flutter, lower bounds, nonconservative systems, symmetrisable matrix.

Strength Analysis of MEMS Micromirror Devices - Effects of Loading Mode and Etching Damage

2005 ◽  
Vol 297-300 ◽  
pp. 527-532 ◽  
Author(s):  
Satoshi Izumi ◽  
Chan Wee Ping ◽  
Makoto Yamaguchi ◽  
Shinsuke Sakai ◽  
Atsushi Suzuki ◽  
...  
Keyword(s):  
Evaluation Method ◽  
Combined Loading ◽  
Strength Analysis ◽  
Load Factor ◽  
Pure Bending ◽  
Loading Test ◽  
Loading Mode ◽  
Safe Side ◽  
The Difference ◽  
Torsion Strength

Strength evaluation method for MEMS micromirror has been proposed. Pure bending and combined loading tests have been performed and torsion strength has been estimated from those results. Two-parameter Weibull distribution was used to evaluate the fractured stresses estimated from FEM model. There exists the difference in strength between pure bending and combined loading. From the load factor analysis, it is found that both geometry and stress distribution have to be considered to estimate the strength of MEMS since flaw population is non-uniformly distributed. It is also found torsional strength can be estimated on the safe side by using the result of combined loading test. From the comparison between two kinds of specimen fabricated by different etching conditions, it is found that the fracture strength is greatly affected by the amount of etching damage (notching).

scholarly journals Research on the Method and Model for Calculating Impact Load in the Rockburst Tunnel

Minerals ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 13
Author(s):  
Zhiwei Yan ◽  
Dagang Liu ◽  
Zhilong Wang ◽  
Daming Zhao ◽  
Hongtao Tian
Keyword(s):  
Impact Load ◽  
Design Method ◽  
Pressure Coefficient ◽  
Side Wall ◽  
Calculation Model ◽  
Load Factor ◽  
Circular Tunnel ◽  
Supporting Structure ◽  
The Difference ◽  
The Impact

Among several design methods of tunnel supporting structure, the load-structure method is widely used in different countries, but the determination of load is essential in this design method. The problem of rockburst is becoming more prominent as tunnel engineering enters the deep underground space. However, the research on the impact load on the supporting structure is insufficient in relevant fields. Therefore, from the perspective of energy, this paper deduces the method and model for calculating the impact load of the rockburst tunnel acting on the supporting structure by using the method of structural mechanics first, after the location effect of impact load is determined under different section types and different section sizes. The results indicated that: dynamic load factor K is related to the stiffness EI and supporting size coefficient K0 of the supporting structure, also the difference of impact load in different sections is proved. Tunnel rockburst-prone location is related to lateral pressure coefficient, thus when λ = 1, the probability of rockburst in the whole circular tunnel is the same, while side wall and vault are prone to rockburst in single-track horseshoe tunnel, and the side wall is prone to rockburst in double-track horseshoe tunnel; furthermore when λ > 1, the vault and the inverted arch are prone to rockburst; additionally, when λ < 1, the rockburst is most likely to occur in the arch waist of the circular tunnel and the side walls and the arch waist of the horseshoe tunnel. Finally, the rockburst tunnel’s local load-structure calculation model and the calculation process based on the model are provided.

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