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An upper bound on the total restrained domination number of a tree

JOURNAL OF COMBINATORIAL OPTIMIZATION 2010年第3期20卷 205-223页

作者： Hattingh, Johannes H. Jonck, Elizabeth Joubert, Ernst J. Georgia State Univ Dept Math & Stat Atlanta GA 30303 USA Univ Johannesburg Dept Math ZA-2006 Auckland Pk South Africa

Let G = (V, E) be a graph. A set of vertices S subset of V is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex of V - S is djacent to a vertex in V - S. The total restrained domination number of G, denoted by gamma(tr)(G), is the smallest cardinality of a total restrained dominating set of G. A support vertex of a graph is a vertex of degree at least two which is adjacent to a leaf. We show that gamma(tr)(T) <= [n+2s+l-1/2] where T is a tree of order n >= 3, and s and l are, respectively, the number of support vertices and leaves of T. We also constructively characterize the trees attaining the aforementioned bound.

关键词： Total restrained Domination Trees

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Influence of fibers on drying shrinkage in restrained concrete

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CONSTRUCTION AND BUILDING MATERIALS 2017年 148卷 833-845页

作者： Yousefieh, Negin Joshaghani, Alireza Hajibandeh, Erfan Shekarchi, Mohammad Univ Tehran CMI Tehran Iran Texas A&M Univ Zachry Dept Civil Engn College Stn TX 77843 USA Amirkabir Univ Technol Tehran Iran Univ Tehran Dept Civil Engn CMI Tehran Iran

Drying shrinkage cracks mainly start to develop at the exposed surface of the concrete elements due to the shrinkage strain caused by self-desiccation. For the purpose of controlling drying shrinkage cracks additions and fibers are used in fresh concretes in order to provide high early age mechanical capacity for moderating the crack development. The purpose of this study is to evaluate the performance of using different fibers in reducing the drying shrinkage and cracking under restrained conditions. To investigate the effectiveness of using both polymeric and metal fibers in concrete, three different types of fibers, including polypropylene fiber, polyolefin fibers, and steel fiber were used in this study. The maximum drying shrinkage strength was highly dependent on fibers' module of elasticity. The average length cracking and its pattern in fiber reinforced concretes were different than control concrete. The physical properties of fibers have direct effects on reducing the cracking width. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Shrinkage restrained Drying Concrete Fibers Crack Polypropylene Polyolefin Image processing

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EXPERIMENTAL BEHAVIOR OF PARTIALLY restrained STEEL COLUMNS

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PROCEEDINGS OF THE INSTITUTION OF CIVIL ENGINEERS-STRUCTURES AND BUILDINGS 1993年第1期99卷 29-42页

作者： GIBBONS, C KIRBY, PA NETHERCOT, DA UNIV NOTTINGHAM NOTTINGHAM NG7 2RDENGLAND UNIV SHEFFIELD SHEFFIELD S10 2TNS YORKSHIREENGLAND

The planning, design, conduct and appraisal of a series of full-scale tests on steel column subassemblages is presented. Ten tests, incorporating a range of semi-rigid beam to column joints, were performed. Special procedures were developed to monitor three-dimensional deformation and internal load components, as well to produce a controlled degree of initial out-of-straightness in the specimens. The results clearly illustrate complex changes to the distribution of moments throughout the system as column failure is approached. These were reproduced in a specially written finite-element computer program which gave very good predictions of behaviour for all the tests. Comparisons with the conventional design approach of BS 5950: Part 1 for this class of construction show large reserves of strength, attributable principally to the beneficial effects of rotational end restraint outweighing the deleterious effect of moment transfer.

关键词： OVE ARUP , SHEFFIELD UNIVERSITY , NOTTINGHAM UNIVERSITY COLUMNS , STEEL , PARTIALLY , restrained , EXPERIMENTAL , BEHAVIOUR , TESTS , SUBASSEMBLAGES , SEMI RIGID , BEAMS , JOINTS , THREE DIMENSIONAL , DEFORMATION , LOADS , DISTRIBUTION , MOMENTS , FAILURES , FINITE ELEMENTS , COMPUTERS , PROGRAMS , STEELWORK , JOINTS , CONNECTIONS , WEBS , CLEATS , FLANGES , PLATES

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Buckling behavior of cold-formed zed-purlins partially restrained by steel sheeting

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THIN-WALLED STRUCTURES 2002年第10期40卷 853-864页

作者： Ye, ZM Kettle, RJ Li, LY Schafer, BW Aston Univ Sch Engn & Appl Sci Birmingham B4 7ET W Midlands England Shanghai Univ Dept Civil Engn Shanghai 200072 Peoples R China Johns Hopkins Univ Dept Civil Engn Baltimore MD 21218 USA

This paper presents a study on the buckling behaviour of purlin-sheeting systems under wind uplift loading. The restraint provided by the sheeting to the purlin is modeled by using two springs representing the translational and rotational restraints. The analysis is performed using finite strip methods in which the pre-buckling stress is calculated based on the same model used for the buckling analysis rather than taken as the 'pure bending' stress. The results obtained from this study show that, for both local and distortional buckling, the restraints have significant influence on the critical loads through their influence on the pre-buckling stress rather than directly on the buckling modes. While for lateral-torsional buckling, the influence of the restraints on the critical loads is mainly due to their influence on the buckling modes rather than the pre-buckling stress. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： cold-formed purlin steel thin-walled restrained sheeting buckling instability

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AN APPRAISAL OF PARTIALLY restrained COLUMN BEHAVIOR IN NON-SWAY STEEL FRAMES

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PROCEEDINGS OF THE INSTITUTION OF CIVIL ENGINEERS-STRUCTURES AND BUILDINGS 1993年第1期99卷 15-28页

作者： GIBBONS, C NETHERCOT, DA KIRBY, PA WANG, YC UNIV NOTTINGHAM NOTTINGHAM NG7 2RDENGLAND UNIV SHEFFIELD SHEFFIELD S10 2TNS YORKSHIREENGLAND BLDG RES ESTAB LONDONENGLAND

This Paper describes a parametric study which was conducted as part of a more extensive investigation into the behaviour of three-dimensional, non-sway, semi-rigid frames. The study comprised finite element modelling of column subassemblages, employing both web cleat and fully rigid connections, when subjected to practical combinations of loading. One of the specific objectives was to quantify the adverse effect of the moment transferred through simple beam to column connections on column capacity. The results of the study show that in many cases, the benefit of the rotational restraint offered by the connection outweighs the detrimental effect of the moment transferred through it. The Paper goes on to show that the present methods of simple frame design are highly conservative and it questions the suitability of interaction formulae for predicting the ultimate capacity of columns in 'real frames'.

关键词： OVE ARUP , NOTTINGHAM UNIVERSITY , SHEFFIELD UNIVERSITY , BUILDING RESEARCH ESTABLISHMENT , BRE FRAMES , STEEL , PARTIALLY , restrained , COLUMNS , BEHAVIOUR , PARAMETRIC , STUDIES , THREE DIMENSIONAL , SEMI RIGID , FINITE ELEMENTS , MODELLING , RESTRAINT , ROTATION , MOMENTS , CONNECTIONS , SUBASSEMBLAGES , PARAMETERS , WEBS , BEAMS , CLEATS , LOADS , CAPACITY , FAILURES , DESIGN , METHODS

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Arching action strength enhancement in laterally-restrained slab strips

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PROCEEDINGS OF THE INSTITUTION OF CIVIL ENGINEERS-STRUCTURES AND BUILDINGS 1997年第4期122卷 461-467页

作者： Rankin, GIB Long, AE QUEENS UNIV BELFAST NO IRELAND TECHNOL CTRCONSTRUCT DIVBELFAST BT7 1NNANTRIMNORTH IRELAND QUEENS UNIV BELFAST SCH BUILT ENVIRONMBELFAST BT7 1NNANTRIMNORTH IRELAND

The behaviour and ultimate load capacity of laterally-restrained reinforced concrete slabs can be considerably enhanced by the development of arching or compressive membrane action, This paper presents a simple method for predicting the enhanced ultimate load capacity of laterally-restrained slab strips, The method is based on deformation theory and utilizes an elastic-plastic stress-strain criterion for concrete, The loads carried by bending and arching action are calculated separately and then added to give the total ultimate load capacity, A simple equivalent strip approach, based on a three-hinged arch analogy, allows for the degree of lateral restraint, The method of prediction has been validated by correlation with a wide range of test results from various sources.

关键词： QUEENS UNIVERSITY BELFAST CONCRETE , SLABS , ARCHING , ACTION , STRENGTH , ENHANCEMENT , LATERALLY , restrained , RESTRAINT , LATERAL , STRIP , BEHAVIOUR , ULTIMATE , LOADS , CAPACITY , REINFORCED , DEVELOPMENT , COMPRESSIVE , MEMBRANES , METHODS , PREDICTION , ENHANCED , DEFORMATION , THEORY , ELASTIC PLASTIC , STRESS , STRAIN , CRITERIA , BENDING , CALCULATIONS , EQUIVALENT , THREE HINGED , TESTS , MATERIALS , PROPERTIES , INTERACTION , CORRELATION

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Load deflection behaviour of partially restrained slab strips

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ENGINEERING STRUCTURES 2007年第5期29卷 663-674页

作者： Muthu, K. U. Amarnath, K. Ibrahim, Azmi Mattarneh, Hashem MSRIT Dept Civil Engn Res Ctr Bangalore 560054 Karnataka India Univ Teknol MARA Dept Civil Engn Selangor Malaysia

The paper gives the results of an analytical method proposed to predict the load deflection behaviour of partially restrained slab strips. The effect of deflection prior to yield line load on the development of compressive membrane forces was incorporated in the theoretical analysis. An experimental programme was designed to cast and test ten partially restrained slab strips with different edge rigidity. A comparison has been made between the results of the proposed and one of the other methods available in the literature. The results indicate that the proposed method can predict the load deflection behaviour satisfactorily. A parametric study has been made on the load enhancement beyond yield line load and the results are presented. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： analysis concrete comparison deflection experiments partially restrained parameters slabs ultimate load

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Nordhaus-Gaddum results for restrained domination and total restrained domination in graphs

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DISCRETE MATHEMATICS 2008年第7期308卷 1080-1087页

作者： Hattingh, Johannes H. Jonck, Elizabeth Joubert, Ernst J. Plummer, Andrew R. Georgia State Univ Dept Math & Stat Atlanta GA 30303 USA Univ Johannesburg Dept Math ZA-2006 Auckland Pk South Africa

Let G = (V, E) be a graph. A set S subset of V is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex of V - S is adjacent to a vertex in V - S. A set S subset of V is a restrained dominating set if every vertex in V - S is adjacent to a vertex in S and to a vertex in V - S. The total restrained domination number of G (restrained domination number of G, respectively), denoted by gamma(tr)(G) (gamma(r)(G), respectively), is the smallest cardinality of a total restrained dominating set (restrained dominating set, respectively) of G. We bound the sum of the total restrained domination numbers of a graph and its complement, and provide characterizations of the extremal graphs achieving these bounds. It is known (see [G.S. Domke, J.H. Hattingh, S.T. Hedetniemi, R.C. Laskar, L.R. Markus, restrained domination in graphs, Discrete Math. 203 (1999) 61-69.]) that if G is a graph of order n >= 2 such that both G and (G) over bar are not isomorphic to P-3, then 4 <= gamma(r)(G) + gamma(r)((G) over bar) <= n + 2. We also provide characterizations of the extremal graphs G of order n achieving these bounds. (C) 2007 Elsevier B.V. All rights reserved.

关键词： restrained total domination Nordhaus-Gaddum

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Analysis of cold-formed zed-purlins partially restrained by steel sheeting

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COMPUTERS & STRUCTURES 2004年第9-10期82卷 731-739页

作者： Ye, ZM Kettle, R Li, LY Aston Univ Sch Engn & Appl Sci Birmingham B4 7ET W Midlands England Shanghai Univ Dept Civil Engn Shanghai 200072 Peoples R China

This paper presents an analysis model for cold-formed purlin-sheeting systems subjected to wind uplift loading in which the restraint of the sheeting to the purlin is taken into account by using two springs representing the translational and rotational restraints provided by the sheeting. The model yields a set of three differential equations corresponding to one torsion and two bending equations. The set of equations is solved by means of trigonometric series. The influence of spring stiffness and fixing position of the purlin and sheeting on the stresses resulted in the cross-section of the purlin is discussed. The results obtained from this study not only highlight the influence of the sheeting restraints on the results of stresses but also can be used as an input to the finite strip code for carrying out the linear elastic buckling analysis of the sections. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： cold-formed purlin steel thin-walled strength restrained sheeting bending

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THE NATURE AND SOURCE OF THE HEAD-INJURIES SUSTAINED BY restrained FRONT-SEAT CAR OCCUPANTS IN FRONTAL COLLISIONS

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ACCIDENT ANALYSIS AND PREVENTION 1995年第4期27卷 561-570页

作者： THOMAS, P BRADFORD, M ICE ERGON VEHICLE SAFETY RES CTRLOUGHBOROUGHLEICSENGLAND

The paper examines the types of head injury sustained by restrained front-seat car occupants in frontal collisions. Injuries are classified into soft tissue, diffuse and focal brain injuries and facial bone or skull fractures. Survivors seldom sustain focal injuries although these are common amongst fatalities. The contact sources within the car are described. Intruding structures and high crash severities are typically associated with high rates of the more severe injuries from steering wheel contact, although some are sustained with intrusion below 11 cm. Low-speed impact testing on nondeployed airbag-equipped wheels is suggested. Toughened glass windscreens are overrepresented amongst those sustaining injuries from glazing materials. Test procedures to reduce injuries from pillar contacts should take account of the dynamic effects of an intruding pillar. Contacts with objects outside the car caused higher rates of severe fractures and brain injury;however, the total numbers are greater from interior contacts.

关键词： HEAD CAR restrained MECHANISMS

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