Alexander Dubček University of Trenčín Izhevsk State Technical University · Alexander Dubček University of Trenčín Izhevsk State Technical University Publishing House:

Alexander Dubček University of Trenčín

Izhevsk State Technical University

Publishing House:Alexander Dubček University of Trenčín

(The international scientific journal founded by two universities from Slovak Republic and Russian Federation)

This journal originated with kindly support of Ministry of Education of the Slovak Republic

Editor-in-Chief

Miroslav Mečár, Assoc. prof., Ing., PhD., Alexander Dubček University of Trenčín

Science Editor

Dubovská Rozmarína, Prof. Ing., DrSc., Alexander Dubček University of Trenčín

Honorary Editors

Miroslav Mečár, Assoc. prof., Ing., PhD.rector, Alexander Dubček University of Trenčín, Slovak Republic

Jakimovič Boris Anatoľjevič, Prof., DrSc., rector, Izhevsk State Technical University, Russian Federation

Members

Alexy Július, Prof. Ing., PhD. Gulášová Ivica, Assoc.prof., PhDr., PhD.Jóna Eugen, Prof. Ing., DrSc.Letko Ivan, Prof. Ing., PhD.Maňas Pavel, Assoc.prof., Ing., PhD. Mečár Miroslav, Assoc.prof., Ing., PhD.Melník Milan, Prof. Ing., DrSc. Obmaščík Michal, Prof. Ing., PhD. Zgodavová Kristína, Prof. Ing., PhD.

Jakimovič Boris Anatoľjevič, Prof., DrSc. Alijev Ali Vejsovič, Prof., DrSc. Turygin Jurij Vasiľjevič, Prof., DrSc. Ščenjatskij Aleksej Valerjevič, Prof., DrSc. Kuznecov Andrej Leonidovič, Prof., DrSc. Fiľkin Nikolaj Michajlovič, Prof., DrSc. Sivcev Nikolaj Sergejevič, Prof., DrSc. Senilov Michail Andrejevič, Prof., DrSc. Klekovkin Viktor Sergejevič, Prof., DrSc.Trubačev Jevgenij Semenovič, Prof., DrSc.

Alexander Dubček University of Trenčín Slovak Republic

Izhevsk State Technical UniversityRussian Federation

Editorial Office

Študentská 1, 911 50 Trenčín, Tel.: 032/7 400 279, 032/7 400 [email protected], [email protected]

Bodorová Janka, Mgr.

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Publishing House

University Review Vol. 2, No. 3Trenčín: Alexander Dubček University of Trenčín2008, 90 p.ISSN 1337-6047EV 2579/08

Alexander Dubček University of Trenčín, Študentská 2, 911 50 Trenčín

3z SOLUTIONS - Zuzana Slezáková, www.3zs.sk

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© 2008 All rights reserved.Alexander Dubček University of Trenčín, Slovak Republic

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Contributors

contents

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51

39

35

31

3

18

S. Isic, V. Dolecek, A.Voloder

S. Roth, V. Skakalova

An Analysis of Postbuckling Frequency Change of Beam Structures Using Finite Elements Method

Carbon Nanotubes In Electronics

41

13

M. Bodnicki, H. J. HawłasContactless Angle Transducer Dedicated For DC Micromotor

V. Lapkovsky, V. Mironov, V. Zemchenkov, I. Boyko

Tubular Metal Powder Permeable Materials With Anisotropic Structure And Their Applications

P. PadevětRewiev of Destructive Methods of Testing of The Cement Paste And Concrete

V. Mironov, I. Boyko, V. LapkovskyProperties And Quality of The Surface of Iron-Copper Powder Details

H.F. El-Maghraby, O. Gedeon, A.A. Khalil

Microstructure And Mechanical Properties of Poly(Vinyl Alcohol)-Plaster Composites

J. Jasiński, G. Walczak, K. Kaczmarek, J. P. Jasiński Investigations of Microstructure of The Forging Die After Using – A Case Study

23

6

P. KoudelkaEvaulation And Future The Ulimate Limit State Design in Geomechanics

M. Kosek, T. Mikolanda, A. Richter, P. Skop

Intelligent Mechatronical System Using Repulsive Force Produced by Permannet Magnets

Dean´s Foreword

7

1

7

84

81

72



68

M. Bodnicki, H. J. Hawłas


P. Padevět

V. Mironov, I. Boyko, V. Lapkovsky

H.F. El-Maghraby, O. Gedeon, A.A. Khalil

J. Jasiński, G. Walczak, K. Kaczmarek, J. P. Jasiński

77


2

65

60

56J. Jasiński, G. Walczak, K. Kaczmarek, J. P. Jasiński

M. Szota, J. Jasinski

P. Wieczorek, J. Lis, A. K. Lis

A. K. Lis, N. Wolańska, C. Kolan

Z. Jonšta, P. Jonšta, V. Vodárek, K. Mazanec

G. Marunić

O. Šuba, J. Jurčiová

M. Greger, L. Kander, B. Kuřetová

Mechanica Load And Microstructure of Discharge Jet For Compresion Ignition Engine

Neural Networks Modeling Carbonizing Proces In Fluidized Bed

The Study of Microstructure of Precipitation-Strengthening HSLA Steel With Copper Addition

Hot Ductility of Low Carbon Steel (S235JR)

Evaluation of Microstructure of Nickel Superalloy Inconel 792-5A After Long Term Exploitation

Rim Stress Distribution of Thin-Rimmed Gear

Mechanical Design of Thermoplastic Shells of Small Wastewater Treatment Systems

Platic Forming of Ecap Processed En Aw 6082 Aluminum Alloy

3

contributors

S. Roth, Max Planck Institute for Solid State Research, Stuttgart, Germany, Sineurop Nanotech GmbH, Stuttgart, Germanye-mail: [email protected]. Skakalova, Max Planck Institute for Solid State Research, Stuttgart, Germany, Danubia Nanotech s.r.o., Bratislava, Slovakia

S. Isic, Faculty of Mechanical Engineering, Mostar, Bosnia and Herzegovinae-mail: [email protected], V. Dolecek Faculty of Mechanical Engineering, Sarajevo, Bosnia and Herzegovinae-mail: [email protected]: [email protected]

M. Kosek, T. Mikolanda, A. RichterTechnical University of Liberec, Liberec, Czech Republice-mail: [email protected]: [email protected]: [email protected]. Skop, Research Institute of Textile Machines, Liberec, Czech Republice-mail: [email protected]

P. Koudelka, Institute of Theoretical and Applied Mechanicsm Prague, Czech Republice-mail: [email protected]

M. Bodnicki, Institute of Micromechanics and Photonics, Warsaw University of Technology; Warszawa, Polande-mail: [email protected]. J. Hawłas, Institute of Precision and Biomedical Engineering, Warsaw University of Technology, Warszawa, Polande-mail: [email protected]

G. MarunićUniversity of Rijeka Faculty of Engineering, Rijeka, Croatiae-mail: [email protected]

4

V. Lapkovsky, V. Mironov, I. BoykoRiga Technical University, Riga, Latviae-mail: [email protected] e-mail: [email protected]: [email protected] V. Zemchenkov, TETA Ltd, Riga, Latviae-mail: [email protected]

contributors

P. Padevět, CTU in Prague, Faculty of Civil Engineering, Prague, Czech Republice-mail: [email protected]

H.F. El-Maghraby, O. Gedeon, Department of Glass and Ceramics, Institute of Chemical Technology, Prague, Czech Republice-mail: [email protected]: [email protected]. Khalil, Department of Refractories, Ceramics, and Building Materials, National Re-search Centre, Cairo, Egypte-mail: [email protected]

J. Jasiński, G. Walczak, K. Kaczmarek, J. P. Jasiński Czestochowa University of Technology, Materials Engineering Institute, Biomaterials and Surface Layers Research Institute, Czestochowa, Polande-mail: [email protected] e-mail: [email protected]

M. Szota, J. JasinskiCzestochowa University of Technology, Materials Engineering Institute, Czestochowa, Polande-mail: [email protected]

Z. Jonšta, P. Jonšta, V. Vodárek, K. MazanecVSB-Technical University of Ostrava, Ostrava-Poruba, Czech Republice-mail: [email protected]

5

P. Wieczorek, J. Lis, A. K. LisInstitute of Materials Engineering, Technical University of Czestochowa, Czestochowa, Poland e-mail: [email protected]: [email protected]

A. K. Lis, N. Wolańska, C. KolanCzestochowa University of Technology, Częstochowa, Polande-mail: [email protected]: [email protected]: [email protected]

O. Šuba, T. Bata University in Zlin, Faculty of Technology, Zlín, Czech Republice-mail: [email protected]. Jurčiová, Faculty of Industrial Technologies, Alexander Dubček University of Trenčín, Púchov, Slovak Republice-mail: [email protected]

M. Greger, B. Kuřetová, VŠB-Technical University Ostrava, Ostrava, Czech Republice-mail: [email protected]: barbora. [email protected]. Kander, Material & Metallurgical Research Ltd, Ostrava, Czech Republice-mail: [email protected]

Reviewers

Prof. RNDr. Pavol Koštial, PhD.Prof. Ing. Vendelín Macho, DrSc.Prof. Ing. Eugen Jóna, DrSc.

Prof. RNDr. Juraj Slabeycius, PhD.Prof. Ing. Ivan Letko, PhD.

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The long-term cooperation between Polish and Slovak researchers in the field of machine design and materials engineering resulted in nine meetings heldin Poland and Slovakia since 1996 un-der the common name “Theoretical and Experimental Problems of Materials Engineering”. Czech researchers have been involved in organization of these conferences since 2003 and have been honoured by organization of the jubilee 10th meeting in Rožnov, 2005 (PiME05). Last conference was located in the beautiful spa region of the town Rajecké Teplice in Slovakia. The conference was organized by the Faculty of industrial technologies in Púchov, University of Alexander Dubček in Trenčín in the period August 25th - 28th 2008.

The purpose of the conference is to present current results in materials engineering, chemistry and mechanics of materials, mechanics and design in applications.

The conference topics :

A. Physicaland chemical properties of materials, nanomaterials

B. Mechanical properties of materials

C. Experimental methods in materials engineering

D. Mechanicsand computer simulation

The first part of proceedings is oriented mainly in mechanics of materials, materials engineering and design.

dean´s foreword

prof. RNDr. Pavel Koštial, PhD.

7

Some people claim that carbon nanotubes will be the most important material of the 21st century. The future will tell us whether this is true, but the past teaches that most predic-tions are wrong. In any case, carbon nanotubes

certainly are the most popular material of the present: Since their discovery in 1991 [1] some 20 000 publications have appeared and some 1000 patents have been filed. Fig. 1 shows the computer model of a carbon nanotube.

carbon nanotubes in eLectronics


Carbon nanotubes have been discovered about 15 years ago. Meanwhile some 30 000 papers have been published on this topic and carbon nanotubes are often claimed to be the most promising ma-terial of the 21st century. This paper will give an introduction into the physical phenomena which can be studied in these materials (conductance quantisation, single-electron effects, ballistic trans-port, van Hove singularities, zero-gap semiconductor, bipolar transport, linear dispersion relation, degenerate sublattices ...). Carbon nanotubes will be discused with respect to their attractiveness for studies in fundamental physics as well as their perspectives for technological applications (car-bon electronics, tube-transistors, sensors, interconnects, vias, nanoelectromechanical devices ...).

Abstract

carbon nanotubes

Key words

Fig. 1: Computer model of a single-walled carbon nanotube

8

Carbon nanotubes are seamless tubes of graph-itic monolayers, about 1 or 2 nanometers in di-ameter and up to several micrometers or even millimeters long. Depending on the diameter and on the details of seamless joining, the nano-tubes are metallic or semiconducting. Because of the strong carbon-carbon bond and because of phase space arguments in narrow constric-tions, there are only few scattering events in na-notubes and the conductivity is mainly ballistic, which for practical purposes means, for metal-lic nanotubes it is very high. The energy gap of semiconducting nanotubes can range from a few meV up to 1 eV. There are single-walled and multi-walled carbon nanotubes. Multi-walled nanotubes consist of up to 70 concentric tubes. For monographs on carbon nanotubes see Refs. [2-5].

If there are semiconducting nanotubes, it is tempting to make nanotube transistors. Sev-eral groups have prepared and investigated such transistors [6-11]. These transistors are expected to be smaller than silicon transistors, faster, and less energy-consuming. Fig. 2 shows a schematic diagram of a nanotube field-effect

transistor (TUBE-FET): A semiconducting single-walled carbon nanotube is placed on the oxide layer of a doped silicon chip. Gold leads are ap-plied by electron beam lithography as source and as drain contacts. Usually the nanotube is already p-doped from the purification process (which generally involves an oxidation step) or it gets p-doped by interaction with the gold leads (different work function between carbon and gold). Consequently the nanotube is con-ducting and the transistor is in the “on” state. To switch the transistor off, a voltage is applied between the nanotube and the doped silicon chip (which serves as a gate contact). The on-off ratio of such a transistor can be as large as 5 or 6 orders of magnitude and it has been shown that these nanotube transistors outperform the best silicon transistors also with respect to other parameter. Fig. 3 shows an AFM image of a single-walled carbon nanotubes placed over 4 gold leads prepared by electron beam lithogra-phy [12]. Any two of the gold leads can be used as the source and the drain contact of the field-effect transistor.

Fig. 2: Schematic diagram of nanotube field-effect transistor

Fig. 3: AFM image of a carbon nanotube laying over 4 gold leads prepared by electron beam lithography [12]

9

Fig. 4 presents the “all-carbon” transistor, where the gate is also a carbon nanotube [11]. This transistor has been “synthesized by wet-chemical methods”, and in principle it would allow for really nanometer-sized devices and extremely high integration density. Phaedon Avouris’ group at IBM has prepared a compli-mentary field-effect device consisting of a na-notube over tree gold electrodes and of which one part is p-doped and the other n-doped [13]. n-doping has been achieved by covering one part of the nanotube by a polymer film and exposing the other to ammonia, so that there the original p-doping is overcompensated (Fig. 5). Such a device can serve as a voltage inverter

(or as a logic NOT gate). An other way of sav-ing space and going to higher integration densi-ties is to put the transistors vertical and to use a wrap-around gate. Such transistors have been patented by Infineon and by Samsung. An art-ist’s view is shown in Fig. 6 [14]. Today we have quite a good understanding on how transistors can be made from individual nanotubes and on how individual nanotubes behave compared to silicon, but we lack a technique of selecting the wanted type of nanotubes and then positioning it in the right place. Developing a technology which could one day replace large scale inte-grated silicon circuits is an endeavour of dec-ades, not of years.

Fig. 4: “All-carbon” transistor with nanotube not only as conducting channel but also with nanotube gate. The dielectric is a linker molecule at the T-junction. The device has been “synthesized by wet-chemical methods” and adsorbed on a silicon chip prior to the application of the lithographic gold leads [11]

Fig. 5: Voltage inverter consisting of a p-type and an n-type carbon nanotube field-effect transistor [13]

10

The limiting problem of today’s electronics is not the active elements (transistors), it is wir-ing. Wiring at all levels, from the cables be-tween computer and peripherals down to inter-connects between the transistors on a chip. A special challenge are VIAs (vertical interconnect access), connecting different layers on a chip. It is very difficult to pass high current densi-ties through very thin wires of conventional metals because of surface and grain boundary scattering. In addition, such thin wires tend to decompose, releasing small metal particles which migrate around within the circuitry (elec-tromigration). Because of the strong covalent bonds between carbon atoms, as compared to the rather week metallic bonds, there is much less electromigration from carbon nanotubes,

and the maximum current density in carbon na-notubes is by three orders of magnitude higher than in copper wires. Therefore several compa-nies are working on VIAs based on carbon nano-tubes. Fig. 7 shows the electronmicrograph of a multi-walled nanotube growing out of a hole etched into a silicon chip [15]. Experts believe that a hybrid technology - with active elements based on silicon and with interconnects based on carbon - could be ready within a few years. An “all-carbon” technology with metallic nano-tubes connecting transistors from semiconduct-ing nanotubes is a dream for a very far future. Yet, a disordered version of this dream has al-ready been realized today: the transparent na-notube transistor.

Fig. 6: Vertical nanotube field-effect transistor with wrap-around gate electrode [14]

Fig. 7: Multi-walled carbon nanotube growing out of a hole etched into a silicon chip,first step towards nanotube-based VIAs [15]

11

Individual nanotubes are difficult to handle. But there are many applications in which large en-sembles of nanotubes are used. This is particu-larly true for nanotube-polymer composites, i.e. for polymers filled with carbon nanotubes. Such filling might improve the electrical and mechan-ical properties of the polymers. Of course, poly-mers filled with larger particles do already exist (e.g. aluminium flakes, silver beats, or stainless steel fibres as conductive fillers, carbon fibres for mechanical reinforcement), and non-tubular nanoparticles have also been known for a long time as polymer fillers (carbon black for chemi-cal purposes in car tires, carbon black as pig-ments, carbon black as conductive fillers). Con-ductive polymers can be used for dissipation of electrostatic charges, for electromagnetic shielding, and for electrical heating (of car seats or of outside mirrors). There are certain advan-tages if the fillers are thin and long (lower per-colation threshold, so that less filler material is needed) and there are certain advantages if the filler particles are nanometer size (homogeneity down to nanometer scale as needed in ultrathin adhesive layers).

Because of the low percolation threshold that can be obtained with nanotube filling, com-bined with nanoscale homogeneity, transpar-ent conductive films can be made. These films can compete with ITO layers (indium-tin oxide), which is the standard material for transparent electrodes (needed in solar cells and in light

emitting devices). A very interesting example of the application of transparent nanotube net-works is the flexible transparent nanotube tran-sistor [16]. A photograph of such a transistor is shown in Fig. 8. and a schematic drawing in Fig. 9. The essential feature of this transistor is that there are two transparent nanotube layers, separated by a thin insulating layer of parylene. Both layers consist of a mixture of metallic and semiconducting nanotubes (Today only mix-tures of nanotubes can be synthesized and there is no efficient way of separating them). For the lower layer the nanotube concentra-tion is chosen such that the metallic nanotubes form a continuous network. This layer behaves like a metal and serves as the gate electrode of the transistor. In the upper nanotube layer the concentration of the tubes is only half as large. Now most metallic nanotubes do not touch and the network is only continuous if both metallic and semiconducting nanotubes are taken into account. This network behaves semiconductor-like and forms the conducting channel of the transistor. Actually, this layer can be considered as a random ensemble of individual semicon-ducting nanotubes, each connected by metallic nanotubes as local source and drain contacts.

The works were realised under support of project Excgange Pragramme DAAD-MSSR (D/07/01257).

Fig. 8: Photograph of flexible trans-parent nanotube transistor [16]

Fig. 9: Schematic drawing of flexible transparent nanotube transistor [16]

Gold Source-Drain Contacts Parylene N (Insulating Layer)

Rare Nanotube Network as Source-Drain Channel

Dense Nanotube Network as Gate Layer

Gold Contactsto the Gate

Flexible PE substrate

12

IIJIMA, S.: Helical microtubulus of graphitic carbon. Nature 354, 56-58 (1991).1. EBBESEN, T.W. (Ed.): “Carbon Nanotubes - Preparation and Properties” CRC Press (1997). 2. DRESSELHAUS, M.S., DRESSELHAUS, G., AVOURIS, Ph. (Eds.) “Carbon Nanotubes” Springer 3. (2000). HARRIS, P.J.F.: “Carbon Nanotubes and Related Structures” Cambridge University Press (1999). 4. SAITO, R., DRESSELHAUS, G., DRESSELHAUS, M.S.: “Physical Properties of Carbon Nanotubes” 5. Imperial College Press, London (1998).TANS, S.J., VERSCHUEREN, A.R.M., DEKKER, C.: Room-temperature transistor based on a single 6. carbon nanotube. Nature 393, 49–52 (1998).H.W.C., POSTMA, T., TEEPEN, Z., YAO, M., GRIFONI, C. DEKKER,: Carbon nanotbe single-electron 7. transistors at room temperature. Science 293, 76–79 (2001).MARTEL, R., SCHMIDT, T., SHEA, H.R., HERTEL, T., AVOURIS, Ph.: Single- and multi-wall carbon 8. nanotube field-effect transistors. Applied Physics Letters 73, 2447-2449 (1998).HEINZE, S., TERSOFF, J., MARTEL, R., DERYCKE, V., APPENZELLER, J., AVOURIS, Ph.: Carbon nano-9. tubes as Schottky barrier transistors. Physical Review Letters 89, 106801-1 -106801-4 (2002).JAVEY, A., GUO, J., WANG, Q., LUNDSTROM, M., DAI, H.: Ballistic carbon nanotube field-effect 10. transistors. Nature 424, 654–657 (2003).CHIU, P.W., KAEMPGEN, M., ROTH, S.: Band-structure modulation in carbon nanotube T-junc-11. tions. Physical Review Letters 92, 246802-1 - 246802-4 (2004).J. MUSTER, M. BURGHARD, S. ROTH, G.S. DUESBERG, E. HERNÁNDEZ, AND A. RUBIO. Scanning 12. force microscopy characterization of individual carbon nanotubes on electrode arrays. Journal of Vacuum Science and Technology B 16, 2796 (1998).AVOURIS, Ph., MARTEL, R., DERYCKE, V., APPENZELLER, J.: Carbon nanotube transistors and 13. logic circuits, d 10598, USA, Physica B 323,6-14 (2002).KREUPL, F., DUESBERG, G.S., GRAHAM, A.P., LIEBAU, M., UNGER, E., SEIDEL, R., PAMLER, W., 14. HÖNLEIN, W.: “Carbon nanotubes in microelectronic applications”. In: Physics, Chemistry and Application of Nanostructures : Reviews and Short Notes to Nanomeeting 2003 Minsk, Belarus 20-23 May 2003. S.V. Gaponenko, V.S. Gurin (Eds.). World Scientific Pub Co Inc (2003/04)KREUPL, F., GRAHAM, A.P., LIEBAU, M., DUESBERG, G.S., SEIDEL, R., UNGER, E.: IEDM Tech. Dig., 15. pp. 683 - 686, December 2004, cond-mat/0412537.ARTUKOVIC, E., KAEMPGEN, M., HECHT, D.S., ROTH, S., GRÜNER, G.: Transparent and flexible 16. carbon nanotube transistors. Nano Letters 5, 757-760 (2005).

Literature

Gold Contactsto the Gate

13

An analysis of eigenfrequencies of the small vibration of beam structures defines char-acter of stability of the current equilibrium position [1]. For critical load, the lowest eigen-frequency becomes zero, and any small per-turbation leads to buckling of a beam. For load greater than critical, linear analysis indicates imaginary value of the frequency. It is already known that beam structure has stable equilib-rium postbuckling positions [2], and frequency should have real values. It is necessary to intro-duce non-linear analysis for its calculation. For analytic calculation of the frequency of buckled beam, perturbation method may be used [1]. It

respectable mathematical problem for systems with many d.o.f-s, because of that, solutions ex-ist for simplified beam models with two d.o.f. [4], [5]. Some numerical method must be used in the case of an analysis of complex systems.

This paper presents analysis of vibrations fre-quency of beams in a postbuckling states using finite elements method. A non-linear equation of postbuckling vibration is derived taking into account higher order terms (up to third order) of a stiffness and stress stiffening. A non-linear equation of vibration is solved using direct in-tegration methods and frequencies of vibration are calculated by transformation of the obtained

an anaLYsis of PostbucKLinG freQuencY cHanGe of beaM structures usinG finite eLeMents MetHod


This paper presents analysis of vibrations frequency of axially loaded beams in a postbuckling states, using finite elements method. Non-linear equation of motion takes into account up to third order terms of stiffness and stress stiffening. Non-linear equation of vibration is solved using di-rect integration methods and frequencies of vibration are calculated by transformation of the ob-tained solutions to frequency domain. According to assumption that beam buckles in the form of first buckling eigenmode, it is derived single non-linear differential equation of vibration, which is enough simple for analytical or numerical analysis. This equation gives results which agree well with solution obtained using direct integration methods of complete finite element equation of vibration. Obtained results shows increasing of the postbuckling frequency with increasing of axial force and initial displacement from straight-line position.

Abstract

beam, finite elements method, postbuckling, frequency

Key words

14

solutions from time to frequency domain. This is combination of two time consuming calcula-tions, and to make it applicable some accelera-tion of the process should be used. According to assumption that beam buckles in the form of first buckling eigenmode, it is derived single non-linear differential equation of vibration, which is enough simple for analysis using ana-lytical perturbation methods or method for nu-merical integration. This equation gives results which agree well with solution obtained using direct integration methods of complete finite element equation of vibration. A content of the spectrum and frequency change in postbuckling states of a beam is calculated for different val-ues of axial force greater than critical, and also for different initial condition of a beam.

finite eLeMents anaLYsisequation of motion

Lets consider axially loaded beam as shown in the Fig. 1. Beam is loaded by axial force P which is constant in value and direction. When

beam looses stability, beam departs from ini-tial straight-line position and vibrates around new buckled configuration. It is supposed that elastic properties of the system remain linear for this value of large displacements. Bended shape of the beam and axial displacements u of the elastic line caused by buckling are uniquely determined by lateral displacements w(s) meas-ured in the natural coordinate system of the beam [2].

The beam is discretized on n standard Euler beam elements with two nodes and four d.o.f. in the element displacement vector {d}ei = {w1 w1,s w2 w2,s }

T Using derivatives w1,s and w2,s as nodal displacements (which represent sine of slope angles) instead slope angles θ1 and θ2 al-lows usage of the same function of interpola-tion and shape function as in linear analysis [2].

Considering third order polynomial interpola-tion function, displacement of arbitrary point could be calculated from nodal displacements as

where [N] are element shape matrix as in case of linear analysis of bending and stability [3].

Potential energy of deformation caused by beam bending may be calculated as

where κ is curvature of the elastic line in natural coordinate system, and B is bending stiffness.

Fig. 1: Buckled simple beam and beam finite element with large displacements

(1)

(2)2

15

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

Expanding (2) in power series (limiting third order), and inserting equation for displacement (1), we get the following expression for the deformation energy concentrated in the beam under bending

Variation of deformation energy is then given by

where matrix epresents element stiffness matrix [k]ei , known in linear analysis [3], and matrix [k1] is element matrix of nonlinear effects on beam stiffness, given by

Axial displacement ΔL of the end of beam, where acts axial force, is given by

where in power series expansion are used members up to forth power.

Using (6) and inserting expression for interpolation of displacements (1), potential energy of the axial force may be written in the form

Variation of the potential energy of the axial force may be written as

where is stress stiffening matrix of the beam finite element [kσ]ei [3], and matrix [kσ]

ei is ma-trix of nonlinear effects on stress stiffening of the beam with second order coefficients, given by

Because of small axial displacements and low vibration frequency, variation of kinetic energy T of the motion in the vertical direction is given by linear expression known from analysis of small vibration

where [m]ei is consistent mass matrix of the beam finite element [3]. An equation of motion of the beam is derived on the basis of Hamilton’s principle.

16

(11)

(12)

(14)

(15)

(13)

Supposing that displacement vector {D} receives arbitrary perturbation δ{D}, which vanishes at the boundaries of the time interval [t1, t2], equation of motion could be written in the form

where [M], [K], [Kσ], [K1] and [Kσ1] are matrices of the structural size, created by standard finite ele-ments procedure from corresponding element matrices [m]ei, [k]ei, [ks]ei, [k1]ei and [kσ1]

ei [3].

direct integration of the equation of motion

Equation (12) is solved by using implicit direct integration method. Starting from initial condition {D}(0), {D}(0) and chosen time step Δt, displacement vector {D}(i+1), is calculated from equation

This solution by direct integration method is time consuming, because et every time step i calcula-tion of displacement requires additional subiterations. It may be very helpful if approximate solu-tion exists which predicts nature of the solutions with acceptable accuracy. In this purpose, lets consider that {D}0 is buckling eigenvector, and b is chosen representative displacement (e.g. middle point displacement in the case of the simple beam). Buckling eigenvector then may be written as

where is scaled by value of representative displacement b in {D}0.

Considering displacement vector {D} in shape of buckling eigenvector [5, 6], and multiplying (12) by , we get one differential equation in the form

Fig. 2: Phase orbit of the beam middle point for different value of axial force

w/L w/L

17

Equation of motion is now equation of one un-known variable b, and for it is neccessarry to cal-culate given matrix products only once, usung results of linear stability analysis.

On the Fig. 2 are presented results of inte-gration of the equation of motion (12) for mid-dle point of the simple beam, obtained by using both equations (13) and (15). Results are given through phase plane of the point for two values of axial force and initial position in the buckled shape where middle point has displacement L/100. Following data are used: E = 210 [GPa], L = 0.34 [m], I = 0.216·10-10 [m4], Δt = 0.0003 [s]. Re-sults show that simplified equation (15) may be used for value of axial force lower then 1.05Pcr (which is also limit of accuracy of the equation of motion containing third order terms).

resuLts discussion

Fig. 3. presents content of frequency spectrum of postcritical vibration (a) and change of the base frequency for different value of axial force and initial displacement (b) given through ratio of postbuckling frequency and frequency of free vibrations. Frequencies are calculated ap-plying Fourier Transform (FFT) to the solutions of equation (12). Zero frequency in the spec-trrum shows existence of departure from initial straight-line equilibrium position, and first and second higher harmonics of base frequency show large displacement. Increasing of axial force causes increasing of the base frequency. Increasing of the initial displacement causes increasing of the frequency also, because of ef-fects of nonlinear stiffness and stress stiffening terms in equation of motion.

concLusions

Finite element analysis of posbuckling frequen-cy change is presented. It is derived nonlinear equation of motion and solved using direct inte-gration method. Frequency is calculated by FFT trans-formation of obtained numerical resultsin time domain. Significant decreasing of calcula-tion efforts is obtained by simplified equation of motion, given by single nonlinear differential

equation. Obtained results show slow increasing of base frequency with increasing of axial force and initial displacement from initial stright-line position, what points to stable equilibrium con-figuration of buckled beam.

Fig. 3: Frequency spectrum and frequency change of buckled simple beam

18

Fig. 3: Frequency spectrum and frequency change of buckled simple beam

THOMSEN, J.J.: “Vibration and Stability – Order&Chaos, Technical University of Denmark, Lyn-1. gby, 1994.THOMPSON, J.M.T., HUNT, G.W.: A General Theory of Elastic Stability, John Wiley & Sons, 1973.2. COOK, R., MALKUS, D.S., PLESHA, M.: ‘’Concepts and Application of Finite Element Analyses’’, 3. John Willey & Sons, New York, 1988.THOMSEN, J.J.: “Chaotic Dynamics of Partially Follower-Loaded Elastic Double Pendulum”, Jour-4. nal of Sound and Vibration, Volume 188, Issue 3, Pages 385-405, October 1994. ISIC, S., DOLECEK, V., KARABEGOVIC, I.: “Bifurcation Analysis of Elastic Systems Based on Fre-5. quency Spectrum of Large Vibrations“,The 17th International DAAAM Symposium “Intelligent Manufacturing & Automation: Focus on Mechatronics & Robotics”, Wien, Austria, 8-11th No-vember 2006ISIĆ, S., DOLEČEK, V., KARABEGOVIĆ, I.: “An Identification of Bifurcation Type Using Postcritical 6. Motion Analysis “, Proceedings of 5th International Congress of Croatian Society of Mechanics, September, 21-23, 2006, Trogir/Split, Croatia, Pages 83-84.

Literature

inteLLiGent MecHatronicaL sYsteM usinG rePuLsiVe force Produced bY PerMannet MaGnets


Two permanent magnets can be used for both the breaking of moving object and sensing its posi-tion. Such system design and analysis need the exact calculation of magnetic field. The robust com-putational method uses integral form of Biot-Savart Law working with coupled volume and surface currents derived from magnetization. Either the simplest assumption of uniform magnetization shows a good agreement between calculated flux density and experimental results, with an excep-tion of the field near magnet edges. This assumption also allows the reliable calculation of repulsive force. The calculated dependence of axial and radial components of flux density on distance be-tween magnets exhibits a maximum for suitable Hall probe position. Since the maximum position is different, the distance measurement is possible by using two Hall probes. The calculations give all data necessary for the design of controller that allows the correct operation of this simple but robust mechatronical system.

Abstract

19

The advantage of mechatronical systems is that they connect both the mechanical act-ing part and electronic control. The system for mechanical breaking based on repulsive force permanent magnets contains both the parts in a very simple way. The magnetic flux due to the permanent magnets produces the force. Since its value depends on magnet position, it can be simultaneously used for device position meas-urement and control. The ideal measuring ele-ment is the Hall probe and the exact control can be realised by smart sensors or microprocessor controller. However, the most important prop-erty of the new solution is simplicity, reliability and robustness, since only two permanent mag-nets of simple ring shape are used.

The use of permanent magnets for breaking force realisation is a new idea; therefore, there are practically no experiences with it. A simple and relatively cheap way is to model the device, estimate its parameters and simulate its action. The parallel simple experiments must be made in order to verify the models. The modelling of the system is a subject of this paper. The paper outlines basic theory, mentions the experiment, presents the results of numerical calculation, compares them with experiment and discusses future use.

tHeorY

The magnet is given very simply by its geometri-cal parameters and magnetization M that fully describes its magnetic properties. There are two basic ways how to calculate all the magnet effects. They can be derived by superposition either from elementary magnets of magnetic momentum MdV in the magnet volume or from the coupled elementary volume imdV and sur-

face jmdS currents that are derived from volume distribution of magnetization in the sample. In basic textbooks of electromagnetism there is a proof that the effect of coupled currents is equivalent to the action of magnetic dipoles. We have preferred the method of elementary coupled currents, since the (free) currents are used frequently in electrical engineering. The magnetic flux density B due to both the coupled currents is given by formula

where im and jm are coupled volume and surface current density, respectively, S and V are the surface and volume of the magnet, respectively, r is a position vector of the point, where the flux density B(r) is calculated, r0 is the position vec-tor of surface and volume elements dS and dV, respectively. The formula requires numerical in-tegration and can be used for the calculation of magnetic force as well as for the measured the Hall probe field dependence on the position of magnet.

The magnetic force between two perma-nent magnets can be calculated at least by three methods: by the superposition of forces between elementary magnetic dipoles, the superposition of forces between elements of surface and volume coupled currents and by the superposition of forces, by which the field of one magnet acts on the elementary coupled currents of the second magnet. We preferred the third method because of its universality.

retarding force, position sensor, magnetic force, permanent magnet, Hall probe

Key words

(1)

20

The fixed magnet produces the field. The for-mula for resulting force F for moving magnet at position r can be written as

where B(r0) is the magnetic field at position r0 of surface and volume elements dS and dV, re-spectively, jm and im are coupled surface and vol-ume current densities, respectively, S and V are the surface and volume of the moving magnet, respectively.

In the simplest case we consider the uniform magnetisation, since it is the only value given by a producer. As a consequence, the coupled vol-ume currents are zero and surface ones are of uniform density. The flux density and magnetic force should be calculated by numerical integra-tion either for very simple magnet shape, cylin-der or ring.

eXPeriMent

The commercial ring magnet used in prelimi-nary experiments had geometrical dimensions: thickness of 4 mm, inner radius of 25 mm and outer one of 70 mm. The magnetization was 1.2 T, approximately. We have made measurement of the magnetic flux density and repulsive force. Both the experiments were made on fully auto-mated apparatus.

The measurement of magnetic field was made by commercial Hall probe instrument that is automatically moved in a plane parallel to

magnet main surface. Since the Hall probe di-mensions are relatively large, the average value of magnetic flux density was measured, instead of the strict local value. A relatively low number of measured points were reached. The experi-ment with Hall probe for the measurement of magnet position was not realized yet.

The repulsive force was measured by pi-ezoelectric sensor and the position of moving magnet was scanned by a commercial LVDT (Lin-ear Variable Differential Transformer). A high number of measured values were processed by standard statistical methods.

resuLts

The calculation of magnetic flux density and re-pulsive force was made by numerical integration in MATLAB. Since there were a large number of nested cycles, the computation time was relatively long, tens of minutes in complicated cases. Only typical results and comparison with experiment will be presented here.

The comparison of calculated and measured magnetic field is in Fig. 1. The flux density is calculated across the magnet diameter at two distances: just on the magnet surface and at the distance 5 mm from it. Measured values are given by crosses. The calculated values were averaged in order to take into account final di-mension of the sensing element. With except of a magnet edge, the agreement with experiment is good. The total coupled surface current is also shown in Fig. 1. Its value cannot be realised in practice, probably.

Fig. 1: Calculated and measured magnetic flux densityx [mm] x [mm]

(2)

21

The dependence of total force between mag-nets on the distance between them is in Fig. 2. According to the experiment three magnets were considered. This choice is an optimum se-lection, as the calculations revealed. The total coupled surface current is very high – 12 kA.

Only a small part of experimental points, de-noted by crosses, is used for comparison. The repulsive axial force has a relatively high value and there is a relatively good agreement with experiment. Nevertheless, small systematic de-viation exists.

The equilibrium for repulsive force is unstable. Any small deviation of the moving magnet from perfect axis position leads to the momentum that tries to rotate the magnet into the position of attractive force which has a minimum of po-tential energy. If the rotation is not possible, the radial force acts on the bar in the hole. The de-pendence of radial force of the deviation from equilibrium position is in the right hand part of Fig. 2. The force is not high in comparison with axial one, nevertheless its negative effects, for

instance the friction, should be taken into ac-count in the design of the device. The measure-ment of radial force is difficult; therefore no comparison with experiment is presented.

Hall probe positioned in fixed point can be used for the measurement of the distance between magnets. However, the flux density depends on the probe position. We have con-sidered several positions of the probe in the up-per plane of fixed magnet outside the external

Fig. 2: Axial and radial forces between magnets and a comparison with experiment for axial force

Fig. 3: Dependence of flux density on distance between magnets for 2 positions of Hall probe

700

600

500

400

300

200

100

0

z [mm]

Comparison with experiment ... Brem = 1.3 T Radial force ... Im 12 kA

F z [N

]

z [mm]

22

Fig. 3: Dependence of flux density on distance between magnets for 2 positions of Hall probe

diameter. The Hall voltage is proportional to the magnetic flux density. The dependence of flux density (and Hall voltage) on the distance be-tween magnets for near and far probe position is given in Fig 3.

Both the curves, for axial (Bz) and radial (Bx) component of magnetic flux density, exhibit a maximum at some distance between magnets. The position of maximum is given by vertical lines in Fig. 3. Maximums are shifted to higher positions with increasing distance of the probe from magnet. Unfortunately, the probe sensi-tivity decreases dramatically.

Since the curves have maximums, the two distances between magnets will be obtained from one Hall voltage for one component. For-

tunately, the maximums are not identical; the unambiguous distance can be obtained from both the components. For comparison, basic parameters for several probe position are sum-marised in Tab. 1 for several probe position xp from outer contour of fixed magnet in its upper plane. The second column shows the minimum distance that can be measured by radial probe. The total radial field change is in the third col-umn. Analogically, the fourth column contains maximum distance that can be measured by axial probe and in the last column there is the corresponding probe sensitivity. The sensitiv-ity decreases rapidly, as the distance of probe increases.

discussion

The outlined method needs only geometrical dimension of magnets and one material pa-rameter, magnetization. If we take into account very simple inputs and no corrections, the agreement with experiment is good and can be used in technical praxis. The agreement can be improved if we refine the model. The most im-portant neglect was the uniform magnetisation. The more correct magnetisation distribution can be assumed, while the calculations change only slightly. Unfortunately, there is not a simple and straightforward way how to find the correct distribution of magnetization. Method of trials and errors appears as the only one solution.

We have used the model of coupled currents and integral formulae for the calculations. Usu-ally the finite element method is preferred. Our approach has several advantages. The program-ming is relatively simple, the user has full check

at all steps of computation, and there are no problems with boundary conditions especially in infinity. All the quantities can be calculated at any given point and the accuracy can increase to any reasonable value. The only disadvantage is relatively long computation time, but the clus-ter can be used if necessary.

The main advantage of the new solution is that the magnetic field is used for two purposes: creating a repulsive force and, simultaneously, a voltage that determines the distance between magnets. Both the quantities depend on dis-tance nonlinearly. Furthermore, the correct value of distance needs both the components of flux density, axial and radial one. The precise calculation of force and Hall voltage characteris-tics for a given probe position, which was made by authors, can be used in the programming of the controller.

xp [mm] rmin [mm] ΔBr [mT] rmax [mm] ΔBz [mT]

3 1.5 116 12 149

6 4 48 21 79

9 6 28 26 49

15 11 11.5 36 26

Tab. 1: Parameters of probes for distance measurement

Radial force ... Im 12 kA

z [mm]

23

concLusion

The simple and exact method for complete anal-ysis of mechatronic system based on application of repulsive force between permanent magnets was realized. Even the simplest assumption of uniform magnetisation leads to acceptable re-sults for technical design. The simulation of the

dynamic behaviour of the whole system is pos-sible at present time. To authors’ knowledge no similar method was found in literature.

acKnowLedGeMent

Thanks to the fund of the Ministry of Industry FT-TA3/017.

KOŠEK, M., MIKOLANDA, T., RICHTER, A.: In: Proceedings of Technical Computing. 2007, Prague, 1. Czech Republic, 78. ISBN 978-80-7080-658-6.

Literature

eVaLuation and future tHe uLiMate LiMit state desiGnin GeoMecHanics

P. Koudelka

The introduction of seven out of eight EUROCODES (1-6, 8) was not so difficult like EUROCODE 7 (Geotechnical design) which has met theoretical problems. The problems do exist in the applica-tion of the limit states theory to the field of geotechnical design. The problems appeared clearly at IWS Dublin 2005 on Evaluation and Implementation of EC7-1 (final draft EN 1997-1) “Geootech-nical design: Part 1 – General rules” (great discussion forum for a general international evalua-tion of the final draft). This theory was formulated for geomechanics after 1950 (most probably it is possible to refer to Brinch Hansen, 1953) with, however, one fundamental fatal error, i.e. the introduction of substitute material physical characteristics to computation models which is at variance with the fundamental principles of mechanics. Almost all problems of geotechnics are significantly and complexly non-linear and the behaviour of theoretical models with different characteristics is different. This conclusion was attained in the Czech Republic after several dec-ades of limit states design application to geotechnics and after far-reaching theoretical studies. The paper presents an evaluation both of the “IWS Dublin 2005” results and the followed develop-ment in geomechanical designs. Some conclusions for theoretical research and practice are sub-mitted.

Abstract

24

geomechanical design, Ultimate Limit States, partial material factor, probability-based design, advanced numerical models

Key words

In mechanics (except for the geotechnical Limit States Designs) it is generally respected that in the cases of non-linear behaviour of the struc-ture (2nd order theory, elasticplastic state) the principle of superposition is not applicable and the computation of individual effects cannot be based on coefficients or additions of individual effects. In such cases every possible dangerous state and each of design situations must be ana-lysed separately.

The present basis of the LSD theory in geo-technics does not take the non-linear behaviour of soils and rocks into account. The little ac-ceptable derivation concept of property design values (analogously with man-made structures) applies particularly to the ULS (its unacceptabil-ity for Serviceability Limit State was recognized earlier). The definition of the statistically de-rived characteristic value as the value with the 5 % probability of occurrence of worse value governing the occurrence of the limit state, at variance with its term („characteristic“) chang-es the physical characteristics of the analysed model towards a low probability of the design model. The partial factors on ground properties further change the strength characteristics of soils and rocks towards even lower probability. When applied in the process of computation these modifications of design values radically change the properties of the analysed soil mass model, i.e. the properties of a structural system with non-linear behaviour, which, in the end, is improbable and almost dissimilar to actual sys-tem.

The above-described situation results in the fact, which can be called the Substitutive Properties Paradox, which can be defined as follows:

In a structural system with non-linear behaviour we analyse a not very probable (or almost im-probable) state, paying no attention to the most probable behaviour of the soil (rock) structure. Thus we do not know the actual reliability (or risk) of the soil (rock) structure, because this reliability and risk do not correspond with the combination of coefficients used.

This appears the problem hearth of geotech-nical designs according to the Limit State Design Theory and according to EC7-1 especially being long decades. Due to it the final draft of EC7-1 was evaluated on a base of wide international collaboration. The base for the evaluation was an International Workshop on the “Evaluation of Eurocode 7” (IWS Dublin 2005).

iws dubLin 2005

The workshop was held in Trinity College Dublin on 31st March and 1st April 2005. This workshop was organised by the European Regional Techni-cal Committee 10 (ERTC 10) of the International Society for Soil Mechanics and Geotechbnical Engineering (ISSMGE), by the Department of Civil, Structural and Environmental Engineering, Trinity College Dublin and Technical Committee 23 (TC23) of ISSMGE. A total of 55 participants attended the Workshop from 18 countries, 16 of these being European countries. And the situ-ation of the time?

The EC7-1 development had reached a very important stage, it had received a positive for-mal vote and thus been ratified by the CEN member states in April 2004 and CEN had is-sued the definitive text of EC7-1 in November 2004, this date is known as the Date of Avail-ability (DAV). Following the DAV, there was a two-years National Calibration Period, i.e. until

25

November 2006, during which each national standard organisation had to prepare its Na-tional Annex with its Nationally Determined Parameters (NDPs), i.e. partial factor values and values of other factors, so that EC7-1 can be im-plemented in its country.

concept of the workshop

Prior to the Workshop, 10 geotechnical design examples involving 5 different ranges of geo-technical design were distributed to the mem-bers of ERTC 10, Geotechnet WP2 and TC 23. These examples include 2 spread foundations, 2 pile foundations, 3 retaining walls, 2 designs against hydraulic failure and a road embank-ment on soft ground. A large number of solu-tions were received to these examples, which were prepared by geotechnical engineers from many countries. The solutions were sent to five reporters who were asked to examine the re-ceived solutions and identify the reasons for the scatter, i.e. ranges of solutions, and determine if this was the different interpretations of EC7-1 or due to other reasons (G. Scarpelli, V.M.E. Fruzzetti, R. Frank, B. Simpson, T. Orr and U. Bergdahl).

Given examples

The workshop organizers prepared the follow-ing set of geotechnical design examples:

1. Pad Foundation with vertical load only:Situation: embedment depth of 0.8 m, Jgroundwater at the foundation base, al-lowable settlement of 25 mm. Actions: G J k = 900 kN, Qk = 600 kN, con-crete weight density = 24 kN/m3.Ground properties: c J uk = 200 kPa, c´ = 0 kPa, Ф´k = 35° kPa, γ = 22 kN/m

3, SPT N= 40, mvk = 0.015 m2/MN.Require foundation width B to satisfy Jboth ULS and SLS.

2. Pad Foundation with an inclined and ec-centric load:

Situation: embedment depth of 0.8 m, Jgroundwater at great depth, allowable

settlement of 25 mm and maximum tilt is 1/2000.Actions: G J k = 3000 kN, Qvk = 2000 kN, Qhk = 400 kN at a height of 4 m above the ground surface. Variable loads are inde-pendent to each other.Ground properties: c´ J k = 0 kPa, Ф´k = 32° kPa, γ = 20 kN/m, E´k = 40 MPa. Require foundation width B. J

3. Pile Foundation designed from soil param-eter values:

Situation: bored pile of 0.6 m diameter, Jgroundwater at depth of 2 m below the ground surface. Actions: G J k = 1200 kN, Qk = 200 kN, con-crete weight density = 24 kN/m3. Ground properties: c´ J k = 0 kPa, Ф´k = 35° kPa, γ = 21 kN/m3, SPT N ´25. Require pile length L. J

4. Pile Foundation designed from pile load tests:

Situation: driven piles, diameter = 0.4 m, JLength = 15 m, allowable settlement of 10 mm, no transfer the load. Actions: G J k = 20000 kN, Qk = 5000 kN. Pile resistance: 2.static pile load tests, Jloaded beyond a settlement of 40 mm to give limit load. Require number of piles needed to satisfy Jboth ULS and SLS.

5. Cantilever Gravity Retaining Wall: Situation: height of 6 m, base and wall Jthickness = 0.4 m, embedment depth of 0.75 m, groundwater at depth below the base, ground behind the wall slopes up-wards at 20°. Actions: characteristic surcharge behind Jwall 15 kPa. Ground properties: sand beneath wall: c J ´k = 0 kPa, Ф´k = 34° kPa, γ = 19 kN/m

3. Fill behind wall: c´ J k = 0 kPa, Ф´k = 38° kPa, γ = 20 kN/m3. Require width of wall foundation B, de- Jsign shear force S and bending moment M in the wall.

6. Embedded Sheet Pile Retaining Wall:Situation: excavation depth of 3 m. J Actions: characteristic surcharge behind J

26

wall 10 kPa, groundwater level at depth of 1.5 m below ground surface behind wall and at the excavation surface in front of wall. Ground properties: sand beneath wall: c´ J k = 0 kPa, Ф´k = 37° kPa, γ = 20 kN/m

3. Require depth of wall embedment D, de- Jsign bending moment M in the wall.

7. Anchored Sheet Pile Quay Wall: Situation: quay height of 8 m, horizontal Jtie bar anchor placed 1.5 m under sur-face. Actions: characteristic surcharge behind Jwall 10 kPa, groundwater levels at depth of 4.7/5.0 m below ground surface be-hind/in front of wall resp. Ground properties: sand beneath wall: c´ J k = 0 kPa, Ф´k = 35° kPa, γ = 18 kN/m

3. Require depth of wall embedment D, de- Jsign bending moment M in the wall.

8. Uplift of a Deep Basement: Situation: Long structure, 15 m wide, with Ja 5 m deep basement. Actions: characteristic structural loading Jgk = 40 kPa, concrete weight density γ = 24 kN/m3, wall thickness = 0.3 m. Ground properties: sand beneath wall: c´ J k = 0 kPa, Ф´k = 35° kPa, γ = 20 kN/m

3. Require: thickness of base slab, D for safe- Jty against uplift.

9. Failure by Hydraulic Heave:Situation: Seepage around an embed- Jded sheet piles retaining wall, excava-tion depth of 7 m. Ground water level 1.0 m above ground surface in front of the wall. Actions: No other. JGround properties: γ = 20 kN/m J 3. Require: Maximal height, H of water be- Jhind the wall above ground surface in front of the wall to ensure safety against hydraulic heave.

10. Road Embankment: Situation: A road embankment with width Jat the top of 13 m is to be constructed over soft clay, side slopes keep relation of 1:2.

Actions: Traffic load on embankment q J k = 10 kPa. Ground properties: Fill for embankment: Jc´k = 0 kPa, Ф´k = 37° kPa, γ = 19 kN/m

3. Clay: c J uk = 15 kPa, γ = 17 kN/m

3. Require: maximal height, H of embank- Jment.

These individual examples, of course, could not show solutions of the tasks through all param-eters scales. However, despite it, the solution large number brought very worth knowledge on an international design practice and the code applicability. Let us to have a look at the results.

tHe worKsHoP resuLts

Geotechnical engineers from many countries prepared a large number of solutions to these above-presented examples. It was found that there was considerable scatter in the solutions received for the most of these design examples. T.L.L. Orr presented the ranges in the ultimate limit state solutions received for the examples in the form of how much the maximum or mini-mum values for the requested parameter are greater or less than the mean of the maximum and minimum values, expressed as a percent-age of mean of these values. The result range can obtain also using another point of view if we compare the maximal value to the minimal ones and express the scatter in percentage of the minimum. Both approaches are involved in Tab. 1.

T.L.L. Orr prepared a set of fully worked model solutions, using his preferred calculation models and design assumptions. The results of the model solutions are summarised in Tab. 2 with model solutions for ULS design, using the three Design Approaches where relevant, pre-sented in bold. The ranges of the model solu-tions due to the different Design Approaches are much smaller than the ranges of the received solutions in Tab. 1. This is caused obviously due to the unified procedure, partial factors and al-gorithms.

27

eVaLuation

The solutions of contributors were evaluated by the reporters respective to the examples. A presentation of the complete workshop evalua-tion of EC7-1 is out of the Paper range. However, let we look at results of the examples 6 (Fig. 1) and 10 (Fig. 2) more in detail.

example 6: embedded retaining wall

The given situation, inputs and require are pre-sented in Chapt. 2, the following Fig. 1 shows the example in general. B. SImpson ś evalua-tion can be find in Fig. 3 further. Points on the graph are annotated as follows to represent the various EC7-1 design approaches (DA): 1 – DA 1, taking the worst case of Combination 1 and 2; 2 – DA 2; 3 – DA 3 and N – an existing National method. The horizontal axis gives a scale to re-

Example Type Parameter Range of Re-ceived Solutions

% Range

T. Orr to minim.

1 Spread Foudation, vert. load B - foundation width 1.4 - 2.3m ±24% 64%

2 Spread Foudation, incl.ecc.load B - foundation width 3.4 -5.6m ±24% 65%

3 Pile Foundation - from soil para. L - pile length 10.0 - 4.2.8m ±62% 328%

4 Pile Foundation - from pile tests N - number of piles 9 - 10 ±5% 11%

5 Gravity Retaining Wall B - wall base width 3.1 - 5.2m ±37% 68%

6 Embedded Retainig Wall D - embedment depth 3.9 - 6.9m ±37% 77%

7 Anchored Retaining Wall D - embedment depth 2.3 - 7.0m ±51% 204%

8 Uplift T - slab thickness 0.42 - 0.85m ±33% 102%

9 Heave H - hydraulic height 3.3 - 8.8m ±45% 167%

10 Embankment on soft ground H - embankment height

1.6 - 3.4m ±36% 113%

Tab. 1: Ranges of received ULS solutions for the examples using EC7-1 (After T.L.L. Orr)

Tab. 2: Summary of model solutions with ranges of model solutions for ULS design (by Orr)

quired embedment values in meters, a country denotation of the contributors are added to the vertical axis however, it is not obvious.

If we do not consider the lowest national far-off value on the first horizontal line (about 2.6m what is obviously too low) the scatter of ex-ample calculations is between values of 3.2 m and 6.9 m. The difference between the lowest considerable value and the low limit of the scat-ter presented by T. Orr in Tab. 1 (3.9 m) is not negligible. This fact shows that both Tab. 1 and Tab. 2 include solutions according to EC7-1 only and that generally the solutions ranges are sig-nificantly wider.

We can see the National solutions (N) give the more effective results generally. The accord-ance of the most their results about embed-ment of 4m is remarkable. The lower effective-ness of the designs according to the all EC7-1 approaches is clearly obvious.

The author’s calculations are placed in the lower half of Fig. 3 between two red lines. The presented black annotation of two designs ac-cording to EC7-1 is not correct: the design de-noted black “b” accords with DA 2 (marked red – value of 3.5m) and similarly design denoted black “1” with DA 3 (red – value of 3.9m). Two other designs according to Czech standards de-noted “N” (in red circles) respect two different theoretical accesses: the one accords to the optimal values of active earth pressure for the peak shear strength state (short-term retain-ing structures - value of 3.2m), the other rep-resents design for the residual shear strength state (longer-term retaining structures - value of 4.2m).

All four designs belong to the most effective ones of the whole set.

example 10: embankment on soft Ground

The material data of the example are given probably according to a local experience but not in accordance to theoretical and physical principles: shear strength of embankment are given in terms of effective stress however, shear strength of clay is given in term of undrained value. Thus, without any doubt, the results are influenced due to this incorrectness and have not full validity.

28

Fig. 1: Given example 6: Embedded Retaining Wall

Fig. 2: Given example 10: Embankment on soft ground

29

Despite it let us to have a look at evaluation in Tab. 3. The results are sorted according to the design approaches used in 7 groups named like Country:

Country 1 - approach DIN 1054; bearing capac-ity formula.

Country 2 - approaches of EC7-1: DA1-2, DA2, DA3, OFS; bearing capacity formula, Annex D, analysis according to Bishop simplified method of slices.

Country 3 - approach of EC7-1: DA3; bearing ca-pacity formula, Annex D.

Country 4 - approaches of EC7-1: DA1a-b-2a-b, DA3a-b; computing programme PostoGRAF v. 3.0 (Bishop method of slices).

Country 5 - approach and Global Bearing analy-sis by Taylor and Swisscode;

Country 6 - approaches of EC7-1: DA1-2; over all stability analysis for slopes (SLOPE W).

Country 7 - approaches of EC7-1: DA2 and by National Code; analysis according to Swedish slip circle.

Tab. 3 shows the wide scatter of the results. The most of them around embankment height of 2.2m are probably in accordance with the local experience of the example author. This experience includes doubtless also other ma-terial properties and local peculiarities (pore pressure, moisture, soil grains, geological de-velopment and others). If the clay undrained shear strength is substituted by effective stress values for soils of the group F7 according to CSN 73 1001 (Czech Standard) then a solution leads to the values in red circles. The difference be-tween the both solutions (EC7-1/Safety Factor Design) is also very wide and shows the lower effectiveness of ULS design according to EC7-1. The example does not appear to be suitable for the evaluation.

concLusion to uLs desiGn

The workshop evaluation of EC7-1 is very im-portant and has brought very important knowl-edge. The evaluation is not the only one. An ear-lier evaluation of four basic geotechnical tasks (slope stability, earth pressure, shallow and pile foundations) has been carried out at the Insti-tute of Theoretical and Applied Mechanic of Czech Academy of Sciences. These four studies analyzed the problems not example by example but in wide usual scales of all parameters. These analyses brought the wide valid results and sim-ilar conclusions as the workshop. The general conclusion can be formulated as follows.

Theoretical base of the ULS geotechnical de-sign is not in concordance with the principles of mechanics and this fact has a principal influence

Fig. 3: Results of the Ex.6: Embedded Retaining Wall - embedment in m

30

for design. Except it, the theoretical ULS design concept of EC7-1 and Limit State Design Theory (quasi-probabilistic method) after long-term development (about 50 years) does not corre-spond to contemporary technical and theoreti-cal possibilities of state of the art.

future of GeotecHnicaL desiGn

An more long-term application of the contem-porary ULS Design on quasi-probabilistic con-cept based appears counter-productive and problematic without some corrections of EC7-1. These can be carried out in the National annex-es. The concentrated attention need especially the characteristic value definition, both material partial factors and partial factors for resistances in Annex A, concept of earth pressure and some less important other. That corrected code would be used some time until development finish of a new fully modern concept and a code.

From contemporary point of view there can be found that a good concept of geotechnical de-sign for the future appears in fully probabilistic methods. These methods are applied more and more in other ranges of structure mechanics.

acKnowLedGeMent

The Grant Agency of the Czech Republic and the Grant Agency of the Czech Academy of Sciences provided financial support of the connected re-search (GP Nos.103/2002/0956, 103/2005/2130, 103/07/0557, 103/08/1617 and No. A2071302 resp.). The author would like to thank them all for support.

Tab. 3: Results of the Ex.10: Embankment on Soft Ground - embankment height in m

ČSN 73 1001 Shallow foundations, CSNI, Prague, 1987.1. EUROCODE 7 November 2004. Geotechnical design – Part 1: General rules (Final draft). Brus-2. sels, CEN/ TC 250/SC7-WG1.ORR T.L.L. et al.: Evaluation of Eurocode 7. Proceedings of the International Workshop. 2005, 3. Dublin, Ireland.

Literature

31

Application of mechanical commutators in DC micromotors causes pulsation of the current passing in the armature circuit. Its fre-quency is dependent on the number of commu-tator sectors. Number of pulses per one revolu-tion of the rotor is determined by the formula n = 2k, where: n – number of pulses, k – number of commutator sectors. They had various de-sign solutions of the commutator, among other things, various brush units (graphitoidal brush-es, metal brushes collaborating with cylinder segments or ring sectors).

Positive side of the current pulses could be us-ing them to the identification of the angular position of the micromotors rotor. With the positive effect was made in Institute of Micro-mechanics and Photonics the study of the new transducer - transforming pulses of the current into the digital measuring signal. The first idea of the measuring path has been presented in papers [1-3].

In Institute of Micromechanics and Photon-ics [4] made complex experimental analysis of influences of kind of micromotor, conditions of work, their wear on changes of resistance. The

contactLess anGLe transducer dedicatedfor dc MicroMotor

M. Bodnicki, H. J. Hawłas

Presented transducer realizes idea of detection of mechanical quantities in electric micromachines on basis of electrical signals. Changes of the resistance cause pulsation of the current passing in the armature circuit and its frequency is dependent on the number of commutator sectors. One decided to examine a possibility of using a transducer, determining the angular position of the ro-tor on the basis of modulations of the armature current mentioned above. The LEM (based on Hall Effect) sensors are used as current/voltage transducers. The advantage is elimination of galvanic contact between armature and measurement unit. The originality of new solution is method of the elimination of component proportional to mechanical load from the current signal. Proposed method was testing on computer simulation way and in physical experiment then the prototype was built. New transducer is proposed for control application in high dynamic DC drive systems of small size mechatronic devices.

Abstract

angular position, measurement, contactless transducer, mechatronics, DC micromotor

Key words

32

examples of signals, which are representative for those examinations are presented on Fig. 1 (those signals are in fact input signals for meas-uring unit).

There are following conclusions for this anal-ysis:

High frequency noises are the effect of Jfriction in pair: brushes and segment of commutator; For typical supply voltage (higher than J 1/6 of nominal value) amplitude of the noise

is constant (under the load ½ to nominal value; but its value is higher then in no-load situation); Work under extremely load is dangerous Jfor lifetime of the motor (big currents and sparking; Constant component depend on load (its Jalso clear from mathematical model of DC micromotor) The firs harmonic is an effect of eccentric Jof the rotor – this harmonic could be hard to elimination.

aLGoritHM of tHe new trans-ducer

As a first step the analysis of the high limit of the frequencies of the commutation phenom-ena was done. For the DC motors with no-load speed to 20.000 rpm (estimated) and to 13 sec-tions in commutator the high limit of the pulsa-tion could be circa 50 kHz. It means – the higher components in the current signal could be take as noise.

The following algorithm was than proposed:

Filtering of the high frequency noises;a. Detecting and separation of the “medium b. signal” (component proportional to load of the micromotor, determined on way of filtering “step a” signal); Subtraction of the “medium signal” from c. the filtering (step a) signal – generation of the differential signal;Digitalization of the differential signal - d. generation of the TTL pulses;

a) b)

c)

Fig. 1: Input signals for measuring unit obtained during work various kinds of DC micromotors [4]: a) Ordinary micromo-tor (for popular electric toy); b) world famous manufacture, long work under load; c) world famous manufacture

33

Then the test on prototype was done. The op-timization of the filter parameters was made

successfully. The exemplary results are pre-sented on Fig. 3.

a) b)

a)

b)

The structure of the measuring unit is present-ed on Fig. 2. The LEM (based on Hall Effect) sensors are used as current/voltage transduc-

ers. The advantage is elimination of galvanic contact between armature and measurement unit.

The transducer of angular position, simplified this way, was laboratory tested within the range of observing the shape of the output signal from

the transducer while staring the micromotor, as well as under steady-state conditions of its op-eration. During these studies, one selected also

Fig. 2: Structure of the measuring path: a) basic version, b) advanced version with additional filtering and buffering.

Fig. 3: Elements of the optimization of the filtering block:a) too small frequency limit, b) final effect of optimization

34

suMMarY and concLusion

The laboratory test of prototype was done. Transducer works correct. There are the follow-ing advantages of the unit:

galvanic isolation from the motor arma- Jture good detection of the first pulse in dy- Jnamic applications the tuning in wide range and fitting to the Jspecific micromotor is possible; constant length of the output pulses (and Jdistance between following two is pro-portional to the angular speed of the mo-tors rotor).

Now the next version – optimized from point of view of miniaturizing – is taken in to considera-tion.

a)

b)

Fig. 4: Signal generated by LEM transducer and finally output signal of the encoder:a) dynamic situation (start-up of the DC motor), b) work with stabile angular speed of the DC motor

the triggering level of the flip-flop digitizing the signal. The effect was positive. The system op-erates correctly under variable conditions of loading. In accordance with the expectations, the trend within the input signal, resulted by

an instantaneous value of the torque braking the motor, is being eliminated correctly. The system is more effective the old version with measuring resistance [1].

35

BODNICKI, M.: Encoder Using Pulsation of the Current in DC Micromotor - Model Tests. Hydrau-1. lika a Pneumatika, v.2, no. 2, 2000, pp. 35-36.BODNICKI, M.: Additional effects of commutation phenomena in DC micromotor - identification 2. and application for positioning. In Proceedings of the 47. Internationales Wissenschaftliches Kolloquium Technische Universität Ilmenau, 23-26.09.2002, Ilmenau (Germany), pp. 143-144 (Full text on CD).BODNICKI, M., ROMANOWSKI, J.: Przetwornik położenia kątowego wirnika mikrosilnika. Pomi-3. ary. Automatyka.Robotyka. no. 7/8, 2001, pp. 46-51.ROMANOWSKI, J.: Opracowanie metody i układu badawczego do identyfikacji położenia 4. siłownika mikromodułu napędowego. MSc Thesis, IMiF PW, Warszawa, 2000.WIERCIAK, J.: Model mikrosilnika prądu stałego w pomiarach jego charakterystyk obciążeniowych. 5. Zeszyty Naukowe Politechniki Śląskiej no. 1230, pp. 401-407. Gliwice 1994.

Literature

tubuLar MetaL Powder PerMeabLe MateriaLs witH ani-sotroPic structure and tHeir aPPLications


The review of the theory and known methods of producing of porous powder materials (PPM) with anisotropic structure is revealed. The new devices for water and gases filtration with filtering elements from PMM with anisotropic structure and the examples or their perspective application is offered. The advantages of the PMM with anisotropic structure in comparison with PMM with isotropic structure are proved. Special attention is given to the producing of the tubular metal pow-der anisotropic materials by the magnetic-pulse compacting. The possibilities of changing of the porous structure and properties of detail from compacted powder material during deformation in pulse electromagnetic field are offered. The examples of producing of the permanent connections of the tubular and rod details are shown.

Abstract

36

metal powder goods, permeable materials, anisotropic structure, magnetic-pulse compacting

Key words

The intensive development of industry, agri-culture, and cities require creation and intro-duction of new highly effective equipment for the purification of drinkable, sewage and indus-trial water, foodstuffs, other liquid and gaseous media from the pollution and toxic substances, the protection from noise of industrial instal-lations and transport means. Porous powder materials (PPM) and articles have many applica-tions in various industrial fields. A production of such materials requires the special technol-ogy of material synthesis and preparation [1], moulding, sintering and treatment [5,8]. On the basis of PPM the articles for the protection of environment (aerators and dispersers for the systems of the preparation for drinking water and purification of waste water, filters, sound suppressors and others are developed [6].

Production of tHe anisotroPic PerMeabLe MateriaLs bY tHe MetHod MioM (MaGnetic PuLsa-tion treatMent of MetaLs)

Magnetic-pulse extrusion

PPM are characterised by a number of the struc-tural and operational parameters, which are de-termined by the properties of initial powders. The method of magnetic-pulse extrusion PPM proved its expediency with the manufacture of lengthy and thin-walled porous and multilayer articles [2,7]. In this case molding article in the inductor without its displacement (Fig. 1a) and step molding (Fig. 1b) are distinguished.

During the extrusion of powder according to the first diagram a certain change in the poros-ity of models occurs, which is connected with a change in the electromagnetic pressure at the ends of the pipe (Fig. 2). In this case the intro-duction into the cavity of the inductor of the bil-let as a result of the manifestation of axial skin

effect is observed a local increase in the pres-sure, and consequently increase in the density. This pressure increment negatively affects the quality of articles. The most effective combat means with this phenomenon is the screening of ends cast.

Fig. 1: The diagram MIOM (magnetic pulsation treatment of metals) of powder in the shell without the displacement (a) and step molding (b) 1- inductor; 2- electrically conducting shell; 3- silencer; 4- powder

37

The more complex nature of the distribution of the density (porosity) of article in the radial sec-tion. The estimation of this phenomenon was accomplished by measurement of Vickers hard-ness (depression of diamond pyramid with the effort 50 N [4]).

Measurements shown the decrease of the density (hardness) towards the centre of the sample. In this case the anisotropy of properties in the radial direction grows with an increase in the energy level of extrusion. The study of the properties of tubular models with the small wall thickness proves the possibility of achieving the uniform distribution of properties.

step molding

For preparation of the lengthy components with length-diameter ratio from 10 and more find the so-called radial- sequential methods of packing (or step-packing) is used. The actual stress state, that appear in the transition zones, depends on the geometric relationships, which determine the angle of taper, the conditions for boundary friction powder- shell and powder- mount, and also from the deformation rate. In the known method of step packing the suc-cessive pressing of the elements of article with the step is provided. In this case in the places of passage the seam is formed, which appearance is explained by edge effects and strengthening of material. We proposed the method of step packing, where packing divided into two several motions with the increased step (Fig. 1b).

aPPLications of PPMProduction of the porous vaporizers

Studies were conducted on the powders of ti-tanium of the stamp PTES-1 (ПТЭС-1) of frac-tion from 63 to 300 mkm. Specific area of the particle was 0.24 – 0.46 m3/g., and bulk density varied in the range from 710 to 860 kg/m3. Po-rosity, permeability according to the results of mercury porosimetry are given in Tab.1.

Sintering was conducted in the vacuum. a study of pore structure was conducted by mean of the mercury porosimeter of Mikrometriks (USA). The samples of articles show the high coeffi-cient of permeability on all ranges of porosity. PPM from the powder of titanium were success-fully tested for preparing the vaporizers of the

camera of vapour plating. With the production of the complex constructions the method of welding separate elements was applied.

Fig. 2: Change of electromagnetic pressure along the axis of inductor - without the component (1); with the shell, but without the powder (2); with the powder (3)

Size of particles, mm

General porosity, %

Coefficient of permeability,

k*1013 m2

Size of pores (Max), mkm

Size of pores (Average),

mkm

Average size of pores by mean of mercury porosimetry, mkm

-315 +200 32 34 40 19 19.4

-200 +160 31 10 21 12 14.4

-100 +63 44 7 14 9 9.5

Tab. 1: Properties of articles made of the powder of titanium according to the method MIOM (magnetic pulsation treat-ment of metals)

38

Production of thermal pipe ele-ments

As is known [8] the widest application find thermal cylindrical pipes with the porous layer, fixed on the internal wall of pipe. In this case to similar elements are presented the high de-mands relative to the reliable metallic bond of the particles of the powder and pipe, open-ness of capillary structure and high permeabil-ity, and also uniformity of properties along the length. From many materials, suitable for pre-paring the body of thermal of pipe, copper and aluminium are processed by pulse the magnet. The centering steel support was established inside the pipe with a diameter of 16-20 mm and with a thickness of the wall of 0.5-1.0 mm and the powder of bronze was filled up (10% of Zn). The length of tube reached 600 mm. pack-ing of powder it was achieved by mean of the device, described in the work [4]. Microstruc-tural studies (Fig. 3) confirm the presence of a good contact between the particles of powder and the wall of pipe.

Maximally attainable porosity 62-74%. For shaping of the surface of filtration perpendicu-lar to the direction of pore channel were used the caprone filaments and fusible wires. We

for the first time developed also the method of obtaining the permeable articles from the variable surface of filtration, situated at angle with respect to the pore channels [3].

concLusions

MIOM (magnetic pulsation treatment of 1. metals) technique makes it possible to produce the anisotropic permeable ma-terials with the small, average and high porosity.MIOM obtained practical use with the 2. production of the elements of vaporizers and thermal pipes.

Hoganas iron and steel powders for sintered components. Hoganas, 1998, 246 p.1. MIRONOV, V: Pulververdichten mit Magnetimpulsen. – Planseebericht, 1976, Bd 24, s. 175-2. 190MIRONOV, V., LAPKOVSKY, V.: Tubular articles with the high permeably by uses of the MIOM 3. technology. In proceeding of 8th Int. Baltic conf. “Engineering materials and Tribology-2004”, Riga, Latvia, Sept. 2004, p. 201-205.SCHATT, W. Einfuhrung in die Werkstoffwissenschaft.Leipzig.1984, 480 s.4. БЕЛОВ С.В.:Пористые металлы в машиностроении.М.Машиностроение.1981,-247 с.5. ЖЕРНОКЛЕВ, А.К., ПИЛИНЕВИЧ, Л.П.,САВИЧ, В.В.: Аэрация и озонирование в процессах 6. очистки воды.Минск, , Беларусь, Тонпик,128 с.МИРОНОВ, В.А.: Магнитно-импульсное прессование порошков.Рига ,Зинатне ,1980,196 с.7. ПИЛИНЕВИЧ, Л.П., МАЗЮК, В.В.,РАК, А.Л., САВИЧ, В.В., ТУМИЛОВИЧ, М.В.: Пористые 8. порошковые материалы с анизотропной структурой для фильтрации жидкостей и газов. . Минск, Беларусь, Тонпик, 250 с.

Literature

Fig. 3. Microstructure of the sintered element on the border shell (copper) and powder (bronze), porosity 40%; magnification 200x.

39

Paper is focused on review of destructive methods of testing of the concrete. Basic methods useable in laboratory are described. Finally, methods used in laboratory, and meth-ods recommended by standard are compared.

destructiVe MetHods of testinG

Material properties of concrete are possible observe by next destructive methods of test-ing. Methodical procedures adduced in stand-ards describe which properties are possible get. Norm procedure do isn’t interest for properties which is possible get by analysis of data. Prima-ry goal of norm procedure is provide similarity of process of testing.

In Czech Republic were valid Czech technical standards. In nineties years of last century start process of unification of the standards with European technical standards. The harmoniza-tion of the standards of testing of the concrete properties was finished, and new standards are marked like the ISO standards.

determination of compressive strength

Probably is most used test for getting the mate-rial properties. Standard unambiguously defined sizes of specimens, shapes of specimens, meth-od of loading, and method of achieve of results. Sizes of specimens are described in standard

rewieV of destructiVe MetHods of testinG of tHe ceMent Paste and concrete

P. Padevět

Abstract describe of the methods for destructive testing of concrete. For testing material proper-ties are used methods: Determination of compressive strength of test specimens, Determination of flexural strength of test specimens, Determination of tensile splitting strength of test specimens, Determination of tensile strength of concrete, Determination of static modulus of elasticity in com-pression. Most important for well results of the properties of concrete are determination of size of specimens, determination of suitable equipment for testing and definition of precise boundary conditions. For definition of compressive strength is needed choose suitable shape of specimen (cube, cylinder or prism) and its size. Same conditions are important for determination of proper-ties in tension, for splitting strength and for static modulus of elasticity too.

Abstract

strength, modulus of elasticity, properties of concrete

Key words

40

ISO 1920. In the ISO 1920 are defined sizes of specimen, their shapes, form of using and de-viation of testing specimens. Next are defined for the compression test specimens with cubic or prism shape, eventually fragments of prisms. Length of cube edge is possible choose 100, 150, 200, 250 or 300 mm. Depth of specimen depend at the diameter of specimen. Standard recommend depth like a double size of base of prism. Second variation of specimen diameter is between 100, 150, 200, 250 or 300 mm. Third variation is use prism specimen. In this case is possible choose prism with edge 100, 150, 200, 250 or 300 mm. Length of prism is defined like a quadruple, eventually 5ty multiple of edge size. Standard recommended suitable sizes of speci-mens, for cube are suitable size of edge 150 mm, for cylinder 150 mm edge and 300 mm depth. For prisms is recommended length of edge 150 mm and depth 600 mm or longer.

Standard of test in compression describe flat-ness and kind of finish of the specimen. Are pos-sible finish compression plates of specimen with cement mortar. Range of testing equipment is defined. Strength of specimen must be minimal-ly 10 % of range of equipment. Loading plates must by same size or bigger than specimen. One of both plates must be connected with equip-ment by hinge. Standard define rate of testing, it must be from 0.2 to 1 MPa/s.

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