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Détails du magazine
Format
Magazine
eISSN
2083-831X
Première publication
09 Nov 2012
Période de publication
4 fois par an
Langues
Anglais

Chercher

Volume 41 (2019): Edition 1 (April 2019)

Détails du magazine
Format
Magazine
eISSN
2083-831X
Première publication
09 Nov 2012
Période de publication
4 fois par an
Langues
Anglais

Chercher

5 Articles

Research Article

Accès libre

Analysis of thin-walled beams with variable monosymmetric cross section by means of Legendre polynomials

Publié en ligne: 26 Mar 2019
Pages: 1 - 12

Résumé

Abstract

This article deals with the vibrations of a nonprismatic thin-walled beam with an open cross section and any geometrical parameters. The thin-walled beam model presented in this article was described using the membrane shell theory, whilst the equations were derived based on the Vlasov theory assumptions. The model is a generalisation of the model presented by Wilde (1968) in ‘The torsion of thin-walled bars with variable cross-section’, Archives of Mechanics, 4, 20, pp. 431–443. The Hamilton principle was used to derive equations describing the vibrations of the beam. The equations were derived relative to an arbitrary rectilinear reference axis, taking into account the curving of the beam axis and the axis formed by the shear centres of the beam cross sections. In most works known to the present authors, the equations describing the nonprismatic thin-walled beam vibration problem do not take into account the effects stemming from the curving (the inclination of the walls of the thin-walledcross section towards to the beam axis) of the analysed systems. The recurrence algorithm described in Lewanowicz’s work (1976) ‘Construction of a recurrence relation of the lowest order for coefficients of the Gegenbauer series’, Applicationes Mathematicae, XV(3), pp. 345–396, was used to solve the derived equations with variable coefficients. The obtained solutions of the equations have the form of series relative to Legendre polynomials. A numerical example dealing with the free vibrations of the beam was solved to verify the model and the effectiveness of the presented solution method. The results were compared with the results yielded by finite elements method (FEM).

Mots clés

  • thin-walled
  • free vibrations
  • nonprismatic
  • Legendre polynomials
Accès libre

Global Stability For Double-Diffusive Convection In A Couple-Stress Fluid Saturating A Porous Medium

Publié en ligne: 08 Apr 2019
Pages: 13 - 20

Résumé

Abstract

We show that the global non-linear stability threshold for convection in a double-diffusive couple-stress fluid saturating a porous medium is exactly the same as the linear instability boundary. The optimal result is important because it shows that linearized instability theory has captured completely the physics of the onset of convection. It is also found that couple-stress fluid saturating a porous medium is thermally more stable than the ordinary viscous fluid, and the effects of couple-stress parameter (F ) , solute gradient ( S f ) and Brinkman number ( D a ) on the onset of convection is also analyzed.

Mots clés

  • couple-stress parameter
  • solute gradient
  • Brinkman number
Accès libre

Complex analysis of uniaxial compressive tests of the Mórágy granitic rock formation (Hungary)

Publié en ligne: 12 Apr 2019
Pages: 21 - 32

Résumé

Abstract

Understanding the quality of intact rock is one of the most important parts of any engineering projects in the field of rock mechanics. The expression of correlations between the engineering properties of intact rock has always been the scope of experimental research, driven by the need to depict the actual behaviour of rock and to calculate most accurately the design parameters. To determine the behaviour of intact rock, the value of important mechanical parameters such as Young’s modulus (E), Poisson’s ratio (ν) and the strength of rock (σcd) was calculated. Recently, for modelling the behaviour of intact rock, the crack initiation stress (σci) is another important parameter, together with the strain (σ). The ratio of Young’s modulus and the strength of rock is the modulus ratio (MR), which can be used for calculations. These parameters are extensively used in rock engineering when the deformation of different structural elements of underground storage, caverns, tunnels or mining opening must be computed. The objective of this paper is to investigate the relationship between these parameters for Hungarian granitic rock samples. To achieve this goal, the modulus ratio (MR = Ec) of 50 granitic rocks collected from Bátaapáti radioactive waste repository was examined. Fifty high-precision uniaxial compressive tests were conducted on strong (σc >100 MPa) rock samples, exhibiting the wide range of elastic modulus (E = 57.425–88.937 GPa), uniaxial compressive strength (σc = 133.34–213.04 MPa) and Poisson’s ratio (ν = 0.18–0.32). The observed value (MR = 326–597) and mean value of MR = 439.4 are compared with the results of similar previous researches. Moreover, the statistical analysis for all studied rocks was performed and the relationshipbetween MR and other mechanical parameters such as maximum axial strain (εa,max)$\left( {{\varepsilon }_{\text{a,}\,\text{max}}} \right)$for studied rocks was discussed.

Mots clés

  • uniaxial compressive test
  • modulus ratio ()
  • maximum axial strain(ε)
  • crack damage stress(σ)
  • crack initiation stress (σ)
  • Mórágy granite formation.
Accès libre

Experimental bearing capacity of eccentrically loaded foundation near a slope

Publié en ligne: 11 Feb 2019
Pages: 33 - 41

Résumé

Abstract

Based on the response of small-scale model square footing, the present paper shows the results of an experimental bearing capacity of eccentrically loaded square footing, near a slope sand bed. To reach this aim, a steel model square footing of (150 mm × 150 mm) and a varied sand relative density of 30%, 50% and 70% are used. The bearing capacity-settlement relationship of footing located at the edge of a slope and the effect of various parameters such as eccentricity (e) and dimensions report (b/B) were studied. Test results indicate that ultimate bearing capacity decreases with increasing load eccentricity to the core boundary of footing and that as far as the footing is distant from the crest, the bearing capacity increases. Furthermore, the results also prove that there is a clear proportional relation between relative densities –bearing capacity. The model test provides qualitative information on parameters influencing the bearing capacity of square footing. These tests can be used to check the bearing capacity estimated by the conventional methods.

Mots clés

  • Square footing
  • bearing capacity
  • slope
  • relative density
  • eccentric load
Accès libre

Effective Width Rule in the Analysis of Footing on Reinforced Sand Slope

Publié en ligne: 08 Apr 2019
Pages: 42 - 55

Résumé

Abstract

This paper presents the results obtained from an experimental programme and numerical investigations conducted on model tests of strip footing resting on reinforced and unreinforced sand slopes. The study focused on the determination of ultimate bearing capacity of strip footing subjected to eccentric load located either towards or opposite to the slope facing. Strip footing models were tested under different eccentricities of vertical load. The obtained results from tests conducted on unreinforced sand slope showed that the increase in eccentricity of applied load towards the slope facing decreases the ultimate bearing capacity of footing. Predictions of the ultimate bearing capacity obtained by the effective width rule are in good agreement with those proposed from the consideration of total width of footing subjected to eccentric load. The ultimate bearing capacity of an eccentrically loaded footing on a reinforced sand slope can be derived from that of axially loaded footing resting on horizontal sand ground when adopting the effective width rule and the coefficient of reduction due to the slope. When increasing the distance between the footing border to the slope crest, for unreinforced and reinforced ground slope by geogrids, the ultimate bearing capacity of footing is no more affected by the slope ground.

Mots clés

  • bearing capacity
  • eccentricity
  • footing
  • geogrid
  • model test
  • slope
5 Articles

Research Article

Accès libre

Analysis of thin-walled beams with variable monosymmetric cross section by means of Legendre polynomials

Publié en ligne: 26 Mar 2019
Pages: 1 - 12

Résumé

Abstract

This article deals with the vibrations of a nonprismatic thin-walled beam with an open cross section and any geometrical parameters. The thin-walled beam model presented in this article was described using the membrane shell theory, whilst the equations were derived based on the Vlasov theory assumptions. The model is a generalisation of the model presented by Wilde (1968) in ‘The torsion of thin-walled bars with variable cross-section’, Archives of Mechanics, 4, 20, pp. 431–443. The Hamilton principle was used to derive equations describing the vibrations of the beam. The equations were derived relative to an arbitrary rectilinear reference axis, taking into account the curving of the beam axis and the axis formed by the shear centres of the beam cross sections. In most works known to the present authors, the equations describing the nonprismatic thin-walled beam vibration problem do not take into account the effects stemming from the curving (the inclination of the walls of the thin-walledcross section towards to the beam axis) of the analysed systems. The recurrence algorithm described in Lewanowicz’s work (1976) ‘Construction of a recurrence relation of the lowest order for coefficients of the Gegenbauer series’, Applicationes Mathematicae, XV(3), pp. 345–396, was used to solve the derived equations with variable coefficients. The obtained solutions of the equations have the form of series relative to Legendre polynomials. A numerical example dealing with the free vibrations of the beam was solved to verify the model and the effectiveness of the presented solution method. The results were compared with the results yielded by finite elements method (FEM).

Mots clés

  • thin-walled
  • free vibrations
  • nonprismatic
  • Legendre polynomials
Accès libre

Global Stability For Double-Diffusive Convection In A Couple-Stress Fluid Saturating A Porous Medium

Publié en ligne: 08 Apr 2019
Pages: 13 - 20

Résumé

Abstract

We show that the global non-linear stability threshold for convection in a double-diffusive couple-stress fluid saturating a porous medium is exactly the same as the linear instability boundary. The optimal result is important because it shows that linearized instability theory has captured completely the physics of the onset of convection. It is also found that couple-stress fluid saturating a porous medium is thermally more stable than the ordinary viscous fluid, and the effects of couple-stress parameter (F ) , solute gradient ( S f ) and Brinkman number ( D a ) on the onset of convection is also analyzed.

Mots clés

  • couple-stress parameter
  • solute gradient
  • Brinkman number
Accès libre

Complex analysis of uniaxial compressive tests of the Mórágy granitic rock formation (Hungary)

Publié en ligne: 12 Apr 2019
Pages: 21 - 32

Résumé

Abstract

Understanding the quality of intact rock is one of the most important parts of any engineering projects in the field of rock mechanics. The expression of correlations between the engineering properties of intact rock has always been the scope of experimental research, driven by the need to depict the actual behaviour of rock and to calculate most accurately the design parameters. To determine the behaviour of intact rock, the value of important mechanical parameters such as Young’s modulus (E), Poisson’s ratio (ν) and the strength of rock (σcd) was calculated. Recently, for modelling the behaviour of intact rock, the crack initiation stress (σci) is another important parameter, together with the strain (σ). The ratio of Young’s modulus and the strength of rock is the modulus ratio (MR), which can be used for calculations. These parameters are extensively used in rock engineering when the deformation of different structural elements of underground storage, caverns, tunnels or mining opening must be computed. The objective of this paper is to investigate the relationship between these parameters for Hungarian granitic rock samples. To achieve this goal, the modulus ratio (MR = Ec) of 50 granitic rocks collected from Bátaapáti radioactive waste repository was examined. Fifty high-precision uniaxial compressive tests were conducted on strong (σc >100 MPa) rock samples, exhibiting the wide range of elastic modulus (E = 57.425–88.937 GPa), uniaxial compressive strength (σc = 133.34–213.04 MPa) and Poisson’s ratio (ν = 0.18–0.32). The observed value (MR = 326–597) and mean value of MR = 439.4 are compared with the results of similar previous researches. Moreover, the statistical analysis for all studied rocks was performed and the relationshipbetween MR and other mechanical parameters such as maximum axial strain (εa,max)$\left( {{\varepsilon }_{\text{a,}\,\text{max}}} \right)$for studied rocks was discussed.

Mots clés

  • uniaxial compressive test
  • modulus ratio ()
  • maximum axial strain(ε)
  • crack damage stress(σ)
  • crack initiation stress (σ)
  • Mórágy granite formation.
Accès libre

Experimental bearing capacity of eccentrically loaded foundation near a slope

Publié en ligne: 11 Feb 2019
Pages: 33 - 41

Résumé

Abstract

Based on the response of small-scale model square footing, the present paper shows the results of an experimental bearing capacity of eccentrically loaded square footing, near a slope sand bed. To reach this aim, a steel model square footing of (150 mm × 150 mm) and a varied sand relative density of 30%, 50% and 70% are used. The bearing capacity-settlement relationship of footing located at the edge of a slope and the effect of various parameters such as eccentricity (e) and dimensions report (b/B) were studied. Test results indicate that ultimate bearing capacity decreases with increasing load eccentricity to the core boundary of footing and that as far as the footing is distant from the crest, the bearing capacity increases. Furthermore, the results also prove that there is a clear proportional relation between relative densities –bearing capacity. The model test provides qualitative information on parameters influencing the bearing capacity of square footing. These tests can be used to check the bearing capacity estimated by the conventional methods.

Mots clés

  • Square footing
  • bearing capacity
  • slope
  • relative density
  • eccentric load
Accès libre

Effective Width Rule in the Analysis of Footing on Reinforced Sand Slope

Publié en ligne: 08 Apr 2019
Pages: 42 - 55

Résumé

Abstract

This paper presents the results obtained from an experimental programme and numerical investigations conducted on model tests of strip footing resting on reinforced and unreinforced sand slopes. The study focused on the determination of ultimate bearing capacity of strip footing subjected to eccentric load located either towards or opposite to the slope facing. Strip footing models were tested under different eccentricities of vertical load. The obtained results from tests conducted on unreinforced sand slope showed that the increase in eccentricity of applied load towards the slope facing decreases the ultimate bearing capacity of footing. Predictions of the ultimate bearing capacity obtained by the effective width rule are in good agreement with those proposed from the consideration of total width of footing subjected to eccentric load. The ultimate bearing capacity of an eccentrically loaded footing on a reinforced sand slope can be derived from that of axially loaded footing resting on horizontal sand ground when adopting the effective width rule and the coefficient of reduction due to the slope. When increasing the distance between the footing border to the slope crest, for unreinforced and reinforced ground slope by geogrids, the ultimate bearing capacity of footing is no more affected by the slope ground.

Mots clés

  • bearing capacity
  • eccentricity
  • footing
  • geogrid
  • model test
  • slope

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