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

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).

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.

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 (σ_cd) was calculated. Recently, for modelling the behaviour of intact rock, the crack initiation stress (σ_ci) is another important parameter, together with the strain (σ). The ratio of Young’s modulus and the strength of rock is the modulus ratio (M_R), 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 (M_R = E/σ_c) of 50 granitic rocks collected from Bátaapáti radioactive waste repository was examined. Fifty high-precision uniaxial compressive tests were conducted on strong (σ_c >100 MPa) rock samples, exhibiting the wide range of elastic modulus (E = 57.425–88.937 GPa), uniaxial compressive strength (σ_c = 133.34–213.04 MPa) and Poisson’s ratio (ν = 0.18–0.32). The observed value (M_R = 326–597) and mean value of M_R = 439.4 are compared with the results of similar previous researches. Moreover, the statistical analysis for all studied rocks was performed and the relationshipbetween M_R and other mechanical parameters such as maximum axial strain (εa, max)$\left( {{\varepsilon }_{\text{a,}\,\text{max}}} \right)$for studied rocks was discussed.

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.

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.