Bending the Foundation Beam on Elastic Base by Two Reaction Coefficient of Winkler’s Subgrade

A new method for analysis of counter beams is presented in the paper. The analysis has taken into account their stiffness EI, Winkler’s space with modulus of subgrade reaction k and equality deformities of the foundation beam with the ground. The solution is found by using the numerical analysis of the Winkler’s model, with variation of different moduli of the subgrade reaction k2 outside the force zone r, while under the force P exists the modulus of the subgrade reaction k, up to the definition of minimum bending moments. The exponential function k2(r), as the geometric position of the minimum moments is approximately assumed. From the potential energy conditions of the reciprocity of displacement and reaction, the width of the zone r and the modulus of the subgrade reaction k2 are explicitly determined, introducing in the calculation initial and calculation soil displacement wsi successively. At the end of the paper, it presented numerical example in which the influence of k and k2 values on bending moments of the counter beam is analyzed. The essential idea of this paper is to decrease the quantity of the reinforcement in the foundations, beams, i.e. to obtain a cost-efficient foundation construction.

Fusion Reaction Rate Coefficient for Different Beam and Target Scenarios

Fusion power output is proportional not only to the fuel particle number densities participating in reaction but also to the fusion reaction rate coefficient （or reactivity）, which is dependent on reactant velocity distribution functions. They are usuMly assumed to be dual Maxwellian distribution functions with the same temperature for thermal nuclear fusion circumstances. However, if high power neutral beam injection and minority ion species ICRF plasma heating, or multi-pinched plasma beam head-on collision, in a converging region are required and investigated in future large scale fusion reactors, then the fractions of the injected energetic fast ion tail resulting from ionization or charge exchange will be large enough and their contribution to the non-Maxwellian distribution functions is not negligible, hence to the fusion reaction rate coefficient or calculation of fusion power. In such cases, beam-target, and beam-beam reaction enhancement effect contributions should play very important roles. In this paper, several useful formulae to calculate the fusion reaction rate coefticient for different beam and target combination scenarios are derived in detail

Rate Coecients and Kinetic Isotope E ects of Cl+XCl→XCl+Cl(X=H,D,Mu)Reactions from Ring Polymer Molecular Dynamics

The ring-polymer molecular dynamics(RPMD)was used to calculate the thermal rate coefficients and kinetic isotope effects of the heavy-light-heavy abstract reaction Cl+XCl→XCl+Cl(X=H,D,Mu).For the Cl+HCl reaction,the excellent agreement between the RPMD and experimental values provides a strong proof for the accuracy of the RPMD theory.And the RPMD results are also consistent with results from other theoretical methods including improved-canonical-variational-theory and quantum dynamics.The most novel finding is that there is a double peak in Cl+MuCl reaction near the transition state,leaving a free energy well.It comes from the mode softening of the reaction system at the peak of the potential energy surface.Such an explicit free energy well suggests strongly there is an observable resonance.And for the Cl+DCl reaction,the RPMD rate coefficient again gives very accurate results compared with experimental values.The only exception is at the temperature of 312.5 K,results from RPMD and all other theoretical methods are close to each other but slightly lower than the experimental value,which indicates experimental or potential energy surface deficiency.

Oxide coating mechanism during fluidized bed reduction: solid-state reaction characteristics between iron ore particles and MgO

Experiments on the solid-state reaction between iron ore particles and MgO were performed to investigate the coating mechanism of MgO on the iron ore particles＇ surface during fluidized bed reduction. MgO powders and iron ore particles were mixed and compressed into briquettes and, subsequently, roasted at different temperatures and for different time periods. A Mg-containing layer was observed on the outer edge of the iron ore particles when the roasting temperature was greater than 1173 K. The concentration of Fe in the Mg-containing layer was evenly distributed and was approximately 10wt%, regardless of the temperature change. Boundary layers of Mg and Fe were observed outside of the iron ore particles. The change in concentration of Fe in the boundary layers was simulated using a gas–solid diffusion model, and the diffusion coefficients of Fe and Mg in these layers at different temperatures were calculated. The diffusion activation energies of Fe and Mg in the boundary layers in these experiments were evaluated to be approximately 176 and 172 k J/mol, respectively.

Numerical study on transverse deformation characteristics of shield tunnel subject to local soil loosening

In this study,a refined numerical model for segmental lining of a shield tunnel,which contains detailed models of reinforcement and connecting bolts,is established using finite element software.The model is first validated by the results from a full-scale model test.Then,based on the load-structure method,this numerical model is adopted to investigate the internal force distribution and the transverse deformation characteristics of the shield tunnel when it is subject to local soil loosening.The influence of loosening position,loosening range,and loosening extent on the mechanical response is extensively studied through comprehensive numerical analyses.The results show that the main influence of local soil loosening on the ring is to disturb the force balance and change the constraint conditions,thus changing the deformation pattern and force state.After the loosening occurs,the bending moment of the ring in the loosening range increases and the axial force decreases.The vertical convergence of the ring is the largest and the equivalent stiffness of the ring is the smallest when the local soil loosened at the haunch and the loosening range a is 90°.The vertical convergence of the ring increases with increasing of the loosening extent,and the equivalent stiffness decreases linearly with increasing of the loosening extent.The results can enhance our understanding of mechanical behaviors of segmental lining associated soil loosening,and will show a possible way for detecting soil loosening based on the measured deformation and internal forces.