Scaling of residual displacements in terms of elastic and inelastic spectral displacements for existing SDOF systems

Structures undergoing inelastic displacements during earthquake ground motions are known to sustain some amount of residual displacements, which may make them unusable or unsafe. In this study an attempt is made to estimate residual displacements for elastic-perfectly-plastic single-degree-of-freedom oscillators with a given lateral strength ratio. It is observed in the case of a class of ground motions that there are no trends in the dependence of residual displacement on the temporal features of the ground motion, and thus any estimation of residual displacements should be carried out only in the statistical sense. Statistical estimation of residual displacement spectrum via normalization with respect to inelastic or elastic spectral displacements is considered, and it is found that normalization with respect to inelastic spectral displacements is preferable. Expressions for residual displacement spectra are proposed for both types of normalizations and for the givenlateral-strength-ratio type oscillators.

THE MECHANICAL METHOD OF CONSTRUCTING THE DISPLACEMENT FUNCTIONS IN ELASTICITY

In this Paper we have proven the general solution to the equations of linear operatorsAu=f as u=Cv+e . where v satisfies the equation Dv=g and D is adiagonal matrix. Basing on the consstructive proof of Hilbert Nullstellensat=. we haregiven the mechanical method of constucting C. D and e.and some of the mechanicalalgorithm displacement functions in elasticity are given by this method also .

Dynamic Modeling and Analysis of 5‑PSS/UPU Parallel Mechanism with Elastically Active Branched Chains

To study the characteristics of the 5-prismatic–spherical–spherical(PSS)/universal–prismatic–universal(UPU)parallel mechanism with elastically active branched chains,the dynamics modeling and solutions of the parallel mechanism were investigated.First,the active branched chains and screw sliders were considered as spatial beam elements and plane beam element models,respectively,and the dynamic equations of each element model were derived using the Lagrange method.Second,the equations of the 5-PSS/UPU parallel mechanism were obtained according to the kinematic coupling relationship between the active branched chains and moving platform.Finally,based on the parallel mechanism dynamic equations,the natural frequency distribution of the 5-PSS/UPU parallel mechanism in the working space and elastic displacement of the moving platform were obtained.The results show that the natural frequency of the 5-PSS/UPU parallel mechanism under a given motion situation is greater than its operating frequency.The maximum position error is -0.096 mm in direction Y,and the maximum orientation error is -0.29°around the X-axis.The study provides important information for analyzing the dynamic performance,dynamic optimization design,and dynamic control of the 5-PSS/UPU parallel mechanism with elastically active branched chains.

Bolt support mechanism based on elastic theory

Mechanical model of anchorage surrounding rock considering tray effect was established based on elastic theory,in order to study the mechanism of bolt supporting.Elastic solutions of normal force at point in the interior of a semi-infnite solid were obtained by means of classical displacement function method in elasticity.The factors which influence stress of bolted surrounding rock,such as the length of bolt and tray effect,were analyzed.The absolute value of stress along bolt axes decreased rapidly with an increase in radical distance and the maximum appeared near ends of bolt.With increasing radical distance,the value of radical stress changed from positive to negative roughly and then increased to zero,with maximum at the middle of bolt.The evolution of hoop stress as radical distance increasing was similar with stress along bolt axes.With an increase in depth,the radical effect ranges of all normal stress components were reduced.These suggest that the effect from tray on stress along bolt axes of bolted surrounding rock could be neglected,except near surface of surrounding rock.

Elastic solutions for partially embedded single piles subjected to simultaneous axial and lateral loading

In order to improve the design level of partially embedded single piles under simultaneous axial and lateral loads, the differential solutions were deduced, in which the soil was treated as an ideal, elastic, homogeneous, semi-infinite isotropic medium. A comparison was made between model test results and the obtained solutions to show their validity. The calculation results indicate that the horizontal displacement and bending moment of the pile increase with increases of the axial and lateral loads. The maximum horizontal displacement and bending moment decrease by 37.9% and 13.9%, respectively, when the elastic modulus of soil increases from 4 MPa to 20 MPa. The Poisson ratio of soil plays a marginal role in pile responses. There is a critical pile length under the ground, beyond which the pile behaves as though it was infinitely long. The presented solutions can make allowance for the continuous nature of soil, and if condition permits, they can approach exact ones.

Pressure-controlled elliptical cavity expansion under anisotropic initial stress: Elastic solution and its application

This paper presents an elastic solution to the pressure-controlled elliptical cavity expansion problem under the anisotropic stress conditions. The problem is formulated by the assumption that an initial elliptical cavity is expanded under a uniform pressure and subjected to an in-plane initial horizontal pressure Kσ_0 and vertical pressure σ_0 at infinity. A conformal mapping technique is used to map the outer region of the initial elliptical cavity in the physical plane onto the inner region of a unit circle in the phase plane. Using the complex variable theory, the stress functions are derived; hence, the stress and displacement distributions around the elliptical cavity wall can be obtained. Furthermore, a closed-form solution to the pressure-expansion relationship is presented based on the elastic solution to the stress and displacement. Next, the proposed analytical solutions are validated by comparing with the Kirsch's solution and the finite element method(FEM). The solution to the presented pressure-controlled elliptical cavity expansion can be applied to two cases in practice. One is to employ the solution to the interpretation of the shear modulus of the soil or rocks and the in-situ stress in the pre-bored pressuremeter test under the lateral anisotropic initial stress condition. The other is the interpretation of the membrane expansion of a flat dilatometer test using the pressure-controlled elliptical cavity expansion solution. The two cases in practice confirm the usefulness of the present analytical solution.