Computer modelling of R.C. shear walls-comparative analyses at different values of the reduction coefficient. Internal forces values

Purpose. Reference data in technical literature about such characteristics as stiffness and elasticity of rail threads at torsion are rather contradictory. This is due to the absence of correct analytical solution of this task and because of complexity of experimental studies of this problem under combined action of vertical and horizontal lateral forces. The article presents the new method of solving the task of calculation the real values of stiffness and elasticity modules of rail thread when torsion under combined action of vertical and horizontal lateral forces. Methodology. The complex method of solving the problem was used in the paper. It includes the theoretical part and the results of the experiment. Using the experiment the characteristics of horizontal lateral stiffness of the rail threads of the head and bottom at different constructions of the modern rail fastenings was measured. The second task of determination of the real values of elasticity and stiffness modulus of the rail thread when torsion was solved by the theoretical methods. Findings. New values of stiffness characteristics and elasticity module of rail thread when torsion for the modern rail constrictions Р65, UIC60, Р50 and the rail fastenings of the types КПП, КБ, ДО, under combined action of vertical and horizontal forces and torsion were obtained. Originality. For the first time in domestic research it was carried out the experimental and theoretical solution of the task for determination of the real values of the stiffness and elasticity modulus of rail thread when torsion under combined action of vertical and horizontal forces of the wheel loadings. The solution is represented in the functional dependence on the correlation of vertical and horizontal forces ; acting together. The solution is carried out for the modern designs of the rails of domestic standard P65, P50, P43 and international standard UIC60. Practical value. The obtained results make it possible to carry out calculations of the real acting strains and deformations in the rails of different types under the joint action of vertical and horizontal forces for railway track on concrete and wooden sleepers with different designs of rigid and elastic rail fastenings КБ, КПП, Д0 with higher accuracy as compared to the current calculation methodology.

A macroscopic model evaluating shear behavior is necessary to simulate the failure process of shear walls under different axial compression ratios and different out-of-plane bending moments. Accordingly, based on the results of experiments and numerical simulations, a three-segment skeleton curve model was established to reflect the relationship between shear force and deformation when a reinforced concrete shear wall is subjected to axial and horizontal force. Corresponding hysteresis rules were proposed to obtain a macroscopic hysteresis model of the shear wall. Comparison between numerical and experimental results showed that the peak displacement, ductility, and hysteresis characteristics determined using the macroscopic model matched the experimental results well. The numerical results of the macroscopic shear model showed that the in-plane shear performance of a shear wall is almost unchanged when the out-of-plane displacement is very small, but if the displacement along the thickness direction increases, the in-plane shear bearing capacity and the deformation ability of a shear wall will notably decrease. The results can be used for structural design or collapse simulation.

The performance of the bridges during seismic occurrences is a key problem for curved highway bridges, where the curve angle and other variables complicate the study. Though several research studies have been conducted on this subject, many fail to consider the effects of the direction of seismic motion on the reactions along the pile depth in curved decks. This omission must be addressed to get a deeper knowledge of how bridges respond to seismic loads. So, this study focuses on the analysis of the straight and curved box-girder bridge decks supported by shaft piles using the finite element method, with an emphasis on time history analysis to evaluate the seismic responses. The curvature angle ranges from 0 to 60 degrees. Ground motion data from the 1940 Imperial Valley earthquake (7 Mw) at El Centro is used to assess the seismic response, which is obtained from the PEER database. This research investigates the relationship between pile depth and responses (axial force, shear force, torsional moment, bending moments, and deflections) in all three pile directions. The ground movements are taken into account in all three directions, with the excitation vertically being scaled to two-thirds of the total ground motion. With notable responses seen in the top part of the pile, the results show that vertical excitation is crucial to pile design. The highest reactions for axial force, shear force, torsional moment, bending moment, and deflection happen during lateral stimulation, but the curvature angle has the most effect during longitudinal ground motion. The curve angle effect is more at the upper part of the pier, and then this effect is decreased with the pile depth. The results show that, in contrast to straight bridges, curved bridges require more robust design standards for their fundamental parts.

Recently in Japan, many experimental studies have been made on the behavior of beam-column-connective zones (or panel zones) of rigid frames subjected to horizontal forces, and it has been reported that in such cases these zones sometimes show a considerable degree of deformation by shearing force taking place due to the bending moments at the juncture of the beams and columns. The author proposes an attroximation method of calculating multi-story frame analysis, including considerations of shear deformation of panel zones. The method is as follows : 1) When a horizontal force is applied to each floor level, the panel zones show a deformation expressed by eq.3, assuming that the inflection points are at the center of the beam spans. 2) From the continuity of the rotation angle at the inflection points of the columns, eq.13, the equation of bending moments of columns can be deduced and solved by using the end condition at the base and the roof. Simultaneously, the rotation angle of the member of each column can be expressed by eq.15. 3) From these equations and the conditions of a constant shearing force of each story column, and of equal dimensions of columns and beams, we may say that D-values, or the shearing force distribution coefficients, are expressed by eq.22. The papers for D-Values, which, however, do not include considerations of the deformation of the panel zone, have already been reported most fully by Dr. Kiyoshi Muto, at the World Conference on Earthquake Engineering in 1956. in Berkeley California, U.S.A. Lastly, this author shows an example of a seven-story rigid frame subjected to the constant shearing force for each story column, and compares the results obtained therein with the results obtained without considerations of the panel zone deformation.

The article presents the results of numerical simulation of the interaction of drilled shafts with rock mass under the action on its head of horizontal load or bending moment. The studies were carried out using finite element method with the use of factor analysis (method of experiment planning). Numerical calculations allowed to obtain the factor dependencies (regression equation) that connect the response functions (the bearing capacity of the shaft and the displacement of its head) with the selected independent factors that have the significant effect on the behavior of shafts. As factors were taken: the ratio of modulus of elasticity of shaft to modulus of deformation of intact rock, ratio of length of the pile to its diameter and RQD of the rock mass. The equations allow to construct graphs of dependence of displacements of the head of the shaft from applied loads: horizontal force or bending moment. Considering that the regression equations are very cumbersome, for convenience of their use nomograms were constructed. On the base of the study were also obtained two factor dependencies (regression equations) that take into account the character of the shaft interaction with the rock mass. One regression equation is used to define the line separating two regions of different interaction of shafts with rock mass. The one region is the region of "short" shafts that deform into rock with rotation and the bearing capacity of this kind of shafts depends on strength of the rock. The other region is the region of "long" shafts. The bearing capacity and horizontal displacements of this kind of shafts is determined only by the strength of the shaft material. The second regression equation allows to find the boundary into the rock mass below which the shaft doesn't work (no displacements of shaft). For the convenience of use of the obtained regression equations were constructed nomograms.

The article presents an analysis of the stress–strain state of rigid airfield pavement structures under the load of the heavy aircraft An-225 Mriya. The results of determining the bearing capacity and calculating the stress–strain state of rigid airfield pavements were obtained. Based on the performed calculations, constructive solutions and proposals for the restoration of rigid airfield pavements are provided. Isolines of vertical displacements, bending moments, and shear forces in rigid airfield pavement slabs under the load of the An-225 aircraft were obtained. The values of the classification parameters (PCR) of rigid airfield pavements were determined. A set of numerical experimental studies made it possible to solve the scientific problem of assessing the stress–strain state of rigid airfield pavement structures, taking into account the spatial load of aircraft. The purpose of the study is to determine the bearing capacity and investigate the stress–strain state of rigid airfield pavement structures considering real spatial loads and soil foundation properties, on the basis of which constructive proposals and engineering solutions for airfield pavements are provided. Methodology. The research methods include literature review, the ACR–PCR classification parameter method, and the finite element method. Results. Calculations of rigid airfield pavement structures under the load of the heavy An-225 aircraft were performed. Numerical experiments using the finite element method and the ACR–PCR method made it possible to determine the bearing capacity of the pavement and assess its stress–strain state. The calculations showed that the existing runway structure of Hostomel International Airport does not ensure the operation of the An-225 even with minimal take-off intensity. The need to increase the thickness of the upper layer of cement concrete pavement to 350–391 mm depending on the number of take-offs was established. The proposed constructive solutions are aimed at improving the strength and durability of airfield pavements, taking into account real spatial loads and soil foundation properties. Scientific novelty. The scientific novelty lies in the implementation of a fundamentally new approach to the study of the stress–strain state of rigid airfield pavements based on the finite element method, considering real spatial loads and the influence of soil foundations. Practical relevance. The practical significance of the work lies in the possibility of applying the results of stress–strain calculations of rigid airfield pavement structures under real spatial aircraft loads in the design and construction of airfield elements.

The designs of modern electronic technology are complex mechanical systems with many rigid bonds, and their microminiature in many cases has reached the physical limit of the dimensional, charge and energy quantization of components. For such mechanical systems, with non-classical methods for mechanics of fastening of separate structural elements, it is difficult to build a design model, simple enough and at the same time one that well reflects physical and dynamic properties. To ensure mechanical strength of interconnects and ultra-thin electronic components, it is necessary to determine the stress-strain state of structural elements. These reasons necessitate the use of numerical methods to calculate the dynamic parameters of the design of electronic equipment interconnections, which will improve the reliability of the developed tools that meet the requirements of regulatory technical documentation on mechanical characteristics, shorten the time and cost of their creation. Subject matter of this work is the study of beam deformation of constant cross section under the action of axial forces, bending moments and torque relative to the longitudinal axis. Goal this work is to determine the deformation of the elements of the structure of the devices using the stiffness matrix with a known vector of external forces. To achieve this goal, it is necessary to solve the following tasks: to consider the existing methods of description and analysis, which take into account the specificity of the structures and technological processes used to manufacture specific structures MEMS; explore the nature of these methods; calculate displacements and deformations using the finite element method; using the stiffness matrix to determine the deformation of the structural elements of the devices; to calculate the deformation of the beam of constant cross-section under the action of axial forces, bending moments and torque relative to the longitudinal axis. Conclusions: stiffness matrix, constructed using functional analysis, allows for the calculation of deformation of MEMS elements and electronic interconnect flexible.

In engineering, many pressure pipes are made of steels with good plasticity, which are subject to internal pressure, axial force, shear force, bending moment, torsion moment or their combined loads. The plastic limit load is an important indicator of the load capacity of pressure pipe. According to Hill yield function, the theoretical solutions of limit load of orthotropic cylindrical pipe under various combined loads under internal pressure, axial force, shear force, torsion moment, and bending moment have been derived on the basis of elastic perfectly plastic constitutive model. The effects of radial stress on different combined limit loads of cylindrical pipe are explored and these results show that the radial stress should be considered about the limit load calculation especially for thick-walled cylindrical pipe. The interactions of various load combination are analyzed in detail and drawn with the interaction curves. For isotropic cylindrical pipe, the limit load increases with the yield strength. For the orthotropic cylindrical pipe, the limit loads of cylindrical pipe under axial force, bending moment, shear force, and torsion moment without internal pressure are only related to the axial yield strength. The limit bending moment is mainly dependent on the axial yield strength when internal pressure is lower, while the impact of the circumferential yield strength of orthotropic cylindrical pipe is obvious when internal pressure is some higher. When the axial yield strength of orthotropic cylindrical pipe is the same, the circumferential yield strength can enhance the limit axial load, limit torsion moment, and limit shear load. Under the different load conditions including internal pressure, bending moment, axial force, shear force, and torsion moment or their combined loads, the relation of limit bending moment with yield strength ratio is diverse, which is decide by the load combination, the circumferential yield strength, and the axial yield strength.

Many numerical methods--transfer matrix, finite difference and finite difference and finite element methods--which take piece-wise account of the variation of the input-datas over the length of the ship hull, such as area, weight, etc., are now available. Most of these methods give deflection and rotation as output in the eigenvalue problem or in the modal analysis, from which vibratory bending moments and shear forces for given exciting forces and moments are obtained after numerical differentiation of deflections and rotations of cross-sections. In order to avoid this numerical differentiation after the modal analysis, the force method can be employed, instead of the usual deformation method, for improved accuracy in ship hull vibration analysis. In this paper, the necessary differential equations of vibrations are derived and analogies between the force method and deformation method are established so that the existing programs in deformation quantities can be used. Moreover, the eigenfunctions of shear force and bending moment and the envelopes of their maximums for an impact force and moment under vertical vibrations are presented for an ice-going ship.

Due to its advantages (fast and accurate calculations), the Hyperstatic Reaction Method (HRM) was used to calculate the internal forces of circular tunnel linings in former works. This paper presents an improved HRM method that is developed to estimate the internal forces induced in square and rectangular tunnel linings. Based on the comparison of the internal forces induced in these linings obtained from the HRM method and the finite element method (FEM), the improved HRM method was validated. An extensive parametric analysis of the tunnel lining and ground parameters was then carried out using both the HRM and FEM. The results indicated a great influence of the lateral earth pressure coefficient K0, and the tunnel lining flexibility ratio F on the internal forces induced. Accordingly, the bending moments M, normal forces N, and shear forces T, induced in the tunnel lining decrease when the flexibility ratio of tunnel lining F increases. The maximum bending moment is observed at the tunnel sides that are perpendicular with the larger principal stress direction.

This paper is about behavior assessment of moment frames with CFT composite columns under seismic loads, knowing of their behavior, and also how to determine their behavior coefficient. For this purpose, structures with this type of composite columns in three different types with different stories (4 story, 8 story and 12 story) and with 5 span are considered. Variables are the lengths of the spans and the height of the structure. These structures analyzed using Opensees software and applying dead, live and earthquake loads by nonlinear dynamic time-history analysis and structural analysis results are presented with consideration of seven different earthquake records. Finally, the responses of maximum shear force and the maximum bending moment which were formed in the column and floors of structure by applied loads are compared and the behavior coefficient is also analyzed in this study. The results show that the value of shear force, bending moment and behavior coefficient of structure change with the deformation of the sections, for example, the shear force obtained in the model with elliptic sections is less than that of other models.

Behaviour and design of steel members with web openings under combined bending, shear and compression

The theoretical basis and the main results of a design procedure, which attempts to provide the optimal layout of ordinary reinforcement in prestressed concrete beams, subjected to bending moment and shear force are presented. The difficulties encountered in simulating the actual behaviour of prestressed concrete beam in presence of coupled forces bending moment - shear force are discussed; particular emphasis is put on plastic models and stress fields approaches. A unified model for reinforced and prestressed concrete beams under axial force - bending moment - shear force interaction is provided. This analytical model is validated against both experimental results collected in literature and nonlinear numerical analyses. Finally, for illustrating the applicability of the proposed procedure, an example of design for a full-scale prestressed concrete beam is shown.

Internal Forces and Moments in Beams

Functionally graded and laminated piezoelectric cantilever actuators are investigated. Eachmaterial parameter of the functionally graded actuator can be an arbitrary continuousfunction of the thickness coordinate of the beam, while the property of each layer in thelaminated actuator is uniform. Piezoelectricity solutions for the two actuatorssubjected to a constant electric potential difference are presented. Firstly, the partialdifferential equations for the plane problem of functionally graded piezoelectricmaterials, which govern the stress function and electric displacement function, arederived. Secondly, the stress function is assumed to be an undetermined function ofthe thickness coordinate, and the electric displacement function is assumed asa linear function of the longitudinal coordinate. In such a case, the stress andelectric displacement function can be acquired through successive integrations. Theanalytical expressions of axial force, bending moment, shear force, displacements,electric displacements and electric potential are then deduced. The analyticalsolutions are finally obtained, with the integral constants completely determined fromthe boundary conditions. Comparisons of the present analytical solutions withbeam theory, finite element method and experiments indicate that the analyticalsolutions are effective and exact, while certain deviations of the beam theory can befound.