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1

Shear force distribution law of inclined webs box girder under live load

Cui Yujun, Wu Longqing, Wang Weiqi, Cao Wei, Xue Xingwei

Archives of Civil Engineering

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2022

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Vol. 68, nr 2

593--610

EN

Inclined web box girders are widely used in urban areas because of their attractive appearance. However, there are few studies on the vehicle shear force distribution of this type of bridge. In this study, we established 62 three-dimensional finite element models in which the shear force of each web of the box girder can be extracted; furthermore, we investigated the shear force distribution law in webs of the box girder under live loads, including single-chamber and multichamber inclined web box girders. The main parameters studied include the number of vehicle lanes and chambers, slope of the inclined webs, and support conditions. The results reveal that an uneven distribution of web shear force exists in both the single-chamber box girder and multichamber girder under live loads, and the maximum value of the vehicle shear force distribution factor is greater than the average shear value shared by all webs. Therefore, the uneven distribution of shear force in the webs of the box girder cannot be ignored under eccentric vehicle loads. These values greatly exceed the safety factor of 1.15 that is used in conventional calculations.

2

Static bending of isotropic circular cylindrical shells based on the higher order shear deformation theory of Reddy and Liu

Nwoji C. U., Ani D. G., Oguaghamba O. A., Ibeabuchi V. T.

International Journal of Applied Mechanics and Engineering

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2021

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Vol. 26, no. 3

141--162

EN

In this paper, a displacement based shear deformation theory formulated on the cubic in-plane displacement field equation of Reddy and Liu is presented for the static bending analysis of isotropic circular cylindrical shells. The adopted displacement field accounts for a quadratic (parabolic) distribution of the transverse shear through the shell thickness as well as satisfies the need for a stress free upper and lower boundary surfaces of the shell. The equations of static equilibrium are obtained on application of the principle of virtual work. Numerical results of the bending analysis for the displacements and stresses are presented for the simply supported shell. A comparison made to those of the Kirchhoff-Love theory for varying shell length to mean – radius of curvature ratios, shows good agreement for thin shells irrespective of the shell length to radius of curvature ratio [...]. The transverse sharing effect is found to be noticeable in the deformation of thick shells, however, this effect diminishes with a continuous increase in [...] ratios.

3

Nonlocal zigzag analytical solution for Laplacian hygrothermal stress analysis of annular sandwich macro/nanoplates with poor adhesions and 2D-FGM porous cores

Alipour M. M., Shariyat M.

Archives of Civil and Mechanical Engineering

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2019

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Vol. 19, no. 4

1211--1234

EN

A zigzag nonlocal model is presented for annular/circular sandwich macro- and nanoplates with bidimensional graded porous cores and weak interfacial adhesions. This is the first time that a stress analysis is performed in the framework of Eringen's nonlocality concept. In this regard, after determination of the displacements by utilizing a power series solution, the governing Laplacian equations of the stress components in terms of the displacement components are solved in a post-processing stage, using a power series solution in terms of stress parameters. Effects of the thermal stresses and material degradation and deterio-ration due to the temperature rise and moisture absorption are also taken into account. To guarantee continuity of the transverse shear and normal stresses, the bonding layers are modeled by spring elements. To present a general model, it is assumed that the core porosity changes in both radial and transverse directions. It is the first time that the effects of the porosity are investigated on transverse distributions of the displacement and stress com-ponents. The results have captured the significant effects of the nonlocality, moisture absorption, and bond strength on the stress and lateral deflection results, and especially, the abrupt changes in the in-plane displacement and stress components at the interfaces.

4

Finite elements analysis of the side grooved I-beam specimen for mode II fatigue crack growth rates determination

Lenkovskiy T. M., Kulyk V. V., Duriagina Z. A., Dzyubyk L. V., Vira V. V., Dzyubyk A. R., Tepla T. L.

Journal of Achievements in Materials and Manufacturing Engineering

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2018

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Vol. 86, nr 2

70--77

EN

Purpose: Carefully investigate the stress-strain state of the side grooved I-beam specimen with edge crack and determine the effect of crack length and crack faces friction on stress intensity factor at transverse shear. Design/methodology/approach: The finite element method was used to estimate the stress-strain state of I-beam specimen at transverse shear. For this purpose, a fullscale, three-dimensional model of the specimen was created, which precisely reproduces its geometry and fatigue crack faces contact. For the correct reproduction of the stress singularity at the crack tip, a special sub-model was used, which has been tested earlier in solving similar problems of fracture mechanics. In order to improve the accuracy of the calculations, for crack plane and cross-section of the specimen on the crack extension modeling, an algorithm for changing the crack length without changing the total number of elements in the model was developed and applied. Young's modulus and Poisson's ratio of structural steels were specified for the model material. The static loading of the model was realized assuming small scale yielding condition. The stress intensity factor was found through the displacement of nodes in the prismatic elements adjacent to the plane and the front of the crack. Findings: Mathematical dependences, which show an increase of stress intensity factor in the I-beam specimen with an increase in the crack length, and its decrease with an increase of crack faces friction factor at transverse shear, were established. The results are compared with the partial cases known from the literature and their good convergence was shown. Research limitations/implications: By analyzing the obtained graphical dependences, it is established that for relative crack lengths less than 0.4 there is a significant influence of the initial notch on the stress-strain state of the specimen, and for the lengths greater than 0.9 an influence of constrained gripping part took place. For this reason, all subsequent calculations were carried out in the range of relative crack length from 0.4 to 0.9, which represents the applicability range of the final calculation formula. Increasing of the crack faces friction factor from 0 to 1 monotonically reduces the stress at the crack tip. For a short crack, this effect is 1.5 times greater than for a long one, which is reflected by the calculation formula. Practical implications: Using the proposed calculation formula, one can calculate the stress intensity factor in the I-beam specimen, and to determine the crack growth resistance characteristics of structural steels at transverse shear. Originality/value: A new, easy-to-use in engineering calculations formula is proposed for stress intensity factor determination in the I-beam specimen at transverse shear. The formula takes into account crack faces friction for various crack lengths.

5

Mode I and mode II fatigue crack growth resistance characteristics of high tempered 65G steel

Lenkovskiy T. M., Kulyk V. V., Duriagina Z. A., Kovalchuk R. A., Topilnytskyy V. H., Vira V. V., Tepla T. L.

Archives of Materials Science and Engineering

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2017

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Vol. 84, nr 1

34--41

EN

Purpose: To investigate the fatigue crack growth at normal tension and transverse shear of 65G steel with the high tempered martensite microstructure and to build an appropriate fatigue crack growth rate curves. To determine the main and auxiliary fatigue crack growth resistance characteristics, which are necessary for machine parts life-time estimation at rolling contact fatigue conditions. Design/methodology/approach: For determination of fatigue crack growth resistance at normal tension a standard compact specimens with edge crack were tested using a hydraulic testing machine and fatigue testing at transverse shear were performed on the I-beam specimens with the edge longitudinal crack using the original testing setup. For crack growth measurement an optical cathetometer B-630 was used. The crack growth rate V was calculated as crack length increment during loading cycles. The stress intensity factor range K was determined by dependence "K = (1 – R)Kmax accordingly to the standard test methods. To establish crack faces friction factor at transverse shear fragments of fractured beam specimen containing crack faces were cut out and tested as a friction pair according to Amontons Coulomb's law. On the base of test results the fatigue crack growth rate curves in logarithmic coordinates "K vs. V were built. These graphical dependencies for normal tension and transverse shear were used for determination of fatigue crack growth resistance characteristics: fatigue threshold "Kth, fracture toughness "Kfc, "K1-2 and "K2-3 which indicates the beginning and the end of middle-amplitude region of curve, "K*, parameters C and n of Paris’s equation. Metallographic and fractographic analyses were performed on the scanning electronic microscope Zeiss EVO 40XVP. Findings: Empirical dependences of the stress intensity factor range on fatigue crack growth rate at normal tension and transverse shear of 65G steel with the high tempered martensite microstructure are obtained. Based on these graphical dependencies the fatigue thresholds and fracture toughness as well as the parameters of Paris’s equation are determined. Research limitations/implications: The fatigue crack growth on 65G steel under low-, medium- and high-amplitude cyclic loading at normal tension and transverse shear was investigated. The fatigue crack growth rate values for a wide range of stress intensity factor are estimated. On the base of fractographical analysis the features of fracture of high tempered martensite in 65G steel at transverse shear are studied. It is shown that the transverse shear crack faces friction factor for high tempered martensite structure is less than for low tempered martensite. Practical implications: Using the fatigue crack growth resistance characteristics of 65G steel at normal tension and transverse shear and related fatigue crack growth rate curves it is possible to predict the life-time of machine parts made of steels with high tempered martensite structure, working at rolling contact fatigue conditions. Originality/value: Complete fatigue crack growth rate curves of 65G steel with tempered martensite structure at normal tension and transverse shear are built and the fatigue crack growth resistance characteristics for both modes of fracture are determined for the first time.

6

Influence of 65G steel microstructure on crack faces friction factor under mode II fatigue fracture

Ivanytskyj Y. L., Lenkovskiy T. M., Molkov Y. V., Kulyk V. V., Duriagina Z. A.

Archives of Materials Science and Engineering

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2016

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Vol. 82, nr 2

49--56

EN

Purpose: The aim of the paper is to evaluate the dependence of microstructure parameters, strength and plasticity of steel on crack faces friction factor. Design/methodology/approach: The specimens for the investigation were cut out from the 10 mm thick hot-rolled plate of 65G steel used as a model material for fatigue and durability testing of whole-rolled railway wheels. The mechanical characteristics of the steel were determined according to the state standard using cylindrical specimens of diameter 5 mm and effective length 50 mm. The specimens were heat-treated at the mentioned conditions. Fatigue testing under mode II loading was carried out on a special rigid loading machine in the standard laboratory conditions at symmetric sinusoidal cycle with a frequency of 12 Hz in the range of fatigue crack growth rates da/dN = 5∙10⁻⁸…5∙10⁻⁷ m/cycle until its reaches relative length l/b ≥ 0.8. The obtained microsections were investigated using the optical metallographic microscope Neophot 9 equipped with a digital camera Nikon D50 and electronic scanning microscope Zeiss EVO 40XVP. Hardness of the specimens with different microstructure was determined using durometer TK-2. The crack faces friction factor was determined using original device for fractured surfaces sliding under certain compression force realization. Findings: The dependences of microstructure parameters, strength and plasticity of steel on crack faces friction factor are obtained. Research limitations/implications: The investigation of the influence of microstructure parameters, strength and plasticity of real wheel steels on crack faces friction factor at the mode II fatigue crack growth will be carried out. Practical implications: The value of crack faces friction factor have strong impact on stress intensity at the crack tip and must be taken into account at crack growth rates curves plotting. Originality/value: Mode II fatigue crack faces friction factor of steel is firstly experimentally determined.

7

Odporność na pękanie betonów z kruszywami naturalnymi i łamanymi

Golewski G., Sadowski T.

Przegląd Budowlany

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2005

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R. 76, nr 10

31-37

8

Optimization of sandwich structures having FRP faces

Muc A., Zuchara P.

Archives of Civil Engineering

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1999

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Vol. 45, nr 2

289-304

EN

The paper establishes an approach for analyzing the effect of shear deformations in sandwich plates and panels having fibre reinforced plastic faces using a formulation based on the Hamilton principle. Six variants of different governing relations have been proposed both for the laminatewise theories as well as the layerwise theories. Those equations have been applied in the optimization problems. The maximization of buckling loads with respect to laminate configurations is the objective function in the analysis of axially compressed plates or cylindrical panels. Design variables are treated herein as discrete ones. Various numerical examples demonstrate the effects of the used plate/shell theories on optimization solution and the effectiveness of the used genetic algorithms in discussed optimization problems.

PL

W pracy omówiona jest analiza efektów poprzecznego ścinania w konstrukcjach przekładkowych. Rozważania dotyczą płyt i powłok warstwowych o okładzinach kompozytowych, z wykorzystaniem zasady Hamiltona. Zaproponowano sześć teorii kinematycznych w podejściu globalnym i lokalnym. Do prób optymalizacji zastosowano związki kinematyczne. W ściskanych osiowo płytach i powłokach cylindrycznych funkcją celu jest maksymalna siła wyboczenia, gdzie zmiennymi optymalizacji są kierunki i ułożenia włókien. Zmienne optymalizacyjne traktowane są jako zmienne dyskretne. Zaprezentowano również przykłady numeryczne rozwiązań optymalnych badanych płyt i powłok oraz wykorzystano algorytmy genetyczne w problemie optymalizacji.