• Title/Summary/Keyword: shear stress-strain

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Analytical Solutions for the Inelastic Lateral-Torsional Buckling of I-Beams Under Pure Bending via Plate-Beam Theory

  • Zhang, Wenfu;Gardner, Leroy;Wadee, M. Ahmer;Zhang, Minghao
    • International journal of steel structures
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    • v.18 no.4
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    • pp.1440-1463
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    • 2018
  • The Wagner coefficient is a key parameter used to describe the inelastic lateral-torsional buckling (LTB) behaviour of the I-beam, since even for a doubly-symmetric I-section with residual stress, it becomes a monosymmetric I-section due to the characteristics of the non-symmetrical distribution of plastic regions. However, so far no theoretical derivation on the energy equation and Wagner's coefficient have been presented due to the limitation of Vlasov's buckling theory. In order to simplify the nonlinear analysis and calculation, this paper presents a simplified mechanical model and an analytical solution for doubly-symmetric I-beams under pure bending, in which residual stresses and yielding are taken into account. According to the plate-beam theory proposed by the lead author, the energy equation for the inelastic LTB of an I-beam is derived in detail, using only the Euler-Bernoulli beam model and the Kirchhoff-plate model. In this derivation, the concept of the instantaneous shear centre is used and its position can be determined naturally by the condition that the coefficient of the cross-term in the strain energy should be zero; formulae for both the critical moment and the corresponding critical beam length are proposed based upon the analytical buckling equation. An analytical formula of the Wagner coefficient is obtained and the validity of Wagner hypothesis is reconfirmed. Finally, the accuracy of the analytical solution is verified by a FEM solution based upon a bi-modulus model of I-beams. It is found that the critical moments given by the analytical solution almost is identical to those given by Trahair's formulae, and hence the analytical solution can be used as a benchmark to verify the results obtained by other numerical algorithms for inelastic LTB behaviour.

Crack initiation mechanism and meso-crack evolution of pre-fabricated cracked sandstone specimens under uniaxial loading

  • Bing Sun;Haowei Yang;Sheng Zeng;Yu Yin;Junwei Fan
    • Geomechanics and Engineering
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    • v.33 no.6
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    • pp.597-609
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    • 2023
  • The instability and failure of engineered rock masses are influenced by crack initiation and propagation. Uniaxial compression and acoustic emission (AE) experiments were conducted on cracked sandstone. The effect of the crack's dip on the crack initiation was investigated using fracture mechanics. The crack propagation was investigated based on stress-strain curves, AE multi-parameter characteristics, and failure modes. The results show that the crack initiation occurs at the tip of the pre-fabricated crack, and the crack initiation angle increases from 0° to 70° as the dip angle increases from 0° to 90°. The fracture strength kcr is derived varies in a U-shaped pattern as β increased, and the superior crack angle βm is between 36.2 and 36.6 and is influenced by the properties of the rock and the crack surface. Low-strength, large-scale tensile cracks form during the crack initiation in the cracked sandstone, corresponding to the start of the AE energy, the first decrease in the b-value, and a low r-value. When macroscopic surface cracks form in the cracked sandstone, high-strength, large-scale shear cracks form, resulting in a rapid increase in the AE energy, a second decrease in the b-value and an abrupt increase in the r-value. This research has significant theoretical implications for rock failure mechanisms and establishment of damage indicators in underground engineering.

Compressive Strength and Environmental Investigation for Beneficial Use of Dredged Sediments (준설퇴적물 유효활용을 위한 압축강도 및 환경성 평가)

  • Yoon, Gil Lim;Bae, Yoon Shin;Yoon, Yeo Won;Kim, Suk Hyun
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.30 no.2C
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    • pp.119-131
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    • 2010
  • In this study, beneficial use of ocean contaminated sediments were investigated by laboratory and environmental tests, and their prototypes were released. Dredged material from Ulsan port is used for making cement treated samples and lightweight foamed samples, and various engineering tests were performed to identify the compressibility and stress-strain behaviors. Environmental tests were also performed for the beneficial uses. The values of Cu are a little higher than the suggested standard possible for reusing dredged material and equal to the suggested standard alarming for reusing dredged material, which shows environmental harmfulness for the reuse of construction material. In addition, particle size distribution, compaction test, Atterberg limit tests, specific gravity test, and unit weight test were performed to investigate the use of landfill cover materials. The shear strengths of cement treated soils were found to be enough for reclamation works.

Nonlinear free and forced vibrations of oblique stiffened porous FG shallow shells embedded in a nonlinear elastic foundation

  • Kamran Foroutan;Liming Dai
    • Structural Engineering and Mechanics
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    • v.89 no.1
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    • pp.33-46
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    • 2024
  • The present research delves into the analysis of nonlinear free and forced vibrations of porous functionally graded (FG) shallow shells reinforced with oblique stiffeners, which are embedded in a nonlinear elastic foundation (NEF) subjected to external excitation. Two distinct types of PFG shallow shells, characterized by even and uneven porosity distribution along the thickness direction, are considered in the research. In order to model the stiffeners, Lekhnitskii's smeared stiffeners technique is implemented. With the stress function and first-order shear deformation theory (FSDT), the nonlinear model of the oblique stiffened shallow shells is established. The strain-displacement relationships for the system are derived via the FSDT and utilization of the von-Kármán's geometric assumptions. To discretize the nonlinear governing equations, the Galerkin method is employed. The model such developed allows analysis of the effects of the stiffeners with various angles as desired, in addition to the quantitative investigation on the influence of the surrounding nonlinear elastic foundations. To numerically solve the problem of vibrations, the 4th-order P-T method is used, as this method, known for its enhanced accuracy and reliability, proves to be an effective choice. The validation of the present research findings includes a comprehensive comparison with outcomes documented in existing literature. Additionally, a comparative analysis of the numerical results against those obtained using the 4th Runge-Kutta method is performed. The impact of stiffeners with varying angles and material parameters on the vibration characteristics of the present system is also explored. The researchers and engineers working in this field may use the results of this study as benchmarks in their design and research for the considered shell systems.

A Study on the Behaviour of Prebored and Precast Steel Pipe Piles from Full-Scale Field Tests and Class-A and C1 Type Numerical Analyses (현장시험과 Class-A 및 C1 type 수치해석을 통한 강관매입말뚝의 거동에 대한 연구)

  • Kim, Sung-Hee;Jung, Gyoung-Ja;Jeong, Sang-Seom;Jeon, Young-Jin;Kim, Jeong-Sub;Lee, Cheol-Ju
    • Journal of the Korean GEO-environmental Society
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    • v.18 no.7
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    • pp.37-47
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    • 2017
  • In this study, a series of full-scale field tests on prebored and precast steel pipe piles and the corresponding numerical analysis have been conducted in order to study the characteristics of pile load-settlement relations and shear stress transfer at the pile-soil interface. Dynamic pile load tests (EOID and restrike) have been performed on the piles and the estimated design pile loads from EOID and restrike tests were analysed. Class-A type numerical analyses conducted prior to the pile loading tests were 56~105%, 65~121% and 38~142% respectively of those obtained from static load tests. In addition, design loads estimated from the restrike tests indicate increases of 12~60% compared to those estimated in the EOID tests. The EOID tests show large end bearing capacity while the restrike tests demonstrate increased skin friction. When impact energy is insufficient during the restrike tests, the end bearing capacity may be underestimated. It has been found that total pile capacity would be reasonably estimated if skin friction from the restrike tests and end bearing capacity from the EOID are combined. The load-settlement relation measured from the static pile load tests and estimated from the numerical modelling is in general agreement until yielding occurs, after which results from the numerical analyses substantially deviated away from those obtained from the static load tests. The measured pile behaviour from the static load tests shows somewhat similar behaviour of perfectly-elastic plastic materials after yielding with a small increase in the pile load, while the numerical analyses demonstrates a gradual increase in the pile load associated with strain hardening approaching ultimate pile load. It has been discussed that the load-settlement relation mainly depends upon the stiffness of the ground, whilst the shear transfer mechanism depends on shear strength parameters.

Damage Analysis of Nearby Structures with the Consideration of Tunnel Construction Conditions in Sandy and Clayey Ground (모래 및 점토지반에서 터널시공조건을 고려한 인접구조물의 손상도 분석)

  • Son, Moorak;Yun, Jongcheol
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.31 no.1C
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    • pp.53-63
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    • 2011
  • This paper investigates the effects of tunnelling-induced ground movements on nearby structures, considering soil-structure interactions of different ground (loose sand, dense sand, soft clay, stiff clay) and construction conditions (ground loss). The response of four-story block structures, which are subjected to tunnelling-induced ground movements, has been investigated in different ground and construction conditions (ground loss) using numerical analysis. The structures for numerical analysis has been modelled using Discrete Element Method (DEM) to have real cracks when the shear and tensile stress exceed the maximum shear and tensile strength. The response of four-story block structures has been investigated with a ground movement magnitude and compared in terms of ground and construction conditions (ground loss) considering the magnitude of deformations and cracks in structures. In addition, the damage levels, which are possibly induced in structures, has been provided in terms of ground and construction conditions (ground loss) using the state of strain damage estimation criterion (Son and Cording, 2005). The results of this study will provide a background for better understandings for controlling and minimizing building damage on nearby structures due to tunnelling-induced ground movements.

High Strength Nanostructured Metastable Alloys

  • Eckert, Jurgen;Bartusch, Birgit;Schurack, Frank;He, Guo;Schultz, Ludwig
    • Journal of Powder Materials
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    • v.9 no.6
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    • pp.394-408
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    • 2002
  • Nanostructured high strength metastable Al-, Mg- and Ti-based alloys containing different amorphous, quasicrystalline and nanocrystalline phases are synthesized by non-equilibrium processing techniques. Such alloys can be prepared by quenching from the melt or by powder metallurgy techniques. This paper focuses on one hand on mechanically alloyed and ball milled powders containing different volume fractions of amorphous or nano-(quasi)crystalline phases, consolidated bulk specimens and, on the other hand. on cast specimens containing different constituent phases with different length-scale. As one example. $Mg_{55}Y_{15}Cu_{30}$- based metallic glass matrix composites are produced by mechanical alloying of elemental powder mixtures containing up to 30 vol.% $Y_2O_3$ particles. The comparison with the particle-free metallic glass reveals that the nanosized second phase oxide particles do not significantly affect the glass-forming ability upon mechanical alloying despite some limited particle dissolution. A supercooled liquid region with an extension of about 50 K can be maintained in the presence of the oxides. The distinct viscosity decrease in the supercooled liquid regime allows to consolidate the powders into bulk samples by uniaxial hot pressing. The $Y_2O_3$ additions increase the mechanical strength of the composites compared to the $Mg_{55}Y_{15}Cu_{30}$ metallic glass. The second example deals with Al-Mn-Ce and Al-Cu-Fe composites with quasicrystalline particles as reinforcements, which are prepared by quenching from the melt and by powder metallurgy. $Al_{98-x}Mn_xCe_2$ (x =5,6,7) melt-spun ribbons containing a major quasicrystalline phase coexisting with an Al-matrix on a nanometer scale are pulverized by ball milling. The powders are consolidated by hot extrusion. Grain growth during consolidation causes the formation of a micrometer-scale microstructure. Mechanical alloying of $Al_{63}Cu_{25}Fe_{12}$ leads to single-phase quasicrystalline powders. which are blended with different volume fractions of pure Al-powder and hot extruded forming $Al_{100-x}$$(Al_{0.63}Cu_{0.25}Fe_{0.12})_x$ (x = 40,50,60,80) micrometer-scale composites. Compression test data reveal a high yield strength of ${\sigma}_y{\geq}$700 MPa and a ductility of ${\varepsilon}_{pl}{\geq}$5% for than the Al-Mn-Ce bulk samples. The strength level of the Al-Cu-Fe alloys is ${\sigma}_y{\leq}$550 MPa significantly lower. By the addition of different amounts of aluminum, the mechanical properties can be tuned to a wide range. Finally, a bulk metallic glass-forming Ti-Cu-Ni-Sn alloy with in situ formed composite microstructure prepared by both centrifugal and injection casting presents more than 6% plastic strain under compressive stress at room temperature. The in situ formed composite contains dendritic hcp Ti solid solution precipitates and a few $Ti_3Sn,\;{\beta}$-(Cu, Sn) grains dispersed in a glassy matrix. The composite micro- structure can avoid the development of the highly localized shear bands typical for the room temperature defor-mation of monolithic glasses. Instead, widely developed shear bands with evident protuberance are observed. resulting in significant yielding and homogeneous plastic deformation over the entire sample.

Geotechnical Characteristics of the Ulleung Basin Sediment, East Sea (1) - Cosolidation and Shear Waves Velocity (동해 울릉분지 심해토의 지반공학적 특성(1) - 압밀 특성, 전단파 특성에 관한 연구)

  • Kim, Youngmoon;Lee, Jongsub;Lee, Jooyong;Lee, Changho
    • Journal of the Korean GEO-environmental Society
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    • v.14 no.5
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    • pp.33-39
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    • 2013
  • A drilling exploration in deep sea is being processed to develop new energy resource in the world. In 2007, the presence of the gas hydrate had been confirmed during the UBGH1 (Ulleung Basin Gas Hydrate Expedition 1) in the Ulleung Basin. Geotechnical properties of the deep marine sediment are important factors for assessing the safety of gas production facility and productivity from the hydrate bearing sediment. In this study, comprehensive laboratory tests are conducted to investigate the geotechnical engineering characteristics of the deep marine sediments recovered from the hydrate occurrence regions during the UBGH2 (Ulleung Basin Gas Hydrate Expedition 2) in the Ulleung Basin, East Sea, Korea. The index properties of the specimens including the specific gravity, atterberg limits, specific surface, and particle size distribution are measured, and these are compared to the results reported by previous studies. A zero-lateral strain cell, which houses bender elements, is used to determine stress-dependant characteristics and shear wave velocities with the vertical effective stresses. Furthermore, the hydraulic conductivity is calculated based on the consolidation test results.

CHARACTERIZATION OF GEOTECHNICAL SITES BY MULTI-CHANNEL ANALSIS OF SURFACE WAVES(MCASW) (지표층의 탄성계수 측정을 위한 새로운 탄성파 방법)

  • 박춘병
    • Proceedings of the Korean Geotechical Society Conference
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    • 1995.10a
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    • pp.15.2-22
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    • 1995
  • Evaluating stiffness of near-surface materials has been one of the critically important tasks in many civil engineering works. It is the main goal of geotechnical characterization. The so-called deflection-response method evaluates the stiffness by measuring stress-strain behavior of the materials caused by static or dynamic load. This method, however, evaluates the overall stiffness and the stiffness variation with depth cannot be obtained. Furthermore, evaluation of a large-area geotechnical site by this method can be time-consuming, expensive, and damaging to many surface points of the site. Wave-propagation method, on the other hand, measures seismic velocities at different depths and stiffness profile (stiffness change with depth) can be obtained from the measured velocity data. The stiffness profile is often expressed by shear-wave (S-wave) velocity change with depth because S-wave velocity is proportional to the shear modulus. that is a direct indicator of stiffiiess. The crosshole and downhole method measures the seismic velocity by placing sources and receivers (geophones) at different depths in a borehole. Requirement of borehole installation makes this method also time-consuming, expensive, and damaging to the sites. Spectral-Analysis-of-Surface-Waves (SASW) method places both source and receivers at the surface, and records horizontally-propagating surface waves. Based upon the theory of surfacewave dispersion, the seismic velocities at different depths are calculated by analyzing the recorded surface-wave data. This method can be nondestructive to the sites. However, because only two receivers are used, the method requires multiple measurements with different field setups and, therefore, the method often becomes time-consuming and labor-intensive. Furthermore. the inclusion of noise wavefields cannot be handled properly, and this may cause the results by this method inaccurate. When multi-channel recording method is employed during the measurement of surface-waves, there are several benefits. First, usually single measurement is enough because multiple number (twelve or more) of receivers are used. Second, noise inclusion can be detected by coherency checking on the multi-channel data and handled properly so that it does not decrease the accuracy of the result. Third, various kinds of multi-channel processing techniques can be applied to f1lter unwanted noise wavefields and also to analyze the surface-wavefields more accurately and efficiently. In this way, the accuracy of the result by the method can be significantly improved. Fourth, the entire system of source, receivers, and recording-processing device can be tied into one unit, and the unit can be pulled by a small vehicle, making the survey speed very fast. In all these senses, multi-channel recording of surface waves is best suited for a routine method for geotechnical characterization in most of civil engineering works.

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Dynamic Fracture Analysis of High-speed Impact on Granite with Peridynamic Plasticity (페리다이나믹 소성 모델을 통한 화강암의 고속 충돌 파괴 해석)

  • Ha, Youn Doh
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.32 no.1
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    • pp.37-44
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    • 2019
  • A bond-based peridynamic model has been reported dynamic fracture characteristic of brittle materials through a simple constitutive model. In the model, each bond is assumed to be a simple spring operating independently. As a result, this simple bond interaction modeling restricts the material behavior having a fixed Poisson's ratio of 1/4 and not being capable of expressing shear deformation. We consider a state-based peridynamics as a generalized peridynamic model. Constitutive models in the state-based peridynamics are corresponding to those in continuum theory. In state-based peridynamics, thus, the response of a material particle depends collectively on deformation of all bonds connected to other particles. So, a state-based peridynamic theory can represent the volume and shear changes of the material. In this paper, the perfect plasticity is considered to express plastic deformation of material by the state-based peridynamic constitutive model with perfect plastic flow rule. The elastic-plastic behavior of the material is verified through the stress-strain curves of the flat plate example. Furthermore, we simulate the high-speed impact on 3D granite model with a nonlocal contact modeling. It is observed that the damage patterns obtained by peridynamics are similar to experimental observations.