• 한국공간구조학회논문집
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• 제18권1호
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• pp.127-134
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• 2018

This study suggests the tangent modulus $E_t$ associated with partially yielded section of steel member under axially compressed. The provisions for column strength does not provide a information about failure mode of structural system. So, designers can not evaluate that a failure comes from member buckling or material yielding. The material of the axially compressed column under inelastic behavior reaches yielding point before the axial force renders the column bent. If axial members yields not by buckling effect but gradually yielding effect of material, the design code should accept related tangent modulus Et which is based on gradual yielding effect of material. This study provides the new effective tangent modulus $E_t$ derived in the case that residual stress is 30 percent and 50 percent of yielding stress respectively. The study considers idealized I section of steel which ignores web and general I section of steel with web respectively and makes conclude that tangent modulus $E_t$ with idealized I section of steel is rational.

• Advances in concrete construction
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• 제14권2호
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• pp.93-102
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• 2022

In this study, limestone powder (LS) and fly ash (FA) were used as powder materials in self-compacting concrete (SCC) in increasing quantities in addition to cement, so that the two powders commonly used in the production of SCC could be compared in the same study. Considering the reduction of the maximum aggregate size in SCC, 10 mm or 16 mm was selected as the coarse aggregate size. The properties of fresh concrete were determined by slump flow (including T₅₀₀ time), V-funnel and J-ring experiments. The experimental results showed that as the amount of both LS and FA increased, the slump flow also increased. The increase in powder material had a negative effect on V-funnel flow times, causing it to increase; however, the increase in FA concretes was smaller compared to LS ones. The increase in the powder content reduced the amount of blockage in the J-ring test for both aggregate sizes. As the hardened concrete properties, the compressive and splitting strengths as well as the modulus of elasticity were determined. Longitudinal and transverse deformations were measured by attaching a special frame to the cylindrical specimens and the values of Poisson's ratio, initiation and critical stresses were obtained. Despite having a similar W/C ratio, all SCC exhibited higher compressive strength than NVC. Compressive strength increased with increasing powder content for both LS and FA; however, the increase of the FA was higher than the LS due to the pozzolanic effect. SCC with a coarse aggregate size of 16 mm showed higher strength than 10 mm for both powders. Similarly, the modulus of elasticity increased with the amount of powder material. Inelastic properties, which are rarely found in the literature for SCC, were determined by measuring the initial and critical stresses. Crack formation in SCC begins under lower stresses (corresponding to lower initial stresses) than in normal concretes, while critical stresses indicate a more brittle behavior by taking higher values.

• 국제강구조저널
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• 제18권4호
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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.

• 소성∙가공
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• 제22권4호
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• pp.216-222
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• 2013

Solid polymers exhibit rate-dependent deformation behavior such as nonlinear strain rate sensitivity and stress relaxation like metallic materials. Despite the different microstructures of polymeric and metallic materials, they have common properties with respect to inelastic deformation. Unlike most metallic materials, solid polymers and shape memory alloys (SMAs) exhibit highly nonlinear stress-strain behavior upon unloading. The present work employs the viscoplasticity theory [K. Ho, 2011, Trans. Mater. Process. 20, 350-356] developed for the pseudoelastic behavior of SMAs, which is based on unified state variable theory for the rate-dependent inelastic deformation behavior of typical metallic materials, to depict the curved unloading behavior of polyphenylene oxide (PPO). The constitutive equations are characterized by the evolution laws of two state variables that are related to the elastic modulus and the back stress. The simulation results are compared with the experimental data obtained by Krempl and Khan [2003, Int. J. Plasticity 19, 1069-1095].

• 한국구조물진단유지관리공학회 논문집
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• 제22권2호
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• pp.161-168
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• 2018

이 연구는 CRC기둥강도곡선의 비탄성영역에 대한 해석적 고찰이다. CRC기둥강도곡선의 비탄성영역은 최대 잔류응력 크기 $0.5{\sigma}_y$와 Bleich이론을 기초로 하고 있다. 이는 실제로 알려진 최대 압축 잔류응력의 크기가 $0.3{\sigma}_y$인 경우 보다 다소 보수적이다. 본 연구는 열압연강재의 최대 압축 잔류응력의 크기를 $0.3{\sigma}_y$으로 고려하여 그에 따른 기둥강도곡선과 접선탄성계수 Et를 제안하고 이를 CRC에서 제안하고 있는 값들과 각각 비교 고찰한다. 축 압축력을 받는 비탄성 기둥의 응력은 기둥에 작용하는 하중이 좌굴을 일으키기 전에 재료의 비례한도를 넘어 항복점에 도달할 것이다. 따라서 점차적인 단면의 항복 상태에 따른 기둥강도곡선을 검토할 필요가 있다. 본 연구는 최대 압축 잔류응력 ${\sigma}_r=0.5{\sigma}_y$을 사용하여 재료의 항복에 따른 임계하중 곡선식을 유도하고 이를 CRC기둥강도곡선과 비교 고찰한다.

• 한국지진공학회:학술대회논문집
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• 한국지진공학회 2003년도 추계 학술발표회논문집
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• pp.303-310
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• 2003

Small-scale models have been frequently used for experimental evaluation of seismic performance because of limited testing facilities and economic reasons. However, there are not enough studies on similitude law for analogizing prototype structures accurately with small-scale models, although conventional similitude law based on geometry is not well consistent in the inelastic seismic behavior. When fabricating prototype and small-scale model of reinforced concrete structures by using the same material, added mass is demanded from a volumetric change and scale factor could be limited due to size of aggregate. Therefore, it is desirable that different material is used for small-scale models. Thus, a modified similitude law could be derived depending on geometric scale factor and equivalent modulus ratio. In this study, compressive strength tests are conducted to analyze equivalent modulus ratio of micro-concrete to normal-concrete. Equivalent modulus ratios are divided into elastic, weak nonlinear and strong nonlinear phases, which are based on ultimate strain level. Therefore, an algorithm adaptable to the pseudodynamic test, considering equivalent three phase similitude law based on seismic damage levels, is developed. In addition, prior to tile experiment, it is verified numerically if tile algorithm is applicable to the pseudodynamic test.

• 한국전산구조공학회논문집
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• 제29권3호
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• pp.237-244
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• 2016

본 연구는 재료비선형 문제를 다루기 위한 비선형 MLS 차분법의 정식화 과정을 제시한다. MLS 차분법은 절점모델을 기반으로 고속 미분근사식을 활용하여 지배 미분방정식을 직접 이산화 하는데, 변수를 변위로 일원화한 Navier 방정식을 사용하여 탄성재료 문제를 다룬 기존의 MLS 차분법은 재료의 구성방정식을 별도로 고려할 수 없다. 본 연구에서는 비선형 재료의 구성방정식을 반영할 수 있는 강정식화를 위해 1차 미분근사를 반복 사용하는 겹미분근사를 고안했다. 응력의 발산으로 표현되는 평형방정식을 그대로 이산화하고 Newton 방법을 적용하여 반복계산을 통해 수렴해를 찾는 비선형 알고리즘을 제시했다. 응력 계산과 내부변수의 갱신은 return mapping 알고리즘을 활용하였고, 알고리즘 접선계수(algorithmic tangent modulus)의 적용을 통해 빠르고 안정적인 반복계산이 가능하도록 하였다. 재생성 시험을 통해 겹미분근사의 정당성을 검증했고, 비선형재료에 대한 인장문제의 해석을 통해 개발된 비선형 MLS 차분 알고리즘의 정확성과 안정성을 확인하였다.

• Computers and Concrete
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• 제2권3호
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• pp.177-188
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• 2005

This paper presents a numerical model developed to evaluate the load-deflection and moment-curvature relationship for concrete beams strengthened externally with four different Fiber Reinforced Polymer (FRP) composite systems. The developed model considers the inelastic behavior of concrete section subjected to a combined axial force and bending moment. The model accounts for tensile strength of concrete as defined by the modulus of rupture of concrete. Based on the adopted material constitutive relations, the model evaluates the sectional curvature as a function of the applied axial load and bending moment. Deflections along the beam are evaluated using a finite difference technique taking into account support conditions. The developed numerical technique has been tested on a cantilever beam with a transverse load applied at its end. A study of the behavior of the beam with tension reinforcement compared to that with FRP areas giving an equivalent ultimate moment has been carried out. Moreover, cracking of the section in the tensile region at ultimate load has also been considered. The results indicated that beams reinforced with FRP systems possess more ductility than those reinforced with steel. This ductility, however, can be tuned by increasing the area of FRP or by combining different FRP layers.

• Steel and Composite Structures
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• 제3권3호
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• pp.185-198
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• 2003

The concept of performance based seismic design has been gradually accepted by the earthquake engineering profession recently, in which the cost-effectiveness criterion is one of the most important principles and more attention is paid to the structural performance at the inelastic stage. Since there are many uncertainties in seismic design, reliability analysis is a major task in performance based seismic design. However, structural reliability analysis may be very costly and time consuming because the limit state function is usually a highly nonlinear implicit function with respect to the basic design variables, especially for the complex large-scale structures for dynamic and nonlinear analysis. Understanding statistical properties of the structural inelastic deformation, which is the aim of the present paper, is helpful to develop an efficient approximate approach of reliability analysis. The present paper studies the statistical properties of the maximum elastoplastic story drift of steel frames subjected to earthquake load. The randomness of earthquake load, dead load, live load, steel elastic modulus, yield strength and structural member dimensions are considered. Possible probability distributions for the maximum story are evaluated using K-S test. The results show that the choice of the probability distribution for the maximum elastoplastic story drift of steel frames is related to the mean value of the maximum elastoplastic story drift. When the mean drift is small (less than 0.3%), an extreme value type I distribution is the best choice. However, for large drifts (more than 0.35%), an extreme value type II distribution is best.

• 대한조선학회논문집
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• 제47권6호
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• pp.843-849
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• 2010

This paper presents definition of symmetry of a ship section where three symmetries are proposed: material, geometric, and load symmetries. Precise terminologies of centroid, moment plane, and neutral axis plane are also defined. It is suggested that force vector equilibrium as well as force equilibrium are necessary condition to determine new position of neutral axis due to translational and rotational mobility. It is also stated that new reference datum of ENMP(elastic neutral moment plane), PNMP(fully plastic moment plane), ENAP(elastic neutral axis plane), and INAP(inelastic neutral moment plane) are required to define asymmetric section properties such as second moment of area, elastic section modulus, yield moment, fully plastic moment, and ultimate moment. Since collision-induced damage and flooding-induced biaxial bending moment produce typical asymmetry of section, the section properties are calculated for a typical VLCC. Geometry asymmetry is determined from ABS and DNV rules and two moment planes of 0/30 degs are assumed for load asymmetry. It is proved that the property reduction ratios directly calculated from second moment of area are usually larger than area reduction ratio. Reduction ratio of ultimate moment capacity shows almost linearly proportional to area reduction ratio. Mobility of elastic and inelastic neutral axis planes is visually provided.