• Structural Engineering and Mechanics
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• 제40권5호
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• pp.689-703
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• 2011

A new perturbation method is introduced to study the undamped free vibration of a non-prismatic Timoshenko beam for its natural frequencies and vibration modes. For simplicity, the natural modes of vibration of its corresponding prismatic Euler-Bernoulli beam with the same length and boundary conditions are used as Ritz base functions with necessary modifications to account for shear strain in the Timoshenko beam. The new method can transform two coupled partial differential equations governing the transverse vibration of the non-prismatic Timoshenko beam into a set of nonlinear algebraic equations. It significantly simplifies the solution process and is applicable to non-prismatic beams with various boundary conditions. Three examples indicated that the new method is more accurate than the previous perturbation methods. It successfully takes into account the effect of shear deformation of Timoshenko beams particularly at the free end of cantilever structures.

• Structural Engineering and Mechanics
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• 제52권4호
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• pp.723-738
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• 2014

Prestressing is the most commonly employed technique in bridges and long span beams in commercial buildings as prestressing results in slender section with higher load carrying capacities. This work is an attempt to study the performance of a minimum weight prestressed concrete beam adopting a non-prismatic section so that there will be a reduction in the volume of concrete which in turn reduces the self-weight of the structure. The effect of adopting a non-prismatic section on parameters like prestressing force, area of prestressing steel, bending stresses, shear stresses and percentage loss of prestress are established theoretically. The analysis of non-prismatic prestressed beams is based on the assumption of pure bending theory. Equations are derived for dead load bending moment, eccentricity, and depth at any required section. Based on these equations an algorithm is developed which does the stress checks for the given section for every 500 mm interval of the span. Limit state method is used for the design of beam and finite difference method is used for finding out the deflection of a non-prismatic beam. All the parameters of nonprismatic prestressed concrete beams are compared with that of the rectangular prestressed concrete members and observed that minimum weight design and economical design are not same. Minimum weight design results in the increase in required area of prestressing steel.

• 한국방재학회 논문집
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• 제7권5호
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• pp.27-35
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• 2007

본 연구는 지진운동의 영향 하에서 강제 모멘트 골조로 이루어진 post-Northridge 연결부를 갖는 보의 탄성 및 비탄성 거동을 모델하기 위한 부등단면 보 요소를 제시한다. 단면감소 연결부를 갖는 부등단면 보의 탄성강성 행렬은 수치적분이 필요치 많은 수식으로 표현된다. 소성모델은 분포형이며 강체링크로 연결된 일련의 비선형 힌지로 구성 되어있고 경화법칙은 단조 및 임의 주기 하중에 대한 비탄성 거동과 국부좌굴의 효과를 고려할 수 있다. 모델의 대조와 검증은 동반논문에 제시되어있다.

• 한국강구조학회 논문집
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• 제16권6호통권73호
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• pp.833-846
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• 2004

포스트-노스리지 연결부를 사용하는 강재 보의 탄성거동을 모델하기 위한 부등 단면 보 요소가 제안된다. 감소 단면 (RBS) 연결부를 갖는 부등단면 부재에 대한 탄성 강성 매트릭스는 수치적분이 필요치 않는 수식으로 표현되고 전단 효과를 포함하고 있다. 또한 균일 단면 보 요소를 사용하여 RBS 연결부를 갖는 보를 모델 하는 간략 방법이 제안된다. 이 방법의 장점은 기존의 보 요소를 사용하여 RBS 연결부를 사용하는 강재 모멘트 골조의 최대 층간 상대 변위 비를 상당히 정확하게 예측할 수 있다는데 있다. 강재 모멘트 골조의 탄성 강성에 감소 단면 연결부가 미치는 영향이 조사되었고, 절점에서의 변형을 고려하기 위한 적절한 모델 선정이 골조의 최대 층간 상대변위 비를 정확히 예측하는데 감소 단면 연결부보다 중요한 역할을 하였다.

• 한국방재학회 논문집
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• 제7권5호
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• pp.37-46
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• 2007

본 연구는 강재 모멘트 골조의 비선형 지진 해석을 위한 부등단면 보 요소에 관한 두 개의 동반논문 중에서 두 번째 논문이다. 동반논문에서는 지진운동 하의 단면감소(RBS) 강재 보의 탄성 및 비탄성 거동을 정의하기 위한 부등단면 보(RBS 보) 요소를 제시하였고 본 연구에서는 RBS 보 요소에 대한 항복면, 강성 변수, 그리고 경화(혹은 연화) 법칙 변수의 결정과정을 기술하였고 RBS 보 요소의 해석결과를 실험 및 유한요소 해석(FEM) 결과와 비교하였다. RBS 보 요소의 해석결과는 실험 및 FEM 결과와 좋은 상관관계를 보였다.

• Smart Structures and Systems
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• 제14권4호
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• pp.699-718
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• 2014

The indirect displacement estimation using acceleration and strain (IDEAS) method is extended to various types of beam structures beyond the previous validation on the prismatic or near-prismatic beams. By fusing different types of responses, the IDEAS method is able to estimate displacements containing pseudo-static components with high frequency noise to be significantly reduced. However, the concerns to the IDEAS method come from possible disagreement of the assumed sinusoidal mode shapes to the actual mode shapes, which allows the IDEAS method to be valid only for simply-supported prismatic beams and limits its applicability to real world problems. In this paper, the extension of the IDEAS method to the general types of beams is investigated by the mathematical formulation of the modal mapping matrix only for the monitored substructure, so-called monitoring span. The formulation particularly considers continuous and wide beams to extend the IDEAS method to general beam structures that reflect many real bridges. Numerical simulations using four types of beams with various irregularities are presented to show the effectiveness and accuracy of the IDEAS method in estimating displacements.

• 한국구조물진단유지관리공학회 논문집
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• 제28권1호
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• pp.61-69
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• 2024

고가의 혼화재 투입 없이 원심성형 공정 활용으로 콘크리트의 수밀성 증대를 통한 콘크리트 압축강도가 100MPa급인 초고강도 프리스트레스 각형보를 개발하였다. 피암터널 상부구조로 개발된 원심성형 각형보를 지역 소하천의 라멘교에 시공하였으며, 본 연구에서는 정적재하시험을 통하여 계측한 결과와 대상 구조물의 수치해석 결과를 바탕으로 비교, 분석하여 원심성형 각형보 라멘교의 공용내하력과 안전성을 평가하였다. 본 교량의 정·동적 재하시험과 수치해석 결과가 유사하게 나타났으며 원심성형 각형보의 거동을 잘 모사하는 것으로 확인되었다. 합성 라멘교를 구성하는 모든 원심성형 각형보는 설계활하중 하에서 충분한 내하력을 확보하는 것으로 평가되었고 안전성을 확보하여 구조적인 신뢰성을 입증하였다.

• Steel and Composite Structures
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• 제4권4호
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• pp.281-301
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• 2004

The paper begins by presenting a unified variational approach to the lateral-torsional buckling (LTB) analysis of doubly symmetric prismatic and tapered thin-walled beams with open cross-sections, which accounts for the influence of the pre-buckling deflections. This approach (i) extends the kinematical assumptions usually adopted for prismatic beams, (ii) consistently uses shell membrane theory in general coordinates and (iii) adopts Trefftz's criterion to perform the bifurcation analysis. The proposed formulation is then applied to investigate the influence of the pre-buckling deflections on the LTB behaviour of prismatic and web-tapered I-section simply supported beams and cantilevers. After establishing an interesting analytical result, valid for prismatic members with shear centre loading, several elastic critical moments/loads are presented, discussed and, when possible, also compared with values reported in the literature. These numerical results, which are obtained by means of the Rayleigh-Ritz method, (i) highlight the qualitative differences existing between the LTB behaviours of simply supported beams and cantilevers and (ii) illustrate how the influence of the pre-buckling deflections on LTB is affected by a number of factors, namely ($ii_1$) the minor-to-major inertia ratio, ($ii_2$) the beam length, ($ii_3$) the location of the load point of application and ($ii_4$) the bending moment diagram shape.

• Structural Engineering and Mechanics
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• 제43권5호
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• pp.561-582
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• 2012

Despite popularity of FEM in analysis of static and dynamic structural problems and the routine applicability of FE softwares, analytical methods based on simple mathematical relations is still largely sought by many researchers and practicing engineers around the world. Development of such analytical methods for analysis of free vibration of non-prismatic beams is also of primary concern. In this paper a new and simple method is proposed for determination of vibration frequencies of non-prismatic beams under variable axial forces. The governing differential equation is first obtained and, according to a harmonic vibration, is converted into a single variable equation in terms of location. Through repetitive integrations, integral equation for the weak form of governing equation is derived. The integration constants are determined using the boundary conditions applied to the problem. The mode shape functions are approximated by a power series. Substitution of the power series into the integral equation transforms it into a system of linear algebraic equations. Natural frequencies are determined using a non-trivial solution for system of equations. Presented method is formulated for beams having various end conditions and is extended for determination of the buckling load of non-prismatic beams. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained to those obtained using available finite element software.

• Structural Engineering and Mechanics
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• 제33권6호
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• pp.675-696
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• 2009

In this paper, a unified solution method is presented for the classical beam theory. In Strength of Materials approach, the geometry, material properties and load system are known and related with the unknowns of forces, moments, slopes and deformations by applying a classical differential analysis in addition to equilibrium, constitutive, and kinematic laws. All these relations are expressed in a unified formulation for the classical beam theory. In the special case of simple beams, a system of four linear ordinary differential equations of first order represents the general mechanical behaviour of a straight beam. These equations are solved using the numerical differential quadrature method (DQM). The application of DQM has the advantages of mathematical consistency and conceptual simplicity. The numerical procedure is simple and gives clear understanding. This systematic way of obtaining influence line, bending moment, shear force diagrams and deformed shape for the beams with geometric and load discontinuities has been discussed in this paper. Buckling loads and natural frequencies of any beam prismatic or non-prismatic with any type of support conditions can be evaluated with ease.