• 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.

• 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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• 제67권4호
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• pp.347-358
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• 2018

The main aim of this research was to investigate the shear strength of non-prismatic steel fiber reinforced concrete beams under monotonic loading considering different parameters. Experimental program included tests on fifteen non-prismatic reinforced concrete beams divided into three groups. For the first and the second groups, different parameters were taken into consideration which are: steel fibers content, shear span to minimum depth ratio ($a/d_{min}$) and tapering angle (${\alpha}$). The third group was designed mainly to optimize the geometry of the non-prismatic concrete beams with the same concrete volume while the steel fiber ratio and the shear span were left constant in this group. The presence of steel fibers in concrete led to an increase in the load-carrying capacity in a range of 10.25%-103%. Also, the energy absorption capacity was increased due to the addition of steel fibers in a range of 18.17%-993.18% and the failure mode was changed from brittle to ductile. Tapering angle had a clear effect on the shear strength of test specimens. The increase in tapering angle from ($7^{\circ}$) to ($12^{\circ}$) caused an increase in the ultimate shear capacity for the test specimens. The maximum increase in ultimate load was 45.49%. The addition of steel fibers had a significant impact on the post-cracking behavior of the test specimens. Empirical equation for shear strength prediction at cracking limit state was proposed. The predicted cracking shear strength was in good agreement with the experimental findings.

• Structural Engineering and Mechanics
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• 제42권6호
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• pp.849-866
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• 2012

Single span historic bridges often contain non-prismatic members identified with a varying depth along their span lengths. Commonly, the symmetric parabolic height variations having the constant haunch length ratio of 0.5 have been selected to lower the stresses at the high bending moment points and to maintain the deflections within the acceptable limits. Due to their non-prismatic geometrical configuration, their assessment, particularly the computation of fixed-end horizontal forces (FEFs) and fixed-end moments (FEMs) becomes a complex problem. Therefore, this study aimed to investigate the behavior of non-prismatic beams with symmetrical parabolic haunches (NBSPH) having the constant haunch length ratio of 0.5 using finite element analyses (FEA). FEFs and FEMs due to vertical loadings as well as the stiffness coefficients and the carry-over factors were computed through a comprehensive parametric study using FEA. It was demonstrated that the conventional methods using frame elements can lead to significant errors, and the deviations can reach to unacceptable levels for these types of structures. Despite the robustness of FEA, the generation of FEFs and FEMs using the nodal outputs of the detailed finite element mesh still remains an intricate task. Therefore, this study advances to propose effective formulas and dimensionless estimation coefficients to predict the FEFs, FEMs, stiffness coefficients and carry-over factors with reasonable accuracy for the analysis and re-evaluation of the NBSPH. Using the proposed approach, the fixed-end reactions due to vertical loads, and also the stiffness coefficients and the carry-over factors of the NBSPH can be determined without necessitating the detailed FEA.

• 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.

• Structural Engineering and Mechanics
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• 제56권5호
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• pp.787-796
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• 2015

When the temperature of a structure varies, there is a tendency to produce changes in the shape of the structure. The resulting actions may be of considerable importance in the analysis of the structures having non-prismatic members. The computation of design forces for the non-prismatic beams having symmetrical parabolic haunches (NBSPH) is fairly difficult because of the parabolic change of the cross section. Due to their non-prismatic geometrical configuration, their assessment, particularly the computation of fixed-end horizontal forces and fixed-end moments becomes a complex problem. In this study, the efficiency of the Artificial Neural Networks (ANN) and Adaptive Neuro Fuzzy Inference Systems (ANFIS) in predicting the design forces and the design moments of the NBSPH due to temperature changes was investigated. Previously obtained finite element analyses results in the literature were used to train and test the ANN and ANFIS models. The performances of the different models were evaluated by comparing the corresponding values of mean squared errors (MSE) and decisive coefficients ($R^2$). In addition to this, the comparison of ANN and ANFIS with traditional methods was made by setting up Linear-regression (LR) model.

• Structural Engineering and Mechanics
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• 제28권2호
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• pp.221-238
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• 2008

Numerical solution to buckling analysis of beams and columns are obtained by the method of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for various support conditions considering the variation of flexural rigidity. The solution technique is applied to find the buckling load of fully or partially embedded columns such as piles. A simple semi- inverse method of DQ or HDQ is proposed for determining the flexural rigidities at various sections of non-prismatic column ( pile) partially and fully embedded given the buckling load, buckled shape and sub-grade reaction of the soil. The obtained results are compared with the existing solutions available from other numerical methods and analytical results. In addition, this paper also uses a recently developed technique, known as the differential transformation (DT) to determine the critical buckling load of fully or partially supported heavy prismatic piles as well as fully supported non-prismatic piles. In solving the problem, governing differential equation is converted to algebraic equations using differential transformation methods (DT) which must be solved together with applied boundary conditions. The symbolic programming package, Mathematica is ideally suitable to solve such recursive equations by considering fairly large number of terms.

• Advances in Computational Design
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• 제3권2호
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• pp.165-190
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• 2018

In this article, the static behavior of non-prismatic sandwich beams composed of functionally graded (FG) materials is investigated for the first time. Two types of beams in which the variation of elastic modulus follows a power-law form are studied. The principle of minimum total potential energy is applied along with the Ritz method to derive and solve the governing equations. Considering conventional boundary conditions, Chebyshev polynomials of the first kind are used as auxiliary shape functions. The formulation is developed within the framework of well-known Timoshenko and Reddy beam theories (TBT, RBT). Since the beams are simultaneously tapered and functionally graded, bending and shear stress pushover curves are presented to get a profound insight into the variation of stresses along the beam. The proposed formulations and solution scheme are verified through benchmark problems. In this context, excellent agreement is observed. Numerical results are included considering beams with various cross sectional types to inspect the effects of taper ratio and gradient index on deflections and stresses. It is observed that the boundary conditions, taper ratio, gradient index value and core to the thickness ratio significantly influence the stress and deflection responses.

• 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.