Abstract
This paper is focused on fractal analysis of the surface cracking, a new tool for safety evaluation of corroded reinforced concrete (RC) beams. Comprehensive experimental investigations, including flexural tests, coupon tests on strength evaluation of corroded concrete and rusty rebar, and pullout tests to determine bond strength between concrete and rebar were carried out on nine Corroded Reinforced Concrete Beams (CRCB) exposed to an aggressive environment for more than 10 years. In combination with test results from a previous study on CRCBs fabricated in the laboratory from accelerated methods, it is found that, for both types of beams, the surface cracking distributions are fractal in character at loading and failure stages. Fractal dimension is calculated for all specimens at different corrosion states based on fractal analysis method. Relationships between the fractal dimension and mechanical properties of corroded concrete, rebar corrosion ratio, and ductility of CRCBs are discussed in detail. It is concluded that the fractal dimension can act as a damage index and can be efficiently used to describe the corrosion state of CRCBs.
Abstract
In this study, element loading matrices are defined for static application of classical MŸller-Breslau principle to finite element method. The loading matrices are derived from existing element matrices using Betti? law and known governing equations of F.E.M. Thus, the ordinates of influence lines and influence surfaces may be easily obtained from structural analysis for the loading matrices derived from governing equations, instead of through introduced unit force or displacement techniques. An algorithm for a computer program and comparative numerical examples are also presented to illustrate the procedure for determination of influence line and surface ordinates.
Key Words
influence lines; influence surfaces; Betti? law, Muller-Breslau principle, finite element method.
Address
Faculty of Civil Engineering, Technical University of .Istanbul, 34469 Ayazaga, Istanbul, Turkey
Abstract
In this paper, free vibration of rotating beam with random properties is studied. The cross-sectional area, elasticity modulus, moment of inertia, shear modulus and density are modeled as random fields and the rotational speed as a random variable. To study uncertainty, stochastic finite element method based on second order perturbation method is applied. To discretize random fields, the three methods of midpoint, interpolation and local average are applied and compared. The effects of rotational speed, setting angle, random property variances, discretization scheme, number of elements, correlation of random fields, correlation function form and correlation length on ?oefficient of Variation?(C.O.V.) of first mode eigenvalue are investigated completely. To determine the significant random properties on the variation of first mode eigenvalue the sensitivity analysis is performed. The results are studied for both Timoshenko and Bernoulli-Euler rotating beam. It is shown that the C.O.V. of first mode eigenvalue of Timoshenko and Bernoulli-Euler rotating beams are approximately identical. Also, compared to uncorrelated random fields, the correlated case has larger C.O.V. value. Another important result is, where correlation length is small, the convergence rate is lower and more number of elements are necessary for convergence of final response.
Key Words
rotating beam; random properties; random fields; stochastic finite element method; second order perturbation.
Address
Department of Mechanical Engineering, Tarbiat Modarres University, P.O. Box 14115-177, Tehran, Iran
Abstract
The paper presents a new approach for the analysis of slope stability that is based on the numerical solution of a differential equation, which describes the thrust force distribution within the potential sliding mass. It is based on the evaluation of the thrust force value at the endpoint of the slip line. A coupled approximation of the slip and thrust lines is applied. The model is based on subdivision of the sliding mass into slices that are normal to the slip line and the equilibrium differential equation is obtained as the slice width approaches zero. Opposed to common iterative limit equilibrium procedures the present method is straightforward and gives an estimate of slope stability at the value of the safety factor prescribed in advance by standard requirements. Considering the location of the thrust line within the soil mass above the trial slip line eliminates the possible development of a tensile thrust force in the stable and critical states of the slope. The location of the upper boundary point of the thrust line is determined by the equilibrium of the upper triangular slice. The method can be applied to any smooth shape of a slip line, i.e., to a slip line without break points. An approximation of the slip and thrust lines by quadratic parabolas is used in the numerical examples for a series of slopes.
Abstract
The T-stress of cracks in elastic sheets is solved by using the fractal finite element method (FFEM). The FFEM, which had been developed to determine the stress intensity factors of cracks, is re-applied to evaluate the T-stress which is one of the important fracture parameters. The FFEM combines an exterior finite element model with a localized inner model near the crack tip. The mesh geometry of the latter is self-similar in radial layers around the tip. The higher order Williams series is used to condense the large numbers of nodal displacements at the inner model near the crack tip to a small set of unknown coefficients. Numerical examples revealed that the present approach is simple and accurate for calculating the T-stresses and the stress intensity factors. Some errors of the T-stress solutions shown in the previous literature are identified and the new solutions for the T-stress calculations are presented.
Abstract
The input energy to a base-isolated (BI) building during an earthquake is considered and formulated in the frequency domain. The frequency-domain approach for input energy computation has some notable advantages over the conventional time-domain approach. Sensitivities of the input energy to the BI building are derived with respect to uncertain parameters in the base-isolation system. It is demonstrated that the input energy can be of a compact form via the frequency integration of the product between the input component (Fourier amplitude spectrum of acceleration) and the structural model component (so-called energy transfer function). With the help of this compact form, it is shown that the formulation of earthquake input energy in the frequency domain is essential for deriving the sensitivities of the input energy to the BI building with respect to uncertain parameters. The sensitivity expressions provide us with information on the most unfavorable combination of the uncertain parameters which leads to the maximum energy input.
Abstract
The cable tension plays an important role in the construction, assessment and long-term health monitoring of cable structures. The cable vibration equation is nonlinear if cable sag and bending stiffness are included. The engineering implementation of a vibration-based cable tension evaluation is mostly carried out by the simple taut string theory. However, the simple theory may cause unacceptable errors in many applications since the cable sag and bending stiffness are ignored. From the practical point of view, it is necessary to have empirical formulas if they are simple and yet accurate. Based on the solutions by means of energy method and fitting the exact solutions of cable vibration equations where the cable sag and bending stiffness are respectively taken into account, the empirical formulas are proposed in the paper to estimate cable tension based on the cable fundamental frequency only. The applicability of the proposed formulas is verified by comparing the results with those reported in the literatures and with the experimental results carried out on the stay cables in the laboratory. The proposed formulas are straightforward and they are convenient for practical engineers to fast estimate the cable tension by the cable fundamental frequency.
Key Words
cable structure; fundamental frequency; cable tension; practical formulas; vibration method; cable sag; cable bending stiffness.
Address
Wei-Xin Ren; Department of Civil Engineering, Fuzhou University, Fuzhou, Fujian Province, 350002, P.R. China (Department of Civil Engineering, Central South University, Changsha, Hunan Province 410075, P.R.China) Gang Chen and Wei-Hua Hu; Department of Civil Engineering, Fuzhou University, Fuzhou, Fujian Province, 350002, P.R. China
Abstract
The structural analysis of space frames in most cases is not practical because of some complications in data preparation and interpretation of results. Therefore the analysis of reinforced concrete and steel structures realized sometimes by idealization of them as plane frames although they are space frames. This approach seems to be sufficient for the design of structures and can be applied to the idealized plane frames provided that at least one of the principal axes of the elements (beams and columns) is laying in the plane of frame. Although the beams of the frames generally do satisfy this condition the columns may or may not satisfy. For these types of columns the frame plane and bending plane are not coinciding and the columns are actually being under the effect of asymmetric bending. For the structural analysis of such frames the frame must be taken as a space frame (Kuo and Yang 1993, Aristazabal-Ochoa 2003), or a special plane frame analysis technique (Kim and Lee 2000, Nunes and Soriano 2003) which takes into consideration the asymmetric bending of columns must be used. In this work a displacement type of finite element method is proposed for a plane frame having columns which has principal axes not in the plane of frame. The global axes of the plane frame (X, Y, Z ) and the local axes of column 1 are shown in Fig. 1. In the analysis of a frame using the method of Finite Elements it is sufficient to define the stiffness matrix of the column in the X, Y system. The local displacements and the forces can be determined by transformation.
Key Words
finite element; plane frames; principal axes not in the plane; space frames.
Address
Department of Civil Engineering, Osmangazi University, Eski ehir, Turkey