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Article

K.A. Patel, Sandeep Chaudhary and A.K. Nagpal

The purpose of this paper is to develop, for use in everyday design, a procedure that incorporates the effect of concrete cracking in reinforced concrete (RC) beams at…

Abstract

Purpose

The purpose of this paper is to develop, for use in everyday design, a procedure that incorporates the effect of concrete cracking in reinforced concrete (RC) beams at service load and requires computational efforts which is a fraction of that required for the available methods. Further for ease of use in everyday design the reinforcement input data is minimized. The procedure has been demonstrated for continuous beams and is under development for tall building frames.

Design/methodology/approach

The procedure is analytical at the element level and numerical at the structural level. A cracked span length beam element consisting of three cracked zones and two uncracked zones has been used. Closed form expressions for flexibility coefficients, end displacements, crack lengths, and mid-span deflection of the cracked span length beam element have been presented. In order to keep the procedure analytical at the element level, average tension stiffening characteristics are arrived at for cracked zones.

Findings

The proposed procedure, at minimal computation effort and minimal reinforcement input data, yields results that are close to experimental and finite element method results.

Practical implications

The procedure can be used in everyday design since it requires minimal computational effort and minimal reinforcement input data.

Originality/value

A procedure that requires minimal computational effort and minimal reinforcement input data for incorporating concrete cracking effects in RC structures at service load has been developed for use in everyday design.

Details

Engineering Computations, vol. 31 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

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Article

C.J. Burgoyne

The paper describes the use of a microcomputer to determine the behaviour of continuous beams. Three procedures are described: the analysis of continuous beams subject to…

Abstract

The paper describes the use of a microcomputer to determine the behaviour of continuous beams. Three procedures are described: the analysis of continuous beams subject to generalized loadings using Macauley's method, the extension to include the production of influence lines, and the analysis of these influence lines to comply with a loading code. Results are presented to show how different assumptions about partial factors applied to dead loads can produce ranges of moments for which the structure must be designed. The implications for the designer of the complexities of a modern highway design code are considered in some detail, and the methods used to produce bending moment and shear force envelopes for structures designed to these rules are discussed.

Details

Engineering Computations, vol. 4 no. 3
Type: Research Article
ISSN: 0264-4401

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Article

Yasser Sharifi and Hamed Aviz

Nowadays, with the expansion of terrorist operations around the world and also the dangers of accidental explosions, the need to design structures resistant to this…

Abstract

Purpose

Nowadays, with the expansion of terrorist operations around the world and also the dangers of accidental explosions, the need to design structures resistant to this phenomenon for the protection and safety of its citizens is inevitable. Tall buildings are one of the most important issues because of which those behavior should be investigated against the blast loading.

Design/methodology/approach

In this paper, the authors used a simple method for investigating the dynamic response of tall buildings with the combined system of framed tube, shear core and outrigger-belt truss located at different heights of the building’s that were subjected to blast loading. This proposed model is based on the development of a continuum model and the ruling equations that have been obtained using the energy principle predict the whole structure idealized as a shear and flexural cantilever beam with rotational springs at the belt truss location.

Findings

The mathematical procedure shows a good understanding of the structural behavior and is suitable for a quick evaluation during the preliminary design stage, which requires less time. Moreover, it was concluded that the present blast load idealization can be used to reasonably assess the response of tall buildings subjected to blast load.

Originality/value

The comparative analysis in this paper could give other engineers a simple analysis method for the preliminary analysis and design of tall building analysis. Numerical example is given to illustrate the ease of application and the accuracy of the suggested model.

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Article

Hassan Samami and S. Olutunde Oyadiji

The purpose of this paper is to employ analytical and numerical techniques to generate modal displacement data of damaged beams containing very small crack-like surface…

Abstract

Purpose

The purpose of this paper is to employ analytical and numerical techniques to generate modal displacement data of damaged beams containing very small crack-like surface flaws or slots and to use the data in the development of damage detection methodology. The detection method involves the use of double differentiation of the modal data for identification of the flaw location and magnitude.

Design/methodology/approach

The modal displacements of damaged beams are simulated analytically using the Bernoulli-Euler theory and numerically using the finite element method. The principle used in the analytical approach is based on changes in the transverse displacement due to the localized reduction of the flexural rigidity of the beam. Curvature analysis is employed to identify and locate the structural flaws from the modal data. The curvature mode shapes are calculated using a central difference approximation. The effects of random noise on the detectability of the structural flaws are also computed.

Findings

The analytical approach is much more robust in simulating modal displacement data for beams with crack-like surface flaws or slots than the finite element analysis (FEA) approach especially for crack-like surface flaws or slots of very small depths. The structural flaws are detectable in the presence of random noise of up to 5 per cent.

Originality/value

Simulating the effects of small crack-like surface flaws is important because it is essential to develop techniques to detect cracks at an early stage of their development. The FEA approach can only simulate the effects of crack-like surface flaws or slots with depth ratio greater than 10 per cent. On the other hand, the analytical approach using the Bernoulli-Euler theory can simulate the effects of crack-like surface flaws or slots with depth ratio as small as 2 per cent.

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Article

SRINIVAS KODIYALAM, S. ADALI and I.S. SADEK

The optimal thickness distribution of a two‐span continuous beam is determined with the objectives of minimizing the maximum stress, maximizing the fundamental frequency…

Abstract

The optimal thickness distribution of a two‐span continuous beam is determined with the objectives of minimizing the maximum stress, maximizing the fundamental frequency and frequency separation between adjacent frequencies. The self‐weight of the beam is included in the computations. The multiobjective design problem is solved by using the concept of Pareto optimality. The beam thickness is approximated by constant splines. The stress distribution and the frequencies are determined by the finite element method. The optimization of the beam is carried out by the feasible direction method and by employing a quadratic approximation of the thickness function. Numerical results are given for two‐objective design problems. Optimal trade‐off curves, thickness distributions and stress distributions of optimally designed beams are presented in graphical form. The effects of self‐weight and different design objectives on the thickness distribution are investigated.

Details

Engineering Computations, vol. 9 no. 5
Type: Research Article
ISSN: 0264-4401

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Article

Jaroslav Mackerle

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the…

Abstract

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

Details

Engineering Computations, vol. 14 no. 4
Type: Research Article
ISSN: 0264-4401

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Article

Leslie P. Dudley

PROBLEMS relating to built‐in or rigid‐end members under transverse loading are frequently encountered by the aircraft engineer. In the following paper discussion of…

Abstract

PROBLEMS relating to built‐in or rigid‐end members under transverse loading are frequently encountered by the aircraft engineer. In the following paper discussion of relevant theorems leads to the development of Clapeyron's Theorem of Three Moments. The latter is particularly valuable in, for example, estimating the crankshaft bearing loads in a non‐radial engine. Attention is also drawn to Wilson's method of solving continuous beam problems. This simple method produces results identical with those given by the Theorem of Three Moments and deserves wider recognition.

Details

Aircraft Engineering and Aerospace Technology, vol. 14 no. 11
Type: Research Article
ISSN: 0002-2667

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Article

Victor Rizov

This paper is concerned with analysis of the time-dependent strain energy release rate for a longitudinal crack in a beam subjected to linear relaxation. A viscoelastic…

Abstract

Purpose

This paper is concerned with analysis of the time-dependent strain energy release rate for a longitudinal crack in a beam subjected to linear relaxation. A viscoelastic model with an arbitrary number of parallel units is used for treating the relaxation. Each unit has one dashpot and two springs. A stress-strain-time relationship is derived for the case when the coefficient of viscosity in each unit of the viscoelastic model changes continuously with time. The beam exhibits continuous material inhomogeneity along the thickness. Thus, the moduli of elasticity and the coefficients of viscosity vary continuously in the thickness direction. The aim of the present paper is to obtain time-dependent solutions to the strain energy release rate that take into account the relaxation when the coefficient of viscosity changes with time.

Design/methodology/approach

Time-dependent solutions to the strain energy release rate are derived by considering the time-dependent strain energy and also by using the compliance method. The two solutions produce identical results.

Findings

The variation of the strain energy release rate with time due to the relaxation is analysed. The influence of material inhomogeneity and the crack location along the beam width on the strain energy release rate are evaluated. The effects of change of the coefficients of viscosity with time and the number of units in the viscoelastic model on the strain energy release rate are assessed by applying the solutions derived.

Originality/value

The time-dependent strain energy release rate for a longitudinal vertical crack in a beam under relaxation is analysed for the case when the coefficients of viscosity change with time.

Details

World Journal of Engineering, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 1708-5284

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Article

V. Yevko, C.B. Park, G. Zak, T.W. Coyle and B. Benhabib

Current commercial rapid prototyping systems can be used for fabricating layered models for subsequent creation of fully‐dense metal parts using investment casting. Due to…

Abstract

Current commercial rapid prototyping systems can be used for fabricating layered models for subsequent creation of fully‐dense metal parts using investment casting. Due to increased demand for shortened product development cycles however, there exists a demand to rapidly fabricate functional fully‐dense metal parts without hard tooling. A possible solution to this problem is direct layered rapid manufacturing of such parts, for example, via laser‐beam fusion of the metal powder. The rapid manufacturing process discussed herein is based on this approach. It involves selective laser‐beam scanning of a predeposited metal‐powder layer, forming fully‐dense claddings as the basic building block of individual layers. This paper specifically addresses only one of the fundamental issues of the rapid manufacturing process under investigation at the University of Toronto, namely the fabrication of single claddings. Our theoretical investigation of the influence of the process parameters on cladding’s geometrical properties employed thermal modeling and computer process simulation. Numerous experiments, involving fabrication of single claddings, were also carried out with varying process parameters. Comparisons of the process simulations and experimental results showed good agreement in terms of overall trends.

Details

Rapid Prototyping Journal, vol. 4 no. 4
Type: Research Article
ISSN: 1355-2546

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Article

Hillal Ayas, Lyes Amara and Mohamed Chabaat

In this paper, an approximate analytical approach is developed for the determination of natural longitudinal frequencies of a cantilever-cracked beam based on the Lagrange…

Abstract

Purpose

In this paper, an approximate analytical approach is developed for the determination of natural longitudinal frequencies of a cantilever-cracked beam based on the Lagrange inversion theorem.

Design/methodology/approach

The crack is modeled by an equivalent axial spring with stiffness according to Castigliano's theorem. Thus, an implicit frequency equation corresponding to cantilever-cracked bar is obtained. The resulting equation is solved using the Lagrange inversion theorem.

Findings

effect of different crack depths and crack positions on natural frequencies of the cracked beam is analyzed. It is shown that an increase in the crack depth ratio produces a decrease in the fundamental longitudinal natural frequency of a cracked bar. Furthermore, approximate analytical results are compared with those obtained numerically as well as from experimental tests.

Originality/value

A new approximate analytical expression of a fundamental longitudinal frequency, as a function of crack depth and crack location, is obtained.

Details

International Journal of Structural Integrity, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 1757-9864

Keywords

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