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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.

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.

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

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

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.

This article presents a geometrically non-linear finite element formulation for the analysis of planar two-layer beam-columns taking into account the inter-layer slip and uplift.

The co-rotational method is adopted, in which the motion of the element is decomposed into a rigid body motion and a small deformational one. The geometrically linear formulation can be used in the local frame and automatically be transformed into a geometrically nonlinear one. In co-rotational frame, both layers are assumed to be discretely connected at the element ends. Slips and uplifts are assumed to be small. Consequently, the condition of non interpenetration between the layers can be treated using a node-to-node contact algorithm. The resolution methods such as penalty (PM) and augmented Lagrangian method (ALM) with Uzawa updating scheme can be used.

The non-penetration condition between the layers of composite beams can be formulated by using contact law. It is found that despite a low convergence rate of augmented Lagrangian method compared to penalty method, the former prevents the unrealistic penetration. Besides, it is shown that the buckling load of the composite beam-column is largely affected by the uplift stiffness of the connectors.

The proposed finite element model is capable of simulating accurately the geometrically non-linear behavior of planar two-layer beam-columns taking into account the inter-layer slip and uplift. Regarding uplift, the non-penetration condition is strictly enforced by considering rigorous contact conditions at the interface. The constraint problem is solved using the penalty method or the augmented Lagrangian method with the Uzawa updating scheme.

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.

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.

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.

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.

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.

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.

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.

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.

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.

This study aims to investigate the effects of using circular spirals as the longitudinal reinforcing bars on the performance of the concrete beams subjected to four-point bending load.

The effects of using circular spirals as the longitudinal reinforcing bars on the performance of the concrete beams subjected to four-point bending load are investigated in this study. Employing circular spirals as the main longitudinal reinforcement is a novel idea presented in this paper. In this regard, a finite element model of the beam with spiral longitudinal reinforcement was developed. After model verification, several configurations of concrete beams reinforced by longitudinal spirals were simulated under the four-point loading condition.

Obtained results showed that using the longitudinal spirals in place of the conventional longitudinal reinforcing bars can improve the bearing capacity of the concrete beam, but at the same time, increases its ductility unacceptably. In other words, the spirals reduce the initial stiffness of the beam significantly. To solve the problem, the authors decided to use the longitudinal spirals as the auxiliary bars added to the main conventional longitudinal bars in the beams. New gained results were satisfactory. By adding the longitudinal spirals to the conventional bars, not only the bearing capacity of the beam increases between 24% and 63%, but also the initial stiffness and ductility of the beam raises between 11%–29% and 3%–57%, respectively, in comparison to the corresponding beam reinforced with conventional longitudinal bars.

Employing circular spirals as the main longitudinal reinforcement is a novel idea presented in this paper.

This research study focuses on investigating the seismic performance of non-straight beams in steel structures and exploring the mechanism by which plastic hinges are formed within these beams. The findings contribute to the understanding of their behaviour under seismic loads and offer insights into their potential for enhancing the lateral resistance of the structure. The abstract of the study highlights the significance of corners in structural plans, where non-coaxial columns, diagonal elements or beams deviating from a straight path are commonly observed. Typically, these non-straight beams are connected to the columns using pinned connections, despite their unknown seismic behaviour. Recognizing the importance of generating plastic hinges in special moment resisting frames and the lack of previous research on the involvement of these non-straight beams, this study aims to address this knowledge gap.

This study examines the seismic behaviour and plastic hinge formation of non-straight beams in steel structures. Non-straight beams are beams that connect non-coaxial columns and diagonal elements, or deviate from a linear path. They are usually pinned to the columns, and their seismic contribution is unknown. A critical case with a 12-m non-straight beam is analysed using Abaqus software. Different models are created with varying cross-section shapes and connection types between the non-straight beams. The models are subjected to lateral monotonic and cyclic loads in one direction. The results show that non-straight beams increase the lateral stiffness, strength and energy dissipation of the models compared to disconnected beams that act as two cantilevers.

The analysis results reveal several key findings. The inclusion of non-straight beams in the models leads to increased lateral stiffness, strength and energy dissipation compared to the scenario where the beams are disconnected and act as two cantilever beams. Plastic hinges are formed at both ends of the non-straight beam when a 3% drift is reached, contributing to energy damping and introducing plasticity into the structure. These results strongly suggest that non-straight beams play a significant role in enhancing the lateral resistance of the system. Based on the seismic analysis results, this study recommends the utilization of non-straight beams in special moment frames due to the formation of plastic hinges within these beams and their effective participation in resisting lateral seismic loads. This research fills a critical gap in understanding the behaviour of non-straight beams and provides valuable insights for structural engineers involved in the design and analysis of steel structures.

The authors believe that this research will greatly contribute to the knowledge and understanding of the seismic performance of non-straight beams in steel structures.

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.

The purpose of this study is to explore the seismic damage mechanism of the Dayemaling Bridge during the Maduo earthquake and discuss the seismic damage characteristics of the high-pier curved girder bridge.

In this study, the numerical simulation method is used to analyze the seismic response using synthetic near-field ground motion records.

The near-field ground motion of the Maduo earthquake has an obvious directional effect, it is more likely to cause bridge seismic damage. Considering the longitudinal slope of the bridge and adopting the continuous girder bridge form, the beam end displacement of the curved bridge can be effectively reduced, and the collision force of the block and the bending moment of the pier bottom are reduced, so the curved bridge with longitudinal slope is adopted.

Combined with the seismic damage phenomenon of bridges in real earthquakes, the seismic damage mechanism and vulnerability characteristics of high-pier curved girder bridges are discussed by the numerical simulation method, which provides technical support for the application of such bridges in high seismic intensity areas.

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.