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The paper reports experiments carried out on beams in pure bending. The material used was a cast magnesium alloy AZ855. The beam sections were rectangular, circular, I‐section, T‐scction and diamond. One series of tests was carried out up to 1 per cent fibre strain. A second series of tests was carried out up to fracture. Tension and compression tests were also made on the material. The experimental results show conclusively that the usual theory of plastic bending is correct and that the tension‐compression stress‐strain curve of the material may be used to determine the bending moment‐curvature relationships, etc., for a beam. Measurements of neutral axis shift also confirm the predictions of plastic bending theory.

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.

The purpose of this paper is to solve temperature stress for bending beam with different moduli under different constraints subject to nonlinear temperature.

The equations of neutral axis position, normal stress, and displacement of bending beam with different moduli subjected to nonlinear temperature were derived based on different moduli elasticity theory. Meanwhile, iterative procedure was programmed to solve the nonlinear equations. The analytical solution can return back into the result of the same modulus theory, and the analytical solution was compared with finite element numerical solution. It shows that the analytical model proposed in this paper is reliable to use. Furthermore, the influence of different moduli characteristics on the temperature stress and deformation is discussed.

The mechanical behavior of the bending beam with different moduli subject to nonlinear temperature is quite different from the one that is subjected to force. The bending beam maybe exist two neutral axis, and the reasonable selection of tension modulus and compression modulus can improve the distribution of the normal stress and reduce the maximum tensile stress or the maximum compressive stress.

The crack produced by temperature stress will affect the integrity and the durability of the structure. The solution for temperature problem with different moduli theory is rarely reported at home and board. In view of this, this paper will do some exploratory research-temperature stress for bending beam with different moduli.

The purpose of this study is to show how gradual strength degradation of metal beams under cyclic bending up to fatigue failure is simulated based on a new elastoplasticity model free of any yield criterion.

A new approach is proposed toward accurately and explicitly prescribing evolution of non-uniform stress distribution on beam cross-section under cyclic bending and, as such, gradual degradation of the bending strength can be directly determined.

Explicit results for the bending response in a whole cyclic process up to fatigue failure are obtained and the fatigue characteristic curve is for the first time simulated directly between the curvature amplitude and the cycle number to failure.

First, explicit and accurate determination of the non-uniform stress distribution on beam cross-section is achieved with asymptotic softening effects. Second, degradation of the bending strength can be directly deduced cycle by cycle. Finally, the relationship between the bending moment and the curvature is calculated using new and efficient numerical algorithms, thus bypassing usual time-consuming calculations with finite element procedures. Numerical results are presented and in good agreement with experimental data.

Tapered steel sections are widely used in house building design due to their structural efficiency and aesthetic appearance. Due to the practical usage of web tapering specifications in the metal building industry, fabrication and material expenses are analyzed to achieve geometric and economic productivity. The purpose of this study is to investigate the effectiveness of utilizing web profiles with openings in reducing the weight of steel beams.

In this paper, the nonlinear analysis of the bending behavior of a tapered steel section with an opening was studied by finite element analysis. The results were then compared with those of the tapered steel section without an opening in terms of displacement and yield moment.

The bending capacity of a tapered steel section was analyzed using finite element analysis. Results showed that the tapered steel section without openings had a higher bending capacity compared to the section with various sizes of web openings. The results also showed that decreasing the number of openings would increase the bending capacity, whereas increasing the size of the opening would decrease it. The difference in the yield moment between the tapered steel section with and without openings was only 15.818%. A total of 60 nonlinear analyses were conducted to investigate the effect of the number and size of web openings, flange thickness and web thickness on the bending behavior. However, this study showed that web opening with octagon shape and 0.6D size of web opening, where D is the depth of section, showed the best section in terms of yield moment and volume reduction compared to other opening size and shape.

It is also found that tapered steel section has better moment resistance in thicker flange and web. The study is valuable for engineers and designers who work with steel structures and need to optimize the performance of tapered steel sections with web openings.

There exists a clear paucity of models for curved bi-directional functionally graded (BDFG) beams wherein the material properties vary along the axis and thickness of the beam simultaneously; such structures may help fulfil practical design requirements of the future and improve structural efficiency. In this context, the purpose of this paper is to extend the analytical model developed earlier to thick BDFG circular beams by using first-order shear deformation theory which allows for a non-zero shear strain distribution through the thickness of the beam.

Smooth functional variations of the material properties have been assumed along the axis and thickness of the beam simultaneously. The governing equations developed have been solved analytically for some representative determinate circular beams. In order to ascertain the effects of shear deformation in these structures, the total strain energy has been decomposed into its bending and shear components and the effects of the beam thickness and the arch angle on the shear energy component have been studied.

Closed-form exact solutions involving through-the-thickness integrals carried out numerically are presented for the bending of circular beams under the action of a variety of concentrated/distributed loads.

The results clearly indicate the importance of capturing shear deformation in thick BDFG beams and demonstrate the capability of tuning the response of these beams to fit a wide variety of structural requirements.

This paper aims to investigate the fire performance of composite beams when considering the hogging moment resistance of the fin-plate beam-to-girder joints including the effect of continuity of reinforcements.

Experiments on composite beams with fin-plate joints protected only at the beam ends are conducted. The test parameter is the specification of reinforcement, which affects the rotational restraint of the beam ends. In addition, a simple method for predicting the failure time of the beam using an evaluation model based on the bending moment resistance of the beam considering the hogging moment resistance of the fin-plate joint and the reinforcement is also presented.

The test results indicate that the failure time of the beam is extended by the hogging moment resistance of the joints. This is particularly noticeable when using a reinforcing bar with a large plastic deformation capability. The predicted failure times based on the evaluation method corresponded well with the test results.

Recent studies have proposed large deformation analysis methods using FEM that can be used for fire-resistant design of beams including joints, but these cannot always be applicable in practice due to the cost and its complexity. Our method can consider the hogging moment resistance of the joint and the temperature distribution in the axial direction using a simple method without requirement of FEM.

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.

The purpose of this paper is to study the buckling and the vibration of the beam induced by atom/molecule adsorption using the nonlocal Euler‐Bernoulli beam model with initial axial stress.

The nonlocal parameter associated with adsorbed mass and bending rigidity variations of the beam induced by adsorbates are taken into account, and the buckling and dynamic behaviors are obtained via the Hamilton's principle, in which the potential energy between adsorbates and surfaces of the beam, the bending energy, the external work and the kinetic energy are summed as the Lagrangian function.

The results show that, for both buckling and resonant frequency, the nonlocal effect should be considered when the beam scales down to several hundreds of nanometres, especially for higher mode numbers.

The present paper gives the exact expressions for the buckling and resonant frequency of a simple‐supported nonlocal beam with initial axial stress. Different from previous works, the mass increasing and bending rigidity of the beam are found size‐dependent (nonlocal effect), resulting in possible different static and dynamic behaviors of the beam when atom/molecular adsorption occurs. The exact expressions obtained for the buckling and resonant frequency may be helpful to the design and application of micro‐ and nanobeam‐based sensors/resonators.

A slender beam with slight geometrical curvature is divided in bays with different cross‐sections subjected to uniformly distributed and concentrated transverse loads. Combined with the conditions which hold at the first and last point of the beam, the bending moments at tbe ends of the bays will be determined by three moment equations, or, when uniformly distributed transverse loads are operative, graphically by use of polar co‐ordinates. Knowing these moments a polar diagram can be completed for each bay. Further, a convenient method is shown for the solution of deflexions of the beam. An additional remark deals also with the beam under tension. Finally numerical examples give an illustration of the procedure.