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WE define as an open tube a thin‐walled structure, the cross‐section of which does not include any closed circuit. This property is common, for example, to the curved channel, the interspar wing cut‐out and the panel stiffened with Z‐sections, illustrated in FIG. 1 (a, b, c). But the interspar cut‐out with nose cell (FIG. 1d) is not an open tube in the present definition. All structures discussed in this paper are assumed to be cylindrical and to have a constant cross‐section. It is relatively simple to extend the results to conical taper and longitudinally varying thickness, but this would be beyond the scope and space of the present analysis (see, however, ref. 5).

This paper continues the theme of the opening Part I by analysing a number of problems designed to illustrate some particular aspects of the general theory. Three are concerned with thermal stresses and the last applies inter alia the theorems on maxima and minima to find lower and upper bounds to the St Venant torsional stiffness of a thin solid section.

DURING the last few years a programme of creep tests under general stress systems at high temperatures has been carried out at the N.P.L., using four metallic alloys which were chosen as being representative of basic groups of materials used in practice in machinery operating at high temperatures. This work, it was hoped, would fulfil, at least partly, the great need for experimental data in this field, as opposed to the comparative abundance of theoretical work available, and also enable a critical examination of the merits of this theoretical work to be made. The materials chosen in order of examination were a cast 0–17 per cent carbon steel, an aluminium alloy (R.R. 59), a magnesium alloy (containing 2 per cent aluminium), and a nickel‐chromium alloy (Nimonic 75). Each material was tested at temperatures lying within the normal working range of the material in question. Thus the 0–17 per cent carbon steel was tested at 350, 450 and 550 dcg. C. (662, 842 and 1,022 deg. F.), the aluminium alloy at 150 and 200 deg. C. (302 and 392 dcg. F.), the magnesium alloy at 20 and 50 deg. C. (68 and 122 dcg. F.), and the nickel‐chromium alloy at 550 and 650 dcg. C. (1,022 and 1,202 deg. F.).

THE work described in this paper is part of a programme concerned with the plastic, creep, and relaxation properties of metals under complex stress systems at elevated temperatures.which is being carried out in the Engineering Division of the N.P.L. It comprises data on the criterion of departure from elastic behaviour, of a low carbon steel over the temperature range 20–550 deg. C, and of an aluminium alloy over the temperature range 20–200 deg. C, and the creep properties under complex stress systems of the low carbon steel at 350 deg. C, and of the aluminium alloy at 150 and 200 deg. C.

This paper presents a preliminary analysis of the effects of kinetic healing at supersonic speeds on the torsional and flexural stiffnesses of thin solid wings. The main investigation is based on the small deflexion theory, but the scope of the analysis for torsion is extended to cover the effects of large deformations.

The purpose of this paper is to present a design sensitivity analysis continuum formulation for the cross-section properties of thin-walled laminated composite beams. These properties are expressed as integrals based on the cross-section geometry, on the warping functions for torsion, on shear bending and shear warping, and on the individual stiffness of the laminates constituting the cross-section.

In order to determine its properties, the cross-section geometry is modeled by quadratic isoparametric finite elements. For design sensitivity calculations, the cross-section is modeled throughout design elements to which the element sensitivity equations correspond. Geometrically, the design elements may coincide with the laminates that constitute the cross-section.

The developed formulation is based on the concept of adjoint system, which suffers a specific adjoint warping for each of the properties depending on warping. The lamina orientation and the laminate thickness are selected as design variables.

The developed formulation can be applied in a unified way to open, closed or hybrid cross-sections.

THE St. Venant theory as applied to long beams of constant cross‐section could generally be used with sufficient accuracy for the solution of the structures encountered in aircraft until the last few years. The wings of high‐speed aircraft, with smaller aspect ratios, large angles of sweep‐back, and small thickness/chord ratios, introduce a new problem. There is an extensive literature on the subject, and all the methods which have been proposed are necessarily studies of redundant systems, the degree of redundancy varying according to the accuracy required. As these solutions require that the scantlings of the structure be known in advance, it was thought interesting to establish a simple method which would determine to a good approximation the skin thicknesses required. This is based on the application of the theorem of least work, which gives exact solutions of elasticity problems so long as all the terms in the strain energy expression are taken into account.

IN these days of metal construction, the aircraft designer frequently uses the so‐called Batho theory of the torsion of thin shells. This simple and well‐known theory is a ecial case, applicable to tubes and boxes of any cross‐section, of the general St. Venant torsion theory. The same theory, applied to thin “ open ” sections, of which a channel is a mplc example, gives the result that the torsional strength and rigidity are very small. While it is true that such a section tends always to be weak in torsion in comparison with a closed section of similar dimensions, subject to certain conditions as regards fixing of the ends it is capable of transmitting an appreciable torque. The method of transmission can be described as differential bending of the two langes, in the case of the channel. Calculation of differential bending stresses in a two‐spar wing under torsion is a simple procedure, but alien the two members in differential bend form part of a continuous section, the conditions are somewhat altered. The general theory applicable to such cases may be called the theory of torsion‐bending. The results of this theory will be summarised, and the proofs given in the Appendix.

To present a new constitutive model for capturing inelastic behavior of brittle materials.

The multi‐surface plasticity theory is employed to describe the damage‐induced mechanisms. An original feature in that respect concerns the multi‐surface criterion which limits the principle values of elastic strains, which is equivalent to Saint‐Venant plasticity model. The latter allows to represent the damage both in tension and in compression.

Provides a quite realistic description of cracking phenomena in brittle materials, with a very few parameters, leading to a very useful tool for analyzing practical engineering problems.

The model is recast in terms of stress resultants and employed within a flat shell elements in order to provide a very efficient tool for analysis of cellular structures. Moreover, a detailed description of the numerical implementation is given.

The purpose of this work is to perform the finite element analysis (FEA) for the numerical discretization of sections with different arrangements of Web openings to investigate the torsion behavior. Typical hexagonal and circular Web opening sections are extensively used in steel construction due to economic development in building design. However, the use of sections with different arrangements of Web opening had improved the performance of the section with Web opening in terms of structural behavior which leads to economic design compared to typical I-beam.

The accuracy of FE results allows extensive numerical analysis of stress concentration magnitude for sections with Web openings, concentrating on the sizes and positions of the Web opening. Five shapes and three sizes of Web opening are used in this work. The shapes involved are c-hexagon, hexagon, octagon, circular and square, whereas the sizes of the Web opening involved are 0.67 D, 0.75 D and 0.80 D where D is the height of the Web. Two types of models for 200 × 100 × 8×6 mm steel section involved which is Model 1, where the section with 50 mm edge and 150 mm center-to-center distance and Model 2, where the section with 100 mm edge and 200 mm center-to-center distance.

It was found that these configurations affect the section with various shapes of Web openings sizes (0.67 D, 0.75 D, and 0.80 D). This also includes the spacing distances, with 50 mm edge and 150 mm center-to-center distance and also a section with 100 mm edge and 200 mm center-to-center distance. Through the FEA results of Model 1 and Model 2, it is found that 50% reduction in horizontal member length in hexagon Web opening, from 50 mm to 20 mm, caused increment about 30%–53% stress concentration in Web for c-hexagon. However, for a stress analysis of c-hexagon, geometry resulted in a lower stress concentration in the Web than other Web opening.

Additionally, the work emphasized the efficiency of Web opening shapes by using an appropriate Web opening radius in section with c-hexagon, hexagon, octagon, square and circular shapes. The final results show the contribution of appropriate Web opening radius to increase the section torsional capacity. It is observed that the torsional capacity at certain loading condition and its angle of twist is analysed.