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A DSIR Sponsored Research Programme on the Development and Application of the Matrix Force Method and the Digital Computer. This work presents a rational method for the structural analysis of stressed skin fuselages for application in conjunction with the digital computer. The theory is a development of the matrix force method which permits a close integration of the analysis and the programming for a computer operating with a matrix interpretive scheme. The structural geometry covered by the analysis is sufficiently arbitrary to include most cases encountered in practice, and allows for non‐conical taper, double‐cell cross‐sections and doubly connected rings. An attempt has been made to produce a highly standardized procedure requiring as input information only the simplest geometrical and elastic data. An essential feature is the use of the elimination and modification technique subsequent to the main analysis of the regularized structure in which all cutouts have been filled in. Current Summary A critical historical appraisal of previous work in the Western World on fuselage analysis is given in the present issue together with an outline of the ideas underlying the new theory.

THE work of Johnson, Mathur and Henderson on the ‘Creep Deflexion of Magnesium Alloy Struts’ raised the question in the present writer's mind of the stress distribution in the beam cross‐section, and the variation of this distribution with time. The precise computation of the stress distribution in an eccentrically loaded strut appears to be a very difficult problem, and the present note is concerned with the much simpler case of a beam subjected to a constant bending moment.

METHOD for the stress analysis of the circular conical fuselage with flexible frames, subjected to a fairly general type of load distribution, was recently developed by the present writer in a paper published in the Journal of the Royal Aeronautical Society. This paper did not, however, make any attempt to deal with the question of cut‐outs, and for the reason given below it later transpired that certain modifications of the basic theory were required before this problem could be solved.

THE strain energy (UF) in a frame is expressed by the equation

IN this part we shall consider the effect of non‐uniformity (with respect to k) in the longitudinal members, with particular reference to the case of four longerons, and we shall then go on to discuss the treatment of cut‐outs.

THE case now to be considered is shown diagrammatically in FIG. 12, which also gives the additional notation required. The problem is to determine how a bending moment, applied at one end to the longer‐ons only, is diffused into the whole section, being finally distributed according to the usual beam theory of bending. The differential equation to be satisfied by the displacement w is equation B(2), and if we take the origin at the centre we may take s=Rψ, h=r, x=R sin ψ and y=R cos ψ. Equation B(2) then becomes:

WE now come to the case shown in fig. 14. This is intended to represent a simplification of a two‐spar wing, having an outer portion skin‐covered and an inner open portion, the two spars being built‐in at the inner end. The top and bottom skins will usually be reinforced with spanwise stiffeners and the application of torque to the box will induce end loads in these stiffeners, in addition to bending moments in the spars. These end loads are essentially a local effect, localized near the inner end of the skin‐covered portion of the wing, and at sections remote from the inner end the torsional stresses in the box will be given by the ordinary Batho formula.

THIS problem is similar to that treated in section C, but now the stringers will be treated as discrete members separated by panels of skin which transmit only shear stress. The method of solution is quite different from that hitherto employed, it having been found that the result was most conveniently obtained by the principle of minimum strain energy. The problem is shown diagrammatically in FIG. 16, where the notation to be used is also given.

A PROBLEM arises in the matrix analysis of highly redundant structures, and no doubt often occurs in other engineering and scientific contexts, in which a set of linear simultaneous equations, which has already been solved for one particular set of values of the coefficients, has to be solved again when some of the coefficients are altered. In the structural context the problem is to find the effect of altering the sizes of some of the members of a structure. This alters the matrix of coefficients of the equations for the unknowns (the redundancies) in a rather special way, but in other problems the alterations in the matrix may be of a more general character. It was accordingly decided to investigate the general problem of matrix modification to sec if some method could be devised which did not involve the complete solution of the altered equations ab initio, but which made use of the work already done in solving the original equations. It seemed reasonable to suppose that the amount of work involved in finding the solution of the modified equations could be related to the number of altered coefficients, so that if only a few of the coefficients were altered the amount of additional work to obtain the new solution would be correspondingly small.

IT is known that if a thin circular ring is subjected to a uniform normal loading in its own plane, of amount σ per unit length of circumference, it will become elastically unstable when σ=—3B/R3, σ being taken to be positive when acting outwards. The theory on which this result is based assumes that the cross‐sectional dimensions of the ring and the change in radius are small compared with the initial radius, and is the counterpart of the elementary buckling theory of straight compression members. If the ring is initially perfectly circular it remains so at any numerically smaller value of σ, and it remains circular for any positive value of σ.