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IF a beam is laterally resting on a continuous elastic foundation then it is usually assumed in the technical literature that the intensity of lateral pressure p(u) is proportional to the deflexion v(u)

The Differential Equation of the Problem and the Solution. A RECTANGULAR plate of length a with simply supported edges is reinforced by equal longitudinal ribs at equal distances b and is submitted to the action of uniformly distributed compressive forces N along the x‐axis (Fig. 1). For every strip b we have the differential equation for the deflection w

LET us consider a tube of length L of doubly symmetrical rectangular cross section, built‐in or simply supported at one end and free at the other. The tube is affected by uniformly distributed torques along the length and by a tip applied torque and torques at intermediate points.

LET us consider a continuous beam with an even number of spans. The spans are each of length l, a constant cross‐section of area A with a constant moment of inertia I about the axis of buckling and are subjected to the compressive force P. The elastic stiffnesses of all intermediate supports are equal and the elastic stiffnesses of the two end supports are also equal but generally different from those of the other supports. We set out to determine the buckling condition for the beam and the relationship between the critical load and the elastic stiffness of the supports. E is Young's Modulus of the material of the beam or the momentary modulus corresponding to the stress at the buckling load.

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.

WHEN the fixed, forward‐firing guns of a fighter aircraft are installed in such a position that the recoil forces have an effective moment about the Centre of Gravity, then the aircraft will develop a pitching motion as a direct result of the discharge of the guns. The projectiles in any given burst will then be dispersed across, instead of concentrated on, the target. A theoretical expression for this dispersion of projectiles is developed, and hypothetical data, corresponding approximately to a modern, single‐engine, single‐seat fighter, is used to derive typical values of the dispersion at two ranges. These values are then considered in conjunction with the two main forms of attack, and it is deduced that the discharge of more than two rounds per gun is valueless since the dispersion of projectiles then exceeds the radius of the target. Other disadvantages attendant on the wing‐installation of guns are also noted and the conclusion is reached that, by mounting the armament in a battery in the nose, lengthy bursts of accurate, concentrated fire at long range are possible. Finally, the use of telescopic sights is envisaged if the potentialities of such a phenomenal increase in the operational efficiency of fighter aircraft are to be fully exploited.

FAILURE of panels under static compression, or for that matter under any loads, involves a vast array of problems ranging from properties of material to initial instability and post‐buckling phenomena as occurring in various types of panels. It is not intended here to do justice to all these aspects of the subject but to select a single—but at the same time very important—topic, develop its analysis as fully as possible, and present the results in a readily applicable form. The structure investigated is the single skin stiffened panel under compression and the mode of failure considered, denoted by flexural cum torsional failure, involves predominantly flexure and torsion of the stringer with a wavelength of greater order of magnitude than stringer height and pitch. By torsional deformation of the stringer we understand a rotation of its undistorted cross‐section about a longitudinal axis R in the plane of the plate, the position of which will be selected later on (see FIG. 1b). The panel may, of course, also fail in a local mode of stringer and plate with a short wave‐length of the order of magnitude of stringer height and pitch, but the analysis of this case is not included here (see, however, Argyris and Dunne). Note that a local mode of deformation of a stringer formed by straight walls is commonly defined as a distortion of the cross‐section in which the longitudinal edges where two adjacent walls meet remain straight (see FIG. 1c).