ALBERT

Description: The theory of Lagrangian multipliers is applied to the problem of finding both upper and lower limits to the true compressive buckling stress of a clamped rectangular plate. The upper and lower limits thus bracket the truss, which cannot be exactly found by the differential-equation approach. The procedure for obtaining the upper limit, which is believed to be new, presents certain advantages over the classical Raleigh-Rite method of finding upper limits. The theory of the lower-limit procedure has been given by Trefftz but, in the present application, the method differs from that of Trefftz in a way that makes it inherently more quickly convergent. It is expected that in other buckling problems and in some vibration problems problems the Lagrangian multiplier method finding upper and lower limits may be advantageously applied to the calculation of buckling stresses and natural frequencies.

Description: Theoretical and experimental investigations were made of the distribution of strains in a plywood sheet-stringer combination used as the chord member of a box beam acted upon by bending loads. The theoretical solution was obtained with the help of the principle of minimum potential energy and certain simplifying assumptions. Strain measurements were made on a build-up box beam by means of electrical-resistance strain gages connected with strain indicators. A very satisfactory agreement between the theoretical and experimental strains was obtained.

Description: The stresses in circular frames of constant bending stiffnesses, as encountered in thin-wall shells, are investigated from the point of view of finite depth of sectional area of frame. The solution is carried out for four fundamental load conditions. The method is illustrated on a worked out example.

Description: The solution of von Karman's fundamental equations for large deflections of plates is presented for the case of a simply supported rectangular plate under combined edge compression and lateral loading. Numerical solutions are given for square plates and for rectangular plates with a width-span ratio of 3:1. The effective widths under edge compression are compared with effective widths according to von Karman, Bengston, Marguerre, and Cox and with experimental results by Ramberg, McPherson, and Levy. The deflections for a square plate under lateral pressure are compared with experimental and theoretical results by Kaiser. It is found that the effective widths agree closely with Marguerre's formula and with the experimentally observed values and that the deflections agree with the experimental results and with Kaiser's work.

Description: A sturdy stiffener is defined as a stiffener of such proportions that it does not suffer cross-sectional distortion when moments are applied to some part of the cross section. When such a stiffener is attached to one edge of a plate, it will resist rotation of that edge of the plate by means of its torsional properties. A formula is given for the restraint coefficient provided the plate by such a stiffener. This coefficient is required for the calculation of the critical compressive stress of the plate.

Description: Compression tests were conducted on 247 panels with Z-section stiffeners and 304 panels with hat-section stiffeners. Specimens were constructed from artificially aged Alclad 24S aluminum alloy with minimum guaranteed yield strengths of 64 and 57 ksi for stiffeners and sheet materials, respectively. Height, thickness, and spacing of stiffeners, sheet thickness, and length of specimens were varied systematically to show effects of changes in these dimensions on panel strength. Results show average stresses at buckling load and maximum load.

Description: The investigation of machine-countersunk flush rivets for aircraft described in reference 1 revealed the necessity of having the height of the rivet heads greater than the depth of the countersunk holes if tightly riveted joints were to be obtained. If ordinary roundhead rivets were inserted from the opposite side of the joint and the countersunk heads formed in the driving of the rivets filled the countersunk holes completely, still tighter joints were obtained. In either case the rivets protruded above the skin surface after driving, and the protruding portion of the rivet heads had to be removed in order to obtain flush rivets. A number of requests have been received for a description of the tool used to mill off the protruding portion of the rivet heads. This report contains assembly and detail drawings of the latest flush-rivet milling tool used at the NACA Structures Research Laboratory. Figure 6 shows the tool in operation. This tool is quite satisfactory for 1/8-inch rivets, but a more powerful motor is recommended for use with larger rivets.

Description: A comprehensive series of compression tests on skin-stiffener panels with Z-section stiffeners formed from flat sheet is being made in order to show the importance of the relative dimensions in determining the strength of the panels. The results obtained to date in this investigation are presented in this report.

Description: Cylindrical shells of arbitrary section, reinforced by longitudinal and transverse members (stringers and ribs) are considered by us, for a sufficiently close spacing of the ribs, as in our previously published papers (references 1 end 2), as thin-walled orthotropic spatial systems at the cross-sections of which only axial (normal and shearing) forces can arise. The longitudinal bending and twisting moments, due to their weak effect on the stress state of the shell, are taken equal to zero. Along the longitudinal sections of the shell there may arise transverse forces in addition to the normal ~d shearing forces. Under the so-called static assumptions there is taken for the computation model of the shell a thin-walled spatial system consisting along its length (along a generator) of an infinite number of elementary strips capable of bending. Each of these strips is likened to a curved rod operating in each of its sections not only in tension (compression)but also in transverse bending and shear. The interaction between two adjoining transverse strips in the shell expresses itself in the transmission from one strip to the other of only the normal and shearing stresses. The static structure of the computation model here described is shown in figure 1, where the connections through which the normal and shearing stresses transmitted from one transverse strip to smother are indicated schematically by the rods located in the middle surface of the shell. In addition to the static hypothesis we introduce also geometric hypotheses. According to the latter the elongational deformations of the shell along lines parallel to the generator of its middle surface and the shear deformations in the middle surface, as ma+gitudes having . little effect on the state of the fundamental internal forces of the shell, are taken equal to zero. The deformations of the shell in our computational model are such that in the first place the lines of this surface perpendicular to the generator are inextensible at each point end in the second place the angles between the lines of principal curvature (the coordinate lines) which are straight before the deformation remain straight after the deformation.

Description: This article explains results developed from the following research: 'The Stability of Plates and Shells beyond the Elastic Limit.' A significant improvement is found in the derivation of the relations between the stress factors and the strains resulting from the instability of plates and shells. In a strict analysis, the problem reduces to the solution of two simultaneous nonlinear partial differential equations of the fourth order in the deflection and stress function, and in the approximate analysis to a single linear equation of the Bryan type. Solutions are given for the special cases of a rectangular plate buckling into a cylindrical form, and of an arbitrarily shaped plate under uniform compression. These solutions indicate that the accuracy obtained by the approximate method is satisfactory.

Description: The present paper deals with the computation and methods of reinforcement of stiffened panels with cutouts under bending loads such as are applied to the sides of a fuselage. A comparison is maade between the computed and test results. Results are presented of tests on panels with cutouts under tensile and compressive loads.

Description: Stress-rupture data for four heat-resisting alloys are analyzed according to equations of the theory of rate processes. A method for determining the four parameters of structure and composition is demonstrated and the four parameters are determined for each of the alloys: forged S816, cast S816, cast S590, and cast Vitallium. It is concluded that parameters can be determined for an alloy provided sufficient reliable experimental data are available.

Description: We consider a prismatic shell consisting of a finite number of narrow rectangular plates and having in the cross-section a finite number of closed contours (fig. 1(a)). We shall assume that the rectangular plates composing the shell are rigidly joined so that there is no motion of any kind of one plate relative to the others meeting at a given connecting line. The position of a point on the middle prismatic surface is considered to be defined by the coordinate z, the distance to a certain initial cross-section z = O, end the coordinate s determining its position on the contour of the cross-section.

Description: This technical memorandum is a mathematical investigation of the problem of overspeeded disks. New methods must be sought for obtaining a satisfactory stress equalization in the cross section of these disks.

Description: In the years after the First World war a very rapid development, which even today has by no means come to an end, took place in the field of welding; here also, as in most technical innovations, failures made their appearance. Thereupon comprehensive Investigations were undertaken by steel manufacturers and consumers with cooperation of the authorities. b most cases the reasons for failure could be determined and eliminated and further occurrences avoided by the use of new test methods.

Description: Tests have been conducted to determine the drive-motor torque and the static force and moment characteristics of the AN/SPS-1 radar antenna. Shifting the longitudinal position of the antenna had very little effect on the drive-motor torque, which reached a maximum value expressed in terms of dynamic pressure (T/q)(sub max) of 1.15 at an azimuth angle of 245 deg. The maximum observed values of rolling, pitching, and yawing moments in terms of dynamic pressure are -29.0, 66.6, and 13.4, respectively.

Description: A sturdy stiffener is defined as a stiffener of such proportions that it does not suffer cross-sectional distortion when moments are applied to some part of the cross section. When such a stiffener is attached to one edge of a plate, it will resist rotation of that edge of the plate by means of its torsional properties. A formula is given for the restraint coefficient provided the plate by such a stiffener. This coefficient is required for the calculation of the critical compressive stress of the plate.

Description: The test indicate that "an indiscriminate single application of the Southwell method (for analyzing Exp. Observations in problems of elastic stability)--can result in definite and measurable errors" The test also indicate "that the effect of curvature due to bending on the critical load for the compression flange material of a box beam is probably small and can be neglected." We have not found this to be true in our tests. It is believed that the effect of curvature, together with a small amount of fixity at the ribs, tends to force the stiffeners to bow in each bay thus effectively increasing their end fixity and thereby raising their allowable loads.

Description: This report contains a theoretical discussion of the load distribution in bolted or riveted joints in light-alloy structures which is applicable not only for loads below the limit of proportionality but also for loads above this limit. The theory is developed for double and single shear joints. The methods given are illustrated by numerical examples and the values assumed for the bolt (or rivet) stiffnesses are based partly on theory and partly on known experimental values. It is shown that the load distribution does not vary greatly with the bolt (or rivet) stiffnesses and that for design purposes it is usually sufficient to know their order of magnitude. The theory may also be directly used for spot-welded structures and, with small modifications, for seam-welded structures, The computational work involved in the methods described is simple and may be completed in a reasonable time for most practical problems. A summary of earlier theoretical and experimental investigations on the subject is included in the report.

Description: Column and plate compressive strengths of extruded 24S-T aluminum alloy were determined both within and beyond the elastic range from tests of thin-strip columns and local-instability tests of H-, Z-,and channel-section columns. These tests are part of an extensive research investigation to provide data on the' structural strength of various aircraft materials. The results are presented in the form of curves and charts that are suitable for use in the design and analysis of aircraft structures.

Description: In the present paper is examined the method of investigating the stability of plates and shells beyond the elastic limit, that proceeds from the generalization of the Hencky-Mises theory of elastico-plastic deformations given in the works of Smirnov-Alyayev, Schmidt, and in our papers.