On the bending of lengthy anisotropic plates moving in a gas at constant supersonic velocity
Approximate solution for bending of long, narrow anisotropic plate moving in gas at supersonic velocity
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Approximate solution for bending of long, narrow anisotropic plate moving in gas at supersonic velocity
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Eighteen 24S-T alclad cylinders of 20-inch diameter, with skin thickness varying between 0.012 inch and 0.025 inch and length varying between 40.5 inches and 64 inches, were tested in pure bending. They were reinforced with either 16 or 28 stringers and either 5 or 6 rings. One of the purposes of the investigation was to establish the critical value above which failure would occur by general instability and below which panel instability would take place. This value was found to be between 20 and 40 for cylinders with 16 stringers and between 16 and 74 for cylinders with 28 stringers.
This report examines the stipulation contained in the 1918 BLV, that a girder subjected to longitudinal compression under the influence of half of the specified breaking load, along with Euler bending safety with an initial deflection of 1/200 of the length of the girder can, at most, be subjected to half the stipulated breaking strength.
This report deals with the calculation of the bending moments in and the distortions of fuselage rings upon which known concentrated and distributed loads are acting. In the procedure suggested, the ring is divided into a number of beams each having a constant radius of curvature. The forces and moments caused in the end sections of the beams by individual unit displacements of the end sections are listed in a table designated as the operations table in conformity with Southwell's nomenclature. The operations table and the external loads are equivalent to a set of linear equations. For their solution the following three procedures are presented: 1) Southwell's method of systematic relaxations. This is a step-by-step approximation procedure guided by the physical interpretation of the changes in the values of the unknown. 2) The growing unit procedure in which the individual beams are combined successively into beams of increasing length until finally the entire ring becomes a single beam. In each step of the procedure a set of not more than three simultaneous linear equations is solved. 3) Solution of the entire set of simultaneous equations by the methods of the matrix calculus. In order to demonstrate the manner in which the calculations may be carried out, the following numerical examples are worked out: 1) Curved beam with both its end sections rigidly fixed. The load is a concentrated force. 2) Egg-shape ring with symmetric concentrated loads. 3) Circular ring with antisymmetric concentrated loads and shear flow (torsion of the fuselage). 4) Same with V-braces incorporated in the ring. 5) Egg-shape ring with antisymmetric concentrated loads and shear flow (torsion of the fuselage). 6) Same with V-braces incorporated in the ring. The results of these calculations are checked, whenever possible, by calculations carried out according to known methods of analysis. The agreement is found to be good. The amount of work necessary for the solution of ring problems by the methods described in the present report is practically independent of the degree of redundancy of the structure. For this reason the methods are recommended for use particularly in problems of rings having one or more internal bracing elements.
Ten 24S-T alclad cylinders of 20-inch diameter, 45- or 58-inch length, and 0.012-inch wall thickness, reinforced with 24S-T aluminum alloy stringers and rings were tested in pure bending. In the middle of the compression side of the cylinders there was a cutout extending over 19 inches in the longitudinal direction, and over an angle of 45 degrees, 90 degrees, or 135 degrees in the circumferential direction. The strain in the stringers and in the sheet covering was measured with metal electric strain gages. The stress distribution in the cylinders deviate considerably from the linear law valid for cylinders without a cutout. The maximum strain measured was about four-thirds of the value calculated from the Mc/I formula when I was taken as the moment of inertia of the cross section of the portion of the cylinder where the cutout was situated. A diagram is presented containing the strain factors defined as the ratios of measured strain to strain calculated with the Mc/I formula. All the 10 cylinders tested failed in general instability. Two symmetric and one antisymmetric pattern of buckling were observed and the buckling load appeared to be independent of the method of manufacture and the length of the cylinder. The buckling load of the cylinders having cutouts extending over 45 degrees, 90 degrees, and 135 degrees was 66, 47, and 31 percent, respectively, of the buckling load of the cylinder without a cutout.