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Bending of Beams of Thin Sections

Description: The tendency toward economy of material and lightness of structure has long since led to the increased application of beams having large ratios of moment of area W to cross-sectional area F. This paper tries to provide an answer to how thin the beams can be.
Date: April 1936
Creator: Huber, Maximilian T.
Partner: UNT Libraries Government Documents Department

Effect of change in cross section upon stress distribution in circular shell-supported frames

Description: From Summary: "Bending-stress and bending-moment coefficients are presented for application to design of circular shell-supported fuselage frames of variable cross section for applied radial load, applied moment, and applied tangential load. A ring which is properly reinforced in the region of maximum bending moment is shown to have a structural efficiency higher than that of a similar ring of uniform cross section. The structural efficiency is given in terms of the relative weights of the reinforced and nonreinforced rings."
Date: July 1946
Creator: Nelson, David H.
Partner: UNT Libraries Government Documents Department

Bending tests of a monocoque box

Description: A monocoque box beam consisting of a 24S-T aluminum-alloy sheet reinforced by four bulkheads and by longitudinal stringers and corner posts was subjected to bending loads as follows: pure bending about the lift axis, cantilever bending about the lift axis, and pure bending about both lift and drag axis. Longitudinal strains were measured for loads up to a load at which permanent set became measurable. The loads were sufficient to produce buckling of the sheet between stringers on the compression side of the box. The only noticeable effect of this buckling was a small increase in extreme-fiber strain on the compression side. The measured strains and measured deflections differed less than 10 percent from those computed from the simple beam theory after taking account of the effective width of the buckled sheet. The effect of the bulkheads on the distribution of stringer strain was negligible.
Date: November 1942
Creator: McPherson, Albert E.; Ramberg, Walter & Levy, Samuel
Partner: UNT Libraries Government Documents Department

Bending tests of circular cylinders of corrugated aluminum-alloy sheet

Description: Bending tests were made of two circular cylinders of corrugated aluminum-alloy sheet. In each test failure occurred by bending of the corrugations in a plane normal to the skin. It was found, after analysis of the effect of short end bays, that the computed stress on the extreme fiber of a corrugated cylinder is in excess of that for a flat panel of the same basic pattern and panel length tested as a pin-ended column. It is concluded that this increased strength was due to the effects of curvature of the pitch line. It is also concluded from the tests that light bulkheads closely spaced strengthen corrugated cylinders very materially.
Date: March 1937
Creator: Niles, Alfred S.; Buckwalter, John C. & Reed, Warren D.
Partner: UNT Libraries Government Documents Department

Stresses in and general instability of monocoque cylinders with cutouts 5: calculation of the stresses in cylinders with side cutout

Description: "Stresses were calculated by a numerical method in three reinforced monocoque cylinders subjected to pure bending. The cylinders were of circular cross section and were reinforced with 8 rings and either 8 or 16 stringers. There was a cutout on one side of each cylinder located symmetrically to the neutral plane and extending over 45, 90, or 135 degrees" (p. 1).
Date: January 1948
Creator: Hoff, N. J. & Klein, Bertram
Partner: UNT Libraries Government Documents Department

A numerical approach to the instability problem of monocoque cylinders

Description: Report presenting two closely related methods which employ operations tables that have been developed and used in the calculation of buckling load of a monocoque cylinder subjected to pure bending. The buckling loads of three cylinders with very different characteristics were calculated using the methods.
Date: April 1951
Creator: Boley, Bruno A.; Kempner, Joseph & Mayers, J.
Partner: UNT Libraries Government Documents Department

Strength tests of thin-walled elliptic duralumin cylinders in pure bending and in combined pure bending and torsion

Description: An analysis is presented of the results of tests made by the Massachusetts Institute of Technology and by the National Advisory Committee for Aeronautics on an investigation of the strength of thin-walled circular and elliptic cylinders in pure bending and in combined torsion and bending. In each of the loading conditions, the bending moments were applied in the plane of the major axis of the ellipse.
Date: June 1942
Creator: Lundquist, Eugene E. & Stowell, Elbridge Z.
Partner: UNT Libraries Government Documents Department

Numerical procedures for the calculation of the stresses in monocoques 3: calculation of the bending moments in fuselage frames

Description: "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" (p. 1).
Date: April 1946
Creator: Hoff, N. J.; Libby, Paul A. & Klein, Bertram
Partner: UNT Libraries Government Documents Department

Experimental stress analysis of stiffened cylinders with cutouts: Pure bending

Description: Bending tests were made on a cylindrical semimonocoque shell of circular cross section. The cylinder was tested without a cutout and then with a rectangular cutout which was successively enlarged through six sizes varying from 30 degrees to 130 degrees in circumference and from 1 to 2 bays in length. Strain measurements were made with resistance-type wire strain gages near the cutout on the stringers, the skin, and the rings for each size of cutout, and the stresses obtained are presented in tables. (author).
Date: March 1954
Creator: Schlechte, Floyd R. & Rosecrans, Richard
Partner: UNT Libraries Government Documents Department

Bending Stresses Due to Torsion in Cantilever Box Beams

Description: "The paper beings with a brief discussion on the origin of the bending stresses in cantilever box beams under torsion. A critical survey of existing theory is followed by a summary of design formulas; this summary is based on the most complete solution published but omits all refinements considered unnecessary at the present state of development. Strain-gage tests made by NACA to obtained some experimental verification of the formulas are described next. Finally, the formulas are applied to a series of box beams previously static-tested by the U.S. Army Air Corps; the results show that the bending stresses due to torsion are responsible to a large extent for the free-edge type of failure frequently experienced in these tests" (p. 1).
Date: June 1935
Creator: Kuhn, Paul
Partner: UNT Libraries Government Documents Department

Bending of Rectangular Plates With Large Deflections

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" (p. 1).
Date: May 27, 1941
Creator: Levy, Samuel
Partner: UNT Libraries Government Documents Department

A Method of Calculating Bending Stresses Due to Torsion

Description: Report presenting a method for analyzing bending stresses due to torsion in a box with variable cross section and loading by means of a recurrence formula leading to a set of equations identical in form with the well-known three-moment equations. An approximate form of the general method of analysis is presented that eliminates the need of solving a system of equations.
Date: December 1942
Creator: Kuhn, Paul
Partner: UNT Libraries Government Documents Department

Some Notes on the Numerical Solution of Shear-Lag and Mathematically Related Problems

Description: "The analysis of box beams with shear deformation of the flanges can be reduced to the solution of a differential equation. The same equation is met in other problems of stress analysis. No analytical solutions of this equation can be given for practical cases, and numerical methods of evaluation must be used. Available methods are briefly discussed. Two numerical examples show the application of the step-by-step method of integration to shear-lag problems" (p. 1).
Date: May 1939
Creator: Kuhn, Paul
Partner: UNT Libraries Government Documents Department

Simplified Procedures and Charts for the Rapid Estimation of Bending Frequencies of Rotating Beams

Description: Note presenting a Rayleigh energy approach utilizing the bending mode of the nonrotating beam in the determination of the bending frequency of the rotating beam, which is evaluated and is found to give good practical results for helicopter blades. Charts are presented for the rapid estimation of the first three bending frequencies for rotating and nonrotating cantilever and hinged beams.
Date: June 1955
Creator: Yntema, Robert T.
Partner: UNT Libraries Government Documents Department

Torsion and Transverse Bending of Cantilever Plates

Description: "The problem of combined bending and torsion of cantilever plates of variable thickness, such as might be considered for solid thin high-speed airplane or missile wings, is considered in this paper. The deflections of the plate are assumed to vary linearly across the chord; minimization of the potential energy by means of the calculus of variations then leads to two ordinary linear differential equations for the bending deflections and the twist of the plate. Because the cantilever is analyzed as a plate rather than as a beam, the effect of constraint against axial warping in torsion is inherently included" (p. 1).
Date: June 1951
Creator: Reissner, Eric & Stein, Manuel
Partner: UNT Libraries Government Documents Department

An Investigation of Bending-Moment Distribution on a Model Helicopter Rotor Blade and a Comparison With Theory

Description: Note presenting bending-moment distributions that were measured on a model helicopter rotor blade under hovering and simulated forward-flight conditions. curves of maximum-bending-moment distribution are presented for all test conditions. Resonance studies have also been made on three sets of blades of different stiffnesses for the purpose of comparing the experimentally determined resonance peaks with those indicated by theory.
Date: February 1952
Creator: Meyer, John R., Jr.
Partner: UNT Libraries Government Documents Department

Deformation Analysis of Wing Structures

Description: Note presenting theories of bending and torsion as applied to the problem of calculating the deflections in aircraft shell structures, particularly of wings. Bending as well as torsional deflections are discussed for wings without or with cut-outs.
Date: July 1947
Creator: Kuhn, Paul
Partner: UNT Libraries Government Documents Department

Deflections of a Simply Supported Rectangular Sandwich Plate Subjected to Transverse Loads

Description: "The differential equations of the bending of sandwich plates were integrated to obtain the deflections when the four edges of the plate are simply supported and the loading consists of either a uniformly distributed transverse load or a concentrated load applied at the center of the panel. The deflection patterns are shown in diagrams and the maximum deflection of the plate is presented in a number of graphs" (p. 1).
Date: December 1951
Creator: Yen, Kuo Tai; Gunturkun, Sadettin & Pohle, Frederick V.
Partner: UNT Libraries Government Documents Department

Creep Bending and Buckling of Linearly Viscoelastic Columns

Description: Note presenting the general dynamic equation of creep bending of a beam loaded laterally and axially as derived for a linearly viscoelastic material whose mechanical properties can be characterized by four parameters. The equation derived was used to obtain the creep bending deflection of a beam in pure bending and of a column with initial sinusoidal deviation from straightness.
Date: January 1954
Creator: Kempner, Joseph
Partner: UNT Libraries Government Documents Department

Rapid Estimation of Bending Frequencies of Rotating Beams

Description: Memorandum presenting a procedure in the form of charts which permits the rapid estimation of the natural bending frequencies of helicopter rotor blades, both rotating and nonrotating. An evaluation of the method with regard to such things as higher modes, blade offset, and variable mass and stiffness distributions is also given. The valuation shows that, when nonrotating beam bending modes are used, Southwell's equation yields reasonably accurate bending frequencies for rotating helicopter blades.
Date: August 18, 1954
Creator: Yntema, Robert T.
Partner: UNT Libraries Government Documents Department

The Influence of Bulkhead Spacing on Bending Stresses Due to Torsion

Description: Report presenting the reasons for the existence of bending stresses due to torsion and the theoretical formulas applying to rectangular boxes with finite bulkhead spacing. Tests are described which were made to verify the theory, strains being measured on a rectangular torsion box with four bulkhead spacings. Results regarding normal stresses are provided.
Date: May 1942
Creator: Kuhn, Paul
Partner: UNT Libraries Government Documents Department