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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1943

Least-work analysis of the problem of shear lag in box beams

The distribution of stress in the cover sheets of thin-wall box beams is analyzed, with regard to the effect of shear deformation in the cover sheets, by the method of least work. Explicit results are obtained for a number of representative cases that show the influence of the following factors on the stress patterns. (1) Variation of stress in spanwise direction as given by elementary beam theory. (2) Value of a parameter called shear-lag aspect ratio which designates the product of span-width ratio of the beam and of the square root of the ratio of effective shear modulus and tensing modulus of the cover sheets. (3) Value of ratio of cover-sheet stiffness to side-web stiffness. (4) Variation of beam height in span direction. (5) Variation of beam width in span direction. (6) Variation of cover-sheet thickness in span direction. General conclusions are drawn from the results obtained. Among them the most important one appears to be the fact that the shear-lag effect depends primarily on the following tow quantities: (1) the value of the shear-lag aspect ratio. (2) the shape of the curve representing the product of the stress of elementary beam theory and of the cover-sheet thickness.

STRESS CALCULATIONS, LEAST-WORK↗
NASA NTRS1942

Shear Lag in Box Beams Methods of Analysis and Experimental Investigations

The bending stresses in the covers of box beams or wide-flange beams differ appreciably from the stresses predicted by the ordinary bending theory on account of shear deformation of the flanges. The problem of predicting these differences has become known as the shear-lag problem. The first part of this paper deals with methods of shear-lag analysis suitable for practical use. The second part of the paper describes strain-gage tests made by the NACA to verify the theory. Three tests published by other investigators are also analyzed by the proposed method. The third part of the paper gives numerical examples illustrating the methods of analysis. An appendix gives comparisons with other methods, particularly with the method of Ebner and Koller.

Kuhn, Paul↗
NASA NTRS1943

The exact solution of shear-lag problems in flat panels and box beams assumed rigid in the transverse direction

A mathematical procedure is herein developed for obtaining exact solutions of shear-lag problems in flat panels and box beams: the method is based on the assumption that the amount of stretching of the sheets in the direction perpendicular to the direction of essential normal stresses is negligible. Explicit solutions, including the treatment of cut-outs, are given for several cases and numerical results are presented in graphic and tabular form. The general theory is presented in a from which further solutions can be readily obtained. The extension of the theory to cover certain cases of non-uniform cross section is indicated. Although the solutions are obtained in terms of infinite series, the present developments differ from those previously given in that, in practical cases, the series usually converge so rapidly that sufficient accuracy is afforded by a small number of terms. Comparisons are made in several cases between the present results and the corresponding solutions obtained by approximate procedures devised by Reissner and by Kuhn and Chiarito.

STRESSED SKIN-PLATES, FLAT↗
NASA NTRS1991

Longitudinal splitting in epoxy and K-polymer composites - Shear lag analysis including the effect of fiber bridging

The shear-lag model used previously by Nairn (1988) to derive a fracture mechanics analysis of longitudinal splitting in double-edge notched unidirectional composites was used to investigate the effect of fibers bridging across the longitudinal split in these composites. Using the new analysis, the longitudinal splitting fracture toughness, G(Lc), was determined for Hercules AS4/3501-6 graphite/epoxy laminates and for K-polymer based laminates containing Magnamite IM-6 as the graphite reinforcing fiber. Results show that the inclusion of the fiber bridging in the fracture analysis significantly affects the reported fracture toughness.

Nairn, John A.↗
NASA NTRS1939

Some notes on the numerical solution of shear-lag and mathematically related problems

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.

Kuhn, Paul↗
NASA NTRS1939

A recurrence formula for shear-lag problems

The analysis of the bending action in box beams with appreciable shear deformation of the flanges becomes very difficult in the general case of variable cross section and loading. This paper presents a convenient method of solving the problem by the familiar method of dividing the beam into a number of bays that can be assumed to have constant cross section and loading. Application of formerly derived shear-lag formulas leads to a general equation closely analogous in form to the well-known three-moment equation. A numerical example and two comparisons between calculation and experimental results are included.

Kuhn, Paul↗
NASA NTRS1984

Shear-lag analysis of notched laminates with interlaminar debonding

The fracture behavior of a debonded zone of finite width with no longitudinal damage in the unidirectional ply is predicted and the solution is then extended to include longitudinal matrix yielding and splitting in the unidirectional ply at the crack tip. The shear-lag assumption is used to describe the shear transfer between fibers. The fracture behavior of the laminate is studied as a function of initial crack length, constraint ratio, and width of the debonded zone. Results indicate that debonding can reduce the maximum fiber stress at the crack tip on the order of ten percent. This effect is maximum for a debond width of two or three fiber spacings and is independent of the initial crack length. As the debond width grows beyond this point, the maximum stress increases. For widths of about ten fiber spacings or more, the maximum fiber stress is larger than for the fully bonded case. In the presence of longitudinal matrix damage the same general behavior is found; however, the location of the maximum fiber stress is quite complex.

Goree, J. G.↗
NASA NTRS1985

Shear-lag analysis of notched laminates with interlaminar debonding

The fracture behavior of a debonded zone of finite width with no longitudinal damage in the unidirectional ply is predicted and the solution is then extended to include longitudinal matrix yielding and splitting in the unidirectional ply at the crack tip. The shear-lag assumption is used to describe the shear transfer between fibers. The fracture behavior of the laminate is studied as a function of initial crack length, constraint ratio, and width of the debonded zone. Results indicate that debonding can reduce the maximum fiber stress at the crack tip on the order of ten percent. This effect is maximum for a debonded width of two or three fiber spacings and is independent of the initial crack length. As the debond width grows beyond this point, the maximum stress increases. For widths of about ten fiber spacings or more, the maximum fiber stress is larger than for the fully bonded case. In the presence of longitudinal matrix damage the same general behavior is found; however, the location of the maximum fiber stress is quite complex.

Kaw, A. K.↗
NASA NTRS1983

Shear-lag analysis of a hybrid, unidirectional composite with fiber damage

Development of a method of analysis capable of predicting accurately the fracture behavior of unidirectional hybrid (buffer strip) composite laminates was studied. Three particular solutions are discussed in detail: broken fibers in a unidirectional half-plane; adjoined half planes of different fiber and matrix properties; and the solution of two half planes bounding a third distinct region of finite width. This finite width region represents a buffer strip and primary attention is given to the potential of this strip to arrest a crack that originates in one of the half planes. A materials modeling approach using the classical shear lag assumption to describe the stress transfer between fibers was analyzed. Explicit fiber and matrix properties of the three regions are retained, and changes in the laminate behavior as a function of the relative material properties, buffer strip width, and initial crack length are discussed.

Goree, J. G.↗