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At least 127 records · Page 7

Shear strains in a graphite-PEEK beam by moire interferometry with carrier fringes

A multispan quasi-isotropic graphite-PEEK beam exhibited dramatic shear strains in the interlaminar region between plies. Shear strains in the plies themselves varied in basic accord with fiber direction. Large anomalous shear strains developed near the center of the beam height, where shear stresses were large. High-sensitivity moire interferometry with 2400 lines/mm was used. A new technique of data extraction was developed, using carrier fringes to transform the pattern to one in which fringe slopes are proportional to derivatives of displacement. It enhanced detection and measurement of highly localized shear-strain gradients.

Post, Daniel↗

The Influence of the Form of a Wooden Beam on Its Stiffness and Strength I : Deflection of Beams with Special Reference to Shear Deformations

The purpose of this investigation was to determine to what extent ordinary deflection formulas, which neglect shear deformations, are in error when applied to beams of various sections, and to develop reasonably accurate yet comparatively simple formulas which take into account such deformations. A great many tests were made to determine the amount of shear deformation for beams of various sections tested over many different spans. As the span over which the beam is tested is increased the error introduced by neglecting shear deformations becomes less, and the values obtained by substituting measured deflections in the ordinary formulas approach more nearly the modulus of elasticity in tension and compression. For short spans the error is considerable and increases rapidly as the span is reduced. Two formulas were developed for estimating the magnitude of shear deformations, both of which have been verified by tests. The first assumes the parabolic distribution of shear on a cross section of a beam and, starting with a differential volume, the distortion due to shear is determined by the ordinary methods of summarizing the work. The second assumes that the deflections due to shear in any two beams of the same length, height, and moment of inertia, which are similarly loaded, are proportional to the summations of the shear stresses on their respective vertical sections. Both formulas check experimental results very closely when the calculations are made with great refinement.

Newlin, J A↗

Buckling of composite beams (CDDF)

Presented are the results of an investigation of the twisting/warping deformation occurring in open-section composite beams. A series of C and L channels were manufactured using both hand layup and the innovative 'hot-drape forming' techniques. A transverse tip load was applied at the free end of the cantilevered open-section beams. The test setup allowed the tip load to be applied at various locations along the plane of and at the beam's shear center. Charts are included in this report depicting various angles of ply layups, loads applied, and load application points. A major verification resulting from this study is that the shear center of an open section composite beam can be altered, if not completely controlled, through laminate layup. Also, it was observed that the choice of the material system does not have an effect on the amount of deformation, as expected, and the material affects the location of an unsymmetric open section composite beam's true shear center. The results from this study have provided a foundation for further investigation into the apparent shifting of the shear center location in open-section composite beams.

Thompson, P.↗

Effects of organized turbulence structures on the phase distortion in a coherent optical beam propagating through a turbulent shear flow

Phase distortion in a coherent optical beam propagating through a turbulent shear flow is studied. The instantaneous distribution of the index refraction is represented by a passive-scalar field in a computed homogeneous shear flow. The flow contains organized vortical structures (hairpin eddies), which are characteristic of turbulent shear flows. The phase distortion induced by turbulent fluctuations is calculated from the optical path difference through the flow. A conceptual model is proposed for the distribution of scalar fluctuations produced by the hairpin vortices in the shear flow. It is shown that the phase distortion of an optical beam can be minimized by propagating the beam at an angle approximately normal to the organized vortical structures in a turbulent shear flow.

Truman, C. Randall↗

Kinetic equilibria of plasma shear layers

The analysis of plasma beam and shear problems in magnetic fields is usually based on a hydromagnetic fluid model. In a low-density collisionless plasma, however, the kinetic effects of the plasma, such as finite Larmor radius effects, are not yet clearly understood. In this paper, the kinetic equilibria of plasma shears in a uniform and fixed magnetic field, with full ion motion, are discussed by solving the Vlasov equation with a given electric field and drift velocity. In this model, the ion density profile through the plasma shear layer is quite different from the one predicted by a hydromagnetic model. As a result of a complicated ion gyromotion through the shear layer, single- and double-humped ion density profiles are obtained. The dependence on the temperature and the strength of the shear will be discussed. The results show a significant difference between positive and negative shears.

Cai, D.↗

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↗

Gravitational lensing by a smoothly variable three-dimensional mass distribution

A smooth three-dimensional mass distribution is approximated by a model with multiple thin screens, with surface mass density varying smoothly on each screen. It is found that 16 screens are sufficient for a good approximation of the three-dimensional distribution of matter. It is also found that in this multiscreen model the distribution of amplifications of single images is dominated by the convergence due to matter within the beam. The shear caused by matter outside the beam has no significant effect. This finding considerably simplifies the modeling of lensing by a smooth three-dimensional mass distribution by effectively reducing the problem to one dimension, as it is sufficient to know the mass distribution along a straight light ray.

Lee, Man Hoi↗

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↗

Free Vibration of Uncertain Unsymmetrically Laminated Beams

Monte Carlo Simulation and Stochastic FEA are used to predict randomness in the free vibration response of thin unsymmetrically laminated beams. For the present study, it is assumed that randomness in the response is only caused by uncertainties in the ply orientations. The ply orientations may become random or uncertain during the manufacturing process. A new 16-dof beam element, based on the first-order shear deformation beam theory, is used to study the stochastic nature of the natural frequencies. Using variational principles, the element stiffness matrix and mass matrix are obtained through analytical integration. Using a random sequence a large data set is generated, containing possible random ply-orientations. This data is assumed to be symmetric. The stochastic-based finite element model for free vibrations predicts the relation between the randomness in fundamental natural frequencies and the randomness in ply-orientation. The sensitivity derivatives are calculated numerically through an exact formulation. The squared fundamental natural frequencies are expressed in terms of deterministic and probabilistic quantities, allowing to determine how sensitive they are to variations in ply angles. The predicted mean-valued fundamental natural frequency squared and the variance of the present model are in good agreement with Monte Carlo Simulation. Results, also, show that variations between plus or minus 5 degrees in ply-angles can affect free vibration response of unsymmetrically and symmetrically laminated beams.

Kapania, Rakesh K.↗