In-plane response of laminates with spatially varying fiber orientations - Variable stiffness concept
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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.
The general aim of the investigation described in this report is the achievement of efficient design in wing beams. The purpose of the tests was to determine factors to apply to the usual beam formula in order that the properties of wood based on tests of rectangular sections might be used as a basis of design for beams of any sections and if practical to develop formulas for determining such factors and to verify them by experiment. Such factors for various sections have been determined from test by comparing properties of the beam in question to similar properties of matched beams 2 by 2 inches in section. Furthermore, formulas were worked out, more or less empirical in character, which check all of these test values remarkably well.
The general purpose in this study was to determine the stresses in a wooden member subjected to combined beam and column action. What may be considered the specific purpose, as it relates more directly to the problem of design, was to determine the particular stress that obtains at maximum load which, for combined loading, does not occur simultaneously with maximum stress.
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