Shear-lag tests of a box beam with a highly cambered cover in tension
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BEAMS, BOX - BENDING↗
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Shear-Lag Tests of Two Box Beams with Corrugated Covers Loaded to Failure
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STRESSED SKIN - BEAMS, BOX↗
Comparison of several analytical solutions to the shear lag problem with experimental data Progress report no. 5
Stress distribution in flat stiffened panel under axial load - comparison of analytical solutions with experimental data
PANEL↗
Shear Lag in a Plywood Sheet-stringer Combination Used for the Chord Member of a Box Beam
Theoretical and experimental investigations were made of the distribution of strains in a plywood sheet-stringer combination used as the chord member of a box beam acted upon by bending loads. The theoretical solution was obtained with the help of the principle of minimum potential energy and certain simplifying assumptions. Strain measurements were made on a build-up box beam by means of electrical-resistance strain gages connected with strain indicators. A very satisfactory agreement between the theoretical and experimental strains was obtained.
LOADS - BEAMS, BOX↗
Shear lag study of three integrally stiffened panels Progress report no. 4
Stress distribution measurements of integrally stiffened panels
STIFF STRUCTURE↗
Shear Lag in Corrugated Sheets Used for the Chord Member of a Box Beam
The problem of the distribution of normal stress across a wide corrugated sheet used as the chord of a box-beam-like structure is investigated theoretically and experimentally. Expressions are developed giving the stress distribution in beams, symmetrical or unsymmetrical, about a plane passed spanwise through the center of the sheet. The experiments were arranged to insure bending without torsion and surveys of the normal stresses were made by means of mechanical and electrical strain gages. The experimental data showed very good agreement with the new b of the theoretical curves, especially at the highly stressed sections, for both the symmetrical and unsymmetrical beams. Several suggestions for future research are included.
Newell, Joseph S↗
A substitute-stringer approach for including shear-lag effects in box-beam vibrations
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Davenport, William W↗
Experimental evaluation of longitudinal splitting in unidirectional composites
An experimental study was conducted to determine the fracture behavior of centernotched, unidirectional graphite/epoxy laminates when subjected to tensile loading. The actual behavior is compared to the behavior predicted by a mathematical model based on classical shear-lag assumptions. Experimental results show the fracture behavior to consist of two modes of longitudinal matrix splitting. After split initiation, a region of slow, stable split growth occurs. This is followed by a distinct transition into a rapid split growth region. However, the shear-lag model predicts a single region of rapid longitudinal split growth behavior with unbounded splitting occurring after approximately a ten percent increase in the applied stress over the split initiation stress. It is therefore concluded that the classical shear-lag model does not accurately predict the complete longitudinal split growth behavior in a brittle matrix composite. This shortcoming in the model and some results obtained from related elasticity solutions are discussed and it is suggested that the slow, stable split growth region is likely dominated by transverse matrix normal stresses which are not accounted for in the classical shear-lag model.
Wolla, Jeffrey M.↗
Transverse vibrations of hollow thin-walled cylindrical beams
The variational principle, differential equations, and boundary conditions considered appropriate to the analysis of transverse vibrations of hollow thin-walled cylindrical beams are shown. General solutions for the modes and frequencies of cantilever and free-free cylindrical beams of arbitrary cross section but of uniform thickness are given. The combined influence of the secondary effects of transverse shear deformation, shear lag, and secondary effects of transverse shear deformation, shear lag, and longitudinal inertia is shown in the form of curves for cylinders of rectangular cross section and uniform thickness. The contribution of each of the secondary effects to the total reduction in the actual frequency is also indicated. (author)
Budiansky, Bernard↗
Analysis of the progressive failure of brittle matrix composites
This report investigates two of the most common modes of localized failures, namely, periodic fiber-bridged matrix cracks and transverse matrix cracks. A modification of Daniels' bundle theory is combined with Weibull's weakest link theory to model the statistical distribution of the periodic matrix cracking strength for an individual layer. Results of the model predictions are compared with experimental data from the open literature. Extensions to the model are made to account for possible imperfections within the layer (i.e., nonuniform fiber lengths, irregular crack spacing, and degraded in-situ fiber properties), and the results of these studies are presented. A generalized shear-lag analysis is derived which is capable of modeling the development of transverse matrix cracks in material systems having a general multilayer configuration and under states of full in-plane load. A method for computing the effective elastic properties for the damaged layer at the global level is detailed based upon the solution for the effects of the damage at the local level. This methodology is general in nature and is therefore also applicable to (0(sub m)/90(sub n))(sub s) systems. The characteristic stress-strain response for more general cases is shown to be qualitatively correct (experimental data is not available for a quantitative evaluation), and the damage evolution is recorded in terms of the matrix crack density as a function of the applied strain. Probabilistic effects are introduced to account for the statistical nature of the material strengths, thus allowing cumulative distribution curves for the probability of failure to be generated for each of the example laminates. Additionally, Oh and Finney's classic work on fracture location in brittle materials is extended and combined with the shear-lag analysis. The result is an analytical form for predicting the probability density function for the location of the next transverse crack occurrence within a crack bounded region. The results of this study verified qualitatively the validity of assuming a uniform crack spacing (as was done in the shear-lag model).
Thomas, David J.↗
Active plate and wing research using EDAP elements
The deflection characteristics of structures using directionally attached piezoelectric (DAP) and enhanced DAP (EDAP) elements are investigated analytically and experimentally. It is shown that directional attachment can be achieved by partial attachment, transverse shear lag, and differential stiffness bonding. The effective stiffnesses of DAP elements can be accurately modeled by an active element area estimation of partial attachment with a shear lag modification. Methods of integrating DAP and EDAP elements in missile wings and ways of alleviating such difficulties as control power degradation and adverse coupling are discussed.
Barrett, Ron↗
Comparison of Micromechanics Theories for Modeling Discontinuous Long Fiber Reinforced Composites
Two micromechanics theories, the high fidelity generalized method of cells and Carrera Unified Formulation, are used to model a repeating unit cell of a discrete long fiber composite. The models are used to predict the effective properties of a single fiber with varying fiber-to-fiber end gap lengths, as well as the local stresses in the fiber and matrix. Both models produced similar results and demonstrated that they could capture the complex local load transfer due to the shear lag effect.
discrete long fiber composites↗
Analysis of a unidirectional, symmetric buffer strip laminate with damage
A method for predicting the fracture behavior of hybrid buffer strip laminates is presented in which the classical shear-lag model is used to represent the shear stress distribution between adjacent fibers. The method is demonstrated by applying it to a notched graphite/epoxy laminate, and the results show clearly the manner in which the most efficient combination of buffer strip properties can be selected in order to arrest the crack. The ultimate failure stress of the laminate is plotted vs the buffer strip width. It is shown that in the case of graphite-epoxy and S-glass epoxy laminates, the optimum buffer strip spacing to width ratio should be about four to one.
Dharani, L. R.↗
Comparison of the Effects of Debonds and Voids in Adhesive Joints
An analytical model is developed to compare the effects of voids an debonds on the interfacial shear stresses between the adherends and the adhesive in simple lap joints. Since the adhesive material above the debond may undergo some extension (either due to applied load or thermal expansion or both), a modified shear lag model, where the adhesive can take an extensional as well as shear deformation, is used in the analysis. The adherends take on only axial loads and act as membranes. Two coupled nondimensional differential equations are derived, and in general, five parameters govern the stress distribution in the overlap region. As expected, the major differences between the debond and the void occur for the stresses near the edge of the defect itself. Whether the defect is a debond or a void, is hardly discernible by the stresses at the overlap region. If the defect occurs precisely at or very close to either end of the overlap, however, differences of the order of 20 percent in the peak stresses can be obtained.
Rossettos, J. N.↗
Aeroelastic Stability of Modern Bearingless Rotors: A Parametric Investigation
The University of Maryland Advanced Rotorcraft Code (UMARC) is utilized to study the effects of blade design parameters on the aeroelastic stability of an isolated modern bearingless rotor blade in hover. The McDonnell Douglas Advanced Rotor Technology (MDART) Rotor is the baseline rotor investigated. Results indicate that kinematic pitch-lag coupling introduced through the control system geometry and the damping levels of the shear lag dampers strongly affect the hover inplane damping of the baseline rotor blade. Hub precone, pitchcase chordwise stiffness, and blade fundamental torsion frequency have small to moderate influence on the inplane damping, while blade pre-twist and placements of blade fundamental flapwise and chord-wise frequencies have negligible effects. A damperless configuration with a leading edge pitch-link, 15 deg of pitch-link cant angle, and reduced pitch-link stiffness is shown to be stable with an inplane damping level in excess of 2.7 percent critical at the full hover tip speed.
Nguyen, Khanh Q.↗
Direct Measurements of the Mechanical Strength of Carbon Nanotube - Aluminum Interfaces
Interfacial load transfer plays a critical role in the bulk mechanical performance of nanofiber-reinforced metallic-matrix nanocomposites (MMNC). In this paper, we investigate the mechanical strength of interfaces in double-walled carbon nanotube (CNT)-reinforced aluminum (Al) nanocomposites by using in situ electron microscopy nanomechanical single-tube pull-out techniques. The nanomechanical measurements reveal the shear lag effect on the CNT-Al interface that is found to possess an average interfacial shear strength (IFSS) of about 28.7 MPa. The study also shows that thermal annealing results in substantially higher binding strength interfaces between CNTs and Al matrices. The average IFSS of CNT-Al interfaces that were thermally annealed at 400 °C is found to reach about 35.3 MPa, a 23% increase from that of the non-annealed interfaces. The maximum load bearing capacity of the annealed interfaces reaches about 304 nN, a 40.1% increase from that of the non-annealed ones (about 217 nN). The findings are useful to better understand the load transfer mechanism in CNT-reinforced MMNC and the tuning and optimization of the reinforcing performance through thermal processing.
Interfacial strength↗
Damage tolerance of woven graphite-epoxy buffer strip panels
Graphite-epoxy panels with S glass buffer strips were tested in tension and shear to measure their residual strengths with crack-like damage. The buffer strips were regularly spaced narrow strips of continuous S glass. Panels were made with a uniweave graphite cloth where the S glass buffer material was woven directly into the cloth. Panels were made with different width and thickness buffer strips. The panels were loaded to failure while remote strain, strain at the end of the slit, and crack opening displacement were monitoring. The notched region and nearby buffer strips were radiographed periodically to reveal crack growth and damage. Except for panels with short slits, the buffer strips arrested the propagating crack. The strength (or failing strain) of the panels was significantly higher than the strength of all-graphite panels with the same length slit. Panels with wide, thick buffer strips were stronger than panels with thin, narrow buffer strips. A shear-lag model predicted the failing strength of tension panels with wide buffer strips accurately, but over-estimated the strength of the shear panels and the tension panels with narrow buffer strips.
Kennedy, John M.↗
Microstructural non-uniformity as related to unidirectional compression performance
The compression performance of unidirectional composite laminates (UDCLs) is related not only to intrinsic or local strength, but also to a sample's ability to resist propagaton of initial damage. This paper introduces a simple shear lag model which is applied to a compression loaded UDCL with initial damage. Among the information obtained are axial overload and matrix layer shear strain factors in the neighborhood of the damage zone. These factors indicate that propagation may occur with relatively little initial damage and emphasize the need for a more complete understanding of compression behavior than currently exists.
Majors, Patrick S.↗