Bending moment

About: Bending moment is a research topic. Over the lifetime, 14577 publications have been published within this topic receiving 158834 citations. The topic is also known as: bending moment.

An analytical solution for the magneto-electro-elastic bimorph beam forced vibrations problem

Abstract: Based on the Timoshenko beam theory and on the assumption that the electric and magnetic fields can be treated as steady, since elastic waves propagate very slowly with respect to electromagnetic ones, a general analytical solution for the transient analysis of a magneto-electro-elastic bimorph beam is obtained. General magneto-electric boundary conditions can be applied on the top and bottom surfaces of the beam, allowing us to study the response of the bilayer structure to electromagnetic stimuli. The model reveals that the magneto-electric loads enter the solution as an equivalent external bending moment per unit length and as time-dependent mechanical boundary conditions through the definition of the bending moment. Moreover, the influences of the electro-mechanic, magneto-mechanic and electromagnetic coupling on the stiffness of the bimorph stem from the computation of the beam equivalent stiffness constants. Free and forced vibration analyses of both multiphase and laminated magneto-electro-elastic composite beams are carried out to check the effectiveness and reliability of the proposed analytic solution.

The strength of the cervical spine in compression and bending

Abstract: Introduction: Little is known about how the cervical spine resists the high complex loading to which it is often subjected in life. In this study, such loading was applied to cadaveric cervical motion segments in order to a) measure their strength in forward and backwards bending, b) indicate which structures resist bending most strongly, and c) indicate how compressive injury influences the bending properties. Methods: Ten human cervical spines aged 65–88yrs were obtained post-mortem, dissected into 14 motion segments, and stored at −20°C. Subsequently, motion segments were defrosted and secured in dental plaster for testing on a hydraulic materials testing machine. An optical motion capture system recorded specimen movement simultaneously. Specimens were loaded in 2.5sec in combined bending and compression to reach their elastic limit in flexion, and then extension. Experiments were repeated following creep loading, removal of spinous processes, removal of apophyseal joints, and vertebral body compressive damage. Results: On average, full flexion was reached at an angle of 7.2° and a bending moment of 6.8Nm. Full extension occurred at 9.2° and 9.0Nm. Creep loading reduced specimen height by 0.37mm, increased flexion by 1.5° (P Conclusion: Cervical motion segments have approximately 20% of the bending strength, and 45% of the compressive strength, of lumbar specimens of similar age. The relative weakness of the cervical spine in bending may influence the patterns of injury seen in “whiplash”.

Onset of Nonlinearity in the Elastic Bending of Blocks

Abstract: The classical flexure problem of nonlinear incompressible elasticity is revisited assuming that the bending angle suffered by the block is specified instead of the usual applied moment. The general moment-bending angle relationship is then obtained and is shown to be dependent on only one nondimensional parameter: the product of the aspect ratio of the block and the bending angle. A Maclaurin series expansion in this parameter is then found. The first-order term is proportional to , the shear modulus of linear elasticity; the second-order term is identically zero because the moment is an odd function of the angle; and the third-order term is proportional to 41, where is the nonlinear shear coefficient, involving third-order and fourth-order elasticity constants. It follows that bending experiments provide an alternative way of estimating this coefficient and the results of one such experiment are presented. In passing, the coefficients of Rivlin’s expansion in exact nonlinear elasticity are connected to those of Landau in weakly (fourth-order) nonlinear elasticity. DOI: 10.1115/1.4001282