On Timoshenko's correction for shear in vibrating beams

Kaneko, T.

doi:10.1088/0022-3727/8/16/003

Cited by 265 publications

(106 citation statements)

References 30 publications

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“…For example, the TBT with KP =5/6 (e.g. Kaneko, 1975;Timoshenko, 1922Timoshenko, , 1921Murthy, 1981;Reissner, 1975;Shi, 2007Shi, , 2011) is in essential equivalent to the third-order model (i.e. Model-A) because of Eq.…”

Section: Shear Correction Factorsmentioning

confidence: 99%

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The Unified Solution for a Beam of Rectangular Cross-Section with Different Higher-Order Shear Deformation Models

Duan

2016

Lat. Am. j. solids struct.

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The unified solution is studied for a beam of rectangular cross section. With the rotation defined in the average sense over the cross section, the kinematics with higher-order shear deformation models in axial displacement is first expressed in a unified form by using the fundamental higher-order term with some properties. The shear correction factor is then derived and discussed for the four commonly used higher-order shear deformation models including the third-order model, the sine model, the hyperbolic sine model and the exponential model. The unified solution is finally obtained for a beam subjected to an arbitrarily distributed load. The relation with that from the conventional beam theory is established, and therefore the difference is reasonably explained. A very good agreement with the elasticity theory validates the present solution.

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Section: Shear Correction Factorsmentioning

confidence: 99%

“…In virtue of this, much attention was paid to evaluating the shear correction factor (e.g. Cowper, 1966;Dong et al, 2013Dong et al, , 2010Gruttmann and Wagner, 2001;Gruttmann et al, 1999;Hutchinson, 2001;Jensen, 1983;Kaneko, 1975;Pai and Schulz, 1999).…”

Section: Introductionmentioning

confidence: 99%

The Unified Solution for a Beam of Rectangular Cross-Section with Different Higher-Order Shear Deformation Models

Duan

2016

Lat. Am. j. solids struct.

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“…For instance, in the Timoshenko beam theory (TBT), the shear strain distribution is incorrectly assumed to be constant throughout the beam height; e.g., considering a simple rectangular cross-section, such hypothesis does not respect the zero shear strain and stress boundary conditions at its top and bottom. Therefore, a shear correction factor is required to accurately determine the strain energy of deformation, which has deserved the attention of researchers since the 1950s up to the present day [9,10,14,16]. Within the framework of this chapter, classical beam theories are considered to be of the first-order, i.e., those in which the displacement fields inside the cross-section are linear functions on each of the cross-sectional coordinates.…”

Section: Introductionmentioning

confidence: 99%

Computational Methods in Earthquake Engineering

Eichmann¹

2017

Computational Methods in Applied Sciences

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When one of the dimensions of a structural member is not clearly larger than the two orthogonal ones, engineers are usually compelled to simulate it with refined meshes of shell or solid finite elements that typically impose a large computational burden. The alternative use of classical beam theories, either based on Euler-Bernoulli or Timoshenko's assumptions, will in general not accurately capture important deformation mechanisms such as shear, warping, distortion, flexural-shear-torsional interaction, etc. However, higher-order beam theories are a still largely disregarded avenue that requires an acceptable computational demand and simultaneously has the potential to account for the above mentioned deformation mechanisms, some of which can also be relevant in slender members. This chapter starts by recalling the main theoretical features of a recently developed higher-order beam element, which was combined for the first time with a force-based formulation. The latter strictly verifies the advanced form of beam equilibrium expressed in the governing differential equations. The main innovative theoretical aspects of the proposed element are accompanied by an illustrative application to members with linear elastic behaviour. In particular, the ability of the model to simulate the effect of different boundary conditions on the response of an axially loaded member is addressed, which is then followed by an application to a case where flexural-shear-torsional interaction takes place. The beam performance is assessed by comparison against refined solid finite element analyses, classical beam theory results, and approximate numerical solutions. Finally, with a view to a future extension to earthquake engineering, an example of the element behaviour with inelastic response is also carried out.

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“…Mindlin (1952) proposed constant and Poisson-ratiodependent shear correction factors based on the free vibration data of the homogeneous and isotropic plates. An overview and elaborate discussion on the correction factors for flexural vibrations of the Timoshenko beams was presented by Kaneko (1975). Some shear correction factors had been derived for beams with various cross sections (Cowper, 1966;Murthy, 1970;Hutchinson, 1981;Rebello et al, 1983;Wittrick, 1987;Stephen, 1997;Pai and Schulz, 1999;Gruttmann and Wagner, 2001).…”

Section: Introductionmentioning

confidence: 99%

Novel Layerwise Shear Correction Factors for Zigzag Theories of Circular Sandwich Plates with Functionally Graded Layers

Shariyat

2015

Lat. Am. j. solids struct.

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The available shear correction factors have mainly been proposed for single-layer rectangular plates with zero shear tractions and isotropic homogenous materials. The present analytical shear factors are especially suitable for the first-order zigzag or layerwise theories of circular sandwich plates with functionally graded cores/face sheets and simultaneous normal and shear tractions. Although the present layerwise correction factors are general, they are evaluated for the modal analyses where effects of the shear correction are more remarkable than those of the stress analyses. It is the first time that the concept of the local shear correction factor is introduced. To present more accurate results, the MoriTanaka micromechanical-based material properties model is used instead of the traditional rule of mixtures. The governing equations are solved using the analytical Taylor transform method. Comparisons made among results associated with the known shear correction factors, present results, and results of the threedimensional theory of elasticity reveal that significant enhancements may occur through using the proposed analytical shear correction factors.

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On Timoshenko's correction for shear in vibrating beams

Cited by 265 publications

References 30 publications

The Unified Solution for a Beam of Rectangular Cross-Section with Different Higher-Order Shear Deformation Models

The Unified Solution for a Beam of Rectangular Cross-Section with Different Higher-Order Shear Deformation Models

Computational Methods in Earthquake Engineering

Novel Layerwise Shear Correction Factors for Zigzag Theories of Circular Sandwich Plates with Functionally Graded Layers

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