The Shear Coefficient in Timoshenko’s Beam Theory

Cowper, G.R.

doi:10.1115/1.3625046

Cited by 1,564 publications

(613 citation statements)

References 0 publications

Supporting

Mentioning

588

Contrasting

Unclassified

Order By: Relevance

“…On the other hand, the value k ¼ 5 6 provides a prediction always lower than the exact, at least over the range considered, with a maximum error of À2%. Experimental evidence in support of the value k ¼ 5ð1 þ nÞ=ð6 þ 5nÞ has recently been provided by Me´ndez-Sa´nchez et al [17], although they also note that a two-coefficient theory presented by Stephen and Levinson [18], and which incorporates both this, and Cowper's value [19] of k ¼ 10ð1 þ nÞ=ð12 þ 11nÞ, provides marginally better agreement with their experimental results.…”

Section: Numerical Examplementioning

confidence: 47%

The second spectrum of Timoshenko beam theory—Further assessment

Stephen

2006

Journal of Sound and Vibration

View full text Add to dashboard Cite

A review of contributions and views on the second spectrum of Timoshenko beam theory (TBT) over the past two decades, together with some new results, are presented. It is shown that the Timoshenko frequency equation factorises not solely for hinged-hinged end conditions, as is often claimed, but also for guided-guided and guided-hinged; these new cases may be regarded as portions of a multi-span hinged-hinged beam. A higher-derivative Lagrangian that leads directly to the well-known fourth-order Timoshenko beam equation is reviewed. A simple relationship between the so-called Ostrogradski energy and the mechanical energy is derived for hinged-hinged end conditions. It is shown that the Ostrogradski energy is positive for the first spectrum but negative for the second; within some branches of physics, this would be sufficient to conclude that the second spectrum is ''unphysical''. A numerical example presented by Levinson and Cooke is re-examined using both TBT and exact plane stress elastodynamic theory. Agreement is excellent for the first spectrum. However, the second spectrum predictions are not in consistent agreement with any single mode of vibration. For long wavelength it is very close to the second asymmetric mode, but as wavelength shortens, it becomes closer to the second symmetric, then the third asymmetric modes. The conclusion remains unchanged: the second spectrum predictions of TBT should be disregarded. r

show abstract

Section: Numerical Examplementioning

confidence: 47%

The second spectrum of Timoshenko beam theory—Further assessment

Stephen

2006

Journal of Sound and Vibration

View full text Add to dashboard Cite

show abstract

“…The shear deformation coefficients are evaluated using an energy approach, instead of Timoshenko's [21] and Cowper's [22] definitions, for which several authors [23] have pointed out that one obtains unsatisfactory results or definitions given by other researchers [24,25], for which these factors take negative values.…”

Section: Introductionmentioning

confidence: 99%

Shear deformation effect in non-linear analysis of composite beams of variable cross section

Sapountzakis¹,

Panagos²

2008

International Journal of Non-Linear Mechanics

View full text Add to dashboard Cite

A c c e p t e d m a n u s c r i p t2 displacement and to two stress functions and solved using the Analog EquationMethod. Application of the boundary element technique yields a system of nonlinear equations from which the transverse and axial displacements are computed by an iterative process. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress functions using only boundary integration. Numerical examples are worked out to illustrate the efficiency, the accuracy, the range of applications of the developed method and the influence of the shear deformation effect.

show abstract

“…The effect of a cross section on flutter stability is considered in Table 3, where values of a critical flutter load are presented with respect to the changes in the cross section type. Shear correction factor in circular cross section is a function of inner and outer radius of hollow beam (Cowper, 1966): Table 3: Effect of radius ratio on critical follower force of stubby and slender beams.…”

Section: L/h Present Methods Timoshenkomentioning

confidence: 99%

Flutter Instability of Timoshenko Cantilever Beam Carrying Concentrated Mass on Various Locations

Sohrabian

Ahmadian

Fathi

2016

Lat. Am. j. solids struct.

View full text Add to dashboard Cite

This paper presents effects of shear deformation on flutter instability of cantilever beam subject to a concentrated follower force. The discrete form of equation of motion is formulated based on the Lagrange. In the presented formulation, the beam is modeled using Timoshenko beam theory, and constant shear distribution through the thickness of the beam is considered. Consistent interpolation scheme is adopted to avoid the shear locking for thin beams. Consequently, convergence of the finite element simulation is enhanced. The effect of rotary inertial term is considered in the flutter study, which has significant influence on the beam behavior as the beam thickness increases. The axial degrees of freedom are taken into account in energy expressions, to improve the accuracy of the results. Results presented for different beam geometries. The numerical results show high efficiency and good convergence characteristic. The effect of concentrated mass on the flutter instability of beam is considered and results are presented for various locations and values of concentrated masses. Furthermore, the shear effects are highlighted in this study by comparing the results obtained from the Euler-Bernoulli with those obtained from the Timoshenko beam model.

show abstract

The Shear Coefficient in Timoshenko’s Beam Theory

Cited by 1,564 publications

References 0 publications

The second spectrum of Timoshenko beam theory—Further assessment

The second spectrum of Timoshenko beam theory—Further assessment

Shear deformation effect in non-linear analysis of composite beams of variable cross section

Flutter Instability of Timoshenko Cantilever Beam Carrying Concentrated Mass on Various Locations

Contact Info

Product

Resources

About