Calculation of stresses in shells under local loads by the method of S. P. Timoshenko

Ol'shanskii, V. P.

doi:10.1007/bf01523075

Cited by 7 publications

(6 citation statements)

References 2 publications

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“…In this case, the strain, calculated from the theory of pure bending of a plate to a cylindrical surface valid between the inner loading points, is equal to ε = 3dz 5a 2 , where d is thickness, z is the displacement of the inner loading bars and a is the distance between the first and second points of the four-point bending load cell (a = 10 mm) [12]. The GF T was calculated for the four upward cycles of the z displacement versus time and resistance curves experimentally acquired for each one of the samples.…”

Section: Electromechanical Characterization Of Composites 241 Testing...mentioning

confidence: 99%

The piezoresistive effect in polypropylene—carbon nanofibre composites obtained by shear extrusion

Paleo

Hattum

Nunes-Pereira

et al. 2010

Smart Mater. Struct.

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The piezoresistive effect on poly(propylene) (PP)-carbon nanofibre (CNF) composites fabricated by twin-screw extrusion and compression moulding has been investigated. The electrical and mechanical properties of PP/CNF composites have been obtained as a function of CNF concentration. Electrical conductivity exhibited low thresholds and values close to the required levels for EMI shielding applications at 2.4 vol%. Meanwhile the elastic modulus showed an enhancement with a maximum up to 130% for one of the composites at 0.9 vol% loading. Further, the piezoresistive response has been evaluated in four-point bending. Positive gauge factors between 2 and 2.5 have been obtained. The highest gauge factors are found within the percolation threshold. The characteristics of the materials and the production technique make them suitable for large scale applications.

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Section: Electromechanical Characterization Of Composites 241 Testing...mentioning

confidence: 99%

The piezoresistive effect in polypropylene—carbon nanofibre composites obtained by shear extrusion

Paleo

Hattum

Nunes-Pereira

et al. 2010

Smart Mater. Struct.

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“…where M and κ = dϕ/ds are the bending moment and the curvature at any point of the beam, respectively, and I is the moment of inertia of the beam cross section about the neutral axis [2][3][4]. We will consider the deflections of a cantilever beam subjected to one vertical concentrated load at the free end by supposing that the deflection due to its self-weight is zero.…”

Section: Theoretical Analysismentioning

confidence: 99%

“…The mathematical treatment of the equilibrium of cantilever beams does not involve a great degree of difficulty [2][3][4]. Nevertheless, unless small deflections are considered, an analytical solution does not exist, since for large deflections a differential equation with a non-linear term must be solved.…”

Section: Introductionmentioning

confidence: 99%

Large and small deflections of a cantilever beam

Beléndez¹,

Neipp²

2002

Eur. J. Phys.

231

162

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The classical problem of deflection of a cantilever beam of linear elastic material, under the action of an external vertical concentrated load at the free end, is analyzed.We present the differential equation governing the behaviour of this physical system and show that this equation, although straightforward in appearance, is in fact rather difficult to solve due to the presence of a non-linear term. In this sense, this system is similar to another well known physical system: the simple pendulum. An approximation of the behaviour of a cantilever beam for small deflections was obtained from the equation for large deflections, and we present various numerical results for both cases. Finally, we compared the theoretical results with the experimental results obtained in the laboratory.BELÉNDEZ, Tarsicio; NEIPP, Cristian; BELÉNDEZ, Augusto. "Large and small deflections of a cantilever beam". European Journal of Physics. Vol. 23, No. 3 (May 2002 1.-IntroductionIn this paper we shall analyze an example of a simple physical system, the deflections of a cantilever beam. We shall see that it is not complicated to formulate the equations governing its behaviour or to study it in a physics laboratory at university level. However, a differential equation with a non-linear term is also obtained. Moreover -as occurs with the simple pendulum for small oscillations- [1] when small deflections of the cantilever beam are considered, it is possible to find a simple analytical solution to the problem. In this sense, the study of large and small deflections of a cantilever beam presents a certain analogy with the study of large and small oscillations of a simple pendulum.The mathematical treatment of the equilibrium of cantilever beams does not involve a great difficulty [2][3][4]. Nevertheless, unless small deflections are considered, an analytical solution does not exist, since for large deflections a differential equation with a non-linear term must be solved. The problem is said to involve geometrical non-linearity [5,6]. An excellent treatment of the problem of deflection of a beam, built-it at one end and loaded at the other with a vertical concentrated force, can be found in "The Feynmann Lectures on Physics" [2], as well as in other university textbooks on physics, mechanics and elementary strength of materials. However, in these books the discussion is limited to the consideration of small deflections and they present a formula for the vertical deflection of the end free of the cantilever beam that shows a relation of proportionality between this deflection and the external force applied [2,4]. The analysis of large deflections of these types of cantilever beams of elastic material can be found in Landau's book on elasticity [5], and the solution in terms of elliptic integrals was obtained by Bisshopp and Drucker [7]. Nevertheless, the developments presented in these last references are difficult for first year university students.In this paper we analyze the problem of the deflection of a cantilever beam, in the ...

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“…Recent work by (Paglietti and Carta, 2009) has concerns over the use of such method. The theoretical basis for stress distributions in tapered beams in elastic range is investigated (Timoshenko, 1930; Oden, 1967).…”

Section: Shear Strength Verificationmentioning

confidence: 99%

Parametrical analysis of the tapered steel section with elliptical perforation: shear behaviour effects

De’nan

Hashim

Sua

2022

WJE

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Purpose With the vast advancement of structural steel properties over the recent decades, structural steel has become the dominate material for the construction of bridges, stadiums, factories and high rise buildings. This paper aims to present the study of structural behaviour and efficiency of tapered steel section with elliptical perforation under shear loading conditions. Design/methodology/approach The effect of various elliptical perforation configurations such as tapering ratio, perforation size, perforation orientation and perforation layout on the shear behaviour of tapered steel section has been investigated by using finite element method. A total of 112 models are simulated via LUSAS software. Findings It has been found that the most efficient model is the tapered steel section with tapering ratio of 0.3 and vertical elliptical perforation of 0.2 times the section depths which are arranged in Layout 3. The most efficient model has a shear efficiency of 1,094.35 kN, which is 4.12% less than the tapered steel section without perforation, but it could achieve a 0.32% of weight reduction. Originality/value The smaller tapering ratio and perforation size contributed to the higher shear buckling capacity and efficiency for the elliptical perforated tapered steel section.

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Calculation of stresses in shells under local loads by the method of S. P. Timoshenko

Cited by 7 publications

References 2 publications

The piezoresistive effect in polypropylene—carbon nanofibre composites obtained by shear extrusion

The piezoresistive effect in polypropylene—carbon nanofibre composites obtained by shear extrusion

Large and small deflections of a cantilever beam

Parametrical analysis of the tapered steel section with elliptical perforation: shear behaviour effects

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