In-plane behaviour of web-tapered beams

Trahair, Nicholas S.; Ansourian, P.

doi:10.1016/j.engstruct.2015.11.010

Cited by 18 publications

(9 citation statements)

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“…In 1944, Saksena [12] used a similar approach to evaluate the shear stresses in elements for aerospace applications and provided examples for rectangular, circular and I-shaped cross-sections. Many other works in the second half of the 20 th century addressed the problem via similar approaches [13][14][15][16][17][18][28][29][30][31][32][33]. Krahula [13] compared the results of Singer's formula [32] with those of the linear elastic solutions for the infinite wedge [7].…”

Section: A Short Survey Of Shear Formulas After Jourawskimentioning

confidence: 99%

“…In the case of the hollow cross-section in Figure 2 (right), for instance, equation ( 29) provides the sum of the shear flows through AB and CD. The partition of the domain and its boundaries, plus the definition of the shear flow (29), also apply to multi-connected cross-sections, although they are not shown in Figure 2. Equation (29), plus ( 8)- (10) and standard integration techniques based on Green's formulas, yield…”

Section: Shear Formula For Bi-tapered Beamsmentioning

confidence: 99%

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A new shear formula for tapered beamlike solids undergoing large displacements

Migliaccio

Ruta²,

Barsotti

et al. 2022

Meccanica

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In many engineering applications it is often necessary to determine the flow of shear stresses in the cross-sections of beam-like bodies. Taking a cue from Jourawski's well-known formula, several scholars have proposed expressions for evaluating the shear stresses in non-prismatic linear elastic beams, where longitudinal variations in the size and shape of the cross-sections produces complex stress fields. In the present paper, a new shear formula, derived using a mechanical model developed in a previous work, is presented for tapered beams subject to even large displacements and small strains. Numerical examples and comparisons with results obtained using other formulas in the literature and non-linear 3D-FEM simulations show how the new formula constitutes an important generalization of the previous ones and is able to provide particularly accurate results.

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Section: A Short Survey Of Shear Formulas After Jourawskimentioning

confidence: 99%

Section: Shear Formula For Bi-tapered Beamsmentioning

confidence: 99%

A new shear formula for tapered beamlike solids undergoing large displacements

Migliaccio

Ruta²,

Barsotti

et al. 2022

Meccanica

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“…Bleich (1932) derived the shear stress of linearly tapered beams based on a generalization of the parabolic shear stress distribution of prismatic beams, also known as Jourawski's formula (Jourawski 1856). Subsequently, many investigations proposed shear stress recovery procedures to infinite wedge elements via Theory of Elasticity approaches (Michell 1900;Carothers 1914;Timoshenko and Goodier 1951), and later to truncated linearly tapered beams (Krahula 1975), including that of I-sections (Blodgett 1966;Vu-Quoc and Léger 1992;Trahair and Ansourian 2016;Balduzzi et al 2017b). Boley (1963), using Airy's stress function, examined the limits of a linear longitudinal stress distribution in non-prismatic beams under pure bending, and concluded that the error associated with Navier's hypothesis escalates with the taper angle, such that a 10 • -taper results in 7.5% of error in predicting the longitudinal stress.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stress recovery of laminated non-prismatic beams under layerwise traction and body forces

Vilar

Hadjiloizi

Masjedi

2022

Int J Mech Mater Des

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Emerging manufacturing technologies, including 3D printing and additive layer manufacturing, offer scope for making slender heterogeneous structures with complex geometry. Modern applications include tapered sandwich beams employed in the aeronautical industry, wind turbine blades and concrete beams used in construction. It is noteworthy that state-of-the-art closed form solutions for stresses are often excessively simple to be representative of real laminated tapered beams. For example, centroidal variation with respect to the neutral axis is neglected, and the transverse direct stress component is disregarded. Also, non-classical terms arise due to interactions between stiffness and external load distributions. Another drawback is that the external load is assumed to react uniformly through the cross-section in classical beam formulations, which is an inaccurate assumption for slender structures loaded on only a sub-section of the entire cross-section. To address these limitations, a simple and efficient yet accurate analytical stress recovery method is presented for laminated non-prismatic beams with arbitrary cross-sectional shapes under layerwise body forces and traction loads. Moreover, closed-form solutions are deduced for rectangular cross-sections. The proposed method invokes Cauchy stress equilibrium followed by implementing appropriate interfacial boundary conditions. The main novelties comprise the 2D transverse stress field recovery considering centroidal variation with respect to the neutral axis, application of layerwise external loads, and consideration of effects where stiffness and external load distributions differ. A state of plane stress under small linear-elastic strains is assumed, for cases where beam thickness taper is restricted to $$15^{\circ }$$ 15 ∘ . The model is validated by comparison with finite element analysis and relevant analytical formulations.

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“…Subse-quently, Krahula [12] compared the predictions of Bleich's formula -even though not citing directly [8] but referring to Timoshenko and Gere [13] and the solution of a two-dimensional elasticity problem for a tapered cantilever beam loaded by a concentrated shear force at its free end. Elasticity theory has been used to model tapered beams also by Knops and Villaggio [14], and more recently by Trahair and Ansourian [15].…”

Section: Introductionmentioning

confidence: 99%

Stresses in constant tapered beams with thin-walled rectangular and circular cross sections

Bertolini

Eder

Taglialegne

et al. 2019

Thin-Walled Structures

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Tapered beams are widely employed in efficient flexure dominated structures. In this paper, analytical expressions are derived for the six Cauchy stress components in untwisted, straight, thin-walled beams with rectangular and circular cross sections characterised by constant taper and subjected to three cross-section forces. These expressions pertain to homogeneous, isotropic, linear elastic materials and small strains. In fact, taper not only alters stress magnitudes and distributions but also evokes stress components, which are zero in prismatic beams. A parametric study shows that increasing taper decreases the von Mises stress based fatigue life, suggesting that step-wise prismatic approximations entail non-conservative designs.

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In-plane behaviour of web-tapered beams

Cited by 18 publications

References 0 publications

A new shear formula for tapered beamlike solids undergoing large displacements

A new shear formula for tapered beamlike solids undergoing large displacements

Stress recovery of laminated non-prismatic beams under layerwise traction and body forces

Stresses in constant tapered beams with thin-walled rectangular and circular cross sections

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