General Stiffness Matrix for a Thin-Walled, Open-Section Beam Structure

Alsheikh, Abdelraouf M. Sami; Rees, D. Andrew S.

doi:10.4236/wjm.2021.1111015

Cited by 4 publications

(3 citation statements)

References 19 publications

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“…This beam element transformation amends earlier forms [6] [8] [13] [15] in allowing for bimoment terms within T ij T     . As a sequel to the authors' previous paper [20], the combined work provided a complete solution to the response of a thin-walled beam structure under any combination of applied loading including axial and transverse forces, flexural bending, and axial torsion. The physical form of the structure may appear as a beam or as a long torsional section having ends that are free or position fixed.…”

Section: Discussionmentioning

confidence: 95%

“…The displacements and internal forces developed due to the theory of thin-walled structures, are related to the principal sectorial pole, see [2] [12], and Alsheikh and Rees [20], also Alsheikh and Sharman [21]. In other words, in a complete stiffness matrix, which includes bending, shear and twisting modes, the terms from the bending modes are relative to transverse forces through the shear centre, and those due to axial modes are relative to forces through the centroid.…”

Section: Theoretical Developmentmentioning

confidence: 99%

“…where K ii is the 12 × 12 element stiffness matrix which is the combination, of bending modes as given in many texts, see Zienkiewicz [23], Weaver and Gere [24], and the St Venant torsional mode, given in reference [20] Table 1. That combination has been assembled in the 14 × 14 matrix given by Alsheikh and Rees [20]…”

Section: Transformation Of the Stiffness Matrixmentioning

confidence: 99%

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Transformation Matrix for Combined Loads Applied to Thin-Walled Structures

Alsheikh¹,

Rees²

2022

WJM

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This paper transforms combined loads, applied at an arbitrary point of a thin-walled open section beam, to the shear centre of the cross-section of the beam. Therein, a generalized transformation matrix for loads with respect to the shear centre is derived, this accounting for the bimoments that develop due to the way the combined loads are applied. This and the authors' earlier paper (World Journal of Mechanics 2021, 11, 205-236) provide a full solution to the theory of thin-walled, open-section structures bearing combined loading. The earlier work identified arbitrary loading with the section's area properties that are necessary to axial and shear stress calculations within the structure's thin walls. In the previous paper attention is paid to the relevant axes of loading and to the transformations of loading required between axes for stress calculations arising from tension/compression, bending, torsion and shear. The derivation of the general transformation matrix applies to all types of loadings including, axial tensile and compression forces, transverse shear, longitudinal bending. One application, representing all these load cases, is given of a simple channel cantilever with an eccentrically located end load.

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Section: Discussionmentioning

confidence: 95%

Section: Theoretical Developmentmentioning

confidence: 99%

Section: Transformation Of the Stiffness Matrixmentioning

confidence: 99%

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Transformation Matrix for Combined Loads Applied to Thin-Walled Structures

Alsheikh¹,

Rees²

2022

WJM

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Center of Stiffness, Principal Axes and Principal Start Point of Thin-Walled Open-Sections of Cores: A New Modified Calculation Technique Based on Vlasov Torsion Theory

Makarios

Athanatopoulou

2022

Buildings

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The present paper deals with the exact calculation of the Principal Elastic Reference System of R/C Cores, which have thin-walled open section. A new modified technique based on Vlasov torsion theory is developed that examines the warping phenomenon of cores. The exact position of the elastic center (or shear center) of a core and the orientation of the principal axes of elasticity, as well as the exact calculation of warping constant, are special parameters since, on the one hand it strongly affects the in plan stiffness distribution of the building members, and on the other hand it affects the values of the building eigen-frequencies and mode-shapes. These parameters are particularly critical in seismic design of asymmetric multistorey buildings. Based on Vlasov torsion theory of cores with thin-walled open sections, a repetitive mathematical procedure about the calculation of the location of the elastic center of core and the principal start point of the section is proposed. This new modified technique can be applied to cores of any shape. Afterwards, the exact diagram of sectorial coordinates of the section, as well as the warping constant, are calculated. All the above-mentioned parameters are very useful in the simulation of the cores in numerical models that are going to use in linear and nonlinear seismic analysis of the structures. Knowing all mentioned parameters, the numerical accuracy of the finite element method on cores can be checked. Finally, a numerical example, where the proposed new modified technique is applied on a fully asymmetric core, is presented.

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Theory of Flexural Shear, Bending and Torsion for a Thin-Walled Beam of Open Section

Rees,

Alsheikh

2024

WJM

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General Stiffness Matrix for a Thin-Walled, Open-Section Beam Structure

Cited by 4 publications

References 19 publications

Transformation Matrix for Combined Loads Applied to Thin-Walled Structures

Transformation Matrix for Combined Loads Applied to Thin-Walled Structures

Center of Stiffness, Principal Axes and Principal Start Point of Thin-Walled Open-Sections of Cores: A New Modified Calculation Technique Based on Vlasov Torsion Theory

Theory of Flexural Shear, Bending and Torsion for a Thin-Walled Beam of Open Section

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