Shear Center | ScienceGate

A shear center demonstration model using 3D-printing

International Journal of Mechanical Engineering Education ◽

10.1177/03064190211057429 ◽

2021 ◽

pp. 030641902110574

Author(s):

Lawrence N Virgin

Keyword(s):

3D Printing ◽

Cross Section ◽

Cross Sections ◽

Principal Axis ◽

Practical Importance ◽

Bending Moment ◽

Shear Center ◽

Cross Sectional ◽

Thin Walls ◽

Section Profile

Locating the shear, or flexural, center of non-symmetric cross-sectional beams is a key element in the teaching of structural mechanics. That is, establishing the point on the plane of the cross-section where an applied load, generating a bending moment about a principal axis, results in uni-directional deflection, and no twisting. For example, in aerospace structures it is particularly important to assess the propensity of an airfoil section profile to resist bending and torsion under the action of aerodynamic forces. Cross-sections made of thin-walls, whether of open or closed form are of special practical importance and form the basis of the material in this paper. The advent of 3D-printing allows the development of tactile demonstration models based on non-trivial geometry and direct observation.

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On Torsion and Transverse Flexure of Orthotropic Elastic Plates

Journal of Applied Mechanics ◽

10.1115/1.3153802 ◽

1980 ◽

Vol 47 (4) ◽

pp. 855-860 ◽

Cited By ~ 4

Author(s):

E. Reissner

Keyword(s):

Cross Section ◽

Beam Theory ◽

Bending Moment ◽

Rate Of Change ◽

Elastic Plates ◽

Shear Center ◽

Explicit Consideration ◽

The Difference ◽

Shear Deformable ◽

Shear Deformable Plates

The equations of transverse bending of shear-deformable plates are used for the derivation of a system of one-dimensional equations for beams with unsymmetrical cross section, with account for warping stiffness, in addition to bending, shearing, and twisting stiffness. Significant results of the analysis include the observation that the rate of change of differential bending moment is given by the difference between torque contribution due to plate twisting moments and torque contribution due to plate shear stress resultants; a formula for shear center location which generalizes a result by Griffith and Taylor so as to account for transverse shear deformability and end-section warping restraint; a second-order compatibility equation for the differential bending moment; a contracted boundary condition of support for unsymmetrical cross-section beam theory in place of an explicit consideration of the warping deformation boundary layer; and construction of a problem where the effect of the conditions of support of the beam is such as to give noncoincident shear center and twist center locations.

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