The elastic coupling between longitudinal and transversal vibrations of isotropic rods I. Rods of square and rectangular cross-section

1960 ◽  
Vol 10 (5) ◽  
pp. 366-382 ◽  
Author(s):  
M. Brdička ◽  
Z. Dvořáček ◽  
M. Nováková-Dvorská
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Elastic Coupling ◽  
Transversal Vibrations

Analysis of Anisotropic Beams: An Analytic Approach

2000 ◽  
Vol 68 (4) ◽  
pp. 674-678 ◽  
Author(s):  
V. Rovenski ◽  
O. Rand
Keyword(s):  
Stress Tensor ◽  
Trigonometric Series ◽  
Cross Section ◽  
Analytic Solution ◽  
Rectangular Cross Section ◽  
Composite Beams ◽  
Elastic Response ◽  
Elastic Coupling ◽  
Exponential Functions ◽  
Coupling Mechanisms

An analytic solution for the elastic response of anisotropic composite beams of rectangular cross section is presented. The formulation is based on the expression of the stress tensor components as trigonometric series and exponential functions. The ability to predict the elastic response and the corresponding elastic coupling mechanisms is well demonstrated and discussed.

scholarly journals Designing for People’s Safety on Flooded Streets: Uncertainties and the Influence of the Cross-Section Shape, Roughness and Slopes on Hazard Criteria

Water ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2119
Author(s):  
Luís Mesquita David ◽  
Rita Fernandes de Carvalho
Keyword(s):  
Cross Section ◽  
Overland Flow ◽  
Rectangular Cross Section ◽  
Safety Hazard ◽  
Cross Section Shape ◽  
Section Shape ◽  
Flood Flows ◽  
The Cross ◽  
Flooding Risk

Designing for exceedance events consists in designing a continuous route for overland flow to deal with flows exceeding the sewer system’s capacity and to mitigate flooding risk. A review is carried out here on flood safety/hazard criteria, which generally establish thresholds for the water depth and flood velocity, or a relationship between them. The effects of the cross-section shape, roughness and slope of streets in meeting the criteria are evaluated based on equations, graphical results and one case study. An expedited method for the verification of safety criteria based solely on flow is presented, saving efforts in detailing models and increasing confidence in the results from simplified models. The method is valid for 0.1 m2/s 0.5 m2/s. The results showed that a street with a 1.8% slope, 75 m1/3s−1 and a rectangular cross-section complies with the threshold 0.3 m2/s for twice the flow of a street with the same width but with a conventional cross-section shape. The flow will be four times greater for a 15% street slope. The results also highlighted that the flood flows can vary significantly along the streets depending on the sewers’ roughness and the flow transfers between the major and minor systems, such that the effort detailing a street’s cross-section must be balanced with all of the other sources of uncertainty.

The Exact One-Dimensional Theory for End-Loaded Fully Anisotropic Beams of Narrow Rectangular Cross Section

2001 ◽  
Vol 68 (6) ◽  
pp. 865-868 ◽  
Author(s):  
P. Ladeve`ze ◽  
J. G. Simmonds
Keyword(s):  
Cross Section ◽  
Plane Stress ◽  
Rectangular Cross Section ◽  
Dimensional Theory ◽  
Explicit Formulas ◽  
Cross Sectional ◽  
Rectangular Shape ◽  
One Dimensional ◽  
Anisotropic Elastic ◽  
Derivatives Of

The exact theory of linearly elastic beams developed by Ladeve`ze and Ladeve`ze and Simmonds is illustrated using the equations of plane stress for a fully anisotropic elastic body of rectangular shape. Explicit formulas are given for the cross-sectional material operators that appear in the special Saint-Venant solutions of Ladeve`ze and Simmonds and in the overall beamlike stress-strain relations between forces and a moment (the generalized stress) and derivatives of certain one-dimensional displacements and a rotation (the generalized displacement). A new definition is proposed for built-in boundary conditions in which the generalized displacement vanishes rather than pointwise displacements or geometric averages.

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