scholarly journals Discussion: “Nonlinear Creep Deformations of Columns of Rectangular Cross Section” (Bleich, H. H., and Dillon, Jr., O. W., 1959, ASME J. Appl. Mech., 26, pp. 517–525)

1960 ◽  
Vol 27 (2) ◽  
pp. 371-372
Author(s):  
H. G. McComb
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Nonlinear Creep ◽  
Creep Deformations

Nonlinear Creep Deformations of Columns of Rectangular Cross Section

1959 ◽  
Vol 26 (4) ◽  
pp. 517-525
Author(s):  
H. H. Bleich ◽  
O. W. Dillon
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Critical Time ◽  
Bending Moment ◽  
Qualitative Reasoning ◽  
Upper And Lower Bounds ◽  
Nonlinear Creep ◽  
Essential Point ◽  
History Of ◽  
Creep Deformations

Abstract Creep deformations of columns of rectangular cross section are studied for the case of materials following the nonlinear law ϵ̇ = (1/E) σ̇ + λσk. The essential point of the paper is the following: The time rate of the curvature κ̇ of an element of a bar loaded by a constant force P and an increasing bending moment M(t) has bounds, which depend on P and on the instantaneous values of M and Ṁ, but not on the history of M. In combination with the collocation method, this permits the formulation of ordinary differential equations for upper and lower bounds on the deformations. Closed solutions for the critical time are obtained for one bound, while the other requires numerical integration. The bounds which are a function of the initial eccentricity are reasonably close and are presented in tables and graphs. By qualitative reasoning it is further shown that the location of the actual critical time with respect to the two bounds is governed by the ratio of the column load P and the nominal Euler buckling load PE of the column if it were elastic.

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.

Electrokinetics of polymeric fluids in narrow rectangular confinements

Soft Matter ◽  
2021 ◽  
Author(s):  
Aditya Natu ◽  
Uddipta Ghosh
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Double Layers ◽  
Polymeric Fluids ◽  
Polymeric Liquids ◽  
Electrical Double Layers

Flow of polymeric liquids in narrow confinements of rectangular cross section, in the presence of electrical double layers is analyzed here. Our analysis is motivated by the fact that many...

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