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Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

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Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
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The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...
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The fineness modulus (FM) of aggregate is a numerical index that measures the coarseness or fineness of the particles. It is calculated by adding the cumulative percentages of aggregate retained on each of a specified series of sieves and dividing the sum by 100.
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Flexural Stress01:16

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Flexural Rigidity Measurements of Biopolymers Using Gliding Assays
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Generalized flexibility-rigidity index.

Duc Duy Nguyen1, Kelin Xia1, Guo-Wei Wei1

  • 1Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, USA.

The Journal of Chemical Physics
|June 24, 2016
PubMed
Summary
This summary is machine-generated.

A new method, generalized Flexibility-Rigidity Index (gFRI), improves macromolecular thermal fluctuation analysis and B-factor prediction. gFRI offers a robust, accurate, and efficient approach for understanding protein flexibility and fluctuation.

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Area of Science:

  • Computational biology
  • Structural bioinformatics
  • Biophysics

Background:

  • The Flexibility-Rigidity Index (FRI) is a key method for analyzing macromolecular thermal fluctuations and predicting B-factors.
  • The accuracy of FRI is contingent upon its specific formulations for rigidity and flexibility indices.

Purpose of the Study:

  • To introduce novel formulations for rigidity and flexibility indices to enhance the Flexibility-Rigidity Index (FRI).
  • To develop a generalized FRI (gFRI) framework for improved macromolecular analysis.

Main Methods:

  • Utilized classic Gaussian surface structures to create a new rigidity index, generating novel rigidity densities.
  • Developed a new flexibility index based on the domain indicator property of normalized rigidity density.
  • Validated generalized FRI (gFRI) methods through B-factor predictions for 364 proteins.

Main Results:

  • The generalized FRI (gFRI) methods demonstrated superior performance compared to the classic Gaussian network model.
  • gFRI achieved significant improvements in B-factor predictions across a diverse set of proteins.
  • Demonstrated the capability of gFRI for molecular surface generation and flexibility visualization.

Conclusions:

  • gFRI represents a new generation of methodologies for the accurate, robust, and efficient analysis of protein flexibility and fluctuation.
  • The developed gFRI framework offers enhanced capabilities for structural bioinformatics and computational biology applications.