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Distribution of Stresses in a Narrow Rectangular Beam

Distribution of Stresses in a Narrow Rectangular Beam

In studying beam stress distribution, examining an elemental section is essential. To determine the average shearing stress on this face, the calculated shear is divided by the surface area. Importantly, shearing stresses on the beam's transverse and horizontal planes mirror each other, indicating a consistent stress distribution along the upper region of the beam. Notably, shearing stresses are absent at the beam's upper and lower surfaces due to the absence of applied forces in these...

Shearing Stresses in a Beam: Problem Solving

Shearing Stresses in a Beam: Problem Solving

A cantilever beam with a rectangular cross-section under distributed and point loads experiences shearing stresses. The analysis begins by identifying the loads acting on the beam. Then, the reactions at the beam's fixed end are calculated using equilibrium equations. The vertical reaction is a combination of the distributed and point loads, while the moment reaction is the sum of their moments. The shear force distribution along the beam, resulting from these loads, is established by creating...

Elastic Strain Energy for Shearing Stresses

Elastic Strain Energy for Shearing Stresses

As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...

Stresses under Combined Loadings

Stresses under Combined Loadings

When analyzing a bent tube with a circular cross-section subjected to multiple forces, it is crucial to determine the stress distribution in order to maintain structural integrity under varied load conditions.
The process begins by slicing the tube at critical points and analyzing the internal forces and stress components at these sections, focusing on the centroid. Normal stresses, generated by axial forces and bending moments, are either compressive or tensile and vary across the section from...

Shearing Strain

Shearing Strain

The shearing strain represents a cubic element's angular change when subjected to shearing stress. This type of stress can transform a cube into an oblique parallelepiped without influencing normal strains. The cubic element experiences a significant transformation when exposed solely to shearing stress. Its shape alters from a perfect cube into a rhomboid, clearly demonstrating the effect of shearing strain. The degree of this strain is considered positive if it reduces the angle between the...

Principal Stresses: Problem Solving

Principal Stresses: Problem Solving

When analyzing two planes intersecting at right angles under the influence of shearing, tensile, and compressive stresses, it is essential to identify principal planes, maximum shearing stress, and principal stresses. To find the principal planes, apply a formula that equates them to twice the shearing stress divided by the difference between tensile and compressive stresses.

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Related Experiment Video

Updated: Nov 27, 2025

Finite Element Modeling for the Simulation of the Quasi-Static Compression of Corrugated Tapered Tubes

Finite Element Modeling for the Simulation of the Quasi-Static Compression of Corrugated Tapered Tubes

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Modeling Bed Shear Stress Distribution in Rectangular Channels Using the Entropic Parameter.

Domenica Mirauda¹, Maria Grazia Russo²

¹School of Engineering, Basilicata University, Viale dell'Ateneo Lucano 10, 85100 Potenza, Italy.

Entropy (Basel, Switzerland)

|December 8, 2020

Summary

This study introduces a new method using Tsallis entropy to estimate bed shear stress distribution in open channels. The approach simplifies calculations and accurately predicts sediment and pollutant transport.

Keywords:

Tsallis entropy bed shear stress distribution entropic parameter error analysis flow velocity rectangular channels

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Last Updated: Nov 27, 2025

Finite Element Modeling for the Simulation of the Quasi-Static Compression of Corrugated Tapered Tubes

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Area of Science:

* Fluid Mechanics
* Environmental Engineering
* Information Theory Applications

Background:

* Accurate bed shear stress distribution is crucial for predicting sediment/pollutant transport and designing stable open channels.
* Traditional methods are complex due to dependencies on velocity fields, cross-section shape, and bed roughness.
* Information theory, specifically entropy models, has shown promise for estimating shear stress but requires complex calculations.

Purpose of the Study:

* To propose a novel formulation for estimating bed shear stress distribution in open-channel flows.
* To simplify the calculation of Lagrange coefficients using Tsallis entropy maximization.
* To establish a relationship between dimensionless mean shear stress and an entropic parameter.

Main Methods:

* Developed a new formulation based on the maximization of Tsallis entropy.
* Introduced a relationship linking dimensionless mean shear stress to an entropic parameter derived from velocity ratios.
* Validated the formulation using extensive laboratory measurements from literature.

Main Results:

* The proposed Tsallis entropy-based formulation simplifies Lagrange coefficient calculations.
* The new method demonstrates good agreement with experimental data across various roughness and flow conditions.
* Successfully linked small-scale dynamic processes to large-scale kinematic ones.

Conclusions:

* The novel Tsallis entropy formulation provides a reliable and simplified approach for estimating bed shear stress distribution.
* This method enhances the prediction of sediment and pollutant transport in open channels.
* The findings contribute to improved design of stable open channel systems.