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Related Concept Videos

Unsymmetric Loading of Thin-Walled Members01:23

Unsymmetric Loading of Thin-Walled Members

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Thin-walled members with non-symmetrical cross-sections are vital to engineering structures, offering material efficiency and structural integrity. However, unsymmetrical loading on these members leads to complex stress distributions, resulting in simultaneous bending and twisting can cause deformation or structural failure. The interaction between bending and twisting requires detailed analysis to ensure structural resilience.
The concept of the shear center is crucial in countering the...
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Thin-Walled Hollow Shafts01:15

Thin-Walled Hollow Shafts

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In analyzing a thin-walled hollow shaft subjected to torsional loading, a segment with width dx is isolated for examination. Despite its equilibrium state, this segment faces torsional shearing forces at its ends. These forces are quantitatively described by the product of the longitudinal shearing stress on the segment's minor surface and the area of this surface, leading to the concept of shear flow. This shear flow is consistent throughout the structure, indicating a uniform distribution of...
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Yield Criteria for Ductile Materials under Plane Stress01:25

Yield Criteria for Ductile Materials under Plane Stress

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In designing structural elements and machine parts using ductile materials, it is crucial to ensure that these components withstand applied stresses without yielding. Yielding is initially determined through a tensile test, which evaluates the material's response to uniaxial stress. However, tensile stress is insufficient when components face biaxial or plane stress conditions This condition requires advanced criteria to predict failure.
The Maximum Shearing Stress Criterion, also known as...
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Unsymmetric Loading of Thin-Walled Members: Problem Solving01:07

Unsymmetric Loading of Thin-Walled Members: Problem Solving

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The shear center of a channel section with uniform thickness, height, and width, is determined by computing the shear force in the member and calculating the moments of inertia of the sections.
To compute the shear forces, find the shear flow at a specific distance from the endpoint using the vertical shear and the moment of inertia values. The total shear force on the flange is calculated by integrating the shear flow from one end of the flange to the other.
Next, calculate the moments of...
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Principal Stresses: Problem Solving01:15

Principal Stresses: Problem Solving

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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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Shearing Stress01:19

Shearing Stress

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Shearing stress, denoted by the Greek letter tau (τ), is stress caused by forces acting transversely on an object. These forces create internal ones within the entity in the plane where the external forces are applied. The resultant of these internal forces is the shear in the section.
The average shearing stress can be calculated by dividing the shear by the area of the cross-section.
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Cutting Procedures, Tensile Testing, and Ageing of Flexible Unidirectional Composite Laminates
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Predicting tearing paths in thin sheets.

A Ibarra1, J F Fuentealba1, B Roman2

  • 1Departamento de Física Universidad de Santiago de Chile, Avenida Ecuador 3493, 9170124 Estación Central, Santiago, Chile.

Physical Review. E
|October 3, 2019
PubMed
Summary
This summary is machine-generated.

This study examines how thin sheets tear when pulled. In anisotropic materials, the crack path deviates from the predicted tearing vector to minimize fracture energy, a finding supported by a new differential equation.

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Area of Science:

  • Materials Science
  • Solid Mechanics
  • Fracture Mechanics

Background:

  • Investigates crack propagation in thin notched sheets under tension.
  • Reviews concepts governing crack trajectory in anisotropic materials.

Purpose of the Study:

  • To analyze the tearing behavior of anisotropic materials.
  • To develop a model for predicting crack trajectory under tension.

Main Methods:

  • Defined a geometric "tearing vector" for crack tip and pulling points.
  • Applied Griffiths's criterion and maximum energy release rate (MERR).
  • Derived a differential equation for crack trajectory in weakly anisotropic cases.

Main Results:

  • In isotropic cases, fracture path aligns with the tearing vector.
  • In anisotropic cases, MERR predicts deviation from the tearing vector.
  • The derived differential equation accurately predicts crack trajectory in weak anisotropy.

Conclusions:

  • Crack path in anisotropic materials is influenced by energy minimization.
  • The new model provides accurate predictions for tearing trajectories.
  • Findings align with existing experimental observations in fracture mechanics.