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Related Concept Videos

Euler's Formula for Pin-Ended Columns01:21

Euler's Formula for Pin-Ended Columns

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In structural engineering, the stability of columns under compressive axial loads is a critical consideration, described as buckling. A typical example involves a column PQ, which is pin-connected at both ends and subjected to a centric axial load F applied at one end, with a reaction force of F' = -F at the other end. Here, it is crucial to understand that when an applied load exceeds the critical load, buckling occurs as the system becomes unstable.
To calculate the critical load,...
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Excess Pressure Inside a Drop and a Bubble01:13

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The shape of a small drop of liquid can be considered spherical, neglecting the effect of gravity. This drop can further be considered as two equal hemispherical drops put together due to surface tension. The forces acting on the spherical drop are due to the pressure of the liquid inside the drop, the pressure due to air outside the drop, and the force due to the surface tension acting on the two hemispherical drops.
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Euler's Formula to Columns with Other End Conditions01:15

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Euler's formula is very important in the field of structural engineering, providing a foundation for understanding the critical loading conditions of pin-ended columns. This formula links the modulus of elasticity, the moment of inertia of the cross-section, and the column's length, offering a precise calculation of the critical load at which a column is prone to buckling.
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Euler's Formula to Columns: Problem Solving01:23

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Euler's formula is used in structural engineering to determine the buckling load of columns under various conditions. However, when dealing with systems that incorporate both rigid elements and elastic components, such as springs, the analysis requires a finer approach to determine the critical load. The problem described involves two rigid bars connected at a pivot point with a spring attached and a vertical load applied at one end.
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Design of Columns under a Centric Load01:17

Design of Columns under a Centric Load

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The design of columns under centric load is a fundamental aspect of structural engineering and is critical for ensuring the stability and integrity of structures. Euler's and Secant's formulas are central to understanding and calculating the critical load and deformation behaviors of columns, providing a basis for safe and effective structural design.
Euler's formula is applicable under the assumption that the column is a perfect, straight, homogenous prism, and it is operating...
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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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Non-Classical Euler Buckling and Brazier Instability in Cylindrical Liquid Droplets.

Emery Hsu1, Daeyeon Lee1, Eli Sloutskin2

  • 1Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States.

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Researchers studied the elastic properties of crystalline monolayers on oil-in-water emulsion droplets. They discovered a nonclassical relationship between Young

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Area of Science:

  • Physics
  • Materials Science
  • Nanotechnology

Background:

  • Crystalline monolayers are found in nature and technology.
  • Their elastic properties are crucial for various scientific fields.
  • Understanding these properties is key to advancing nanotechnology.

Purpose of the Study:

  • To investigate the elastic characteristics of crystalline monolayers.
  • To explore the conditions governing Euler buckling and Brazier kink formation.
  • To uncover nonclassical elasticity mechanisms in tubular interfacial crystals.

Main Methods:

  • Utilizing oil-in-water emulsion droplets that undergo shape transitions to cylindrical forms.
  • Straining elongating cylindrical droplets within microfluidic wells.
  • Analyzing the resulting buckling and kink formation.

Main Results:

  • A nonclassical relationship between Young's modulus and bending modulus was observed.
  • This relationship was found to be dependent on the cylindrical crystal's radius.
  • The findings suggest a novel mechanism for tuning elasticity.

Conclusions:

  • The study reveals a nonclassical elasticity in crystalline monolayers.
  • The radius-dependent relationship offers new possibilities for nanotechnology.
  • This work provides fundamental insights into interfacial crystal mechanics.