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Related Concept Videos

Design of Columns under an Eccentric Load01:21

Design of Columns under an Eccentric Load

Designing columns to withstand eccentric loads is a critical aspect of structural engineering, ensuring structures can support off-center loads without failure. This design process must account for the additional normal stresses introduced by eccentric loading, which can significantly influence a column's stress distribution and overall stability. An eccentric load applied to a column induces normal stresses that can be conceptualized as a combination of stresses due to an equivalent centric...
Design of Columns under a Centric Load01:17

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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.
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Method of Joints: Problem Solving II01:30

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Consider a truss structure with frictionless joints fixed to a wall and roller support. If a force of 150 N is applied to joint A, the forces in each member of the truss can be determined using the method of joints.
Euler's Formula for Pin-Ended Columns01:21

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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.
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Nonequilibrium scale selection mechanism for columnar jointing.

Lucas Goehring1, L Mahadevan, Stephen W Morris

  • 1Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario, Canada. lg352@cam.ac.uk

Proceedings of the National Academy of Sciences of the United States of America
|January 9, 2009
PubMed
Summary
This summary is machine-generated.

Drying cornstarch cracks mimic geological columnar joints. A unified theory explains these crack patterns, revealing a single dynamical law governing both phenomena.

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Area of Science:

  • Geophysics
  • Materials Science
  • Rheology

Background:

  • Columnar jointing in cooling lava and drying crack patterns in cornstarch exhibit striking geometric similarities.
  • Understanding the formation mechanisms of these natural crack patterns is crucial for materials science and geology.

Purpose of the Study:

  • To investigate the underlying mathematical and dynamical similarities between crack patterns in drying cornstarch and cooling lava.
  • To develop a unified theory explaining the formation of geometrically similar crack patterns in different physical systems.
  • To establish scaling relations for crack spacing and explore implications for crack pattern control.

Main Methods:

  • Laboratory experiments on thick cornstarch samples under controlled drying conditions.
  • Analysis of crack spacing measurements from both laboratory experiments and geological sites (e.g., Giant's Causeway).
  • Development and application of a mathematical theory for cracking induced by differential drying or cooling.

Main Results:

  • Crack spacing data from both cornstarch and geological samples collapse onto a single master scaling curve.
  • A unified dynamical law, rooted in nonequilibrium physics, explains the formation of these similar crack patterns.
  • Quantitative explanation provided for the geometric similarity observed across different phenomena.

Conclusions:

  • The formation of columnar joints and drying cracks share a common underlying physical principle.
  • The developed theory offers a predictive framework for crack spacing in various materials and conditions.
  • Results have implications for controlling crack formation in thin and thick solid films.