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Related Concept Videos

Unsymmetric Bending - Angle of Neutral Axis01:15

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Unsymmetrical bending occurs when a structural member is subjected to bending moments in a plane that does not align with the member's principal axes. This scenario typically arises in beams and other structural components when loads are applied at non-ideal angles, introducing complexities in stress analysis.
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An electric motor applies a torque of 700 N·m to an aluminum shaft, triggering a stable rotation. Two pulleys, B and C, are subjected to torques of 300 N·m and 400 N·m, respectively. The modulus of rigidity is provided as 25 GPa. With the knowledge of the length and diameter of each segment, the twist angle between the two pulleys can be computed. First, a section cut is made between pulleys B and C, and the cut cross-section is analyzed using a free-body diagram. Given that the...
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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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Consider a cylindrical shaft with a length denoted by L and a consistent cross-sectional radius referred to as r. This shaft undergoes a torque at the free end. The highest shearing strain within the shaft is directly proportional to the twist angle and the radial distance from the shaft axis. When the shaft behaves elastically, this shearing strain can be articulated using variables such as the applied torque, radial distance, the polar moment of inertia, and the modulus of rigidity. By...
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Circular shafts undergoing torsional stress maintain their cross-sectional integrity due to their axisymmetric nature. This symmetry ensures an even distribution of stress, allowing the shaft to withstand torsion without distorting. In contrast, square bars, lacking this axial symmetry, experience significant distortion across their cross-sections when subjected to torsion, with the exception of along their diagonals and at lines connecting midpoints. A detailed examination of a cubic element...
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Unsymmetrical bending occurs when the bending moment applied to a structural member does not align with its principal axis. This misalignment leads to complex stress distributions and deflection patterns that differ from those in symmetrical bending, and are essential for designing structures to withstand different loading conditions. In unsymmetrical bending, the neutral axis—where stress is zero—does not necessarily align with the geometric axes of the cross-section. The...
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Fibonacci spirals may not need the Golden Angle.

Xiaofeng Yin1,2, Hirokazu Tsukaya1

  • 1Department of Biological Sciences, Graduate School of Science, The University of Tokyo, Tokyo, Japan.

Quantitative Plant Biology
|April 20, 2023
PubMed
Summary

Plant phyllotaxis, the arrangement of leaves, can follow Fibonacci spirals. New research suggests auxin dynamics, not just the Golden Angle, guide this patterning in plants like gerbera.

Keywords:
auxincapitulumparastichypattern transitionphyllotaxis

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Area of Science:

  • Plant biology
  • Developmental biology
  • Quantitative biology

Background:

  • Phyllotaxis describes the regular arrangement of plant lateral organs.
  • Models often focus on spiral phyllotaxis and its relation to the Golden Angle.
  • However, some patterns, like in Asteraceae, deviate from this strict geometric dependency.

Purpose of the Study:

  • To explore the mechanisms underlying phyllotactic patterning, particularly Fibonacci spirals.
  • To investigate the role of auxin dynamics in guiding phyllotaxis.
  • To understand the transition between different phyllotaxis modes.

Main Methods:

  • Analysis of phyllotactic patterning in *Gerbera hybrida*.
  • Investigating the influence of auxin dynamics on organ primordia arrangement.
  • Observing the expansion and contraction of the capitulum meristem.

Main Results:

  • Auxin dynamics and the dynamic ring of the capitulum are key to Fibonacci spiral formation in gerbera.
  • Distinct phases of phyllotactic patterning and mode transitions were identified.
  • Local interactions among primordia play a significant role in patterning.

Conclusions:

  • Fibonacci spirals in phyllotaxis may not strictly require the Golden Angle.
  • Auxin dynamics are a crucial factor in guiding phyllotactic patterns.
  • Understanding these mechanisms offers new insights into plant development.