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Unsymmetric Bending

Unsymmetric Bending

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 orientation of the...

Unsymmetric Bending - Angle of Neutral Axis

Unsymmetric Bending - Angle of Neutral Axis

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.
When a bending moment is applied at an angle θ concerning the vertical axis of a symmetrical member, it can be resolved into components along the member's principal centroidal axes. The...

Angle of Twist - Elastic Range

Angle of Twist - Elastic Range

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...

Deformations in a Symmetric Member in Bending

Deformations in a Symmetric Member in Bending

When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
When the member is segmented into tiny cubic elements, it is observed that the primary stress...

Bending and Torsional Moments

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Bending and torsional moments are two fundamental concepts in structural engineering. They play an important role in understanding the behavior of materials and structures under different loading conditions.
The reaction developed in a structural element when subjected to an external force causes the element to bend. When a structural element bends upwards, it creates compressive normal forces on the top and tensile normal forces on the bottom, resulting in a couple that determines the bending...

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Related Experiment Video

Updated: May 26, 2026

High-Contrast and Fast Photorheological Switching of a Twist-Bend Nematic Liquid Crystal

High-Contrast and Fast Photorheological Switching of a Twist-Bend Nematic Liquid Crystal

Published on: October 31, 2019

Nematic disclinations as twisted ribbons.

Simon Copar¹, Tine Porenta, Slobodan Zumer

¹Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|December 21, 2011

Summary

This summary is machine-generated.

Topological rules govern disclination loops in nematics. Changing parameters like spacing and pitch affects loop geometry, explained by liquid crystal elasticity.

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Area of Science:

Soft Matter Physics
Liquid Crystal Science
Colloidal Systems

Background:

Disclination loops in nematic liquid crystals are topological defects.
These defects entangle colloidal structures, with their geometry dictated by topological rules.
Understanding these rules is key to controlling colloidal assembly in liquid crystals.

Purpose of the Study:

To investigate how geometric properties of disclination loops are affected by system parameters.
To analyze the interplay between writhe and twist in colloidal dimers within nematics.
To correlate observed geometric trends with liquid crystal elasticity and symmetry.

Main Methods:

Utilized finite difference numerical simulations.
Studied colloidal dimers as the model system.
Varied intercolloidal spacing, cell twist angle, and cholesteric pitch.

Main Results:

Demonstrated that writhe and twist of disclination loops are constrained to sum to a constant.
Showed how intercolloidal spacing, cell twist, and cholesteric pitch influence loop geometry.
Observed trends in loop geometry were consistent with liquid crystal elasticity theory.

Conclusions:

The geometric configurations of disclination loops are topologically stabilized.
Liquid crystal elasticity and symmetry principles explain the observed trends in loop geometry.
This work provides insights into the topological and elastic control of colloidal structures in nematics.