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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...

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...

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...

Bending of Curved Members - Strain Analysis

Bending of Curved Members - Strain Analysis

The mechanics of deformation in curved members, such as beams or arches, under bending moments, involve complex responses. When such a member, symmetric about the y-axis and shaped like a segment of a circle centered at point C, is subjected to equal and opposite forces, its curvature and surface lengths change significantly. This alteration results in the shift of the curvature's center from C to C', indicating a tighter curve.
The important part of bending analysis for such a member...

Residual Stresses in Bending

Residual Stresses in Bending

In the study of elastoplastic members subjected to bending moments, understanding the loading and unloading phases is crucial for assessing material behavior and structural integrity. During the loading phase, as the bending moment increases, the material initially responds elastically, adhering to Hooke's Law, where stress is directly proportional to strain. When the load exceeds the yield strength, plastic deformation occurs, resulting in permanent strain and deformation that remains even...

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...

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Related Experiment Video

Updated: Jul 19, 2025

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

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Published on: August 12, 2013

Flexible stitching interferometry for gull-wing asphere using variable-sign curvature compensation.

Yi Zong, Caiyun Yu, Yixuan Liu

|August 15, 2023

Summary

Accurate testing of gull-wing aspheres (GWA) is now possible using flexible stitching interferometry (FSI) with variable-sign curvature compensation (VSCC). This novel method enables high-precision GWA testing for advanced optical systems.

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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

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Published on: August 12, 2013

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Area of Science:

Optical Engineering
Metrology
Aspheric Optics

Background:

Aspheres are crucial components in modern optical systems.
High-precision testing of gull-wing aspheres (GWA) presents significant challenges.

Purpose of the Study:

To introduce a novel method for accurate GWA testing.
To address the limitations of current GWA metrology techniques.

Main Methods:

Flexible stitching interferometry (FSI) combined with variable-sign curvature compensation (VSCC).
Relative translation of VSCC to adjust outgoing wavefront curvature for subaperture compensation.
Alternating optimization stitching for full-aperture absolute phase retrieval.

Main Results:

Experimental demonstration of the feasibility and performance of the proposed FSI-VSCC method.
Successful high-precision testing of GWAs.
Accurate full-aperture absolute phase retrieval achieved.

Conclusions:

The FSI-VSCC method offers a new solution for accurate GWA testing.
This technique represents a first-time application of VSCC in stitching interferometry for aspheric testing.
The method has potential applications in general aspheric interferometry.