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Design of Prismatic Beams for Bending

Design of Prismatic Beams for Bending

The design of prismatic beams, structural elements with a uniform cross-section, focuses on ensuring safety and structural integrity under load. The design process begins by determining the allowable stress, either from material properties tables, or by dividing the material's ultimate strength by a safety factor. This safety factor is essential for accommodating uncertainties, and varies depending on the material—timber, steel, or concrete—with each having unique strength and stress...

Bending of Curved Members - Neutral Surface

Bending of Curved Members - Neutral Surface

In curved beams, unlike straight beams, the stress distribution across the cross-section is not uniform due to the beam's curvature. This non-uniformity arises because the neutral axis, where stress is zero, does not align with the centroid of the section. In a curved beam, the strain varies along the section as a function of the distance from the neutral axis.
Consider the curved member described in the previous lesson. According to Hooke's law, which relates stress to strain within the...

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.
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Plastic Deformation in Circular Shafts

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When materials are subjected to forces that surpass their yield strength, they undergo a process known as plastic deformation. This results in a permanent alteration or strain in their structure. This concept can be specifically applied to circular shafts, where the deformation leads to a change in its shape. The precise evaluation of this plastic deformation requires understanding the stress distribution within the circular shaft, which is achieved by calculating the maximum shearing stress in...

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.
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Related Experiment Video

Updated: May 10, 2026

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

Published on: March 20, 2017

Beam shaping system design using double freeform optical surfaces.

Zexin Feng¹, Lei Huang, Mali Gong

¹Center for Photonics and Electronics, State Key Laboratory of Tribology, Department of Precision Instruments, Tsinghua University, Beijing 100084, China.

|June 22, 2013

Summary

This summary is machine-generated.

This study introduces a numerical method for designing double-freeform optical surfaces to shape laser beams. The technique effectively transforms Gaussian beams into uniform rectangular profiles while preserving wavefront quality.

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Last Updated: May 10, 2026

Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

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Published on: March 20, 2017

Fabrication of a Low-Cost, Fiber-Coupled, and Air-Spaced Fabry-Pérot Etalon

Fabrication of a Low-Cost, Fiber-Coupled, and Air-Spaced Fabry-Pérot Etalon

Published on: February 3, 2023

Area of Science:

Optics
Optical Engineering
Computational Optics

Background:

Laser beam shaping is crucial for various applications.
Designing freeform optical surfaces requires sophisticated methods.
Existing methods may lack efficiency or applicability for complex beam profiles.

Purpose of the Study:

To propose a numerical double-freeform-optical-surface design method for beam shaping.
To account for both irradiance distribution and wavefront of the output beam.
To develop a practical and computationally efficient design approach.

Main Methods:

Numerical design using energy conservation and variable separation for ray mapping.
Simultaneous, point-by-point construction of two freeform surfaces using Snell's law and optical path length constancy.
Application to separable irradiance distributions, simplifying computation.

Main Results:

Successfully designed a two-plano-freeform-lens system for Gaussian to uniform rectangular beam transformation.
Achieved high uniformity with relative root mean square deviation from 0.0652 to 0.326.
Maintained high power concentration (97.5% to 88.3%) over a significant propagation distance.

Conclusions:

The proposed numerical method is effective for specific laser beam shaping applications.
The method offers a practical solution for designing freeform optics with separable irradiance distributions.
The technique demonstrates potential for efficient and accurate beam transformation systems.