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Deflection of a Beam

Deflection of a Beam

Accurately determining beam deflection and slope under various loading conditions in structural engineering is crucial for ensuring safety and structural integrity. Singularity functions offer a streamlined approach to analyzing beams, especially when multiple loading functions complicate the bending moment equation.
Singularity functions, described in an earlier lesson, are powerful mathematical tools that represent discontinuities within a function commonly encountered in structural loading...

Beams with Symmetric Loadings

Beams with Symmetric Loadings

The moment-area method is an analytical tool used in structural engineering to determine the slope and deflection of beams under various loads. Consider a cantilever with a concentrated load and moment at the free end. The first step is constructing a free-body diagram to calculate the reactions at the fixed end. Next, the bending moment diagram is plotted to visualize how the bending moment varies along the beam's length, focusing on points where the bending moment equals zero.
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Impact Loading on a Cantilever Beam

Impact Loading on a Cantilever Beam

The analysis of a cantilever beam with a circular cross-section subjected to impact loading at its free end illustrates the conversion of potential energy from a dropped object into kinetic energy, which is then absorbed by the beam as strain energy. This process is crucial for understanding how materials behave under dynamic loads, which is important in fields such as construction and aerospace.
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Beams with Unsymmetric Loadings

Beams with Unsymmetric Loadings

Analyzing a supported beam under unsymmetrical loadings is essential in structural engineering to understand how beams respond to varied force distributions. This analysis involves calculating the deflection and identifying points where the slope of the beam is zero, which are crucial for ensuring structural stability and functionality.
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Deformation of a Beam under Transverse Loading

Deformation of a Beam under Transverse Loading

Understanding beam deflection, particularly for indeterminate beams with overhanging segments and multiple concentrated loads, is crucial for ensuring structural integrity and functionality. The process begins with constructing an accurate free-body diagram, which helps identify the forces and moments acting on the beam. This diagram is vital for visualizing how bending moments vary along the beam's length, influencing its curvature.
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Shear on the Horizontal Face of a Beam Element

Shear on the Horizontal Face of a Beam Element

To understand shear on the flat side of a prismatic beam element, consider the vertical and horizontal shearing forces, and the normal forces, acting on the element. The element's upper (U) and lower (L) sections, which are divided by the beam's neutral axis, are examined. The equilibrium of these forces is determined by applying the equilibrium equation, which helps identify the horizontal shearing force. This force is directly related to the bending moments and the cross-section's...

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Related Experiment Video

Updated: Mar 7, 2026

Demonstration of Equal-Intensity Beam Generation by Dielectric Metasurfaces

Demonstration of Equal-Intensity Beam Generation by Dielectric Metasurfaces

Published on: June 7, 2019

Dynamical beam manipulation based on 2-bit digitally-controlled coding metasurface.

Cheng Huang¹, Bo Sun¹, Wenbo Pan¹

¹State Key Laboratory of Optical Technologies on Nano-Fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Science, P. O. Box 350, Chengdu 610209, China.

Scientific Reports

|February 9, 2017

Summary

This summary is machine-generated.

This study introduces a 2-bit digitally-controlled coding metasurface capable of manipulating electromagnetic waves. This novel metasurface enables arbitrary control over reflected beams for applications in advanced antenna systems.

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Area of Science:

Electromagnetics and Metamaterials
Applied Physics

Background:

Digital metamaterials offer novel ways to control electromagnetic fields.
Metasurfaces provide a platform for manipulating wave propagation with subwavelength structures.

Purpose of the Study:

To design and demonstrate a 2-bit digitally-controlled coding metasurface.
To achieve arbitrary control over scattered electromagnetic waves and far-field beam patterns.

Main Methods:

Each meta-atom integrates two pin diodes for four distinct phase responses (0, π/2, π, 3π/2).
A coding sequence of digital elements ('00', '01', '10', '11') is designed to control the metasurface's phase profile.
Programmable electric source enables dynamic switching of scattering patterns.

Main Results:

The 2-bit coding metasurface successfully modulates scattered electromagnetic waves.
Demonstrated capabilities include beam deflection, multi-beam generation, and beam diffusion.
Dynamical switching between different scattering patterns was achieved.

Conclusions:

The proposed 2-bit digitally-controlled coding metasurface offers flexible and dynamic control of electromagnetic wave scattering.
This technology has potential applications in reconfigurable antennas and advanced radar systems.