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Beams

Beams

Beams are integral components of structural engineering and construction, designed to support loads applied at various points along their length. These long, straight members can be classified based on geometry, cross-section, support type, and equilibrium condition.
Based on geometry, beams can be straight, tapered, or curved. Straight beams are the most common type and have a constant cross-section throughout their length. Tapered beams, on the other hand, have a varying cross-section along...

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.
The first moment-area theorem determines the slope at any point on the beam. This theorem indicates that the change in slope between two points on a beam...

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...

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 first...

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.
The M/EI...

Prismatic Beams: Problem Solving

Prismatic Beams: Problem Solving

In the design of a supported timber beam subjected to a distributed load, both the beam's physical dimensions and the timber's characteristics, such as its grade and species, are critical. These factors determine the allowable stress values, which are crucial for calculating the necessary beam depth to ensure structural integrity and safety.
The design begins with analyzing the beam as a free body to identify moments and force balances, thereby determining support reactions. Next, the designer...

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Related Experiment Video

Updated: Jul 10, 2026

Design and Building of a Customizable, Single-Objective, Light-Sheet Fluorescence Microscope for the Visualization of Cytoskeleton Networks

Design and Building of a Customizable, Single-Objective, Light-Sheet Fluorescence Microscope for the Visualization of Cytoskeleton Networks

Published on: January 26, 2024

Light beams with flat-topped profiles.

|November 21, 2007

Summary

This summary is machine-generated.

A new condition is proposed for creating optical beams with uniform profiles. This leads to novel flat-topped beams constructed from fundamental Gaussian modes, offering an alternative to existing flattened Gaussian beam models.

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Demonstration of Equal-Intensity Beam Generation by Dielectric Metasurfaces

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Published on: June 7, 2019

Area of Science:

Optics and Photonics
Laser Physics

Background:

Generating optical beams with uniform intensity profiles is crucial for various applications.
Existing models for flattened Gaussian beams have limitations.

Purpose of the Study:

To propose a necessary condition for generating optical beams with nearly uniform transverse profiles.
To introduce a novel set of light beams with flat-topped profiles based on this condition.

Main Methods:

Derivation of a necessary condition for uniform beam profiles.
Mathematical representation of the new beams as a finite series of Gaussian modes (TEM00).
Investigation and comparison of the new beam characteristics with existing models.

Main Results:

A novel set of flat-topped optical beams is introduced.
These beams are expressed as a series expansion of fundamental Gaussian modes.
Key features of the proposed beams are analyzed and contrasted with prior models.

Conclusions:

The proposed condition provides a method for generating uniform optical beams.
The new set of flat-topped beams offers a potentially advantageous alternative to existing flattened Gaussian beams.