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Related Concept Videos

Beams01:30

Beams

2.1K
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...
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Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

504
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...
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Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

504
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...
504
Distribution of Stresses in a Narrow Rectangular Beam01:11

Distribution of Stresses in a Narrow Rectangular Beam

697
In studying beam stress distribution, examining an elemental section is essential. To determine the average shearing stress on this face, the calculated shear is divided by the surface area. Importantly, shearing stresses on the beam's transverse and horizontal planes mirror each other, indicating a consistent stress distribution along the upper region of the beam. Notably, shearing stresses are absent at the beam's upper and lower surfaces due to the absence of applied forces in these...
697
Prismatic Beams: Problem Solving01:15

Prismatic Beams: Problem Solving

541
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...
541
Shearing Stresses in a Beam: Problem Solving01:14

Shearing Stresses in a Beam: Problem Solving

838
A cantilever beam with a rectangular cross-section under distributed and point loads experiences shearing stresses. The analysis begins by identifying the loads acting on the beam. Then, the reactions at the beam's fixed end are calculated using equilibrium equations. The vertical reaction is a combination of the distributed and point loads, while the moment reaction is the sum of their moments. The shear force distribution along the beam, resulting from these loads, is established by creating...
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Related Experiment Video

Updated: Apr 15, 2026

Author Spotlight: Introduction to Active Probe Atomic Force Microscopy with Quattro-Parallel Cantilever Arrays
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Free space self-similar beams.

Nan Gao, Changqing Xie

    Optics Letters
    |April 2, 2015
    PubMed
    Summary
    This summary is machine-generated.

    Self-similar beams can propagate in linear systems, unlike nonlinear systems. This research introduces a method for creating and controlling these beams in linear wave dynamics using superposition.

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    Area of Science:

    • Wave dynamics
    • Linear systems
    • Quantum mechanics

    Background:

    • Self-similar wave dynamics typically require nonlinearity and diffraction.
    • Extrapolation to linear systems often yields trivial solutions.
    • Linear systems present unique challenges for self-similar beam propagation.

    Purpose of the Study:

    • To demonstrate self-similar beam propagation in linear wave systems.
    • To explore methods for constructing and controlling such beams.
    • To present a technique for manipulating wave propagation in linear environments.

    Main Methods:

    • Governing linear wave equations: paraxial wave equation and free particle Schrödinger equation.
    • Utilizing the principle of superposition inherent in linear systems.
    • Employing transformed coordinates to find exact or approximate solutions.

    Main Results:

    • A broad class of self-similar beams can propagate in linear systems.
    • Superposition in linear free space enables beam construction and eliminates instabilities.
    • The proposed technique offers a viable method for manipulating linear wave propagation.

    Conclusions:

    • Self-similar beam propagation is achievable in linear systems.
    • Linearity offers advantages like stability and constructability via superposition.
    • The presented coordinate transformation technique is valuable for controlling waves in linear systems.