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Related Concept Videos

Shearing Stresses in a Beam: Problem Solving01:14

Shearing Stresses in a Beam: Problem Solving

418
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...
418
Prismatic Beams: Problem Solving01:15

Prismatic Beams: Problem Solving

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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...
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Design of Prismatic Beams for Bending01:23

Design of Prismatic Beams for Bending

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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...
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Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

281
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

313
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...
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Shear on the Horizontal Face of a Beam Element01:16

Shear on the Horizontal Face of a Beam Element

398
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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Hierarchical Multiobjective Heuristic for PCB Assembly Optimization in a Beam-Head Surface Mounter.

Huijun Gao, Zhengkai Li, Xinghu Yu

    IEEE Transactions on Cybernetics
    |January 15, 2021
    PubMed
    Summary
    This summary is machine-generated.

    A new hierarchical multiobjective heuristic (HMOH) optimizes printed-circuit board assembly (PCBA) by decomposing complex tasks. This method enhances efficiency for high-mix, low-volume production lines.

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    Area of Science:

    • Manufacturing Engineering
    • Operations Research
    • Artificial Intelligence

    Background:

    • The beam-head surface mounter is critical for high-mix, low-volume printed-circuit board assembly (PCBA) lines.
    • Optimizing PCBA on these machines presents a complex, multiobjective combinatorial challenge.
    • Existing studies have not provided a comprehensive framework for optimizing all interrelated objectives.

    Purpose of the Study:

    • To propose a novel hierarchical multiobjective heuristic (HMOH) for optimizing PCBA on single beam-head surface mounters.
    • To develop a framework that addresses the complete and interrelated objectives in PCBA optimization.
    • To improve the efficiency and decision-making process in high-mix, low-volume PCBA production.

    Main Methods:

    • A novel decomposition strategy models the problem as Head Task Assignment Problem (HTAP) and Pickup-and-Place Sequencing Problem (PAPSP).
    • HTAP includes nozzle assignment and component allocation; PAPSP includes place allocation, feeder set assignment, and place sequencing.
    • The HMOH employs a lexicographic method to solve subproblems in descending order of objective importance, utilizing expert knowledge for heuristic design.

    Main Results:

    • The proposed HMOH effectively models real-world PCBA factors, including pickup-and-place cycles, nozzle changes, simultaneous pickups, and distances.
    • The method achieves complete and optimal PCBA decision-making in real time.
    • Comparative analysis using industrial PCB datasets demonstrates the superiority of HMOH over the Samsung SM482's built-in optimizer.

    Conclusions:

    • The HMOH provides a significant advancement in optimizing PCBA processes for beam-head surface mounters.
    • This approach offers a comprehensive solution for complex, multiobjective PCBA optimization challenges.
    • The HMOH enhances real-time decision-making and operational efficiency in high-mix, low-volume manufacturing environments.