Name: equivalent resultant loads on beams
Uploaded: 2023-09-22T11:49:23.000Z
Duration: 1 min 21 s
Channel: JoVE

한쪽 끝에 고정되고 분산 하중을 받는 테이퍼 빔 OB를 고려하십시오.
다양한 하중의 등가 결과력을 결정하고 빔에서 해당 위치를 찾습니다.
먼저, 분산된 하중을 두 개의 삼각형 영역으로 나눕니다.
다음으로, 왼쪽 및 오른쪽 삼각형 영역의 등가 결과 하중의 크기는 각 삼각형의 면적과 같습니다.
각 결과 하중은 삼각형의 수직 측면 AD에서 기본 길이의 1/3에 위치한 중심에서 작용합니다.
등가 결과 하중은 각 삼각형 영역의 개별 결과 하중을 더하여 결정할 수 있습니다.
점 O에 대한 모멘트는 각 결과 하중으로 인해 작용하는 개별 모멘트를 더하여 결정할 수 있습니다.
점 O에 대한 등가 결과 하중의 모멘트가 등가 결과 하중의 곱과 점 O로부터의 거리와 같다는 모멘트 원리를 기억하십시오.
방정식의 값을 대체하면 등가 결과 하중의 위치를 결정할 수 있습니다.

<ol>
	<li>히벨러, R.C. (2016). Engineering Mechanics \u2012 정역학 및 동역학. 뉴저지 호보켄: Pearson Prentice Hall, pp. 194-195</li>
</ol>

분산 하중: 문제 해결

빔은 다양한 하중 전달 용량이 필요한 엔지니어링 응용 분야에 일반적으로 사용되는 구조 요소입니다. 분산 하중을 받는 빔을 해석하는 첫 번째 단계는 하중을 더 작은 영역으로 나누어 문제를 단순화하는 것입니다. 이를 통해 각 영역을 개별적으로 고려하고 빔의 각 부분에 작용하는 등가 합성 하중의 크기를 계산할 수 있습니다. 각 영역의 등가 합성 하중의 크기는 각 영역의 하중에 의해 가해지는 힘을 나타내는 각 영역의 면적을 계산하여 결정할 수 있습니다.
다음으로, 빔에서 각 결과 하중의 위치를 찾습니다. 이는 영역의 질량이 집중된 것으로 간주될 수 있는 지점인 영역의 중심을 찾아 수행할 수 있습니다. 개별 결과 하중은 이러한 중심에 작용하여 빔을 따라 특정 지점에 힘을 가합니다.
결정된 개별 합성하중의 크기와 위치를 이용하여 전체 보에 대한 등가 합성하중을 계산할 수 있습니다. 여기에는 빔에 작용하는 전체 등가 합성 하중을 얻기 위해 다양한 영역의 개별 합성 하중을 추가하는 작업이 포함됩니다.
다음 단계는 특정 지점, 일반적으로 빔의 고정된 끝 부분에 대한 모멘트를 결정하는 것입니다. 모멘트는 빔에 작용하는 힘의 회전 효과를 측정합니다. 결과 모멘트는 각 하중으로 인해 작용하는 개별 모멘트를 추가하여 결정할 수 있습니다. 각 하중의 모멘트는 힘과 지정된 지점으로부터의 거리의 곱과 같습니다.
<img alt="Equation 1" src="/files/ftp_upload/14280/14280_PT_Equation_1.svg" style="text-align: center; height: 11px;" />
모멘트 원리를 떠올려 특정 지점에 대한 등가 합성 하중의 모멘트는 등가 합성 하중과 해당 지점으로부터의 거리를 곱한 것과 같습니다.
<img alt="Equation 2" src="/files/ftp_upload/14280/14280_PT_Equation_2.svg" style="text-align: center; height: 13px;" />
방정식을 재배열하고 항을 대체하면 빔을 따라 등가 합성 하중의 위치를 결정할 수 있습니다.
<img alt="Equation 3" src="/files/ftp_upload/14280/14280_PT_Equation_3.svg" style="text-align: center; height: 35px;" />

빔은 다양한 하중 전달 능력을 필요로 하는 엔지니어링 응용 분야에 일반적으로 사용되는 구조 요소입니다. 분석의 첫 번째 단계 ...

Education

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JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Force System Resultants

힘 체계의 합력

KEY TERMS AND CONCEPTS

주요 용어 및 개념

Distributed Loads: Problem Solving

equivalent resultant loads on beams

Equivalent resultant loads on beams can be found by breaking a distributed load into smaller regions. This makes the beam easier to analyze. Each region can then be handled on its own before the results are combined.

The magnitude of the equivalent resultant load for each region comes from the area of that region. In this setting, area represents the force applied by the distributed load over that part of the beam. After finding the force for each region, the position of each resultant load must be located.

The position is found by using the centroid of each region. A centroid is the point where the region’s mass can be treated as concentrated. The individual resultant loads act at these centroids, so each force is placed at a specific point along the beam.

Once the separate forces and locations are known, they are combined to find the equivalent resultant load for the full beam. This is done by adding the individual resultant loads from the different regions. The result gives the overall force acting on the beam.

The next step is to determine the moment about a chosen point, usually the fixed end of the beam. A moment is the turning effect of a force. The total moment comes from adding the moments created by each load, and each moment equals force times distance from the chosen point.

By using the moment principle, the moment of the equivalent resultant load about that point must equal the force multiplied by its distance from the point. Rearranging that relationship makes it possible to find where the single equivalent load acts along the beam. This gives both the size and location of the load that replaces the distributed loading.

Equivalent Resultant Loads on Beams

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cartesian form for vector formulation

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Resultant moment describes the total turning effect of multiple forces acting on an object. It shows how several forces can combine to make a body rotate about a point. In physics, moment is the tendency of a force to cause rotation. The resultant moment of a force system is a vector quantity. That means it can be added and subtracted like other vectors. For a system with two forces, F1 and F2, acting on a pole at points A and B, the resultant moment is written as MR = (rA x F1) + (rB x F2).

principle of moments

Resolving Forces in Moment Calculations

The principle of moments, also called Varignon's theorem, explains how a force creates rotation about a point. It is a key idea in physics and engineering. It also helps describe when a rigid body stays in equilibrium under external forces. The moment of a force is found by multiplying the force by the perpendicular distance from the point of application to the point being studied. A larger force or a larger distance gives a larger moment. This makes the idea useful for checking how strongly a...

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Couple Moment in Force Systems

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equivalent couples

Equivalent Couples in Mechanical Systems

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Torque from a Couple: Solving Forces

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Equivalent Force and Moment Systems

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simplification of a force and couple system: ii

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Resultant Force and Wrench Motion

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distributed loads

Load Distribution on Shelves and Dams

Load distribution helps engineers describe how force spreads across a surface or structure. A distributed load is a continuous force per unit area, rather than a single point force. It is a common idea in many practical situations. A bookshelf full of stacked books is one simple example. The weight of the books is spread along the shelf, so the pressure changes across the surface. This pressure is measured in Newtons per square meter, or Pascals. A hydroelectric dam gives another clear...

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Finding Resultant Loads on a Beam

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distributed loads: problem solving

Equivalent resultant loads on beams can be found by breaking a distributed load into smaller regions. This makes the beam easier to analyze. Each region can then be handled on its own before the results are combined. The magnitude of the equivalent resultant load for each region comes from the area of that region. In this setting, area represents the force applied by the distributed load over that part of the beam. After finding the force for each region, the position of each resultant load...

key terms and concepts

Learn how to replace a distributed load with one equivalent resultant force on a beam by using areas, centroids, and moments to find its location.

Equivalent Resultant Loads on Beams | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Equivalent Resultant Loads on Beams

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