Name: finding the resultant of distributed loads
Uploaded: 2023-09-22T11:49:32.000Z
Duration: 1 min 13 s
Channel: JoVE

エンジニアリングアプリケーションでは、ラインに沿った荷重分布を考慮することが重要です。
分布荷重によって加えられる正味の力は、合力と呼ばれる単一のベクトルとして表されます。
均一な荷重を受ける任意の形状の平板を考えてみましょう。
プレート上の極小領域に作用する力は、微分体積要素と同等の大きさを持ちます。
プレートに作用する合力は、プレート表面全体に作用するすべての微分力を合計することによって計算されます。
プレートの面積全体積分により、合力の大きさを計算するための式が得られ、これは分布荷重図の下の総体積にも等しくなります。
合力の位置は、合力のモーメントを、それぞれの軸の周りのすべての微分力のモーメントと比較することによって決定されます。
得られた式は、力の作用線が分布荷重図の下の体積の幾何学的中心または重心を通過することを意味します。

<ol>
	<li>ヒベラー、RC(2016)。エンジニアリングメカニクス:静力学。第14版、ニュージャージー州:ピアソン。セクション9.4、511ページ。</li>
	<li>ビール、FP、ジョンストン、ER、マズレック、DF、コーンウェル、PJおよびセルフ、BP(2016)。エンジニアのためのベクトル力学。第11版、ニューヨーク:マグロウヒル教育。セクション5.3、262ページ。</li>
</ol>

一般的な分布荷重の結果

Resultant of a General Distributed Loading

構造物を非均一な荷重にさらす際には、結果力とその位置を考慮することが重要です。この結果力は、分布荷重によって適用される合力を表す単一のベクトルです。

風による荷重分布や橋の荷重分布などの例は、この概念が変動する荷重条件下で安全で信頼性のある構造物の解析と設計にどのように使用されるかを示しています。ほとんどの建物や橋、タワーなどの構造物は、非均一な風荷重に耐えるように設計されており、風速と風向によって異なります。同様に、橋は車両の重みに耐えるように設計されていますが、車両の重み分布は均一ではなく、橋の一部は他の部分よりもより多くの応力やひずみを受ける可能性があります。建物や橋に作用する結果力を計算する必要があります。これは非均一な荷重分布の問題です。

この力を決定するためには、微小な領域に作用する微分力の大きさを総和して、荷重を受ける表面積で積分する必要があります。この結果力の大きさは、分布荷重図の全体積に等しいです。この結果力の位置は、それぞれの軸に関する微分力のモーメントと比較して、決定することができます。これは、この力の作用線が対象となる体積の幾何学的中心または重心を通ることを意味します。

構造物に適用される力の位置と大きさを知ることで、エンジニアは構造物が目的に適している十分な強度と剛性を確保することができます。これらの値は、荷重条件の変化に基づいても変化する可能性があるため、安全で安全な構造物を設計するためにこれらの潜在的な変化を考慮することが不可欠です。

不均一な荷重にさらされる構造を設計する際には、合力とその位置を考慮することが重要です。この合力は ...

resultant-of-a-general-distributed-loading

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Center of Gravity and Centroid

重心と図心

KEY TERMS AND CONCEPTS

主要用語と概念

finding the resultant of distributed loads

Distributed loads create a force that is spread over a surface instead of acting at one point. To analyze this kind of loading, engineers use a single resultant force. That force represents the net effect of the entire load.

This idea is important in structures that face non-uniform loads. Wind can push on buildings and towers with changing speed and direction, so the load is not evenly spread. Bridges also experience non-uniform loading from vehicles, and some parts of the bridge can feel more stress and strain than others.

To find the resultant force, the small forces acting on tiny areas are added together with integration over the load-bearing surface. The size of the resultant force equals the total area under the distributed-loading diagram. Its location is found by comparing moments, which means the turning effects of the force about an axis.

The line of action of the resultant passes through the geometric center, or centroid, of the volume under the load diagram. Knowing both the size and location of the force helps engineers judge whether a structure has enough strength and rigidity. Because loading can change, these calculations help support safe and reliable design for buildings, bridges, and other structures.

Finding the Resultant of Distributed Loads

finding-the-resultant-of-distributed-loads

center of gravity

Center of Gravity in Balance and Design

The center of gravity is the point where an object’s weight appears to act. It is the spot used to balance the object most evenly. In mechanics, this point helps explain stability and moments of inertia. The center of gravity does not always sit inside the object’s shape. In some cases, it can lie outside the body. That is why the idea is useful for both simple and more complex shapes. Its location can be found with the principle of moments. The object is divided into very small parts, and...

center of mass

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The center of mass helps explain how an object moves through space. It is the point where the total mass of an object can be treated as concentrated. This idea applies to objects of different shapes and sizes. The center of mass is related to the center of gravity, but they are not the same. The center of gravity is the point where an object’s weight seems to be concentrated. It can be used to balance an object perfectly. Knowing the center of mass also helps predict motion. When a ball is...

centroid of a body

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The centroid is the geometric center of a body. It is an important idea in engineering, physics, and mechanics. For many objects, it lies inside the body. A body with holes or cavities can be an exception. For a homogeneous body, the centroid matches the center of mass or the center of gravity. Homogeneous means the material has a uniform density. In that case, the centroid can often be found by balancing the moments of the body’s volume. Symmetry can also help locate the centroid. If a...

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Centroid and Uses of a Paraboloid Shape

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composite bodies

Center of Gravity in Composite Bodies

Composite bodies are made of multiple connected parts that act as one larger object. Each part still has its own weight and center of gravity. To find the center of gravity of the whole body, engineers must account for every part. When the density or specific weight is constant, the center of gravity matches the centroid. The centroid is the geometric center of a shape. This idea is useful when analyzing parts that behave as a single unit. Composite bodies are common in mechanical engineering.

theorems of pappus and guldinus

Surface Area and Volume by Centroid Paths

Pappus and Guldinus theorems help find the surface area and volume of bodies of revolution. A body of revolution is formed when a plane curve or plane area is turned around an axis that does not intersect it. For surface area, a curve is revolved around a non-intersecting axis. A small line element on the curve creates a thin ring as it moves. Adding these ring areas gives the total surface area of the solid. The first theorem says that this surface area equals the length of the generating...

theorems of pappus and guldinus: problem solving

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Pappus and Guldinus Theorems for Surface Area

Pappus and Guldinus's theorems help find the surface area and volume of composite shapes. These rules are useful when a solid is made from simple parts that are hard to measure directly. A cylindrical storage tank with a conical top is one example. The tank can be split into two simple shapes: a cylinder and a cone. To find surface area, the first theorem is used for the solid formed by revolving each generating curve around a non-intersecting axis. The calculation uses the length of the...

resultant of a general distributed loading

Distributed loads create a force that is spread over a surface instead of acting at one point. To analyze this kind of loading, engineers use a single resultant force. That force represents the net effect of the entire load. This idea is important in structures that face non-uniform loads. Wind can push on buildings and towers with changing speed and direction, so the load is not evenly spread. Bridges also experience non-uniform loading from vehicles, and some parts of the bridge can feel...

fluid pressure

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fluid pressure over curved plate of constant width

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Finding Force on a Curved Plate in Water

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fluid pressure over flat plate of variable width

fluid-pressure-over-flat-plate-of-variable-width

A submerged flat plate experiences fluid pressure that changes with depth. This pressure can create effects such as drag and buoyancy. To study a flat plate with variable width, the pressure distribution across the plate must be analyzed first. The force on a small strip of the plate is found by multiplying the pressure by the strip’s differential area. The pressure can also be written using the fluid’s specific weight and the depth of that strip below the surface. To find the total, or...

key terms and concepts

Learn how engineers combine non-uniform loads into one resultant force, find its location with moments, and apply the idea to bridges and buildings.

Finding the Resultant of Distributed Loads | JoVE K12

JoVE Core 機械工学は、平衡、力、トラス解析、構造力学などの重要なトピックをカバーする簡潔でわかりやすいアニメーション ビデオを提供します。実際のアプリケーションを探索し、科学者主導の実験を通じてこれらのコンセプトが実際に動作しているのを目撃してください。

Finding the Resultant of Distributed Loads

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