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

엔지니어링 응용 분야에서는 라인을 따라 하중 분포를 고려하는 것이 중요합니다.
분산 하중으로 인해 가해지는 알짜 힘은 결과 힘이라고 하는 단일 벡터로 표시됩니다.
균일한 하중을 받는 임의 모양의 평판을 생각해 보십시오.
플레이트의 무한소 영역에 작용하는 힘은 차동 부피 요소와 동일한 크기를 갖습니다.
플레이트에 작용하는 결과적인 힘은 전체 플레이트 표면에 작용하는 모든 차동 힘을 합산하여 계산됩니다.
플레이트의 면적을 적분하면 결과 힘의 크기를 계산하는 표현식을 얻을 수 있으며, 이는 분산 하중 다이어그램 아래의 총 부피와도 같습니다.
결과적인 힘의 위치는 결과적인 힘의 모멘트를 각각의 축에 대한 모든 차동 힘의 모멘트와 비교하여 결정됩니다.
얻어진 표현식은 힘의 작용선이 분산 하중 다이어그램 아래 부피의 기하학적 중심 또는 중심을 통과한다는 것을 의미합니다.

<ol>
	<li>히벨러, R.C. (2016). 엔지니어링 역학: 정적. 14판, 뉴저지: 피어슨. 섹션 9.4, 511쪽.</li>
	<li>Beer, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. 및 Self, B.P. (2016). 엔지니어를 위한 벡터 역학. 제 11 판, 뉴욕 : McGraw-Hill Education. 섹션 5.3 262쪽.</li>
</ol>

일반 분산 하중의 결과

Resultant of a General Distributed Loading

불균일 하중에 노출되는 구조물을 설계할 때 합력과 그 위치를 고려하는 것이 매우 중요합니다. 이 합력은 분산하중으로 인해 가해지는 알짜힘을 나타내는 단일 벡터입니다.
바람에 의한 하중 분포와 교량의 하중 분포와 같은 예는 이 개념이 가변 하중 조건에서 안전하고 신뢰할 수 있는 구조물을 분석하고 설계하는 데 어떻게 사용되는지 보여줍니다. 주거용 건물, 교량 및 타워와 같은 대부분의 구조물은 풍속과 방향에 따라 달라지는 불균일한 바람 하중을 견딜 수 있도록 설계되었습니다. 마찬가지로 교량도 차량이 지나가는 무게를 견딜 수 있도록 설계되었습니다. 그러나 차량의 무게 분포가 균일하지 않고 교량의 일부 부분은 다른 부분보다 더 많은 스트레스와 변형을 겪을 수 있습니다. 건물이나 교량에 작용하는 합력을 계산해야 하는데, 이는 불균일한 하중 분포 문제입니다. 
이 힘을 결정하기 위해서는 무한대의 면적에 작용하는 각 미분력의 크기를 합산하여 하중을 받는 표면적에 적분해야 합니다. 이 합력의 크기는 분산하중 도표의 전체 부피와 같습니다. 이 결과적인 힘의 위치는 각 축에 대한 모든 미분력의 모멘트와 비교하여 알 수 있습니다. 이는 이 힘의 작용선이 고려 중인 부피의 기하학적 중심이나 중심을 통과할 것임을 의미합니다.
구조물에 어디에 어느 정도의 힘이 가해지는지를 알면 엔지니어는 구조물이 목적에 맞게 적합하도록 충분한 강도와 강성을 보장할 수 있습니다. 이러한 값은 또한 가변 하중 조건에 따라 변경될 수 있으므로 안전하고 안정적인 구조를 설계하기 위해 이러한 잠재적인 변화를 고려하는 것이 필수적입니다.

불균일한 하중에 노출된 구조물을 설계할 때는 그에 따른 힘과 그 위치를 고려하는 것이 중요합니다. 이 결과적인 힘은 단일 ...

resultant-of-a-general-distributed-loading

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Center of Gravity and Centroid

무게중심과 도심

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

Center of Mass in Motion

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

Finding the Center of a Body

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...

centroid of a body: problem solving

Centroid of a Quarter Circle Wire

The centroid of a quarter circle wire shows how balance points can be found for curved shapes. In physics and engineering, the centroid helps describe stability, balance, and design. For a thin wire bent into a quarter circular arc, the goal is to find the centroid coordinates of the arc itself. Polar coordinates are used to solve this centroid problem. The wire is divided into small differential elements, and each element has a length equal to the radius times the differential angle. The x-...

centroid for the paraboloid of revolution

centroid-for-the-paraboloid-of-revolution

Centroid and Uses of a Paraboloid Shape

The centroid of a paraboloid of revolution is the point where its mass is balanced. A paraboloid of revolution is an axially symmetric surface made by rotating a parabola around its axis. In engineering, this location matters because it helps show how forces spread across the shape. Knowing the centroid can help when building parts that must handle stress and pressure reliably. The paraboloid shape has useful structural properties, including rotational symmetry and strength against stress...

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

theorems-of-pappus-and-guldinus-problem-solving

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

How Depth Changes Fluid Pressure

Fluid pressure changes with depth in liquids used in engineering systems. It matters in hydraulic systems, pumps, and valves, where the forces from moving and resting fluid must be considered to prevent damage or failure. For a fluid at rest, Pascal’s law says the pressure is equal in all directions. Pressure is force per unit area. Its size depends on the fluid’s specific weight, or mass density, and on how deep the measurement point is below the fluid surface. This relationship can be...

fluid pressure over flat plate of constant width

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

Center of Pressure on a Submerged Plate

Fluid pressure on a submerged flat plate depends on depth and shape. A plate under water experiences pressure acting normal to its surface, and the force is spread across the whole area. For a rectangular plate of constant width, this pressure increases from the top edge to the bottom edge. Because the pressure rises with depth, the loading forms a trapezoidal distribution. The resultant force on the plate comes from the trapezoidal volume of water with a specific weight. The line of action of...

fluid pressure over curved plate of constant width

fluid-pressure-over-curved-plate-of-constant-width

Finding Force on a Curved Plate in Water

Fluid pressure on a curved plate of constant width changes in both size and direction. That makes the total force hard to find directly. A common method is to split the force into horizontal and vertical parts and then combine them. The calculation becomes simpler by replacing the distributed load with an equivalent two-dimensional loading. The first step is to include the weight of the liquid inside the block. That force equals the specific weight of the liquid times the plate thickness and...

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 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

Finding the Resultant of Distributed Loads

Description

Transcript