Name: checking force balance in 3d structures
Uploaded: 2023-09-22T11:49:23.000Z
Duration: 1 min 30 s
Channel: JoVE

바닥에 놓인 삼각대를 생각해 보십시오. 다리는 A에서 볼과 소켓 조인트를 사용하여 연결되고 다른 쪽 끝 B는 바닥에 있습니다.
다리에 작용하는 결과적인 힘과 결과적인 커플 모멘트가 0일 때, 다리는 평형 상태에 있다고 하며 평형 방정식의 도움으로 표현될 수 있습니다.
다리는 평형 상태에 있기 때문에 평형의 벡터와 스칼라 방정식을 충족합니다.
평형의 벡터 방정식에 따르면 다리에 작용하는 모든 외력은 벡터 합이 0이어야 합니다. 모든 커플 모멘트의 벡터 합과 한 점에 대한 모든 힘의 모멘트도 0과 같아야 합니다.
평형의 스칼라 방정식에 따르면 외부 힘이 데카르트 형태로 표현되면 각 방향을 따른 힘 구성 요소의 합은 0이어야 합니다.
마찬가지로, x, y, z축에서 모멘트의 성분에 대한 스칼라 합계도 0이어야 합니다.

<ol>
	<li>히벨러, R.C. (2016). Engineering Mechanics \u2012 정역학 및 동역학. 뉴저지 호보켄: 피어슨 프렌티스 홀. 250쪽</li>
</ol>

3차원 평형 방정식

Equations of Equilibrium in Three Dimensions

정지된 구조나 시스템을 분석할 때는 평형 상태인지 확인하는 것이 필요합니다. 여기서 벡터 및 스칼라 평형 방정식이 작용합니다. 이러한 방정식은 구조가 안정적이고 붕괴되거나 붕괴되지 않도록 하는 데 중요합니다. 벡터 및 스칼라 평형 방정식은 물체에 작용하는 힘을 분석하기 위한 틀을 제공합니다.
평형의 벡터 방정식에 따르면 물체에 작용하는 모든 외부 힘의 벡터 합은 0과 같아야 합니다. 또한, 쌍모멘트와 한 점에 대한 모든 힘의 모멘트의 벡터 합도 0과 같아야 합니다.
<img alt="Equation 1" src="/files/ftp_upload/14275/14275_Equation_1v2.svg" style="text-align: center; height: 33px;" />
평형의 스칼라 방정식에 따르면 외부 힘이 데카르트 형식으로 표현되면 각 방향을 따르는 힘의 구성요소의 합은 0이 되어야 합니다.
<img alt="Equation 2" src="/files/ftp_upload/14275/14275_Equation_2v2.svg" style="text-align: center; height: 55px;" />
마찬가지로 x, y, z 축에 있는 순간 구성 요소의 스칼라 합도 0이어야 합니다.
<img alt="Equation 3" src="/files/ftp_upload/14275/14275_Equation_3v2.svg" style="text-align: center; height: 55px;" />
이러한 방정식은 기계 공학의 기본이며 구조의 안전과 안정성을 보장합니다.

정지 상태의 구조나 시스템을 분석할 때는 이들이 평형 상태에 있는지 확인해야 합니다. 이것은 의 벡터와 스칼라 방정식이 있는 곳입니다 ...

equations-of-equilibrium-in-three-dimensions

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Equilibrium of a Rigid Body

강체의 평형

KEY TERMS AND CONCEPTS

주요 용어 및 개념

checking force balance in 3d structures

Checking force balance in 3D structures is a key step when a system is at rest. The vector and scalar equations of equilibrium are used to test whether a body is stable and will not collapse or fall apart. These equations give a clear way to study the forces acting on a body.

The vector equations of equilibrium require the vector sum of all external forces on a body to equal zero. They also require the vector sum of the couple moments and the moments of all forces about a point to equal zero. A couple moment is a turning effect produced by a pair of forces.

The scalar equations of equilibrium use Cartesian form, which means the forces are written in x, y, and z components. In that form, the sum of the force components along each direction must be zero. The scalar sum of the moment components about the x, y, and z axes must also be zero. These conditions are fundamental in mechanical engineering because they help show that structures are safe and stable.

Checking Force Balance in 3D Structures

conditions of equilibrium

Rigid Body Force Balance in Equilibrium

Rigid body equilibrium depends on a balance of external forces and moments. A rigid body is in equilibrium when it has no translational motion and no rotational motion. This happens when the net force and the net couple acting on the body are both zero. Internal forces are not used when checking equilibrium. These forces act in equal and opposite pairs inside the body, so they cancel each other. Because of that, they do not affect the overall motion or change in motion of the rigid body. The...

support reactions

Types of Structural Supports

Types of structural supports control how a coplanar force system moves and reacts under load. A coplanar force system is a set of forces that all lie in the same plane. The supports create reactions at the point of contact. These reactions help keep a structure stable under external forces. Supports work by stopping translation with an equal and opposite force. They can also stop rotation by applying a couple moment in the opposite direction. In structural design, these reactions are important...

internal forces and center of gravity

Forces Inside a Body and Balance

Internal forces and the center of gravity help explain how objects stay in balance. These mechanics ideas matter for structures, machines, and vehicles that must remain stable under different loads and conditions. Internal forces are created inside a body when its particles interact. They can appear as tension, compression, or shear forces. These forces act in collinear pairs with equal magnitude and opposite direction. Between connected parts, they cancel each other and help keep the body in...

alternative sets of equilibrium equations

alternative-sets-of-equilibrium-equations

Equilibrium Conditions for a Supported Plate

Equilibrium conditions for a supported plate are used to describe when forces and moments balance. In this state, the plate has no net movement and no rotation. Engineers use these equations to study how structures behave under external loads. In many cases, the standard equilibrium equations are enough. But some systems need an alternative set of equations to match the geometry of the support points. A rectangular plate supported at points A, B, and C is one example. For this plate, the...

two force member

Two-Force Body Equilibrium

A two-force body is a rigid body acted on by only two external forces. In equilibrium, those two forces must have the same magnitude, the same line of action, and opposite directions. This balance is what keeps the body at rest. For a plate with forces F1 and F2 applied at points A and B, equilibrium means the sum of moments about any axis is zero. If moments are summed about point A, the moment from F2 must be zero. That means the line of action of F2 must pass through point A. The same idea...

three force member

Solving a Three-Force Member Example

A three-force member is a rigid body acted on by three forces at three points. The forces must have concurrent lines of action. If the forces are parallel, their lines of action stay parallel instead. A dumpster provides the example used here. It is connected to a pin support at point A and to a pin on a hydraulic cylinder at point B. The hydraulic cylinder acts as a two-force member in equilibrium. The dumpster weight acts through the center of gravity, and the support reaction acts at point...

equations of equilibrium in three dimensions

Checking force balance in 3D structures is a key step when a system is at rest. The vector and scalar equations of equilibrium are used to test whether a body is stable and will not collapse or fall apart. These equations give a clear way to study the forces acting on a body. The vector equations of equilibrium require the vector sum of all external forces on a body to equal zero. They also require the vector sum of the couple moments and the moments of all forces about a point to equal zero.

support reactions in three dimensions

3D Support Types for Stability and Motion

Support reactions in three dimensions keep structures stable and in equilibrium. They stop unwanted translation and rotation, so a design can handle external forces safely and work as intended. These reactions are important in many structures and systems. A ball and socket joint is one support that allows free rotation about any axis. It does not provide a moment that resists turning. At the same time, it restricts motion in space with three reaction forces along the three dimensions. A...

constraints and statical determinacy

Constraints in Structural Equilibrium

Constraints in structural engineering control how a body can move and help keep it in mechanical equilibrium. A constraint is a restriction on motion. When the right number of constraints is used, the system can stay balanced with the fewest supports needed. A system with the proper number of supports is called statically determinate. In that case, the unknown reaction forces can be found from equations of equilibrium. These systems are the easiest to analyze and design because the forces can...

key terms and concepts

Learn how vector and scalar equilibrium equations keep 3D structures stable by balancing forces and moments in x, y, and z directions.

Checking Force Balance in 3D Structures | 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

Checking Force Balance in 3D Structures

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