Name: constraints in structural equilibrium
Uploaded: 2023-09-22T11:49:23.000Z
Duration: 1 min 26 s
Channel: JoVE

시스템의 평형은 방정식에 의해서뿐만 아니라 제약 조건의 도움으로 정의됩니다. 제약 조건은 시스템 동작에 대한 제한을 나타냅니다.
시스템이 평형을 보장하기 위해 최소한의 제약 조건으로 유지되는 경우, 정적으로 결정된다고 합니다.
이러한 시스템의 경우, 미지의 반응 지지체는 평형 방정식을 사용하여 추정할 수 있습니다.
평형을 유지하기 위해 추가 중복 지지부가 시스템에 추가되면 정적으로 불확정 상태가 됩니다. 이는 시스템에 작용하는 제약 조건의 수가 해당 해에 사용할 수 있는 평형 방정식의 수보다 크다는 것을 의미합니다.
반면에, C 지점 과 D 지점에서 두 개의 핀 지지대에 연결된 부재 AB를 고려하여 반동력의 작용선이 C 지점에서 동시에 이루어진다고 가정합니다.
적용된 하중은 빔을 부분적으로 구속하는 경향이 있는데, 평형 방정식이 하중 조건에 대해 충족되지 않기 때문입니다.
마찬가지로, 모든 반작용력이 서로 평행하면 부적절하게 구속됩니다.

<ol>
	<li> 히벨러, R.C. (2016). Engineering Mechanics \u2012 정역학 및 동역학. 뉴저지 호보켄: 피어슨 프렌티스 홀. 251-254쪽. </li>
</ol>

제약조건과 통계적 결정성

Constraints and Statical Determinacy

구조공학에서 시스템의 평형은 평형방정식 뿐만 아니라 제약조건의 도움으로 결정됩니다. 제약조건은 시스템의 운동에 대한 제약조건을 의미합니다. 제약조건의 적절한 조합은 시스템이 기계적 평형 상태를 유지하는 데 필요한 제약조건의 총 수를 최소화할 수 있습니다. 이런 일이 일어나면 시스템은 정적으로 결정된다고 합니다. 이러한 시스템의 경우 알 수 없는 반응지원은 평형방정식을 사용하여 추정할 수 있습니다. 
정적으로 결정되는 시스템은 특정 수의 평형 방정식을 사용하여 시스템에 작용하는 모든 힘을 결정할 수 있기 때문에 분석하고 설계하기가 가장 쉽습니다. 일반적으로 평형 방정식은 시스템에 작용하는 모든 힘의 합과 0과 같은 모든 순간의 합을 포함합니다.
그러나 평형을 유지하기 위해 추가적인 중복 지원이 시스템에 추가되면 정적으로 불확정적이 됩니다. 이는 솔루션에 사용할 수 있는 평형 방정식보다 더 많은 제약이 시스템에 작용하고 있음을 의미합니다. 정적으로 불확정적인 시스템에서는 추가적인 지원이 시스템의 움직임을 제한하지만 추가적인 방정식도 생성합니다. 이러한 추가적인 방정식은 일반적으로 재료의 역학 하에서 처리되는 시스템의 변형에 의해 얻어집니다. 정적으로 불확정적인 시스템의 과제는 시스템에 추가할 정확한 중복 지원의 수를 찾는 것입니다. 
또한 부적절한 제약조건은 모든 반응력이 한 지점에서 만나거나 공통축을 통과하거나 평행이 되는 상황을 말합니다. 이러한 조건은 구조에 불안정성을 유발할 수 있으므로 엔지니어링 실무에서 피해야 합니다. 반응력이 한 지점에서 교차하거나 공통축을 따를 때 신체를 균형 밖으로 밀어 넘어뜨릴 수 있습니다. 마찬가지로 서로 평행한 힘은 평형을 유지하지 못할 수 있으며 구조적인 실패를 초래할 수 있습니다. 불안정한 조건과 잠재적인 위험을 방지하기 위해 부적절한 제약조건을 피하는 것이 필수적입니다.

구조 공학에서 시스템의 평형은 평형 방정식에 의해서만 결정되는 것이 아니라 제약 조건의 도움에 의해서도 결정됩니다. ...

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

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 be solved from a fixed set of equilibrium equations.

The usual equilibrium equations include the sum of all forces equal to zero and the sum of all moments equal to zero. If extra, redundant supports are added, the system becomes statically indeterminate. That means there are more constraints than equilibrium equations, so the extra reactions cannot be found from equilibrium alone.

For statically indeterminate systems, the extra equations usually come from deformation. This topic is handled in mechanics of materials. The main challenge is choosing the correct number of redundant supports so the structure stays in equilibrium without becoming overconstrained.

Improper constraints can also create instability. This happens when all reactive forces meet at a single point, pass through a common axis, or become parallel. In those cases, the structure may topple or fail to stay balanced, so engineers avoid these conditions in practice.

Constraints in Structural Equilibrium

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

equations-of-equilibrium-in-three-dimensions

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.

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 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 constraints affect structural equilibrium, including statically determinate and indeterminate systems, redundant supports, and unstable constraint patterns.

Constraints in Structural Equilibrium | 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

Constraints in Structural Equilibrium

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