Name: rigid body force balance in equilibrium
Uploaded: 2023-09-22T11:49:22.000Z
Duration: 1 min 28 s
Channel: JoVE

刚体在外力作用下不会发生任何形变。
考虑一个旋转木马，在垂直径向距离为 r 的位置受到一个外力 F 的作用，从而在点 O 处产生力矩。
当多个力作用在旋转木马上时，若作用在其上的所有外力之和为零，则达到平衡条件。
平衡的另一个条件指出，关于点 O 的所有力矩之和必须等于零。
当在点 A 测量力矩时，它可以表示为点 O 处的力矩与垂直距离和所施加力的叉积之和。
这些条件确保物体在静态平衡下不发生任何平动或转动。
此处仅考虑外力，因为刚体内部的内力大小相等、方向相反，根据牛顿第三运动定律会相互抵消。

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	<li>比尔，F.P.;约翰斯顿，ER;马祖克，DF;克伦威尔，PJ 和塞尔夫，BP（2019 年）。工程师的矢量力学 \u2012 静力学和动力学。纽约:麦格劳-希尔。页码 170</li>
</ol>

平衡条件

Conditions of Equilibrium

平衡是指刚体不受任何平移或旋转运动的状态。当作用在刚体上的力和力矩等于零时，便达到了平衡状态。当外力系统的净效应等于零时，刚体则会被认为是处于平衡状态的。 平衡条件不考虑内力，因为它们在体内以相等且相反的方式出现，并且在效果上是相互抵消的。因此，这些内力不会对刚体的整体运动或变化产生影响。平衡的状态是由作用在刚体上的外力和力矩的平衡来进行决定的，因为它们能够负责引起平移或旋转运动。 平衡的必要和充分条件可以通过将合力和力矩设为零来进行确定。此外，通过将每个力和力矩分解为它们在直角坐标系中的分量，可以用六个标量方程来代替向量方程。这意味着外力在x、y和z方向上的分量是平衡的，并且外力关于x、y和z轴的力矩也是平衡的。如果刚体是处于平衡状态的，则外力系统对刚体不会产生平移或旋转运动。 要写出刚体的平衡方程，首先要确定作用在刚体上的所有力，并绘制相应的受力分析图。除了施加在结构上的力之外，还要考虑支撑在结构上的反作用力。并且正确识别每个反作用力来帮助解决其中未知的力和反作用力。 对刚体平衡条件的了解对于分析与刚体有关的问题至关重要。通过确定未知的力和反作用力，并利用平衡的充分必要条件，可以预测刚体的行为。

平衡是指刚体不受任何平动或转动作用的状态。当作用在物体上的合力与合力矩均为零时，即可实现这一状态。

Education

教育

JoVE Core

Mechanical Engineering

机械工程

Unit 1

第一单元

Equilibrium of a Rigid Body

刚体的平衡

KEY TERMS AND CONCEPTS

关键术语与概念

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 external forces and moments determine whether the body stays balanced. These are the forces that can cause translation or rotation. The necessary and sufficient conditions for equilibrium are found by setting the resultant force and the resultant moment equal to zero.

The vector equations for equilibrium can also be written as six scalar equations. Each force and moment is resolved into rectangular components. This means the external force components in the x, y, and z directions must balance, and the moments about the x, y, and z axes must also balance.

To write equilibrium equations for a rigid body, first identify all forces acting on it. Then draw a free-body diagram. The reactions from supports must also be included. Correctly identifying each reaction helps solve unknown forces and reactions in structures.

Rigid Body Force Balance in Equilibrium

conditions of 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 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 rigid body equilibrium is determined by balanced external forces and moments, free-body diagrams, and support reactions in high school physics.

Rigid Body Force Balance in 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

Rigid Body Force Balance in Equilibrium

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