Name: two-force body equilibrium
Uploaded: 2025-05-22T09:06:02.000Z
Duration: 1 min 30 s
Channel: JoVE

考虑一盏灯通过其上端被夹住，垂直悬挂在支架上。
若杆件被隔离，且仅有两个力分别作用于两点 A 和 B，中间无其他载荷，则该杆件称为二力构件。此时，力的性质仅为拉力或压力。
对于二力构件处于平衡状态，力 FA 和 FB &#160;必须大小相等，方向相反。
为了满足力矩平衡条件，FA 和 FB&#160; 必须具有相同的力作用线。
通常，二力构件在点 A 和 B 上可能受到多个力的作用，这些力可表示为点 A 和 B 处的合力。
如果已知一侧力的大小和方向，则可计算出另一侧的力。这会减少平衡方程中的未知数个数。
二力构件不一定为直杆；它可以是弯曲或弧形的，用于分析桁架、框架和机械结构的受力情况。

<ol>
	<li>希伯勒，RC（2016 年）。工程力学 \u2012 静力学和动力学。 新泽西州霍博肯:Pearson Prentice Hall。第 230 页。</li>
	<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。第 195 页。</li>
</ol>

两力构件

Two Force Member

两力构件的平衡是实际应用中经常遇到的特殊情况。两力物体是一个只受到两个外力作用的刚体。对于这样一个处于平衡状态的体系，两个力必须具有相同的大小，并且具有相同的作用线和相反的方向。 <img alt="Figure 2" src="/files/ftp_upload/14273/14273_PT_Figure_1v2.svg" style="text-align: center; height: 350px;"> 假设有任何一个受到两个力F1和F2作用的板块，它们作用于A点和B点。如果板块处于平衡状态，则F1和F2关于任何一根轴线的力矩之和必须为零。对A点的力矩进行求和，我们可以得出F2的力矩必须为零。因此，它的作用线必须通过A点。同样，对B点的力矩进行求和，我们可以得出F1的作用线必须通过B点。这意味着两个力都具有相同的作用线——连接A点和B点的线。 此外，可以证明这两个力具有相同的大小和相反的方向。这可以从方程ΣFx = 0和ΣFy = 0中可以看出，其中的这些力是相互抵消的。 当多个力作用于A点和B点时，作用在A点的力可以由它们的合力F1来进行替代，作用在B点的力可以由它们的合力F2来进行替代。一个两力构件可以一般地定义为一个受到作用于仅含有两个点的力的刚体。重要的是要注意，无论何种情况，为了保证体系的平衡，F1和F2的合力必须具有大小相同和方向相反的作用线。

二力体的平衡是在实际应用中经常遇到的一个特殊情况。二力体是指仅受两个力作用的刚体，该刚体……

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

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 works at point B. Summing the moments about point B shows that the line of action of F1 must pass through point B. So both forces lie on the line joining A and B.

The force balance also requires ΣFx = 0 and ΣFy = 0. These equations show that the two forces have the same magnitude and opposite directions, so they cancel each other out. When several forces act at A and B, each group can be replaced by a resultant force. Those resultants must still share the same line of action, the same magnitude, and opposite directions for the body to stay in equilibrium.

Two-Force Body 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

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 a two-force body stays in equilibrium by using moment balance, force balance, and the rules for line of action, magnitude, and direction.

Two-Force Body 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

Two-Force Body Equilibrium

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