Name: solving a three-force member example
Uploaded: 2023-09-22T11:49:22.000Z
Duration: 1 min 27 s
Channel: JoVE

一个刚体若受到三个作用在三个不同点上的力，则称为三力构件。
这些力的作用线必须共点，除非是作用线相互平行的平行力。
考虑一个在点处连接到销钉支座的垃圾箱 A 以及一个在点处连接到液压缸的销钉 B.
液压缸是一个处于平衡状态的二力构件。由重力产生的力通过重心作用，而由支撑产生的反作用力则作用于点 A。
第一步是绘制包含作用在垃圾箱上所有力的系统受力分析图。
可以利用力和力矩平衡方程来确定未知力 FA 和 FCB。
然后，根据点 A 的力矩平衡条件计算力 FCB。
沿垂直方向的力平衡条件给出了垂直反作用力。
同样，根据水平方向的力平衡条件可得水平反作用力。

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	<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 196 页</li>
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三力构件

Three Force Member

作用在三个点上的三个力的刚体被称为三力杆。这些力必须具有并行的作用线，但平行力除外，平行力的作用线是平行的。 例如，假设有一个液压缸在A点处连接到销的支撑点，并在B点处连接到液压缸的销。 <img alt="Figure 1" src="/files/ftp_upload/14274/14274_Figure_1v3.jpg" style="text-align: center; height: 300px;"> 在这种情况下，液压缸是一个处于平衡状态的双力元件。在由重力产生的作用下，可以支撑位于A处所产生的反作用力。 为了求解未知力FA和FCB的值，第一步涉及到了创建整个系统的受力分析图，同时还包括作用在液压缸上的所有力。 <img alt="Figure 2" src="/files/ftp_upload/14274/14274_Figure_2v2.png" style="text-align: center; height: 250px;"> 接下来，可以使用力和力矩平衡方程来确定其未知力的值。 <img alt="Equation 1" src="/files/ftp_upload/14274/14274_PT_Equation_1v2.svg" style="text-align: center; height: 13px;"> <img alt="Equation 2" src="/files/ftp_upload/14274/14274_PT_Equation_2v2.svg" style="text-align: center; height: 13px;"> <img alt="Equation 3" p="" src="/files/ftp_upload/14274/14274_PT_Equation_3v2.svg" style="text-align: center; height: 13px;">

位于点A处力矩的平衡条件给出了力FCB的值为24.08 kN。与此同时，竖直方向上力的平衡条件确定了竖直方向反作用力FAy为9.74kN。类似地，在水平方向上力的平衡条件得到了水平方向的反作用力FAx为25.74kN。

受三个作用点上力作用的刚体称为三力构件。这些力的作用线必须共点，除非……

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

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 A.

The solution starts with a free-body diagram of the entire system. That diagram includes every force acting on the dumpster. Then the force and moment equilibrium equations are used to solve for the unknown forces.

Taking moments about point A gives the cylinder force F CB as 24.08 kN. The vertical force equilibrium condition gives the vertical reaction F Ay as 9.74 kN. The horizontal force equilibrium condition gives the horizontal reaction F Ax as 25.74 kN.

Solving a Three-Force Member Example

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

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 to analyze a three-force member with a free-body diagram, equilibrium equations, and a dumpster example to find unknown reaction forces.

Solving a Three-Force Member Example | JoVE K12

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mechanical engineering

Solving a Three-Force Member Example

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