Name: equivalent resultant loads on beams
Uploaded: 2023-09-22T11:49:23.000Z
Duration: 1 min 21 s
Channel: JoVE

考虑一端固定的锥形梁OB，并承受分布载荷。
确定可变载荷的等效力，并确定其在梁上的位置。
首先，将分布载荷分为两个三角形区域。
接下来，左右三角形区域的等效合力大小等于各个三角形的面积。
每个合成载荷作用于形心，该形心位于三角形垂直边 AD 的底边长度的三分之一处。
可以通过将每个三角形区域的单独合力相加来确定等效合力。
关于点 O 的力矩可通过将每个合力载荷所产生的力矩分别相加来确定。
回顾力矩原理，该原理指出：等效合力关于点 O 的力矩等于等效合力与其到点 O 距离的乘积。
通过代入方程中的数值，可确定等效合力作用点的位置。

<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 194-195 页</li>
</ol>

分布载荷：求解问题

Distributed Loads: Problem Solving

梁是通常用于在工程应用中需要不同承载能力的的结构元件。如果要分析受分布载荷作用的梁，第一步是通过将载荷划分为较小的区域来对问题进行简化，从而来独立考虑其每个区域，并计算作用在梁上与合载荷等效的大小。每个区域与合载荷等效的大小可以通过计算相应区域的面积来进行确定，该面积表示了载荷在每个区域中所施加的力。 接下来，确定在梁上每个等效合载荷的位置。可以通过找到各个区域的质心来进行实现，质心是可以被认为是质量集中区域处的点。各个等效合载荷在这些质心处发挥作用，并在梁上的特定点处施加力。 可以通过已经确定的各个等效合载荷的大小和位置来计算整个梁上的等效合载荷。这涉及到将不同区域的各个等效合载荷进行相加，以获得作用在梁上的整体等效合载荷。 下一步是确定位于特定点（通常为梁的固定端）处的力矩。力矩可以测量作用在梁上的力所产生的旋转效果。可以通过将每个载荷产生的各个力矩进行相加来确定其结果力矩。每个载荷的力矩等于力与其距离指定点处的乘积。 <img alt="Equation 1" src="/files/ftp_upload/14280/14280_PT_Equation_1.svg" style="text-align: center; height: 11px;"> 根据力矩原理可以得知，等效合载荷关于指定点的力矩等于等效合载荷与该点距离之间的乘积。 <img alt="Equation 2" src="/files/ftp_upload/14280/14280_PT_Equation_2.svg" style="text-align: center; height: 13px;"> 通过对其进行重新排列方程并替换术语，可以确定等效合载荷是沿着梁的位置。 <img alt="Equation 3" src="/files/ftp_upload/14280/14280_PT_Equation_3.svg" style="text-align: center; height: 35px;">

梁是工程应用中常用的结构元件，需具备不同的承载能力。分析梁的第一步是……

Education

教育

JoVE Core

Mechanical Engineering

机械工程

Unit 1

第一单元

Force System Resultants

力系合力

KEY TERMS AND CONCEPTS

关键术语与概念

equivalent resultant loads on beams

Equivalent resultant loads on beams can be found by breaking a distributed load into smaller regions. This makes the beam easier to analyze. Each region can then be handled on its own before the results are combined.

The magnitude of the equivalent resultant load for each region comes from the area of that region. In this setting, area represents the force applied by the distributed load over that part of the beam. After finding the force for each region, the position of each resultant load must be located.

The position is found by using the centroid of each region. A centroid is the point where the region’s mass can be treated as concentrated. The individual resultant loads act at these centroids, so each force is placed at a specific point along the beam.

Once the separate forces and locations are known, they are combined to find the equivalent resultant load for the full beam. This is done by adding the individual resultant loads from the different regions. The result gives the overall force acting on the beam.

The next step is to determine the moment about a chosen point, usually the fixed end of the beam. A moment is the turning effect of a force. The total moment comes from adding the moments created by each load, and each moment equals force times distance from the chosen point.

By using the moment principle, the moment of the equivalent resultant load about that point must equal the force multiplied by its distance from the point. Rearranging that relationship makes it possible to find where the single equivalent load acts along the beam. This gives both the size and location of the load that replaces the distributed loading.

Equivalent Resultant Loads on Beams

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Equivalent resultant loads on beams can be found by breaking a distributed load into smaller regions. This makes the beam easier to analyze. Each region can then be handled on its own before the results are combined. The magnitude of the equivalent resultant load for each region comes from the area of that region. In this setting, area represents the force applied by the distributed load over that part of the beam. After finding the force for each region, the position of each resultant load...

key terms and concepts

Learn how to replace a distributed load with one equivalent resultant force on a beam by using areas, centroids, and moments to find its location.

Equivalent Resultant Loads on Beams | JoVE K12

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Equivalent Resultant Loads on Beams

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