Name: truss member force analysis by sections
Uploaded: 2025-05-22T09:06:03.000Z
Duration: 1 min 30 s
Channel: JoVE

考虑一个桁架结构。力 F1 和 F2 分别作用于点 B 和 D 处。
截面法用于确定作用在桁架少数杆件上的力。该方法基于以下原理：处于平衡状态的桁架，其各个部分也均处于平衡状态。
考虑桁架的受力图，以计算作用在杆件 EF、DC 和 DF 上的力。
关于点 A 的力矩平衡方程可用于计算点 E 处的支座反力。
现在，沿一个截面平面进行切割，该平面最多与三个构件相交。
绘制该截面的受力分析图，假设未知力为拉力。
对 D 点取矩可求得作用在 EF 上的力。
未知的倾斜力被分解为水平分量和垂直分量。
水平和竖直方向上所受力的平衡条件可得到两个方程。
解联立方程，可计算出沿 DC 和 DF 的力。

<ol>
	<li>R. C.，Hibbeler Engineering Mechanics Statics，皮尔逊，第 291-293 页</li>
	<li>F.P. Beer， E.R. Johnston， D.F. Mazurek， P.J. Cornwell， B.P. Self， 工程师的矢量力学 静力学和动力学 工程力学静力学， Mc Graw-Hill Education.第 217 页</li>
</ol>

分段法

考虑一个桁架结构，如图所示。 <img alt="Figure 1" src="/files/ftp_upload/14285/14285_PT_Fig_1v2.svg" style="text-align: center; height: 350px;"> 

对于力F1和F2施加在接合点B和D上。可以使用分段法来确定作用在桁架特定构件上的力，如EF，DC和DF。这种方法基于一个原理，即处于平衡状态的桁架的每个部分也处于平衡状态。 

为了计算这些构件上的力，需要绘制桁架的受力分析图。可以将关节A点周围的力矩平衡方程应用于关节E点处的反支撑力。

<img alt="Equation 1" src="/files/ftp_upload/14285/14285_PT_Equation_1v2.svg" style="text-align: center; height: 13px;"> 

沿着最多与三个构件相交的截面进行切割：EF，DC和DF。然后，绘制切割区域右侧的受力分析图，假设未知力为拉力。


<img alt="Figure 2" src="/files/ftp_upload/14285/14285_PT_Fig_2v2.svg" style="text-align: center; height: 350px;"> 

对关节D点的力矩进行求和可以得出作用在构件EF上的力。

<img alt="Equation 2" src="/files/ftp_upload/14285/14285_PT_Equation_2v2.svg" style="text-align: center; height: 13px;"> 

未知的倾斜力FDC和FDF被分解为水平和垂直分量。可以通过水平方向和垂直方向上力的平衡条件来得出两个单独的方程。

<img alt="Equation 3" src="/files/ftp_upload/14285/14285_PT_Equation_3v2.svg" style="text-align: center; height: 13px;"> <img alt="Equation 4" src="/files/ftp_upload/14285/14285_PT_Equation_4v2.svg" style="text-align: center; height: 13px;"> 

沿构件DC和DF方向的力可以通过联立这些方程并对其进行求解来进行估算。

考虑如图所示的桁架结构。

力 F1 和 F2 分别作用于节点 B 和 D。可采用截面法来……

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Structural Analysis

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Method of Sections

truss member force analysis by sections

Truss member force analysis by sections finds the force in selected members of a truss. In this problem, forces F1 and F2 act at joints B and D. The goal is to determine the forces in members EF, DC, and DF.

The method uses the idea that a truss in equilibrium also has each of its sections in equilibrium. A free-body diagram of the whole truss is drawn first. The moment equation about joint A is then used to estimate the support reaction at point E.

Next, a cut is made along a sectional plane that passes through no more than three members. Here, the cut intersects EF, DC, and DF. A free-body diagram of the right side of the cut section is then drawn, and the unknown member forces are assumed to be tensile, or pulling away from the cut.

The force in member EF is found by summing moments about joint D. The inclined forces in members DC and DF are then split into horizontal and vertical parts. Finally, equilibrium in the horizontal and vertical directions gives two equations, and solving them gives the forces in DC and DF.

Truss Member Force Analysis by Sections

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Learn how the method of sections uses free-body diagrams, moments, and force balance to find unknown forces in truss members EF, DC, and DF.

Truss Member Force Analysis by Sections | 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.

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Truss Member Force Analysis by Sections

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