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

考虑一个由对角杆、竖直杆和水平杆组成的任意桁架结构，该结构固定在墙上。
可以使用截面法来计算作用在构件 CB、GB 和 GH 上的力。
此处，水平杆件和竖直杆件的载荷及其长度均为已知参数。
沿一个与 CB、GB 和 GH 杆件相交的平面进行切割，并绘制右侧截面的受力分析图。
关于点的力矩平衡方程 G 沿方向提供力 CB正号表示构件中的拉力。&#160;
现在，FGB 可通过 BCG 中的斜率三角形表示，而 FGH 可通过 CEG 中的斜率三角形表示。
根据竖向力和水平力的总和，可写出力的平衡方程。
将 FCB 的值代入。&#160; 联立求解力的平衡方程，得到沿 GH 和 GB 杆件的力。
FGH 的负号表示该力为压力，而 FGB 的正号表示拉力。

<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>

截面法：问题求解 ii

假设有一个由对角线、垂直线和水平线所组成的任意桁架结构，这些线条能够固定在墙壁上。如果要计算成员CB、GB和GH上的受力，则可以使用截面法来进行求解。水平线和垂直线的负荷和长度都是已知参数，如图所示。 

<img alt="Figure 1" src="/files/ftp_upload/14287/14287_PT_Fig_1v2.svg" style="text-align: center; height: 350px;"> 

首先，沿着与CB、GB和GH成员相交的平面来进行切割，然后可以绘制处其右侧截面的受力分析图。 

<img alt="Figure 2" src="/files/ftp_upload/14287/14287_PT_Fig_2v2.svg" style="text-align: center; height: 350px;"> 

使用关于G点的力矩平衡方程。 

<img alt="Equation 1" src="/files/ftp_upload/14287/14287_PT_Equation_1v2.svg" style="text-align: center; height: 13px;"> 

可以得出成员CB上的力为4kN，其中的正号表示了该成员受到了拉力。 

现在，可以使用BCG中的斜三角形来表示FCB，并且可以使用CEG中的斜三角形来表示FGH。通过计算出垂直方向和水平方向上力的总和，可以将力的平衡方程写为以下形式： 

<img alt="Equation 2" src="/files/ftp_upload/14287/14287_PT_Equation_2v2.svg" style="text-align: center; height: 15px;"> 

<img alt="Equation 3" src="/files/ftp_upload/14287/14287_PT_Equation_3v2.svg" style="text-align: center; height: 13px;"> 

在替换了FCB的值后，同时也得出了力的平衡方程。FGH的结果为-7.454kN，FGB的结果为3.772kN。FGH的负号表示了该力是压缩力，而FGB的正号则表示该力是拉力。

截面法：问题求解 II

考虑一个由斜向、竖直和水平杆件组成的任意桁架结构，该结构固定于墙体。为计算作用在杆件上的力……

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Method of Sections: Problem Solving II

truss member force analysis by sections

Truss member force analysis by sections finds the forces in selected members of a wall-mounted truss. The structure here includes diagonal, vertical, and horizontal members. The known loads and member lengths are used to solve for the forces in CB, GB, and GH.

A cut is made through members CB, GB, and GH. The right side of the truss is then isolated as a free-body diagram. Next, the moment equilibrium equation is taken about point G. This step gives the force in member CB as 4 kN, and the positive sign shows that CB is in tension.

The force in CB is then written with a slope triangle in triangle BCG. The force in GH is written with a slope triangle in triangle CEG. After that, the sums of vertical and horizontal forces are set equal to zero. The equation for CB is substituted, and the remaining equations are solved at the same time.

The final values are FGH = -7.454 kN and FGB = 3.772 kN. The negative sign for GH means the member is in compression. The positive sign for GB means the member is in tension.

Truss Member Force Analysis by Sections

truss-force-analysis-using-method-of-sections

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Truss Member Force Analysis by Sections

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