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

Rozważ konstrukcję kratownicy. Siły F1 i F2 działają w punktach B i D.
Metoda przekrojów służy do określania sił działających na kilka elementów kratownicy. Opiera się na zasadzie, że kratownica w równowadze ma każdy ze swoich segmentów w równowadze.
Wykres swobodnego ciała kratownicy jest brany pod uwagę w celu obliczenia sił działających na pręt EF, DC i DF.
Równanie równowagi dla momentów wokół punktu A można wykorzystać do obliczenia reakcji podparcia w punkcie E.
Teraz cięcie jest wykonywane wzdłuż płaszczyzny przekroju przecinającej maksymalnie trzy pręty.
Rysowany jest diagram swobodnego ciała przekroju, przy założeniu nieznanych sił rozciągających.
Sumowanie momentów wokół D daje rozwiązanie dla siły działającej na EF.
Nieznane nachylone siły są rozdzielane na składowe poziome i pionowe.
Warunek równowagi dla sił przyłożonych wzdłuż kierunku poziomego i pionowego daje wynik dwóch równań.
Rozwiązując równania jednoczesne, można obliczyć siłę wzdłuż DC i DF.

<ol>
	<li>R. C., Hibbeler Inżynieria Mechanika Statyka, Pearson. Str. 291-293</li>
	<li>F.P. Beer, E.R. Johnston, D.F. Mazurek, P.J. Cornwell, B.P. Self, Mechanika wektorowa dla inżynierów, statyka i dynamika, mechanika inżynierska, Edukacja Mc Graw-Hill. Str. 217</li>
</ol>

metoda przekrojów

Rozważ strukturę kratownicową, jak pokazano na rysunku.

<img alt="Figure 1" src="/files/ftp_upload/14285/14285_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" />

Siły F1 i F2 działają na węzły B i D, odpowiednio. Metoda przekrojów może być używana do wyznaczania sił działających na konkretne elementy kratownicy, takie jak EF, DC i DF. To podejście opiera się na zasadzie, że kratownica w równowadze ma również każdy ze swoich segmentów w równowadze.

Aby obliczyć siły działające na te elementy, rozważane jest diagram ciała swobodnego kratownicy. Równanie równowagi dla momentów względem węzła A może być stosowane do oszacowania reakcji podparcia w punkcie E.

<img alt="Equation 1" src="/files/ftp_upload/14285/14285_PT_Equation_1v2.svg" style="text-align: center; height: 13px;" />

Wykonywane jest cięcie wzdłuż płaszczyzny przekroju, która przekształca się na trzy elementy: EF, DC i DF. Następnie rysowany jest diagram swobodnego ciała prawej strony przekroju cięcia, przyjmując, że nieznane siły działają jako siły rozciągające.

<img alt="Figure 2" src="/files/ftp_upload/14285/14285_PT_Fig_2v2.svg" style="text-align: center; height: 350px;" />

Rozwiązanie dla siły działającej na element EF można otrzymać, sumując momenty względem węzła D.

<img alt="Equation 2" src="/files/ftp_upload/14285/14285_PT_Equation_2v2.svg" style="text-align: center; height: 13px;" />

Nieznane siły pochylone, FDCDC i FDF, są rozkładane na składowe poziome i pionowe. Zastosowanie warunku równowagi dla sił w kierunkach poziomych i pionowych prowadzi do dwóch oddzielnych równań.

<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;" />

Siły wzdłuż elementów DC i DF można oszacować, rozwiązując te równania jednocześnie.

Metoda przekrojów

Rozważmy konstrukcję kratownicy, jak pokazano na rysunku.

Siły F1 i F2 działają odpowiednio na stawach B i D. Metodę przekrojów można zastosować do ...

Education

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Mechanical Engineering

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Unit 1

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Structural Analysis

Analiza strukturalna

KEY TERMS AND CONCEPTS

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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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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...

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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.

mechanical engineering

Truss Member Force Analysis by Sections

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