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

Rozważmy dowolną konstrukcję kratownicy składającą się z ukośnych, pionowych i poziomych prętów przymocowanych do ściany.
Metodę przekrojów można wykorzystać do obliczenia siły działającej na pręty CB, GB i GH.
W tym przypadku znanymi parametrami są obciążenia i długości prętów poziomych i pionowych.
Wykonuje się cięcie wzdłuż płaszczyzny przecinającej pręty CB, GB i GH i rysuje się schemat swobodnego ciała sekcji prawej strony.
Równanie równowagi momentu wokół punktu G daje siłę wzdłuż CB. Znak dodatni wskazuje na napięcie w członku. 
Teraz FGB można wyrazić za pomocą trójkąta nachylenia w BCG, podczas gdy FGH można wyrazić za pomocą trójkąta nachylenia w CEG.
Biorąc pod uwagę sumę sił pionowych i poziomych, można zapisać równania równowagi sił.
Podstawiana jest wartość FCB. Równania równowagi sił są rozwiązywane jednocześnie, aby uzyskać siłę wzdłuż prętów GH i GB.
Ujemny znak FGH wskazuje, że siła jest ściskająca, podczas gdy dodatni znak FGB wskazuje siłę rozciągającą.

<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: rozwiązywanie problemów ii

Rozważ abstrakcyjną konstrukcję kratownicy składającą się z przekątnych, pionowych i poziomych elementów przymocowanych do ściany. Aby obliczyć siły działające na elementy CB, GB, i GH, można użyć metody przekrojów. Obciążenia i długości elementów poziomych i pionowych są znane, jak pokazano na rysunku.

<img alt="Figure 1" src="/files/ftp_upload/14287/14287_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" />

Aby rozpocząć, wykonuje się przekrój wzdłuż płaszczyzny przecinającej elementy CB, GB, i GH, a następnie rysuje diagram ciała swobodnego części prawej strony.

<img alt="Figure 2" src="/files/ftp_upload/14287/14287_PT_Fig_2v2.svg" style="text-align: center; height: 350px;" />

Zastosowana jest równowaga momentów wokół punktu G.

<img alt="Equation 1" src="/files/ftp_upload/14287/14287_PT_Equation_1v2.svg" style="text-align: center; height: 13px;" />

Wynik daje siłę wzdłuż elementu CB równą 4 kN, z dodatnim znakiem oznaczającym naciąg w elemencie.

Obecnie moc FCB może być wyrażona przy użyciu trójkąta nachylenia w BCG, podczas gdy FGH może być wyrażone przy użyciu trójkąta nachylenia w CEG. Zważywszy na sumę sił pionowych i poziomych, równania równowagi siły można zapisać następująco:

<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;" />

Wartość FCB jest zastępowana, a równania równowagi siły są rozwiązywane jednocześnie. Wynik daje siłę FGH równą -7,454 kN i siłę FGB równą 3,772 kN. Negatywny znak FGH wskazuje na siłę ściskającą, podczas gdy dodatni znak FGB wskazuje na siłę rozciągającą.

Metoda przekrojów: Rozwiązywanie problemów II

Rozważmy dowolną konstrukcję kratownicy składającą się z ukośnych, pionowych i poziomych prętów przymocowanych do ściany. Aby obliczyć siłę działającą na pręty ...

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Mechanical Engineering

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Unit 1

Jednostka 1

Structural Analysis

Analiza strukturalna

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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 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...

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key terms and concepts

Learn how the method of sections isolates a truss cut, uses moment and force balance, and identifies tension or compression in members CB, GB, and GH.

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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