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

Considera una struttura a traliccio. Le forze F1 e F2 agiscono nei punti B e D.
Il metodo delle sezioni viene utilizzato per determinare le forze che agiscono su alcuni membri di un traliccio. Si basa sul principio che un traliccio in equilibrio ha ciascuno dei suoi segmenti in equilibrio.
Un diagramma a corpo libero della trave reticolare è considerato per calcolare le forze agenti sull'asta EF, DC e DF.
L'equazione di equilibrio per i momenti intorno al punto A può essere utilizzata per calcolare la reazione vincolare nel punto E.
A questo punto, viene eseguito un taglio lungo un piano di sezione che interseca un massimo di tre aste.
Viene disegnato un diagramma a corpo libero della sezione, assumendo che le forze incognite siano di trazione.
Sommando i momenti intorno a D si ottiene una soluzione per la forza che agisce su EF.
Le forze inclinate incognite vengono risolte nelle componenti orizzontale e verticale.
La condizione di equilibrio per le forze applicate lungo le direzioni orizzontale e verticale risulta in due equazioni.
Risolvendo le equazioni simultanee, è possibile calcolare la forza lungo DC e DF.

<ol>
	<li>R. C., Hibbeler Engineering Mechanics Statics, Pearson. pp. 291-293</li>
	<li>F.P. Beer, E.R. Johnston, D.F. Mazurek, P.J. Cornwell, B.P. Self, Meccanica vettoriale per ingegneri Statica e dinamica Ingegneria meccanica Statica, Mc Graw-Hill Education. Pagine 217</li>
</ol>

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metodo delle sezioni

Considera una struttura a capriata, come mostrato nella figura.

<img alt="Figure 1" src="/files/ftp_upload/14285/14285_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" />

Forze F1 e F2 agiscono rispettivamente sui giunti B e D. Può essere utilizzato il metodo delle sezioni per determinare le forze che agiscono su membri specifici della trave, come EF, DC e DF. Questo approccio si basa sul principio che una trave in equilibrio, ha anche ciascuno dei suoi segmenti in equilibrio.

Per calcolare le forze che agiscono su questi membri, viene considerato un diagramma di corpo libero della trave. L'equazione di equilibrio per i momenti sul giunto A, può essere applicata per stimare la reazione di supporto nel punto E.

<img alt="Equation 1" src="/files/ftp_upload/14285/14285_PT_Equation_1v2.svg" style="text-align: center; height: 13px;" />

Viene effettuato un taglio lungo un piano di sezione che interseca un massimo di tre membri: EF, DC e DF. Successivamente, viene disegnato un diagramma di corpo libero del lato destro della sezione tagliata, assumendo le forze sconosciute come tensioni.

<img alt="Figure 2" src="/files/ftp_upload/14285/14285_PT_Fig_2v2.svg" style="text-align: center; height: 350px;" />

Una soluzione per la forza che agisce sul membro EF, può essere ottenuta sommando i momenti sul giunto D.

<img alt="Equation 2" src="/files/ftp_upload/14285/14285_PT_Equation_2v2.svg" style="text-align: center; height: 13px;" />

Le forze inclinate sconosciute, FDC e FDF, vengono risolte in componenti orizzontali e verticali. Applicando la condizione di equilibrio per le forze lungo le direzioni orizzontale e verticale, si ottengono due equazioni separate.

<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;" />

Le forze lungo i membri DC e DF, possono essere stimate risolvendo queste equazioni simultanee.

Metodo delle sezioni

Si consideri una struttura a traliccio, come mostrato nella figura.

Le forze F1 e F2 agiscono rispettivamente in corrispondenza delle articolazioni B e D. Il metodo delle sezioni può essere impiegato per ...

Education

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Mechanical Engineering

Ingegneria Meccanica

Unit 1

Unità 1

Structural Analysis

Analisi Strutturale

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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.

mechanical engineering

Truss Member Force Analysis by Sections

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