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

Consider a truss structure. Forces F1 and F2 are acting at points B and D.
The method of sections is used to determine the forces acting on a few members of a truss. It is based on the principle that a truss in equilibrium has each of its segments in equilibrium.
A free-body diagram of the truss is considered to calculate the forces acting on the member EF, DC and DF.
The equilibrium equation for moments about point A can be used to calculate the support reaction at point E.
Now, a cut is made along a sectional plane intersecting a maximum of three members.
A free-body diagram of the section, assuming the unknown forces as tensile, is drawn.
Summing moments about D yields a solution for the force acting on EF.
The unknown inclined forces are resolved into the horizontal and vertical components.
The equilibrium condition for the forces applied along the horizontal and vertical directions results in two equations.
Solving the simultaneous equations, the force along DC and DF can be calculated.

methode van secties

Overweg een vakwerkconstructie, zoals weergegeven in de figuur. <img alt="Figure 1" src="/files/ftp_upload/14285/14285_PT_Fig_1v2.svg" style="text-align: center; height: 350px;"> Forces F1 en F2 werken op de knooppunten B en D. De methode van secties kan worden toegepast om de krachten te bepalen die werken op specifieke onderdelen van het vakwerk, zoals EF, DC en DF. Deze benadering is gebaseerd op het principe dat een vakwerk in evenwicht ieder van zijn segmenten ook in evenwicht heeft. Om de krachten op deze onderdelen te berekenen, wordt een vrije krachtdiagram van het vakwerk overwogen. De evenwichtsvergelijking voor momenten rond het knooppunt A kan worden toegepast om de ondersteuningsreactie bij punt E te schatten. <img alt="Equation 1" src="/files/ftp_upload/14285/14285_PT_Equation_1v2.svg" style="text-align: center; height: 13px;"> Er wordt een snede gemaakt langs een doorsnede die maximaal drie onderdelen doorkruist: EF, DC en DF. Vervolgens wordt een vrije krachtdiagram van de rechterzijde van het doorsnede gedeelte getekend, waarbij de onbekende krachten als trekkrachten worden verondersteld. <img alt="Figure 2" src="/files/ftp_upload/14285/14285_PT_Fig_2v2.svg" style="text-align: center; height: 350px;"> Een oplossing voor de kracht werkend op onderdeel EF kan worden verkregen door momenten rond knooppunt D op te tellen. <img alt="Equation 2" src="/files/ftp_upload/14285/14285_PT_Equation_2v2.svg" style="text-align: center; height: 13px;"> De onbekende schuine krachten, FDC en FDF, worden opgelost in horizontale en verticale componenten. Door de evenwichtsvoorwaarde toe te passen voor de krachten in de horizontale en verticale richtingen, ontstaan er twee aparte vergelijkingen. <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;"> De krachten langs onderdelen DC en DF kunnen worden geschat door deze simultane vergelijkingen op te lossen.

Methode van Secties

Consider a truss structure, as shown in the figure.

Forces F1 and F2 act at joints B and D, respectively. The method of sections can be employed to ...

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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

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Truss Member Force Analysis by Sections

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