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6.7: Method of Sections

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Mechanical Engineering

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Method of Sections
 
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6.7: Method of Sections

Consider a truss structure, as shown in the figure.

Figure 1

Forces F1 and F2 act at joints B and D, respectively. The method of sections can be employed to determine the forces acting on specific members of the truss, such as EF, DC, and DF. This approach is based on the principle that a truss in equilibrium also has each of its segments in equilibrium.

To calculate the forces acting on these members, a free-body diagram of the truss is considered. The equilibrium equation for moments about joint A can be applied to estimate the support reaction at point E.

Equation 1

A cut is made along a sectional plane that intersects a maximum of three members: EF, DC, and DF. Next, a free-body diagram of the right side of the cut section is drawn, assuming the unknown forces as tensile.

Figure 2

A solution for the force acting on member EF can be obtained by summing moments about joint D.

Equation 2

The unknown inclined forces, FDC and FDF, are resolved into horizontal and vertical components. Applying the equilibrium condition for the forces along the horizontal and vertical directions results in two separate equations.

Equation 3

Equation 4

The forces along members DC and DF can be estimated by solving these simultaneous equations.


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Keywords: Method Of Sections Truss Structure Free-body Diagram Equilibrium Support Reaction Sectional Plane Inclined Forces Simultaneous Equations

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