Questions: Method of Sections for Truss Analysis

Question 1

A section cut passes through three members of a Pratt truss: a top chord, a diagonal, and a bottom chord. You want to find the bottom chord force in a single equation. Where should you take moments?

• A. At the point where the cut crosses the bottom chord
• B. At the support reaction on the left end
• C. At the intersection of the top chord and the diagonal member's lines of action
• D. At the midpoint of the cut panel

Answer: (C)

Taking moments about the intersection of the top chord and diagonal forces means those two unknown forces produce zero moment — their lines of action pass through the moment center. Only the bottom chord force has a moment arm about that point, so the equilibrium equation contains exactly one unknown and can be solved directly. Choosing any other point would leave two or three unknowns in the equation, requiring simultaneous solution.

Question 2

A student needs to find the force in one interior diagonal of a 20-panel Pratt truss. Which method is most efficient?

• A. Method of joints, starting from the left support and working inward joint by joint
• B. Method of sections — cut through the panel containing the diagonal and solve with a moment equation
• C. Calculate all member forces using the full stiffness matrix
• D. Method of joints, starting from the right support to reduce the number of steps

Answer: (B)

The method of sections allows you to isolate any interior member's force directly, without working through all preceding joints. For a single target member deep in a large truss, this eliminates many sequential steps. This is precisely the use case the method of sections was designed for. Joint-by-joint analysis from either support would require solving through many intermediate joints before reaching the target.

Question 3

In the method of sections, a cut through a statically determinate truss must pass through no more than three members, because three equilibrium equations can solve for at most three unknowns.

• T. True
• F. False

Answer: True

True. Three equilibrium equations (ΣFx = 0, ΣFy = 0, ΣM = 0) can solve for at most three unknowns. If the cut exposes more than three unknown member forces, the free body is statically indeterminate and cannot be solved by equilibrium alone. The three-member cut is the key practical constraint on where you can make the section.

Question 4

The method of sections replaces the method of joints and should be used for most truss analysis problems.

• T. True
• F. False

Answer: False

False. The two methods are complementary, not mutually exclusive. The method of sections is efficient for finding forces in a small number of interior members without analyzing the whole truss. The method of joints is preferable when all member forces are needed, or for simple trusses where joint analysis terminates quickly. Engineers routinely combine both: section cuts for key interior members, joint equations to fill in the rest.

Question 5

What is the key strategic choice in applying the method of sections, and how does it eliminate the need to solve simultaneous equations?

Model answer: The key choice is the location of the moment center. By taking moments about the point where two of the three cut member forces intersect (i.e., their lines of action pass through that point), those two forces produce zero moment. Only the third force has a moment arm and appears in the equation — one unknown, one equation, solved directly. Without this strategic choice, all three unknowns appear and simultaneous equations are required.

Any force passing through the moment center contributes zero to the moment equation, effectively eliminating it. Choosing the center to simultaneously eliminate two unknowns transforms a three-equation, three-unknown system into a single equation. This is the core skill: not the section itself, but knowing where to take the moment.