You need to find the force in a single diagonal member near the center of a large Pratt truss. Which approach is more efficient?
AMethod of joints starting from a support — it's more systematic and less error-prone
BMethod of sections — pass a cut through the target member and at most two others, then apply equilibrium to one half
CBoth methods require the same number of steps for a single target member
DMethod of joints is faster because each joint uses only two equilibrium equations
The method of sections is specifically designed for this situation: finding a specific member force without analyzing every joint. A cut through the target member and two others produces a free body that can be solved with three equilibrium equations. The method of joints, by contrast, requires solving every joint between the support and the target member — potentially a dozen or more joints. The method of sections lets you jump directly to the answer.
Question 2 Multiple Choice
A cutting plane exposes two horizontal chord members (upper and lower) and one diagonal member. You want to find the force in the diagonal. Which equilibrium equation isolates it most directly?
AΣFx = 0 — the diagonal's horizontal component is larger than those of the chord members
BΣFy = 0 — the horizontal chord members have no vertical components, so only the diagonal appears
CΣM = 0 about a point on the diagonal — this eliminates the diagonal force from the equation
DSolve all three equations simultaneously; there is no shortcut for this configuration
The two horizontal chord members lie along the x-axis, so they contribute zero to a vertical force balance. ΣFy = 0 therefore contains only the diagonal member's vertical component (plus any external vertical loads), isolating the diagonal force in a single equation. Taking moments about the intersection of the two chords would also work if they intersect, but ΣFy = 0 is more direct here. Option C is backwards — you'd take moments about a point on the diagonal's line of action to eliminate the diagonal, not to find it.
Question 3 True / False
Support reactions must be determined before applying the method of sections.
TTrue
FFalse
Answer: True
True. The free body created by the cut includes all external forces on that half of the truss, including support reactions. If the reactions are unknown, you cannot write a complete equilibrium equation — the system will have more unknowns than equations. Solving the entire truss for support reactions using the global free body is always the first step, regardless of which internal analysis method follows.
Question 4 True / False
The method of sections can be applied to a cutting plane that exposes four unknown member forces, provided you use most three equilibrium equations.
TTrue
FFalse
Answer: False
False. A 2D equilibrium problem yields exactly three independent equations (ΣFx = 0, ΣFy = 0, ΣM = 0). With four unknowns and three equations, the system is underdetermined — there is no unique solution. The cut must expose at most three unknown member forces. If your cut exposes four unknowns, you must redesign the cut: try a different cutting plane orientation that passes through fewer members.
Question 5 Short Answer
Why does taking moments about the intersection point of two unknown member forces isolate the third unknown in a single equation?
Think about your answer, then reveal below.
Model answer: The moment of a force about a point equals the force magnitude times its perpendicular distance (moment arm) from that point. If two unknown forces pass through the chosen moment point, their moment arms are zero — they produce no moment about that point regardless of their magnitude. The ΣM = 0 equation about that point therefore contains only the third unknown force, which can be solved directly without first finding the other two. This is the core strategic advantage of the method of sections over a brute-force simultaneous system.
Concretely: for a truss with two chord members that converge at a panel point, taking moments about that panel point eliminates both chord forces from the moment equation, leaving only the diagonal member force. This reduces a 3×3 system to a 1×1 equation — the difference between a single calculation and a multi-step solve. Choosing the best moment point is the skill that separates efficient sections analysis from laborious algebra.