Statics and Dynamics Quiz: Trusses Method Of Sections

What this quiz covers

This quiz focuses on Trusses Method Of Sections, giving you a quick way to practice the rules, question types, and explanations that matter most for Statics and Dynamics.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. The analyst must use the perpendicular distance from the moment center to the line of action of the top chord force (not the vertical truss height), because if the top chord is horizontal its moment arm equals the vertical distance from the moment center to the top chord's line of action—which is the same as the truss height only if the moment center lies directly below the top chord.
2. The analyst must resolve the bottom chord force into horizontal and vertical components before writing the moment equation, because the sloped bottom chord's line of action does not pass through the same point as the vertical chord force does in a flat-chord truss, shifting the effective moment center unpredictably.
3. The analyst must account for the fact that the sloped bottom chord introduces a vertical component of force that alters the external shear that the diagonal must carry, so the diagonal force cannot be found from vertical equilibrium alone without first knowing the bottom chord force.
4. The analyst must locate the actual geometric intersection of the diagonal's and the bottom chord's lines of action (which may lie outside the truss panel) to use as the moment center, and the perpendicular distance from this point to the horizontal top chord is the correct moment arm—which differs from the nominal truss height of 4 m unless the moment center lies at the panel joint. (correct answer)

Question 2

1. The force in the remaining member can always be determined uniquely from a single equilibrium equation, because the two zero-force members contribute nothing to any equation and the remaining member is always the only unknown regardless of its geometric orientation relative to the applied loads.
2. The force in the remaining member can be determined only if its line of action is not parallel to the resultant of all external forces on the free-body; if parallel, the force-sum equation along that direction is trivially satisfied and the moment equation must be used instead, though it too may be trivial in degenerate cases.
3. The force in the remaining member cannot be determined from the equilibrium equations alone, because having only one unknown in three equations makes the system over-determined; the analyst must verify consistency across all three equations, and any contradiction signals that the zero-force assumption for the other two members must be re-examined.
4. The force in the remaining member can be determined from any single non-trivial equilibrium equation, since with only one unknown the three equations are consistent by construction for a statically determinate truss. The one caveat is that the chosen equation must have a nonzero coefficient for the unknown — a condition that fails only in the rare geometric case where the member's line of action is concurrent with all external forces on the free-body, making every moment equation trivial. (correct answer)

Question 3

1. Linear dependence arises because the three linking members are all parallel; two parallel members contribute identical force directions, reducing the rank of the equilibrium matrix. The remedy is to cut a different set of members that are not all parallel so that the three equilibrium equations become independent.
2. Linear dependence arises because the three linking members are concurrent (their lines of action all pass through one point), which causes the moment equation about that point to degenerate. The remedy is to take moments about two different points and combine the resulting equations with the force-sum equations to recover three independent relations. (correct answer)
3. Linear dependence of the three equilibrium equations is impossible for a statically determinate planar truss cut by exactly three members; the engineer must have made an algebra error. Re-deriving the equations from scratch will resolve the apparent dependence without changing the approach.
4. Linear dependence arises because the free-body diagram has been drawn with an incorrect external loading; the distributed reaction at the cut face must be resolved into its components before the equilibrium equations become independent, and doing so will yield a full-rank system.

Question 4

1. The net shear is $+62.5\text{ kN}$ upward. The left reaction is 100 kN, each end joint carries 20 kN, and each interior joint carries 40 kN. After subtracting the loads at joints 0 and 1, the shear is $100 - 20 - 40 = 40\text{ kN}$, but a partial-panel correction factor raises this to 62.5 kN.
2. The net shear is $+40\text{ kN}$ upward. The total load is 200 kN, giving reactions of 100 kN each. Converting the UDL: end joints 0 and 5 each receive $10 \times 4/2 = 20\text{ kN}$, and interior joints 1–4 each receive $10 \times 4 = 40\text{ kN}$. The left free-body (cut through panel 2) contains joints 0 and 1, so the net shear is $100 - 20 - 40 = 40\text{ kN}$. (correct answer)
3. The net shear is $+60\text{ kN}$ upward. The left reaction is 100 kN. Since the end joint at the support transfers its load directly into the reaction, the 20 kN at joint 0 does not appear as a separate force on the free-body; only the 40 kN at joint 1 is subtracted, giving $100 - 40 = 60\text{ kN}$.
4. The net shear is $+20\text{ kN}$ upward. The left reaction is 100 kN. The cut between panels 2 and 3 places joints 0, 1, and 2 inside the left free-body, so all three joint loads must be subtracted: $100 - 20 - 40 - 20 = 20\text{ kN}$.