At a truss joint with no external load, exactly two members meet at a non-collinear angle. What can you immediately conclude by inspection?
ABoth members are in compression — joints without external loads always develop compressive forces
BBoth members carry zero force — the zero-force member rule for two non-collinear members at an unloaded joint
COne member is in tension and one in compression, balancing each other
DNothing can be concluded without solving the full equilibrium equations
This is the first zero-force member rule: if exactly two non-collinear members meet at a joint with no external load applied, both members must carry zero force. The reasoning comes directly from equilibrium: ΣFx = 0 and ΣFy = 0 at the joint. If the two members are not collinear (their axes are not along the same line), the only solution satisfying both equations simultaneously is that both forces equal zero. Identifying this by inspection eliminates those unknowns immediately, simplifying the subsequent joint-by-joint analysis considerably.
Question 2 Multiple Choice
You assume a truss member is in tension (positive) and solve the equilibrium equations at a joint. The algebra gives a result of −15 kN. What does this mean?
AYou made an arithmetic error — member forces cannot be negative if you assumed tension
BThe member carries 15 kN in compression — the negative sign indicates your tension assumption was wrong
CThe member is a zero-force member because the magnitude is indeterminate
DYou should re-solve the joint using a compression assumption and the answer will be +15 kN
A negative result is not an error — it is meaningful information. The standard method assumes all unknown member forces are in tension (pulling away from the joint). A positive result confirms tension; a negative result means the member is actually in compression, with magnitude equal to the absolute value of the result. The member carries 15 kN in compression. You do not need to re-solve; you simply report the member as −15 kN (or 15 kN compression). Identifying compression members is practically important: long, slender compression members can buckle at loads well below their yield strength, a failure mode tension members don't face.
Question 3 True / False
Truss members resist only axial (tension or compression) forces, not bending moments or shear forces.
TTrue
FFalse
Answer: True
This is the defining idealization that makes truss analysis tractable. A truss member is modeled as a two-force member: pinned at both ends, loaded only at the pins. Because the pin cannot transmit a moment, and because the member is in static equilibrium, the forces at each end must be equal, opposite, and directed along the member's axis. No transverse loads are applied between pins, so no bending or shear develops. This idealization reduces each member to a single scalar unknown (the axial force, positive = tension, negative = compression), which is what allows the method of joints to work with just ΣFx = 0 and ΣFy = 0.
Question 4 True / False
If you get a negative member force when solving by method of joints, you should re-do the calculation assuming compression.
TTrue
FFalse
Answer: False
A negative member force is not an error requiring re-calculation — it is the answer. The method of joints assumes all unknown forces are tension (positive). If the algebra produces a negative value, the result tells you directly that the member is in compression, with magnitude equal to the absolute value. Re-doing the calculation with a compression assumption would yield a positive number of the same magnitude, but you gain no new information. The sign convention is consistent throughout: report positive values as tension, negative values as compression.
Question 5 Short Answer
Why should zero-force members be identified before beginning joint-by-joint analysis, and what is the practical consequence of missing them?
Think about your answer, then reveal below.
Model answer: Zero-force members are identified by inspection using two geometric rules: (1) two non-collinear members at an unloaded joint both carry zero force; (2) three members at an unloaded joint where two are collinear means the third carries zero force. Identifying them first eliminates unknowns from the analysis — a joint that appears to have three unknowns may reduce to two once a zero-force member is identified, making it immediately solvable. Missing zero-force members forces you to start at a more complex joint or solve a larger system of equations simultaneously, which is more error-prone and time-consuming. In design, recognizing zero-force members also identifies where material could be eliminated without loss of structural function.
Zero-force members seem counterintuitive — why does a structural member carry no load? They appear in trusses either to provide rigidity for load cases other than the one being analyzed, or to brace compression members against buckling, or simply because the geometry required them. They are real members doing real structural work — just not carrying axial load in the specific loading case under analysis. This is why they are left in the design but can be skipped analytically.