What fundamentally distinguishes a multi-force member (in a frame) from a two-force member (in a truss)?
AMulti-force members are always longer and carry more load than two-force members
BTwo-force members are straight; multi-force members can be curved or angled
CTwo-force members carry only axial force along their length; multi-force members also carry forces not along their axis, generating moments at connections
DMulti-force members must be made of steel; two-force members can be made of any material
The defining distinction is mechanical, not geometric. A two-force member has forces applied at exactly two points and both forces must be equal, opposite, and collinear — so only axial tension or compression is transmitted. A multi-force member has forces or moments applied at three or more points, or has distributed loads, meaning the forces at connections can be in any direction and generate bending moments. This is why truss analysis is simpler (method of joints uses only force equations) while frame analysis requires treating each member as a full rigid body with its own moment equation.
Question 2 Multiple Choice
You isolate member AB in a frame and find that at pin C (shared with member CD), member CD exerts a force of (6, −4) N on member AB. What force does member AB exert on member CD at pin C?
A(6, −4) N — the same force, because both members must carry the same load at the pin
B(−6, 4) N — equal in magnitude but opposite in direction, by Newton's third law
C(0, 0) N — internal forces cancel each other out at the pin
DCannot be determined without knowing the external loads on the full structure
Newton's third law applies directly at every pin connection: if member CD exerts force (6, −4) N on member AB, then member AB exerts the equal and opposite force (−6, 4) N on member CD. This is not optional — it is a fundamental law. When drawing the FBD of each member, you must explicitly show these action-reaction pairs with opposite signs. Forgetting to flip the sign is the single most common error in frame analysis and produces equations that are internally inconsistent or give wrong force values.
Question 3 True / False
To analyze a frame, it is sufficient to draw a free-body diagram of the entire structure and apply equilibrium equations — you do not need to isolate individual members.
TTrue
FFalse
Answer: False
The whole-structure FBD is only the first step, and it can only find the external support reactions. The internal pin forces between members — the forces members exert on each other at connections — are invisible in a whole-structure FBD because they are internal to the system and cancel out. To find these internal forces, you must disassemble the structure and draw a separate FBD for each member. This is the essential and new step in frame analysis that goes beyond single-body equilibrium.
Question 4 True / False
In a machine, the mechanical advantage (ratio of output force to input force) depends entirely on the geometry of the members — specifically the moment arms — not on the material or cross-sectional area of the members.
TTrue
FFalse
Answer: True
Mechanical advantage is a purely geometric quantity determined by moment arm ratios. By applying moment equilibrium to each member, the input force times its moment arm equals the output force times its moment arm. A machine that amplifies force by a factor of 5 does so because the input moment arm is 5 times longer than the output moment arm — regardless of whether the parts are steel or aluminum, thick or thin. Material properties affect whether the machine will fail under load, but they do not change the mechanical advantage of a working machine.
Question 5 Short Answer
Why must the internal pin force between two connected frame members be shown with opposite signs in the FBD of each member? What physical law requires this?
Think about your answer, then reveal below.
Model answer: Newton's third law requires that for every force exerted by body A on body B, body B exerts an equal and opposite force on body A. At a shared pin, member A pushes member B with some force (Cx, Cy); therefore member B pushes back on member A with (−Cx, −Cy). Each member's FBD must show the force that the other member exerts on it — these forces are opposite in sign because they are an action-reaction pair. If both FBDs showed the same force in the same direction, you would be violating Newton's third law and the resulting equilibrium equations would be inconsistent.
This sign discipline is the core bookkeeping challenge of frame analysis. The pin force components (Cx, Cy) are unknowns you are solving for. Once you solve for them in one member's equations, the values plug into the other member's equations with flipped signs. Getting this right ensures the system of equations is consistent and the solution satisfies equilibrium everywhere in the structure.