7 Free Body Diagram Mistakes That Cost You Points
The free body diagram (FBD) is the foundation of every statics, dynamics, and structural analysis problem. Get the FBD wrong, and the entire solution falls apart. After reviewing thousands of student solutions, these are the seven most common FBD mistakes that lead to wrong answers on the FE exam.
Mistake 1: Forgetting a Force
The most basic mistake is leaving a force off the diagram. Common forces that get forgotten include:
- Weight (self-weight): Unless the problem states to neglect the weight of the member, include it as a concentrated force at the centroid.
- Friction forces: When surfaces are in contact and there is potential for sliding, friction forces exist.
- Normal forces: At every contact point with another surface, a normal force exists perpendicular to the contact surface.
- Internal forces at cuts: When you cut through a member to analyze a section, include all internal forces (axial, shear, moment) at the cut.
Solution: After drawing your FBD, systematically check every contact point, support, and applied load. Ask yourself: "Is there any physical interaction I have not shown?"
Mistake 2: Wrong Direction for Support Reactions
Different support types provide different reactions. Common errors include:
- Showing a moment reaction at a pin support (pins allow rotation, so they have no moment reaction)
- Showing a horizontal reaction at a roller (rollers provide reaction perpendicular to the rolling surface only)
- Forgetting the moment reaction at a fixed support
- Showing a compression force in a cable (cables can only pull, never push)
Solution: Memorize the reactions provided by each support type: pin (two force reactions), roller (one force reaction), fixed (two forces and one moment), cable (one tension force along the cable).
Mistake 3: Including Internal Forces as External Forces
When drawing an FBD of the entire structure, only external forces appear. Internal forces (forces between connected members of the same structure) cancel out and should not be shown. This mistake typically happens when:
- Showing forces at internal pins of a multi-member structure on the overall FBD
- Including member-to-member forces on the whole-structure diagram
Solution: Internal forces appear only when you isolate a portion of the structure (when you "cut" through the structure). On the complete structure FBD, show only external loads and support reactions.
Mistake 4: Wrong Distributed Load Representation
When converting distributed loads to equivalent concentrated forces for analysis:
- The resultant force of a uniform load (w per unit length over length L) is w*L, acting at the midpoint of the loaded region.
- The resultant force of a triangular load is (1/2)*w_max*L, acting at one-third of the length from the maximum end.
- A common error is placing the resultant of a triangular load at the midpoint instead of at the one-third point.
Solution: For uniform loads, the resultant acts at the center. For triangular loads, the resultant acts at one-third from the heavy end. Sketch the load shape to verify your placement.
Mistake 5: Assuming Force Directions
Some students try to guess the correct direction of unknown forces before solving. If they guess wrong, negative values appear in the solution, which can cause confusion and errors in subsequent calculations.
Solution: Assume a direction for each unknown force (positive x, positive y, or your chosen convention). If the solution gives a negative value, the actual direction is opposite to your assumption. The magnitude is still correct; just reverse the direction. Being consistent with your assumed directions is more important than guessing correctly.
Mistake 6: Not Isolating the Correct Body
When analyzing a specific member or section of a structure, you must completely isolate it from everything else. Common errors include:
- Including forces that act on other members, not the isolated body
- Forgetting to "cut" through all connections when isolating a section
- Confusing the forces acting on the body with the forces the body exerts on other things
Solution: Draw a clear boundary around the body you are analyzing. Everything outside that boundary is removed and replaced by the forces it exerts on the isolated body. Be meticulous about what is inside and outside your boundary.
Mistake 7: Ignoring the Third Dimension
Most FE exam problems are two-dimensional, but some involve 3D effects or out-of-plane loading. A less obvious version of this mistake is forgetting that forces and moments are vectors with both magnitude and direction. When resolving forces into components:
- Use trigonometry carefully; mixing up sine and cosine is easy when angles are measured differently.
- Verify that your components add up to the original force magnitude using the Pythagorean theorem.
- When taking moments, include the moment arm (perpendicular distance) correctly, not just the force times any distance.
Solution: Always use the perpendicular distance (moment arm) when calculating moments. If the geometry makes this difficult, resolve the force into components and calculate the moment of each component separately (Varignon's theorem).
How to Build Good FBD Habits
- Draw the FBD before writing any equations. Never start with equations and try to figure out the FBD later.
- Use a checklist. After drawing the FBD, check: (1) Are all external forces shown? (2) Are support reactions correct for the support type? (3) Are dimensions and angles labeled? (4) Are internal forces excluded from the overall FBD?
- Practice with diverse problems. The more different configurations you draw FBDs for, the better your intuition becomes.
- Compare with solutions. When practicing, compare your FBD with the solution's FBD before proceeding with calculations. Catching FBD errors early saves time.
A correct free body diagram is worth more than any formula on the FE exam. If your FBD is right, the rest is just algebra. If it is wrong, no amount of calculation can save you. Take the time to draw it carefully and verify it before proceeding.