Statics on the FE Exam
Statics is a fundamental topic that appears on nearly every FE exam discipline. It typically accounts for 7 to 11% of the exam and serves as the foundation for mechanics of materials, structural analysis, and other advanced topics. A strong understanding of statics principles is essential for FE exam success.
Force Systems and Equilibrium
The most important concept in statics is equilibrium. A body is in static equilibrium when the sum of all forces and the sum of all moments acting on it equal zero. For a two-dimensional system, this gives three equilibrium equations:
- Sum of forces in the x-direction equals zero
- Sum of forces in the y-direction equals zero
- Sum of moments about any point equals zero
For three-dimensional systems, you have six equilibrium equations (three force equations and three moment equations). Most FE exam problems involve two-dimensional systems, but be prepared for occasional 3D problems.
Free Body Diagrams
Drawing accurate free body diagrams (FBDs) is the most critical skill in statics. Every statics problem should begin with a clear FBD showing all external forces, support reactions, and dimensions. Common errors include forgetting reaction components at supports, incorrectly identifying support types, and missing distributed loads.
Know the reactions at different support types: a pin support provides two force reactions (horizontal and vertical), a roller provides one force reaction (perpendicular to the surface), and a fixed support provides two force reactions plus a moment reaction.
Trusses
Truss analysis problems appear frequently on the FE exam. Know both the method of joints and the method of sections:
Method of Joints
Analyze one joint at a time, applying equilibrium equations at each joint. This method works well when you need to find forces in all members or in members near the supports. Start at a joint with at most two unknown member forces.
Method of Sections
Cut through the truss and analyze one section as a free body. This method is efficient when you need to find the force in a specific member deep within the truss. The cut should pass through no more than three members with unknown forces.
Remember to identify zero-force members before starting your analysis. A member is a zero-force member if it connects two collinear members at an unloaded joint, or if it is one of two non-collinear members at an unloaded joint.
Centroids and Moments of Inertia
Centroid calculations are essential for beam analysis and other structural problems. For composite areas, calculate the centroid using the weighted average formula: the total first moment of area divided by the total area. Break complex shapes into simple geometric shapes (rectangles, triangles, circles) and use tabulated centroid locations.
Moments of inertia (second moments of area) determine a cross-section's resistance to bending and buckling. Know how to calculate moments of inertia for basic shapes and use the parallel axis theorem to transfer moments of inertia to different axes. The parallel axis theorem states that the moment of inertia about any axis equals the moment of inertia about the centroidal axis plus the area times the square of the distance between the axes.
Friction
Static friction problems involve determining whether a body will slide or tip under applied loads. The maximum static friction force equals the coefficient of static friction times the normal force. Know how to solve wedge problems, belt friction problems, and inclined plane problems using equilibrium equations combined with friction relationships.
Problem-Solving Tips
Always start with a free body diagram. Choose your coordinate system wisely to minimize the number of unknown components in each equation. When solving for support reactions, take moments about a point where multiple unknown forces intersect to eliminate those unknowns from the equation. Check your answers by verifying that all equilibrium equations are satisfied.