Structural Analysis for the FE Exam
Structural analysis is one of the most heavily weighted topics on the FE Civil exam and appears in various forms across other disciplines. It builds directly on statics fundamentals, extending them to analyze the internal forces and deformations of structural members and systems.
Beam Analysis
Beams are structural members that resist loads primarily through bending. Analyzing beams involves finding support reactions, internal shear forces, and internal bending moments.
Types of Beams
- Simply supported beam: Supported by a pin at one end and a roller at the other. The most common beam type on the FE exam.
- Cantilever beam: Fixed at one end and free at the other.
- Overhanging beam: Extends beyond one or both supports.
- Continuous beam: Supported at more than two points (statically indeterminate).
Finding Support Reactions
For statically determinate beams (the most common type on the FE exam), use the three equilibrium equations:
- Sum of horizontal forces = 0
- Sum of vertical forces = 0
- Sum of moments about any point = 0
Choose your moment point strategically. Taking moments about a support eliminates that support's vertical reaction from the equation, making the math simpler.
Shear and Moment Diagrams
Shear and moment diagrams show how internal forces vary along the length of a beam. To construct them:
- Start from the left end of the beam
- At each point, the shear V equals the sum of all forces to the left of that point
- At each point, the moment M equals the sum of moments of all forces to the left
- Concentrated loads cause jumps in the shear diagram
- Distributed loads cause linear (uniform) or curved (varying) changes in shear
- The moment diagram is the integral of the shear diagram
- The maximum moment occurs where shear equals zero or changes sign
Truss Analysis
A truss is a structure composed of members connected at joints (nodes). Each member carries only axial force (tension or compression). Two primary methods are used for truss analysis:
Method of Joints
Isolate each joint and apply equilibrium equations (sum of forces in x = 0, sum of forces in y = 0). Start at a joint with at most two unknown member forces. Solve for the unknowns, then move to the next joint. This method works well when you need to find forces in all or most members.
Method of Sections
Cut through the truss, isolating a section. Apply the three equilibrium equations to find forces in the cut members. This method is efficient when you need the force in a specific member without solving the entire truss. Choose your section cut to pass through no more than three members with unknown forces.
Zero-Force Members
Some truss members carry no force under certain loading conditions. Identifying zero-force members quickly saves time:
- At a joint with only two members and no external load, if the members are not collinear, both are zero-force members.
- At a joint with three members and no external load, if two members are collinear, the third is a zero-force member.
Frame Analysis
Frames differ from trusses in that their members can carry axial forces, shear forces, and bending moments. Analyze frames by:
- Drawing a free body diagram of the entire frame to find external reactions
- Disassembling the frame at connection points
- Drawing free body diagrams of individual members
- Applying equilibrium equations to each member
At pin connections between members, equal and opposite forces act on the connected members (Newton's third law).
Influence Lines
An influence line shows how a specific response (reaction, shear, or moment at a point) varies as a unit load moves across the structure. Key applications:
- Finding the maximum reaction due to moving loads
- Determining critical load positions for maximum shear or moment
- Analyzing bridges and structures subject to traffic loading
Deflection Methods
The reference handbook provides deflection formulas for common beam configurations. For the FE exam, know how to:
- Use standard deflection formulas from the handbook tables
- Apply superposition to combine deflections from multiple loads
- Understand the double-integration method conceptually
Statically Indeterminate Structures
Structures with more unknown reactions than equilibrium equations are statically indeterminate. While the FE exam focuses primarily on determinate structures, you should understand the concept and know basic methods such as:
- Compatibility equations (matching deformations at supports)
- Force method (removing redundant supports and applying compatibility)
Practice Tips for Structural Analysis
- Draw complete free body diagrams for every problem
- Practice constructing shear and moment diagrams until the process is automatic
- Use method of sections whenever you need only one or two member forces in a truss
- Know the standard beam deflection formulas in the reference handbook
- Practice identifying zero-force members quickly
Structural analysis is a topic that rewards systematic, methodical work. Rushing through free body diagrams or skipping steps in equilibrium calculations leads to errors. Take the time to set up each problem correctly, and the solution will follow.