Structural Analysis on the FE Civil Exam
Structural engineering is one of the highest-weighted content areas on the FE Civil exam, accounting for 9 to 14% of the questions. Structural analysis involves determining internal forces (axial, shear, and moment) in beams, frames, and trusses, as well as calculating deflections and understanding load paths.
Determinacy and Stability
Before analyzing a structure, determine whether it is statically determinate, statically indeterminate, or unstable. For a 2D structure, compare the number of unknown reactions plus internal unknowns to the number of available equilibrium equations. If the number of unknowns exceeds the number of equations, the structure is statically indeterminate and requires additional compatibility equations for solution.
A structure is unstable if the supports do not provide sufficient constraints or if the support reactions are concurrent or parallel. Recognizing instability quickly on the exam saves time by eliminating the need for detailed analysis.
Shear and Moment Diagrams
Constructing shear and bending moment diagrams is a fundamental skill tested extensively on the FE Civil exam. Key relationships:
- The slope of the shear diagram equals the negative of the distributed load intensity
- The slope of the moment diagram equals the shear value
- A concentrated force causes a jump in the shear diagram
- A concentrated moment causes a jump in the moment diagram
- The change in shear between two points equals the negative of the area under the load diagram between those points
- The change in moment between two points equals the area under the shear diagram between those points
Practice drawing shear and moment diagrams for common loading cases: simply supported beams with concentrated loads, uniformly distributed loads, triangularly distributed loads, and overhanging beams. Know the shapes of the diagrams for each loading type.
Influence Lines
Influence lines show how a response quantity (reaction, shear, or moment at a specific point) varies as a unit load moves across the structure. For statically determinate structures, influence lines are composed of straight-line segments.
To construct an influence line, place a unit load at various positions along the beam and calculate the response quantity for each position. Alternatively, use the Muller-Breslau principle, which states that the influence line for a response quantity has the same shape as the deflected shape of the structure when a small deformation is introduced corresponding to that response quantity.
Influence lines are used to determine the critical position of moving loads (such as truck loads on a bridge) that produce the maximum response at a point of interest.
Frame Analysis
Frames differ from trusses in that frame members carry axial forces, shear forces, and bending moments. Analyze frames by first finding support reactions using equilibrium of the entire structure, then cutting through members and analyzing individual sections.
For portal frames and rigid frames, draw free body diagrams of individual members and apply equilibrium at each joint. Remember that at a rigid connection, the moment is transmitted between members.
Deflection Methods
Several methods for calculating deflections may appear on the FE exam:
Double Integration Method
Integrate the moment equation twice to obtain the deflection equation. Apply boundary conditions to solve for the constants of integration. This method is straightforward but can be tedious for complex loading.
Moment-Area Method
Two theorems relate the tangent lines and vertical deviations to the area under the M/EI diagram. These theorems are particularly useful for beams with simple M/EI diagrams.
Virtual Work Method
Apply a virtual unit load at the point where deflection is desired. Calculate the real and virtual internal forces, then integrate the product of real and virtual forces divided by EI (for bending) or AE (for axial) to find the deflection.
Load Combinations
Structural design requires considering multiple load types simultaneously. The FE exam may reference load combinations from building codes, including dead load (D), live load (L), wind load (W), earthquake load (E), and snow load (S). Know the basic concept that structures must be designed for the most critical combination of these loads.
Study Approach
Practice is essential for structural analysis. Work through many problems involving shear and moment diagram construction, truss analysis, and deflection calculations. Time yourself to build speed, as structural analysis problems on the FE exam can be time-consuming if you are not efficient with your methods.