Overview
This lecture covers key concepts and problem-solving strategies for the FE Civil exam's structural analysis section, focusing on statically determinate and indeterminate structures, deflection methods, truss analysis, column buckling, and stability.
Structural Analysis Overview
- Structural engineering is divided into analysis (finding forces, moments, deflections) and design (sizing members).
- FE Civil covers statics, mechanics of materials, and structural analysis topics.
- Problems involve beams, columns, trusses, and frames—often building from statics concepts.
Truss Analysis & Method of Sections
- Truss problems often ignore self-weight and focus on applied loads.
- Use the method of sections to solve for member forces by cutting through the truss and using equilibrium equations.
- Always assume members are in tension; a negative value indicates compression.
- Sum moments about a point where lines of action intersect to simplify calculations.
Frame and Beam Analysis
- For frames with internal pins, separate members and draw free-body diagrams to analyze reactions.
- Equal and opposite forces appear on either side of a pin.
- Use equations of equilibrium to solve for reactions and internal moments.
- For uniformly loaded simply supported beams, reactions are wL/2 at each support.
Deflections in Structures
- Deflections in beams/trusses can be found using formulas in the FE Reference Handbook.
- For cantilever beams under uniform load: δ_max = 7wL⁴ / 384EI.
- Use consistent units and convert as needed (e.g., feet to inches).
- For trusses, the principle of virtual work uses δ = Σ(F_i f_i L_i/AE).
- Zero-force members do not contribute to deflection calculations.
Column Buckling & Euler's Formula
- Euler’s critical buckling load: P_cr = π²EI / (KL)², where K is the effective length factor.
- Identify strong/weak axes and corresponding moments of inertia (I_x or I_y).
- The axis with the lower buckling load controls failure.
Structural Determinacy and Stability
- Stable, statically determinate structures: reactions = 3 × (number of members).
- More reactions than 3m: statically indeterminate; fewer: unstable.
- Draw all reaction forces and check stability by considering possible movement.
Stability Analysis (e.g., Dams)
- Check sliding: horizontal water force must be less than base friction.
- Check overturning: resisting moments from the structure's weight must exceed overturning moments from water pressure.
Statically Indeterminate Structures
- Use superposition and compatibility (set deflections to zero at supports) to solve for unknown support reactions.
- Fixed-end moment tables and beam deflection formulas assist in analysis.
- For multi-support beams, symmetry and equilibrium help distribute reactions.
Key Terms & Definitions
- Statically Determinate — Structure solvable using only equilibrium equations.
- Statically Indeterminate — Structure with more unknowns than equilibrium equations.
- Method of Sections — Technique to solve truss member forces by "cutting" a section.
- Zero Force Member — Truss element carrying no force under given loading.
- Principle of Virtual Work — Method using virtual (unit) loads to compute deflections.
- Effective Length Factor (K) — Multiplier adjusting column length for buckling calculations.
- Radius of Gyration (r) — √(I/A), used in slenderness ratio for columns.
Action Items / Next Steps
- Review the FE Reference Handbook: locate key beam, truss, and column formulas.
- Practice drawing free-body diagrams for complex frames and trusses.
- Complete sample problems on deflections, determinacy, and column buckling.
- Prepare for next week: structural design (concrete and steel).