Structural Engineering: Analysis and Limit-State Design
Structural Engineering in this examination tests analysis of beams, frames and trusses, limit-state design of reinforced concrete and steel members, and detailing to the codes used in Sri Lankan practice - BS 8110, ACI 318 and increasingly Eurocode 2 with EN 1991 actions, and IS 800 or EC3 for steel.
Analysis
- Determinate structures: three equilibrium equations; draw the SFD and BMD and check that shear is the derivative of moment.
- Indeterminate structures: stiffness or moment distribution; confirm the degree of redundancy before starting.
Limit-state design of reinforced concrete
- BS 8110 ultimate combination is 1.4Gk + 1.6Qk; EC2 uses 1.35Gk + 1.5Qk.
- Design as under-reinforced: keep xu/d below the code limit (about 0.53 for Fe 415) so steel yields before concrete crushes.
- Basic span/effective-depth ratios (simply supported 20, continuous 26, cantilever 7) give a quick deflection check.
- Minimum shear links and 0.13% minimum tension steel are detailing requirements, not options.
Worked example
Simply supported beam, span 6 m, w_ult = 30 kN/m. M = wl²/8 = 30 × 36/8 = 135 kNm. With b = 300 mm, D = 500 mm, 25 mm bars and 10 mm links, d = 500 − 40 − 10 − 12.5 = 437.5 mm. Take z ≈ 0.95d = 415.6 mm. As = M/(0.87 fy z) = 135 × 10⁶/(0.87 × 460 × 415.6) ≈ 812 mm², so 2T25 (982 mm²) is adequate.
Traps
- Forgetting self-weight of beam and slab.
- Working in kNm while the resistance formula needs N·mm - a 10⁶ error.
- Using overall depth instead of effective depth.
- Assuming singly reinforced design when xu/d exceeds the limit; add compression steel instead.
- Sri Lanka's low seismicity does not remove wind loading and ductile detailing checks.