Sri Lanka Engineering Service Exam cheat sheet

Concrete mix design by IS/BS absolute volume method: Vc = 1 - (C/Sc + W/1 + a/1000), where a is entrapped air percentage and Sc is cement specific gravity (3.15).

One bag of cement = 50 kg = 0.035 m³ loose volume; nominal 1:2:4 mix yields roughly 0.28 m³ concrete per bag with w/c ≈ 0.5 by mass.

BOD₅ removal in a conventional activated sludge plant: 85–95%; primary sedimentation removes 25–40% BOD and 50–70% suspended solids.

Darcy's law for seepage: q = k i A; coefficient of permeability k (cm/s) for clean sand ≈ 10⁻³–10⁻², silt ≈ 10⁻⁵–10⁻⁴, clay < 10⁻⁷.

Sri Lanka Road Development Authority (RDA) asphalt wearing course: 40–50 mm dense bituminous macadam over 60–100 mm base; compaction to ≥ 98% of maximum dry density (modified Proctor).

Hydraulic design of sewers uses Manning's n ≈ 0.013 for concrete, minimum self-cleansing velocity 0.6–0.75 m/s at full-flow, and partial-flow ratio d/D ≈ 0.7–0.8 at peak.

Surveying: levelling reduces staff readings to a datum; rise = previous staff − current staff; fall = current staff − previous staff; check sum of rises − falls = last RL − first RL.

Rational method peak discharge: Q = C·i·A/360 (Q in m³/s, i in mm/h, A in ha); runoff coefficient C ≈ 0.85–0.95 for roofs and pavements, 0.10–0.30 for lawns.

Simply supported beam, uniformly distributed load w over span L: maximum bending moment M = wL²/8 at midspan; maximum shear V = wL/2 at supports.

Cantilever with point load P at free end: M = PL at fixed support, deflection δ = PL³/(3EI); with UDL w: M = wL²/2, δ = wL⁴/(8EI).

Euler buckling load: Pcr = π²EI/(KL)²; effective length factor K = 1.0 pinned-pinned, 0.5 fixed-fixed, 0.7 fixed-pinned, 2.0 fixed-free.

Reinforced concrete, BS 8110/EC2 singly reinforced section: lever arm z ≈ 0.95d, As = M/(0.87 fy z); balanced ratio ρb = 0.85β₁ f'c/fy × (εcu/(εcu+εy)).

Shear reinforcement in beams: nominal links Asv/sv ≥ 0.4bw/fyv (BS 8110); minimum shear stress vmin = 0.4 N/mm² for concrete grades ≤ C35/45.

Slenderness limit for short columns: λ = le/h ≤ 15 (BS 8110 braced); above this, second-order moments must be added.

Steel tension member design: capacity = min(fy·Ag/γM0, fu·Anet/γM2); bolt bearing resistance Fb,Rd = 2.5·αb·fu·d·t/γM2.

Truss analysis by method of joints: at a joint with two non-collinear members and no external load, both member forces are zero; three members with two collinear, the third is zero.

Three-phase power: P = √3·VL·IL·cosφ; for balanced star connection VL = √3 Vph, IL = Iph; for delta VL = Vph, IL = √3 Iph.

Transformer efficiency peaks when copper loss equals iron (core) loss; η = output/(output + Pcu + Pfe).

Induction motor synchronous speed Ns = 120f/P; slip s = (Ns − Nr)/Ns, typically 2–5% at full load.

Transmission line surge impedance Zc = √(L/C), roughly 400 Ω overhead and 40–60 Ω cable; natural (SIL) power = V²/Zc.

Per-unit system: Zpu = Zactual/Zbase, Zbase = Vbase²/Sbase; base change Zpu,new = Zpu,old × (Vold/Vnew)² × (Snew/Sold).

Power factor correction capacitor kVAR = P (tanφ1 − tanφ2); raising pf from 0.8 to 0.95 needs about 0.42 × kW of capacitive kVAR.

Kirchhoff's laws: ΣI = 0 at a node; ΣV = 0 around a loop; Thevenin equivalent Vth = open-circuit voltage, Rth = Vth/Isc.

Earthing: resistance of a single rod R = (ρ/2πL)[ln(4L/d) − 1]; Sri Lanka CEB LV supply is 400/230 V, 50 Hz, TN-S/TN-C-S earthing.

Otto cycle efficiency η = 1 − 1/r^(γ−1), r = compression ratio; Diesel cycle η = 1 − [1/(γ r^(γ−1))]·[(ρ^γ − 1)/(ρ − 1)], ρ = cut-off ratio.

Carnot efficiency η = 1 − Tc/Th (absolute temperatures); no real engine between the same reservoirs can exceed it.

Rankine cycle: pump work ≈ vf·(p2 − p1); thermal efficiency = (h1 − h2) − (h4 − h3) over (h1 − h4).

Heat conduction through a plane wall: Q = kA(T1 − T2)/L; for composite walls, resistances add: R = L/(kA).

Bernoulli with head loss: p1/ρg + v1²/2g + z1 = p2/ρg + v2²/2g + z2 + hf; Darcy–Weisbach hf = f·(L/D)·v²/2g.

Refrigeration COP = QL/W; for a Carnot refrigerator COP = Tc/(Th − Tc).

Belt drive: (T1 − T2) = P/v; ratio T1/T2 = e^(μθ/sinβ) for a V-belt with groove angle 2β.

Stress in thin cylinder: hoop σh = pD/(2t), longitudinal σl = pD/(4t); maximum shear = pD/(8t).

SI base units: metre, kilogram, second, ampere, kelvin, mole, candela; force in newtons (kg·m/s²), pressure in pascals (N/m²), work in joules (N·m).

Concrete cube strength at 28 days is the acceptance criterion; characteristic strength means 5% of results may fall below it.

Slump test (BS EN 12350-2) classes: S1 10–40 mm, S2 50–90 mm, S3 100–150 mm, S4 160–210 mm; suitable for normal structural work.

Steel reinforcement grades in Sri Lanka: fy = 460 N/mm² (BS 4449 grade 460) or 500 N/mm² (BS 4449:2005 grade B500B); check mill certificates before use.

Quality control: acceptance sampling uses AQL; a control chart flags action when a point falls outside ±3σ or 7 consecutive points trend one way.

Engineering drawing conventions: first-angle projection places the plan below the elevation; third-angle places plan above; Sri Lanka generally uses first-angle (BS 8888).

Health and safety: a permit-to-work is required for confined-space entry, hot work, and excavation deeper than 1.2 m; scaffolding inspection at least every 7 days.

Measurement and payment in Sri Lankan public works follows CIDA/ICTAD standard specifications and SBD conditions; variations require written instruction before execution.

Percentage change = (new − old)/old × 100; successive changes a% then b% give net change a + b + ab/100.

Simple interest I = PRT/100; compound amount A = P(1 + R/100)^T; for half-yearly compounding use R/2 and 2T.

Speed, time, distance: d = st; for a train of length L crossing a pole, time = L/s; crossing a platform of length P, time = (L + P)/s.

Work: if A alone takes a days and B alone b days, together they take ab/(a + b) days; combined rate = 1/a + 1/b.

Ratio and mixture: alligation rule gives ratio of quantities = (mean − cheaper) : (dearer − mean).

Permutations and combinations: nPr = n!/(n−r)!; nCr = nPr/r!; number of arrangements of n items with p identical = n!/p!.

Series: sum of first n natural numbers n(n+1)/2; sum of squares n(n+1)(2n+1)/6; arithmetic mean of AP = (first + last)/2.

Data interpretation: mean = Σx/n; median is the middle value of ordered data; mode is most frequent; for grouped data mean = Σfx/Σf.

Sri Lanka gained independence on 4 February 1948 (Ceylon); the republic was declared on 22 May 1972 and the current constitution promulgated in 1978.

The Parliament of Sri Lanka has 225 members: 196 elected by proportional representation in districts and 29 from the national list.

Sri Lanka's highest peak is Pidurutalagala (2,524 m); longest river is the Mahaweli (335 km), which supports major hydropower schemes.

The Central Bank of Sri Lanka was established in 1950; the rupee (LKR) is issued in notes of 20, 50, 100, 200, 500, 1000, 5000.

Major infrastructure: Port of Colombo, Bandaranaike International Airport (Katunayake), Southern Expressway (E01), and the Colombo–Kandy (A1) road.

Sri Lanka is a member of SAARC, BIMSTEC, the Commonwealth, the UN, and the World Trade Organization; it is not a member of ASEAN.

Administrative structure: 9 provinces, 25 districts, and 331 divisional secretariats; the capital is Sri Jayawardenepura Kotte, and Colombo is the commercial capital.

CIDA (Construction Industry Development Authority) registers contractors in grades C1–C10 by financial capacity; public contracts above threshold require ICTAD/CIDA-registered contractors.