BTSC JE Civil cheat sheet

Standard brick (modular): 190 × 90 × 90 mm; conventional field brick 230 × 110 × 70 mm including mortar joint; 10 mm mortar joint assumed in modular sizing.

Brick classification by compressive strength (IS 1077): class 35, 30, 25, 20, 17.5, 15, 12.5, 10, 7.5, 5, 3.5 N/mm²; water absorption ≤ 20% for class 12.5 and above, ≤ 1/5 of weight for first-class bricks.

Lime: fat lime slakes vigorously and doubles in volume (used for whitewashing); hydraulic lime sets under water due to clay impurities; quicklime is CaO, slaked lime is Ca(OH)2.

Cement mortar 1:3 to 1:6 for masonry; 1:4 to 1:6 for plastering; mortar strength depends on cement content and water-cement ratio, not on sand grading alone.

Timber: seasoning reduces shrinkage and warping; air seasoning is slow, kiln seasoning faster and controlled; moisture content at fibre saturation point ≈ 25–30%.

Paint: primer improves adhesion and inhibits corrosion; putty fills pores; distemper is water-based; enamel is oil-based and gives glossy, washable finish.

Damp proof course (DPC): placed at plinth level, minimum 100–150 mm thick; materials include bitumen felt, cement concrete 1:2:4 with waterproofing compound, or polythene sheet.

Bond types: English bond (alternate header and stretcher courses, strongest), Flemish bond (header and stretcher alternate in each course), stretcher bond for half-brick walls, rat-trap bond for economy.

Stress σ = P/A; strain ε = δ/L; Young's modulus E = σ/ε; Poisson's ratio μ = lateral strain / longitudinal strain (≈0.3 for steel, 0.15–0.2 for concrete).

Hooke's law valid within proportional limit; yield stress is the stress at which strain increases without load increase; ultimate stress is maximum stress before rupture.

Bending: M/I = σ/y = E/R; for rectangular section σ_max = 6M/(bd²); section modulus Z = I/y_max.

Shear stress in beam: τ = VQ/(Ib); maximum at neutral axis for rectangular section = 1.5 V/(bd); average shear = V/(bd).

Deflection of simply supported beam under central point load: δ = WL³/(48EI); under UDL: δ = 5wL⁴/(384EI); cantilever with end load: δ = WL³/(3EI).

Torsion of circular shaft: T/J = τ/r = Gθ/L; power transmitted P = 2πNT/60.

Euler buckling load P_cr = π²EI/L_eff²; effective length factors: both ends pinned 1.0, fixed-fixed 0.5, fixed-pinned 0.7, fixed-free 2.0.

Analysis: degree of static indeterminacy = (3m + r) − 3j for plane frames; influence line ordinate gives response per unit moving load; Maxwell–Betti reciprocal theorem applies to linear elastic structures.

M20 means characteristic cube compressive strength 20 N/mm² at 28 days; target mean strength f_ck + 1.65 × standard deviation.

Water-cement ratio controls strength and durability; IS 456 limits w/c to 0.45–0.55 depending on exposure class (mild to severe).

Workability tests: slump (concrete), compaction factor, Vee-Bee; slump 25–75 mm typical for normal RCC work.

Curing: minimum 7 days for OPC concrete, 10 days for blended cement; strength gain continues with adequate moisture and temperature.

Design philosophies: working stress method (elastic, permissible stresses), limit state method (partial safety factors, collapse and serviceability limit states) - limit state is current IS 456 practice.

Singly reinforced rectangular section: M_u = 0.87 f_y A_st d (1 − f_y A_st/(f_ck b d)); limiting neutral axis depth ratio x_u,max/d = 0.53 for Fe415, 0.48 for Fe500.

Shear design: nominal shear stress τ_v = V_u/(bd); τ_c from IS 456 Table 19; minimum shear reinforcement = 0.4/(0.87 f_y) × b s.

Development length L_d = φ σ_s/(4 τ_bd); lap length in tension = 1.3 L_d for flexural members; anchorage requirements govern detailing.

Structural steel grades: Fe 410 (yield 250 MPa), Fe 540 (yield 410 MPa) per IS 2062; E = 2 × 10⁵ N/mm², G = 0.8 × 10⁵ N/mm².

Limit state design (IS 800:2007): partial safety factor for material γ_m0 = 1.10 for yielding, γ_m1 = 1.25 for ultimate resistance; load factors 1.5 dead/live, 0.9 dead opposing uplift.

Design bending strength M_d = β_b Z_p f_y/γ_m0, with β_b = 1.0 for plastic and compact sections, less for semi-compact.

Classification of cross-sections: plastic (b/t limits), compact, semi-compact, slender; depends on width-to-thickness ratio of flange and web.

Design shear strength V_d = V_p/γ_m0, where V_p = f_yw A_v/√3; shear area A_v = h t_w for rolled I-sections.

Bolted connections: nominal shear capacity of bolt V_nsb = f_ub A_nb/(√3 γ_mb); bearing capacity V_npb = 2.5 k_b d t f_u/γ_mb.

Weld design: throat thickness = 0.7 × size for fillet weld; design strength of fillet weld = f_u/(√3 γ_mw) with γ_mw = 1.25 (shop) or 1.50 (site).

Lacing and battening for built-up compression members; slenderness ratio KL/r limited to 180 for main compression members, 250 for secondary members.

Phase relations: void ratio e = V_v/V_s; porosity n = e/(1+e); degree of saturation S = V_w/V_v; γ = (G + Se)γ_w/(1+e).

Atterberg limits: liquid limit, plastic limit, shrinkage limit; plasticity index PI = LL − PL; consistency index = (LL − w)/PI.

Compaction: standard Proctor (light) vs modified Proctor (heavy, higher energy); OMC decreases and γ_d,max increases with greater compaction energy.

Terzaghi bearing capacity (strip footing): q_u = c N_c + γ D_f N_q + 0.5 γ B N_γ; N factors depend on φ.

Effective stress σ' = σ − u; capillary rise increases effective stress; quick sand condition when hydraulic gradient i = (G−1)/(1+e) = critical gradient.

Consolidation: C_v = T_v H²/t; coefficient of consolidation from time-settlement curve; primary consolidation followed by secondary compression.

Shear strength: τ = c + σ' tan φ (Mohr–Coulomb); UU test gives c_u with φ_u = 0; CU test with pore pressure measurement gives c', φ'.

Pile capacity: ultimate load = end bearing (q_b A_b) + skin friction (Σ f_s A_s); negative skin friction reduces capacity in consolidating fill.

Hydrostatic pressure p = ρgh; total force on vertical rectangular gate = 0.5 ρ g H² b; centre of pressure at 2H/3 from surface.

Continuity: A₁V₁ = A₂V₂; Bernoulli: p/γ + V²/(2g) + z = constant along a streamline for ideal flow.

Reynolds number Re = ρVD/μ = VD/ν; laminar pipe flow Re < 2000, turbulent Re > 4000; critical zone between.

Darcy–Weisbach head loss h_f = f L V²/(2gD); friction factor f = 64/Re for laminar flow; Moody diagram relates f to Re and relative roughness.

Hagen–Poiseuille laminar discharge Q = πΔp D⁴/(128 μ L); velocity profile parabolic, maximum at centre = 2 × average.

Orifice: Q = C_d A √(2gH); C_d = C_v × C_c; typical C_d ≈ 0.62 for sharp-edged orifice.

Notches and weirs: rectangular weir Q = (2/3) C_d b √(2g) H^{3/2}; triangular (V-notch) Q = (8/15) C_d √(2g) tan(θ/2) H^{5/2}.

Hydraulic jump: conjugate depth relation y₂/y₁ = 0.5(√(1 + 8F₁²) − 1); energy loss = (y₂ − y₁)³/(4 y₁ y₂).

Rainfall–runoff: rational method Q = C i A/3.6 (Q in m³/s, i in mm/h, A in km²); C depends on land use and slope.

Unit hydrograph: direct runoff hydrograph for 1 cm of rainfall in unit duration; volume under UH = 1 cm × catchment area.

S-curve method converts unit hydrograph of one duration to another; time base of UH ≈ 5–6 times time of concentration.

Infiltration: Horton equation f = f_c + (f_0 − f_c) e^{−kt}; φ-index is average rainfall intensity equal to infiltration capacity.

Irrigation: duty D (ha/cumec) and delta Δ (m) relation Δ = 8.64 B/D where B is base period in days; duty increases with canal lining and decreases with canal length.

Crop water requirement: consumptive use = evapotranspiration; net irrigation requirement = CU − effective rainfall; gross requirement accounts for application efficiency.

Canal design: Kennedy's formula V = 0.55 m y^0.64; Lacey's regime equations V = (Q f²/140)^{1/6}, R = 0.47 (Q/f)^{1/3}.

Dams and spillways: ogee spillway profile follows downstream face of standard crest; stilling basin dissipates energy via hydraulic jump; freeboard depends on wave height and wind setup.

Highway geometric design: design speed, superelevation e = V²/(127R) − f (V in km/h, R in m); maximum superelevation 7% for plain terrain, 10% for hilly.

Stopping sight distance SSD = 0.278 V t + V²/(254 (f ± g)); reaction time 2.5 s; overtaking sight distance is longer for two-lane roads.

Pavement: flexible pavement layered structure (wearing course, base, sub-base, subgrade); rigid pavement uses concrete slab with joints (expansion, contraction, construction).

CBR test: California Bearing Ratio = (test load / standard load) × 100; standard loads 1370 kg (2.5 mm) and 2055 kg (5 mm); used in flexible pavement design.

Design traffic: cumulative standard axles N = 365 A [(1 + r)^n − 1]/r × VDF; used with IRC 37 pavement design charts.

Railway: sleeper density, creep of rails, cant e = GV²/(127R); points and crossings; coning of wheels 1 in 20.

Airport: runway orientation by wind rose; basic runway length corrected for elevation, temperature and gradient; clearway and stopway definitions.

Traffic engineering: PCU (passenger car unit) converts mixed traffic; LOS categories A–F; traffic volume studies, spot speed, and origin-destination surveys.

Water demand: per capita demand 135 lpcd (domestic, IS 1172); peak factor 1.5–2.0; fire demand by Kuichling's formula Q = 3182 √P (L/min, P in thousands).

Water treatment train: screening → aeration → coagulation-flocculation → sedimentation → filtration → disinfection; chlorination is the final disinfection step.

Coagulants: alum, ferric chloride, polyelectrolytes; optimum pH for alum coagulation ≈ 6.5–7.5; rapid mix followed by slow flocculation.

Sedimentation: overflow rate = Q/A; detention time = V/Q; Stokes' law settling velocity v = g(ρ_s − ρ)d²/(18μ).

Filtration: rapid sand filter rate 100–150 L/m²/min, slow sand filter 100–200 L/m²/day; backwashing when head loss exceeds limit.

Disinfection: chlorine dose depends on breakpoint chlorination; residual free chlorine 0.2–0.5 mg/L at consumer end; CT concept for pathogen inactivation.

Sewerage: self-cleansing velocity 0.6–0.75 m/s minimum; maximum velocity 3 m/s; BOD₅ of domestic sewage ≈ 200–300 mg/L; COD/BOD ratio indicates biodegradability.

Wastewater treatment: primary sedimentation removes 60–70% SS; activated sludge process with sludge age and F/M ratio; trickling filter, oxidation pond, and septic tank for rural areas.

Chain surveying: ranging, offsets (perpendicular and oblique); principle of working from whole to part; limiting length of offset depends on scale.

Compass surveying: WCB (whole circle bearing) and RB (reduced bearing) conversions; local attraction detected by fore/back bearing difference; magnetic declination varies with time and place.

Levelling: height of instrument (HI) method and rise-fall method; curvature correction = 0.0785 d² m (d in km); refraction correction = 1/7 of curvature correction.

Theodolite: horizontal and vertical angles; face left/right observations; repetition and reiteration methods; transit rule for balancing traverse.

Traverse computations: latitude = L cos θ, departure = L sin θ; closing error e = √(ΣL² + ΣD²); Bowditch rule distributes error proportional to side length.

Tacheometry: distance D = k s + C (stadia); anallatic lens keeps additive constant zero; staff held vertical for accuracy.

Contouring: contour interval depends on scale and terrain; characteristics - contours never cross except at overhanging cliff; closer contours indicate steeper slope.

Modern surveying: total station combines EDM and theodolite; GPS/GNSS gives 3D coordinates; remote sensing and GIS for large-area mapping.

Types of estimate: approximate (plinth area, cubic content, unit rate), detailed estimate, revised estimate, supplementary estimate; detailed estimate uses measurement sheets and abstract of cost.

Plinth area rate method: cost = plinth area × plinth area rate; suitable for preliminary estimates only.

Measurement units: earthwork in excavation - m³; brickwork - m³; plastering - m²; painting - m²; steel reinforcement - kg or tonne; doors and windows - number.

Centre line method and long wall–short wall method for building quantity take-off; centre line method suits walls of uniform thickness.

Rate analysis: labour, material, plant, overheads and contractor profit; task work or out-turn per day per mason; standard schedule of rates (SSR) used.

PERT and CPM: CPM is activity-oriented with deterministic durations; PERT is event-oriented with three time estimates (optimistic, most likely, pessimistic); expected time = (O + 4M + P)/6.

Network: critical path has zero float; total float = LS − ES = LF − EF; free float = total float − head event slack.

Construction contracts: lump sum, item rate, percentage rate, cost plus; earnest money deposit (EMD) and security deposit; escalation clause for price variation.

Indian Constitution: adopted 26 November 1949, came into force 26 January 1950; fundamental rights in Part III, directive principles in Part IV.

Bihar-specific: state formed in 1912 as Bihar and Orissa, separated in 1936; capital Patna; major rivers Ganga, Gandak, Kosi, Son; Kosi known as 'sorrow of Bihar'.

Indian geography: Tropic of Cancer passes through 8 states; Western Ghats and Eastern Ghats; monsoon onset over Kerala around 1 June.

Indian economy: NITI Aayog replaced Planning Commission in 2015; GDP, inflation measured by CPI; Reserve Bank of India regulates monetary policy.

Science basics: SI units (newton, pascal, joule, watt); pH scale 0–14; photosynthesis converts CO₂ and water to glucose using sunlight.

Indian history: Mauryan and Gupta empires; 1857 revolt; Indian National Congress founded 1885; independence 1947.

Current affairs awareness: national infrastructure missions, environmental conventions (Paris Agreement), and disaster management frameworks (NDMA).

Percentage: x% of y = xy/100; successive percentage change a% then b% gives net change a + b + ab/100.

Profit and loss: profit% = (SP − CP)/CP × 100; discount% on marked price; successive discounts combine multiplicatively, not additively.

Time, speed and distance: distance = speed × time; relative speed adds for opposite direction, subtracts for same direction; average speed = total distance/total time.

Time and work: if A does work in x days and B in y days, together they finish in xy/(x + y) days; efficiency inversely proportional to time.

Simple and compound interest: SI = PRT/100; CI = P(1 + R/100)^T − P; difference between CI and SI for 2 years = P(R/100)².

Ratio and proportion: if a:b = c:d then ad = bc; partnership profit shares proportional to capital × time.

Number series and coding-decoding: identify arithmetic/geometric patterns; alphabet positions A=1 to Z=26; mirror-image and letter-shift coding.

Permutation and combination: nPr = n!/(n−r)!; nCr = n!/(r!(n−r)!); probability = favourable outcomes/total outcomes.