MEngC R.S.E Part-I Civil cheat sheet

Degree of static indeterminacy for a planar frame: DSI = 3m + r - 3j, where m = number of members, r = number of reaction components, j = number of joints.

For a simply supported beam with a central point load P and span L, maximum bending moment = PL/4 and maximum deflection = PL^3/(48EI).

Castigliano's second theorem: deflection at a point = partial derivative of total strain energy with respect to a force applied at that point in the direction of the deflection.

Slope-deflection equation for member AB: M_AB = (2EI/L)(2θ_A + θ_B - 3Δ/L) + FEM_AB, where Δ is relative lateral displacement.

Moment distribution method: distribute unbalanced moment at a joint in proportion to member stiffness factors (4EI/L for far end fixed, 3EI/L for far end pinned); carry-over factor is 0.5 for fixed far end and 0 for pinned.

Influence line for shear at a section: ordinate equals shear at that section when unit load is at the ordinate location; maximum shear occurs with load placed over the positive ordinate region.

Euler buckling load for a pin-ended column: P_cr = π^2 EI / L^2; effective length factors K: pinned-pinned 1.0, fixed-fixed 0.5, fixed-pinned 0.7, fixed-free 2.0.

For a linear elastic truss, member force due to a unit load at a joint (virtual work method): Δ = Σ (F u L)/(AE), where F = actual member force, u = virtual member force.

Limit state of collapse in flexure (IS 456): design moment M_u = 0.36 f_ck b x_u (d - 0.42 x_u), with x_u limited to 0.53d for Fe415 steel to ensure ductile failure.

Minimum tension reinforcement in beams: A_st,min = 0.85 b d / f_y (IS 456 clause 26.5.1.1); maximum tension reinforcement = 0.04 b D.

Shear design: nominal shear stress τ_v = V_u / (b d) must not exceed τ_c,max = 0.62 √f_ck; shear reinforcement provided when τ_v > τ_c.

Development length L_d = φ σ_s / (4 τ_bd), where τ_bd = bond stress (1.6 MPa for plain bars, 1.9 MPa for deformed bars in tension, IS 456).

Serviceability: deflection limits per IS 456: span/250 for total deflection, span/350 for deflection after partitions; crack width limit 0.3 mm for moderate exposure.

Column design: minimum eccentricity e_min = L/500 + D/30, subject to minimum 20 mm; axial capacity P_u = 0.4 f_ck A_c + 0.67 f_y A_sc for tied columns.

Flat slab: total design moment M_o = w L_n^2 / 8 (direct design method); negative moment at column = 0.65 M_o, positive moment = 0.35 M_o for interior panel.

Ductile detailing (IS 13920): minimum grade of concrete M20; minimum grade of steel Fe415; confining reinforcement in plastic hinge region with spacing ≤ min(D/4, 8φ_long, 100 mm).

Design bending strength of a laterally supported beam (IS 800:2007): M_d = β_b Z_p f_y / γ_m0, where β_b = 1.0 for plastic section, Z_p = plastic section modulus, γ_m0 = 1.10.

Shear capacity of a steel section: V_d = A_v f_yw / (√3 γ_m0), where A_v = shear area, f_yw = yield strength of web.

Design compressive strength of a column: P_d = A_g f_y / γ_m0 for stocky (plastic) section, or governed by buckling curve (Perry-Robertson) for slender sections.

Bolted connection: design shear capacity of a bolt V_dsb = (f_ub / (√3 γ_mb)) (n_n A_nb + n_s A_sb), where n_n = number of shear planes with threads intercepting, n_s = without threads.

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

Limiting width-to-thickness ratios for plastic design: outstanding flange b/t_f ≤ 9.4ε, web d/t_w ≤ 84ε for a plastic section, where ε = √(250/f_y).

Lateral torsional buckling: design bending strength M_d = β_b Z_p f_bd, with f_bd = f_y / γ_m0 for L_LT ≤ L_LT,lim; otherwise reduced per IS 800 clause 8.2.2.

Column base plate: area required A = P_u / (0.6 f_ck) for concrete bearing; plate thickness t = √(3w(a^2 - b^2)/f_y) for cantilever projection.

Terzaghi's bearing capacity for a strip footing: q_u = c N_c + q N_q + 0.5 γ B N_γ, with N_c, N_q, N_γ depending on the angle of internal friction φ.

Standard penetration test: N-value corrected for overburden: N_1(60) = N × (C_N × C_E × C_R × C_B), where C_N = √(100/σ'_v) (σ'_v in kPa).

Allowable bearing pressure from plate load test: q_allow = q_ult / FOS, with FOS = 2.5 to 3.0; settlement of footing = settlement of plate × (B_f / B_p) for clay.

Pile capacity: ultimate load Q_u = Q_p + Q_s = q_p A_p + Σ f_s A_s; for driven piles in sand, q_p = 0.5 N_q tanφ × effective overburden at tip.

Liquefaction susceptibility: factor of safety against liquefaction F_L = CRR / CSR, where CSR = 0.65 (σ_v/σ'_v) (a_max/g) r_d; F_L < 1 indicates liquefaction.

Effective stress principle: σ' = σ - u; for a soil with water table at depth z_w, effective stress at depth z is σ' = γ z - γ_w (z - z_w) when z > z_w.

Consolidation settlement: S_c = (C_c H / (1 + e_0)) log10((σ'_0 + Δσ)/σ'_0), where C_c = compression index, e_0 = initial void ratio.

Slope stability: factor of safety F = resisting moment / disturbing moment (method of slices); for a c-φ soil, F = (c L + N tanφ) / T, where N and T are normal and tangential components.

Natural frequency of a single-degree-of-freedom system: ω_n = √(k/m); period T = 2π/ω_n = 2π√(m/k).

Response spectrum: peak pseudo-acceleration S_a = ω^2 S_d; base shear V_b = A_h W, where A_h = Z I S_a / (2 R g) per IS 1893.

IS 1893 seismic zone factor Z: Zone II 0.10, Zone III 0.16, Zone IV 0.24, Zone V 0.36; importance factor I = 1.5 for critical buildings, 1.0 for ordinary.

Response reduction factor R: 5.0 for special moment resisting RC frame, 3.0 for ordinary RC frame, 4.0 for steel special moment frame (IS 1893 Table 9).

Damping ratio: critical damping c_c = 2√(km) = 2mω_n; typical values: steel 2%, RC 5%, masonry 10%.

Time period of a building (empirical, IS 1893): T = 0.075 h^0.75 for RC moment resisting frames, where h = height in metres.

Ductility demand: for a structure with response reduction factor R, the design seismic force is reduced by R, but the structure must be detailed for ductility to sustain inelastic deformation.

Seismic weight calculation: W = dead load + 25% of imposed load for live load ≤ 3 kN/m² (IS 1893 clause 7.3.1); for heavier live loads, 50% is considered.

Concrete mix design (IS 10262): target mean strength f'_ck = f_ck + 1.65 s, where s = standard deviation (e.g., 4 MPa for M20, 5 MPa for M25).

Water-cement ratio limits (IS 456): 0.50 for mild exposure, 0.45 for moderate, 0.40 for severe, 0.35 for very severe, 0.30 for extreme exposure.

Slump test: workability measure; typical slumps: 25-75 mm for normal RCC, 75-125 mm for pumped concrete, 125-200 mm for self-compacting concrete.

Compressive strength of concrete: cube strength at 28 days = characteristic strength f_ck; acceptance criteria: mean of 4 consecutive tests ≥ f_ck + 0.825 s, individual ≥ f_ck - 4 MPa.

Steel reinforcement: Fe415 means yield strength 415 MPa; elongation at fracture minimum 14.5% for Fe415, 12% for Fe500 (IS 1786).

Bitumen grade: penetration grade 60/70 means penetration between 60 and 70 (0.1 mm) at 25°C; viscosity grade VG-30 has kinematic viscosity 300 ± 60 cSt at 135°C.

Non-destructive testing: rebound hammer gives surface hardness index; ultrasonic pulse velocity (UPV) > 4.5 km/s indicates good quality concrete, 3.5-4.5 km/s is medium, < 3.5 km/s is doubtful.

Curing: minimum 7 days for ordinary Portland cement concrete, 10 days for OPC with mineral admixtures, 14 days for concrete with pozzolana (IS 456 clause 13.5).

Critical path method: total float = LS - ES = LF - EF; critical path has zero total float; project duration = sum of durations on critical path.

PERT: expected time t_e = (t_o + 4t_m + t_p)/6; variance σ^2 = ((t_p - t_o)/6)^2; probability of completion Z = (T - T_e)/σ_project.

Earned value management: Cost Performance Index CPI = EV/AC; Schedule Performance Index SPI = EV/PV; CPI < 1 means over budget.

Resource levelling: adjust start times of non-critical activities within their float to reduce peak resource demand; resource smoothing does not change project duration.

Contract types: lump-sum (fixed price), item-rate (BOQ-based), cost-plus (actual cost + fee); item-rate contracts are common in Indian public works.

Safety: minimum PPE includes helmet, safety shoes, harness for work at height > 1.8 m; scaffolding must be inspected before use and after alteration.

Quality control: cube samples taken at rate of 1 per 5 m³ of concrete or 1 per 100 m² of slab area, whichever is greater (IS 456 clause 15.2).

Delay analysis: concurrent delay does not entitle contractor to extension of time if both parties caused delay; force majeure may allow time extension without cost.

Centre line method: total length = sum of centre line lengths of all walls; quantity = total length × width × height; suitable for walls of same thickness.

Trapezoidal rule for area: A = (d/2)[(y_0 + y_n)/2 + y_1 + y_2 + ... + y_{n-1}], where d = common interval, y_i = ordinates.

Prismoidal rule for volume: V = (L/6)(A_1 + 4A_m + A_2), where A_m = mid-section area; more accurate than trapezoidal for varying cross-sections.

Rate analysis: rate per unit = (material cost + labour cost + plant cost + overheads + profit)/quantity; contractor's profit typically 10-15%.

Bar bending schedule: cutting length of a bar = length of straight portion + (number of bends × bend allowance) - (number of hooks × hook allowance); standard hook allowance = 9d for 90° bend.

Quantity of cement in 1 m³ of concrete: for M20 (1:1.5:3), dry volume = 1.54 m³; cement = (1/5.5) × 1.54 × 1440 = 403 kg/m³.

Earthwork excavation: volume = (A + √(A B) + B) × h/3 for a frustum of a rectangular pit, where A and B are top and bottom areas, h = depth.

Deduction for openings in masonry: no deduction for opening area ≤ 0.1 m²; deduction for full opening when area > 0.1 m² and ≤ 3 m²; for larger openings, deduct opening and add lintel/sill.

IS 456:2000 governs plain and reinforced concrete design; IS 800:2007 governs general steel construction; IS 1893 (Part 1):2016 governs seismic design of buildings.

National Building Code of India (NBC 2016) Part 4 covers fire and life safety; Part 3 covers development control rules; Part 6 covers structural design.

Professional ethics: engineer must not accept compensation from more than one party for the same service; must disclose conflicts of interest.

Code of conduct for engineers: duty to public safety, competence, confidentiality, and avoidance of deceptive acts; violation may lead to disciplinary action by the institution.

Building permit process: submit drawings, structural calculations, and soil report to local authority; approval required before commencement; occupancy certificate after completion.

IS 875 (Parts 1-5) gives design loads: dead loads, imposed loads, wind loads, snow loads, and special loads; wind load depends on basic wind speed and terrain category.

Fire safety: minimum width of staircase 1.5 m for buildings > 30 m height; fire resistance rating of structural elements: 2 hours for high-rise buildings.

Contract documents: bill of quantities, drawings, specifications, conditions of contract, and letter of acceptance form the contract; precedence typically: contract agreement > letter of acceptance > conditions > specifications > drawings > BOQ.

Levelling: height of instrument HI = RL of benchmark + backsight; RL of new point = HI - foresight; arithmetic check: ΣBS - ΣFS = last RL - first RL.

Theodolite: horizontal angle measurement by repetition method; face left and face right readings average to eliminate collimation error.

Total station: measures horizontal and vertical angles and slope distance; coordinates computed as X = X_0 + D sinθ, Y = Y_0 + D cosθ, where D = horizontal distance.

Contouring: contour interval depends on scale and terrain; for flat terrain 0.25-0.5 m, for hilly terrain 1-2 m; contours close together indicate steep slope.

AutoCAD: layer management, blocks, and xrefs; dimension style scale factor (DIMSCALE) should be set to reciprocal of plot scale.

Structural analysis software (STAAD.Pro, ETABS, SAP2000): model with nodes, members, supports, and loads; check equilibrium and deformation before interpreting results.

Building information modelling (BIM): uses 3D parametric models with data attributes; clash detection identifies conflicts between structural and MEP elements.

Global positioning system (GPS) surveying: uses trilateration from satellites; accuracy depends on PDOP and ionospheric corrections; real-time kinematic (RTK) gives centimetre accuracy.