WRD Maharashtra JE cheat sheet

Working stress method: modular ratio m = 280/(3σ_cbc); lever arm z = jd with j = 1 − k/3 where k = mσ_cbc/(mσ_cbc + σ_st).

Limit state of collapse, singly reinforced balanced section (Fe415): x_u/d limited to 0.48; for Fe250 it is 0.53 and for Fe500 it is 0.46 as per IS 456.

Nominal shear stress τ_v = V_u/(b·d); for slabs τ_v uses b = 1000 mm. Design shear strength τ_c depends on percentage steel p_t = 100A_st/(b·d).

Minimum shear reinforcement: A_sv/(b·s_v) ≥ 0.4/(0.87 f_y); maximum spacing 0.75d or 300 mm, whichever is smaller.

One-way slab: span/effective depth limits (IS 456 cl. 23.2.1) - simply supported 20, continuous 26, cantilever 7, with modification factor for tension steel.

Soil: Terzaghi bearing capacity for strip footing q_u = cN_c + γD_f N_q + 0.5γBN_γ; for square footing the last term becomes 0.4γBN_γ.

Compaction: Standard Proctor energy ≈ 594 kJ/m³ (25 blows, 3 layers, 2.5 kg rammer, 310 mm drop); Modified Proctor ≈ 2703 kJ/m³ (4.5 kg rammer, 457 mm drop).

Concrete mix: IS 10262 uses target mean strength f_ck' = f_ck + 1.65 s; water-cement ratio selected from IS 456 Table 5 durability exposure limits, not strength alone.

Otto cycle efficiency η = 1 − 1/r^(γ−1); Diesel cycle additionally depends on cut-off ratio ρ = V_3/V_2.

Carnot COP for refrigeration = T_L/(T_H − T_L) with absolute temperatures in kelvin; actual COP = refrigerating effect/compressor work.

Three-phase power: P = √3 V_L I_L cos φ; for balanced star connection V_L = √3 V_ph and I_L = I_ph; for delta V_L = V_ph and I_L = √3 I_ph.

Transformer: EMF per turn E_t = 4.44 f Φ_m; ratio V_1/V_2 = N_1/N_2 = I_2/I_1; efficiency peaks when copper loss equals iron loss.

Induction motor synchronous speed N_s = 120f/P; slip s = (N_s − N_r)/N_s; rotor frequency = s·f.

DC machine EMF E = (PΦNZ)/(60A) for generator, and E = V − I_a R_a for a motor (back EMF).

Belt drive: velocity ratio = (D_1 + t)/(D_2 + t) for crossed belts; slip reduces ratio; centrifugal tension T_c = m·v².

Hydraulic turbines: specific speed N_s = N√P/H^(5/4); Pelton for high head/low discharge, Francis for medium, Kaplan for low head/high discharge.

Kennedy's silt theory: critical velocity V_0 = 0.55 m·y^0.64 (m = 1 for Kennedy's original, 1 for B/D ratio > 1); regime condition means no silting and no scouring.

Lacey's regime equations: P = 4.75√Q, A = Q/V, V = (Q f²/140)^(1/6), where f is the silt factor = 1.76√d_mm.

Manning's equation: V = (1/n)R^(2/3)S^(1/2); use for lined canals and unlined channel design checks.

Duty D (ha/cumec) = 8.64 B/Δ (Δ in m); delta Δ (m) = 8.64 B/D; base period B in days.

Canal lining reduces seepage and increases capacity but does not change the required discharge duty; design discharge Q = A/D.

Dam safety: as per the Maharashtra Dam Safety framework and the national Dam Safety Act 2021, dams are classified by hazard (large/small, high/low hazard) determining inspection frequency and EAP requirements.

Reservoir routing: use the continuity equation I − O = dS/dt with the storage-elevation and elevation-discharge curves; flood routing through a spillway uses the standard step method.

Cross-drainage works: aqueduct carries canal over drain; superpassage carries drain over canal; level crossing allows both to share water level; selection depends on relative bed levels and HFL.

Maharashtra has 36 districts and 6 revenue divisions (Konkan, Nashik, Pune, Aurangabad/Sambhajinagar, Amravati, Nagpur); the state was formed on 1 May 1960 by the Bombay Reorganisation Act, 1960.

Maharashtra Legislature is bicameral: Legislative Assembly (Vidhan Sabha, 288 seats) and Legislative Council (Vidhan Parishad, 78 seats), with the Council partially renewed every two years (one-third).

The Maharashtra Right to Public Services Act, 2015 mandates time-bound delivery of notified services with a first appeal and second appeal mechanism; the Maharashtra Lokayukta handles corruption complaints.

Maharashtra Zilla Parishad and Panchayat Samiti are governed by the Maharashtra Zilla Parishads and Panchayat Samitis Act, 1961; Gram Panchayat by the Maharashtra Village Panchayats Act, 1959.

Marathi grammar essentials: 3 genders (पुल्लिंग, स्त्रीलिंग, नपुंसकलिंग), 2 numbers (एकवचन, अनेकवचन), and 8 cases (विभक्ती); the विभक्ती markers include -ने (कर्ता), -ला/-स (कर्म), -चा/-ची/-चे (षष्ठी).

Marathi official terminology: शासन (Government), विभाग (Department), सचिव (Secretary), मुख्य अभियंता (Chief Engineer), अंदाजपत्रक (Budget), निविदा (Tender), कार्यकारी अभियंता (Executive Engineer).

Maharashtra Public Service Commission (MPSC) and the Maharashtra Engineering Services conduct JE recruitment; the Water Resources Department (जलसंपदा विभाग) recruits through the Maharashtra Engineering Services Examination.

Maharashtra geography: Western Ghats (Sahyadri) run north-south; major rivers are Godavari, Krishna, Bhima, Tapi, Narmada (partly); the state's highest peak is Kalsubai (1,646 m).