RPSC AE Civil cheat sheet

Concrete mix design (IS 10262): target mean strength f'ck = fck + 1.65·s, where s is the assumed standard deviation (e.g., 4 N/mm² for M20–M25); water-cement ratio is then selected from IS 456 durability limits and adjusted for exposure.

IS 456 workability/durability limits: minimum cement content and maximum free w/c ratio depend on exposure (Mild, Moderate, Severe, Very Severe, Extreme); e.g., severe exposure typically requires max w/c 0.50 and min cement 320 kg/m³ for reinforced concrete.

Nominal shear strength of concrete τc from IS 456 Table 19 depends on percentage steel pt = 100·Ast/(b·d) and concrete grade; maximum shear stress τc,max (Table 20) caps design regardless of stirrups.

Singly reinforced section: Mu,lim = 0.36·fck·b·xu,lim·(d − 0.42·xu,lim), with xu,lim/d = 0.53 for Fe 250, 0.48 for Fe 415, 0.46 for Fe 500.

Design of a two-way slab (IS 456 Annex D): short-span moment coefficient αx and long-span αy depend on ly/lx ratio and edge conditions; ly/lx ≥ 2 is designed as one-way.

Effective span of a simply supported beam = clear span + effective depth, or centre-to-centre distance of supports, whichever is smaller; for cantilever it is length to face of support plus half effective depth.

Lacing and battening for built-up steel columns (IS 800): lacing slenderness ratio of the component ≤ 50, and lacing flat angle ≤ 45° to the longitudinal axis; batten plates designed for transverse shear 2.5% of axial force.

Bending stress in steel sections (IS 800 LSD): Md = βb·Zp·fbd/γm0, with βb = 1.0 for plastic (compact) sections; design shear Vd = Vp/γm0 where Vp = Av·fy/√3.

Surveying: horizontal distance by tacheometry (fixed hair) D = (f/i)·s + (f + d), where s is staff intercept, f/i is multiplying constant (usually 100), and (f + d) is additive constant.

Level book arithmetic check: ΣBS − ΣFS = last RL − first RL; ΣBS − ΣFS = ΣRise − ΣFall.

Open-channel flow: Manning's equation V = (1/n)·R^(2/3)·S^(1/2); Chezy's V = C√(RS); hydraulic mean depth R = A/P.

Most economical trapezoidal channel: half top width equals side slope length, giving hydraulic radius R = y/2 for a given side slope; discharge Q = A·V with A = y(b + zy).

Darcy's law for one-dimensional seepage q = k·i·A; constant-head permeability test k = QL/(A·h·t); falling head k = (a·L/(A·t))·ln(h1/h2).

Terzaghi bearing capacity (strip footing): qu = c·Nc + q·Nq + 0.5·γ·B·Nγ; for local shear use reduced c' = 2c/3 and tan φ' = (2/3)tan φ.

Standard Proctor vs Modified Proctor: modified uses heavier hammer (4.5 kg, 450 mm drop, 25 blows, 5 layers) giving higher γd,max and lower OMC than standard (2.6 kg, 310 mm drop).

Highway geometric design (IRC): superelevation e = V²/(127R) − f; extra widening at curves = (n·L²)/(2R) + V/(9.5√R); stopping sight distance SSD = 0.278·V·t + V²/(254f).