ESE CE Prelims cheat sheet

Civil Engineering - Structural Analysis, RCC/Steel Design, Geotech, Hydraulics, Surveying

• Degree of static indeterminacy: Ds = 3m + r − 3j for plane rigid frames (m = members, r = reactions, j = joints); for trusses Ds = m + r − 2j. Degree of kinematic indeterminacy = number of unrestrained joint displacements (3 per plane rigid joint, 2 per truss joint, 1 per roller direction).

• Slope-deflection and moment-distribution both rely on stiffness 4EI/L (far end fixed) and 2EI/L (far end pinned); carry-over factor is 0.5 for a fixed far end and 0 for a pinned far end. Distribution factor at a joint = member stiffness / sum of stiffnesses.

• Influence-line ordinate for a simply supported beam of span L at section distance a from left support: maximum shear = 1 − a/L (or a/L), maximum bending ordinate = a(L − a)/L. Absolute maximum BM under a single point load = PL/4 at midspan.

• Euler buckling: Pcr = π²EI/(KL)²; effective length factor K ≈ 1.0 pinned-pinned, 0.5 fixed-fixed, 0.7 fixed-pinned, 2.0 cantilever. Slenderness ratio λ = KL/r; buckling stress σcr = π²E/λ² (elastic range only).

• Limit state of collapse (IS 456): Mu,lim for singly reinforced rectangular section = 0.36 fck b xu,lim (d − 0.42 xu,lim), with xu,lim/d = 0.53 for Fe 415, 0.48 for Fe 500, 0.46 for Fe 550. Balanced steel percentage pt,lim = 41.4 fck/fy approximately for Fe 415.

• Shear design: τv = Vu/(b·d) must not exceed τc,max (3.1 MPa for M25, 3.5 MPa for M30, 4.0 MPa for M35 and above). Minimum shear reinforcement Asv/(b·sv) ≥ 0.4/(0.87 fy). Nominal cover per IS 456: 20 mm slab, 25 mm beam, 40 mm column, 50 mm footing (mild exposure 20 mm, moderate 30 mm).

• Terzaghi bearing capacity (strip footing): qu = c·Nc + q·Nq + 0.5·γ·B·Nγ; for square footing replace 0.5γBNγ with 0.4γBNγ and add 1.3cNc. Net safe bearing capacity qns = (qu − γDf)/FOS + γDf. Immediate settlement uses elastic formula Si = q·B(1 − μ²)·If/Es.

• Open-channel flow: Manning V = (1/n)·R^(2/3)·S^(1/2), where R = A/P; Chezy V = C√(RS). Most efficient trapezoidal section: half top width equals side slope length, hydraulic radius = y/2. Critical depth in rectangular channel yc = (q²/g)^(1/3). Hydraulic jump conjugate depths satisfy y2/y1 = 0.5(√(1 + 8Fr1²) − 1).

• Surveying: horizontal distance by stadia D = 100·s·cos²θ + (f + c) for inclined sights; curvature correction = 0.0785 D² m (D in km), refraction = 1/7 of curvature, combined correction = −0.0673 D². Traverse closing error e = √(ΣL² + ΣD²), precision = 1 in perimeter/e. Contour interval = (max elevation difference)/(number of contours).