UPSC ESE /Gate ( Civil engineering)
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Q3/3: A rectangular tank of length 4 m containing water accelerates uniformly at 3 m/s2 horizontally on a level surface. The difference in water surface levels between the rear and front ends is:
Q2/3: A vertical cut in saturated clay (phi = 0) has cohesion c = 30 kN/m2 and unit weight gamma = 19 kN/m3. The depth of the tension crack (where active earth pressure becomes zero) is:
Q1/3: A flat slab with 400x400 mm interior column has effective depth d = 250 mm and factored shear force Vu = 800 kN. As per IS 456 Cl 31.6.3, the punching shear stress on the critical section (perimeter at d/2 from column face) is:
📚 ESE Cracker — Day 76/174: Curve Setting (Simple, Compound & Reverse Curves) 📍 Surveying
Tuesday = Surveying day. Curves ka poora game ek image mein — formulas, worked examples aur self-check trick.
💡 Key: deflection angle from PC to any point = arc/2 — at PT total deflection MUST equal Δ/2. Agar nahi aa raha, setting-out galat hai.
✅ Simple: T = R tan(Δ/2), δ = 1718.9l/R min
✅ Compound: same direction, different R — PCC joins the arcs
✅ Reverse: opposite direction — parallel tracks d = (R1+R2)(1−cosΔ)
#ESEPrep #CivilEngineering #SyllabusCrusher #ESE2027 #Surveying
A circular curve of radius 300 m has a deflection angle of 60 degrees. As per Rankine's method, the external distance of the curve (mid-point of curve to intersection of tangents) is:
A 3 x 3 pile group has 600 mm diameter piles at 1.8 m centre-to-centre spacing. As per the Converse-Labarre formula, the pile group efficiency is:
A singly reinforced beam (M20, Fe 415) has b = 250 mm, d = 400 mm and 1.0% tension steel. As per IS 456 Table 19, the design shear strength of the concrete section (Vc) is:
📚 ESE Cracker — Day 75/174
📐 RCC — Singly Reinforced Beam Design (IS 456:2000, LSM)
Today's cracker covers:
• When a beam stays singly reinforced (Mu ≤ Mu,lim gate)
• xu,max/d ladder — 0.53 (Fe250) / 0.48 (Fe415) / 0.46 (Fe500)
• Mu,lim = 0.138 fck b d² (Fe415) + full lever-arm equation set
• Worked design: Mu = 120 kN·m, M20/Fe415 → b 250 mm, D 500 mm, 3-20φ, 8φ-4L stirrups @ 200 c/c (all arithmetic verified)
• Shear + deflection checks tacked on, "148-138-133" & "53-48-46" mnemonics
• ❌/✅ common mistakes: D vs d, grade-blind coefficients, skipping xu/d
#ESEPrep #CivilEngineering #SyllabusCrusher #ESE2027
Q3 [Water Resources]: Using the Rational Method, estimate the peak runoff from a catchment of 5 ha with runoff coefficient C = 0.60 and design rainfall intensity i = 40 mm/hr. Peak discharge Q is:
Q2 [Geotechnical]: In an oedometer test, a 20 mm thick clay sample (double drainage) reached 50% consolidation in 20 min. A field clay layer 4 m thick with single drainage is loaded to the same stress increment. Time for 50% consolidation in the field:
Q1 [Structural/Steel]: A 16 mm thick gusset plate of Fe 410 (fu = 410 N/mm2) fails in block shear. Net shear area Anv = 2000 mm2, net tension area Ant = 600 mm2. As per IS 800:2007 Cl 6.4, the block shear design strength Vdb is:
Q3: Water flows at 2 m/s in a 500 m long rigid pipe (K = 2.1 GPa). The valve is closed in 0.4 s. The Joukowsky pressure rise is (rho = 1000 kg/m³):
Q2: A normally consolidated clay (c' = 0) is tested in CU triaxial: cell pressure 200 kPa, deviator stress 300 kPa, pore pressure at failure 100 kPa. The effective friction angle phi' is:
Q1: A steel rod (E = 200 GPa, A = 500 mm², L = 2 m) carries a 10 kN collar dropped from h = 25 mm. The maximum impact stress in the rod is:
📚 ESE Cracker — Day 74/174
📋 Mixed Revision: 5 Quick-Fire Concepts (Week 15)
Days 64–73 recap — 5 cards that carry the highest exam weight:
🔹 Column Buckling — Euler Pcr = π²EI/(KL)², K factors, λc ladder, Rankine for λ < λc
🔹 BOD Kinetics — y_t = L(1−10^−kt), the 68% rule at k=0.1, ThOD ≥ COD ≥ BOD
🔹 Concrete Mix Design — fck+1.65σ, Abrams law, durability w/c caps (M20 0.55 / M25 0.50 / M30 0.45)
🔹 Activated Sludge — F/M, sludge age θc, SVI, recirculation R
🔹 Hill Roads — gradient compensation C = 30/(R+15)%, extra widening
✅ Quick recap: Rankine when λ < λc • BOD5 ≈ 0.684L • F/M uses influent only • compensate on sharp curves
💡 Revisions pe focus — yehi 5 cards har hafte ek baar dohrana.
#ESEPrep #CivilEngineering #SyllabusCrusher #ESE2027
A spherical soap bubble of radius 2.5 mm is formed in air with surface tension 0.03 N/m. The excess pressure inside the bubble is: #ESEPrep #CivilEngineering #TargetPractice #ESE2027
A retaining wall 5 m high retains cohesionless backfill (phi = 30 deg, gamma = 18 kN/m3). A surcharge of 10 kN/m2 acts on the backfill surface. The additional active thrust per metre run due to surcharge is: #ESEPrep #CivilEngineering #TargetPractice #ESE2027
A fixed beam AB of span 6 m carries a point load of 90 kN at 2 m from support A. The fixed-end moment at A is: #ESEPrep #CivilEngineering #TargetPractice #ESE2027
Day 73/174 — Timber: Properties, Seasoning & Defects
Friday = Engineering Materials. Day 72 covered Hill Roads; today it's timber — the OG construction material. Key highlights:
• Fiber Saturation Point (FSP) ≈ 25–30% MC — shrinkage & strength gain start ONLY below this
• MC = (Ww − Wd)/Wd × 100% — denominator is always OVEN-DRY weight
• Shrinkage: Tangential > Radial ≈ 2:1, Longitudinal ≈ 0
• Worked example: 100 kg wet / 60 kg dry → MC = 66.7%; season to 15% → remove 31 kg water
• Seasoning: Air (cheapest, 15–20% MC) | Kiln (fast, 10–15%) | Water (decay-proof but weakens)
• Defects: Knots, Bow/Cup/Twist, Checks & Shakes, Termites, Dry rot
#ESEPrep #CivilEngineering #SyllabusCrusher #ESE2027
Q3 (Transportation Engineering): Stopping sight distance on a level road at 80 km/h, reaction time 2.5 s and f = 0.35 (n = 0) is:
