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Civil Engineering 2021 Paper II 50 marks Compulsory Solve

Paper II — Q1

(a) (i) What is the purpose of first coat of plastering ? (ii) What loads are taken by the formwork apart from its self-weight ?…

(a)
(i)

What is the purpose of first coat of plastering ? (ii) What loads are taken by the formwork apart from its self-weight ? (iii) Label the components (1, 2, 3 & 4) of pitched roof shown in the figure. 10 marks (b) Convert the given A-O-A (Activity on Arrow) to A-O-N (Activity on Node) Network and indicate the critical path. The duration of each activity is shown in the figure. 10 marks (c) The staff reading taken on a staff held at a distance of 80 m from the instrument when the bubble central was 1·455 m. When the bubble is moved 6 divisions out of centre, the staff reading observed is 1·487 m. If the length of one division is 2 mm, find the radius of curvature and the sensitivity of the tube. 10 marks (d) What is vertical curve and its significance ? Draw summit as well as valley curve for the following conditions : (i) Upward gradient (+g₁%) followed by another upward gradient (+g₂%) (ii) Downward gradient (−g₁%) followed by another downward gradient (−g₂%) 10 marks (e) A locomotive on M. G. Track has three pairs of driving wheels each carrying 20 tonnes. What maximum load can it pull on level track with curvature of 2° at 50 km/hr ? Take coefficient of friction = 0·166. 10 marks

हिंदी में प्रश्न पढ़ें
(a)
(i)

प्लास्टर के पहले लेप का उद्देश्य क्या है ? (ii) फर्मवर्क (फॉर्म वर्क) द्वारा अपने स्वयं के भार के अलावा और कौन से भार वहन किए जाते हैं ? (iii) ढालू छत के, दिए गए चित्र में दर्शाए गए अंगों (1, 2, 3, 4) को नामांकित कीजिए । 10 अंक (b) दिए गए ए-ओ-ए (शर पर क्रिया) जाल को ए-ओ-एन (संधि पर क्रिया) जाल में परिवर्तित कीजिए एवं क्रांतिक पथ इंगित कीजिए । प्रत्येक क्रिया की समयावधि चित्र में दर्शाई गई है । 10 अंक (c) उपकरण से 80 m की दूरी पर स्थित गज (स्टाफ) पर गज पाठ्यांक, बुलबुले के केंद्र में होने पर 1·455 m था । जब बुलबुले को केंद्र से 6 भाग बाहर खिसकाया गया, तब गज पाठ्यांक 1·487 m में देखा गया । यदि एक भाग की लंबाई 2 mm है, तो समतलन नलिका की वक्रता की त्रिज्या एवं सुग्राहिता ज्ञात कीजिए । 10 अंक (d) उद्वर्धर वक्र क्या है एवं इसका महत्व क्या है ? निम्नलिखित स्थितियों के लिए शिखर (समिट) वक्र और घाटी वक्र का चित्र बनाइए : (i) उद्वमुखी ढाल (+g₁%) के बाद एक और उद्वमुखी ढाल (+g₂%) (ii) अधोमुखी ढाल (−g₁%) के बाद एक और अधोमुखी ढाल (−g₂%) 10 अंक (e) एम. जी. रेलपथ पर एक रेल इंजिन के तीन जोड़ी चालक पहिये हैं जो प्रत्येक 20 टन वहन कर रहे हैं । एक समतल रेलपथ पर, 2° वक्रता के साथ एवं 50 km/hr पर यह कितना अधिकतम भार खींच पाएगा ? घर्षण गुणांक 0·166 लीजिए । 10 अंक

Q1 of the 2021 UPSC Mains Civil Engineering Paper II, as printed
The question as printed in the 2021 Civil Engineering paper
Evaluate your answer to this question → See all 2021 Civil Engineering questions

The figure this question refers to, in words

The question paper is a scan and the diagram did not survive as text. This is the figure as read from the original page — every component, value and label — so the question can be worked from the text below.

(a) A schematic diagram of a pitched roof structure. The main body is a rectangular prism with a gable roof. The roof has two sloping surfaces meeting at a central ridge. There are four numbered circles indicating specific components: (1) is located on the central ridge line; (2) is located on the upper right sloping surface; (3) is located on the lower right sloping surface near the eaves; (4) is located at the bottom right corner of the roof structure. Arrows indicate the direction of the roof slope. There is a chimney or vertical structure protruding from the front face of the roof.

(b) An Activity-on-Arrow (A-O-A) network diagram. The nodes are numbered 1 through 8. The activities are represented by arrows connecting the nodes, with labels (letters) and durations (numbers) associated with each arrow. The connections are as follows: Node 1 to Node 2 (Activity A, duration 5); Node 1 to Node 4 (Activity B, duration 3); Node 1 to Node 3 (Activity C, duration 8); Node 2 to Node 5 (Activity H, duration 4); Node 4 to Node 5 (Activity G, duration 4); Node 4 to Node 6 (Activity F, duration 6); Node 3 to Node 7 (Activity E, duration 7); Node 5 to Node 8 (Activity L, duration 6); Node 6 to Node 8 (Activity J, duration 2); Node 6 to Node 7 (Activity I, duration 7); Node 7 to Node 8 (Activity K, duration 6).

Model answer

Drafted with AI by UPSC Answer Check against this question's marking rubric, to the expected length. UPSC does not publish answers for Mains — this is one way to score well, not an official key. How we build rubrics and answers.

(a) Plastering, formwork loads and roof parts (10 marks)

(i) First coat. The first (scratch or rendering) coat levels the surface by filling joints and irregularities, and its rough key gives a firm bond for the following coats.

(ii) Loads on formwork besides its self-weight:

  • weight of wet concrete and reinforcement
  • construction live load of workers, materials and equipment
  • lateral pressure of fresh concrete
  • impact and vibration from placing and compaction
  • wind load (and seismic load where relevant)

(iii) Roof components in the plan. (1) Ridge, (2) hip, (3) valley, (4) eaves.

(b) A-O-N network and critical path (10 marks)

Activities and predecessors: A, B and C start the project. H follows A. G and F follow B. E follows C. L follows H and G. J and I follow F. K follows E and I. J, L and K end the project. No dummy is needed.

Forward pass (ES–EF): A 0–5, B 0–3, C 0–8, H 5–9, G 3–7, F 3–9, E 8–15, L 9–15, J 9–11, I 9–16, K 16–22. Project duration = 22.

Backward pass (LS–LF): K 16–22, L 16–22, J 20–22, I 9–16, E 9–16, F 3–9, H 12–16, G 12–16, C 1–9, A 7–12, B 0–3.

Total float: A 7, B 0, C 1, H 7, G 9, F 0, E 1, L 7, J 11, I 0, K 0.

Critical path: B → F → I → K (3 + 6 + 7 + 6 = 22 days).

Diagram: Activity-on-node network with critical path B-F-I-K

(c) Radius and sensitivity of the bubble tube (10 marks)

The staff reading changes by 1.487 − 1.455 = 0.032 m over 80 m, so the tilt of the line of sight is α = 0.032/80 = 4 × 10⁻⁴ rad.

The bubble moves 6 × 2 = 12 mm. For a circular tube, arc = Rα, so R = 12 mm/(4 × 10⁻⁴) = 30,000 mm = 30 m.

Sensitivity is the angle per division = α/6 = 6.67 × 10⁻⁵ rad = 13.75″ per division.

(d) Vertical curves (10 marks)

A vertical curve is a parabolic curve inserted in the longitudinal section where two gradients meet. It gives a smooth change of grade, comfort and safety, and sufficient sight distance (stopping and overtaking), and it avoids sudden jolts and poor drainage.

(i) +g₁% followed by +g₂%: if g₁ > g₂ the gradient flattens, so the curve is convex upward (summit). If g₂ > g₁ the gradient steepens, so the curve is concave upward (valley).

(ii) −g₁% followed by −g₂%: if g₂ > g₁ the fall steepens, so a summit curve is used. If g₁ > g₂ the fall flattens, so a valley curve is used.

Diagram: Summit and valley vertical curves for same-sign gradients

(e) Maximum load the locomotive can pull (10 marks)

Hauling capacity (adhesion) = pairs × load per pair × μ = 3 × 20 × 0.166 = 9.96 t.

Resistance for a train of weight W at V = 50 km/h (standard IR formula):

  • Rolling, speed and air resistance = 0.0016W + 0.00008WV + 0.0000006WV² = W(0.0016 + 0.004 + 0.0015) = 0.0071W.
  • Curve resistance = 0.0004 × D × W = 0.0004 × 2 × W = 0.0008W.
  • Total = 0.0079W.

Equating hauling capacity to resistance: 0.0079W = 9.96, so W ≈ 1,261 tonnes.

How this answer will be evaluated

What earns full marks: All parts answered with correct formulas, clear diagrams, and complete working.

Evaluation rubric

Each sub-part is marked on its own, against the marks and word limit printed on the paper.

  1. (a) Explain plastering purpose, formwork loads, and label roof components. 10 marks

    describe— define → structure or process in order → labelled diagram → significance

    Must cover

    • State purpose of first coat (leveling/adhesion)
    • List loads: dead, live, wind, construction
    • Label the roof parts in the figure: (1) ridge, (2) hip, (3) valley, (4) eaves

    Loses marks

    • Unlabeled or mislabeled roof components
    • Missing specific loads (e.g., omitting wind)

    Earns more

    • Correct component names (ridge, hip, valley, eaves) rather than rafter or purlin

    Extra mark

    • Reference IS 456 for plastering thickness
  2. (b) Convert A-O-A to A-O-N network and identify the critical path. 10 marks

    calculate— given → formula → substitution → result with units → interpretation

    Must cover

    • Draw A-O-N network with correct nodes and activities
    • Calculate Earliest Start (ES) and Latest Finish (LF)
    • Identify and highlight the critical path
    • State the total project duration

    Loses marks

    • Incorrect network topology in A-O-N
    • Critical path not clearly indicated

    Earns more

    • Show slack calculation for non-critical activities

    Extra mark

    • Use standard A-O-N node box format
  3. (c) Determine the radius of curvature and sensitivity of the level tube. 10 marks

    calculate— given → formula → substitution → result with units → interpretation

    Must cover

    • State formula for sensitivity (s = d / (n * D))
    • Calculate sensitivity in radians or arc-seconds
    • State formula for radius (R = D / s)
    • Provide final values with units

    Loses marks

    • Missing unit conversion for staff reading difference
    • Incorrect formula application

    Earns more

    • Show conversion of divisions to radians

    Extra mark

    • Mention standard sensitivity range for level tubes
  4. (d) Define vertical curve, its significance, and draw summit/valley curves. 10 marks

    describe— define → structure or process in order → labelled diagram → significance

    Must cover

    • Define vertical curve and its purpose (smooth transition)
    • Draw summit curve for +g1 to +g2
    • Draw valley curve for -g1 to -g2
    • Label gradients and curve length

    Loses marks

    • Missing or incorrect curve diagrams
    • No mention of significance

    Earns more

    • Mention sight distance requirements

    Extra mark

    • Reference IRC standards for vertical curves
  5. (e) Calculate the maximum load a locomotive can pull on a curved track. 10 marks

    calculate— given → formula → substitution → result with units → interpretation

    Must cover

    • Calculate tractive force (friction * weight)
    • Calculate resistance due to curvature
    • Calculate resistance due to speed (50 km/h)
    • Equate hauling capacity (9.96 t) to total resistance 0.0079 W to get W of about 1,261 t

    Loses marks

    • Missing resistance components (curvature or speed)
    • Incorrect unit conversion for speed

    Earns more

    • Show the curve resistance formula 0.0004 x D x W

    Extra mark

    • Mention specific resistance formulas used
What "Solve" is asking you to do

Choose the method, then carry it through to a final answer. Identifying what kind of problem this is and why that method applies is the first thing marked; a correct figure arrived at invisibly earns almost nothing.

Structure that answers it

Given data and what is required → method chosen, with the reason it applies → set-up (equation, circuit, free body, trial balance) → working, step by step → answer with units and any condition of validity

Where marks are lost

Doing the middle steps mentally and writing only the result. In mathematics papers, a further loss comes from giving a decimal where the exact value in surds or fractions was wanted, or from skipping the justification a part explicitly asks for.

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