(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 (Activ

Question

(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

UPSC Answer Check · Accepted Answer

(a)(i) The first coat of plastering is the base or scratch coat. It fills joints, cracks and surface irregularities, gives a uniform thickness, provides a rough key, and ensures a strong bond with the masonry or concrete substrate so that the finish coat can be smooth and even.

(a)(ii) Apart from its self-weight, formwork must carry:
dead load of wet concrete,
live/construction loads of workers, materials, equipment and stock,
lateral pressure of fresh concrete,
dynamic and impact loads from placing, vibration and compaction,
wind load and other imposed loads.

(a)(iii) From the figure: (1) ridge; (2) rafter; (3) eaves; (4) barge (sloping gable edge).

(b) Method: Critical Path Method on an Activity-on-Node network. The AON nodes are A, B, C, H, G, F, E, L, J, I, K. Precedence: start→A, B, C; A→H; B→G and B→F; C→E; H and G→L; F→J and F→I; E and I→K; J, L and K→end. No dummy activities are needed.

Forward pass, in the given duration units:
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 time units.

Backward pass (LS–LF):
K 16–22, I 9–16, F 3–9, B 0–3;
E 9–16, C 1–8, L 16–22, H 12–16, G 12–16, A 7–12, J 20–22.

Total floats: 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, duration 22 time units.

(c) Method: sensitivity of a circular bubble tube. The staff reading change is Δh = 1.487 m − 1.455 m = 0.032 m at D = 80 m. The line-of-sight tilt is θ = arctan(Δh/D) = arctan(0.032/80) ≈ 0.0004 rad. The bubble moves x = 6 × 2 mm = 12 mm = 0.012 m. For a circular tube, x = Rθ, so R = x/θ = 0.012/0.0004 = 30 m.

Sensitivity is the angle for one division: θ₁ = 0.002 m / 30 m = 1/15000 rad = 6.667×10⁻⁵ rad per division. In seconds of arc, θ₁ = (1/15000) × 206265 = 13.75 arcsec per division.

Radius of curvature = 30 m; sensitivity = 13.75 arcsec per division. Valid for small θ, vertical staff, and a circular tube.

(d) A vertical curve is a transition curve, normally parabolic, introduced between two different gradients. Its significance is to provide a smooth change of grade, vehicle comfort, safety, adequate sight distance, proper drainage, and reduced impact or jolting on vehicles.

(d)(i) For +g₁% followed by +g₂%:
if g₁ > g₂, the grade decreases; draw a summit/crest curve: a convex curve below the PVI, with T.C. and C.T. on the two upward tangents.
if g₂ > g₁, the grade increases; draw a valley/sag curve: a concave curve above the PVI.

(d)(ii) For −g₁% followed by −g₂%:
if g₂ > g₁, the fall becomes steeper, so the grade decreases; draw a summit/crest curve.
if g₁ > g₂, the fall becomes flatter, so the grade increases; draw a valley/sag curve.

In all cases the PVI is the intersection of the two tangent gradients, and the curve is tangent to them at T.C. and C.T.

(e) Method: available adhesive tractive effort divided by standard train resistance. Driving-wheel load = 3 × 20 t = 60 t. Gross tractive effort = μW = 0.166 × 60 = 9.96 tonne-force = 9960 kgf.

Using the usual level-track resistance formula at V = 50 km/h:
R = 0.0033V² + 0.0025V + 0.0001
= 0.0033(50)² + 0.0025(50) + 0.0001
= 8.3751 kgf/tonne.

For a 2° curve, curvature resistance = 0.00005 D V² = 0.00005 × 2 × 50² = 0.25 kgf/tonne.

Total resistance = 8.3751 + 0.25 = 8.6251 kgf/tonne.

Maximum load = 9960 / 8.6251 = 1154.8 t ≈ 1155 tonnes.

Assumptions: level track, no acceleration, standard railway resistance formula, M.G. curve degree D = 2, and gross tractive effort is available for the train.

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