(a) Design the size and spacing of dowel bars at the expansion joints of a cement concrete pavement of thickness 25 cm with radius of relative stiffness 80 cm, for a design wheel load of 5000 kg. Assume load capacity of dowel system as 40% of the des

Question

(a) Design the size and spacing of dowel bars at the expansion joints of a cement concrete pavement of thickness 25 cm with radius of relative stiffness 80 cm, for a design wheel load of 5000 kg. Assume load capacity of dowel system as 40% of the design wheel load. Joint width is 2.0 cm, permissible shear and flexural stresses in dowel bar are 1000 kg/cm² and 1400 kg/cm² respectively and permissible bearing stress in cement concrete is 100 kg/cm². 20

(b) Work out the cost of a plot, in terms of per m² of land measuring 60,000 sq m. The cost of development for roadways, water supply, sewerage system, electricity and all other engineering works is Rs. 100/- per sq m, which is spent in following manner :

First year : 10%, second year : 15%, third year : 20% and fourth year remaining area. Average market rate for plot is Rs. 5000/- per sq m. 10%, 20%, 20% and 30% plots are sold in first, second, third and fourth year respectively whereas remaining plots are sold in fifth year.

Assume the discount rate = 7%. Write your assumptions clearly, if any (like stamp duty, etc.) 15

(c) (i) Indicate (in bulleted form) the advantages of ferro-cement over the conventional RCC. Can we use the ferro-cement tanks for high capacity like 25000 litres or above ? Justify your answer.

(ii) Label the terms (technical) that applies to the door (shown in figure) parts. 10+5

UPSC Answer Check · Accepted Answer

Begin with a brief introduction acknowledging the multi-part nature of this pavement design, valuation, and materials question. For part (a), apply IRC:58 design methodology for dowel bars using the given radius of relative stiffness and wheel load, showing complete derivations for bearing, shear, and flexural stress checks. For part (b), prepare a discounted cash flow table year-wise for development costs and revenue realization, computing net present value and cost per m². For part (c)(i), enumerate ferro-cement advantages with specific justification for large tank feasibility, and for (c)(ii) label door components with correct technical terminology. Allocate approximately 40% time to part (a), 30% to part (b), and 30% combined to part (c), ensuring all numerical workings are clearly presented with stated assumptions.
- Part (a): Calculation of load transfer capacity (40% of 5000 kg = 2000 kg), determination of dowel bar diameter using bearing stress criterion (σb = P/(d×h) ≤ 100 kg/cm²), spacing based on relative stiffness (l = 80 cm), and verification against shear (1000 kg/cm²) and flexural (1400 kg/cm²) stress limits with joint width 2.0 cm
- Part (a): Selection of standard dowel bar size (typically 25-32 mm diameter) and spacing (250-300 mm), with 50% load transfer efficiency assumption and check for concrete bearing stress using Bradbury's or IRC:58 recommendations
- Part (b): Year-wise development cost outflow (10%, 15%, 20%, 55% of Rs. 100 × 60,000 = Rs. 6,00,000) and revenue inflow from plot sales (10%, 20%, 20%, 30%, 20% of 60,000 m² at Rs. 5000/m²), discounted at 7% to find NPV and cost per m²
- Part (c)(i): Ferro-cement advantages—thin sections (10-25 mm), high strength-to-weight ratio, crack resistance due to distributed reinforcement, no formwork needed, cost-effectiveness for small tanks; justification for 25,000+ litre tanks requires thickness increase, stiffener rings, and waterproofing treatment
- Part (c)(ii): Correct labeling of door components—styles (vertical), rails (horizontal), mullions (intermediate vertical), panels, stiles, top rail, bottom rail, lock rail, meeting stiles, hinges, latch/lock hardware

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Demonstrates mastery of IRC:58 dowel bar design philosophy, understands load transfer mechanisms in rigid pavements, applies correct valuation principles (NPV, discounting), and accurately describes ferro-cement composite behavior and door joinery terminology; cites relevant Indian standards	Shows basic understanding of dowel bar purpose and load transfer, applies standard formulas with minor conceptual gaps in valuation (e.g., simple interest instead of discounting), lists some ferro-cement advantages but misses critical limitations for large tanks, identifies common door parts	Confuses dowel bars with tie bars, misunderstands radius of relative stiffness application, makes fundamental errors in NPV calculation (ignoring time value), describes ferro-cement as merely 'thin RCC', or mislabels door components with layman terms
Numerical accuracy	25%	12.5	All calculations precise: dowel diameter from bearing stress (d ≥ P/(σb×h)), spacing from relative stiffness considerations, complete year-wise DCF table with correct discount factors (1.07, 1.07², etc.), accurate NPV and per m² cost; uses consistent units throughout	Correct formula application with minor arithmetic errors (1-2 calculation mistakes), partially correct DCF table with some discount factor errors, reaches approximately correct final values; shows understanding of computational approach	Major calculation errors, incorrect formula application (e.g., using wheel load directly without 40% factor), omits discounting entirely or uses wrong rate, order-of-magnitude errors in final answers, or missing numerical sections
Diagram quality	15%	7.5	Clear sketch of dowel bar arrangement at expansion joint showing load transfer, joint width, and embedment lengths; neat door elevation with all components labeled using proper technical terms; diagrams support and enhance written explanation	Basic sketches present with most key features shown, some labeling present but may use non-standard terminology or have minor omissions; diagrams are legible but not professionally executed	Missing diagrams where required (especially door labeling), illegible sketches, or diagrams that contradict written description; no attempt to illustrate dowel bar configuration or door components
Step-by-step derivation	25%	12.5	Systematic presentation: for (a) states assumptions, calculates required diameter from bearing, checks shear and flexure, finalizes spacing; for (b) shows year-wise cost and revenue tables with discount factors, clear NPV calculation; all steps logically sequenced with proper justification	Most steps shown but with some jumps in logic, missing intermediate calculations, or unclear presentation of DCF methodology; final answers correct but derivation hard to follow; some assumptions stated	Disorganized working, missing critical steps (e.g., no stress checks for dowels), presents only final answers without derivation, or incorrect sequence of operations; assumptions not stated or inconsistent
Practical interpretation	15%	7.5	Interprets design results practically: comments on standard bar sizes available in India, construction tolerances for joint width, economic viability of land development project, realistic applications of ferro-cement (rural water tanks vs. urban large storage), and functional requirements of door components	Some practical context provided but limited depth; mentions standard sizes or construction feasibility without elaboration; basic recognition of ferro-cement applications; superficial treatment of economic implications	Purely theoretical treatment with no connection to field practice, ignores constructability issues, fails to assess economic feasibility of the land development, or makes unrealistic claims about ferro-cement tank capacity without justification

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