Civil Engineering 2022 Paper II 50 marks Solve

Q2

(a) A construction company is planning to purchase an excavation equipment for operating a borrow soil pit that will last 5 years. The soil can be excavated by equipment 'A' or equipment 'B'. Equipment 'A' has an initial cost of ₹ 1·32 lakh and will have no salvage value at the end of the project. Equipment 'B' has an initial cost of ₹ 0·21 lakh. However, to provide the same capacity, 2 numbers of equipment 'B' are required and their operating cost per year together (for 2 numbers of equipment 'B') will be ₹ 0·18 lakh more than the equipment 'A'. Normal service life for equipment 'B' is 3 years with zero salvage value but a 2-year-old equipment 'B' can likely be sold for ₹ 0·05 lakh. If the interest rate is 15%, which equipment (equipment 'A' or 2 numbers of equipment 'B') should be preferred to purchase from the present worth point of view? The estimated salvage value for equipment 'B' must be included as a cash inflow at the end of year 5. (15 marks) (b) Design a flexible pavement for a two-lane undivided carriageway using the following data: Subgrade CBR value = 8%, Lane distribution factor = 0·5, Design Life = 15 years, Planning and Construction period = 1·5 years. Present commercial traffic is as under: Bus (Gross Wt. 15T, 200 vehicles/day, Front Axle – Single, Rear Axle – Dual, Growth Rate 4%), Truck (Gross Wt. 20T, 1512 vehicles/day, Front Axle – Single, Rear Axle – Tandem, Growth Rate 8%). As per IRC 37, 2018 the following pavement composition is desired for CBR of 8% subgrade corresponding to different Design traffic: [Table showing Design Traffic (msa) vs pavement layers]. (15 marks) (c) The following data were obtained from the spot speed study carried out at a city road. Suggest (i) Speed limit for regulation, (ii) Speed to check geometric design elements, (iii) Lower speed group causing congestion. [Table showing Speed Range (km/hr) vs No. of Vehicles]. (15 marks)

हिंदी में प्रश्न पढ़ें

(a) एक निर्माण कम्पनी एक मिट्टी खदान के प्रचालन के लिए एक खुदाई उपकरण के क्रय की योजना बना रही है जो 5 वर्ष तक रहेगा। मिट्टी उपकरण 'A' या उपकरण 'B' के द्वारा खोदी जा सकती है। उपकरण 'A' की प्रारंभिक लागत ₹ 1·32 लाख है तथा परियोजना के अंत में निस्तारण मूल्य कुछ भी नहीं होगा। उपकरण 'B' की प्रारंभिक लागत ₹ 0·21 लाख है। यद्यपि समान क्षमता के लिए 'B' के दो उपकरणों की आवश्यकता होगी तथा उन दोनों की प्रचालन लागत प्रति वर्ष ('B' के दो उपकरण) उपकरण 'A' से ₹ 0·18 लाख अधिक होगी। उपकरण 'B' की सामान्य सेवा आयु 3 वर्ष है और निस्तारण मान शून्य है लेकिन एक 2 वर्ष पुराना उपकरण 'B' ₹ 0·05 लाख में विक्रय किया जा सकता है। यदि ब्याज दर 15% है, तो कौन-से उपकरण को (उपकरण 'A' या 2 संख्या में उपकरण 'B') वर्तमान मूल्य के दृष्टिकोण से क्रय करने हेतु वरीयता देनी चाहिए? उपकरण 'B' का अनुमानित निस्तारण मूल्य 5 वर्ष के अंत में नकदी अंतवाह के रूप में शामिल किया जाना चाहिए। (15 अंक) (b) निम्नलिखित आँकड़ों का उपयोग करते हुए एक अविभाजित दो-लेन मार्ग के लिए एक नम्य कुशिंग का अभिकल्पन कीजिए: सबग्रेड का सी.बी.आर. मान = 8%, लेन वितरण गुणक = 0·5, अभिकल्पन आयु = 15 वर्ष, परिकल्पन तथा निर्माण अवधि = 1·5 वर्ष। वर्तमान व्यावसायिक ट्रैफिक निम्न प्रकार है: बस (सकल भार 15T, 200 वाहन प्रतिदिन, अग्र धुरी – एकल, पश्च धुरी – दोहरी, वृद्धि दर 4%), ट्रक (सकल भार 20T, 1512 वाहन प्रतिदिन, अग्र धुरी – एकल, पश्च धुरी – अग्रपश्च (टैन्डम), वृद्धि दर 8%)। IRC 37, 2018 के अनुसार, सबग्रेड 8% के लिए विभिन्न अभिकल्पित ट्रैफिक के अनुसार निम्नलिखित कुंडिम संयोजन अपेक्षित है: [सारणी दिखाते हुए अभिकल्पित ट्रैफिक (एम.एस.ए.) बनाम परतें]। (15 अंक) (c) एक शहर की सड़क पर किए गए स्थानिक गति अध्ययन से निम्नलिखित आँकड़े प्राप्त किए गए। सुझाइए (i) नियमन के लिए गति सीमा, (ii) ज्यामितीय अभिकल्प घटकों की जाँच के लिए गति, (iii) संकुलन करने वाले निम्न गति समूह। [सारणी दिखाते हुए गति परास (km/hr) बनाम वाहनों की संख्या]। (15 अंक)

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Approach

Solve all three sub-parts systematically: (a) Calculate present worth of costs for Equipment A vs two Equipment B using 15% interest rate, accounting for replacement cycle and salvage value; (b) Design flexible pavement using IRC 37:2018 by computing cumulative standard axles (msa) and selecting layer thicknesses from the provided table; (c) Analyse spot speed data to determine 85th percentile speed for regulation, 98th percentile for geometric design, and identify congested speed groups. Allocate approximately 35% time to part (a) due to complex replacement analysis, 35% to part (b) for detailed traffic calculations, and 30% to part (c) for statistical interpretation. Present each part with clear headings, formulae, calculations, and final recommendations.

Key points expected

  • Part (a): Correct application of present worth factor (PWF) at 15% for 5 years; Equipment A: single investment with annual operating costs; Equipment B: initial purchase plus replacement at year 3 with salvage of old equipment, higher combined operating costs, and final salvage value at year 5 included as cash inflow
  • Part (a): Proper handling of Equipment B's replacement economics - buying new unit at year 3 while selling 2-year-old unit for ₹0.05 lakh, and recognizing that 2 units of B operate throughout
  • Part (b): Correct calculation of design traffic using F=365, lane distribution factor 0.5, vehicle damage factor (VDF) for buses and trucks as per IRC 37:2018, growth factors (4% and 8%), and construction period of 1.5 years
  • Part (b): Accurate computation of cumulative standard axles in msa and selection of appropriate pavement layer thicknesses from IRC 37:2018 table for CBR 8% and calculated design traffic
  • Part (c): Statistical analysis of spot speed data - calculation of cumulative frequency distribution, identification of 85th percentile speed for regulatory speed limit, 98th percentile for geometric design checks, and determination of lower speed group causing congestion (typically below 15th percentile or modal speed range)
  • Part (c): Proper presentation of frequency distribution table and cumulative percentages to justify speed recommendations with clear reasoning for each decision

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%9Demonstrates mastery of engineering economics (present worth analysis with replacement cycles), IRC 37:2018 pavement design methodology including VDF and traffic accumulation, and traffic engineering statistics (percentile speeds); correctly identifies that Equipment B requires replacement analysis and that spot speed percentiles serve different design purposesShows basic understanding of present worth concepts and pavement design steps but makes minor errors in replacement timing, VDF selection, or percentile interpretation; may confuse 85th vs 98th percentile applicationsFundamental misconceptions such as treating annual costs as simple sums without discounting, ignoring replacement needs for Equipment B, using wrong growth period, or applying arbitrary speed limits without statistical basis
Numerical accuracy20%9All calculations precise: correct PWF values [(1.15)^5], accurate Equipment B replacement cost net of salvage, exact msa calculation with proper VDF values (typically 2.5 for bus rear dual, 4.5 for truck rear tandem), correct cumulative frequency calculations for speed data; final numerical answers match expected rangesGenerally correct approach with minor arithmetic errors in discount factors, traffic calculations, or frequency percentages; final answers slightly off but methodologically soundMajor calculation errors such as wrong exponent in present worth, omitting lane distribution factor, incorrect VDF application, or errors in cumulative frequency summation leading to wrong percentile identification
Diagram quality15%7Clear cash flow diagram for part (a) showing timing of all outflows and inflows for both alternatives; neat pavement layer sketch with thicknesses labeled for part (b); well-drawn frequency distribution curve or histogram with percentile markings for part (c); all diagrams properly titled and referencedBasic diagrams present but lacking detail or clarity; cash flows shown without clear time markers, pavement sketch without proper layer identification, or speed distribution without clear percentile markingsMissing essential diagrams or illegible sketches; no visual representation of cash flows, pavement cross-section, or speed distribution; diagrams contradict numerical work
Step-by-step derivation25%11Complete logical flow: explicit formulae stated (PWF, compound growth, standard axle formula), substitution of values shown, intermediate results calculated, clear comparison of Equipment A vs B present worths, detailed traffic calculation table, systematic cumulative frequency table for speed data; each step justified with IRC/code referencesMost steps shown but some shortcuts taken; formulae implied rather than stated, minor skips in calculation chains, or less organized presentation of traffic data; final answers correct but derivation harder to followDisorganized or missing steps; jumps from given data to final answer without showing work; no formulae cited; impossible to verify calculations or identify where errors occur
Practical interpretation20%9Clear equipment selection recommendation with economic justification; pavement design validated against IRC 37:2018 provisions with constructability notes; speed recommendations contextualized for Indian urban road conditions with safety and congestion management rationale; identifies practical constraints like Equipment B's market availability for resaleCorrect recommendations stated but with limited justification; accepts numerical results without discussing practical implications; minimal connection to real-world construction or traffic management scenariosNo clear recommendations or conclusions; ignores practical aspects such as equipment availability, construction feasibility of pavement layers, or enforcement challenges of proposed speed limits; purely theoretical treatment

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