Civil Engineering 2024 Paper II 50 marks Solve

Q2

(a) The network for a construction project is shown in the figure given below. The three time estimates for each activity are given along each activity arrow. Determine the: (i) Expected time of completion of each activity, (ii) Earliest expected time for each event, (iii) Latest allowable occurrence time for each event, (take earliest expected time for last event as the scheduled completion time for the project), (iv) Slack for each event, (v) Critical path of the network. Also, give explanation of dotted arrow shown in the network. What is the significance of critical path? All time estimates are in days. 20 marks (b) What are the functions of tie bars in rigid pavements? A cement concrete pavement has a thickness of 30 cm and lane width 3·75 m. Design the tie bars along the longitudinal joints using the data given below: Allowable working stress in steel tie bars = 1250 kg/cm², Allowable tensile stress in deformed bars (Sₛ) = 2000 kg/cm², Allowable bond stress in plain bars (Sᵦ) = 17·5 kg/cm², Allowable bond stress in deformed bars (Sᵦ) = 24·6 kg/cm², Unit weight of concrete pavement (W) = 2400 kg/m³, Maximum value of friction coefficient (f) = 1·35. 15 marks (c) A high speed B.G. section with a maximum sanctioned speed of 130 kmph is proposed. The section is passing through a transition length with a 2° curve. Calculate the superelevation, maximum permissible speed and transition length for this section at curve. Assume the equilibrium speed as 90 kmph and the booked speed of the goods train to be 60 kmph. Rate of change of Cant or Cant deficiency is 35 mm/sec. Assume any other data suitably. 15 marks

हिंदी में प्रश्न पढ़ें

(a) एक निर्माण परियोजना के लिए जाल (नेटवर्क) नीचे दिए गए चित्र में दर्शाया गया है। प्रत्येक क्रिया के तीन आकलित समय प्रत्येक क्रिया तीर के साथ दिखाए गए हैं। ज्ञात कीजिए: (i) प्रत्येक क्रिया के पूरा होने का अपेक्षित समय, (ii) प्रत्येक घटना के लिए यथाशीघ्र अपेक्षित समय, (iii) प्रत्येक घटना के लिए यथाविलम्बित अनुज्ञेय घटन काल (अंतिम घटना के यथाशीघ्र अपेक्षित समय को परियोजना के लिए निर्धारित समापन समय के रूप में लीजिए), (iv) प्रत्येक घटना का स्लैक, (v) जाल का क्रांतिक पथ। जाल में दर्शाए गए बिंदुकित तीर का स्पष्टीकरण भी दीजिए। क्रांतिक पथ का क्या महत्व है? सभी आकलित समय दिनों में दिए गए हैं। 20 (b) दृढ़ कुंडियों में बंधन छड़ों (टाई बार) के क्या कार्य हैं? एक सीमेंट कंक्रीट कुंडिम की मोटाई 30 सेमी और लेन की चौड़ाई 3·75 मीटर है। नीचे दिए गए आंकड़ों का उपयोग करते हुए अनुदैर्ध्य संधियों में बंधन छड़ों की अभिकल्पना कीजिए: स्टील बंधन छड़ों में अनुज्ञेय कार्यकारी प्रतिबल = 1250 किग्रा/सेमी², विकृत छड़ों में अनुज्ञेय तनन प्रतिबल (Sₛ) = 2000 किग्रा/सेमी², सादा छड़ों में अनुज्ञेय बंध प्रतिबल (Sᵦ) = 17·5 किग्रा/सेमी², विकृत छड़ों में अनुज्ञेय बंध प्रतिबल (Sᵦ) = 24·6 किग्रा/सेमी², कंक्रीट कुंडिम का एकक भार (W) = 2400 किग्रा/मी³, घर्षण गुणांक का अधिकतम मान (f) = 1·35। 15 (c) उच्च गति वाली बड़ी लाइन (बी.जी.) का एक भाग है जिसकी अधिकतम अनुमत गति 130 किमी प्रति घंटा प्रस्तावित है। यह भाग 2° वक्र वाली संक्रमण लंबाई से गुजर रहा है। वक्र पर इस भाग के लिए बाहोत्थान (सुपरएलिवेशन), अधिकतम अनुमत गति और संक्रमण लंबाई की गणना कीजिए। संतुलन गति 90 किमी प्रति घंटा और मालगाड़ी की अभिलेखित गति 60 किमी प्रति घंटा मान लीजिए। कैंट न्यूनता या कैंट के परिवर्तन की दर 35 मिमी प्रति सेकंड है। किन्हीं अन्य आंकड़ों को उपयुक्त रूप से मान लीजिए। 15

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How this answer will be evaluated

Approach

Solve all three sub-parts systematically, allocating approximately 40% time to part (a) given its 20 marks, and 30% each to parts (b) and (c). Begin with clear PERT calculations for (a), followed by tie bar design computations for (b), and superelevation/transition length calculations for (c). Present all numerical work in tabular format where appropriate, with clear labeling of each step.

Key points expected

  • Part (a): Calculate expected activity times using PERT formula (te = (a+4m+b)/6), determine TE and TL for each event, compute slacks, identify critical path, and explain dummy activity significance
  • Part (a): Correct interpretation of dotted arrow as dummy activity showing logical dependency without time/resource consumption, and critical path significance for project scheduling
  • Part (b): State functions of tie bars (prevent longitudinal joint opening, transfer load, maintain slab alignment), then design tie bar diameter, spacing and length using friction coefficient method
  • Part (c): Calculate equilibrium superelevation for 90 kmph, check against maximum (1/12th or 1/8th of gauge), determine cant deficiency for 130 kmph, and compute transition length based on rate of change of cant
  • Part (c): Apply Indian Railways standards for BG track (1750 mm gauge), verify booked speed check for goods train (60 kmph), and ensure maximum permissible speed satisfies all constraints

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly applies PERT methodology for (a), understands tie bar mechanics and IRC design principles for (b), and applies Indian Railways superelevation standards (equilibrium, cant deficiency, transition curve) for (c); no conceptual errors in any sub-partMostly correct concepts with minor errors in one sub-part, such as incorrect PERT formula application or confusion between tie bars and dowel bars, or superelevation calculation errorsFundamental conceptual errors like treating PERT as CPM deterministic, confusing tie bars with load transfer dowels, or applying wrong gauge/standards for BG track
Numerical accuracy25%12.5All calculations precise: correct expected times, TE/TL values, critical path identification for (a); accurate tie bar diameter, spacing, length for (b); correct superelevation, cant deficiency, transition length and verified speeds for (c); proper unit handling throughoutCorrect methodology with minor arithmetic errors in 1-2 sub-parts, or unit conversion mistakes (e.g., kmph to m/s), or rounding errors affecting final values slightlyMajor calculation errors, wrong formulas applied numerically, or inconsistent units leading to unrealistic results (e.g., negative slack, impractical tie bar spacing, excessive cant deficiency)
Diagram quality15%7.5Reproduces clear network diagram for (a) with activities, time estimates, and event numbering; sketches tie bar placement detail for (b); draws transition curve diagram with superelevation development for (c); all diagrams labeled, proportional, and referenced in textBasic diagrams present but lacking detail, poor labeling, or not properly integrated with calculations; or missing one required diagramNo diagrams, or completely unrecognizable sketches; failure to show network structure, tie bar configuration, or transition curve geometry when explicitly needed
Step-by-step derivation25%12.5Systematic presentation: tabular calculation of PERT parameters with forward/backward pass for (a); clear friction force derivation leading to tie bar design for (b); explicit superelevation formula application with speed checks for (c); all formulas stated before substitutionSome steps shown but with gaps in logical flow, missing intermediate calculations, or unclear presentation of forward/backward pass methodologyOnly final answers with no working, or completely jumbled calculations without logical sequence; impossible to follow derivation path
Practical interpretation15%7.5Interprets critical path for project crashing decisions in (a); discusses tie bar corrosion protection and construction practice in (b); evaluates speed restrictions and safety implications for mixed traffic in (c); cites IRC:58, Indian Railways Permanent Way Manual relevanceBrief mention of practical significance without elaboration, or generic statements not tied to specific numerical results obtainedPurely mathematical treatment with no interpretation of what results mean for construction scheduling, pavement performance, or railway operations

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