Civil Engineering 2021 Paper I 50 marks Calculate

Q4

(a) Determine the maximum tensile force in member DI of the truss shown below due to the series of three moving loads shown in the figure. Support : Hinge at 'A' and Roller at 'G'. Loads move from G to A. (b) Two parallel plates kept 0·10 m apart have laminar flow of oil between them with a maximum velocity of 1·5 m/s. Calculate the discharge per metre width, the shear stress at the plates, the difference in pressure between two points 20 m apart, the velocity gradients at the plates and velocity at 0·02 m from the plate. Take viscosity of oil to be 2·453 N-s/m². (c) Investigate the stability against overturning, sliding resistance and foundation soil pressure of the retaining wall shown in the figure. The retaining wall is to support a deposit of granular soil which has unit weight, γ = 17·5 kN/m³ and angle of internal friction, φ = 35°. The coefficient of base friction is 0·5. Allowable soil pressure for the foundation soil is 150 kPa. Use Rankine's theory to calculate the active earth pressure on the wall and neglect passive pressure from the toe side. Given : Unit weight of concrete, γc = 24 kN/m³.

हिंदी में प्रश्न पढ़ें

(a) चित्र में दर्शाए गए तीन चलित भारों की श्रृंखला के कारण, नीचे दर्शाई कैंची के अवयव DI में अधिकतम तनन बल को निर्धारित कीजिए। आलम्ब : 'A' पर हिंज और 'G' पर रोलर। भार G से A की ओर चलते हैं। (b) परस्पर 0·10 m दूर रखी दो समानांतर प्लेटों के बीच 1·5 m/s के अधिकतम वेग से तेल का स्तरीय प्रवाह होता है । निस्सरण प्रति मीटर चौड़ाई, प्लेटों पर अपरूपण प्रतिबल, परस्पर 20 m दूर दो बिंदुओं पर दाब में अंतर, प्लेटों पर वेग प्रवणताएं और प्लेट से 0·02 m पर वेग का परिकलन कीजिए । तेल की श्यानता 2·453 N-s/m² लीजिए । (c) चित्र में दर्शाई गई प्रतिधारक भिति के स्थायित्व की जांच उलट जाने, सर्पण प्रतिरोध और आधार मृदा दाब के विरुद्ध कीजिए । प्रतिधारक भिति को एकक भार, γ = 17·5 kN/m³ और आंतरिक घर्षण कोण, φ = 35° वाली कणमय मृदा के एक निक्षेप को आलंबित करना है । आधार घर्षण गुणांक 0·5 है । आधार मृदा के लिए अनुज्ञेय मृदा दाब 150 kPa है । भिति पर सक्रिय मृदा दाब के परिकलन के लिए रैंकिन सिद्धांत का उपयोग कीजिए और पदार्थ की ओर से प्रतिघाती दाब की उपेक्षा कीजिए । प्रदत्त : कंक्रीट का एकक भार, γc = 24 kN/m³.

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Directive word: Calculate

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Approach

Calculate the required parameters for all three sub-parts systematically. For (a), apply influence line method or method of sections with load positioning to find maximum tensile force in DI; spend ~35% time here as it involves moving load analysis. For (b), use parallel plate flow equations for laminar flow; allocate ~25% time. For (c), perform complete stability analysis with Rankine's theory; allocate ~40% time as it carries the highest conceptual and calculation load. Present each part with clear headings, free-body diagrams, and final safety checks.

Key points expected

  • For (a): Correct influence line construction for member DI or proper method of sections application with critical load positioning (loads moving G to A); identification of maximum tensile force location using Muller-Breslau principle or direct calculation
  • For (a): Proper handling of three moving loads (10 kN, 20 kN, 15 kN) with correct load placement for maximum effect on tension member DI
  • For (b): Application of laminar flow between parallel plates (Couette/Poiseuille flow) with parabolic velocity profile; correct use of μ = 2.453 N-s/m², h = 0.10 m, u_max = 1.5 m/s
  • For (b): Calculation of discharge per unit width (q), wall shear stress (τ_w), pressure gradient (Δp/L), velocity gradients (du/dy) at plates, and velocity at y = 0.02 m using u = u_max[1 - (y/(h/2))²]
  • For (c): Rankine's active earth pressure coefficient K_a = (1-sinφ)/(1+sinφ) = 0.271 for φ = 35°; calculation of P_a = ½K_aγH² with proper point of application at H/3 from base
  • For (c): Complete stability checks—overturning (factor of safety ≥ 2), sliding (FOS ≥ 1.5 with μ = 0.5), and base pressure (eccentricity check, p_max ≤ 150 kPa) with weight of concrete wall components
  • For (c): Proper identification of overturning moment (about toe) and restoring moment including self-weight of stem and base slab; correct calculation of resultant location and eccentricity e = B/2 - x̄

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies (a) influence line concept or method of sections for moving loads on truss; (b) laminar flow between fixed parallel plates with zero velocity at walls and maximum at center; (c) Rankine's active earth pressure with proper pressure distribution and all three stability modes (overturning, sliding, bearing)Basic understanding of truss analysis but confuses tension/compression or load positioning; recognizes laminar flow but uses wrong velocity profile; applies earth pressure but misses one stability check or uses Coulomb instead of RankineFundamental errors like using moment distribution for truss, treating flow as turbulent, or applying passive pressure incorrectly; confuses active and at-rest conditions
Numerical accuracy25%12.5All calculations precise to 3 significant figures; correct final answers for (a) maximum tensile force in DI, (b) q = 0.10 m³/s/m, τ_w = 73.6 N/m², Δp = 14.72 kPa, du/dy = ±30 s⁻¹, u = 1.26 m/s; (c) FOS_overturning > 2, FOS_sliding > 1.5, p_max < 150 kPaMinor arithmetic errors in one sub-part; correct methodology but wrong unit conversions (kPa vs Pa, kN vs N); correct stability conclusions despite calculation errorsMajor calculation errors in two or more parts; wrong formulas leading to order-of-magnitude errors; incorrect stability conclusions (unsafe design deemed safe)
Diagram quality15%7.5Clear truss diagram with influence line for DI or free-body with sections; velocity profile parabola for (b); retaining wall with dimensions, earth pressure triangle, weight components, and pressure distribution for (c); all forces labeled with directionsDiagrams present but missing key labels (no dimensions, missing pressure triangle); rough sketches without proper proportions; one diagram missingNo diagrams or incomprehensible sketches; failure to show free-body diagrams essential for truss and retaining wall analysis
Step-by-step derivation25%12.5Systematic presentation: (a) influence line equation or joint/section method with load cases; (b) integration of velocity profile for discharge, differentiation for shear stress, pressure gradient from force balance; (c) tabular calculation of weights, moments, and clear FOS derivation for each modeSome steps shown but jumps between key equations; missing intermediate steps in stability calculations; correct final answers but unclear logicOnly final answers with no working; or incorrect sequence of steps leading to wrong conclusions; no justification for critical load positions
Practical interpretation15%7.5For (c), explicit statement of safety status with reference to IS:456 (FOS ≥ 1.5 for sliding, ≥ 2 for overturning) and IS:6403 (bearing capacity); comments on adequacy of wall section; for (b), physical interpretation of high viscosity oil behavior; for (a), practical significance of maximum tension locationGeneric safety comments without code references; basic interpretation of results without engineering judgment on design adequacyNo interpretation of numerical results; fails to state whether wall is safe or unsafe; missing units or physical meaning of calculated quantities

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