Civil Engineering 2021 Paper I 50 marks Solve

Q2

(a) Using moment area method, find the slopes and deflection at 'B' for the beam shown in the figure below. Point 'B' is a hinge. (15 marks) (b) A rectangular reinforced concrete column of size 250 mm × 400 mm is used to support an ultimate axial load of 700 kN. The column has an unsupported length of 3·2 m. The column is effectively held in position at both ends and restrained against rotation at one end. Design suitable reinforcements in the column using M 25 grade of concrete and Fe 415 HYSD bars. Also draw the reinforcement details. Use limit state method. (15 marks) (c) A flow of 100 litres/sec flows down in a rectangular laboratory flume of width 0·60 m and having adjustable bottom slope. If Chezy's constant (C) is 56, determine the bottom slope for uniform flow with a depth of flow 0·30 m. Also find the conveyance and state the flow. (20 marks)

हिंदी में प्रश्न पढ़ें

(a) आधृण क्षेत्रफल विधि का उपयोग करके, नीचे चित्र में दर्शाई गई धरन के लिए 'B' पर प्रवणताएँ और विस्थेप ज्ञात कीजिए । बिन्दु 'B' एक हिन्ज है । (15 अंक) (b) 250 mm × 400 mm आमाप के एक आयताकार प्रबलित कंक्रीट स्तम्भ का उपयोग एक 700 kN के चरम अक्षीय भार को आलम्बित करने के लिए किया जाता है । स्तम्भ की अनालम्बित लम्बाई 3·2 m है । स्तम्भ दोनों सिरों पर स्थिति में प्रभावी रूप से आबद्ध है और एक सिरे पर घूर्णन निरोधित है । M 25 ग्रेड के कंक्रीट और Fe 415 एच.वाई.एस.डी. छड़ों का उपयोग करके स्तम्भ में उपयुक्त प्रबलनों की अभिकल्पना कीजिए । प्रबलन विस्तरण भी खींचिए । सीमान्त अवस्था विधि का उपयोग कीजिए । (15 अंक) (c) 100 litres/sec का एक प्रवाह, 0·60 m चौड़ी और समायोज्य तल प्रवणता वाली एक आयताकार प्रयोगशाला अवनालिका (फ्ल्यूम) में प्रवाहित होती है । यदि चेजी नियतांक (C) 56 है, तो 0·30 m की प्रवाह की गहराई के एकसमान प्रवाह के लिए तल प्रवणता का निर्धारण कीजिए । वाहकता (कन्वेयेंस) और प्रवाह की दशा भी ज्ञात कीजिए । (20 अंक)

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Approach

This question demands solving three distinct numerical problems covering structural analysis, R.C.C. design, and open channel hydraulics. Begin with clear identification of given data for each part, present systematic calculations with appropriate formulae, and conclude with final answers and reinforcement detailing for part (b).

Key points expected

  • Part (a): Correct application of moment area theorems with proper handling of internal hinge at B, including M/EI diagram construction and tangential deviation calculations
  • Part (b): Calculation of effective length factor (0.8L for given end conditions), slenderness ratio check, minimum eccentricity verification, and longitudinal reinforcement design using SP-16 or working formula with proper lateral ties
  • Part (c): Application of Chezy's formula V = C√(RS) for slope determination, conveyance K = AC√R calculation, and Froude number computation to classify flow regime
  • Proper use of IS 456:2000 provisions for column design including minimum reinforcement percentage (0.8%) and maximum (4%) checks
  • Correct unit conversions throughout (litres/sec to m³/s, mm to m) and consistent use of SI units in final answers
  • Neat reinforcement detailing showing longitudinal bars, lateral ties with spacing as per IS 456, and clear cover specifications

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies moment area theorems for hinge condition, applies IS 456 effective length factors accurately, and uses Chezy's formula with proper hydraulic radius concept; recognizes that hinge at B creates determinate structure for slope/deflection calculationsMinor errors in theorem selection or effective length factor; confuses Chezy's with Manning's equation; understands basic concepts but misapplies in one partFundamental conceptual errors such as treating hinge as fixed support, using wrong effective length coefficient, or applying Bernoulli's equation instead of uniform flow formula
Numerical accuracy25%12.5All three parts yield correct numerical answers with proper significant figures: slopes in radians, deflection in mm, steel area in mm², slope in suitable ratio (1 in x), conveyance in m³/s; cross-checks slenderness ratio against IS 456 limitsCorrect approach with minor calculation errors in one part; acceptable final answers but missing intermediate checks like minimum eccentricity or Froude numberMajor calculation errors, wrong unit conversions (common: litres/sec error), or order-of-magnitude mistakes; fails to verify column safety against buckling
Diagram quality15%7.5Clear M/EI diagram with proper sign convention for part (a); neat reinforcement detailing to IS 456 showing 12-16mm longitudinal bars, 8mm lateral ties @ ≤300mm c/c, 40mm clear cover; dimensioned cross-section and elevation with bar scheduleAcceptable freehand diagrams missing some dimensions or tie spacing; M/EI diagram lacks proper labeling of key ordinatesMissing diagrams or unrecognizable sketches; no reinforcement detailing provided; failure to show hinge condition in beam diagram
Step-by-step derivation25%12.5Systematic presentation: states formulae, substitutes values with units, shows intermediate steps for moment of M/EI diagram areas, calculates steel area using Pu = 0.4fckAc + 0.67fyAsc with explicit Ag and Asc terms; derives S from Chezy equation stepwiseAdequate steps shown but skips some substitutions or combines steps excessively; missing justification for design choices like bar diameter selectionFinal answers without derivation; jumps to results; no working shown for critical steps like solving quadratic for steel area or calculating hydraulic radius
Practical interpretation15%7.5Classifies flow as subcritical/supercritical using Fr = V/√(gD); comments on column slenderness ratio (lex/D < 12 for short column); suggests practical bar arrangement (4 corners + 2 on each face); notes if slope is mild or steep for flume operationBasic interpretation of results without engineering judgment; states flow type but no discussion of implications for flume designNo interpretation of results; fails to classify flow regime; missing comment on whether column is short or slender; no practical relevance discussed

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