Civil Engineering 2022 Paper I 50 marks Solve

Q4

(a) Find the maximum load P, which the bracket as shown can transmit. The bolt strength of 20 mm dia and 8·8 grade is assumed to be 82 kN, considering shear and bearing under limit state method. (15 marks) (b) A continuous beam ABC has span AB = 6 m and BC = 6 m and carries a uniformly distributed load of 25 kN/m covering both the spans AB and BC. Supports A and C are simple supports. If the load factor is 1·75 and the shape factor is 1·144 for the I-section, determine the section modulus required. Use the yield stress for the material as 245 MPa. (15 marks) (c) Design the vertical stem of a reinforced concrete retaining wall as shown below. The angle of repose of the earth is 30° and its density is 18 kN/m³. Use M25 grade of concrete and Fe500 grade of steel. The wall is safe against stability. Detail the reinforcement in the stem only. Given: | M_u/bd² | 1·5 | 1·6 | 1·7 | 1·8 | 1·9 | 2·0 | 2·1 | 2·2 | 2·3 | 2·4 | 2·5 | |---------|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----| | p_t | 0·373 | 0·40 | 0·427 | 0·455 | 0·484 | 0·512 | 0·541 | 0·571 | 0·601 | 0·631 | 0·662 | Assume nominal cover to reinforcement as 50 mm. Curtailment of bars is not required. Given: | τ_c (MPa) | 0·36 | 0·49 | 0·57 | 0·64 | 0·70 | 0·74 | 0·78 | 0·82 | 0·85 | 0·88 | |-----------|------|------|------|------|------|------|------|------|------|------| | p_t | 0·25 | 0·5 | 0·75 | 1·0 | 1·25 | 1·5 | 1·75 | 2·0 | 2·25 | 2·5 | (20 marks)

हिंदी में प्रश्न पढ़ें

(a) अधिकतम भार P ज्ञात कीजिए, जिसे दर्शाया गया ब्रैकेट प्रेषित कर सकता है। सीमांत अवस्था विधि में अपरूपण और धारण के लिए 20 mm व्यास वाले तथा 8·8 ग्रेड के बोल्ट की सामर्थ्य को 82 kN माना गया है। (15 अंक) (b) एक सतत धरन ABC, विस्तृति AB = 6 m और BC = 6 m, AB तथा BC दोनों की पूरी विस्तृति पर 25 kN/m का एकसमान वितरित भार वहन करती है। आलम्ब A और C शुद्ध आलम्ब हैं। यदि I-परिच्छेद के लिए भार गुणक 1·75 और आकार गुणक 1·144 है, तो आवश्यक परिच्छेद मापांक निर्धारित कीजिए। पदार्थ के लिए प्रारंभ प्रतिबल 245 MPa का उपयोग कीजिए। (15 अंक) (c) दर्शाए अनुसार प्रबलित कंक्रीट की प्रतिधारक भित्ति के उद्व पट्ट का अभिकल्प कीजिए। मृदा का विश्राम-कोण 30° और इसका घनत्व 18 kN/m³ है। M25 ग्रेड कंक्रीट और Fe500 ग्रेड इस्पात का उपयोग कीजिए। भित्ति स्थायित्व के विरुद्ध सुरक्षित है। प्रबलन का विवरण केवल उद्व पट्ट के लिए दीजिए। प्रदत : | M_u/bd² | 1.5 | 1.6 | 1.7 | 1.8 | 1.9 | 2.0 | 2.1 | 2.2 | 2.3 | 2.4 | 2.5 | |---------|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----| | p_t | 0.373 | 0.40 | 0.427 | 0.455 | 0.484 | 0.512 | 0.541 | 0.571 | 0.601 | 0.631 | 0.662 | प्रबलन का अभीष्ट आवरण 50 mm मान लीजिए। छड़ों के छिन्नीकरण की आवश्यकता नहीं है। प्रदत : | τ_c (MPa) | 0.36 | 0.49 | 0.57 | 0.64 | 0.70 | 0.74 | 0.78 | 0.82 | 0.85 | 0.88 | |-----------|------|------|------|------|------|------|------|------|------|------| | p_t | 0.25 | 0.5 | 0.75 | 1.0 | 1.25 | 1.5 | 1.75 | 2.0 | 2.25 | 2.5 | (20 अंक)

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Approach

Solve all three sub-parts systematically, allocating approximately 30% time to part (a) bolted bracket analysis, 30% to part (b) plastic moment capacity of continuous beam, and 40% to part (c) complete RC retaining wall stem design including reinforcement detailing. Begin each part with clear identification of given data, apply relevant IS codes (IS 800:2007 for steel, IS 456:2000 for concrete), show all formulae with substitutions, and conclude with final answers in proper units. For part (c), include a neat sketch showing bar curtailment and spacing.

Key points expected

  • Part (a): Identify bolt group centroid, calculate eccentricity, determine critical bolt under combined direct shear and torsional shear, resolve shear components, check resultant against bolt strength of 82 kN to find maximum load P
  • Part (b): Calculate collapse load factor × working load, determine plastic moment capacity using shape factor and yield stress, apply virtual work or static method for continuous beam collapse mechanism, equate internal and external work to find required section modulus
  • Part (c): Compute active earth pressure coefficient Ka for φ=30°, determine lateral pressure distribution and maximum moment at base of stem, calculate effective depth using cover, find Mu/bd² and interpolate pt from table, calculate steel area and provide distribution steel, check shear stress against permissible τc
  • Correct application of limit state design principles per IS 800:2007 for steel connections and IS 456:2000 for RC design
  • Proper interpretation of given design tables for percentage steel (pt) and permissible shear stress (τc) through linear interpolation where needed
  • Complete reinforcement detailing for stem showing main steel on tension face, distribution steel, and development length considerations

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies eccentric loading on bolt group for (a), plastic collapse mechanism with hinge formation for (b), and active earth pressure with cantilever action for (c); applies proper IS code clauses throughoutIdentifies basic concepts but makes minor errors in collapse mechanism selection or earth pressure coefficient application; some code references missingConfuses concepts (e.g., uses elastic analysis for plastic design, applies passive pressure instead of active), fundamental misunderstanding of bolt group behavior
Numerical accuracy25%12.5All calculations precise to 2-3 decimal places; correct interpolation in tables; final answers with proper units; no arithmetic errors in moment calculations or steel areasMinor calculation errors (±5%) or unit inconsistencies; approximate interpolation; one significant error in final answer but correct methodologyMajor computational errors (>10%), wrong formula substitutions, incorrect unit conversions, or answers without any numerical working
Diagram quality15%7.5Clear free-body diagrams for bracket showing eccentricity and bolt forces; collapse mechanism diagram for continuous beam; pressure diagram and cross-section of stem with reinforcement layout; all dimensions and bar marks labeledDiagrams present but lacking key dimensions or labels; rough sketches without proper scale indication; missing pressure distribution diagramNo diagrams or incomprehensible sketches; failure to show critical sections or reinforcement placement
Step-by-step derivation25%12.5Every formula stated with IS code reference; clear substitution of values; logical progression from given data to final answer; explicit statement of assumptions; proper handling of units throughoutSome steps skipped or combined; missing code references; correct final answer but unclear derivation path; assumptions not statedDisorganized working with no logical flow; missing critical steps; no indication of formula sources; impossible to follow calculation sequence
Practical interpretation15%7.5Comments on practical bolt spacing in (a), checks for ductility in plastic design for (b), and provides constructible reinforcement details with bar diameters, spacing, and development lengths for (c); notes on durability and crack controlBrief concluding remarks without specific practical insights; standard detailing without consideration of construction constraintsNo practical interpretation; purely mathematical solution without engineering judgment; unrealistic or unbuildable reinforcement details

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