Civil Engineering 2025 Paper I 50 marks Solve

Q4

(a) Analyse the frame shown in the figure by the moment distribution method. Draw the Bending Moment Diagram (BMD). Joints 'B' and 'C' are rigid; 'A' and 'D' are fixed. 20 marks (b) A horizontal steel bar of 60 mm diameter is rigidly tied at each end, the ties being 1·25 m apart. A rigid bracket is fixed to the middle of the bar. Determine the maximum radial length of the bracket at which a vertical load of 1400 N can be suspended, if the deflection of the load is not to exceed 0·5 mm. Take E = 2 × 10⁵ N/mm²; G = 7·6 × 10⁴ N/mm². 10 marks (c) (i) For a continuous beam ABCDEFG, show the pattern of loading for the live load for the following : (A) max –ve bending moment at support C (B) max +ve bending moment in span CD (C) max –ve bending moment in span CD (D) max +ve bending moment at support C (ii) Design a (tread and riser) dog-legged staircase of an office building, given the following data : Height between floors = 3·2 m Riser = 160 mm Tread = 270 mm Width of flight = Landing width = 1·25 m Live load = 5 kN/m² Finishes load = 0·6 kN/m² Consider the landing to be supported only on two edges perpendicular to the risers. Take density of concrete = 25 kN/m³. Pt/100 = Ast/bd = fck/2fy [1 - √(1 - 4.598 R/fck)] where R = Mu/bd². 14 marks

हिंदी में प्रश्न पढ़ें

(a) चित्र में दर्शाए गए फ्रेम का विश्लेषण आघूर्ण वितरण विधि द्वारा कीजिए । बंकन आघूर्ण आरेख (बी.एम.डी.) बनाइए । जोड़ 'B' और 'C' दृढ़ हैं; 'A' और 'D' आबद्ध हैं । 20 अंक (b) 60 mm व्यास की एक क्षैतिज इस्पात छड़ प्रत्येक सिरे पर दृढ़ता से आबद्ध है, आबद्धक एक दूसरे से 1·25 m की दूरी पर हैं । एक दृढ़ ब्रैकेट छड़ के मध्य पर आबद्ध है । ब्रैकेट की अधिकतम त्रिज्यीय लंबाई निर्धारित कीजिए जिस पर 1400 N का एक उल्लंबधर भार लटकाया जा सके, यदि भार का विस्थापन 0·5 mm से अधिक नहीं हो पाए । E = 2 × 10⁵ N/mm²; G = 7·6 × 10⁴ N/mm² लीजिए । 10 अंक (c) (i) निम्नलिखित के लिए, एक सतत धरन ABCDEFG के लिए चल भार के भारण के स्वरूप को दर्शाइए : (A) आलम्ब C पर अधिकतम ऋणात्मक बंकन आघूर्ण (B) विस्तृति CD में अधिकतम धनात्मक बंकन आघूर्ण (C) विस्तृति CD में अधिकतम ऋणात्मक बंकन आघूर्ण (D) आलम्ब C पर अधिकतम धनात्मक बंकन आघूर्ण (ii) एक कार्यालय भवन की प्रतिवर्ती सीढ़ी (ट्रेड और राइजर) की अभिकल्पना कीजिए, निम्नलिखित आँकड़े प्रदत हैं : मंजिलों के बीच ऊँचाई = 3·2 m राइजर = 160 mm ट्रेड = 270 mm फ्लाइट की चौड़ाई = लैंडिंग चौड़ाई = 1·25 m चल भार = 5 kN/m² परिष्कृतियों का भार = 0·6 kN/m² लैंडिंग को राइजर के लम्बवत केवल दो सिरों पर आलम्बित मान लीजिए । कंक्रीट का घनत्व = 25 kN/m³ लीजिए । Pt/100 = Ast/bd = fck/2fy [1 - √(1 - 4.598 R/fck)] जहाँ R = Mu/bd² है । 14 अंक

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Approach

This is a multi-part numerical problem requiring systematic solving: begin with the moment distribution frame analysis (a) carrying 20 marks and consuming ~45% time, followed by the torsion-deflection calculation (b) at ~25%, then loading patterns (c)(i) at ~15%, and finally the staircase design (c)(ii) at ~15%. Present each sub-part clearly separated with proper headings, showing all calculations stepwise, and conclude with final answers boxed for each part.

Key points expected

  • Part (a): Correct calculation of stiffness factors, distribution factors, fixed-end moments, and iterative moment distribution until convergence; proper drawing of BMD with values marked at critical sections
  • Part (b): Recognition of combined bending and torsion in the bracket problem; correct application of deflection limit to find maximum radial length using both E and G values
  • Part (c)(i): Correct live load pattern diagrams for all four cases (max -ve BM at C, max +ve BM in CD, max -ve BM in CD, max +ve BM at C) using alternate span loading principle
  • Part (c)(ii): Proper sizing of staircase (number of risers, treads, flights), load calculations (self-weight, live load, finishes), moment calculation for landing as two-way slab, and reinforcement design using given formula
  • Correct use of relative stiffness for members with different end conditions in moment distribution
  • Proper unit consistency throughout (mm, N, MPa) and conversion where needed
  • Clear free-body diagrams and deflected shapes where applicable to support calculations

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness22%10Correctly applies moment distribution fundamentals (stiffness K=4EI/L for far fixed, K=3EI/L for far pinned if applicable), recognizes combined stress state in (b), applies Muller-Breslau principle for load patterns in (c)(i), and treats landing as two-way slab in (c)(ii); no conceptual errors in any sub-partMinor errors in stiffness factor selection (e.g., using 4EI/L instead of 3EI/L where appropriate) or incomplete understanding of torsion-bending interaction; load patterns mostly correct but missing some spansFundamental misunderstanding of moment distribution (e.g., wrong distribution factor calculation), treats (b) as pure bending ignoring torsion, or designs staircase as one-way slab
Numerical accuracy22%10All calculations accurate to 3 significant figures; correct final answers for moment distribution moments, bracket length ~180-200 mm, and staircase reinforcement area; proper substitution in given Pt/100 formulaMinor arithmetic errors in distribution iterations or unit conversion mistakes (m to mm); final answers within 10% of correct value; staircase design approximately correct but rounding errorsMajor calculation errors leading to absurd results (e.g., negative bracket length, moments not balancing at joints); wrong formula application or order-of-magnitude errors
Diagram quality18%8Clear BMD for (a) with values at A, B, C, D and proper curvature; neat loading pattern sketches for (c)(i) with spans clearly marked; staircase plan and section drawings with dimensions; all diagrams labeled with units and valuesBMD drawn but missing some values or incorrect sign convention; loading patterns understandable but poorly spaced; minimal staircase detailingMissing BMD or unrecognizable diagrams; no loading pattern illustrations; diagrams without labels or values making them useless for verification
Step-by-step derivation22%10Tabular moment distribution with at least 2-3 cycles shown, carry-over clearly indicated; explicit derivation of torsion constant J for circular section in (b); complete load calculation table for staircase; all steps logically sequenced with justificationMoment distribution table present but iterations condensed; some intermediate steps skipped in (b) or (c)(ii) but final method discernibleNo working shown—only final answers; or completely disorganized working with no logical flow; missing essential steps like carry-over in moment distribution
Practical interpretation16%6Comments on practical implications: realistic moment values for frame design, check on bracket deflection limit being serviceability critical, appropriate staircase dimensions per IS 456 (riser 150-190mm, tread 250-300mm), and practical bar arrangement in staircaseBrief mention of code compliance or practical checks without elaboration; standard dimensions acknowledged but no explicit code referenceNo practical context provided; purely mathematical exercise with no engineering judgment; unrealistic final answers not flagged (e.g., impractical reinforcement percentage)

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