Civil Engineering 2024 Paper I 50 marks Calculate

Q3

(a) A box culvert ABCD is shown in the above figure. By using member fixed end moments given above; calculate the final end moments in the box culvert using "Moment distribution method." Also sketch these moments only. (20 marks) (b) Design only the flexural reinforcement for a T-beam section to resist a service moment of 200 kNm. The details of the section are given below: Breadth of flange b_f = 1400 mm Breadth of web b_w = 300 mm Effective depth of the T-beam d = 455 mm Overall depth of the T-beam D = 500 mm Depth of flange D_f = 125 mm Use M25 grade concrete and Fe 500 grade steel. Relevant portion of the IS 456 : 2000 is enclosed. (20 marks) (c) A 10 mts long steel pipe is simply supported at both ends. It is having 500 mm external diameter and 20 mm thickness. It is carrying a total uniformly distributed load of 100 kN/m (including the self weight). Calculate the maximum deflection of the pipe. Take E = 200 GPa. (10 marks)

हिंदी में प्रश्न पढ़ें

(a) नीचे चित्र में एक बक्सा पुलिया ABCD दर्शाई गई है। नीचे दिए गए अवयव-आबद्ध-सिरा-आघूर्णों का उपयोग करते हुए; बक्सा पुलिया के लिए अंतिम सिरा आघूर्णों की गणना "आघूर्ण-वितरण विधि" द्वारा कीजिए। केवल इन आघूर्णों का रेखाचित्र भी बनाइये। M_FAB = –13·5 kN-m M_FBC = –37·5 kN-m M_FCD = –9·0 kN-m M_FAD = +90 kN-m M_FBA = +9·0 kN-m M_FCB = +37·5 kN-m M_FDC = +13·5 kN-m M_FDA = –90·0 kN-m (20 marks) (b) एक T-धरन काट में, 200 kNm के सेवा आघूर्ण को वहन के लिए केवल आनमनी प्रबलन का अभिकल्पन कीजिए । काट का विवरण नीचे दिया गया है : प्लेंज की चौड़ाई b_f = 1400 mm वेब की चौड़ाई b_w = 300 mm T-धरन की प्रभावी गहराई d = 455 mm T-धरन की कुल गहराई D = 500 mm प्लेंज की गहराई D_f = 125 mm M25 ग्रेड कंक्रीट एवं Fe 500 ग्रेड इस्पात का उपयोग कीजिए । IS 456 : 2000 का संबंधित भाग संलग्न है । (20 marks) (c) एक 10 मीटर लम्बा स्टील पाइप दोनों सिरों पर शुद्धालम्बित है। इसका बाहरी व्यास 500 mm और मोटाई 20 mm है। यह कुल 100 kN/m का एकसमान वितरित भार वहन कर रहा है (इसमें स्वभार भी सामिल है)। पाइप के अधिकतम विस्थाप की गणना कीजिए। E = 200 GPa लीजिए। (10 marks)

Evaluate your answer to this question → See all 2024 Civil Engineering questions

Directive word: Calculate

This question asks you to calculate. The directive word signals the depth of analysis expected, the structure of your answer, and the weight of evidence you must bring.

See our UPSC directive words guide for a full breakdown of how to respond to each command word.

How this answer will be evaluated

Approach

Calculate the required quantities across all three sub-parts, allocating approximately 40% of effort to part (a) Moment Distribution Method (20 marks), 40% to part (b) T-beam flexural design (20 marks), and 20% to part (c) pipe deflection (10 marks). Begin with clear identification of given data, proceed through systematic calculations with proper formulae from IS 456:2000 and structural mechanics, and conclude with final answers and sketches where demanded. For part (a), show the complete moment distribution table; for part (b), check neutral axis position and design accordingly; for part (c), apply standard deflection formula for UDL.

Key points expected

  • Part (a): Correct application of Moment Distribution Method with proper distribution factors, carry-over factors, and iterative balancing to obtain final end moments for box culvert frame ABCD with given FEM values
  • Part (a): Accurate sketch of bending moment diagram showing hogging and sagging moments at corners and mid-spans of the box culvert
  • Part (b): Correct determination of neutral axis depth by comparing xu with Df using IS 456:2000 Clause 23.1.1, identifying whether flange is in tension or compression zone
  • Part (b): Proper calculation of limiting moment of resistance and required steel area using appropriate equations for T-beam (xu < Df or xu > Df case), with final provision of reinforcement bars
  • Part (c): Correct calculation of moment of inertia for hollow circular section (pipe) using I = π/64 × (D⁴ - d⁴), and application of δmax = 5wL⁴/(384EI) for simply supported UDL
  • Part (c): Proper unit conversion (GPa to kN/m², mm to m) and final deflection value in mm with appropriate significant figures

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Demonstrates flawless understanding of moment distribution fundamentals for indeterminate frames, T-beam flexural behavior per IS 456:2000 (neutral axis classification, effective flange width concepts), and beam deflection theory; correctly identifies when to use xu < Df versus xu > Df formulationShows basic understanding of methods but makes minor errors in identifying T-beam case or applies approximate methods for moment distribution; some conceptual gaps in IS code applicationFundamental misconceptions such as treating T-beam as rectangular, ignoring carry-over in moment distribution, or using wrong deflection formula; confuses service moment with factored moment
Numerical accuracy25%12.5All calculations precise to 3-4 significant figures; correct final end moments in part (a), steel area within ±2% of optimal in part (b), and deflection accurate with proper unit handling; no arithmetic or algebraic errors throughoutMinor calculation errors (±5-10%) in one sub-part, or consistent rounding issues; final answers approximately correct but working shows some slips in distribution factors or section propertiesMajor numerical errors (>15% deviation), wrong formula substitutions, or consistent unit conversion failures; incorrect final answers despite correct method indication
Diagram quality15%7.5Clear, labeled bending moment diagram for box culvert in part (a) showing values at all critical points (supports and mid-spans), proper curvature indication (tension side), and neat free-hand or scaled sketch; dimension lines and moment values explicitly markedDiagram present but lacks clarity in values or has minor labeling omissions; rough sketch without proper moment values or tension side indicationMissing diagram, or diagram completely uninterpretable; no indication of moment distribution pattern or critical values
Step-by-step derivation25%12.5Complete tabular format for moment distribution in (a) showing DF, COF, all balancing cycles, and final moments; systematic IS 456 design steps in (b) with explicit neutral axis check, Mu,lim calculation, and steel computation; clear I calculation and substitution in (c); all formulae stated before useSome steps shown but skips intermediate calculations or lacks proper tabulation; jumps between steps without justification; missing explicit check for T-beam case in (b)No systematic working, only final answers or grossly incomplete derivations; missing essential steps like distribution factor calculation or moment of inertia derivation
Practical interpretation15%7.5Interprets final moments for box culvert design (reinforcement placement), provides practical bar arrangement for T-beam (number and diameter of bars, spacing checks per IS 456), and comments on deflection limits (L/250 or L/500 as per IS 456 serviceability); relates to Indian construction practicesBrief mention of practical implications without detail; standard bar sizes mentioned but no arrangement sketch or spacing verificationNo practical interpretation; purely mathematical exercise with no engineering judgment on constructability, serviceability, or code compliance

Practice this exact question

Write your answer, then get a detailed evaluation from our AI trained on UPSC's answer-writing standards. Free first evaluation — no signup needed to start.

Evaluate my answer →

More from Civil Engineering 2024 Paper I