Civil Engineering 2024 Paper I 50 marks Solve

Q4

(a) A prestressed concrete T-beam having the cross-section of flange 1500 mm wide and 200 mm thick, rib of 300 mm wide and 1200 mm deep. The beam carries a live load of 20 kN/m apart from its dead load, over a simply supported span of 18 m. The beam is prestressed with a straight cable having constant eccentricity 'e'. Assume the losses of prestress as 16%. Determine the initial prestressing force 'Pᵢ' and its eccentricity 'e', if the permissible net stresses are equal to zero and 5 MPa respectively at top and bottom fibres of the beam. The unit weight of concrete is 25 kN/m³. (20 marks) (b) A pin jointed, symmetrically loaded, truss 'ABCDE' is shown in the above figure. Cross-sectional area of each member is 500 mm² and E = 200 GPa. Forces in the members meeting at joint C are also shown in the figure. Calculate the vertical deflection of joint C by unit load method. (20 marks) (c) What are the different modes of failure of a structural steel tension member ? Explain with sketches. (10 marks)

हिंदी में प्रश्न पढ़ें

(a) एक पूर्व प्रतिबलित T-धरन की अनुप्रस्थ काट में फ्लेंज 1500 mm चौड़ी एवं 200 mm मोटी और रिब 300 mm चौड़ी एवं 1200 mm गहरी है। यह धरन अपने अचल भार के अतिरिक्त 20 kN/m का चल भार, 18 m की शुद्धालम्बित विस्तृति पर वहन करती है। इस धरन को नियत उत्केन्द्रता 'e' वाले सीधे तार से पूर्व-प्रतिबलित किया गया है। पूर्व प्रतिबल में ह्रास 16% मान लीजिए। यदि धरन के शीर्ष और तल के तंतुओं में अनुज्ञेय निवल प्रतिबल क्रमशः: शून्य और 5 MPa है तो प्रारंभिक प्रतिबलन बल 'Pᵢ' और इसकी उत्केन्द्रता 'e' निर्धारित कीजिए। कंक्रीट का एकक भार 25 kN/m³ है। (20 marks) (b) नीचे चित्र में एक पिन जोड़ वाली सममित रूप से भारित कैंची ABCDE दर्शाई गई है। प्रत्येक अवयव का अनुप्रस्थ काट क्षेत्रफल 500 mm² और E = 200 GPa है। जोड़ C पर मिलने वाले सभी अवयवों के बलों को चित्र में दर्शाया गया है। एकक-भार-विधि द्वारा जोड़ C के उद्वर्धर विस्थाप की गणना कीजिए। (20 marks) (c) संरचनात्मक इस्पात के एक तनन अवयव में विभिन्न प्रकार की भंग विधाएं क्या हैं ? रेखाचित्रों द्वारा व्याख्या कीजिए । (10 marks)

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How this answer will be evaluated

Approach

Solve this multi-part numerical and descriptive question by allocating approximately 40% time to part (a) prestressed concrete calculations, 35% to part (b) truss deflection analysis, and 25% to part (c) steel tension member failure modes. Begin with clear sectional property calculations for the T-beam, apply Pigeaud's or relevant prestress theory with stress constraints, then use unit load method systematically for the truss, and conclude with well-labelled sketches for failure modes. Present each part distinctly with proper headings and maintain sequential logical flow from given data to final results.

Key points expected

  • Part (a): Calculate section properties of T-beam (area, centroid, moment of inertia) considering flange 1500×200 mm and rib 300×1200 mm; determine dead load as 25 kN/m³ × cross-sectional area
  • Part (a): Apply stress equations at top and bottom fibres using Pᵢ and e with 16% loss factor, setting σ_top = 0 and σ_bottom = 5 MPa under working loads to solve simultaneous equations
  • Part (b): Identify zero-force members and calculate member forces under actual loading and unit load at joint C using method of joints or sections
  • Part (b): Apply unit load method formula Δ = Σ(NnL)/(AE) for all members, tabulating forces N (actual), n (unit), lengths L, and summing contributions
  • Part (c): Enumerate four failure modes: gross section yielding, net section rupture, block shear failure, and shear lag effects with end connections
  • Part (c): Draw clear sketches showing each failure mode with failure planes marked, particularly for bolted/riveted connections typical in Indian bridge girders

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies T-beam as Class 1 prestressed section; applies transformed section properties; recognizes that permissible net stresses refer to working stress condition after losses; for (b) correctly identifies virtual work/unit load methodology; for (c) accurately distinguishes between limit states of yielding vs fracture per IS 800Uses gross section properties without transformation; confuses initial vs effective prestress; applies standard beam formula without eccentricity term; mixes up force and displacement methods for truss; lists failure modes without clear distinction between ductile and brittle failuresTreats T-beam as rectangular section; ignores prestress losses completely; uses wrong sign convention for stresses; applies moment-area theorem instead of unit load method; omits block shear or confuses it with bearing failure
Numerical accuracy25%12.5Accurate section properties: A = 660,000 mm², ȳ ≈ 636 mm from top, I ≈ 1.35×10¹¹ mm⁴; correct Pᵢ ≈ 2500-2600 kN and e ≈ 430-450 mm; for (b) correct deflection ≈ 8-12 mm downward; all calculations show 3-4 significant figures with proper unit handlingMinor errors in I calculation (within 10%); correct approach but arithmetic slips in simultaneous equations; wrong loss factor application (uses 0.16 instead of 0.84); deflection magnitude correct but sign wrong; order of magnitude acceptable for steel failure stressesOrder of magnitude errors in section properties; Pᵢ and e completely unrealistic (>5000 kN or e > 600 mm); deflection calculation missing AE denominator or using wrong E value; numerical answers without any intermediate steps shown
Diagram quality15%7.5Clear T-beam cross-section with dimensions, centroid axis, prestressing cable position marked; truss diagram with joint labels, member forces indicated; part (c) shows four distinct sketches: cup-cone rupture, flat yielding, block shear with shear and tension planes, shear lag with staggered bolts per IS 800 detailingBasic cross-section sketch without key dimensions; truss diagram without force directions; failure mode sketches generic without specific failure planes marked; missing one of the four required sketchesNo diagrams despite sketch requirement; extremely poor freehand drawings unrecognizable; diagrams copied but not referred to in text; part (c) answered entirely in text without any sketches
Step-by-step derivation25%12.5Systematic presentation: section properties → load calculations → stress equations at transfer and service → simultaneous solution for Pᵢ and e; for (b) table format with member identification, L, N, n, NnL/AE columns; clear statement of assumptions (rigid joints, elastic material, etc.)Some steps combined or skipped but logical flow maintained; missing explicit statement of stress equation (σ = P/A ± Pe/Z ± M/Z); table present but incomplete; assumptions implied rather than statedFinal answers appear without derivation; jumps from given data to results; no working shown for simultaneous equations; unit load method stated but not applied; part (c) as bullet points without explanatory derivation of why failures occur
Practical interpretation15%7.5Comments on practical implications: for (a) notes that e ≈ 450 mm is feasible within kern limits and cable placement; discusses camber vs deflection control; for (b) relates deflection to L/250 or L/360 serviceability limits; for (c) connects failure modes to IS 800 design provisions and Indian bridge/ building practiceBrief mention of code compliance without specific clause reference; generic statement about safety without numerical context; acknowledges prestressing is common in long spans without specific Indian exampleNo interpretation of results; answers treated as pure mathematics; fails to note that zero top stress implies no tension which is conservative; no connection to real structures like Howrah Bridge or metro viaducts

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