Civil Engineering 2025 Paper I 50 marks Compulsory Solve

Q1

(a) Draw the free body diagram of link ABCD and determine all reaction forces acting at A, B, C and D of the assembly shown in the figure. (All dimensions are in mm.) 10 marks (b) A horizontal cantilever beam of length 2L has its free end attached to a vertical tie rod of length L and area 'A', which is initially unstrained. If the moment of inertia of the cantilever beam is I, determine the load taken by the tie rod when a uniformly distributed load of 'w' per unit run is placed on the inner half length of the cantilever. Modulus of elasticity for the tie rod and cantilever beam is E. 10 marks (c) Calculate the maximum bending moment at points 'C' and 'D' if the five loads of 160 kN equally spaced at 1·52 m, cross the beam from right to left. 10 marks (d) A tie member of a truss consisting of an angle-iron section ISA 65 × 65 × 6 of Fe 410 grade, is welded to an 8 mm gusset plate. Design the weld to transmit a load equal to the full strength of the member. Assume shop welding. Take weld size as 4 mm and fy = 250 MPa, properties of ISA 65 × 65 × 6 are: A = 744 mm², Cz = 18·1 mm, γm0 = 1·1, γm1 = 1·25. Tdb = [Avg fy/(√3 γm0) + 0·9 Atn fu/γm1] or Tdb = [0·9Avn fu/(√3 γm1) + Atg fy/γm0]. 10 marks (e) The plan of a ground floor column in a building is shown in the figure. It is desired to reduce the longitudinal bar diameter from 30 mm to 20 mm above the second floor level. Design and detail a suitable lap splice. Assume M25 grade concrete and Fe 500 grade steel. 10 marks

हिंदी में प्रश्न पढ़ें

(a) लिंक ABCD का मुक्त पिंड आरेख बनाइए और चित्र में दर्शाए गए समन्वयोजन के A, B, C और D पर लगने वाले सभी प्रतिक्रिया बलों को निर्धारित कीजिए। (सभी विमाएँ mm में हैं) 10 अंक (b) 2L लम्बाई की एक क्षैतिज प्रास धरन का मुक्त सिरा, लम्बाई L और क्षेत्रफल 'A' की ऊर्ध्वाधर तान छड़ जो आरम्भ में तनाव रहित है, से जुड़ा है। यदि प्रास धरन का जड़त्व आघूर्ण I है, तो तान छड़ द्वारा वहन किए जाने वाले भार का निर्धारण कीजिए जब प्रास की आंतरिक अर्ध लम्बाई पर 'w' प्रति एकक लम्बाई का एक एकसमान वितरित भार रखा गया है। तान छड़ और प्रास धरन के लिए प्रत्यास्थता गुणांक E है। 10 अंक (c) बिन्दु 'C' और 'D' पर अधिकतम बंकन आघूर्ण की गणना कीजिए यदि एक दूसरे से 1·52 m की समान दूरी पर स्थित 160 kN के पाँच भार घन को दाएँ से बाएँ की ओर पार करते हैं। 10 अंक (d) Fe 410 ग्रेड के एक लोह-कोण परिच्छेद ISA 65 × 65 × 6 से बना ट्रस का एक तान अवयव 8 mm की संगम पट्टिका से वेल्डित है। अवयव की पूर्ण सामर्थ्य के बराबर के भार को प्रेषित करने के लिए वेल्ड की अभिकल्पना कीजिए। कार्यशाला वेल्डिंग मान लीजिए। वेल्ड आमाप 4 mm और f_y = 250 MPa लीजिए। ISA 65 × 65 × 6 के गुणधर्म हैं: A = 744 mm², Cz = 18·1 mm, γm0 = 1·1, γm1 = 1·25. Tdb = [Avg fy/(√3 γm0) + 0·9 Atn fu/γm1] या Tdb = [0·9Avn fu/(√3 γm1) + Atg fy/γm0]. 10 अंक (e) एक भवन में एक भूतल स्तंभ का अनुविभेद चित्र में दर्शाया गया है। अनुद्देश्य छड़ों के व्यास को, दूसरी मंजिल से ऊपर, 30 mm से घटाकर 20 mm किया जाना वांछित है। एक उपयुक्त चढ़ाव जोड़ पट्टी का अभिकल्पन कीजिए और विवरण दीजिए। M25 ग्रेड कंक्रीट और Fe 500 ग्रेड इस्पात मान लीजिए। 10 अंक

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Approach

Solve all five sub-parts systematically, allocating approximately 20% time to each part since all carry equal marks. Begin with free body diagram construction for part (a), followed by compatibility-based analysis for the indeterminate structure in (b), influence line or absolute maximum moment calculation for (c), weld design using IS 800 provisions for (d), and lap splice detailing per IS 456 for (e). Present derivations stepwise with clear identification of equations used, and conclude each part with final numerical answers and units.

Key points expected

  • Part (a): Correct identification of all external and internal reactions at pins A, B, C, D with properly labeled free body diagram showing forces and moments
  • Part (b): Application of compatibility condition (equal deflection at connection point) to solve the statically indeterminate beam-tie rod system
  • Part (c): Determination of absolute maximum bending moment using influence line concepts or critical load positioning for points C and D
  • Part (d): Calculation of design tensile strength of ISA 65×65×6 angle and proportioning of fillet weld lengths (parallel and transverse) to match member capacity per IS 800:2007
  • Part (e): Design of tension lap splice with development length calculations, staggered bar arrangement, and detailing as per IS 456:2000 clause 26.2.5.1
  • Correct application of partial safety factors γm0 = 1.1 and γm1 = 1.25 in steel design calculations
  • Proper use of M25 concrete (fck = 25 MPa) and Fe 500 steel (fy = 500 MPa) properties for development length in part (e)
  • Dimensional consistency and unit conversion (mm to m, kN to N) across all numerical computations

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Demonstrates flawless application of static equilibrium for (a), force method/compatibility for indeterminate analysis in (b), influence line theory or critical load position for (c), limit state design philosophy per IS 800 for (d), and anchorage and splice provisions per IS 456 for (e); no conceptual errors in identifying determinate vs indeterminate systems or tension vs shear failure modesShows generally correct concepts with minor errors in application, such as incorrect assumption of zero moment at certain points, confusion between gross and net area in weld design, or approximate development length calculation without considering stress reduction factor for bars in tensionFundamental misconceptions evident, such as treating indeterminate structure as determinate, ignoring compatibility conditions, applying bending moment formulas to wrong beam configurations, or using working stress method instead of limit state method for steel design
Numerical accuracy20%10All calculations arithmetically precise with correct final answers; proper significant figures maintained; accurate interpolation of standard values; correct computation of weld strength using given formula and proper application of 0.9 factor for transverse welds; development length calculated precisely with τbd = 1.4 MPa for M25 concreteMinor arithmetic slips (±5% error) or rounding inconsistencies; correct method but final answer slightly off due to calculator error; occasional unit conversion mistakes that don't propagate through entire solutionSignificant computational errors (>10% deviation), wrong formula substitution, missing partial safety factors, or answers without units; gross errors in section properties or failure to use given material properties (E, fy, fu values)
Diagram quality20%10Clear, labeled free body diagram for (a) showing all reaction components with proper direction conventions; neat sketch of beam-tie arrangement for (b); influence line diagram or load position sketch for (c); weld configuration showing parallel and transverse fillets with throat dimensions for (d); detailed lap splice drawing with bar positions, cover, and development lengths for (e); all diagrams dimensioned and annotatedDiagrams present but lacking some labels or dimensions; free body diagram shows forces but omits moment arms; weld sketch shows layout but misses throat thickness indication; splice detail present but bar spacing or cover not indicatedMissing or illegible diagrams; free body diagram with incorrect force directions; no sketch for weld configuration or splice detail; diagrams that contradict written solution or show physically impossible configurations
Step-by-step derivation20%10Logical progression from given data to final answer with explicit statement of equilibrium/compatibility equations; clear identification of unknowns and simultaneous equation solving for (b); systematic load positioning analysis for (c); stepwise weld strength calculation comparing block shear and tearing failure modes; complete development length derivation with stress reduction factor applicationGenerally logical flow with some steps combined or skipped; equations stated but intermediate values not always shown; correct final answer reached but derivation lacks clarity on key transitions such as how compatibility equation is establishedDisorganized presentation with equations scattered; missing crucial steps such as compatibility condition setup or weld resistance calculation; jumps from given data to final answer without showing working; no indication of which IS code clauses are being applied
Practical interpretation20%10Interprets results in context of Indian construction practice: comments on adequacy of 4mm weld size for shop welding conditions, discusses why bar diameter reduction requires lap splice rather than mechanical coupler, notes practical implications of tie rod stiffness on load sharing, and relates absolute maximum moment calculation to bridge deck design scenarios common in Indian highway projectsBrief mention of practical relevance without elaboration; standard concluding statements about safety or economy without specific connection to the calculated values; generic reference to code compliance without explaining why particular provisions applyNo practical interpretation offered; purely mathematical exercise without engineering judgment; fails to comment on whether designed weld or splice is constructible; ignores real-world constraints such as minimum weld spacing or bar congestion in columns

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