Civil Engineering 2022 Paper I 50 marks Compulsory Solve

Q1

(a) A rod shown in the figure below is subjected to a force of 95 kN. Determine the diameter d of the portion ②, if the stress there is not to exceed 115 N/mm². Also, determine the axial deformation of the rod. Use E = 205 GPa : (10 marks) (b) A reinforced concrete beam of 250 mm × 500 mm is reinforced with 3 nos. 16 mm dia bars as tension reinforcement. The nominal cover to the reinforcement is 30 mm and diameter of stirrups is 8 mm. Calculate the moment of resistance of the beam. Use M20 and Fe500. Adopt limit state method of design. (10 marks) (c) A three-hinged parabolic arch of uniform cross-section has a span of 60 m and a central rise of 10 m. It is subjected to a UDL of intensity 15 kN/m covering the whole span. Show that the bending moment is zero at any cross-section of the arch. (10 marks) (d) Use Castigliano's theorems and determine the vertical displacement of point C of the beam shown in the figure below. Take E = 210 GPa and I = 150×10⁶ mm⁴ : (10 marks) (e) A vertical member of a truss consisting of an angle section ISA 75×75×8 of E250 grade is welded to a 10 mm thick gusset plate. The factored tensile and compressive forces in the member are 100 kN and 90 kN respectively. Design the weld connection (shop weld) having weld size of 4 mm; only two sides of the angle are welded. Cᵧ = Cᵤ = 21·4 mm for ISA 75×75×8. (10 marks)

हिंदी में प्रश्न पढ़ें

(a) नीचे चित्र में दर्शाई गई एक छड़ पर 95 kN का एक बल लगा है। भाग ② का व्यास d ज्ञात कीजिए, यदि इसमें प्रतिबल 115 N/mm² से अधिक नहीं हो। छड़ का अक्षीय विरूपण भी ज्ञात कीजिए। E = 205 GPa का उपयोग कीजिए : (10 अंक) (b) एक 250 mm × 500 mm की प्रबलित कंक्रीट धरन को तनन प्रबलन के लिए 16 mm व्यास वाली तीन छड़ों द्वारा प्रबलित किया गया है। प्रबलन का अभिहित आवरण 30 mm है एवं वलयकों का व्यास 8 mm है। धरन के प्रतिरोध-आघूर्ण की गणना कीजिए। M20 एवं Fe500 का उपयोग कीजिए। अभिकल्पना की सीमांत अवस्था विधि का उपयोग कीजिए। (10 अंक) (c) एकसमान अनुप्रस्थ परिच्छेद वाली एक त्रि-कब्जीय परवलयिक डाट की विस्तृति 60 m एवं मध्य उत्थान 10 m है। इसकी पूरी विस्तृति पर 15 kN/m तीव्रता का एकसमान वितरित भार लगा है। दर्शाइए कि डाट के किसी भी अनुप्रस्थ परिच्छेद पर बंकन आघूर्ण शून्य है। (10 अंक) (d) कास्टिग्लियानो के प्रमेयों का उपयोग करके नीचे चित्र में दर्शाई गई धरन के बिंदु C पर उद्वधर विस्थापन को निर्धारित कीजिए। E = 210 GPa एवं I = 150×10⁶ mm⁴ लीजिए : (10 अंक) (e) E250 ग्रेड के एक कोण परिच्छेद ISA 75×75×8 से बना एक कैंची का उद्वधर अवयव 10 mm मोटी गसेट प्लेट से वेल्डित है। अवयव में गुणित तनन एवं संपीडन बल क्रमशः: 100 kN एवं 90 kN हैं। 4 mm वेल्ड आमाप के वेल्ड जोड़ (कार्यशाला वेल्ड) की अभिकल्पना कीजिए; कोण को केवल दो तरफ से वेल्ड किया गया है। ISA 75×75×8 के लिए Cᵧ = Cᵤ = 21·4 mm. (10 अंक)

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Approach

Solve all five sub-parts systematically, allocating approximately 20% time to each since marks are equal. Begin with stating given data and required unknowns for each part, show complete derivations with formulae, perform calculations with proper units, and conclude with final answers. For parts (a), (b), (d), and (e), ensure IS code references (IS 456:2000, IS 800:2007) where applicable. For part (c), provide the mathematical proof of zero bending moment condition.

Key points expected

  • Part (a): Apply stress formula σ = P/A to find diameter d = √(4P/πσ), then use δ = PL/AE for axial deformation with consistent units (mm, N, MPa)
  • Part (b): Calculate effective depth d = 500 - 30 - 8 - 16/2 = 454 mm; determine xu,max = 0.46d for Fe500; check section type and compute Mu using IS 456:2000 Clause 38.1
  • Part (c): Derive horizontal thrust H = wL²/8h = 675 kN; show that moment at any section Mx = VAx - wx²/2 - Hy = 0 for parabolic arch under UDL
  • Part (d): Apply Castigliano's second theorem ∂U/∂P = δ; set up strain energy integral U = ∫(M²/2EI)dx; differentiate under integral sign for vertical displacement at C
  • Part (e): Design fillet weld for combined tension and compression; calculate throat thickness t = 0.7×4 = 2.8 mm; determine required weld length considering eccentricity and IS 800:2007 provisions for shop welds

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies all underlying principles: stress-strain relationship for (a), limit state philosophy and neutral axis depth limits for (b), arch thrust line coinciding with funicular polygon for (c), strain energy and partial differentiation for (d), and weld design with throat area calculations for (e)Identifies most concepts correctly but shows minor confusion in one sub-part, such as using working stress method instead of limit state for (b) or incorrect theorem application for (d)Fundamental misconceptions in multiple sub-parts, such as treating arch as beam for (c), using first instead of second Castigliano theorem for (d), or ignoring weld throat thickness for (e)
Numerical accuracy20%10All calculations precise with correct unit conversions (GPa to MPa, kN to N), proper significant figures, and final answers matching expected ranges: d ≈ 32.4 mm, δ ≈ 2.3 mm for (a); Mu ≈ 85-90 kNm for (b); H = 675 kN for (c)Correct methodology but arithmetic errors in 1-2 sub-parts, such as effective depth calculation error in (b) or unit inconsistency in (a) or (d)Major calculation errors, order-of-magnitude mistakes, or consistent unit confusion (e.g., mixing mm and m) across multiple sub-parts leading to unrealistic answers
Diagram quality20%10Clear free-body diagrams for (a) stepped rod, (b) beam cross-section with strain distribution, (c) arch geometry with loading and reactions at hinges, (d) beam with virtual/unit load setup, and (e) weld configuration with throat dimensions; all properly labeled with forces and dimensionsDiagrams present but missing key labels, or sketchy representations without proper scale indication; one sub-part may lack diagram where essentialMissing critical diagrams for (c), (d), or (e); or diagrams with incorrect force directions, missing hinge symbols, or no indication of coordinate systems
Step-by-step derivation20%10Each sub-part shows complete logical flow: given data → formula with standard reference → substitution → simplification → final answer with units; for (c) includes general equation of parabola and full integration; for (d) shows strain energy expression before differentiationDerivations mostly complete but skips intermediate algebraic steps or assumes known results without proof, particularly for arch equation in (c) or moment expressions in (d)Jumps directly to answers without showing formulae, missing essential steps like section modulus calculation for (b) or partial derivative setup for (d), or presents disconnected calculations
Practical interpretation20%10Demonstrates engineering judgment: comments on standard bar sizes for (a), checks ductility and minimum reinforcement for (b), explains why arches are efficient for bridges in (c), discusses displacement limits for serviceability in (d), and specifies weld quality/inspection for (e) per Indian standardsBrief concluding remarks without substantive connection to design practice, or generic statements not specific to the calculated valuesNo interpretation of results; fails to check answer reasonableness (e.g., extremely large or small deformations without comment) or relate to IS code safety provisions

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