Civil Engineering 2022 Paper I 50 marks Solve

Q3

(a) (i) A simple girder of 20 m span is traversed by a moving uniformly distributed load of 6 m long with an intensity of 2 kN/m, from left to right. Determine the maximum bending moment and shear force at 4 m distant section from the left support. Also, determine the absolute maximum bending moment that may occur anywhere in the girder. (10 marks) (ii) Determine the maximum force that can be developed in member BC of the bridge truss shown in the figure below due to a moving load of 80×10³ N and a moving uniformly distributed load of 8·50 kN/m. The loading is applied at the top chord. (10 marks) (b) A laced column of height 8 m is made of 2 nos. ISMC 350 placed back-to-back. The column is restrained against translation and free against rotation at both ends in both directions. Find the distance between them to carry maximum axial compressive load and calculate the factored load-carrying capacity of the column using limit state method. The properties of ISMC 350 are A = 5440 mm², I_zz = 10000 cm⁴, I_yy = 434 cm⁴, C_y = 24.4 mm. Given: | KL/r | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | |------|----|----|----|----|----|----|----|----|-----| | f_cd (MPa) | 224 | 221 | 198 | 183 | 168 | 152 | 136 | 121 | 107 | | KL/r | 110 | 120 | 130 | 140 | 150 | 160 | 170 | 180 | |------|-----|-----|-----|-----|-----|-----|-----|-----| | f_cd (MPa) | 95 | 84 | 74 | 66 | 59 | 53 | 48 | 44 | (15 marks) (c) A post-tensioned simply supported beam of 300 mm wide × 600 mm depth spans over 10 m and carries a live load of 7 kN/m. The total area of cables is 500 mm² and located at 100 mm from the soffit of the beam. The initial prestress in the cables is 1400 MPa. Compute the net initial and final concrete stresses in the extreme top and bottom fibres at midspan of the beam. Assume loss of prestress = 15%. (15 marks)

हिंदी में प्रश्न पढ़ें

(a) (i) एक 2 kN/m तीव्रता का 6 m लम्बा एकसमान विस्तृत चल भार 20 m की विस्तृति वाले एक साधारण गर्डर पर बायीं से दायीं ओर चलता है। बायीं आलम्ब से 4 m दूर परिच्छेद पर अधिकतम बंकन आघूर्ण और अपरूपण बल निर्धारित कीजिए। गर्डर में कहीं भी उत्पन्न होने वाले निरपेक्ष अधिकतम बंकन आघूर्ण को भी निर्धारित कीजिए। (10 अंक) (ii) एक 80×10³ N के चल भार और 8·50 kN/m के एकसमान वितरित चल भार के कारण नीचे चित्र में दर्शाई गई पुल ट्रस के अवयव BC में उत्पन्न होने वाले अधिकतम बल को निर्धारित कीजिए। भार उपरीजीवा पर लगे हैं। (10 अंक) (b) एक 8 m ऊँचा बंधित स्तंभ सहपृष्ठ स्थिति में रखे दो ISMC 350 से बना है। स्तंभ दोनों सिरों पर दोनों दिशाओं में स्थिति में आबद्ध और घूर्णन के प्रति मुक्त है। सीमान्त अवस्था विधि का उपयोग करते हुए अधिकतम अक्षीय संपीडन भार वहन करने के लिए इनके बीच की दूरी ज्ञात कीजिए और स्तंभ की गुणित भार वहन क्षमता की गणना कीजिए। ISMC 350 के गुणधर्म हैं—A = 5440 mm², I_zz = 10000 cm⁴, I_yy = 434 cm⁴, C_y = 24·4 mm। प्रदत : | KL/r | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | |------|----|----|----|----|----|----|----|----|-----| | f_cd (MPa) | 224 | 221 | 198 | 183 | 168 | 152 | 136 | 121 | 107 | | KL/r | 110 | 120 | 130 | 140 | 150 | 160 | 170 | 180 | |------|-----|-----|-----|-----|-----|-----|-----|-----| | f_cd (MPa) | 95 | 84 | 74 | 66 | 59 | 53 | 48 | 44 | (15 अंक) (c) एक 300 mm चौड़ी × 600 mm गहरी पश्च-तानित शुद्धालम्बित धरन की विस्तृति 10 m है और 7 kN/m का चल भार वहन करती है। केबिलों का कुल क्षेत्रफल 500 mm² है और धरन के अधःस्तल से 100 mm पर स्थित है। केबिल में आरंभिक पूर्व-प्रतिबल 1400 MPa है। धरन की विस्तृति के मध्य में ऊपरी-छोर तंतु और अधो-छोर तंतु में शुद्ध आरंभिक और अंतिम कंक्रीट प्रतिबलों की गणना कीजिए। पूर्व-प्रतिबल में ह्रास = 15% मान लीजिए। (15 अंक)

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Approach

Solve all four sub-parts systematically, allocating time proportionally to marks: ~20 minutes for (a)(i) moving load on girder, ~20 minutes for (a)(ii) truss influence lines, ~30 minutes for (b) laced column design, and ~30 minutes for (c) prestressed concrete stress calculations. Begin each part with clear identification of the method (influence line diagrams for moving loads, IS 800 provisions for steel columns, IS 1343 for prestressed concrete), show complete derivations with formulae, and conclude with boxed final answers.

Key points expected

  • For (a)(i): Correct influence line ordinates at 4m section (0.8 and 0.2), maximum BM when load head is at 8.8m from left support giving BM_max = 38.4 kNm, maximum SF when load head at 4m or tail at 4m giving SF_max = ±4.8 kN, and absolute maximum BM at midspan = 50 kNm
  • For (a)(ii): Proper influence line construction for member BC (zero ordinate at A, maximum at panel point), correct loading positions for maximum force, and final answer incorporating both concentrated and distributed load effects
  • For (b): Correct effective length factor (K=0.65 for fixed-rotation, free-translation ends), optimal spacing calculation using I_yy = 2[I_YY + A(d/2 + C_y)²] with I_zz = I_yy condition, resulting spacing ≈ 180-190 mm, slenderness ratio calculation, interpolation for f_cd, and factored load capacity
  • For (c): Correct section properties (Z_top = Z_bottom = 9×10⁶ mm³), prestressing force P = 700 kN after losses, eccentricity e = 200 mm, stress calculations at transfer and service conditions with proper sign convention
  • Proper use of influence line diagrams with clear sketches showing load positions for critical effects in all moving load problems
  • Application of relevant IS codes: IS 800-2007 for steel column design and IS 1343-1980 for prestressed concrete
  • Clear statement of assumptions and boundary conditions for each structural system

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies influence line theory for moving loads in (a), effective length factors and built-up column behavior in (b), and prestress loss mechanics with stress block concepts in (c); applies Muller-Breslau principle for truss influence linesBasic understanding of influence lines and column buckling but confuses effective length conditions or misapplies prestress loss percentages; minor errors in structural behavior identificationFundamental misconceptions such as treating moving loads as static, ignoring effective length factors, or confusing pre-tensioning with post-tensioning; incorrect identification of critical load positions
Numerical accuracy25%12.5All calculations precise to 2-3 significant figures: (a)(i) BM_max = 38.4 kNm, SF_max = 4.8 kN, absolute BM_max = 50 kNm; (b) optimal spacing ≈ 186 mm, P_d ≈ 1800-1900 kN; (c) stresses at transfer: top = +2.33 MPa, bottom = +10.11 MPa; final: top = +6.22 MPa, bottom = +6.22 MPaCorrect method but arithmetic errors in 1-2 parts; incorrect interpolation for f_cd or wrong section modulus calculation; answers within 10-15% of correct valuesMajor calculation errors, wrong formulae application, unit conversion mistakes (kN-m vs N-mm), or missing critical steps leading to answers off by >25%
Diagram quality15%7.5Clear influence line diagrams for BM and SF at 4m section with ordinates marked, truss with influence line for BC showing proper triangular shape, laced column cross-section with battens/lacing shown, stress distribution diagrams for prestressed beamDiagrams present but poorly labeled or missing critical dimensions; freehand sketches without proper scaling; missing influence line for one partNo diagrams or completely incorrect sketches; failure to show load positions on influence lines; missing cross-sectional details for column design
Step-by-step derivation25%12.5Complete stepwise solutions: influence line equations derived from statics, load position optimization using calculus or geometric reasoning, radius of gyration calculations with clear formula substitution, prestress loss application sequence clearly shownSome steps skipped or combined; final formulae stated without derivation; missing intermediate calculations for slenderness ratio or section propertiesOnly final answers with no working; jumps between steps without justification; incorrect or missing formulae; no indication of how critical load positions were determined
Practical interpretation15%7.5Interprets results for Indian bridge/railway practice: comments on IRC loading relevance for (a), discusses lacing vs battening choice for (b) with reference to IS 800-2007 clause 7.6, evaluates stress limits against IS 1343 permissible stresses for (c), notes serviceability implicationsBrief mention of code compliance without specific clause references; generic statements about safety without relating to calculated valuesNo interpretation or practical relevance; fails to compare calculated stresses with permissible values; no discussion of design adequacy or member selection rationale

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