Civil Engineering 2023 Paper I 50 marks Design

Q3

(a) Design a floor slab to cover a room with internal dimensions of 4·5 m × 6·0 m. The slab is simply supported on all the sides on 230 mm thick masonry walls. The slab carries a live load of 4·0 kN/m² and a dead load due to finishing work of 1·0 kN/m². The corners of the slab are prevented from lifting up. Use M 20 concrete and Fe 415 steel. Assume mild exposure conditions. (20 marks) Table : Bending Moment coefficients when four edges are discontinuous | l_y/l_x | Short span coefficient, α_x | | | | | | Long span coefficient, α_y | |---------|----------------------------|---|---|---|---|---|---------------------------| | | 1·0 | 1·1 | 1·2 | 1·3 | 1·4 | 1·5 | for all values of l_y/l_x | | α_x | 0·056 | 0·064 | 0·072 | 0·079 | 0·085 | 0·089 | 0·056 | Modification Factor for Tension Reinforcement Note : f_s is steel stress of service loads in N/mm² f_s = 0.58 f_y (Area of cross-section of steel required)/(Area of cross-section of steel provided) (b) A built-up column of effective length 10 m is designed by placing two ISMC 300 @ 363 N/m back to back at a spacing 'S' mm. The column is to carry a factored axial load of 1100 kN. Find the economical spacing 'S' of the two channel sections. Also design the batten system for the column. M 20 bolts of grade 4.6 are used for making the connections. Do not design the connections. Use E 250 grade of steel. (20 marks) For connections : Edge distance = 32 mm Gauge distance = 50 mm Properties of ISMC 300 : A = 4630 mm² r_zz = 118 mm, r_yy = 26.0 mm I_zz = 6420 × 10⁴ mm⁴ I_yy = 313 × 10⁴ mm⁴ C_y = 23.5 t_f = 13.6 300 z z t_w=7.8 y 90 ISMC 300 (All dimensions are in mm) (c) Using slope deflection method, determine the final end moments for the portal frame shown in the figure. The frame is fixed at A and D, and has rigid joints at B and C. Take EI as constant. (10 marks)

हिंदी में प्रश्न पढ़ें

(a) 4·5 m × 6·0 m की आंतरिक विमाओं के एक कक्ष के आच्छादन के लिए एक फर्श छतपट की अभिकल्पना कीजिए । छतपट सभी ओर पर 230 mm मोटी चिनाई की दीवारों पर शुड्डालम्बित है । छतपट 4·0 kN/m² का एक चल भार और परिष्करण कार्य के कारण 1·0 kN/m² का एक अचल भार वहन करता है । छतपट के कोनों को ऊपर उठने से रोका गया है । M 20 कंक्रीट और Fe 415 इस्पात का उपयोग कीजिए । हल्की प्रभावन अवस्थाएँ मान लीजिए । (20 अंक) सारणी : बंकन आधुर्ण गुणांक, जब चारों कोर असतत हैं | | लघु विस्तृति गुणांक, αₓ | | | | | | दीर्घ विस्तृति गुणांक, αᵧ | |---|---|---|---|---|---|---|---| | lᵧ/lₓ | 1·0 | 1·1 | 1·2 | 1·3 | 1·4 | 1·5 | lᵧ/lₓ के सभी मानों के लिए | | αₓ | 0·056 | 0·064 | 0·072 | 0·079 | 0·085 | 0·089 | 0·056 | तनन प्रबलन के लिए आशोधन गुणक नोट : f_s सेवा भारों का इस्पात प्रतिबल N/mm² में है f_s = 0.58 f_y आवश्यक इस्पात का अनुप्रस्थ-परिच्छेद क्षेत्रफल —————————————————————— प्रदत इस्पात का अनुप्रस्थ-परिच्छेद क्षेत्रफल (b) दो ISMC 300 @ 363 N/m को 'S' mm के अंतरण पर सहपृष्ठ रखकर, 10 m प्रभावी लंबाई के एक संधित स्तंभ की अभिकल्पना की गई है । स्तंभ को 1100 kN का एक गुणित अक्षीय भार बहन करना है । दो चैनल परिछेदों के मितव्ययी अंतरण 'S' को ज्ञात कीजिए । स्तंभ के लिए बता तंत्र की भी अभिकल्पना कीजिए । जोड़ों को बनाने के लिए 4·6 ग्रेड के M 20 बोल्टों को उपयोग किया गया है । जोड़ों की अभिकल्पना नहीं कीजिए । E 250 ग्रेड इस्पात का उपयोग कीजिए । (20 अंक) जोड़ों के लिए : कोर दूरी = 32 mm गेज दूरी = 50 mm ISMC 300 के गुण : A = 4630 mm² r_zz = 118 mm, r_yy = 26.0 mm I_zz = 6420 × 10⁴ mm⁴ I_yy = 313 × 10⁴ mm⁴ C_y = 23.5 t_f = 13.6 300 z z t_w=7.8 y 90 ISMC 300 (सभी विमाएँ mm में हैं) (c) प्रवणता विषम विधि का उपयोग करके, चित्र में दर्शाए पोर्टल फ्रेम के लिए अंतिम सिरा आघूर्णों को निर्धारित कीजिए। फ्रेम, A और D पर आबद्ध है तथा B और C पर दृढ़ जोड़ हैं। EI को नियत लीजिए। (10 अंक)

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Directive word: Design

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How this answer will be evaluated

Approach

Design requires systematic application of codal provisions across three distinct structural problems. Allocate approximately 40% time to part (a) slab design including load calculations, moment coefficients, and reinforcement detailing; 40% to part (b) built-up column covering spacing optimization and batten design; and 20% to part (c) slope deflection analysis with proper sign convention and equilibrium checks. Present each part sequentially with clear headings, showing all intermediate calculations before final design values.

Key points expected

  • Part (a): Calculate effective spans, determine l_y/l_x ratio = 1.33, interpolate α_x = 0.0763, compute total load = 6.5 kN/m², design moments M_x and M_y, check depth for deflection using modification factor, calculate steel areas for both directions, and provide reinforcement detailing with bar diameter and spacing
  • Part (b): Determine required spacing S by equating slenderness ratios about both axes (r_yy_modified ≈ r_zz), use Perry-Robertson formula or IS 800 buckling curves for E 250 steel, design batten system with spacing ≤ 1.5 times least r_yy of single channel, check batten strength for transverse shear and moment, and specify batten dimensions and connections
  • Part (c): Identify degrees of freedom (θ_B and θ_C), write slope-deflection equations for members AB, BC, and CD considering fixed ends at A and D, apply joint equilibrium at B and C, solve simultaneous equations for unknown rotations, and compute final end moments with proper sign convention (clockwise positive)
  • Correct application of IS 456:2000 for slab design including moment coefficients from Table 26 and deflection control through Clause 23.2.1
  • Correct application of IS 800:2007 for built-up column design including Clause 7.6 for lacing and battening systems
  • Proper use of given material properties: M 20 concrete (f_ck = 20 N/mm²), Fe 415 steel (f_y = 415 N/mm²), E 250 structural steel (f_y = 250 N/mm²)

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies two-way slab action with proper edge conditions; recognizes built-up column design requires equal slenderness about both axes for economy; applies slope-deflection method with correct fixed-end moments and equilibrium conditions; references appropriate IS codes (IS 456, IS 800) for each partIdentifies slab as two-way but uses approximate coefficients; understands batten purpose but confuses spacing criteria; attempts slope-deflection but makes sign convention errors; partial code referencesTreats slab as one-way; fails to recognize built-up column buckling modes; uses moment distribution or other method for part (c); no code references or wrong standards cited
Numerical accuracy25%12.5Accurate interpolation of α_x = 0.0763 for l_y/l_x = 1.33; correct total factored load calculation; precise spacing S ≈ 180-200 mm from slenderness equality; correct batten force calculations; accurate simultaneous equation solution for slope-deflection with moments summing to zero at jointsMinor arithmetic errors in moment calculations; approximate spacing without iteration; batten design with simplified assumptions; correct slope-deflection setup but arithmetic errors in final momentsMajor errors in load factors or span calculations; unrealistic spacing values; incorrect batten spacing (>2×r_yy); wrong fixed-end moments or failure to solve equations
Diagram quality15%7.5Clear slab plan showing span directions, reinforcement layout with bar marks; built-up column cross-section with dimensions S, batten location elevation; portal frame with degrees of freedom labeled, bending moment diagram showing tension sideBasic sketches without dimensions; column section without batten details; frame diagram without deformation shape or moment diagramMissing diagrams or unrecognizable sketches; no reinforcement detailing; no column cross-section; no frame diagram for part (c)
Step-by-step derivation25%12.5Systematic presentation: effective spans → load calculation → moment coefficients → depth check → reinforcement; spacing derivation from r_yy = √(I_yy_modified/A) equality; batten design with shear and moment checks; slope-deflection equations written explicitly, substitution shown, final moments calculatedSome steps combined or skipped; spacing stated without derivation; batten sizing by rule of thumb; slope-deflection with final equations onlyDisorganized calculations; no derivation of spacing; no batten design steps; only final moments stated without equations
Practical interpretation15%7.5Provides practical reinforcement detailing with actual bar diameters (8mm or 10mm) and spacings (multiple of 5mm, ≤3d or 300mm); specifies batten dimensions (typically flat 50-60mm wide) with practical connection layout; discusses constructability of built-up column; notes serviceability implications of moment distributionGeneric reinforcement description; standard batten sizes without justification; limited practical commentaryImpractical reinforcement (single large bar, excessive spacing); no batten dimensions; no practical considerations; purely mathematical treatment

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