GATE-CE-2003 - GATE 2003 CE Civil Engineering Time...

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Unformatted text preview: GATE - 2003 CE: Civil Engineering Time Allowed .- .3 Hours Maximum Marks : 150 QJ — (2.30 CARRY ONE MARK EACH. - 4 2 '1 3 1. Given Matrix {AI = [6 3 4 7'], the rank of the 2 l 0 1 matrix is (a) 4 (b) 3 (C) 2 (t0 1 4. A box contains 10 screws, 3 of which are defective. Two screws are drawn at random with replacement. The probability that none of the two screwsis defective will be (f!) 100% (b) 50% (c) 49% (d) None of these If P, Q and R are three points having coordinates (3, —2, —1), (1, 3, 4), (2, 1, —2) in xrz space, then the distance from point P to plane COR {0 being the origin of the coordinate system) is given by (a) 3 G!) 5 (C) 7 (d) 9 A bar of varying square cross-section is loaded symmetrically as shown in the figure. Loads shown are placed on one of the axes of symmetry of cross section. Ignoring self weight, the maximum tensile stress in N / rnrn2 anywherei's (a) 16.0 (b). 20.0. (c) 25.0 (d) 30.0 Muller Breslau principle in structural analysis is used for- (n) drawing influence line diagram for any force function (0) writing virtual work equation (:5) super-positiOn of load effects (d) none of these The effective length of a column in a reinforced concrete building frame, as per 15 : 456-2000, is independent of the (a) frame type is, braced (no sway) or un-braced _ (with sway) (b) span of the beam 0:) height of the column {d} loads acting on the frame 50 it!“ 10. 11. A curVed member with a straight vertical leg is carrying a vertical load at Z, as shown in-the figure. The streSs resultants in the XY segment are i (a) bending moment. shear l’ force and axial force 2 (b) bending moment and \ axial force only ' (c) bending moment and shear force only Y X -—,—-7 / The working streSS method of design specifies the value of modular ratio, m = 280/ (3 fiche}, where 5:0: is the allowable stress in bending comp reSsion in concrete. To. what extent does the above value of in make any allowance for the creep of concrete? (:2) No compensation (b) Full compensation (0) Partial cornpensation (d) The two are unrelated In the design of lacing system for a built—up steel column, the maximum allowable slendern'ess ratio of a lacing bar is (a) 120 (b) 145 (I?) 180 (d) 250 Which of’the following elements of a pitched roof industrial steel building primarily resists lateral load parallel to me ridge ? (a) bracings (is) purlirls (c) truss (d) Columns Maximum strains in an extreme fibre in concrete- and in the tension reinforcement {F6415 grade and Es : 200 kN/mmz) in a balanced section at limit state of flexur'e are respeCtively (a) 0.0035 and 0.0038 (b) 0.002 and 0.0018 (c) 0.0035-and 0.0041 (11} 0.002 and 0.003! (d) axial force. only ' 23. The tolal irrigation depth of water, required by. a '24. 25. 2'6. 2?. 28. certain crop in its entire growing period (150 days), is 25.92 cm. Tire cullurable command area for a distributary channel is 100,000 hectares. The distributary channel shall be designed for a discharge (a) less than 2 cumecs (b) 2 cumecs (c) 20 cumecs {d} more than 20 cumecs The moisture content of soiI in the root zone of an agricultural crop at certain stage is found to be 0.05. The field capacity of theisoil is 0.15. The root zone depth is 1.1m. The consumptive'use of crop at this stage is 2.5 mm/ day and there is no precipitation during this period. irrigation efficiency is 65%. It is in tended to raise the moisture content to the field capacity in 8 days through irrigation. The necessary depth of irrigation is I (a) l 15 mm (c) 200 mm (b) 159 mm (d) 285 mm The results of analysis of a raw water sample are given below Turbidity 5 mg/l pH 7.4 ‘ Fluorides 2.5 mg/l Total Hardness 300 mgfl Iron 3.0 rag/l MPN 50 per 100 ml From the data given above, it can be inferred that water needs removal of (a) Turbidity followed by disinfection {b} Fluorides and Hardness. (:2) Iron, followed by disinfection (d) BOH’l (b) and (6) Which of the following sewage treatment methods has inherent problems of odour, pending, and fly nuisance ? (a) UASB system (b) Activated sludge process "{c) Tric'kling filters (:1) Stabilization ponds From amongst the following sewage treatment options, largest iand requirements for a given discharge will be needed for (a) trickling filter (b) anaerobic pond {c} oxidation ditch {d1 oxidation pond Zero hardness of water is achieved by I (a) lime soda process (1)) excess lime treatment (:2) ion exchange treatment (if) excess alum and lime treatment 29. 30. Temperature stresses in concrete pavements may cause the slab to crack. If a slab cools uniforml then the crack will develop at the following locations of the slab (a) at centre ([7) near edges (c) at corners id) bfith (b) and (1:) The ”speed ”and delay studies on a defined section of highway are conducted by (a) radar gun (b) traffic counters (c) moving car method (d) enoscope Q. 31490 CARRY TWO MARKS EACH —-——._._.____ 31. 32. 33. If L defines the Laplace Transform of a function, L {sin (at)] will be equal to w a/{sZ—an a» aim?) (c) s/(a2 + .12] (d) 's/(s.2 - a”) The Fourier series expansion of a symmetric and even function, fix) where flx)=1 +(2x/n),—ri < x c t] =1—(2x/it}, D < x < r: willbe (a) i'[4/n2n2](1+ cosna) n=.1 and lb) 2(4/a2nzlfl — cos mi) (6) i(4/n2n2)[1—sinnn) R'=l. (d) i[4/1T2l12)(1 + SinmtEl n=1 A long structural columnfillength = L) with both ends hinged is acted upon by an axial compressive load, P. The differential equation goverrung the bending of column is given by dzy 2 El = — a? P5“ where y is the structural lateral deflection and E1 is the flexural rigidity. The first critical load on column responsible for its buckling is given by in) «313111.? (b) fingEIiL" is) 21t2EIIL2 (d) attain.“ ill. Group I contains some properties of concrete/ cement and Group 2 contains list of some tests on concrete/cement. Match the property with the corresponding test. Group I P workability of concrete Q direct tensile strength of concrete R bond between concrete and steel 5 firmness of cement _ Group H I sillinder splitting test 2. Vee-Bee test 3. surface area test 4 Fineness modulus test 5. pullout test. I Codes : ' P Q R (a) 2 1 5 (b) 4 5 1 5 1 {It-(8mm (c) .2 1 (d) 2 5 4 Group I contains some elements in design of a simply supported plate girder and Group. 2 gives some qualitative locations on the girder. Match the items of two lists as per good design practice and relevant codal provisions. Group I P flange splice Q web splice R bearing stiffeners S horizontal stiffener Group H 1. at supports (minimum) 2. away‘trom centre pf-sp‘an 3. away from support 4. in the middle of span 5. longitudinally somewhere in the compression flange Codes : _ _ - P Q R s (a) "2 3 1 5 (b) 4.. 2 1 3 {c} 3 4 2 1 (d) 1- 5 2 3 A concrete column carries an axial load of 450 RN and a bending moment of 60 RN 111 at its base. An isolated footing of size 2m by 3m, with 3m side along the plane of thebending moment, is prowded under the calm. Centres of gravity of column and fooling eoinsids The net maximum and the minimum pressures in kN/m2 on soil under the fooling are respectively. (a) 95 and 55 (c) is and 55 (b) 95 and 75 (d) 75 and 75 44. Group] shows different loads acting on a beam and Group 2 5.th5 different bending moment clistribolions.~ match the load with the corresponding bending moment diagram. I Gro up 1 P f—hfir—j Codes: _ P , Q R 5 (a) 4 2 1 3 (b) 5 4 1 3 (c) .2 5 3 1 (a) 2- 4 1 3 45. Compaction of an embankment is carried out in 500 mm thick layers. The rammer used for compaction has 21 Foot area of 0.05 sq. m and the energy imparted in every drop of rammer is‘ 400' Nm. Assuming 50% more-energy in each pass over the compacted area due to. oVerlap, the number of passes required to develop compactive energy equivalent to Indian-Standard light compaction for each layer would be (a) 10 (b) 16 (c) 20 (d) 26 A braced cut, 51:: wide and 7.5m deep isproposed in a coh'esionless soil deposit h'aving effective cohesion c' : 0 and effective friction angle, o": 36°. The first row of struts is to. be installed at a depth of 0.5 m below ground surface and spacing be tween the struts should be 1.5m. If the horizontal spacing of struts is 3111 and unit weight of the deposit is 20 kam’, the maximum strut load will be (a) 70.87kN (c) 113.90kN For the soil strata shown in figure, the water table is lowered by drainage by 2111 and if the top 21:: thick silty sand stratum remains saturated by capillary action even after lowering of water table, the increase in effective vertical pressure in RP; at mid—height ofclay layer will be 46. (b) 98.72 RN (to 15136 RN 4?. (n) 0.2 (c) 20 (D) '2 (d) 200 At a reclamation site for which the soil strata is shown in figure, a 3m thick layer of a fill material is to be laid imtantamously-on the top surface. If the coefficient ofvolume compressibility, mu for Emirate 2t2 fxfllO‘4 kaN, the consolidation meno ecla la er'du ' ' ‘ material will be y y e to placmg of fill 49. on some 3'.“ = 2| kwm' c F owr S It‘ :n W = 3-2 x 10" m’i'kl‘l (n) 695 mm (b) 139 mm (C) 223 mm (d) 278 mm For the (3 x 3) pile group show in the figure, the settlement of pile group, 5113 normally consolidated clay stratum having properties as shown in the figure, will be 1 son tN lely Consolidated Char m z 20 mm’ 0.02? Hudfimlam éé . ! Emlyndiu. .c _____ $49-er- as... _._._(:§._¢.fl}._._. I _ _l | Min (-1) 13.2 mm (3:) 12.775 mm {c} 7.345 mm (d) noneofthes'e 50- Match the items of the two lists SL 52; correct answer and sake“ the List I (Boring Methods) Auger Boring Wash Boring Percussion Drilling Rotary Drilling List II (Field Conditions) Below water table in all soil types except hard I‘ soils and rocks P Q 'R s L" 2, Large diameter boreholes over 150 mm in size 3. Explorations for shallow foundations and highways . 4. Bouldery and gravelly strata Codes: P (a) 3 (b) 1 (c) 2 (d) 3 Match the items of List—I with List—II and select the correct answer. List I Q 'l 2 3 I merge-7; S 2 3 1 4 P Modulus of subgrade reaction Q Relative density and strength R Skin friction and point bearing reist'ance 5 Elastic constants List H 1. Cyclic pite load test .2. Pressure meter test 3. Plate load test 4. Standard penetration test 5. Dynamic cone penetration test Codes .- P ' Q R s (a) 1 3 2 5 (b; 1 2 4 3 (c) 2 5 ‘l 3 (d) 3 4 I 2 A horizontal jet strikes a frictionless vertical plate (the Plan View is shown in the figure). It is then divided into two parts, as shown in the figure. If the impact loss can be neglected, what is the value of 8'? 53. (rt) 15‘5 (c) 45° (b) 3.0" (a) 60° A hydraulic jump takes place in a triangular channel of ver tex angle 90°, as shown in figure. The discharge is 1m3/s and the pre-jump depth is 0.5 m. What will be the post-jump depth ?'(Take g = 9.81 m/sz) (a) 0.57m (b) 0.91 m \H \ (c) 1.02 m ’ x%( . (d) 1.57 111 Two pipelines, one carrying oil (mass density 900 kg/m3) and the other water, are connected to a manometer as shown in the figure. By what amount the pressure in the water pipe should be increased so that the mercury levels in both the limbs of the manometer become equal ?' (Mass density of mercury = 13,550 kg/m3 and g: 9.81 m/sz} (ii) 265 kPa (d) 28.9 kPa (a) 24.? kl’a (c) 25.? kPa 55. A solid sphere (diameter 6 mm) is rising- through 56. 57. 59. oil (mass density 900 kg/m3, dynamic viscosity 0.? kg/ms) at a constant velocity of 1 cm/s. What is the specificweight of- the material From which Hie sphere is made ? (Take g = 9.8] 111/52) (s) 4.3 kN/m3 (b) 5.3 kN/m3 (c) a? kam3 (d) 12.3 kN/m3 While applying the Rational formula for computing the design-discharge, the rainfall duratlon is stipulated as the Lime of concentration because (it) this leads to the largest possible rainfall intensity _ (l1) this leads to the smallest possible rainfall . intensity (c) the time of concentrationis the smallest rainfall duration for which the Rational formula is applicable (if) the time (if-concentration. is- the largest rainfall duration for which the Rational formula is applicable While designing a hydraulic structure, the piezometric head at bottom of the floor is computed as 10111. The datum is 3111 below floor bottom. The assured standing water depth above the floor is 2m. The specific gra vily of the floor material 'is 2.5. The floor thickness should be (a) 2.00 m (b) 3.33 m (c) 4.40 m (d) 6.00m The plan area of a reservoir is 1 kmz. The water level in the..reservoir is observed to decline by 20 cm in a certain period. During this period the reservoir receives a surface inflow of 10 hectare- rneters, and 20 hectare-meters are abstracted from the reservoir for irrigation and power. The pan evaporation and rainfall recorded during the same period at a n'ear by meteorological station are 12 cm and 3 cm respectively. The calibrated pan factor is 0.7!, The seepage loss from the reservoir during this period in hectare—meters is (a) 0.0 (b) 1.0 (c) 2.4 (a) 4.6 Match the following : Group I P Rainfall intensity Q Rainfall excess R Rainfall Averaging S Ma55 curve Grbrrp H 1. Isohyets 2- Cumulative rainfall 3. Hymgraph 4. Direct runoff hydrograp'h 60. 6]. Concentration (mg/l} 62-. 63. P Q a 5 (a) 1 3 2 4 (b) 3 4 1 2 (c) 1 2 4 3 (a) 3 4 2 1 Setfljng test on a sample drawn fromAeralionka liquor of ASP (MLSS = 2300 rug/1) was carried Out with 1 litre sample. The test yielded a settled volume of 200 ml. The value of Sludge VOIDme Index shall be (a) 14.0 (c) 71.4 lb) 34-2 (a) 271 Results of a ivater sample analysis are as follows; Equivalent Weight 12.2 20 39 (milliequivalent weight of CaC‘D3 = 50 nag/meg}, Hardness of the water sample in trig/l as CaCO3 is (a) 44.8 (b) 39.5 (c) 179 (d) 358 An ideal horizontal flow settling basin is Sun deeP having surface area 900 m2. Water flows at the rate of 8000 m3/d, at water temperature 20°C {in : 10'3 kg/rns) and p = 1000 kg/m3). Assuming Stokes law to be valid, the proportion {percentage} of Spherical sand particles (0.01 mm in diameter with specific gravity-2.65), that will be removed. is (a). .325 (b) 67 (c) 37.5 (it) 95.5 Match the following : Group I Group II (Characteristics of (Allowable limit, mg/U sewage discharged into inland waters) P 13.0135 1. 250 Q COD. 2. 30 R. 011 and Grease 3. 20 5 Total Suspended Solids 4. 10 5. 5 6. 3 Codes : P Q R 5 (it) 2 5 4 2 (b) 4 1 6 4 (c) 3 1 4 2 (d) 2 1 6' 3 64. Match the following : Group I (Type of water impurity) P Hardness Q Brackish'water from sea R Residual MPN From filters 5 Turbidity Group II (Method of treatment) 1. Reverse Osmosis 2. Chlorination 3. Zeolite Treatment 4. Coagulation and Flocculati'on 5. Coagulation, Flacculation, and Filtration Codes : ‘ P Q R s (a) l ' 2 4 5 (b) 3 2 2 4 (c) 2 1 3 5 (d) 3 l 2 5 65. The design speed for a National Highway is 100 kmph. If the maximum permissible supereleva tion is 0.10 and the coefficient of lateral friction is 0.15, the ruling minimum radius of horizontal curve on the highway should be (a) 250 m (b) 315 m (c) 380 rn (d) 410 m 66. A traffic stream in a particular direction of a two lane road is moving with a constant speed of 50 kmph, with an average headway of 2.52 seconds. The longitudinal distance between two consecutive vehicles is (it) 30 In (b) 35 m (r) 38 m (a) 42 m 67. In the Marshall method of mix design, the coarse aggregates, tine aggregates; filler and bitumen, having respective specific gravities of 2.62, 2.72, 2.70 and 1.02, are mixed in the ratio of 55, 34.6, 4.8. and 5.6 percent, respectively. The theoretical specific gravity of the mix would be (a) 2.36 (b) 2.40 (c) 2.44 (d) 2.50 68. The plate load test conducted with a 75 cm diameter plate on soil subgrade yielded a deflection of 2.5 mm under a stress of 800 N/cmz. The modulus of elasticity of the subgrade soil, in kN/cm2,i.s (a) 141.6 (C) 160.0 (1:). 154.6 (a) 135.4 69. Column Ibelow gives a list of physical properties of aggregates which should be determined tojudge Ll‘telr suitability in road construction. Column ll gives a list of laboratory tests which are conducted to determine these preperties. Column 1 Column II P Hardness ]. Water adsorption Q Porosity 2. Impact test I R Toughness 3. Soundness test 5 Durability 4. Abrasion tEst Which of” the following matches is correct '1' Codes : P Q R S (a) 1 2 3 4 (b) 4 1 2 3 (c) 3 4 1 2 (d) 2 3 it ‘1 Data for Q. 70 — 72 are given below. Solve the problems and choose correct answers. A beam PQRS is-18m long and is simply supported at points Q and R 10m apart. Overhangs PQ and R5 are - 3m and 5m respectively. A train of two point loads of 150 kN and 100 W, 5m apart, crosses this beam from left to right with 100 RM load leading. 20. The maximum sagging moment under the 150 RM ' load anywhere is (a) 500 kNm (c) 400 kNm (b) 450 kNm (d) 375 kNm 71. During the passage of the leads, the maximum and the minimum reactions at support R, lJ'I-kN, are réspectively (:1) '300 and —30 (c) 225 and -30 (b) 300 and —25 (d) 225 and —25 '22. The maximum hogging-moment in the beam anywhere is _ (a) 300 kNm (ta) 450 kNm (c) 50D kNrn (111750 mm Data for Q. 173 — 74 are given below. Solve the problems and choose correct answers. A reinforced concrete beam, size ZOO-mm wide and 300 mm deep overall is simply supported everaspan'oflim. It is subjected to two point loads P of equal magnitude placed at middle third points. The two loads are gradually increased simultaneously. Beam is reinforced with 2 HYSD bars of 16 mm diameter placed at an effective cover of 40 mm on bottom face and nominal shear reinforcement. The characteristic compressrve strength and the bending tensile strength of the concrete are 20.0 N/rorn2 and 2.2N/rnrn2 respechvely. 73. 7'4. 1 'n the resence of tension reinforcement, figrilhoihefiralue 2f load P in kN when the first flexure crack will develop in the beam. (11} 4.5 (b) 5.0 (c) 6.6 (d) 7.5 The theoretical failure load of the beam for attairuhent of limit state of collapse in flexure is (a) 23.7 RN (b) 25.6 m (c) 28.? RN (a) 31.6 m Data for Q. '35 ~—- '?6 aregiven below. Solve the problems and choose correct answers. A truss tie consisting of 2 [SA 75. x 75 x 8 mm carries a pull of 150 kN. At ends the two. angles are connected, one each on either side of a 10 mm thick gusset plate, by 18 mm diameter rivets arranged in one row. The allowable stresses in rivet are fs = 90.0 N/mm2 and {Dr : 250 N/rnmz. r5. Maximum tensile stress in the tie in til/mm2 is (a) 93.6 ' (b) 37.5- (C) 77-2 {d} 66.0 76. Minimum'number of rivets required at each end is (a) 2 (b) 3 (Cl 4 (d) 5 Data for Q. 7'7— 78 are given below. Solve the problems and choose correct answers. A canal having side slopes 1:1 is proposed to be constructed in a cohesive soil to a depth of 10 m below the ground surface. The soil properties are : qr“ =15°.cn = 12 kPa, e :10, Gs = 2.65. 5’7. 78. If Taylor's Stability Number, Sn is 0.08 and if the canal flows fulL the factor of safety with respect to cohesion against failure of the canal bank slopes will be (a) 13.? (C) 1.0 (b) 1.85 (d) None of mesa If there is a sudden 'drawdown of water in'the canal and if Taylor’s Stability Number‘for the reduced value of 43V is 0.126, the factor of safety with respect to cohesion against the failure of bank slopes will be . (a) 1.85 (c) 0.84 (b) 1.18 (d) 0.53 Data for Q. '19 — 30 are given below. Solve the problems and choose correct answers. Figure shows the geometry of a strip footing SuPPOI'ting the load bearing walls of a three storied building and ”the properties of clay layer. ' Hard Stratum 1f the pressure acting gifts; footing isfltll} We, the consolidation settlement of the footing will be {a} 0.89 mm (b) 8.9 mm (c) 89.0 mm ((1) None of these If the elastic modulus and the Poisson's ratio of the clay layer are respectively 50 x 103 kPa and 0.4 and if the influence factor for the strip footing is 1.75, the elastic settlement of the footing will be (a) 0.41 mm (b) 1.41 mm (c) 14.1 mm (18 None of these Data for Q. 81 - 82 are given below. Solve the problems and choose correct answers. A very wide rectangular channel carries a discharge of 3 1113/5 per m width. The channel has ...
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