GATE 2009 Civil Engineering Question Paper. GATE 2009 Civil Engineering Question Paper Q. No Carry One Mark Each

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1 GATE 009 Civil Engineering Quetion Paper GATE CIVIL ENGINEERING 009 (CE) GATE 009 Civil Engineering Quetion Paper Q. No. 1 0 Carry One Mark Each 1. A quare matrix B i kew ymmetric if (A) B T = B (B) B T = B (C) B 1 = B (D) B 1 = B T. For a calar function f(x, y, z) = x + x, the gradient at the point P (1,, 1) i (A) i 6 j 4k (B) i 1 j 4k (C) i 1 j 4k (D) 56 z 1. The analytic function f(z) = ha ingularitie at z 1 (A) 1 and 1 (B) 1 and i (C) 1 and i (D) i and i 4. A thin walled cylindrical preure veel having a radiu of 0.5m and wall thickne of 5mm i ubjected to an internal preure of 700kPa. The hoop tre developed i (A) 14MPa (B) 1.4MPa (C) 0.14MPa (D) 0.014MPa 5. The modulu of rupture of concrete in term of it characteritic cube compreive trength (f ck ) in MPa according to IS 456:000 i (A) 5000f ck (B) 0.7f ck (C) 5000 f ck (D) 0.7 f ck 6. In the theory of platic bending of beam, the ratio of platic moment to yield moment i called (A) Shape factor (B) Platic ection modulu (C) Modulu of reilience (D) Rigidity modulu 7. For limit tate of collape, the partial afety factor recommended by IS 456:000 for etimating the deign trength of concrete and reinforcing teel are repectively (A) 1.15 and 1.5 (B) 1.0 and 1.0 (C) 1.5 and 1.15 (D) 1.5 and The point within the cro ectional plane of a beam through which the reultant of the external loading on the beam ha to pa through to enure pure bending without twiting of the cro-ection of the beam i called (A) Moment centre (B) Centroid (C) Shear centre (D) Elatic centre 9. The quare root of the ratio of moment of inertia of the cro ection to it cro ectional area i called (A) Second moment of area (B) Slenderne ratio (C) Section modulu (D) Radiu of gyration 10. Depoit with flocculated tructure i formed when (A) Clay particle ettle on ea bed (B) Clay particle ettle on freh water lake bed (C) Sand particle ettle on river bed (D) Sand particle ettle on ea bed Page 1 of 10

2 GATE 009 Civil Engineering Quetion Paper GATE CIVIL ENGINEERING 009 (CE) 11. Dilatancy correction i required when a trata i (A) Coheive and aturated and alo ha N Value of SPT > 15 (B) Saturated ilt/fine and and N value of SPT < 10 after the overburden correction (C) Saturated ilt/fine and and N value of SPT >15 after the overburden correction (D) Coare and under dry condition and N value of SPT < 10 after the overburden correction 1. A precat concrete pile i driven with a 50kN hammer falling through a height of 1.0m with an efficiency of 0.6. The et value oberved i 4mm per blow and the combined temporary compreion of the pile, cuhion and the ground i 6mm. A per Modified Hiley Formula, the ultimate reitance of the pile i (A) 000kN (B) 485.7kN (C) 8.kN (D) 11905kN 1. Direct tep method of computation for gradually varied flow i (A) Applicable to non-primatic channel (B) Applicable to primatic channel (C) Applicable to both primatic and non-primatic channel (D) Not applicable to both primatic and non-primatic channel 14. The relationhip among pecific yield (Sy), pecific retention (Sr) and poroity (h) of an aquifer i (A) S y = S r + (B) S y = S r (C) S y = S r (D) S y = S r The depth of flow in an alluvial channel i 1.5m. If critical velocity ratio i 1.1 and Manning n i 0.018, the critical velocity of the channel a per Kennedy method i (A) 0.71m/ (B) 0.784m/ (C) 0.879m/ (D) 1.108m/ 16. The reference preure ued I the determination of ound preure level i (A) 0μPa (B) 0db (C) 10μPa (D) 10db 17. Particulate matter (fly ah) carried in effluent gae from the furnace burning foil fuel are better removed by (A) Cotton bag houe filter (B) Electrotatic precipitator (ESP) (C) Cyclone (D) Wet crubber 18. The value of lateral friction or ide friction ued in the deign of horizontal curve a per India Road Congre guideline i (A) 0.40 (B) 0.5 (C) 0.4 (D) During a CBR tet, the load utained by a remolded oil pecimen at 5.0mm penetration i 50kg. The CBR value of the oil will be (A) 10.0% (B) 5.0% (C).6% (D).4% 0. In quadrantal bearing ytem, bearing of a line varie from (A) 0º to 60º (B) 0º to 180º (C) 0º to 90º (D) 0º N to 90º Page of 10

3 GATE 009 Civil Engineering Quetion Paper GATE CIVIL ENGINEERING 009 (CE) Q. No Carry Two Mark Each 1. For a calar function f (x, y, z) = x + y + z, the directional derivative at the point P(1,, -1) in the direction of a vector i j k i (A) 18 (B) 6 (C) 6 (D) 18 co(z). The value of the integral (z 1)(z ) C dx (where C i a cloed curve given by z = 1) i (A) i (B) i 5 (C) i 5 (D) i dy. Solution of the differential equation y + x = - repreent a family of dx (A) ellipe (B) circle (C) parabola (D) hyperbola 4. Laplace tranform for the function f (x) = coh(ax) i (A) a a (B) a (C) a a (D) a 5. In the olution of the following et of linear equation by Gau elimination uing partial pivoting 5x + y + z = 4; 4y z = 1; and 10x y + z = 4. The pivot for elimination of x and y are (A) 10 and 4 (B) 10 and (C) 5 and 4 (D) 5 and The tandard normal probability function can be approximated a 1 F(x N ) = exp( 1.755x x N N Where xn = tandard normal deviate. If mean and tandard deviation of annual precipitation are 10cm and 7cm repectively, the probability that the annual precipitation will be between 90cm and 10cm i (A) 66.7% (B) 50.0% (C).% (D) 16.7% 7. Conider the following tatement: I. On a principal plane, only normal tre act II. On a principal plane, both normal and hear tree act III. On a principal plane, only hear tre act IV. Iotropic tate of tre i independent of frame of reference The TRUE tatement are (A) I and IV (B) II (C) II and IV (D) II and III Page of 10

4 GATE 009 Civil Engineering Quetion Paper GATE CIVIL ENGINEERING 009 (CE) 8. The degree of tatic indeterminacy of a rigidly jointed frame in a horizontal End clamped to rigid wall plane and ubjected to vertical load only, a hown in figure below i (A) 6 (B) 4 (C) (D) 1 9. A 1mm thick plate i connected to two 8mm plate, on either ide through a 16mm diameter power driven field rivet a hown in the figure below. Auming permiible hear tre a 90MPa and permiible bearing tre a 70MPa in the rivet, the rivet value of the joint i P/ 8 mm 1 mm P P/ 8 mm (A) 56.70kN (B) 4.9kN (C) 6.19kN (D) 1.65kN 0. A hollow circular haft ha an outer diameter of 100mm and a wall thickne of 5mm. The allowable hear tre in the haft i 15MPa. The maximum torque the haft can tranmit i (A) 46kN m (B) 4.5kN m (C) kn m (D) 11.5kN m 1. Conider the following tatement for a compreion member: I. The elatic critical tre in compreion increae with decreae in lenderne ratio II. III. IV. The effective length depend on the boundary condition at it end The elatic critical tre in compreion i independent of the lenderne ratio The ratio of the effective length to it radiu of gyration i called a lenderne ratio The TRUE tatement are (A) II and III (B) III and IV (C) II, III and IV (D) I, II and IV Page 4 of 10

5 GATE 009 Civil Engineering Quetion Paper GATE CIVIL ENGINEERING 009 (CE). Group I give the hear force diagram and Group II give the diagram of beam with upport and loading. Match the Group I with Group II Group I P. ql/ + ql/4 + ql/4 ql/ Q. + ql/4 ql/4 + R. q/ + q/ q/ q/ + q/ q/ S. q/ q/ + Group II 1. q/unit length q/unit length l. q/ q q/ l. q/unit length l 4. q/ q/ l (A) P-,Q-1,R-,S-4 (B) P-,Q-4,R-,S-1 (C) P-,Q-1,R-4,S- (D) P-,Q-4,R-,S-4 Page 5 of 10

6 GATE 009 Civil Engineering Quetion Paper GATE CIVIL ENGINEERING 009 (CE). A rectangular concrete beam of width 10mm and depth 00mm i pretreed by pretenioning to a force of 150kN at an eccentricity of 0mm. The cro ectional area of the pretreing teel i 187.5mm. Take modulu of elaticity of teel and concrete a MPa and MPa repectively. The percentage lo of tre in the pretreing teel due to elatic deformation of concrete i (A) 8.75 (B) 6.15 (C) 4.81 (D) Column I give a lit of tet method for evaluating propertie of concrete and Column II give the lit of propertie Column I Column II P. Reonant frequency tet 1. Tenile trength Q. Rebound hammer tet. Dynamic modulu of elaticity R. Split cylinder tet. Workability S. Compacting factor tet 4. Compreive trength The correct match of the tet with the property i (A) P-,Q-4,R-1,S- (B) P-,Q-1,R-4,S- (C) P-,Q-4,R-,S-1 (D) P-4,Q-,R-1,S- 5. The laboratory tet reult of a oil ample are given below: Percentage finer than 4.75 mm = 60 Percentage finer than mm = 0 Liquid Limit = 5% Platic Limit = 7% The oil claification i (A) GM (B) SM (C) GC (D) ML-MI 6. A plate load tet i carried out on a 00mm 00mm plate placed at m below the ground level to determine the bearing capacity of a m m footing placed at ame depth of m on a homogeneou and depoit extending 10m below ground. The ground water table i m below the ground level. Which of the following factor doe not require a correction to the bearing capacity determined baed on the load tet? (A) (B) (C) (D) Abence of the overburden preure during the tet Size of the plate i much maller than the footing ize Influence of the ground water table Settlement i recorded only over a limited period of one or two day 7. Water flow through a 100mm diameter pipe with a velocity of 0.015m/ec. If the kinematic vicoity of water i m / ec, the friction factor of the pipe material i (A) (B) 0.0 (C) 0.07 (D) A rectangular open channel of width 4.5m i carrying a dicharge of 100m/ec. The critical depth of the channel i (A) 7.09m (B).69m (C).16m (D) 1.1m 9. Water ( w = 9.879kN/m ) flow with a flow rate of 0.m /ec through a pipe AB of 10m length and of uniform cro ection. The end B i above end A and the pipe make an angle of 0º to the horizontal. For a preure of 1kN/m at the end B, the correponding preure at the end A i (A) 1.0kN/m (B) 17.0kN/m (C) 56.4kN/m (D) 61.4kN/m Page 6 of 10

7 GATE 009 Civil Engineering Quetion Paper GATE CIVIL ENGINEERING 009 (CE) 40. An agricultural land of 47ha i to be irrigated for a particular crop. The bae period of the crop i 90 day and the total depth of water required by the crop i 105cm. If a rainfall of 15cm occur during the bae period, the duty of irrigation water i (A) 47ha/cumec (B) 486ha/cumec (C) 741ha/cumec (D) 864ha/cumec 41. Column I Column II P. Corioli effect 1. Rotation of earth Q. Fumigation. Lape rate and vertical temperature profile R. Ozone layer. Inverion S. Maximum mixing depth 4. Dobon (mixing height) The correct match of Column I with Column II i (A) P-,Q-1,R-4,S- (B) P-,Q-1,R-,S-4 (C) P-1,Q-,R-,S-4 (D) P-1,Q-,R-4,S- 4. A horizontal flow primary clarifier treat watewater in which 10%, 60% and 0% of particle have ettling velocitie of 0.1mm/, 0.mm/, 0.mm/, and 1.0mm/ repectively. What would be the total percentage of particle removed if clarifier operate at a Surface Overflow Rate (SOR) of 4.m /m.d? (A) 4% (B) 56% (C) 86% (D) 100% 4. An aerobic reactor receive watewater at a flow rate of 500m /d having a COD of 000mg/L. The effluent COD i 400mg/L. Auming that watewater contain 80% biodegradable wate, the daily volume of methane produced by the reactor i (A) 0.4m (B) 0.80m (C) 4m (D) 80m 44. Column I Column II P. Grit chamber 1. Zone ettling Q. Secondary ettling tank. Stoke law R. Activated ludge proce. Aerobic S. Trickling filter 4. Contact tabiliation The correct match of Column I with Column II i (A) P-1,Q-,R-,S-4 (B) P-,Q-1,R-,S-4 (C) P-1,Q-,R-4,S- (D) P-,Q-1,R-4,S- 45. Which of the following tre combination are appropriate in identifying the critical condition for the deign of concrete pavement? Type of Stre Location P. Load 1. Corner Q. Temperature. Edge. Interior (A) P-, Q- (B) P-1, Q- (C) P-, Q-1 (D) P-, Q- 46. A ret vertical curve join two gradient of +% and -% for a deign peed of 80km/h and the correponding topping ight ditance of 10m. The height of driver eye and the object above the road urface are 1.0m and 0.15m repectively. The curve length (which i le than topping ight ditance) to be provided i (A) 10m (B) 15m (C) 16m (D) 40m Page 7 of 10

8 GATE 009 Civil Engineering Quetion Paper GATE CIVIL ENGINEERING 009 (CE) 47. On a pecific highway, the peed-denity relationhip follow the Greenberg model [v = v f ln (k j / k)], where v f and k f are the free flow peed and jam denity repectively. When the highway i operating at capacity, the denity obtained a per thi model i (A) e.k j (B) k j (C) k j / (D) k j / e 48. A three-phae traffic ignal at an interection i deigned for flow hown in the figure below. There are ix group of flow identified by the number 1 through 6. Among thee 1,, 4 and 6 are through flow and, and 5 are right turning. Which phaing cheme i not feaible? Combination choice Phae I Phae II Phae III P 1, 4, 5, 6 Q 1, 4, 5, 6 R, 5 1, 4, 6 S 1, 4, 6, 5 1 (A) P (B) Q (C) R (D) S 49. The magnetic bearing of a line AB wa N 59º 0 W in the year 1967, when the declination wa 4º 10 E. If the preent declination i ºW, the whole circle bearing of the line i (A) 99º 0 (B) 07º 40 (C) 9º 0 (D) 01º Determine the correctne or otherwie of the following Aertion [a] and the Reaon [r] : Aertion [a] : Curvature correction mut be applied when the ight are long Reaon [r] : Line of collimation i not a level line but i tangential to the level line (A) Both [a] and [r] are true and [r] i the correct reaon for [a] (B) Both [a] and [r] are true but [r] i not the correct reaon for [a] (C) Both [a] and [r] are fale (D) [a] i fale but [r] i true Page 8 of 10

9 GATE 009 Civil Engineering Quetion Paper GATE CIVIL ENGINEERING 009 (CE) Common Data Quetion: 51 & 5 Examine the tet arrangement and the oil propertie given below 5m 5m Rigid Steel Beam Concrete block m high G.W.T. Saturated dene and at = 18kN/m = 5, c = 0kPa N = 40 w = 10kN/m 5m 500mm diameter bored pile Angle of friction () = 4 Earth preure coefficient (K) = The maximum preure that can be applied with a factor of afety of through the concrete block, enuring no bearing capacity failure in oil uing Terzaghi bearing capacity equation without conidering the hape factor, depth factor and inclination factor i (A) 6.67kPa (B) 60kPa (C) 90kPa (D) 10kPa 5. The maximum reitance offered by the oil through kin friction while pulling out the pile from the ground i (A) 104.9kN (B) 09.8kN (C) 6kN (D) 47kN Common Data Quetion: 5 & 54 Following chemical pecie were reported for water ample from a well: Special Concentration (milli equivalent/l) Chloride (Cl ) 15 Sulphate (SO 4 ) 15 Carbonate (CO ) 05 Bicarbonate (HCO ) 0 Calcium (Ca + ) 1 Magneium (Mg + ) 18 ph Total hardne in mg/l a CaCO i (A) 1500 (B) 000 (C) 000 (D) Alkalinity preent in the water in mg/l a CaCO i (A) 50 (B) 1500 (C) 1750 (D) 5000 Page 9 of 10

10 GATE 009 Civil Engineering Quetion Paper GATE CIVIL ENGINEERING 009 (CE) Common Data Quetion: 55 & 56 One hour triangular unit hydrograph of a waterhed ha the peak dicharge of 60m /ec.cm at 10hour and time bae of 0 hour. The index i 0.4cm per hour and bae flow i 15m m/ec 55. The catchment area of the waterhed i (A).4km (B).4km (C) 4km (D) 40km 56. If thee i rainfall of 5.4cm in 1 hour, the ordinate of the flood hydrograph at 15 th hour i (A) 5 m /ec (B) 40 m /ec (C) 49 m /ec (D) 58 m /ec Linked Anwer Quetion: Q.57 to Q.60 Carry Two Mark Each Statement for Linked Anwer Quetion: 57 & 58 In the cantilever beam PQR hown in figure below, the egment PQ ha flexural rigidity EI and the egment QR ha infinite flexural rigidity. W El Q Rigid P R 57. The deflection and lope of the beam at 'Q' are repectively (A) 5WL WL WL WL and (B) and 6EI EI EI EI (C) WL WL WL WL and (D) and EI EI EI EI 58. The deflection of the beam at 'R' i (A) 8WL EI (B) 5WL 6EI L (C) 7WL EI (D) 8WL 6EI Statement for Linked Anwer Quetion: 59 & A aturated unditurbed ample from a clay trata ha moiture content of.% and pecific weight of.7. Auming w = 10kN/m, the void ratio and the aturated unit weight of the clay, repectively are (A) 0.6 and kN/m (B) 0. and 0.65kN/m (C) 0.6 and 0.65kN/m (D) 0. and kN/m 60. Uing the propertie of the clay layer derived from the above quetion, the conolidation ettlement of the ame clay layer under a quare footing (neglecting it elf weight) with additional data hown in the figure below (aume the tre ditribution a 1H:V from the edge of the footing and w = 10kN/m ) i 00 kn L G.W.T. 1.0m 1.0m m m 1 Saturated and at = 18kN/m 1.0m Stiff Clay Compreion Index (C c ) = 0.4 Dene and (A).78mm (B) 61.75mm (C) 79.5mm (D) 11.1mm Page 10 of 10