GATE-1997 CIVIL ENGINEERING SECTION A. (100 Marks) 1. For each subquestion given below, for answers viz A,B,C D are provided, out of which only one is correct. Choose the correct answer from A,B,C or D. dy 1.1.For the differential equation, f ( x, y) g ( x. y) 0 to be extract, dx 2 2 f g f g f g a) b) c)f=g d) 2 ans:a y x x y x y2 dy 1.2 The differential equation +Py= Q, is a linear equation of first order only if dx (a) P is a constant but Q is a function of y (b) P and Q are functions of y or constants (c) P is a function of y but Q is a constant (d) P and Q are functions of x or constants ans:c 1.3. For real values of x, cos(x) can be written in one of the forms of a convergent series given below : x 2 x 4 x5 x x x a)cos(x)= 1 b) 1 ...... ...... 2! 4! 5! 1! 2! 3! x3 x5 x 7 x 2 x 2 x3 c) x d) x ans:d ...... ...... 3! 5! 7! 1! 2! 3! 1.4. If A and B are two matrices and if AB exists, then BA exists (a) only if A has as many rows as B has columns (b) only if both A and B are square matrices (c) only if A and B are skew matrices (d) only if both A and B are symmetric ans:a 1 3 2 1.5. If the determinant of matrix 0 5
6 is 26, then the determinant of the matrix 2 7 8
2 7 8 0 5 6 1 3 2 (a) -26
6 is (b) 26 (c) 0 0 1 0
1.6. Inverse of matrix 0 0 1 is
1 0 0
(d) 52
ans:a
0 1 1 1 0 0 1 0 0 0 0 1 (a) 1 0 0 (b) 0 0 1 (c) 0 1 0 (d) 0 1 0 0 1 0 0 1 0 0 0 1 1 0 0 2 1.7. Area bounded by the curve y = x and lines x = 4 and y=0 is given by 128 128 64 (a) 64 (b) c) (d) 3 4 3 1.8. The curve give by the equation x2+y2=3 axy, is (a) symmetrical about x-axis (b) symmetrical about y-axis (c) symmetrical about line y=x (d) tangential to x=y=a/3 x 1.9. e is periodic, with a period of (a) 2π (b) 2i π (c) π (d) i π sin 1.10. Lt , where m is an integer, is one of the following:
ans:a
ans:b
ans:d ans:b
(a) m (b) mπ (c)mθ (d) 1 ans:a 2. For each sub question given below, four answer viz: A,B,C and D are provided, out of which only one is correct. 2.1.the force in the member DE of the truss shown in fig is
a)100.0kN b)zero c)35.5kN d)25.0kN ans:b 2.2 A propped cantilever beam of span L, is loaded with uniformly distributed load of intensity w/unit length, all through the span. Bending moment at the fixed end is wL2 wL2 wL2 wL2 (a) (b) (c) (d) ans:a 8 2 12 24 2.3. The degree of kinematic inderminacy of the rigid frame with clamped ends at A and D shown in the Figure 2.3 is.
(a) 4 (b) 3 (c) 2 (d) zero ans:b 2.4 For the frame shown in the Figure 2.4, the maximum bending moment in the column is
(a) zero
(b) 400 kN m (c) 100 kN m (d) 200 kN m
ans:b
2.5 The order or the flexibility matrix for a structure is (a) equal to the number of redundant forces (b) more than the number of redundant forces (c) less than the number of redundant forces (d) equal of the number of redundant forces plus three ans:a 2.6 A cantilever beam of span ‘L’ is loaded with a concentrated load ‘P’ at the free end. Deflection of the beam at the free end is 5PL3 PL3 PL3 PL3 (a) (b) (c) (d) ans:c 384 EI 6 EI 48 EI 3 EI 2.7 The cylinder strength of the concrete is less than the cube strength because of (a) the difference in the shape of the cross section of the specimens (b) the difference in the slendeness ratio of the specimens (c) the friction between the concrete specimens and the steel plate of the testing machine (d) the cubes are tested without capping but the cylinders are tested with capping. ans:b 2.8 IS 459-1978 recommends to provide certain minimum steel in a RCC beam (a) the difference in the shape of the cross section of the specimens (b) the difference in the slenderness ratio of the specimens (c) the friction between the concrete specimens and the steel plate of the testing machine. (d) the cubes are tested without capping but the cylinders are tested with capping ans:b 2.9 The permissible bending tensile stress in concrete for the vertical wall of an R.C. water tank made of M25 concrete is (a) 8.5N/mm2 (b) 6.0 N/mm2 (c) 2.5 N/mm2 (d) 1.8N/mm2 ans:d 2.10 Permissible bending tensile stress in high yield strength deformed bars of grade 415 N/mm2 in a beam is (a) 190 N/mm2 (b) 230 N/mm2 (c) 140 N/mm2 (d) None of the above ans:b 2.11 A prestressed concrete rectangular beam of size 300 mm x 900 mm is prestressed with an initial prestressing force of 700 kN at an eccentricity of 350 mm at midspan. Stress at top of the due to prestress alone, in N/mm2 is (a) -3.46 9tension) (b) 2.59 (compression) (c) zero (d) 8.64 (compression) ans:a 2.12. Maximum size of a fillet weld for a plate of square edge is (a) 1.5 mm less than the thickness of the plate (b) one half thickness of the plate (c) thickness of the plate itself (d) 1.5 mm more than the thickness of the plate
ans:a
2.13 Factor of safety adopted by IS : 800 – 1984 while arriving at the permissible stress in axial compression is (a) 2.00 (b) 1.00 (c) 1.67 (d) 1.50 ans:c 2.14 Effective length of a rafter member between two nodes at a distance L, perpendicular to the plane of the truss is
(a) 2.00 L (c) 1.50
(b) 0.85 (d) 1.00 L
ans:b
2.15 Allowable average shear stress is an unstiffened web for beams made of steel of grade 250 N/mm2 is (a) 250 N/mm2 (b) 165 N/mm2 (c) 150 N/mm2 (d) 100 N/mm2 ans:d 3. For each sub question given below, four answers viz : A,B,C and D are provided, out of which only one is correct. 3.1 If the porosity of a soil sample is 20%, the void ratio is (a) 0.20 (b) 0.80 (c) 1.00 (d) 0.25 ans:d 3.2 The shape of clay particle is usually (a) angular (b) flaky (c) tubular (d) rounded
ans:b
3.3 Consistency Index for a clayer soil is [LL=Liquid Limit, PL = Plastic Limit, PI = Plasticity Index, W = natural moisture content] LL w w PL (a) (b) (c) LL-PL (d) 0.5 w ans:a PI PI 3.4 According to Darcy’s law for flow through porous media, the velocity is proportional to (a) effective stress (b) hydraulic gradient (c) cohesion (d) stability number ans:b 3.5 A soil mass has coefficients of horizontal and vertical permeability as 9 x 10-7cm/s and 4×10-7 cm/s, respectively. The transformed coefficient of permeability of an equivalent isotropic soil mass is (a) 9×10-7cm/s (b) 4×10-7cm/s -7 (c) 13×10 cm/s (d) 6×10-7cm/s ans:d 3.6 In a compaction test, as the compaction effort is increased, the optimum moisture content (a) decreases (b) remains same (c) increase (e) increases first there after decreases ans:a 3.7 The vertical stress at depth. z directly below the point load p is (k is a constant) p p p p (a) k (b)k 3 (c) k 2 (d)k ans:c z z z z 3.8 The slope of the e-log p curve for a soil mass gives (a) coefficient of permeability, k (b) coefficient of consolidation Cv (c) compression index, Cc (d) coefficient of volume compressibility, mv ans:b 3.9 Sand and drains are used to
(a) reduce the settlement (b) accelerate the consolidation (c) increase the permeability (d) transfer the load ans:a 3.10 Coulomb’s theory of earth’s pressure is based on (a) the theory of elasticity (b) the theory of plasticity (c) empirical rules (d) wedge theory ans:d 3.11. The depth of tension crack in a soft clay (Φu=0) is 4C u 2C u C C (a) (b) (c) u (d) u ans:b 2 3.12 Vane tester is normally used for determining in situ shear strength of (a) soflt clays (b) sand (c) stiff clays (d) gravel ans:a 3.13 The unit for coefficient of subgrade modulus is (a) kN/m3 (b) ku/m2 c) ku/m (d) ku/m ans:a 3.14 The ratio of unconfined compressive strength of an undisturbed sample of soil to that of a remoulded sample, at the same water content, is known as (a) activity (b) damping (c) plasticity (d) sensitivity ` ans:d 3.15 Well foundation are commonly used as foundation for the following structures: (a) Water tanks (b) Bridges (c) Buildings (d) Reciprocating machines ans:b 4. For each sub question given below, four answers viz : A,B,C and are provided, out of which only is correct. 4.1 The unit of dynamic viscosity of a fluid is (a) m2/s (b) Ns/m2 (c) Pa s/m2 (d) kgs2/m2 ans:b 4.2 The centre of pressure of a liquid on a plane surface immersed vertically in a static body of liquid, always lies below the centroid of the surface area, because (a) in liquids the pressure acting is same in all directions (b) there is no shear stress in liquids at rest (c) the liquid pressure is constant over depth (d) the liquid pressure increases linearly with depth ans:d 4.3 One of the following statements is true with regards to bodies that float or are submerged in liquids : (a) For a body wholly submerged in a liquid the stability is ensured if the centre of buoyancy is below the centre of gravity of the body. (b) For a body floating in a liquid the stability is ensured if the centre of buoyancy is below the centre of buoyancy is below the centre of gravity of the body. (c) For a body floating in a liquid the stability is ensured if the centre of buoyancy and the centre of gravity, regardless of the relative positions of the centre of buoyancy and gravity.
(d) For a body floating in a liquid the stability is ensured if the centre of buoyancy is below the centre of gravity and the meta centre is above both the centre of gravity and buoyancy. ans:a 4.4 The kinetic energy correction factor for a fully developed laminar flow through a circular pipe is (a) 1.00 (b) 1.33 (c) 2.00 (d) 1.50 ans:c 4.5 Two flow patterns are represented by their stream functions ψ1 and ψ2 as given below ψ1=X2+Y2, ψ2 = 2xy If these two partners are superposed on one another, the resulting streamline pattern can be represented by one of the following : (a) A family of parallel straight lines (b) A family of circle (c) A family of parabolas (d) A family of hyperbola ans:b 4.6 While deriving an expression for loss of head due to a sudden expansion in a pipe, in addition to the continuity and impulse – momentum equations, one of the following assumptions is made : (a) Head loss due to friction is equal to the head loss in eddying pressure. (b) The mean pressure in eddying fluid is equal to the downstream pressure (c) The mean pressure in eddying fluids is equal to the upstream pressure. (d) Head lost in eddies is neglected. ans:c 4.7 If a single pipe of length L and diameter d is to be replaced by three pipes of same material, same length and equal diameter d (d (a)Both statements are true. (b) Both statements are false. (c) II is true but I false (d) I is true but II is false. 2.9. A cantilever beam of length L and a cross section with shape factor f supports a concentrated load P as shown below :
the length Lp of the plastic zone, when the maximum bending moment, equals the plastic moment Mp’ given by L L 1 (a) p (b) p L(1 f ) L L f Lp L 1 1 1 (c) (d) p 1 L L f f 2.10. For the structure shown below, the vertical deflection at point A is given by
(a)
pL3 81E1
(b)
2 pL3 81E1
pL3 72 E1 2.11. The ultimate bearing capacity of a soil is 300 kN/m2. The depth of foundation is 1m and unit weight of soil is 20 kN/m3. Choosing a factor of safety of 2.5, the net safe bearing capacity is (a) 100 kN/m2 (b) 112 kN/m2 (c) 80 kN/m2 (d) 100.5 kN/m2 2.12. A deep cut of 7m has to be made in a clay with unit weight 16 kN/m3 and a cohesion of 25 kN/m2. What will be the factor of safety if one has to have a slope angle of 300 ? Stability number is given to be 0.178 (from Taylor’s chart) for a depth factor of 3. (a) 0.80 (b) 1.1 (c) 1.25 (d) 1.0 2.13. In a drained triaxial compression test, a saturated specimen of a cohesionless sand fails under a deviatoric stress of 3 kgf/cm2 when the cell pressure is 1 kgf/cm2. The effective angle of shearing resistance of sand is about (a) 370 (b) 450 (c) 530 (d) 200 2.14. Two footings, one circular and the other square, and founded on the surface of a purely cohesionless soil. The diameter of the circular footing is same as that of the side of the square footing. The ratio of their ultimate bearing capacities is (a) 3/4 (b) 4/3 (c) 1.0 (d) 1.3 2.15. To have zero active pressure intensity at the tip of a wall in cohesive soil, one should apply a uniform surcharge intensity of (a) 2 c tan α (b) 2 c cot α (c) -2 c tan α (d) -2 c tan α 2.16. Water flows at a depth of 0.1m with a velocity of 6/m/s in a rectangular channel. The alternate depth is (a) 0.30 m (b) .40 m (c) 0.86 m ( d) 0.81 m 2.17 In an area of 200 hectare, water table drops by 4m. If the porosity is 0.35 and the specific retention is 0.15, change in volume of storage in the aquifer is (a) 160m3 (b) 1.6x106 m 6 3 (c) 8 x 10 m (d) 1.6 x 103 m3 2.18. A tube well having a capacity of 4m3 / hour operates for 20 hours each day during the irrigation season. How much area can be commanded if the irrigation interval is 20 days and depth of irrigation is 7 cm ? (a) 1.71 x104 m2 (b) 1.14 x 104 m2 4 2 (c) 22.9 x 10 m (d) 2.29 x 104 m2 2.19 The parameters in Horton’s infiltration equation [f(t) = fc + (f0-fc)e-kt] are given as, f0 = 7.2 cm/ hour, fc=1.34 cm/hour and k = 4.182/hour. For assumed continuous ponding the comulative infiltration at the end of 2 hours is (a) 2.68 cm (b) 1.50 cm (c) 1.45 cm (d) 4.18 cm 2.20 Water flows at a rate of 10m3/s in a rectangular channel 3 m wide. The critical depth of flow is (c) zero
(d)
(a)1.13 m (b) 2 m (c) 1.45 m (d) 1.04 m 2.21. A circular sewer 2m diameter has to carry a discharge of 2m3/s when flowing nearly full. What is the minimum required slope to initiate the flow ? Assume Manning’s n = 0.015. (a) 0.00023 (b) 0.000036 (c)0 0.000091 (d) 0.000014 2.22 The following characteristics pertain to the sand filters used in water industry. I. Filtration rate is 1 to 4m3/(m2 day). II. Typical duration of operation in one run is 24 to 72 hours. III. Operating cost is low. Which of the above characteristics pertain to slow sand filters ? (a) I, II and III (b) I and II (c) II and III (d) I and II 2.23. The ruling minimum radius of horizontal curve of a national highway in plain terrain for a fuling design speed of 100 km/hour with e = 0.07 and f = 0.15 is close to (a) 250 m (b) 360 m (c) 36 m (d) 300 m 2.24. Design rate of super elevation for horizontal highway curve of radius 450 m for a mixed traffic condition, having a speed of 125 km/hour is (a) 1.0 (b) 0.05 (c) 0.07 (d) 0.154 SECTION B. (75 Marks) This section consists of TWENTY questions of FIVE marks each. ANY FIFTEEN out of them have to be answered. Answers to each questions must be started on a fresh page. If more number of questions are attempted, score off the answers not to be evaluated, else only the first fifteen unscored answer will be considered strictly. (15×5=75) d2y 2 3. Find the solution of the differential equation y cos t k with initial conditions 2 dt , dy y(0)=0, and k are constants. Use either the method of undetermined (0) =0,here dt coefficients or the operator(D=d/dt) based method. 4. A is a square matrix is given by 2 0
A
1
2 0 1 2 One of the eigenvalues of A is given to be equal to 2. Determine the other eigenvalues. Express the eigenvector corresponding to the lowest eigenvalue in the form [1 a b]T and determine a and b. 5. A cantilever beam AB carries a concentrated force P and a moment M = PL/3 at its tip as shown below. Show using Castigliano’s theorem that, if the angle of inclination α = ½, then the displacement of the point B, due to bending will be in the direction of force P.
6. A beam AB is suspended from a wire CB as shown in figure below. The beam carries a central concentrated load P. It may be assumed that E = 7x1010N/m2, I = 800 mm4, A = 1.2 mm2, and P 300 N. Determine, using stiffness matrix approach, the deflection of point B. What would be this deflection if the load P were to be applied upwards, instead of downwards ? The axial deformation of the beam AB may be ignored.
The stiffness matrix fro a beam element is given to be as follows.
AL2 symmetric I 0 12 K
2 EL 0 6 L 4 L L3 AL2 AL2 00 I I 0 12 6 L 12
0 6 L 2 L2 0 6 L 4 L2 7. A simply supported rectangular prestressed concrete beam 200 mm wide and 400 mm deep has an effective span of 12m. the prestressing cable has a triangular profile with zero eccentricity at ends and 70 mm at the midspan as shown in the figure below. The effective prestress is 800 kN after all losses. Determine the value of a point load, the beam can support at the midspan if the pressure line passes through the upper kern of the selection. The weight density of the material of the beam can be taken to be 25 kN/m3
8. A two hinged parabolic arch carries two concentrated moments as shown in the figure below. The moment of inertia of the arch at any particular cross section is equal to the moment of interia at the crown multiplied by the secant of the angle θ, where θ is the angle between the horizontal and the tangent to the arch axis at that particular section. Determine the support reactions.
9. A continuous beam 250 mm x 450 mm carries 6 numbers of 12 mm diameter longitudinal bars as shown. The factored shear force at the point of inflection is 200 kN. Check if the beam is safe in bond. Assume M15 mix with σck = 15 N/mm2 and mild steel with σy= 250 N/mn2. A clear cover of 25 mm can be assumed. The design bond stress for mild steel bars in M15 concrete is specified to be 1.0 N/mm2.
10. A 12mm bracket plate is connected to a column flarge as shown in he figure below. The bracket transmits a load of w = 200 kN to the column flange. A 10 mm fillet weld is provided along AB, BC and CD. If e = 350 mm, b = 200 mm adn d = 650 mm, verify if the size of the weld provided is adequate. Allowable shearing stress in the fillet weld can be taken to be 108 MPa.
11. A 5 m thick clay layer lies between two layers of sand each 4m thick, the top of the upper layer of sand being at ground level. The water table is 2m below the piezometric surface being 4m above ground level. The saturated unit weight of clay is 20 kN/m3 and that of sand is 19 kN/m3. Above the water table unit weight of sand is 16.5 kN/m3. Calculate the effective vertical stresses at the top and bottom of the layer. Also draw the total vertical stress diagram in the given soil layers. 12. In an oedometer test, a specimen of saturated clay 19 mm thick reaches 50% consolidation in 20 minutes. How long it would take a layer of this clay 5m thick to reach the same degree of consolidation under the same stress and drainage conditions ? How long would it take for the clay layer to reach 30% consolidation ? 13. A footing 3m square carries a gross pressure of 350kN/m2 at a depth of 1.2 m in sand. The saturated unit weight of sand is 20 kN/m3 and the unit weight of sand is 20kN/m3 and the unit weight above the water table is 17kN/m3. The shear strength parameters are c’=0 and φ’ = 300. (For φ’ = 300, Nq = 22 and Ng= 20). Determine the factor of safety with respect of shear failure for the following cases : (a) water table is 5m below ground level. (b) water table is at 1.2 m below ground level. 14. For the retaining wall shown in the figure below assume that the wall can yield sufficiently to develop active stage. use Rankine’s active earth pressure theory and determine (a) active force per meter of the wall, and (b) the location of the resultant line of action.
15. A pump is to deliver water at a rate of 1.4 m3/s from a sump to a reservoir which is 10 km away through a steel pipe 1200 mm in diameter for a length of 5 km and the remaining through a PSC pipe of diameter 1000 mm. The elevation difference between the full tank level of the delivery reservoir and the low water level of the sump is 50 m. What is the Break Horse Power (in kW) requirement of the motor ? Assume a pump house loss of 3.75 m and minor losses to be 10% of the friction losses. Use Darcy-Weisbach friction factor (f) of 0.018 for steel pipe and 0.02 for PSC pipe with a pump efficiency of 80%. 16. A 1: 49 scale model of a proposed dam is used to predict prototype flow conditions. The design flood discharge near the spillway is 15000 m3/s. Establish the relation between velocities in the model and prototype. What flow rate should be established in the model to simulate this flow ? If a velocity of 1.2 m/s is measured at a poitn in the model what is the velocity at a corresponding point in the prototype ?
17. An area of 1 hectare is irrigated through a stream of 0.03 m3/s. Depth of the root zone is 1 m and available moisture holding capacity is 16 cm/m. Irrigation water is supplied when 50% of the available moisture is depleted. Water application efficiency is 60% Determine the storage efficiency. 18. A 6 hour unit hydrograph of a watershed is given below. calculate 18 our unit hydrograph using S- curve method and tabulate the results. Time (hour) 6hr unit hydrograph [m3/(cm)] 0 0 6 1.8 12 30.9 18 85.6 24 41.8 30 14.6 36 42 1.8 19. Consider a glucose solution (C6 H12 O6) of molarity 1.75×10-3 that is completely oxidized to CO2 and H2O. Find the amount of oxygen required for this reaction. The chemical mass balance equation for the above reaction is given as C6 H12 O6 6O2 6CO2 + 6H2 O (Atomic weights are : C = 12; H = 1 ;O =16). 20. The dissolved oxygen (DO) in an unseeded sample of diluted waste having an initial DO of 9.5 mg/I is measured to be 3.5 mg/1 after 5 days. The dilution factor is 0.03 and the reaction rate constant, k = 0.22/day (to the base ‘e’ in the decay curve at 200C) Estimate (a) The 5 day BOD of the waste at 200C. (b) Ultimate carbonaceous BOD. (c) Remaining oxygen demand after 5 days. (d) The 5 day BOD of this waste at 250 C assuming a temperature coefficient of 1.047. 21. The load penetration date from a California Bearing Ratio (CBR) test is provided in the following table. Indicate whether any correction is required for the calculated CBR value. Find the CBR value of the soil from the data provided. Table : Load penetration data Penetration (in mm) Load in kgf (kg force) 0 0 0.5 4 1.0 13 1.5 29 2.0 40 2.5 50 3.0 58 4.0 70 5.0 78 7.5 93 10 103 12.5 112
Area of plunger is given as 19.6 cm2. Pressure for standard crushed stones at 2.5 mm and 5.0 mm are 70 kgf/cm2 and 105 kgf/cm2 respectively. 22. As ascending gradient has to be designed for design speed of 80 km/h so as to provide a safe overtaking sight distance of 230 m. Estimate the length of the summit curve.
Civil Engineering
GATE Paper 2001
GATE – 2001 CE: Civil Engineering Section – A (75 Marks) 1. This question consists of TWENTY FIVE sub-questions (1.1-1.25) of ONE mark each. For each of these sub-questions four possible answers (A, B, C and D) are given, out of which only one is correct. 1.1. The number of boundary conditions required to solve the differential equation (A) 2 (B) 0 1.2. Value of the integral I =
is
(C) 4 (D) 1 is
(A)
(C)
(B)
(D)
1.3. Limit of the following series as x approaches is f(x) = x (A)
(C)
(B)
(D) 1
1.4. The degree of static indeterminacy, , and the degree of kinematic indeterminacy, plane frame shown below, assuming axial deformations to be negligible, given by
, for the
Page : 1
Civil Engineering (A) (B)
GATE Paper 2001 (C) (D)
1.5. The bending moment (in kNm units) at the mid-span location X in the beam with overhangs shown below is equal
(A) 0 (B) 10
(C) 15 (D) 20
1.6. Identify the FALSE statement from the following, pertaining to the effects due to a temperature rise ∆T in the bar BD alone in the plane truss shown below:
(A) No reactions develop at supports A and D (B) The bar BD will be subject to a tensile force (C) The bar AC will be subject to a compressive force (D) The bar BC will be subject to a tensile force 1.7. Identify the correct deflection diagram corresponding to the loading in the plane frame shown below:
Page : 2
Civil Engineering
GATE Paper 2001
1.8. Identify the FALSE statement from the following, pertaining to the methods of structural analysis. (A) Influence lines for stress resultants in beams can be drawn using Muller Breslau’s Principle. (B) The Moment Distribution Method is a force method of analysis, not a displacement method. (C) The Principle of Virtual Displacements can be used to establish a condition of equilibrium. (D) The Substitute Frame Method is not applicable to frames subjects to significant sidesway 1.9. Identify the FALSE statement from the following, pertaining to the design of concrete structures. (A) The assumption of a linear strain profile in flexure is made use of in working stress design, but not in ultimate limit state design. Page : 3
Civil Engineering
GATE Paper 2001
(B) Torsional reinforcement is not required to be provided at the corners of simply supported rectangular slabs, if the corners are free to lift up. (C) A rectangular slab, whose length exceeds twice its width, always behaves as a two way slab, regardless of the support conditions. (D) The ‘load balancing’ concept can be applied to select the appropriate tendon profile in a prestressed concrete beam subject to a given pattern of loads. 1.10. Identify the most efficient but joint (with double cover plates) for a plate in tension from the patterns (plan views) shown below, each comprising 6 identical bolts with the same pitch and gauge.
1.11. The following two statements are made with respect to different sand samples having the same relative density. Identify if they are TRUE or FALSE. I. Poorly graded sands will have lower friction angle than the well graded sands. II. The particle size has no influence on the friction angle of sand. (A) II is TRUE but I is FALSE (C) Both are TRUE statements (B) Both are FALSE statements (D) I is TRUE but II is FALSE 1.12. The following two statements are made with reference to the calculation of net bearing capacity of a footing in pure clay soil (ϕ = 0) using Terzaghi’s bearing capacity theory. Identify if they are TRUE or FALSE. I. Increase in footing width will result in increase in bearing capacity. Page : 4
Civil Engineering
GATE Paper 2001
II. Increase in depth of foundation will result in higher bearing capacity. (A) Both statements are TRUE (C) I is TRUE but II is FALSE (B) Both statements are FALSE (D) I is FALSE but II is TRUE 1.13. The width and depth of a footing are 2 and 1.5 m respectively. The water table at the site is at a depth of 3 m below the ground level. The water table correction factor for the calculation of the bearing capacity of soil is (A) 0.875 (C) 0.925 (B) 1.000 (D) 0.500 1.14. The void ratio and specific gravity of a soil are 0.65 and 2.72 respectively. The degree of saturation (in percent) corresponding to water content of 20% is (A) 65.3 (C) 83.7 (B) 20.9 (D) 54.4 1.15. With respect to a c-ϕ soil in an infinite slope, identify if the following two statements are TRUE or FALSE. I. The stable slope angle can be greater than ϕ II. The factor of safety of the slope does not depend on the height of soil in the slope. (A) Both statements are FALSE (C) I is FALSE but II is TRUE (B) I is TRUE but II is FALSE (D) Both statements are TRUE 1.16. In a Bernoulli equation, used in pipe flow, each term represents (A) Energy per unit weight (C) Energy per unit volume (B) Energy per unit mass (D) Energy per unit flow length 1.17. The stage-discharge relation in a river during the passage of flood is measured. If is the discharge at the stage when water surface is falling and is the discharge at the same stage when water surface is rising, then (A) (C) (B) (D) constant for all stages 1.18. Isopleths are lines on a map through points having equal depth of (A) Rainfall (C) Evapotranspiration (B) Infiltration (D) Total runoff 1.19. A linear reservoir is one in which (A) Storage varies linearly with time Page : 5
Civil Engineering
GATE Paper 2001
(B) Storage varies linearly with outflow rate (C) Storage varies linearly with inflow rate (D) Storage varies linearly with elevation 1.20. Aeration of water is done to remove (A) Suspended impurities (B) Colour
(C) Dissolved Salts (D) Dissolve Gases
1.21. The following chemical is used for coagulation (A) Ammonium Chloride (B) Aluminium Chloride
(C) Aluminium Sulphate (D) Copper Sulphate
1.22. The unit in which both sedimentation and digestion processes of sludge take place simultaneously is (A) Skimming Tank (C) Detritus Tank (B) Imhoff Tank (D) Digestion Tank 1.23. The design value of lateral friction coefficient on highway is (A) 1.5 (C) 0.35 (B) 0.50 (D) 0.15 1.24. Camber on highway pavement is provided to take care of (A) Centrifugal Force (C) Sight Distance (B) Drainage (D) Off -Tracking 1.25. The minimum value of CBR(%) required for granular sub-base as per Ministry of Surface Transport (MOST) specification is (A) 5 (C) 15 (B) 10 (D) 20 2. This question consists of Twenty Five sub-questions (2.1-2.25) of TWO marks each. For each of these sub-questions four possible answers (A, B, C and D) are given, out of which only one is correct 2.1. Determinant of the following matrix is (A) 76 (B) 28
(C) 28 (D) 72
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2.2. The inverse Laplace Transformer of
is
(A)
(C)
(B)
(D)
2.3. The solution for the following differential equation with boundary conditions y(0) = 2 and 3 is
(A) y =
(C) y =
(B) y =
(D) y =
2.4. The product [P]
of the following two matrices [P] and [Q] is
(A)
(C)
(B)
(D)
2.5. The given values of the matrix (A) (5.13, 9.42) (B) (3.85, 2.93)
(t) =
are (C) (9.00, 5.00) (D) (10.16, 3.84)
2.6. The frame below shows three beam elements OA, OB and OC, with identical length L and flexural rigidity EI, subject to an external moment M applied at the rigid joint O. The correct set of bending moments that develop at O in the three beam elements OA, OB and OC respectively is,
(A)
(C)
(B)
(D)
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2.7. Identify, from the following, the correct value of the bending moment (in kNm units) at the fixed end A in the statically determinate beam shown below (with internal hinges at B and D), when a uniformly distributed load of 10 kN/m is placed on all spans. (Hint: Sketching the influence line for or applying the Principle of Virtual Displacements makes the solution easy.)
(A) 80 (B) 40
(C) (D) 40
2.8. The end moment (in kNm) units developed in the roof level beams in the laterally loaded frame shown below (with all columns having identical cross-sections), according to the Cantilever Method of simplified analysis, is
(A) 7.5 (B) 15
(C) 20 (D) 30
2.9. Consider the following two statements related to reinforced concrete design, and identify whether they are TRUE or FALSE: I. Curtailment to bars in the flexural tension zone in beams reduces the shear strength at the cutoff locations. II. When a rectangular column section is subject to biaxially eccentric compression, the neutral axis will be parallel to the resultant axis of bending. (A) Both statements I and II are TRUE. (B) Statement I is TRUE, and statement II is FALSE. (C) Statement I is FALSE, and statement II is TRUE. (D) Both statements I and II are FALSE.
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2.10. Consider the following two statements related to structural steel design, and identify whether they are TRUE or FALSE: I. The Euler buckling load of a slender steel column depends on the yield strength of steel II. In the design of laced column, the maximum spacing of the lacing does not depend on the slenderness of column as a whole. (A) Both statements I and II are TRUE (B) Statement I is TRUE and statement II is FALSE (C) Statement I is FALSE and statement II is TRUE (D) Both statements I and II are FALSE 2.11. Identify the two FALSE statements from the following four statements. I. The consolidation of soil happens due to the change in total stress. II. When Standard Penetration Tests are performed in fine sands below the water table, the dilation correction is applied after the overburden correction is applied. III. Over consolidated clays will have predominantly cohesive strength as compared to the frictional strength. IV. Compaction of soils is due to expulsion of water. (A) II and III (B) I and IV
(C) I and III (D) II and IV
2.12. The critical slip circle for a slope is shown below along with the soil properties. The length of the arc of the slip circle is 15.6 m and the area of within the slip circle is 82 . The radius of the slip circles is 10.3 m. The factor of safety against the slip circle failure is nearly equal to
(A) 1.05 (B) 1.22
(C) 0.78 (D) 1.28
2.13. The coefficients permeability of a soil in horizontal and vertical directions are 3.46 and 1.5 m/day respectively. The base length of a concrete dam resting in this soil is 100 m. When the flow net is developed for this soil with 1:25 scale factor in the vertical direction, the reduced base length of the dam will be Page : 9
Civil Engineering (A) 2.63 m (B) 4.00 m
GATE Paper 2001 (C) 6.08 m (D) 5.43 m
2.14. A plate load test was conducted in sand on a 300 mm diameter plate. If the plate settlement was 5 mm at a pressure of 100 kPa, the settlement (in mm) of a 5m × 8 m rectangular footing at the same pressure will be (A) 9.4 (C) 12.7 (B) 18.6 (D) 17.8 2.15. Identify the two TRUE statements from the following four statements. I. Negative skin friction is higher on floating piles than on end bearing piles. II. All other things being the same in footings on sand, the footing with smaller width will have lower settlement at the same pressure. III. The void ratio of soils is always less than 1.0. IV. For determining the depth of embedment of anchored sheet, piles, net moment at the anchor elevation is set to zero. (A) I and IV (C) II and IV (B) I and III (D) II and III 2.16. A 15 cm length of steel rod with relative density of 7.4 is submerged in a two layer fluid. The bottom layer is mercury and the top layer is water. The height of top surface of the rod above the liquid interface in ‘cm’ is (A) 8.24 (C) 7.64 (B) 7.82 (D) 7.38 2.17. The direct runoff hydrograph of a storm obtained from a catchment is triangular in shape and has and catchment area is 86.4 k . The a base period of 80 hours. The peak flow rate is 30 rainfall excess that has resulted the above hydrograph is (A) 5 cm (C) 10 cm (B) 8 cm (D) 16 cm
2.18. A field was supplied water from an irrigation tank at a rate of 120 lit/sec to irrigate an area of 2.5 hectares. The duration of irrigation is 8 hours. It was found that the actual delivery at the field, which is about 4 km from the tank, was 100 lit/sec. The runoff loss in the field was estimated as 800 . The application efficiency in this situation is (A) 62% (C) 76% (B) 72% (D) 80% Page : 10
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2.19. A trapezoidal channel with bottom width of 3 m and side slope of IV: 1.5 H carries a discharge /sec with the flow depth of 1.5 m. The Froude number of the flow is of 8.0 (A) 0.066 (C) 0.265 (B) 0.132 (D) 0.528 2.20. In a 1/50 model of a spillway, the discharge was measured to be 0.3 is prototype discharge in (A) 2.0 (C) 106.0 (B) 15.0 (D) 5303.0
. The corresponding
2.21. If the of waste is 150 mg/L and the reaction rate constant (to the base ‘e’) at 0.35/day, the ultimate BOD in mg/L is (A) 97.5 (C) 212.9 (B) 181.5 (D) 230.5
C is
2.22. The concentration and concentration of a water sample are 160 mg/lit and 40 mg/lit as their ions respectively. The total hardness of this water sample in terms of in mg/lit is approximately equal to (A) 120 (C) 267 (B) 200 (D) 567 2.23. A town has an existing horizontal flow sedimentation tank with an overflow rate of 17 /day/ , and it is desirable to remove particles that have settling velocity of 0.1mm/sec. Assuming the tank is an ideal sedimentation tank, the percentage of particles removal is approximately equal to (A) 30% (C) 70% (B) 50% (D) 90% 2.24. A valley curve has a descending gradient of 1 in 40 followed by an ascending gradient of 1 in 50. The length of the valley curve required for a design speed of 80 km/hour for comfort condition is (A) 199 m (C) 58 m (B) 116 m (D) 37 m 2.25. The radius of relatives stiffness for a 20 cm thick slab with E = 3 × is ratio = 0.15, resting on a subgrade having modulus of 5 kg/ (A) 10 cm (C) 120 cm (B) 80 cm (D) 320 cm
kg/
and poisson’s
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Section – B (75 Marks) This section consists of TWENTY question of FIVE marks each. Any FIFTEEN out of these questions have to be answered. 3. A car having a mass m is travelling at a constant velocity of . At time t = 0, the engine is shut off, assuming that the resistance to the motion of the car is proportion to the square of the instantaneous velocity (v), find v as a function of the distance travelled (x) after the engine is shutt off by setting up the differential equation using the Newton’s principle. 4. Determine the volume of the largest rectangular parallelepiped which can be inscribed in a hemisphere of radius a shown below using the maxima principle of calculus.
5. The figure below shows a cable-supported cantilever beam of span L subject to a concentrated load P at mid-span. (A) Express the bending moment M(x) at any section of the beam AB located at a distance x from the fixed end A, in terms of P, L and the cable tension T. (B) Applying the Theorem of Least Work, derive an expression for T in terms of P, assuming EA =
. Consider only the flexural strain energy in the beam and the axial strain energy in the
cable.
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6. The two-span continuous beam shown below is subject to a clockwise rotation slip = 0.004 radian at the fixed end A. Applying the slope-deflection method of analysis, determine the slope at B. Given that the flexural rigidity EI = 25000 kN and span L = 5m, determine the end moments (in kNm units) in the two spans, the draw the bending moment diagram.
7. The plan of a reinforced concrete column section, and the distribution of strains at the ultimate limit state are shown below. The concrete is of M20 grade and the steel of Fe 250 grade. Also sketched below, for convenience, are the concrete compression stress block and the design stressstrain curve for Fe 250, with all notations as per IS 456. Ignore the reduction in concrete area due to the embedded steel.
(A) Determine the ultimate axial compression capacity (in kN units). (B) Determine the corresponding eccentricity e (in mm units) of loading, with respect to the centroidal axis at the ultimate limit state. 8. The effective spans for a simple one-way slab system, with an overhang, are indicated in the and 4.5 kN/ for figure below. The specified ultimate design loads on the slab are 6.0 kN/ dead loads and live loads respectively considering the possibility of live loads not occurring simultaneously on both spans, determine the maximum spacing (in mm units) of 8 mm diameter bars required as bottom rein forcement in the span AB, assuming an effective depth of 125 mm. Assume M20 concrete and Fe 415 steel.
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9. With reference to the plane frame (portal with overhanging beam) shown below, sketch four possible failure mechanisms, clearly marking the plastic hinge locations and mode of failure in each case. For the case of the ‘combined mechanism’, derive an expression for the collapse load W in terms of the plastic moment capacity (assumed to be constant at all sections) and the dimension L.
10. The relevant cross-sectional details of a compound beam comprising a symmetric I-section and a channel section (with welded connections), proposed for a steel gantry girder, are given below (all dimensions in mm).
(A) Determine the depth of the centroidal axis and the second moments of area, and of the compound section. For computing include the full contribution of the channel section, but only the top flange of the I-section. (B) Determine the maximum compressive stress that develops at a top corner location on account of a vertical bending moment of 550.0 kNm, combined with a horizontal bending moment of 15.0 kNm. Page : 14
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11. (A) For what type of soils would you use falling head and constant head permeability tests to determine the coefficients of permeability (B) Derive the formula to estimate the coefficient of permeability from falling head permeability test. (C) Estimate the flow quantity (in litres per second) through the soil in the pipe shown below. The pressure heads at two locations are shown in the figure. The internal diameter of the pipe is 1m and the coefficient of permeability of soil is 1 × .
12. (A) Referring to consolidated-undrained (C-U) triaxial compression tests, sketch the total stress and the corresponding effective stress Mohr circles along with the failure envelopes for the following soils. (i) Normally consolidated clays (ii) Over consolidated clays Clearly mark the total stress and the effective stress shear strength parameters on the figures. With respect to the slope stability analysis of embankments, when are the total and effective stress parameters used. (B) A C-U triaxial compression test was performed on saturated sand at a cell pressure of 100 kPA. The ultimate deviator stress was 350 kPa and the pore pressure at the peak stress was – 40 kPs (suction). Estimate the total and effective stress shear strength parameters. 13. A concrete gravity type retaining wall, shown below, retains granular soil having a friction angle and dry and saturated unit weights of 16 kN/ and 20 kN/ . The unit weights of of and 10 kN/ respectively. The friction factor at the base of the concrete and water are 24 kN/ wall against lateral sliding is 0.47. Calculate the following quantities for the retaining wall. (i) Factor of safety against lateral sliding, (ii) Factor of safety against overturning, and (iii) Bearing pressure on foundation soil using Meyerhoffs method.
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14. A group of 16 piles (4 in each row) was installed in a layered clay soil deposit shown below. The diameter of each pile is 500 mm and their c/c distance is 1m. The length of the pile group is 18 m. Estimate the safe load capacity of the group with a factor of safety of 2.50. The adhesion factors (α) between the pile and soil in each soil layer are shown in the figure.
15. A spillway has its crest at elevation of +144.0 m and a horizontal apron at an elevation of + 105.0 m on the downstream side. Find the tail water elevation required to form a hydraulic jump when the elevation of energy line above the crest is +146.5 m. The for the flow can be assumed as 0.73. The energy loss over the spillway face may be neglected. 16. The 4-hour unit hydrograph (UH) for a catchment having an area of 536 is shown in the Table below. Find the peak discharge when a 3-hour period of rainfall excess with intensity of 6 mm/hr was realized in the catchment. Assume that there is no base flow. Time UH ordinate Time UH ordinate (hours) (hours) ( /sec) ( /sec) 0 0 11 73 1 10 12 59 2 60 13 48 Page : 16
Civil Engineering
GATE Paper 2001 3 4 5 6 7 8 9 10
120 170 200 180 150 124 104 88
14 15 16 17 18 19 20 21
36 28 20 13 8 3 0 0
17. A well of 300 mm diameter is located in a confined aquifer of 40 m thick. The aquifer has a hydraulic conductivity of 25 m/day and the radius of influence is 300 m. Determine the discharge / hour from the well if the draw down is 3m. Also determine the percentage increase in in discharge if the draw down is 3m. Also determine the percentage increase in discharge if the diameter is made to 450 mm, with other conditions remain same. 18. An area of 40000 ha. has to be irrigated by a canal for growing banana in 15000 ha. and 25000 ha, for growing paddy. The peak water requirements of banana and paddy 12 cm/month and 16 cm/month respectively and these peak demands occur at the same month. Design a suitable canal section using Lacey’s method. Adopt a side slope of 0.5 H:IV. 19. A wastewater treatment plant discharges 1.5 /sec of effluent having an ultimate BOD of 40.0 . Just upstream of the discharge point, the stream has an mg/lit into a stream flowing at 10 ultimate BOD of 3.0 mg/lit. The deoxygenation constant to the base ‘e’ is estimated as 0.32 /day. (A) Assuming complete mixing, find the ultimate BOD of the mixture of waste and stream just downstream of the outfall. (B) Assuming a constant cross-section area for the stream equal of 50 , estimate the BOD of the stream at a point 2.5 km downstream from the outfall. 20. The data of an activated sludge process are as follows: MLSS = 5000 mg/lit Flow = 0.15 SS of inflow = 400 mg/lit Solids settled after 30 min = 25% Volume of Aeration Tank = 3000 /day with VSS of 15000 mg/lit. Sludge Wastage Rate = 120 Calculate Sludge Volume Index (SVI), Sludge Density Index (SDI), Return Sludge Ratio ( and Mean cell residence time ( ).
)
21. The speeds of overtaking and overtaken vehicles on a highway are 85 kmph and 70 kmph respectively. Calculate the overtaking sight-distance needed for two way traffic. Assume the Page : 17
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GATE Paper 2001
acceleration of the overtaking vehicle as 2.5 kmph per second and the speed of the vehicle in the oppsite direction as 85 kmph. 22. Calculate the spacing between contraction joints for a two lane 250 mm thick concrete road having 3.5 m wide slab. Unit weight of concrete = 24 kN/ . Ultimate stress in tension = 0.16 . Coefficients of Friction at interface = 1.5, and the Factor of Safety = 2. Also calculate N/ the spacing between expansion joints if the increase in temperature is 20℃, the expansion joint per ℃. gap is 24 mm and the thermal coefficient = 10 ×
Page : 18
`GATE-2002 CIVIL ENGINEERING SECTION A. (75 Marks) CE1. This question consists of TWENTY FIVE sub-questions(1.1-1.25) of ONE mark each. For each of these sub-question four possible answers (A,B,C and D) are given, out of which ONLY ONE is correct. 1 4 1.1 Eigen values of the following matrix are : 4 1 (a) 3 and -5 (b) -3 and 5 (c) -3 and -5 (d) 3 and 5 2
1.2. The value of the following definite integral is
sin 2 x dx : 1 cos x
2
(a) -2 In2 (b) 2 (c) 0 (d) (In 2)2 1.3. The following function has a local minima at which value of x f(x) = x 5 x 2 5 2
(a)
(c)
5 2
(b)
(d)
5
5 2
1.4 For the loading given in the figure below, two statements (I and II) are made.
I. Member AB carries shear force and bending moment II. Member BC carries axial load and shear force. Which of the following is true ? (a) Statement I is true but II is false (b) Statement I is false but Ii is true (c) Both statements I and II are true (d) Both statements I and II are true 1.5. Read the following statements. I. Maximum strain in concrete at the outermost compression fibre is taken to be 0.0035 in bending II. The maximum compressive strain in concrete in axial compression is taken as 0.002.
Keeping the provisions of IS 456-2000 on limit state design in mind, which of the following is true ? (a) Statement I is true and but II is false (b) Statement I is false but II is true (c) Both statements I and II are true (d) Both statement I and I are false 1.6. As per the provisions of IS 456-2000, the (short term) modulus of elasticity of M25 grade concrete (in N/mm2) can be assumed to be (a) 25000 (b) 28500 (c) 3000 (d) 36000 1.7. The shear modulus (G), modulus of elasticity (E) and the Poisson’s ratio (v) of a (a) G=E/[2(1+v)] (b) E=G/[2(1+v)] (c) G=E/[2(1-v)] (d) G=E/[2(v-1)] 1.8. When designing steel structures, one must ensure that local buckling in webs does not take place. this check may not be very critical when using rolled steel sections because. (a) Quality control at the time of manufacture of rolled sections is very good (b) Web depths available are small (c) Web stiffeners are in-built in rolled sections (d) Depth to thickness ratios (of the web) are appropriately adjusted 1.9. An ISMB 500 is used as a beam in a multi-storey construction. From the viewpoint of structural design, it can be considered be ‘literally restrained’ when, (a) the tension flange is ‘laterally restrained’ (b) the compression flange is ‘laterally restrained’ (c) the web is adequately stiffened (d) the conditions in (A) and (C) are met 1.10. Data from a sieve analysis conducted on a given sample of soil showed that 67% of the particles passed through 75 micron IS sieve. The liquid limit and plastic limit of the finer fraction was found to be 45 and 33 percents respectively. The group symbol of the given soil as per IS : 1498-1970 is (a) SC (b) MI (c) CH (d) MH 1.11. The avoid ratios at the densest, loosest and the natural states of a sand deposit are 0.2, 0.6 and 0.4, respectively. the relative density of the deposit is (a) 100% (b) 75% (c) 50% (d) 25% 1.12. The following data were obtained from a liquid limit test conducted on a soil sample. Number of blows 17 22 25 28 34 Water content ((%) 63.8 63.1 61.9 60.6 60.5 The liquid limit of the soil is (a) 63.1% (b) 62.8% (c) 61.9% (d) 60.6% 1.13. The specific gravity and insitu void ratio of a soil deposit are 2.71 and 0.85 respectively. The value of the critical hydraulic gradient is (a) 0.82 (0/85
(c) 0.92 (d) 0.95 1.14. The observed value of the standard penetration number (N) at 10m depth of a silty sand deposit is 13. The unit weight of the soil is 16 kN/m3. The N value after correcting for the presence of fines will be (a) 12 (b) 13 (c) 14 (d) 15 1.15. The force ‘F’ required at equilibrium on the semi-cylindrical gate shown below is
(a) 9.81kN (b) 0.0kN (c) 19.62 kN (d) none of the above 1.16. Velocity distribution in a boundary layer flow over a plate is given by (u/um) = 1.5η where, η = y/δ; y is the distance measured normal to the plate; δ sis the boundary layer thickness; and um is the maximum velocity at y = δ. If teh shear stress τ, acting on the plate is given by τ = K(μum)/ δ where, μ is the dynamic viscosity of the fluid, K takes the value of (a) 0 (b) 1 (c) 1.5 (d) none of the above 1.17. A 6-hour Unit Hydrograph (UH) of a catchment is triangular in shape with a total time base of 36 hours and a peak discharge of 18m3/s. The area of the catchment (in sq. km) is (a) 233 (b) 117 (c) 12 (d) Sufficient information not available 1.18. When there is an increase in the atmospheric pressure, the water level in a well penetrating in a confined aquifer (a) increases (b) decreases (c) may increase or decrease depending on the nature of the aquifer (d) does not undergo any change 1.19. In a domestic wastewater sample, COD and BOD were measured. Generally which of the following statement is true for their relative magnitude ? (a) COD = BOD (b) COD > BOD (c) COD < BOD (d) Nothing can be said 1.20. In disinfection, which of the following forms of chlorine is most effective in killing the pathogenic bacteria ? (a) CI (b) OCI (c) NH2CI (d) HOCI 1.21. A Trickling filter is designed to remove
(a) Settleable Solids (b) Colloidal Solids (c) Dissolved Organic Matter (d) None of the above 1.22. In natural water, hardness is mainly caused by (a) Ca++ and Mn++ (b) Ca++ and Fe++ (c) Na+ and K+ (d) Ca++ and Mg++ 1.23. Bitumen is derived from (a) destructive distillation of coal tar (b) destructive distillation of petroleum (c) fractional distillation of petroleum (d) naturally occurring ores 1.24. Dowel bars in concrete pavement are placed (a) along the direction of traffic (b) perpendicular to the direction of traffic (c) along 450 to the direction of traffic (d) can be placed along any direction 1.25. Stopping sight distance and frictional co-efficients are (a) directly proportional to each other (b) inversely proportional to each other (c) unrelated (d) either directly or inversely proportional to each other depending on the nature of pavement. CE2. This question consists of TWENTY FIVE sub-questions (2.1-2.25) of TWO marks each. For each of these sub-questions four possible answers (A,B,C and D) are given, out of which only one is correct. Answer each sub-question by darkening the appropriate bubble on the OBJECTIVE RESPONSE SHEET (ORS) using a soft HB pencil. Do not use the ORS for any rough work. You may use the Answer Book for any rough work, if needed. 1
2.1. The value of the following improper inegral is xinx 0
(a) ¼ (b) 0 (c) -1/4 (d) 1 2.2 The directional derivative of the following function at (1,2) in the direction of (4i+3j) is f(x,y) = x2 + y2 (a) 4/5 (b) 4 (c) 2/5 (d) 1 2.3 The Laplace Transform of the following function is sin t for 0 t f (t ) 0 for t 1 1 for all S 0 for all S (a) (b) 2 1 s 1 s2
(c)
1 e s for all S 1 s2
0
(d)
e s for all S 1 s2
0
2.4 The limit of the following sequence as n ∞ is Xn=n1/n (a) 0 (b) 1 (c) ∞ (d) -∞ 2.5 A steel beam (with a constant EI, and span L) is fixed at both ends and carries a uniformly distributed load (w kN/m), which is gradually increased till the beam reaches the stage of plastic collapse (refer to the following figure). Assuming ‘B’ to be at midspan, which of the following is true,
(a) Hinges are formed at A, B and C together. (b) Hinges are formed at B and then at A and C together (c) Hinges are formed A and C together and then at B. (d) Hinges are formed at A and C only. 2.6. As per the provisions of IS 456-2000, in the limit state method for design of beams, the limiting value of the depth of neutral axis in a reinforced concrete beam of effective depth ‘d’ is given as (a) 0.53d (b) 0.48d (c) 0.46d (d) any of the above depending on the different grades of steel. 2.7. ISA 100x100x10mm (Cross sectional area = 1908 mm2) serves as tensile member. This angle is welded to a gusset plate along A and B appropriately as shown. Assuming the yield strength of the steel to be 260 N/mm2 the tensile strength of this member can be taken to be approximately.
(a) 500kN (b) 300kN (c) 225kN (d) 375kN 2.8 ISA 100x100x10 mm (Cross sectional area = 1908 mm2) is welded along A and B (Refer to figure for question 2.7), such that the lengths of the weld along A and B are 1=and 12, respectively. Which of the following is a possibility acceptable combination of 11 and 12. (a) 11= 60 mm and 12 = 150 mm (b) 11= 150 mm and 12 = 60 mm (c) 11= 150 mm and 12 = 150 mm (d) Any of the above, depending on the size of the weld. 2.9. In the propped cantilever beam carrying a uniformly distributed load of w N/m, shown in the following figure, the reaction at the support B is
(a) 5/8 wL.
(b) 3/8 wL
(c) 1/2 wL
(d) 3/4 wL
2.10. An infinite slope is to be constructed in a soil. The effective stress strength parameters of the soil are c’=0 and υ’ = 300. The saturated unit weight of the slope is 20kN/m3 and the unit weight of water is 10kN/m3. Assuming that seepage is occurring parallel to the slope, the maximum slope angle for a factor of safety of 1.5 would be (a) 10.890 (b) 11.300 (c) 12.480 (d) 14.730 2.11. If the effective stress strength parameters of a soil are c’=10kPa and o’ = 300, the shear strength on a plane within the saturated soil mass at a point where the total normal stress is 300kPa and pore water pressure is 150 kPa will be (a) 90.5 kPa (b) 96.6kPa. (c) 101.5 kPa (d) 105.5 kPa 2.12. The time for a clay layer to achieve 85% consolidation is 10 years. If the layer was half as thick, 10 times more permeable and 4 times more compressible then the time that would be required to achieve the same degree of consolidation is (a) 1 year (b) 5 years (c) 12 years (d) 16 years 2.13. In a triaxial test carried, out on a cohesionless soil sample with a cell pressure of 20 kPa, the observed value of applied stress at the point of failure was 40 kPa. The angle of internal friction of the soil is (a) 100 (b) 150
(c) 250 (d) 300 2.14. In a falling head permeability test the initial head of 1.0m dropped to 0.35 m in 3 hours, the diameter of the stand pipe being 5 mm. The soil specimen was 200 mm long and of 100 mm diameter. The coefficient of permeability of the soil is : (a) 4.86×10-5cm/s (b) 4.86×10-6cm/s -7 (c) 4.86×10 cm /s (d) 4.86×10-8cm/s 2.15. In a lined rectangular canal, the Froude number of incoming flow is 3.0. A hydraulic jump forms when it meets the pool of water. The depth of flow after the jump formation is 1.51 m. Froude number of flow after the hydraulic jump is (a) 0.30 (b) 0.71 (c) 0.41 (d) none of these 2.16. A pump can lift water at a discharge of 0.15m3/s to a head of 25 m. The critical cavitation number (σc) for the pump is found to be 0.144. The pump is to be installed at a location where the barometric pressure is 9.8 m of water and the vapour pressure of water is 0.30 of water. The intake pipe friction loss is 0.40m. Using the minimum value of NPSH (Net Positive Suction Head), the maximum allowable elevation above the sump water surface at which the pump can be located is (a) 9:80 m (b) 6.20 m (c) 5.50 m (d) none of the above 2.17. During a 6-hour storm, the rainfall intensity was 0.8 cm/hour on a catchment of area 8.6 km2. The measured runoff volume during this period was 2,56.000 m3. The total rainfall was lost due to infiltration, evaporation, and transpiration (in cm/hour) is (a) 0.80 (b) 0.304 (c) 0.496 (d) sufficient information not available. 2.18 The rainfall on five successive days in a catchment were measured as 3,8,12,6 and 2 cms. If the total runoff at the outlet from the catchment was 15cm, the value of the υindex (in mm/hour) is (a) 0.0 (b) 1.04 (c) 1.53 (d) sufficient information not available 2.19. A canal was designed to supply the irrigation needs of 1200 hectares to land growing rice of 140 days base period having a Delta of 134 cms. If this canal water is used to irrigate wheat of base period 120 days having a Delta of 52 cm, the area (in Hectares) that can be irrigated is (a) 2650 (b) 3608 (c) 543 (d) none of the above 2.20. For a water treatment plant having a flow rate of 432m3/hr, what is the required plan area of a Type I setting tank to remove 90% of the particles having a settling velocity of 0.12 cm/sec is (a) 120m2 (b) 111m2 2 (c) 90m (d) 100m2 2.21. The theoretical oxygen demand of a 0.001 mol/L glucose solution is (a) 180 mg/L (b) 192 mg/L
(c) 90mg/L (d) 96 mg/L 2.22. A wastewater sample has an initial BOD of 222mg/L. The first order BOD decay coefficient is 0.4/day. The BOD consumed (in mg/L) in 5 days is (a) 150 (b) 192 (c) 30 (d) 50 2.23. A car is moving at a speed of 72 km/hr on a road having 2% upward gradient. The driver applies brakes when he sees an obstruction. If his reaction time is 1.5 seconds, assuming that the co-efficient of friction between the pavement and tyre as 0.15, calculate the distance traversed before the car finally stops. (a) 24 m (b) 105 m (c) 1056 m (d) 324 m 2.24. The average daily traffic on a stretch of road is 300 commercial vehicles per lane per day. Design traffic repetitions for 10 years when vehicle damage factor is 2.5 and traffic growth rate is 7%, is (a) 3.8 msa (b) 23.5 msa (c) 45.4 msa (c) 16 msa 2.25. In a concrete pavement (A) temperature stress is tensile at bottom during day time. (B) load stress is compressive at bottom (a) Both the statement (A) and (B) are correct (b) Statement (A) is correct and (B) is wrong (c) Statement (B) is wrong and (A) is correct (d) Both statement (A) and (B) incorrect SECTION B (75 Marks) This section consists of TWENTY question of five marks each. Any FIFTEEN out of these questions need to be answered on the Answer Book provided. CE3. A solid region in the first octant is bounded by the co-ordinate planes and the plane x + y + z = 2. The density of the solid is p (x,y,z) = 2x. Calculate the mass of the solid (50 CE4. The following equation is sometimes used to model the population growth : dN N aN in dt K where, N is the population at time t, a > 0 is growth coefficient and K > 0 is a constant. Given, at t = 0 N = N0 and 0 0.6/d 19. When the outflow from a storage reservoir is uncontrolled as in a freely operating spillway, the of outflow hydrograph occurs at (a.) the point of intersection of the inflow and outflow hydrographs (b.)a point, after the intersection of the inflow and outflow hydrographs (c.) the tail of inflow hydrographs (d.)a point, before the intersection of the inflow and outflow hydrographs 20. The intensity of rainfall and time interval of a typical storm are: Time interval Intensity of rainfall (minutes) (mm/minute) 0-10 0.7 10-20 1.1 20-30 2.2 30-40 1.5 40-50 1.2 50-60 1.3 60-70 0.9 70-80 0.4 The maximum intensity of rainfall for 20 minutes duration of the storm is (a.) 1.5 mm/minute (b.)1.85 mm/minute
(c.) 22 mm/minute (d.)3.7 mm/minute 21. On which of the canal systems, R.G Kennedy, executive engineer in the Punjab Irrigation Department made his observations for proposing his theory on stable channels? (a.)Krishna Western Delta canals (b.)Lower Bad Doab canals (c.) Lower Chenab canals (d.)Upper Bari Doab canals 22. Which one of the following equations represents the downstream profile of Ogee spillway with vertical upstream thee? (x,y) are the coordinates of the point on the downstream profile with origin at the crest of the spillway and Hd is the design head. y a) Hd
x 0.5 Hd
y c) Hd
x 2.0 Hd
1.85
1.85
y b) Hd
x 0.5 Hd
y d) Hd
x 2.0 Hd
1 1.85
1 1.85
23. The length of summit curve on at two lane two way highway depends upon (a.) allowable rate of change of centrifugal acceleration (b.)coefficient of lateral friction (c.) required stopping sight distance (d.)required overtaking sight distance 24. Pradhan Mantri Gram Sadak Yojna (PMGSY), launched in the year 2000, aims to provide rural connectivity with all-weather roads. It is proposed to connect the abitations in plain areas of population more than 500 persons by the year (a.) 2005 (b.)2007 (c.) 2010 (d.)2012 25. List-I contains some properties of bitumen. List-II gives a list of Laboratory Tests conducted on bitumen to determine the properties. Match the property with the corresponding test and select the cot answer using the codes given below the lists : List-I List-II P. Resistance to flow 1. Ductility test Q. Ability to deform under load 2. Penetration test R. Safety 3. Flash and fire point test Codes : P Q R (a.) 2 1 3 (b.) 2 3 1 (c.) 1 2 3 (d.) 3 1 2 26. Bituminous concrete is a mix comprising of (a.) fine aggregate, filler and bitumen
(b.)fine aggregate and bitumen (c.) coarse aggregate, fine aggregate, filler arid bitumen (d.)coarse aggregate, filler and bitumen 27. Consider the matrices X(4 3),Y(4 3) and P(2 3). The order of P X T Y (a.) (2 (b.)(3 (c.) (4 (d.)(3
1
T
PT
will be
2) 3) 3) 4)
28. Consider a non-homogeneous system of linear equations representing mathematically an overdetermined system. Such a system will be (a.) consistent having a unique solution (b.)consistent having many solutions (c.) inconsistent having a unique solution (d.)inconsistent having no solution 29. Which one of the following is NOT true for complex number Z1 and Z2? a) b) | Z1 Z 2 | | Z1 | | Z 2 | c) | Z1 Z 2 | | Z1 | | Z 2 | d) | Z1 Z2 |2
| Z1 Z2 |2 2 | Z1 |2 2 | Z2 |2
30. Which one of the following statements is NOT true? (a.) The measure of skewness is dependent upon the amount of dispersion (b.)In a symmetric distribution, the values of mean, mode and median are the same (c.) In a positively skewed distribution: mean > median > mode (d.)In a negatively skewed distribution: mode > mean > median 31. If principal stresses in a two-dimensional case are –10 MPa and 20 MPa respectively, then maximum shear stress at the point is (a.) 10 MPa (b.)15MPa (c.) 20 MPa (d.)30 MPa 32. The bending moment diagram for a beam is given below: The shear force at sections respectively are of the (a.) 100 kN, 150 kN
aa’ and bb’ magnitude
(b.)zero, 100 kN (c.) zero, 50 kN (d.)100 kN, 100 kN
33. A circular shaft shown in the figure is subjected to torsion T at two points A and B. The torsional rigidity of portions CA and BD is GJ1 and that of portion AB is GJ2. The rotations of shaft at points A and B are 1 and 2. The rotation 1 is a)
TL GJ1 GJ 2
TL GJ1 TL c) GJ 2
b)
d)
TL GJ1 GJ 2
34. Match the following: List-I P. Slope deflection method Q. Moment distribution method R. Method of three moments S. Castigliano’s second theorem Codes : P Q R S (a.) 1 2 1 2 (b.) 1 1 2 2 (c.) 2 2 1 1 (d.) 2 1 2 1
List-II 1. Force method 2. Displacement method
35. All member of the frame shown below have the same flexural rigidity EI and length L. If a moment M is applied at joint B, the rotation of the joint is
ML 12 EI ML c) 8EI a)
ML 11EI ML d) 7 EI b)
Data for Q. 36 & Q.37 are given below. Solve the problems and choose the correct answers. A truss is shown hi the figure. Members are of equal cross section A and same modulus of elasticity E. A vertical force P is applied at point C.
36. Force in the member AB of the truss is
a) P
2
b) P
3
c) P 2
d)P
37. Deflection of the point C is a)
2 2 1 PL 2 EA
b) 2
PL EA
c) 2 2 1
PL EA
d)( 2 1)
PL EA
38. A rectangular column section of250mni x 400mm is reinforced with five steel bars of grade Fe-500, each of 20mm diameters. Concrete mix is M30. Axial load on the column section with minimum eccentricity as per IS:456-2000 using limit state method can be applied upto (a.) 1707.37 (b.)1805.30 (c.) 1806.40 (d.)1903.7 39. A concrete beam of rectangular cross section of 200mm 400mm is prestressed with a force 400kN at eccentricity 100mm. The maximum compressive stress in the concrete is (a.) 12.5N/mm2 (b.)7.5N/mm2 (c.) 5.0N/mm2 (d.)2.5N/mm2 40. The flexural strength of M30 concrete as per IS:456-2000 is (a.) 3.83 MPa (b.)5.47 MPa (c.) 21.23 MPa (d.)30.0 MPa 41. In a random sampling procedure for cube strength of concrete, one sample consists of X number of specimens. These specimens are tested at 28 days and average strength of these X specimens is considered as test result of the sample, provided the individual variation in the strength of specimens is not more than ± Y per cent of the average strength. The values of X and Y as per IS:456-2000 are (a.) 4 and 10 respectively (b.)3 and 10 respectively (c.) 4 and 15 respectively (d.)3 and 15 respectively Data for Q.42 & Q.43 are given below. Solve the problems and choose correct answers. Assume straight line instead of parabola for stress-strain curve of concrete as given below and partial factor of safety as 1.0.
A rectangular under-reinforced concrete section of 300mm width and 500mm effective depth is reinforced with 3 bars of grade Fe-415, each of 16mm diameter. Concrete mix is M20. 42. The depth of the neutral axis from the compression fibre is (a.) 76mm (b.)81mm (c.) 87mm (d.)100mm 43. The depth of the neutral axis obtained as per 15:456-2000 differs from the depth of neutral axis obtained in Q.22 by (a.) 15mm (b.)20mm (c.) 25mm (d.)32mm 44. An unstiffened web I-section is fabricated from a 10mm thick plate by fillet welding as shown in the figure. If yield stress of steel is 250MPa, the maximum shear load that section can take is (a.) 750 kN (b.)350 kN (c.) 337.5 kN (d.)300 kN
45. A fillet-welded joint of 6mm size is shown in the figure. The welded surfaces meet at 60-90 degree and permissible stress in the fillet weld is 108 MPa. The safe load that can be transmitted by the joint is (a.) 162.7 kN (b.)151.6 kN (c.) 113.4 kN (d.)109.5 kN
46. Which one of the following is NOT correct for steel sections as per IS : 800-1984? (a.) The maximum bending stress in tension or in compression in extreme fibre calculated on the effective section of a beam shall not exceed 0.66 fy. (b.)The bearing stress in any part of a beam when calculated on the net area shall not exceed 0.75 c. (c.) The direct stress in compression on the gross sectional area of axially loaded compression member shall not exceed 0.6 fy. (d.)None of the above. 47. A cantilever beam of length l, width b and depth d is loaded with a concentrated vertical load at the tip. If yielding starts at a load P, the collapse load shall be (a.) 2.0 P (b.)1.5 P (c.) 1.2 P (d.)P
48. In a constant head permeameter with cross section area of 10cm2, when the flow was taking place under a hydraulic gradient of 0.5, the amount of water collected in 60 seconds is 600cc. The permeability of the soil is (a.) 0.002 cm/s (b.)0.02 cm/s (c.) 0.2 cm/s (d.)2.0 cm/s 49. Two observation wells penetrated into a confined aquifer and located 1.5km apart in the direction of flow, indicate head of 45m and 20m. If the coefficient of permeability of the aquifer is 30m/day and porosity is 0.25, the time of travel of an inert tracer from one well to another is (a.) 416.7 days (b.)500 days (c.) 750 days (d.)3000 days 50. Assuming that a river bed level does not change and the depth of water in river was 10m, 15 m and 8 m during the months of February, July and December respectively of a particular year. The average bulk density of the soil is 20kN/m3. The density of water is 10kN/m3. The effective stress at a depth of 10m below the river bed during these months would be (a.) 300 kN/m2 in February, 350 kN/m2 July and 320kN/m2 in December (b.)100 kN/m2 in February, 100 kN/m2 July and 100 kN/m2 in December (c.) 200 kN/m2 in February, 250 kN/m2 July and 180 kN/m2 in December (d.)300 kN/m2 in February, 350 kN/m2 July and 280 kN/m2 in December 51. For a triaxial shear test conducted on a sand specimen at a confining pressure of 100 kN/m2 under drained conditions, resulted in a deviator stress ( 1 – 3) at failure of 100kN/m2. The angle of shearing resistance of the soil would be (a.) 18.43° (b.)19.47° (c.) 26.56° (d.)30° 52. A 3m high retaining wall is supporting a saturated sand (saturated due to capillary action) of bulk density 18 kN/m3 and angle of shearing resistance 30°. The change in magnitude of active earth pressure at the base due to rise in ground water table from the base of the footing to the ground surface shall ( w = 10 kN/m3) (a.) increase by 20 kN/m2 (b.)decrease by 20 kN/m2 (c.) increase by 30 kN/m2 (d.)decrease by 30 kN/m2 53. For two infinite slopes (one in dry condition and other in submerged condition) in a sand deposit having the angle of shearing resistance 30°, factor of safety was determined as 1.5 (for both slopes). The slope angles would have been (a.) 21.05° for dry slope and 21.05° for submerged slope (b.)19.47° for dry slope and 18.40° for submerged slope (c.) 18.4° for dry slope and 21.05° for submerged slope (d.)22.6° for dry slope and 19.47° for submerged slope 54. A strip footing (8m wide) is designed for a total settlement of 40mm. The safe bearing capacity (shear) was 150kN/m2 and safe allowable soil pressure was 100kN/m2. Due to importance of the structure, now the footing is to be redesigned for total settlement of 25mm. The new width of the footing will be
(a.) 5 m
(b.)8 m
(c.) 12 m
(d.)12.8 m
55. During the subsurface investigations for design of foundations, a standard penetration test was conducted at 4.5m below the ground surface. The record of number of blows is given below: Penetration depth (cm) Number of blows
0–7.5 3 7.5–15 3 15–22.5 6 22.5–30 6 30–37.5 8 37.5–45 7 Assuming the water table at ground level, soil as fine sand and correction factor for overburden as 1.0, the corrected ‘N’ value for the soil would be (a.)18 (b.)19 (c.)21 (d.)33 56. A soil mass contains 40% gravel, 50% sand and 10% silt. This soil can be classified as (a.) silty sandy gravel having coefficient of uniformity less than 60. (b.)silty gravelly sand having coefficient of uniformity equal to 10. (c.) gravelly silty sand having coefficient of uniformity greater than 60. (d.)Gravelly silty sand and its coefficient of uniformity cannot be determined. 57. A saturated soil mass has a total density 22kN/m3 and a water content of 10%. The bulk density and dry density of this soil are (a.) 12 kN/m3 & 20 kN/m3 respectively (b.)22 kN/m3 & 20 kN/m3 respectively (c.) 19.8 kN/m3 & 19.8 kN/m3 respectively (d.)23.2kN/m3 & 19.8 kN/m3 respectively 2 x 2 y ( x 1) y 2 58. A stream function is given by: The flow rate across a line joining points A(3, 0) and B(0, 2) is (a.) 0.4units (b.)1.1 units (c.) 4 units (d.)5 units
59. The circulation ‘ ’ around a circle of radius 2 units for the velocity field u = 2x + 3y and v = -2y is (a.) - 6 units (b.)- 12 units (c.) - l8 units (d.)- 24 units 60. A tank and a deflector are placed on a frictionless trolley. The tank issues water jet (mass density of water = 1000kg/m3), which strikes the deflector and turns by 45°. If the velocity of jet leaving the deflector is 4mIs and discharge is 0.1m3 /s, the force recorded by the spring will be (a.) 100 N (b.)100 2n (c.) 200 n (d.)200 2N
61. Cross-section of an object (having same section normal to the paper submerged into a fluid consists of a square of sides 2m and triangle as shown in the figure. The object is
hinged at point P that is one meter below the fluid free surface. If the object is to be kept in the position as shown in the figure, the value of ‘x’ should be (a.) 2 3 (b.)4 3 (c.) 4m (d.)8m
62. Critical depth at a section of a rectangular channel is 1.5m. The specific energy at that section is (a.) 0.75m (b.)1.0m (c.) 1.5m (d.)2.25rn 63. A partially open sluice gate discharges water into a rectangular channel The tail water depth in the channel is 3m and Froude number is 1/2 2 If a free hydraulic jump is to be formed at downstream of the sluice gate after the vena contract of the jet coming out from the sluice gate, the sluice gate opening should be (coefficient of contraction Cc = (0.9) (a.) 0.3m (b.)0.4m (c.) 0.69m (d.)0.9m 64. A triangular irrigation lined canal carries a discharge of 25m3/s at bed slope 1/6000 . If the side slopes of the canal are 1 : 1 and Manning’s coefficient is 0.018, the central depth of flow is equal to (a.) 2.98m (b.)3.62m (c.) 4.91m (d.)5.61m 65. If tomato juice is having a pH of 4.1, the hydrogen ion concentration will be (a.) 10.94 X 10–5 mol/L (b.)9.94 X 10–5 mo1/L (c.) 8.94 X 10–5 mol/L (d.)7.94 X 10–5 mo1/L 66. List-I contains some properties of water/waste water and List-II contains list of some tests on water/waste water. Match List-I with List-II and select the correct answer using the codes given below the lists: List-I List-II P. Suspended solids concentration 1. BOD Q. Metabolism of biodegradable organics 2. MPN H. Bacterial concentration 3. Jar test S. Coagulant dose 4. Turbidity Codes : P Q R S (a.) 2 1 4 3 (b.) 4 1 2 3
(c.) 2 4 1 3 (d.) 4 2 1 3 67. Match List-I with List-II and select the correct answer using the codes given below the lists : List-I List-II P. Thickening of sludge by chemical 1. Decrease in volume of oxidation Q. Stabilization of sludge or chemical 2. Separation of water by heat treatment H. Conditioning of sludge 3. Digestion of sludge S. Reduction of sludge floatation or 4. Separation of water by gravity P Q R S (a.) 4 3 1 2 (b.) 3 2 4 1 (c.) 4 3 2 1 (d.) 2 1 3 4 68. A circular primary clarifier processes an average flow of 5005m3/d of municipal waste water. The overflow rate is 35m3/m2/d. The diameter of clarifier shall be (a.) 10.5m (b.)11.5m (c.) 12.5m (d.)13.5m 69. Match List-I with List-II and select the correct answer using the codes given below the lists: List-I List-II P. Release valve 1. Reduce high inlet pressure to lower outlet pressure Q. Check valve 2. Limit the flow of water to single direction R. Gate valve 3. Remove air horn the pipeline S. Pilot valve 4. Stopping the flow of water in the pipeline. Codes : PQRS (a.) 3 2 4 1 (b.) 4 2 1 3 (c.) 3 4 2 1 (d.) 1 2 4 3 70. In a certain situation, waste water discharged into a river mixes with the river water instantaneously and completely. Following is the data available: Waste water DO = 2.00 mg/l Discharge rate = 1.10 m3/s River water DO = 8.3mg/l Flow rate= 8.70m3/s Temperature = 20°C Initial amount of DO in the mixture of waste and river shall be (a.) 5.3mg/l (b.)6.5mg/l (c.) 7.6mg/l (d.)8.4mg/l
Data for Q.71 & Q.72 are given below. Solve the problems and choose correct answers. A city is going to install the rapid sand filter after the sedimentation tanks. Use the following data. Design loading rate to the filter – 200m3/m2d Design flow rate – 0.5 m3/s Surface area per filter box – 50m2 71. The surface area required for the rapid sand filter will be (a.) 210m2 (b.)215m2 (c.) 216m2 (d.)218m2 72. The number of filters required shall be (a.)3 (b.)4 (c.)6 (d.)8 73. The culturable commanded area for a distributary is 2x10 m2. The intensity of irrigation for a crop is 40%. If k or water depth and k or period for the crop are 14cm and 4 weeks, respectively, the peak demand discharge is (a.) 2.63 m3/s (b.)4.63 m3/s (c.) 8.58 m3/s (d.)11.58 m3/s 74. Uplift pressure at points E and D (figure A) of a straight horizontal floor of negligible thickness with a sheet pile at downstream end are 28% and 20%, respectively. If the sheet pile is at upstream end of the floor (figure- B), the uplift pressures at points D1 and C1 are (a.) 68% and 60% respectively (b.)80% and 72% respectively (c.) 8$% and 70% respectively (d.)100% and zero respectively.
75. A launching apron is to he designed at downstream of a weir for discharge intensity of 6.5 m3/s/m. For the design of launching aprons the scour depth is taken two times of Lacey scour depth. The silt factor of the bed material is unity. If the tail water depth is 4.4m, the length of launching apron in the launched position is (a.) 5m (b.)4.7 m (c.) 5 m (d.)5 5m Data for Q.76 & Q.77 are given below. Solve the problems and choose correct answers. A four hour unit hydrograph of a catchment is triangular in shape with base of 80 hours. The area of the catchment is 720km2. The base flow and - index are 30m3/s and 1 mm/h, respectively. A storm of 4 cm occurs uniformly in 4hours over the catchment.
76. The peak discharge of four hour unit hydrograph is (a.) 40 m3/s (b.)50 m3/s (c.) 60 m3/s (d.)70 m3/s 77. The peak flood discharge due to the storm is (a.) 210m3/s (b.)230m3/s (c.) 260m3/s (d.)720m3/s 78. For a 25cm thick cement concrete pavement, analysis of stresses gives the following values: Wheel load stress due to corner loading ………….30kg/cm2 Wheel load stress due to edge loading ………….32kg/cm2 Warping stress at corner region during summer ………….9kg/cm2 Warping stress at corner region during winter ………….7kg/cm2 Warping stress at edge region during summer ………….8kg/cm2 Warping stress at edge region during winter ………….6kg/cm2 Frictional stress during summer ………….5kg/cm2 Frictional stress during winter ………….4kg/cm2 The most critical stress value for this pavement is (a.) 40kg/cm2 (b.)42kg/cm2 (c.) 44kg/cm2 (d.)45kg/cm2 79. The following observations were made of an axle-load survey on a road: Axle load (kN) Repetitions per day 35-45 800 75-85 400 The standard axle-load is 80kN. Equivalent daily numbers of repetitions for the standard axle-load are (a.)450 (b.)480 (c.)800 (d.)1200 80. A transport company operates a scheduled daily truck service between city P and city Q. One-way journey time between these two cities is 85 hours. A minimum layover time of 5 hours is to be provided at each city. How many trucks are required to provide this service? (a.)4 (b.)6 (c.)7 (d.)8
GATE-2006 CE : CIVIL ENGINEERING Q.1-Q.20 Carry One Mark Each 1. Solution for the system by the set of equations 4y+3z=8 ; 2x-z=2; and 3x+2y=5 is (a) x = 0; y = 1; z = 4/3 (b) x=0;y=1; z = 2 (c) x = 1; y = 1/2; z = 2
(d) nonexistent
2. The differential equation dy/dx = 0.25 y2 is to be solved using the backward (iplicit) Euler‟s method with the boundary condition y = 1 at x = 0 and with a step size of 1. What would be the value of y at x = 1? (a) 1.33 (b) 1.67 (c) 2.00 (d) 2.33 3. The necessary and sufficient condition for a surface to be called as a free surface is (a) no stress should be acting on it (b) tensile stress acting on it must be zero (c) shear stress acting on it must be zero (d) no point on it should be under any stress 30 0 4. Mohr‟s circle for the state of stress defined by MPa is a circle with 0 30 (a) center at (0,0) and radius 30 MPa (b) center at (0,0) and radius 60 MPa (c) center at (30,0) and radius 30 MPa (d) center at (30,0) and zero radius 5. The buckling load P = Pcr for the column AB in the figure, as KT approaches infinity, become α π2 EI/L2, where α is equal to
(a) 0.25 (b) 1.00 (c) 2.05 (d) 4.00 6. A long shaft of diameter d is subjected to twisting moment T at its ends. The maximum normal stress acting at its cross-section is equal to (a) zero (b) 16T/ πd3 3 (c) 32T/ πd (d) 64T/ πd3
7. If the characteristic strength of concrete fck is defined a the strength below which not more than 50% of the test results are expected to fall the expression for fck in terms of mean strength fm and standard deviation S would be (a) fm-0.1645S (b) fm-1.645S (c) fm (d) fm+1.645S 8. The range of void ratio between which quick sand conditions occurs in cohesion less granular soil deposits is (a) 0.4-0.5 (b) 0-6-0.7 (c) 0.8-0.9 (d) 1.0-1.1 9. Figure given below shows a smooth vertical gravity retaining wall with cohesionless soil backfill having an angle of internal friction φ In the graphical representation of Rankine‟s active earth pressure for the retaining wall shown in figure, length OP represents
(a) vertical stress at the base (b) vertical stress at a height H/3 from the base (c) lateral earth pressure at the base (d) lateral earth pressure at a height H/3 from the base 10. Which of the following statement is NOT true in the context of capillary pressure in soils ? (a) Water is under tension in capillary zone (b) Pore water pressure is negative in capillary zone (c) Effective stress increases due to capillary pressure (d) Capillary pressure is more in coarse grained soils 11. A channel with a mild slope is followed by a horizontal channel and then by a steep channel. What gradually varied flow profiles will occur ? (a) M1, H1,S1 (b) M2,H2,S2 (c) M1,H2,S3 (d) M1,H2,S2 12. To provide safety against piping failure, with a factor of safety of 5, what should be he maximum permissible exit gradient for soil with specific gravity of 2.5 and porosity of 0.35 ? (a) 0.155 (b) 0.176 (c) 0.195 (d) 0.213 13. Identify the FALSE statement from the following : The specific speed of the pump increases with (a) increase in shaft speed (b) increase in discharge (c) decrease in gravitational acceleration
(d) increase in head 14. For steady flow to a fully penetrating well in a confined acquifer, the drawdowns at radial distances of r1 and r2 from the well have been measured as s1 and s2 respectively, for a pumping rate of Q. The transmissivity of the aquifer is equal to r in 2 r1 Q (a) 2 ( s1 s2 ) Q in(r2 r1 ) (b) 2 ( s1 s2 ) Q in(r2 / r1 ) (c) 2 ( s2 / s1 ) (r r ) (d) 2 Q 2 1 in( s2 / s1 ) 15. To determine the BOD5 of a wastewater sample, 5, 10 and 50 mL aliquots of the wastewater were diluted to 300 mL and incubated at 200C in BOD bottles for 5 days. Sl. No. Wastewater Volume, Initial DO, mg/L DO After 5 days, mg/L 1. 5 9.2 6.9 2. 10 9.1 4.4 5 Based on the data, the average BOD of the wastewater is equal to (a) 139.5 mg/L (b) 126.5 mg/L (c) 109.8 mg/L (d) 72.2 mg/L 16. The cumulative noise power distribution curve at a certain location is given below. The value of L40 is equal to
(a) 90 dBA (b) 80 dBA (c) 70 dBA (d) 60 dBA 17. A synthetic sample of water is prepared by adding 100 mg Kaolinite (a clay minerla), 200 mg glucose, 168 mg NacI, 120 mg MgSO4, and 111 mg CaCI2 to 1 liter of pure water. The concentrations of total solids (TS) and fixed dissolved solids (FDS) respectively in the solution in mg/L are equal to (a) 699 and 599 (b) 599 and 399 (c) 699 and 199 (d) 699 and 399 18. If aggregate size of 50-40 mm is to be tested for finding out the portion of elongated aggregates using length gauge, the slot length of the gauge should be (a) 81 mm (b) 45 mm
(c) 53 mm (d) 90 mm 19. Name the traffic survey data which is plotted by means of “Desire lines”. (a) Accident (b) Classified volume (c) Origin and Destination (d) Speed and Delay 20. In case of governing equations for calculating wheel load stresses using Wesergaard‟s approach, the following statements are made. I. Load stress are inversely proportional to wheel load II. Modulus of subgrade reaction is useful for load stress calculation (a) Both statements are TRUE (b) I is TRUE and II is FALSE (c) Both statements are FALSE (d) I is FALSE AND II is TRUE Q. 21 to Q.75 carry two marks each 2 2 3
1 6 , one of the 1 2 0 eigenvalues is 3. The other two eigenvalues are (a) 2,-5 (b) 3,-5 (c) 2,5 (d) 3,5 22. The directional derivative of f(x,y,z) = 2x2+3y2+z2 at the point P : (2,1,3) in the direction of the vector a = i – 2 k is (a) -2.785 (b) -2.145 (c) – 1.789 (d) 1.000 23. A class of first year B. Tech. students is composed of four bathes A,B,C and D, each consisting of 30 students. It is found that the sessional marks of students in Engineering Drawing in batch C have a mean of 6.6 and standard deviation of 2.3. The mean and standard deviation of the marks for the entire class are 5.5 and 4.2, respectively. It is decided by the course instructor to normalize the marks of the students of all batches to have the same mean and standard deviation as that of the entire class. Due to this, the marks of a student in batch C are changed from 8.5 to (a) 6.0 (b) 7.0 (c) 8.0 (d) 9.0 24. A 2nd degree polynomial, f(x), has values of 1,4, and 15 at x = 0, and 2, respectively. 21. For a given matrix A =
2
2
f ( x)dx is to be estimated by applying the trapezoidal rule to this data.
The integral 0
What is the error (defined as “true value – approximate value”) in the estimate ? (a) -4 /3 (b) -2/3 (c) 0 (d) 2/3 25. What is the area common to the circles r = a and r = 2a cos θ ? (a) 0.524 a2 (b) 0.614 a2 (c) 0.147 a2 (d) 1.228 a2 26. Using Cauchy‟s integral theorem, the value of the integral (integration being taken in counter clock-wise direction is
(a) 2π/81- 4πi (b) π/8-6πi (c) 4π/81 – 6πi (d) 1 27. There are 25 calculators in a box. Two of hem are defective. Suppose 5 calculators are randomly picked for inspecion ((i.e., each has the same chance of being selected), what is the probability that only one of the defective calculators will be included in the inspection ? (a) 1/2 (b) 1/3 (c) 1/4 (d) 1/5 28. A spherical naphthalene ball exposed to the atmosphere loses volume at a rate proportional to is instantaneous surface area due to evaporation. If the initial diameter of the ball is 2 cm and the diameter reduces to 1 cm after 3 months, the ball completely evaporates in (a) 6 months (b) 9 months (c) 12 months (d) infinite time dy 29. The solution of the differential equation, x 2 2 xy x 1 0 given that at x=1,y=0 dx is (a) 1/2-1/x+1/2x2 (b)1/2-1/x-1/2x2 (c)1/2+1/x+1/2x2 (d)-1/2+1/x+1/2x2 30. A simply supported beam AB has the bending moment diagram as shown in the following figure. The beam is possibly under the action of following loads :
(a) Couples of M at C and 2M at D (b) Couples of 2M at C and M at D (c) Concentrated loads of M/L at C and 2M/Lat D (d) Concentrated load of M/L at C and couple of 2M at D. 31. For the section shown below, second moment of the area about an axis d/4 distance above the bottom of the area is
(a) bd3 /48 (b) bd3/12 3 (c) 7bd /48 (d) bd3/3 32. Consider the beam AB shown in the figure below. Part AC of the beam is rigid while Part CB has the flexural rigidity EI. Identify the correct combination of deflection at end B and bending moment.
(a) PL3/3EI,2PL (b)PL3/3EI,PL 3 (c) 8PL /3EI,2PL (d)8PL3/3EI,PL 33. A beam with the cross-section given below is subjected to a positive bending moment (causing compression at the top) of 16 kN-m acting around the horizontal axis. The tensile force acting on the hatched area of the cross-section is
(a) zero (b) 5.9 kN (c) 8.9 kN (d) 17.8 kN 34. T-section of a beam is formed by gluing wooden planks as shown in the figure below. If this beam transmits a constant vertical shear force of 3000 K, the glue at any of the four joints will be subjected to a shear force (in kN per meter length) of
(a) 3.0 (b) 4.0 (c) 8.0 (d) 10.7 35. If a beam of rectangular cross-section is subjected to a vertical shear force V, the shear force carried by the upper one-third of the cross-section is (a) zero (b) 7V/27 (c) 8V /27
(d) V/3
36. A thin-walled long cylindrical tank of inside radius r is subjected simultaneously to internal gas pressure p and axial compressive force F at its ends. In order to produce „pure shear‟ state of stress in the wall of the cylinder, F should be equal to (a) πpr2 (b) 2πpr2 (c) 3πpr2 (d) 4πpr2 37. Vertical reaction developed at B in the frame be-low due to the applied load of 100 kN (with 150, 000mm2 cross-sectional area and 3.125 x 109 mm4 moment of inertia for both members) is
(a) 5.9 kN (b) 302 kN (c) 66.3 kN (d) 94.1 kN 38. Consider the beam ABCD and the influence line as shown below. The inflience the pertains to
(a) reaction at A,RA (b) shear force at B, VB (c) shear force on the left of C,Vc(d) shear force on the right of C,VC+ 39. Carry-over factor CAB for the beam shown in the figure below is
(a) 1/4 (B)1/2 (C)3/4 (D) 1 40. Assuming concrete below the neutral axis to be cracked, the shear stress across the depth of a singly-reinforce rectangular beam section (a) increases parabolically to the neutral axis and then drops suddently to zero value. (b) increases parabolically to the neutral axis and then remains constant over the remaining depth (c) increases linearly to the neutral axis and then remains constant up to the tension steel (d) increases parabolically to the neutral axis and then remains constant up to the tension steel. 41. As per IS : 456-2000, consider the following statements I. The modular ratio considered in the working stress method depends on the type of steel used II. There is an upper limit on the nominal shear stress in beams (even withshear reinforcement) due to the possibility of crushing of concrete in diagonal compression. III. A rectangular slab whose length is equal to its width may not be a two-way slab for some support conditions. The TRUE statements are (a) only I and II (b) only II and III (c) only I and III (d) , II and III 42. In the design of welded tension members, consider the following statements : I. The entire cross-sectional area of the connected leg is assumed to contribute to the effective area in case of angles. II. Two angles back-to-back and tack-welded as per the codal requirements may be assumed to behave as a tee section. III. A check on slenderness ratio may be necessary in some cases. The TRUE statements are
(a) only I and II (b) only II and III (c) only I and III (d) I, II and III 43. Consider the following statements I. Effective length of a battened column is usually increased to account for the additional load on battens due to the lateral expansion of columns. II. As per IS: 800-1984, permissible stress in bending compression depends on both Euler buckling stress and the yield stress of steel. III. As per IS: 800-1984, the effective length of a column effectively held in position at both ends but not restrained against rotation, is taken to be greater than that in the ideal end conditions. The TRUE statements are (a) only I and II (b) only II and III (c) only I and III (d) I, II and III 44. When the triangular section of a beam as shown below becomes a plastic hinge, the compressive force acting on the section (with σy denoting the yiield stress) becomes
(a) (c)
bh 4 bh
y
y
(b) (d)
2bh
y
9
bh
y
2 3 45. Consider the following statements : I. The width-thickness ratio limitations on the plate elements under compression in steel members are imposed by IS: 800-1984 in order to avoid fabrication difficulties. II. In a doubly reinforced concrete beam, the strain in compressive reinforcement is higher than the strain in the adjoining concrete. III. If a cantilever I-section supports slab construction all along its length with sufficient friction between them, the permissible bending stress in compression will be the same as that in tension. The TRUE statements are (a) only I and II (b) only II and III (c) only I and III (d) I, II and III 46. List – I below gives the possible types of failure for a finite soil slope and List – II gives the reasons for these different types of failure. Match the items in List – I with the items in List – II. List – I List-II P Base failure 1. Soils above and below the toe have same strength
Q
Face Failure
2.
Soil above the toe is comparatively weaker R Toe failure 3. Soil above the toe is comparatively stronger (a) P-1 Q-2 R-3 (b) P-2 Q-3 R-1 (c) P-2 Q-1 R-3 (d) P-3 Q-2 R-1 47. For the soil profile shown in figure below, the minimum number of precast concrete piles of 300 mm diameter required to safety carry the load for a given factor of safety of 2.5 (assuming 100% efficiency for the pile group) is equal to
(a) 10 (b) 15 (c) 20 (d) 25 48. In a standard proctor test, 1.8 kg of moist soil was filling the mould (volume = 944 cc) after compaction. A soil sample weighing 23 g was taken from the mould and overdried for 24 hours at a temperature of 1100C. Weight of the dry sample was found to be 20 g. Specific gravity of soil solids is G = 2.7. The theoretical maximum value of the dry unit weight of the soil at that water content is equal to (a) 4.67 kN/m3 (b) 11.5 kN/m3 (c) 16.26 kN/m3 (d) 8.85 kN/m3 49. A sample of saturated cohesionless soil tested in a drained triaxial compression test showed an angle of internal friction of 300. The deviatoric stress at failure for the sample at a confining pressure of 200 kPa is equal to (a) 2000 kPa (b) 400 kPa (c) 600 kPa (d) 800 kPa 50. The thickness of the laminar boundary layer on a flat plate at a point A is 2 cm and at a point B, 1m downstream of A, is 3 cm. What is the distance of A from the leading edge of the plate ? (a) 0.50 m (b) 0.80 m (c) 1.00 m (d) 1.25 m 51. The velocity field for flow is given z ) k and the density varies by V (5 x 6 y 7 z ) i (6 x 5 y 9 z ) j (3x 2 y as 0 exp(-2t). In order that the mass is conserved, the value of λ should be (a) -12 (b) -10 (c) -8 (d) 10 52. In a cultivated area, the soil ahs porosity of 45% and field capacity of 38%. For a particular crop, the root zone depth is 1.0 m, the permanent wilting point is 10% and the
consumptive use is 15 mm/d. If the irrigation efficiency is 60%, what should be the frequency of irrigation such that the moisture content does not fall below 50% of the maximum available moisture ? (a) 5d (b) 6d (b) 9d (d) 15 d 53. A hydraulic jump occurs in a rectangular, horizontal, frictionless channel. What would be the pre-jump depth if the discharge per unit width 2m3/s/m and the energy loss is 1 m ? (a) 0.2 (b) 0.3 m (c) 0.8 m (d) 0.9 m 54. During a 3 hour storm event, it was observed that all abstractions other than infiltration are negligible. The rainfall was idealized as 3 one hour storms of intensity 10 mm/hr, 20 mm/hr and 10 mm/hr respectively and the infiltration was idealized as a Horton curve, f=6.8+8.7 exp (-t) (f in mm/hr and t in hr). What is the effective rainfall ? (a) 10.00 mm (b) 11.33 mm (c) 12.43 mm (d) 13.63 mm 55. A very wide rectangular channel is designed to carry a discharge of 5m3/s per meter width. The design is based on the Manning‟s equation with the roughness coefficient obtained from the grain size using Strickler‟s equation and results in a normal depth of 1.0 m. By mistake, howeve,r the engineer used the grain diameter in mm in the Stickler‟s equation instead of in meter. What should be the correct normal depth ? (a) 0.32 m (b) 0.50 m (c) 2.00 m (d) 3.20 m 56. The flow of glycerin (kinematic viscosity v = 5×10-4 m2/s) in an open channel is to be modeled in a laboratory flume using water (v=10-6m2/s) as the flowing fluid. If both gravity and viscosity are important, what should be the length scale (i.e. ratio of prototype to model dimensions) for maintaining dynamic similarity ? (a) 1 (b) 22 (c) 63 (d) 500 57. The mean indoor airborne chloroform (CHCI3) concentration in a room was determined to be 0.4 ug/m3. Use the following data : T = 293 K, P = 1 atmosphere, R = 82.05 x 10-6 atm.m3/ mol-K, Atomic weights : C = 12, H=1, CI= 35.5. This concentration expressed in parts per billion (volume basis, ppbv) is equal to (a) 1.00 ppbv (b) 0.20 ppbv (c) 0.10 ppbv (d) 0.08 ppbv 58. The composition of a certain MSW sample and specific weights of its various components are given below. Component Percent by Weight Specific Weight (kg/m3) Food waste 50 300 Dirt and Ash 30 500 Plastics 10 65 Wood and Yard waste 10 125 Specific weight (kg/m3) of the MSW sample is (a) 319 (b) 217 (c) 209 (d) 199
59. A subgrade soil sample was tested using standard CBR apparatus and the observations are given below. Load, kg Penetration, mm 60.5 2.5 80.5 5.0 Assuming that the load-penetration curve is convex throughout, the CBR value (%) of the sample is (a) 6.5 (b) 5.5 (c) 4.4 (d) 3.9 60. A vehicle moving at 60 kmph on an ascending gradient of a highway has to come to stop position to avoid collision with a stationary object. The ratio of lag to brake distance is 6 : 5. Considering total reaction time of the driver as 2.5 Considering total reaction time of the driver as 2.5 seconds and the coefficient of longitudinal friction as 0.36, the value of ascending gradient (%) is (a) 3.3 (b) 4.8 (c) 5.3 (d) 6.8 61. For designing a 2-phase fixed type signal at an intersection having North-South and East-West road where only straight ahead traffic permitted, the following data is available. Parameter Design Hour North South East West Flow (PCU/hr) 1000 700 900 550 Saturation Flow (PCU/hr) 2500 2500 3000 3000 Total time lost per cycle is 12 seconds. The cycle length (seconds) as per webster‟s approach is (a) 67 (b) 77 (c) 87 (d) 91 62. On an urban road, the free mean speed was measured as 70 kmph and the average spacing between the vehicles under jam condition as 7.0 m. The speed-flow-density equation is given by
k andq uk kj where U = space-mean speed (kmph); Usf = free mean speed (kmph); k = density (veh/km); kj = jam density (veh/km); q = flow (veh/hr). The maximum flow (veh/hr) per lane for this condition is equal to (a) 2000 (b) 2500 (c) 3000 (d) None of these 63. At a horizontal curve portion of a 4 lane undivided carriageway, a transition curve is to be introduced to attain required superelevation. The design speed is 60 kmph and radius of the curve is 245 m. Assume length of wheel base of a longest vehicle as 6 m, superelevation rate as 5% and rate of introduction of this superelevation as 1 in 150. The length of the transition curve (m) required, if the pavement is rotated about inner edge is. (a) 81.4 (b) 85.0 (c) 91.5 (d) 110.2 64. Using IRC : 37 – 1984 “Guidelines for the Design of Flexible Pavements” and the following data, choose the total thickness of the pavement. U
U sf 1
No. of commercial vehicles when construction is completed = 2723 veh/day Annual growth rate of the traffic = 5.0% Design life of the pavement = 10 years Vehicle damage factor = 2.4 CBR value of the subgrade soil = 5% Data for 5% CBR value No. of Standard Axels, msa Total Thickes, mm 20 620 25 640 30 670 40 700 (a) 620 mm (b) 640 mm (c) 670 mm (d) 700 mm 65. The observed magnetic bearing of a line OE was found to be 1850. It was later discovered that station O had a local attraction of + 1.50. The true bearing of the line OE, considering a magnetic a magnetic declination of 3.50 E shall be (a) 1800 (b) 1870 (c) 1900 (d) 1930 66. A Bench Mark (BM) with Reduced Level (RL) = 155.305 m has been established at the floor of a room. It is required to find out the Rl of the underside of the roof (R) of the room using Spirit Leveling. The Back Sight (BS) to the BM has been observed as 1.500 m whereas the ForeSight (FS) to R has been observed as 0.575 m (Staff held inverted). The RL (m) of R will be (a) 155.880 (b) 156.230 (c) 157.380 (d) 157.860 67. Consider the following figure, which is an extract from a contour map (scale = 1:20,000) of an area. An alignment of a road at a ruling gradient of 4% is to be fixed from the point O and beyond. What should be the radius of the arc with O as the center to get the point of a alignment on the next contour on the map.
(a) 0.025 cm (b) 0.25 cm (c) 2.5 cm (d) 5.0 cm 68. In the figure given below, lengths PQ(WCB:300) and QR (WCB:450) respectively up to three places of decimal are
(a) 273.205, 938.186 (b) 273.205, 551.815 (c) 551.815, 551.815 (d) 551.815, 938.186 69. During a leveling work along a falling gradient using a Dumpy level and a Staff of 3m length, following successive readings were taken : 1.785, 2.935, 0.360, 1.320. What will be the correct order of booking these four readings in a level book ? (BS : Back Sight, IS : Intermediate Sight, FS : Fore Sight) (a) BS, FS, BS, FS (b) BS,IS,FS,FS (c) BS,IS,IS,FS (d) BS,IS,BS,FS Common Data Questions Common Data for Question 70, 71 : Laboratory sieve analysis was carried out on a soil sample using a complete set of standard IS sieves. Out of 500g of soil used in the test, 200g was retained on IS 600μ sieve, 250g was retained on IS 500μ sieve and the remaining 50g was retained on IS 425μ sieve. 70. The coefficient of uniformity of the soil is (a) 0.9 (b) 1.0 (c) 1.1 (d) 1.2 71. The classification of the soil is (a) SP (b) SW (c) GP (d) GW Common Data for Questions 72,73 : For a catchment, the S-curve (or S-hydrograph) due to a rainfall of intensity 1cm/hr is given by Q =1 – (1+t) exp (-1) (t in hr and Q in m3/s). 72. What is the area of the catchment ? (a) 0.01 km2 (b) 0.36 km2 (c) 1.00 km2 (d) 1.28 km2 73. What will be the ordinate of a 2-hour unit hydrograph for this catchment at t=3 hour ? (a) 0.13 m3/s (b) 0.20 m3/s 3 (c) 0.27 m /s (d) 0.54 m3/s Common Data for Questions 74,75: In a rapid sand filter, the time for reaching particle breakthrough (TB) is defined as the time elapsed from start of filter run to the time at which the turbidity of the effluent from the filter is greater than 2.5 NTU. The time for reaching terminal head loss (TH) is defined as the time elapsed from the start of the filter run to the time when head loss across the filter is greater than 3m. 74. The effect of increasing the filter depth (while keeping all other conditions same) on TB and TH is (a) TB increases and TH decreases (b) both TB and TH increase (c) TB decreases and TH increases
(d) both TB and TH decreases Linked Answer questions : Q.76 to Q.85 Carry two marks each Statement of Linked Answer Question 76 and 77 Consider a propped cantilever beam ABC under two loads of magnitude P each as shown in the figure below. Flexural rigidity of the beam is EI.
76. The reaction at C is 77. (a) 9pa/16L(upwards) (b) 9pa/16L(downwards) (c) 9pa/8L(upwards) (d) 9pa/8L(downwads) 77. The rotation at B is (a) 5pLa/16EI (clockwise) (b) 5pLa/16EI(anti clockwise) (c) 59pLa/16EI(clockwise) (d) 59pla/16EI(anticlockwise) Statement for Linked Answer Questions 78 and 79: In the design of beams for the limit state of colapse in flexure as per IS : 456-2000, let the maximum strain in concrete be limited to 0.0025 (in place of 0.0035). For this situation, consider a rectangular beam section with breadth as 250 mm, effective depth as 350 mm, area of tension steel as 1500 mm2, and characteristics strengths of concrete and steel as 30Mpa and 250 MPa respectively. 78. The depth of neutral axis for the balanced failure is (a) 140 mm (b) 156 mm (c) 168 mm (d) 185 mm 79. At the limiting state of collapse in flexure, the force acting on the compression zone of the section is (a) 326 kN (b) 389 kN (c) 424 kN (d) 542 kN Statement for Linked Answer Questions 80 and 81 The average effective overburden pressure on 10 m thick homogeneous saturated clay layer is 150 kPa. Consolidation test on undisturbed soil sample taken from the clay layer showed that the void ratio decreased from 0.6 to 0.5 by increasing the stress intensity from 100 kPa to 300 kPa. (G=2.65) 80. The initial void ratio of the clay layer is (a) 0.209 (b) 0.563 (c) 0.746 (d) 1.000 81. The total consolidation settlement of the clay layer due to the construction of a structure imposing an additional stress intensity of 200 kPa is (a) 0.10 m (b) 0.25 m
(c) 0.35 m (d) 0.50 m Statement for Linked Answer Questions 82 and 83 An upward flow of oil (mass density 800 kg/m3, dynamic viscosity 0.8 kg/m-s) takes place under laminar conditions in an inclined pipe of 0.1 m diameter as shown in the figure. The pressures at section 1 and 2 are measured p1=435 kN/m2 and p2= 200 kN/m2
82. The discharge in the pipe is equal to (a) 0.100 m3/s (b) 0.127 m3/s (c) 0.144 m3/s (d) 0.161 m3/s 83. If the flow is reversed, keeping the same discharge, and the pressure at section 1 is maintained as 435 kN/m2, the pressure at section 2 is equal to (a) 488 kN/m2 (b) 549 kN/m2 2 (c) 586 kN/m (d) 614 kN/m2 Statement for Linked Answer Questions 84 and 85 A water sample contains the following dissolved ions. [Na+]=56 mg/L;[Ca2+]=40 mg/L;Mg2+]= 30mg/L;[A13+] = 3mg/L; [HCO3] Water pH is 7. Atomic weights : Ca:40; Mg: 24;AI:27;H:1, C:12; O:16; Na:23; CI:35.5 84. The total hardness of the sample in mg/L as CaCO3 is (a) 484 (b) 450 (c) 242 (d) 225 85. The non-arbonate hardness of the sample in mg/L as CaCO3 is (a) 225 (b) 156 (c) 86 (d) 0
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GATE 2007 Civil Engineering Question Paper GATE CIVIL ENGINEERING 2007 (CE) GATE 2007 Civil Engineering Question Paper
1.
2.
Q.1 - Q.20 Carry One Mark Each. 1 1 3 The minimum and the maximum eigen velue of the matrix 1 5 1 are -2 and 6, respectively. What 3 1 1 is the other eigen value ? (a) 5 (b) 3 (c) 1 (d) -1 The degree of the differential equation
(a) 3.
0
(b)
d2 x dt 2
1
(c)
The solution for the differential equation (A)
y=
1 e 2x
(B)
2x 3 is 2
(d)
3
dy 2 = x y with the condition that y = 1 at x = 0 is dx
x3 ln(y) = 4 (C) 3
x2 ln(y) = 2
(D)
y=
x3 e3
4.
An axially loaded bar is subjected to a normal stress of 173 MPa. The shear stress in the bar is (a) 75 MPa (b) 86.5 MPa (c) 100 MPa (d) 122.3 MPa
5.
A steel column, pinned at both ends, has a buckling load of 200kN. If the column is restrained against lateral movement at its mid-height, its buckling load will be (A) 200kN (B) 283kN (C) 400kN (D) 800kN
6.
The stiffness coefficient kij indicates (a) force at i due to a unit deformation at j (b) deformation at j due to a unit force at i (c) deformation at i due to a unit force j (s) force at j due to a unit deformation i
7.
For an isotropic material, the relationship between the Young’s modulus (E), shear modulus (G) and Poisson’s ratio () is given by E G (A) G= (B) E 2(1 ) 2(1 ) E E (D) G= (C) G= (1 2) 2(1 )
8.
A clay soil sample is tested in a triaxial apparatus in consolidated-drained conditions at a cell pressure 2 2 of 100 kN/m . What will be the pore water pressure at a deviator stress of 40 kN/m ? 2 2 2 2 (a) 0 kN/m (b) 20 kN/m (c) 40 kN/m (d) 60 kN/m
9.
The number of blows observed in a Standard Penetration Test (SPT) for different penetration depths are given as follows Penetration of sampler Number of blows 0-150 mm 6 150-300 8 300-450 mm 10 The observed N value is (a) 8 (b) 14 (c) 18 (d) 24
Page 1 of 12
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GATE 2007 Civil Engineering Question Paper GATE CIVIL ENGINEERING 2007 (CE) 10.
The vertical stress at some depth below the corner of a 2m x 3m rectangular footing due to a certain 2 2 load intensity is 100 kN/m . What will be the vertical stress in kN/m below the centre of a 4m x 6m rectangular footing at the same depth and same load intensity? (a) 25 (b) 100 (c) 200 (d) 400
11.
There is a free overfall at the end of a long open channel. For a given flow rate, the critical depth is less than the normal depth. What gradually varied flow profile will occur in the channel for this flow rate ? (b) M2 (c) M3 (d) S1 (a) M1
12.
The consumptive use of water for a crop during a particular stage of growth is 2.0 mm/day. The maximum depth of available water in the root zone is 60 mm. Irrigation is required when the amount of available water in the root zone. Frequency of irrigation should be (a) 10 days (b) 15 days (c) 20 days (d) 25 days
13.
As per the Lacey’s method for design of a alluvail channels, identify the true statement from the following (a) Wetted perimeter increases with an increase in design discharge (b) Hydraulic radius increases with an increase in silt factor. (c) Wetted perimeter decreases with an increase in design discharge. (d) Wetted perimeter increases with an increase in silt factor
14.
At two points 1 and 2 in a pipeline the velocities and V and 2V, respectively. Both the points are at the same elevation. The fluid density is . The flow can be assumed to be in compressible, inviscid, steady and irrotational. The difference in pressures P1 and P2 at points at 1 and 2 is 2 2 2 2 (a) 0.5 V (b) 1.5 V (c) 2V (d) 3 V
15.
The presence of hardness in excess of permissible limit causes (a) cardio vascular problems (b) skin discolouration (c) calcium deficiency (d) increased laundry expenses
16.
The dispersion of pollutants in atmosphere is maximum when (a) environmental lapse rate is greater than adiabatic lapse rate (b) environmental lapse rate is less than adiabatic lapse rate (c) environmental lapse rate is equal to adiabatic lapse rate (d) maximum mixing depth is equal to zero
17.
The alkalinity and hardness of a water sample are 250 mg/L and 350 mg/L as CaCO3, respectively. The water has (a) 350 mg/L carbonate hardness and zero non-carbonate hardness. (b) 250 mg/L carbonate hardness and zero non-carbonate hardness. (c) 250 mg/L carbonate hardness and 350 mg/L non-carbonate hardness. (d) 250 mg/L carbonate hardness and 100 mg/L non-carbonate hardness.
18.
The consistency and flow resistance of bitumen can be determined from the following (a) Ductitility test (b) Penetration test (c) Softening point test (d) Viscosity test
Page 2 of 12
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GATE 2007 Civil Engineering Question Paper GATE CIVIL ENGINEERING 2007 (CE) 19.
If a two-lane national highway and a two-lane state highway intersect at right angles, the number of potential conflict points at the intersecton, assuming that both the roads are two-way is (a) 11 (b) 17 (c) 24 (d) 32
20.
In signal design as per Indian Roads Congress specifications, if the sum of the ratios of normal flows to saturation flow of two directional traffic flow is 0.50 and the total lost time per cycle is 10 seconds, the optimum cycle length in seconds is (a) 100 (b) 80 (c) 60 (d) 40
21.
22.
Q. 21 to Q.75 carry two marks each : For what values of α and the following simultaneous equations have an infinite number of solutions? x+y+z = 5; x+3y+3z = 9; x+2y+az = (a) 2,7 (b) 3,8 (c) 8,3 (d) 7,2
A velocity vector is given as V 5 xy i 2 y 2 j 3yz 2 k The divergence of this velocity vector a (1,1,1) is (a) 9 (b) 10 (c)
14
(d)
15
23.
A body originally at 60C cools down to 40C in 15 minutes when kept in air at a temperature of 25C. What will be the temperature of the body at the end of 30 minutes ? (b) 31.5C (c) 28.7C (d) 15C (a) 35.2C
24.
The following equation needs to be numerically solved using the Newton-Raphson method. 3 x +4x-9 = 0 The iterative equation for this purpose is (k indicates the iteration level) 2x k3 9 2 x k2 4 x k 1 x (B) (A) k 1 3x k2 4 3x k2 4 x k 1 x k 3x k2 4
(C)
25.
Evaluate
0
(a) 26.
27.
28.
(D)
x k 1
(c)
/4
4 x k2 3 9 x k2 2
sin t dt t (b)
/2 2
(d)
/3
2
Potential function is given as = x + y . What will be the stream function (ψ) with the condition ψ = 0 at x = y = 0 ? 2 2 2 2 2 2 (a) 2xy (b) x +y (c) x y (d) 2x y 1 The inverse of the 2 2 matrix 5 7 2 7 (A) (B) 5 1 5
2 is 7 2 1 3
(C) 2
1 7 2 3 5 1
(D)
1 7 2 3 5 1
Given that one root of the equation x 10x + 31x 30 = 0 is 5, the other two roots are (a) 2 and 3 (b) 2 and 4 (c) 3 and 4 (d) 2 and 3
Page 3 of 12
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GATE 2007 Civil Engineering Question Paper GATE CIVIL ENGINEERING 2007 (CE) 29.
If the standard deviation of the spot speed of vehicles in a highway is 8.8 kmph and the mean speed of the vehicles is 33 kmph, the coefficient of variation in speed is (a)
30.
32.
33.
(c)
0.2666
(d)
zero
(b)
12 MPa
(c)
24 MPa
(d)
(a)
16.67 kN each
(b)
30 kN and 15 kN
(c)
30 kN and 10 kN
(d)
21.4 kN and 14.3 kN
0.3646
2400 MPa
The maximum and minimum shear stresses in a hollow circular shaft of outer diameter 20 mm and thickness 2mm, subjected to a torque of 92.7 N.m will be (a)
59 MPa and 47.2 MPa
(b)
100 MPa and 80 MPa
(c)
118 MPa and 160 MPa
(d)
200 MPa and 160 MPa
The shear stress at the neutral axis in a beam of triangular section with a base of 40 mm and height 20 mm, subjected to a shear force of 3 kN is 3 MPa
(b)
6 MPa
(c)
10 MPa
(d)
20 MPa
U1 and U2 are the strain energies stored in a prismatic bar due to axial tensile forces P1 and P2, respectively. The strain energy U stored in the same bar due to combined action of P1 and P2 will be. (a)
35.
0.1867
A rigid bar is suspended by three rods made of the same material as shown in the figure. The area and length of the central rod are 3A and L, respectively while that of the two outer rods are 2A and 2L, respectively. If a downward force of 50 kN is applied to the rigid bar, the forces in the central and each of the outer rods will be
(a) 34.
(b)
A metal bar of length 100 mm is inserted between two rigid supports and its temperature is increased -6 by 10C. If the coefficient of thermal expansion is 12 10 per C and the young’s modulus is 2 × 5 10 MPa, the stress in the bar is (a)
31.
0.1517
U = U1 + U 2
(b)
U = U1U2
(c)
U < U1 + U 2
(d)
U > V1 + U2 2
The right triangular truss is made of members having equal cross sectional area of 1550 mm and 5 Young’s modulus of 2 10 MPa. The horizontal deflection of the joint Q is
(a)
2.47 mm
(b)
10.25 mm
(c)
Page 4 of 12
14.31 mm
(d)
15.68 mm
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GATE 2007 Civil Engineering Question Paper GATE CIVIL ENGINEERING 2007 (CE) 36.
The influence line diagram (ILD) shown is for the member
(a) 37.
PS
(b)
RS
(c)
PQ
(d)
QS
Consider the following statements : I.
The compressive strength of concrete decreases with increase in water-cement ratio of the concrete mix.
II.
Water is added to the concrete mix for hydration of cement and workability.
III.
Creep and shrinkage of concrete are independent of the water-cement ratio in the concrete mix.
The true statements are (a) 38.
40.
(b)
I, II and III
(c)
II and III
(d)
only II
The percentage loss of prestress due to anchorage slip of 3 mm in a concrete beam of length 30 m 2 which is post-tensioned by a tendon with an initial stress of 1200 N/mm and modulus of elasticity 5 2 equal to 2.1 x 10 N/mm is (a)
39.
I and II
0.0175
(b)
0.175
(c)
1.75
(d)
17.5
A concrete beam of rectangular cross-section of size 120 mm (width) and 200 mm (depth) is prestressed by a straight tendon to an effective force of 150 kN at an eccentricity of 20 mm (below the centroidal axis in the depth direction). The stresses at the top and bottom fibres of the section are 2
2
2
(a)
2.5 N/mm (compression), 10N/mm (compression), 10N/mm (compression).
(b)
10N/mm (tension), 2.5 N/mm (compression)
(c)
3.75 N/mm (tension), 3.75 N/mm (compression)
(d)
2.75 N/mm (compression), 3.75 N/mm (compression)
2
2
2
2
2
2
Consider the following statements : I.
Modulus of elasticity of concrete increases with increase in compressive strength of concrete.
II.
Brittleness of concrete increases with decrease in compressive strength of concrete.
III.
Shear strength of concrete increases with increase in compressive strength of concrete.
The TRUE statements are (a)
II and III
(b)
I, II and III
(c)
Page 5 of 12
I and II
(d) I and III
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GATE 2007 Civil Engineering Question Paper GATE CIVIL ENGINEERING 2007 (CE) 41.
42.
A steel flat of rectangular section of size 70 6 mm is connected to a gusset plate by three bolts each having a shear capacity of 15 kN in holes having diameter 11.5 mm. If the allowable tensile stress in the flat is 150 MPa, the maximum tension that can be applied to the flat is (a)
42.3 kN
(b)
52.65 kN
(c)
59.5 kN
(d)
63.0 kN
A bracket connection is made with four bolts of 10 mm diameter and supports a load of 10 kN at an eccentricity of 100 m. The maximum force to be resisted by any bolt will be P
10kN
30 30 40 40
(a) 43.
44.
(b)
6.5 kN
(c)
6.8 kN
(d)
7.16 kN
The plastic collapse load Wp for the propped cantilever supporting two point loads as shown in figure terms of plastic moment capacity, Mp is given by (a)
3 Mp/L
(b)
4MP/L
(c)
4MP/L
(d)
6MP/L
Sieve analysis on a dry soil sample of mass 1000 g showed that 980 g and 270 g of soil pass through 4.75 mm and 0.075 mm sieve, respectively. The liquid limit and plastic limits of the soil fraction passing through 425 sieves are 40% and 18% respectively. The soil may be classified as (a)
45.
5 kN
SC
(b)
MI
(c)
CI
(d) SM
The water content of a saturated soil and the specific gravity of soil solids were found to be 30% and 2.70, respectively. Assuming the unit weight of water to be 10 kN/m3, the saturated unit weight 3 (kN/m ) and the void ratio of the soil are (a)
19.4, 0.81
(b)
18.5, 0.30
(c)
Page 6 of 12
19.4, 0.45
(d)
18.5, 0.45
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GATE 2007 Civil Engineering Question Paper GATE CIVIL ENGINEERING 2007 (CE) 46.
The factor of safety of an infinite soil slope shown in the figure having the properties 0 3 3 c = 0, c = 0, = 35 , dry = 16 kN/m and sat = 20 kN/m is approximately equal to
10m
(a) 47.
0.70
(b)
8m 30
0.80
(c)
1.00
(d) 1.20
Match the following groups Group = I
Group - II
P Q R S
Constant head permeability test Consolidation test Pycnometer test Negative skin friction
1. 2. 3. 4.
Pile foundations Specific gravity Clay soil Sand
(a) (c)
P-4, Q-3, R-2, S-1 P-3, Q-4, R-2- S-1
(b) (d)
P-4, Q-2, R-3, S-1 P-4, Q-1, R-2, S-3
48.
The bearing capacity of a rectangular footing of plan dimensions 1.5 m x 3m resting on the surface of 2 2 a sand deposit was estimated s 600 kN/m of a sand deposit was estimated as 600 kN/m when the 2 water table is far below the base of the footing. The bearing capacities in kN/m when the water level rises to depths of 3m, 1.5 m and 0.5 m below the base of the footing are (a) 600, 600, 400 (b) 600, 450, 350 (c) 600, 500, 250 (d) 600, 400, 250
49.
What is the ultimate capacity in kN of the pile group sown in the figure assuming the group to fail as a single block ?
0.4m diameter piles Clay soil
10m
2
Cu = 40kN/m
1.2m c/c
1.2m c/c
(a)
921.6
(b)
1177.6
(c)
Page 7 of 12
2438.6
(d)
3481.6
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GATE 2007 Civil Engineering Question Paper GATE CIVIL ENGINEERING 2007 (CE) 50.
2
A horizontal water jet with a velocity of 10 m/s and cross sectional area of 10 mm strikes a flat plate held normal to the flow direction. The density of water is 1000 kg/m3. The total force on the plate due to the jet is (a)
51.
(d)
0.1 N
3
0.057 m /s
(b)
2
0.08m /s
(c)
3
0.57 m /s
3
(d)
5.7 m /s
3
3
0.08 m /s
(b) 0.11 m /s
(c)
3
3
0.15 m /s
(d) 0.2 m /s 3
2
0.025 N.s/m
(b)
2
0.012 N.s/m
(c)
2
0.00192 N.s/m (d)
2
0.00102 N.s/m
3
The flow rate in a wide rectangular open channel is 2.0 m /s per metre width. The channel bed slope is 0.002. The Manning’s roughness coefficient is 0.012. The slope of the channel is classified as Critical
(b)
Horizontal
(c)
Mild
(d)
Steep
The culturable command area for a distributary channel is 20,000 hectares. Wheat is grown in the entire area and the intensity of irrigation is 50%. The kor period for wheat is 30 days and the kor water depth is 120 mm. The outlet discharge for the distributary should be (a)
56.
1N
3
(a) 55.
(c)
Flow rate of a fluid (density = 1000 kg/m ) in a small diameter tube is 800 mm /s. The length and the diameter of the tube are 2 m and 0.5 mm, respectively. The pressure drop in 2 m length is equal to 2.0 MPa. The viscosity of the fluid is (a)
54.
10 N
A triangular open channel has a vertex angle to 90 and carries flow at a critical depth of 0.30 m. The discharge in the channel is (a)
53.
(b)
A 1: 50scale model of a spillway is to be tested in the laboratory. The discharge in the prototype is 3 1000 M /s. The discharge to be maintained in the model test is (a)
52.
100 N
3
2.85 m /s
(b)
3
3.21 m /s
(c)
3
4.63 m /s
3
(d) 5.23 m /s
An isolated 4-hour storm occurred over a catchment as follows st
Time
nd
rd
th
2 hour 3 hour 4 hour 1 hour Rainfall (mm) 9 28 12 7 The index for the catchment is 10 mm/h. The estimated runoff depth from the catchment due to the above storm is (a) 57.
16 mm
(c)
20 mm
(d)
23 mm
100%
(b)
93%
(c)
80%
(d)
65%
50 g of CO2 and 25 g of CH4 are produced from the decomposition of municipal solid waste (MSW) with a formula weight of 120 g. What is the average per capita green house gas production in a city of 1 million people with a MSW production rate of 500 ton/day ? (a)
59.
(b)
Two electrostatic precipitators (ESPs) are in series. The fractional efficiencies of the upstream and downstream ESPs for size dp are 80% and 65%, respectively. What is the overall efficiency of the system for the same dp? (a)
58.
10 mm
104 g/day
(b)
120 g/day
(c)
208 g/day
(d)
313 g/day
The extra widening required for a two-lane national highway at a horizontal curve of 300 m radius, considering a wheel base of 8 m and a design speed of 100 kmph is (a) 0.42 m (b) 0.62 m (c) 0.82 m (d) 0.92 m
Page 8 of 12
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GATE 2007 Civil Engineering Question Paper GATE CIVIL ENGINEERING 2007 (CE) 60.
While designing a hill road with a ruling gradient of 6%, if a sharp horizontal curve of 50 m radius is encountered, the compensated gradient at the curve as per the Indian Roads Congress specifications should be (a) 4.4% (b) 4.75% (c) 5.0% (d) 5.25%
61.
The design speed on a road is 60 kmph. Assuming the driver reaction time of 2.5 seconds and coefficient of friction of pavement surface as 0.35, the required slopping distance for two-way traffic on a single lane road is (a) 82.1 m (b) 102.4 m (c) 164.2 m (d) 186.4 m
62.
The width of the expansion joint is 20 mm in a cement concrete pavement. The laying temperature is 20C and the maximum slab temperature in summer is 60C. The coefficient of thermal expansion of -6 o concrete is 10×10 mm/mm/ C and the joint filler compresses up to 50% of the thickness. The spacing between expansion joints should be (a) 20 m (b) 25 m (c) 30 m (d) 40 m
63.
The following data pertains to the number of commercial vehicles per day for the design of a flexible pavement for a national highway as per IRC:37-1984 Type of commercial Number of vehicles per day Vehicle Damage Factor Vehicle considering the number f lanes Two axle trucks 2000 5 Tandem axle trucks 200 6 Assuming a traffic growth factor of 7.5% per annum for both the types of vehicles, the cumulative number of standard axle load repetitions (in million) for a design life of ten years is (a) 44.6 (b) 57.8 (c) 62.4 (d) 78.7
64.
Match the following tests on aggregate TEST P. Crushing test Q. Los Angeles abrasion test R. Soundness test S. Angularity test (a) P-2, Q-1, R-4, S-3 (c) P-3, Q-2, R-1, S-4
and its properties PROPERTY 1. Hardness 2. Weathering 3. Shape 4. Strength (b) P-4, Q-2, R-3, S-1 (d) P-4, Q-1, R-2, S-2
65.
The plan of a map was photo copied to a reduced size such that a line originally 100 mm, measures 90 mm. The original scale of the plan was 1 : 1000. The revised scale is (a) 1 : 900 (b) 1 : 111 (c) 1 : 1121 (d) 1: 1221
66.
The following table gives data of consecutive co-ordinates in respect of a closed theodolite traverse PQRSP. Station Northing, m Southing, m Easting, m Westing, m P 400.75 300.5 Q 100.25 199.25 R 199.0 399.75 S 300.0 200.5 The magnitude and direction of error of closure in whole circle bearing are (a) (c)
2.0 m and 45 2.82 m and 315
(b) (d)
Page 9 of 12
2.0 m and 315 3.42 m and 45
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GATE 2007 Civil Engineering Question Paper GATE CIVIL ENGINEERING 2007 (CE) 67.
The following measurements were made during testing a leveling instrument. Instrument at
Staff Reading at Q1 1.700 m 1.800 m
P1 2.800 m 2.700 m
P Q
P1 is close to P and Q1 is close to Q. If the reduced level of station P is 100.000 m, the reduced level of station Q is (a) 68.
(b)
100.000 m
(c)
101.000 m
(d)
102.000 m
Two straight lines intersect at an angle of 60. The radius of a curve joining the two straight lines is 600m. The length of long chord and mid-ordinates in metres of the curve are (a)
69.
99.000 m
8.4, 600.0
(b)
600.0, 80.4
(c)
600.0, 39.89
(d)
40,89, 300
The magnetic bearing of a line AB is S 45 E and the declination is 5 West. The true bearing of the line AB is (a)
S 45 E
(b)
S 40 E
(c)
S 50 E
(d)
S 50 W
COMMON DATA QUESTIONS Common Data for Questions 70,71
Water is flowing through the permeability apparatus as shown in the figure. The coefficient of permeability of the soil is k m/s and the porosity of the soil sample is 0.50.
70.
The total head, elevation head and pressure head in metres of water at the point R shown in the figure are (a) 0.8, 0.4, 0.4 (b) 1.2, 0.4, 0.8 (c) 0.4, 0, 0.4 (d) 1.6, 0.4, 1.2
71.
What are discharge velocity and seepage velocity through the soil sample ? (A) k, 2k (B) 2/3k, 4/3k (C) 2k,k (D)
4/3k, 2/3k
Common Data for Questions 72 and 73 : Ordinates of a 1-hour unit hydrograph at 1 hour intervals, starting from time t = 0, are 0, 2, 6, 4, 2, 1 and 0 3 m /s.
72.
73.
Catchment area represented by this unit hydrograph is 2 2 (a) 1.0 km (b) 2.0 km (c)
2
3.2 km
(d)
Ordinate of a 3-hour unit hydrograph for the catchment at t= 3 hours is 3 3 3 (a) 2.0 m /s (b) 3.0 m /s (c) 4.0 m /s (d)
Page 10 of 12
2
5.4 km 3
5.0 m /s
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GATE 2007 Civil Engineering Question Paper GATE CIVIL ENGINEERING 2007 (CE) Common Data for Questions 74 and 75 : A completely mixed activated sludge process is used to treat a wastewater flow of 1 million litres per day (1 MLD) having a BOD5 of 200 mg/L. The biomass concentration in the aeration tank is 2000 mg/L and the 3 concentration of the net biomass leaving the system is 50 mg/L. The aeration tank has a volume of 200 m .
74.
What is the hydraulic retention time of the wastewater in aeration tank ? (a) 0.2 h (b) 4.8 h (c) 10 h (d)
24 h
75.
What is the average time for which the biomass stays in the system ? (a) 5h (b) 8h (c) 2 days
8 days
(d)
Linked Answer questions : Q.76 to Q.85 carry two marks each. Statement of Linked Answer Questions 76 and 77. A two span continuous beam having equal spans each of length L is subjected to a uniformly distributed load w per unit length. The beam has constant flexural rigidly.
76.
77.
The reaction at the middle support is 5L (a) L (b) 2 The bending moment at the middle support is 2 2 (b) 8wL (a) 4wL
(c)
5L 4
(c)
12wL
2
(d)
L2 16
(d)
16wL
2
Statement for Linked Answer Questions 78 and 79 A singly reinforced rectangular concrete beam has a width of 150 mm and an effective depth of 330 mm. The characteristics compressive strength of concrete is 20 MPa and the characteristics tensile strength of steel is 415 MPa. Adopt the stress block for concrete as given in IS 456-2000 and take limiting value of depth of neutral axis as 0.48 times the effective depth of the beam. 78. The limiting value of the moment of resistance of the beam is kN.m is (A) 0.14 (B) 0.45 (C) 45.08 (D) 156.82
79
2
The limiting area of tension steel in mm is (A) 473.9 (B) 412.3
(C)
373.9
(D)
312.3
Statement for Linked Answer Questions 80 and 81 The ground conditions at a site are as shown in the figure. The water table at the site which was initially at a depth of 5m below the ground level got permanently lowered to a depth of 15m below the ground level due to pumping of water over a few years. Assume the following data 3 i. unit weight of water = 10kN/m 3 ii. unit weight of sand above water table = 18kN/m 3 iii. unit weight of sand and clay below the water table = 20kN/m 2 iv. coefficient of volume compressibility = 0.25m /MN
Page 11 of 12
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GATE 2007 Civil Engineering Question Paper GATE CIVIL ENGINEERING 2007 (CE) 80.
What is the change in the effective stress in kN/m2 at mid-depth of the clay layer due to the lowering of the water table? (A) 0 (B) 20 (C) 80 (D) 100
81.
What is the compression of the clay layer in mm due to the lowering of the water table? (A) 125 (B) 100 (C) 25 (D) 0
Statement for Linked Answer Questions 82 and 83 3 A rectangular open channel needs to be designed to carry a flow of 2.0 m /s under uniform flow conditions. The Manning’s roughness coefficient is 0.018. The channel should be such that the flow depth is equal to half the width, and the Froude number is equal to 0.5
82.
The bed slope of the channel to be provided is (a) 0.0012 (b) 0.0021
83.
Keeping the width, flow depth and roughness the same, if the bed slope of the above channel is doubled, the average, boundary shear stress under uniform flow conditions is 2 2 2 2 (a) 5.6 N/m (b) 10.8 N/m (c) 12.3 N/m (d) 17.2 N/m
(c)
0.0025
(d)
0.0052
Statement for Linked Answer Questions 84 and 85 A plain sedimentation tank with a length of 20m, width of 10 m, and a depth of 3 m is used in a water treatment plant to treat 4 million litres of water per day (4 MLD). The average temperature of water is 20C. 2 3 The dynamic viscosity of water is 1.002 x 10-3 N.s/m at 20C. Density of water is 998.2 kg/M . Average specific gravity of particles is 2.65.
84.
What is the surface overflow rate in the sedimentation tank ? 3 2 3 2 (a) 20 m /m /day (b) 40 m /m /day 3 2 3 2 (d) 133 m /m /day (c) 67 m /m day
85.
What is the minimum diameter of the particle which can be removed with 100% efficiency in the above sedimentation tank? -3 -3 (a) 11.8 10 mm (b) 16.0 10 mm -3 -3 (d) 160 10 mm (c) 50 10
Page 12 of 12
GATE : 2008 CE : Civil Engineering Q.1 – Q.20 carry one mark each. 1. The product of matrices (PQ) 1P is (a) P-1 (b) Q-1 (c) P-1 Q-1 P (d) PQP-1 d2y 2. The general solution of y 0 dx 2 (a) y = P cos x + Q sin x (b) y = P cos x (c) y = P sin x (d) y = P sin2 x 3. A mild steel specimen is under uni-axial tensile stress. Young’s modulus and yield stress for mild steel are 2×105 MPa and 250 MPa respectively. The maximum amount of strain energy per unit volume that can be stored in this specimen without permanent set is (a) 156 Nmm/mm3 (b) 15.6 Nmm/mm3 (c) 1.56 Nmm/mm3 (d) 0.156 Nmm/mm3 4. A reinforced concrete structure has to be constructed along a sea coast. the minimum grade of concrete to be used as per IS : 456-2000 is (a) M 15 (b) M 20 (c) M 25 (d) M 30 5. In the design of a reinforced concrete beam the requirement for bond is not getting satisfied. The economical option to satisfy the requirement for bond is by (a) bundling of bars (b) providing smaller diameter bars more in number (c) providing larger diameter bars less in number (d) providing same diameter bars more in number 6. The shape of the cross-section, which has the largest shape factor, is (a) rectangular (b) I-section (c) diamond (d) solid circular 7. Group symbols assigned to silty sand and clayey sand are respectively (a) SS and CS (b)SM and CS (c) SM and SC (d) MS and CS 8. When a retaining wall moves away from the back-fill, the pressure exerted on the wall is termed as (a) passive earth pressure (b) swelling pressure (c) pore pressure (d) active earth pressure 9. Compaction by vibratory roller is the best method of compaction in case of (a) moist silty sand (b) well graded dry sand (c) clay of medium compressibility (d) silt of high compressibility 10. A person standing on the bank of a canal drops a stone on the water surface. He notices that the disturbance on the water surface in not traveling up-stream. This is because the flow in the canal is (a) sub-critical (b) super-critical
(c) steady (d) uniform 11. A flood wave with a known inflow hydrograph is routed through a large reservoir. The outflow hydrograph will have (a) attenuated peak with reduced time-base (b) attenuated peak with increased time-base (c) increased peak with increased time-base (d) increased peak with reduced time-base 12. A stable channel is to be designed for a discharge of Q m3/s with silt factor as per Lacey’s method. The mean flow velocity (m/s) in the channel is obtained by 13. The base width of an elementary profile of gravity dam of height H is b. The specific gravity of the material of the dam is G and uplift pressure coefficient is K. The correct relationship for no tension at the heel is given by 14. Two primary air pollutants are (a) sulphur oxide and ozone (b) nitrogen oxide and peroxyacetyInitrate (c) sulphur oxide and hydrocarbon (d) ozone and peroxyacetynitrate 15. Two biodegradable components of municipal solid waste are (a) plastics and wood (b) cardboard and glass (c) leather and tin cans (d) food wastes and garden trimmings 16. The specific gravity of paving bitumen as per IS : 73-1992 lies between (a) 1.10 and 1.06 (b) 1.06 and 1.02 (c) 1.02 and 0.97 (d) 0.97 and 0.92 17. A combined value of flakiness and elongation index is to be determined for a sample of aggregates. The sequence in which the two tests are conducted is (a) elongation index test followed by flakiness index test on the whole sample (b) flakiness index test followed by elongation index test on the whole sample (c) flakiness index test followed by elongation index test on the non-flaky aggregates (d) elongation index test followed by flakiness index test on non-elongated aggregates 18. The capacities of “One-way 1.5 m wide sidewalk (persons per hour)” and “One-way 2-lane urban road (PCU per hour, with no frontage access, no standing vehicles and very little cross traffic)” are respectively. (a) 1200 and 2400 (b) 1800 and 2000 (c) 1200 and 1500 (d) 2000 and 1200 19. The shape of the STOP sign according to IRC : 67-2001 is (a) circular (b) triangular (c) octagonal (d) rectangular 20. The type of surveying in which the curvature of the earth is taken into account is called (a) Geodetic surveying (b) Plane surveying (c) Preliminary surveying (d) Topographical surveying Q. 21 to Q. 75 carry two marks each.
2
21. The equation k x 2
To k x
h
2 1
x
2 h h K z 2 x x2
can be transformed
2
h = 0 by substituting x2 3 x
(6 x y )dxdy is
22. The value of 0 0
(a) 13.5 (b) 27.0 (c) 40.5 (d) 54.0 23. Three values of x and y are to fitted in a straight line in the form y=a+bx by the method of least squares. Given: Σx=6, Σx=21, Σx2=14 and Σxy=46, the values of a and b are respectively (a) 2 and 3 (b) 1 and 2 (c) 2 and 1 (d) 3 and 2 24. Solution of dy/dx = - x/y at x = 1 ad y = 3 is Dx y 2 (a) x-y =-2 (b) x+y2 = 4 (c) x2-y2=-2 (d) x2+y2=4 25. If probability density function of a random variable X is ƒ(x) = x2 for -1< x SL (b) LL>PL>SL (c) LL Irfan`s age +saira`s age II. the age difference between Gita and saira is 1 year. However, Gita and saira is 1 year. However Gita is not the oldest and saira is not the youngest III.There are not twins (a) HSIG (b) SGHI (c) IGSH (d) IHSG
GATE:2011 CIVIL ENGINEERING Q.(1-25) CARRY ONE EACH MARK 1.[A] is a square matrix which is neither symmetric nor skew-symmetric and [A]T is its transpose. The sum and differene of these matrices are defined as [s]=[A]+[A]T, and [D]=[A]-[A]T,respectively. Which of the following statements is true? (a) Both [S] and [D] are symmetric (b) Both[S] and [D] are skew-symmetric (c) [S] is skew-symmetric and [D] is symmetric (d) [S] is symmetric and [D] is skew-symmetric 2. The square root of a number N is to be obtained by applying the NewtonRaphson iterations to the equation x2-N=0.if i denotes the iteration index, the correct iterative scheme will be 1 N 1 2 N xi xi (a) xi 1 (b) xi 1 2 xi 2 xi2 (c) xi
1
1 xi 2
N2 xi
(d) xi
1
1 xi 2
N xi
3.There are two containers, with one containing 4 Red and 3 Green balls and the other containing 3 Blue and 4 Green balls. One ball is drawn at random from each container. The probability that one of the balls is Red and the other is Blue will be (a) 1/7 (b) 9/49 (c) 12/49 (d) 3/7 4.For the fillet weld of size `s` shown in the adjoining figure the effective throat thickness is
(a) 0.61s (b) 0.65s (c) 0.70s (d) 0.75s 5.A 16 mm thick plate measuring 650mm 420mm is used as a base plate for an ISHB 300 column subjected to a factored axial compressive load of 2000kN. As per IS 456-2000,The minimum grade of concrete that should be used below the base plate for safely carrying the load is (a) M15 (b)M 20 (c) M30 (d) M40 6.consider a reinforcing bar embedded in concrete. In a marine environment this bar undergoes uniform corrosion, which leads to the deposition of corrosion products on its surface and increase in the apparent volume of the bar. This subjects the surrounding concrete to expansive pressure. As a
result, corrosion induced cracks appear at the surface concrete. Which of the following statements is TRUE? (a) Corrosion cause circumferential tensile stresses in concrete and the cracks will be parallel to the corroded reinforcing bar. (b) corrosion causes radial tensile stesses in concrete and the cracks will be parallel to the corroded reinforcing bar. (c)Corrosion causes circumferential tensile stresses in concrete and the cracks will be perpendicular to the direction of the corroded reinforcing bar. (d) Corrosion cause radial tensile stresses in concrete and the cracks will be perpendicular to the direction of the corroded reinforcing bar. 7.The results for sieve analysis carried out for three types of sand p,Q and R, are gives in the adjoining figure. If the fineness modulus values of the three sands are given as FMp,FMQ and FMR, it can be stated that
(a) FM Q
FM p FM R
(c)FMp>FMQ>FMR
(b) FMQ=0.5(FMp+FMR) (d) FMp SSD. comfort condition with allowablerate of change of centrifugal acceleration = 0.5 m/sec3.
Assume total reaction time = 2.5 seconds; coefficient of longitudinal friction of the pavement= 0.35; height of head light of the vehicle =0.75 m; andbeam angle = 1°. Q.50
What is the length of valley curve (in m) based on the head light sight distance condition? __________
Q.51
What is the length of valley curve (in m)based on the comfort condition? __________
Linked Answer Questions Statement for Linked Answer Questions 52 and 53: A multistory building with a basement is to be constructed. The top 4 m consists of loose silt, below which dense sand layer is present up to a great depth. Ground water table is at the surface. The foundation consists of the basement slab of 6 m width which will rest on the top of dense sand as shown in the figure. For dense sand, saturated unit weight = 20kN/m3, and bearing capacity factors Nq = 40 and N = 45. For loose silt, saturated unit weight = 18kN/m3, Nq = 15 and N = 20.Effective cohesion c' is zero for both soils.Unit weight of water is 10 kN/m3. Neglect shape factor and depth factor. Average elastic modulus E and Poisson’s ratio of dense sand is 60 x 103kN/m2 and 0.3 respectively.
Ground surface Loose silt 4 m
Loose silt
Basement Foundation slab
6 m Dense sand Q.52
Using factor of safety = 3, the net safe bearing capacity (in kN/m2) of the foundation is: (A) 610
Q.53
(C) 983
(D) 693
The foundation slab is subjected to vertical downward stresses equal to net safe bearing capacity derived in the above question. Using influence factor If = 2.0, and neglecting embedment depth and rigidity corrections, the immediate settlement of the dense sand layer will be: (A) 58 mm
CE
(B) 320
(B) 111 mm
(C) 126 mm
(D) 179 mm
14/16
2013
CIVIL ENGINEERING - CE
Statement for Linked Answer Questions 54 and 55:
At a station, Storm I of 5 hour duration with intensity 2 cm/h resulted in a runoff of 4 cm and Storm II of 8 hour duration resulted in a runoff of 8.4 cm. Assume that the ϕ-index is the same for both the storms. Q.54
The ϕ-index (in cm/h) is: (A)1.2
Q.55
(B)1.0
(C)1.6
(D) 1.4
(C)1.50
(D)2.25
The intensity of storm II (in cm/h) is: (A)
2.00
(B)1.75
General Aptitude (GA) Questions
Q. 56 – Q. 60 carry one mark each. Q.56
A number is as much greater than 75 as it is smaller than 117. The number is: (A) 91
Q.57
(C) 89
(D) 96
The professor ordered to the students to go out of the class. I II III IV Which of the above underlined parts of the sentence is grammatically incorrect? (A) I
Q.58
(B) 93
(B) II
(C) III
(D) IV
Which of the following options is the closest in meaning to the word given below: Primeval (A) Modern (C) Primitive
Q.59
(B) Historic (D) Antique
Friendship, no matter how _________it is, has its limitations. (A) cordial (B) intimate (C) secret (D) pleasant
Q.60
Select the pair that best expresses a relationship similar to that expressed in the pair: Medicine: Health (A) Science: Experiment (C) Education: Knowledge
CE
(B) Wealth: Peace (D) Money: Happiness
15/16
2013
CIVIL ENGINEERING - CE
Q. 61 to Q. 65 carry two marks each. Q.61
X and Y are two positive real numbers such that 2 , 3 following values of , the function
6 and 2 8. For which of the 6 will give maximum value?
(A) (4/3, 10/3) (B) (8/3, 20/3) (C) (8/3, 10/3) (D) (4/3, 20/3) Q.62
If |4
7|
(A) 2, 1/3 Q.63
5 then the values of 2 | |
|
(B) 1/2, 3
| is: (C) 3/2, 9
(D) 2/3, 9
Following table provides figures (in rupees) on annual expenditure of a firm for two years - 2010 and 2011. Category
2010
2011
Raw material
5200
6240
Power & fuel
7000
9450
Salary & wages
9000
12600
Plant & machinery
20000
25000
Advertising
15000
19500
Research & Development
22000
26400
In 2011, which of the following two categories have registered increase by same percentage? (A) Raw material and Salary & wages (B) Salary & wages and Advertising (C) Power & fuel and Advertising (D) Raw material and Research & Development Q.64
A firm is selling its product at Rs. 60 per unit. The total cost of production is Rs. 100 and firm is earning total profit of Rs. 500. Later, the total cost increased by 30%. By what percentage the price should be increased to maintained the same profit level. (A) 5
Q.65
(B) 10
(C) 15
(D) 30
Abhishek is elder to Savar. Savar is younger to Anshul. Which of the given conclusions is logically valid and is inferred from the above statements? (A) Abhishek is elder to Anshul (B) Anshul is elder to Abhishek (C) Abhishek and Anshul are of the same age (D) No conclusion follows
END OF THE QUESTION PAPER CE
16/16
Detailed Solutions
of
Civil Engineering
GATE-2014 Morning Session
Write us at
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Expert Opinion
D
ear Students, The Questions of GATE 2014 are based on fundamental and basic concepts of the syllabus. There is no ambiguity
and misprint noticed till now, however, it is an observation based on students feedback. The level and standard of GATE 2014 questions are relatively easier B. Singh (Ex. IES) CMD, MADE EASY Group
1.
than the exam of GATE 2013. There are 3 important observations made by me about GATE 2014 exam.
The GATE 2014 exam is conducted in two seating i.e. morning session and afternoon session. The question papers of both seatings are different. The difficulty level of questions are nearly same and due care has been taken to balance both the papers, however small differences are certainly there. The morning session paper seems to be little easier by 2 to 5%, however, it varies on the perception of person to person also.
The average marks of both the papers should be equated and necessary scaling criteria should be adopted for this purpose.
2.
The GATE 2014 cut-off will be nearly same as that of last year, perhaps it may be little lesser than that of GATE 2013. GATE-2013 cutoff was 33 marks. Though the paper of GATE 2013 was tougher and number of students were less, 6 marks questions were wrongly framed and hence, these 6 marks were awarded to all the candidates, which was certainly a kind of bonus.
Therefore expected cut-off for GATE 2014 may be between 30 to 34 marks (General category). It may be noted that the following formulae is used to evaluate GATE cut-off marks.
Total Marks obtained by all the candidates GATE Cutoff = Total number of candidates
3.
GATE cutoff 0.6 Vs (b) V > 0.7 Vs (c) V > 0.8 Vs (d) V > 0 (a) Clause 9.2.1 IS 800:2007.
Q.6
Ans.
In reservoir with an uncontrolled spillway the peak of the plotted outflow hydrograph (a) Lies outside the plotted inflow hydrograph. (b) Lies on the recession limb of the plotted inflow hydrograph. (c) Lies on the peak of the inflow hydrograph. (d) is higher than peak of the plotted inflow hydrograph. (b)
Inflow hydrograph Recession limb Outflow hydrograph
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GATE-2014 Exam Solutions Civil Engineering (Morning Session) Q.7
Ans.
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Page 3
If y = 5x2 + 3 than the tangent at x = 0 and y = 3 (a) passes through x = 0, y = 0 (b) has a slope +1 (c) is parallel to x-axis (d) has a slope of –1 (c) y = 5x2 + 3 dy = 10 x dx dy dx (0,3) = 10 × 0 = 0
⇒ y
Tangent (0, 3)
x
⇒ tangent is parallel to x-axis.
Q.8
Ans.
The dimension for kinematic viscosity is (a)
L MT
(b)
L T2
(c)
L2 T
(d)
ML T
(c) The SI unit of kinamatic viscosity is m2/sec. ∴ dimension of kinamatic viscosity [ν] = L2/T.
Q.9
The following statements are related to temperature stress developed in concrete pavement slab with four edge (without any restrain) P : The temperature stress will be zero during both day and night time if the pavement slab is considered weight less. Q. : The temperature stress will be compressive at the bottom of the slab during night time if the self weight of the pavement slab is considered. R : The temperature stress will be compressive at the bottom of the slab during day time if the self weight of the pavement slab is considered.
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GATE-2014 Exam Solutions Civil Engineering (Morning Session) The true statement(s) is(are) (a) P only (c) P and Q only Ans.
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Page 4
(b) Q only (d) P and R only
(c) The temperature stress will be tensile at the bottom of the slab during the day time if the self weight of the pavement slab is considered.
Q.10
An incompressible homogeneous fluid flowing steadily in a variable dia pipe having the large and small dia as 15 cm and 5 cm respectively. If velocity at the section of 15 cm dia portion of the pipe is 2.5 m /sec, the velocity of fluid (in m/s) at section falling in 5 cm portion of the pipe is _________.
Sol. π 2 π (5) × V (15)2 × 2.5 = 4 4
V = 2.5 × 9 = 22.5 m/s
⇒
Q.11
The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following figure which of the following are true ? (K percentile is the value such that K % of data fall below that value) Rainfall (mm)
800
650
700 650 600
600
500 400 300
400
200
200
100
100 50 Feb
Mar Apr May
June July
Aug Sep Oct Nov Dec
(i) On average it rains more in July than in Dec. (ii) Every year, the amount of rainfall in August is more than that in January.
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GATE-2014 Exam Solutions Civil Engineering (Morning Session)
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Page 5
(iii) July rainfall can be estimated with better confidence than Feb. rainfall. (iv) In Aug, there is at least 500 mm of rainfall. (a) (i) and (ii) (b) (i) and (iii) (c) (ii) and (iii) (d) (iii) and (iv) Ans.
Q.12
(b)
The potable water is prepared from turbid surface water by adopting the foil treatment square. (a) Turbid surface water → Coagulation → Flocculation → Sedimentation → Filtration → Disinfection → Storage and supply (b) Turbid surface water → Disinfection → Flocculation → Sedimentation → Filteration → Coagulation → Storage and supply (a) Turbid surface water → Filteration → Sedimentation→ Disinfection → Flocculation → Coagulation (a) Turbid surface water → Sedimentation → Flocculation → Coagulation → Disinfection → Filteration
Ans.
Q.13
Ans.
(a)
The minimum value of 15 minutes peak hour factor on a section of a road is (a) 0.1 (b) 0.2 (c) 0.25 (d) 0.33 (c) 15 min. peak hr factor is used for traffic intersection design PHF =
(V/4) V15
⎛ veh. ⎞ V = Peak hourly volume ⎜ in ⎟ ⎝ hr. ⎠
(veh.)
V15 = Maximum 15 minimum volume within the peak hr.
Maximum value is 1.0 and minimum value is 0.25 Normal range is 0.7 – 0.98 = 0.25
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GATE-2014 Exam Solutions Civil Engineering (Morning Session) Q.14
Ans.
Q.15
(d)
The degree of disturbances of a sample collected by sampler is expressed by a term called the area ratio. If outer diameter and inner dia of sample are D0 and Di respecgively, the area ratio is
(c)
Q.16
D20 − D2i
(b)
D2i
D20 − D2i
(d)
D20
D2i − D02 D2i
D2i − D02 D20
(a)
The degree of static indeterminacy of a rigid jointed frame PQR supported as shown is y
R
145°
S
EI
90°
P
Q
EI
(a) 0 (c) 2 Ans.
Page 6
Some of the non-toxic metal normally found in natural water are (a) Arsenic, Lead, Mercury (b) Calcium, Sodium, Silver (c) Cadmium, curomium, copper (d) Iron, Mangnese, Magnesium
(a)
Ans.
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x
(b) 1 (d) 3
(a) Ds = DSe + Dsi = (re – 3) + 3C – rr = (4 – 3) + 3 × 0 – 1 = 0
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GATE-2014 Exam Solutions Civil Engineering (Morning Session) Q.17
Ans.
Q.18
Page 7
The action of negative friction on the pile is to (a) Increase the ultimate load on the pile (b) Reduce the allowable load on the pile (c) Maintain the working load on the pile (d) Reduce the settlement (b)
The ultimate collapse load (Wu) in terms of plastic moment Mp by kinematic approach for a propped cantilever of length L with W acting at its mid span as shown in fig would be W
L/2
(a) (c) Ans.
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L/2
2M p
(b)
L 6M p
(d)
L
4M p L 8M p L
(c) W
L/2
L/2 Wu
θ
θ
Mp θ
θ
Mp
Mp
From principal of virtual work − M pθ − M pθ − M pθ + Wu
⇒
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L θ = 0 2
Wu =
6M p L
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GATE-2014 Exam Solutions Civil Engineering (Morning Session) Q.19
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Page 8
Match the following: Group I
Group II
P. Alidade
1. Chain Survey
Q. Arrow
2. Levelling
R. Bubble tube
3. Plant table surveying
S. Stedia hair
4. Theodolite
(a) P – 3, Q – 2, R – 1, S – 4 (b) P – 2, Q – 4, R – 3, S – 1 (c) P – 1, Q – 2, R – 4, S – 3 (d) P – 3, Q – 1, R – 2, S – 4 Ans.
(d) P – 3, Q – 1, R – 2, S – 4
Q.20
The sum of eigen value matrix [M] is
When
⎡215 650 795⎤ [M] = ⎢⎢655 150 835⎥⎥ ⎢⎣485 355 550⎥⎦
(a) 915 (c) 1640 Ans.
(b) 1355 (d) 2180
(a) Sum of eigen values = trace of matrix = 215 + 150 + 550 = 915
Q.21
The probability density function of evaporation E on any day during a year in watershed is given by
⎧1 ⎪ 0 ≤ E ≤ mm/day f (E) = ⎨ 5 ⎪⎩0 Otherwise The probability that E lies in between 2 and 4 mm/day in a day in watershed is (in decimal) Sol.
⎧1 ⎪ 0 ≤ E ≤ mm/day f (E) = ⎨ 5 ⎪⎩0 Otherwise
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GATE-2014 Exam Solutions Civil Engineering (Morning Session)
4
P (2 < E < 4) =
∫ f (E) dE = 2
=
Q.22
4
1
1
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Page 9
4
∫ 5 dE = 5 [ E]2 2
1 2 (4 − 2) = 5 = 0.4 5
A box of weight 100 kN shown in the figure to be lifted without swinging. If all the forces are coplanar, the magnitude and direction (θ) of force F w.r.t. x axis is ________. y 90 kN
40 kN
F
45° θ
30°
x
100 kN
(a) F = 56.389 kN and θ = 28.28° (b) F = –56.389 kN and θ = –28.28° (c) F = 9.055 kN and θ = 1.1414° (d) F = –9.055 kN and θ = –1.1414° Ans.
(a) For no swinging ∑Fhorizontal = 0 90 kN
40 kN
F
45° θ
30°
x
100 kN
⇒
Q.23
90 cos 30° = 40 cos 45° + F cos θ 49.658 = F cos θ F cos θ from option (a) = 56.389 cos 28.28° = 49.658 kN
The amount of CO2 generated in kg while completely oxidizing one kg of CH4 is ________.
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GATE-2014 Exam Solutions Civil Engineering (Morning Session)
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Page 10
Sol.
CH 4 + 2O 2 → CO2 + 2H 2O 16g
Q.24
44g
⇒
16 g of CH4 when completely oxidized leads to 44 g of CO2
⇒
1 kg of CH4 when completely oxidized leads to
44 × 1 = 2.75 kg CO 2 16
While designing for a steel column of Fe250 grade the base plate resting on a concrete pedestal of M20 grade, the bearing strength of concrete (N/mm2) in LSM of design as per IS 456: 2000 is ..........
Sol. Permissible bearing stress = 0.45 fck = 0.45 × 20 = 9 N/mm2
Q.25
⎡3 2 1⎤ Given J = ⎢⎢ 2 4 2 ⎥⎥ and K = ⎢⎣ 1 2 6 ⎥⎦
⎡ 1⎤ ⎢ 2 ⎥ then product KT JK is _______. ⎢ ⎥ ⎢⎣ −1⎥⎦
Sol.
⎡ 1⎤ ⎡3 2 1⎤ ⎢ 2⎥ ⎢2 4 2⎥ J= ⎢ ⎥, K = ⎢ ⎥ ⎢⎣ −1⎥⎦ ⎢⎣ 1 2 6 ⎥⎦
KT
⎡3 2 1⎤ ⎡ 1⎤ ⎢ ⎥ ⎢ ⎥ JK = [1 2 − 1] ⎢ 2 4 2 ⎥ ⎢ 2 ⎥ ⎢⎣ 1 2 6 ⎥⎦ ⎢⎣ −1⎥⎦ ⎡ 1⎤ ⎢ ⎥ = [ 6 8 − 1 ] ⎢ 2 ⎥ = 6 + 16 + 1 = 23 ⎢⎣ −1⎥⎦
Two Marks Questions Q.26
Three rigid bucket are of identical height and base area. Further assume that each of these buckets have negligible mass and are full of water. The weight of water in these bucket are denoted by W1, W2, W3 respectively. Which of the following option are correct.
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h
h
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h
(a) W2 = W1 = W3 and F2 > F1 > F2 (b) W2 > W1 > W3 and F2 > F1 > F3 (c) W2 = W1 = W3 and F1 = F2 = F3 (d) W2 > W1 > W3 and F2 = F1 = F3 Ans.
(d) Bucket → identical height → identical base area
h
h
h
A
A
A
1
2
3
h
W 2 > W1 > W3
⇒
Force on the base in each case will be equal to = γ w h A Hence,
Q.27
F1 = F2 = F3
If the following equation establishes equilibrium in slightly bent position. d 2y dx
2
+
py = 0 EI
the mid-span deflection of a member shown in figure is y x
P
EI
P
y
M
N
L
[a is the amplitude constant for y] (a) y =
1⎛ 2π x⎞ 1 − a cos ⎜ P⎝ L ⎟⎠
(b) y =
1⎛ 2π x⎞ 1 − a sin ⎜ P⎝ L ⎟⎠
(c) y =
a sin n π x L
(d) y ′ =
a cos n π x L
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(c) d2 y dx
2
= −
P ×y EI
= –m2y ∴ Solution of above differential equation is y = a sin mx + b cos mx at x = 0, y = 0 ⇒ b= 0 at x = L, y = 0 ⇒ 0 = sin mL ⇒ mL = nπ ⇒ ∴
Q.28
m=
nπ L
y = asin
nπx L
A rectangular beam of 230 mm width and effective depth = 450 mm, is reinforced with 4 bars of 12 mm diameter. The grade of concrete is M 20, grade of steel is Fe 500. Given that for M 20 grade of concrete, the ultimate shear strength τ uc = 0.36 N/mm 2 for steel percentage of = 0.25, and
τuc = 0.48 N/mm2 for steel percentage = 0.5. For a factored shear force of 45 kN, the diameter (mm) of Fe 500 steel 2 legged stirrups to be used at spacing of 325 mm should be
Ans.
(a) 8
(b) 10
(c) 12
(d) 16
(a) 230
450
4 × 12φ
τuc = 0.36 N/mm2 [For M20] for
A st × 100 = 0.25 bd
τuc = 0.48 N/mm2 [For M20] for
A st × 100 = 0.5 bd
Factored SF = 45 kN = Vu
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We have to calculate the dia of Fe 500 2-L egged stirrup to be used at a spacing of 325 mm c/c
τv =
Vu 45 × 1000 = = 0.4348 N/mm 2 bd 230 × 450
π (12)2 4 × 100 = 0.437 % % tensile steel = 230 × 450 4×
τc = 0.36 + Since
0.12 × (0.437 − 0.25 ) = 0.45 N/mm 2 0.25
τv – τc < 0
⇒
Min shear reinforcement is required
⇒
Min shear reinforcement is given by 0.4 A sv = 0.87 f bS v y
Asv =
0.4 × (S v )( b ) 0.87 f y
Since we limit fy to 415 N/mm2 hence, Asv = 2 ×
π 0.4 × 325 × 230 ( φ )2 = 0.87 × 415 = 82.814 mm 2 4
φ = 7.26 mm adopt φ = 8 mm
Q.29
Ans.
16 MLD of water is flowing through a 2.5 km long pipe of diameter 45 cm. The chlorine at the rate of 32 kg/d is applied at the entry of this pipe so that disinfected water is obtained at the exit. These is a proposal to increase the flow through the pipe to 22 MLD from 16 mLD. Assume the dilution coefficient n = 1. The minimum amount of chlorine (in kg per day) to be applied to achieve the same degree of disinfection for the enhanced flow is (a) 60.5 (b) 4.4 (c) 38 (d) 23.27 (a) In the disinfection process we have the relationship, tCn = K where
t = time required to kill all organism
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c = concentration of disinfectant n = dilution coefficient k = constant
t1 C1n = t2 C2n
⇒
in our case n = 1 t 1C 1 = t 2 C 2
⇒
L t1 = v 1
L = length of pipe ; V1 = velocity of flow
C1 =
t1 =
L Q1 / A
t1 =
LA Q1
W1 , where W1 = weight of disinfectant per day ; Q1 = discharge per Q1
day ⇒
LA W2 LA W1 × × = Q2 Q2 Q1 Q1 2
⇒
Q.30
Ans.
Q22 ⎛ 22 ⎞ × W1 = ⎜ ⎟ × 32 kg / day = 60.5 kg/day 2 ⎝ 16 ⎠ Q1
W2 =
A rectangular channel flow have bed slope of 0.0001 width = 3 m coefficient n = 0.015, Q = 1 m3/sec given that normal depth of flow ranges between 0.76 m and 0.8 m. The minimum width of throat (in m) that is possible at a given section while ensuring that the prevailing normal depth does not exceed along the reach upstream of the concentration is approximately, equal to (assume negligible loss) (a) 0.64
(b) 0.84
(c) 1.04
(d) 1.24
(b) n = 0.015 Q = 1 m3/s Normal depth of flow between 0.76 m to 0.8 m.
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If prevailing normal depth of flow is not exceeded, there must not be chocking of the section or there must be just chocking. Thus the width of the section should be such that for the prevailing specific energy there should be critical flow at the contracted section i.e.
⇒
3 ⎛ q2 ⎞ 2 ⎜⎝ g ⎟⎠ ⎡⎛ Q ⎞2 ⎤ ⎢ ⎥ 3 ⎢ ⎜⎝ B min ⎟⎠ ⎥ ⎥ 2⎢ g ⎢ ⎥ ⎢ ⎥ ⎣ ⎦
1/3
= EC = Einitial 1/3
= Einitial
Let is now calculate Einitial Q=
1 AR 2/3 S1/2 0 2
⇒
1=
1 ⎛ 3y ⎞ 3y ) ⎜ ( ⎝ 3 + 2y ⎟⎠ 0.015
⇒
y = 0.78 m
⇒
Einitial = y +
2/3
(0.0001)1/2
q2 2gy 2
= 0.78 +
⎛ 1⎞ ⎜⎝ 3 ⎟⎠
2
2 × 9.81 × (0.78)
2
= 0.7893 m
1/3
⇒
⎡⎛ Q ⎞2 ⎤ ⎢ ⎥ 3 ⎢ ⎜⎝ B min ⎟⎠ ⎥ ⎥ 2⎢ g ⎢ ⎥ ⎢ ⎥ ⎣ ⎦
⇒
(1) 3 2 g1/3 ( Bmin )2/3 = 0.7893
= 0.7893
2/3
Bmin = 0.836 m
Q.31
A levelling is carried out to established the reduced level (RL) of point R with respect to the bench mark (BM) at P. The staff reading taken are given below
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Staff station
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BS
IS FS RL − − 1.655 − −0.95 − −1.5 −
P Q R
–
0.75
−
−
If RL of P is + 100 m, then RL (m) of R is (a) 103.355 (b) 103.155 (c) 101.455 (d) 100.355 Ans.
(c) HI = RL + BS and
RL = HI – FS Staff station P Q R
BS
IS FS RL HI RL − − 101.655 1.655 − 100 −0.95 − −1.5 − 102.205 103.155 –
Ans.
0.75
−
−
101.455
RL of R = 101.455 m
∴
Q.32
−
A given cohensionless soil has emax = 0.85, emin = 0.5. In the field, the soil is compacted to a mass density of 1800 kg/m3 at water content of 8%. Take the mass density of water as 1000 kg/m3 and GS = 2.7. (a) 56.43
(b) 60.25
(c) 62.87
(d) 65.41
(d) e max = 0.85 emin = 0.5 ρfield = 1800 kg/m3 at water content = 8% ρw = 1000 kg/m3 G S = 2.7 Relative density, ID = ? ρ= ⇒ ⇒ ⇒
1 + e=
Gρ w (1 + w ) 1+e
=
2.7 × 1000 (1.08 ) 1+e
2.7 × 1000 × 1.08 1800
e = 0.62 e max − e × 100 ID = e max − e min
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=
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0.85 − 0.62 × 100 0.85 − 0.5
= 65.714 %
Q.33
Then tension and shear force (both in kN) at both joints as shown below are respectively
4 5 3 Pu = 250 kN
(a) 30.3 and 20 (c) 33.33 and 20 Ans.
(b) 30.33 and 25 (d) 33.33 and 25
(d)
θ
Pu cos θ =
Tension in each bolt =
tanθ =
3 4
cosθ =
4 5
sinθ =
3 5
Pu cos θ =
3 Pu 5
4 Pu 5
Pu
4Pu 5×6 4 × 250 = 33.33 kN 5×6 3Pu 3 × 250 = 5×6 5×6 = 25 kN
Shear in each bolt =
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GATE-2014 Exam Solutions
Page 18
Civil Engineering (Morning Session) Q.34
For a sample of water with the ionic composition shown below, the Carbonate and Non-carbonate hardness concentration (in mg/l as CaCO3) respectively are. 0
4
meq/l
Ca
meq/l
HCO3
2+
5 Mg
–
7
2+
Na 2–
SO4 3.5
(a) 200 and 500 (c) 75 and 175 Ans.
+
7
(b) 175 and 75 (d) 50 and 200
(c) Carbonate hardness = 3.5 × 10–3 g-eq [if NCH is present sodium alkalinity will be absent i.e. NaHCO3 absent] −3 = 3.5 × 10 ×
50g as CaCO3 l
= 175 mg/l as CaCO3 Non carbonate hardness = total hardness-carbonate hardness Total hardness = 5 × 50 mg/l as CaCO3 [total hardness is due to Ca2 Mg2+]
+
and
= 250 mg/l as CaCO3 ⇒
Q.35
NCH = 250 – 175 = 75 mg/l as CaCO3
Group-I P. Curve J Q. Curve K R. Curve L
Group-II 1. No apparent heaving of soil around the footing. 2. Rankine passive zone develops imperfectly 3. Well defined slip surface extends to ground surface. Load
Settlement
J
(a) P-1, Q-3, R-2 (c) P-3, Q-1, R-2
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K
L
(b) P-3, Q-2, R-1 (d) P-1, Q-2, R-3
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(d) L → General shear failure K → Local shear failure J → Punching shear failure
Q.36
Ans.
A horizontal jet of water with its cross section area 0.0028 m2 hits a fixed vertical plate with a velocity of 5 m/s. After impact the jet split symmetrically in a plane parallel to the plane of the plate. The force of impact (in N) of the jet on the plate is (a) 90
(b) 80
(c) 70
(d) 60
(c)
5 m/s area of jet = 0.0028 m 2
Force on plate = (ρ w a V ) V = ρ w aV 2 = 1000 × 0.0028 × (5)2 = 70 N
Q.37
In a simply supported beam of length L four influence line diagram for shear at a section located at a distance of L/4 from the left support marked (P, Q, R, S) are shown below the correct, ILD is 0.75
P.
L/4
0.6
3L/4
Q.
L/4
3L/4
0.6
0.25 0.5
R.
L/4
3L/4
S. L/4
3L/4
0.5
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(b) Q (d) S
(a) X B
A L/4
3L/4
1 unit 0.75 + – 0.25 1 unit
X
ILD for SF at X-X i.e., option (a)
Q.38
Ans.
A long slope is formed in a soil with shear strength parameter C′ = 0, φ′ = 34°. Firm strate lies below the slope and it is assumed that water table may occasionally rise to the surface, with seepage taking place parallel to the slope. Use γsat = 18 kN/m3 and γw = 10 kN/m3. maximum slope angle (in degree) to ensure the factor of safety 1.5. Assuming a potential failure surface parallel to the slope would be (a) 45.3
(b) 44.7
(c) 12.3
(d) 11.3
(d)
C′ = 0 φ = 34°
γsat = 18 kN/m γw = 10 kN/m
3
3
β
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Page 21
γ sub . tan φ FOS = γ sat tan β
⇒
⎛ γ sub tan φ ⎞ . tan β = ⎜ ⎝ γ sat FOS ⎟⎠
⇒
γ sub . tan φ tan β = γ 1.5 sat
tan β =
18 × 1.5
β = 11.30°
⇒
Q.39
(18 − 10) × tan 34°
For the truss shown below, the member PQ is short by 3 mm. The magnitude of the vertical displacement of joint R in mm is ________. R
3m
Q
P
4m
4m
Sol. PQ is short by 3 mm We have to find out vertical displacement of joint R in mm Δ R = ∑u (λ) Let in apply unit load at R as shown below R uPR
P
θ
R
Q
u PQ
1/2
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1/2
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uPR sin θ =
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Page 22
1 2
uPQ + uPR cos θ = 0 u P Q = –uPR cos θ = − uPQ = −
−1 × 4 / 3 −2 1 = cot θ = 2 2 3
Δ R = u PQ × λ PQ =
Q.40
1 . cos θ 2 sin θ
−2 ( −3) = 2 mm upwards 3
The smallest angle of a triangle is equal to two third of the smallest angle of a quadrilateral. The ratio between the angle of the quadrilateral is 3 : 4 : 5 : 6. The largest angle of the triangle is twice its smallest angle, what is the sum, in degrees of the second largest angle of the triangle and the largest angle of the quadrilateral.
Sol. θ2 θ3
3α
4α
5α
6α
θ1
18α = 360 α = 20°
Largest angle of quadrilateral = 120° Smallest angle of quadrilateral = 60° ⇒
Smallest angle of triangle =
2 × (2 × 20) = 40° 3
Largest angle of triangle = 2 × 40 = 80° ⇒
Third angle of triangle = 60°
⇒ Sum of largest angle of quadrilateral and second largest angle of triangle = 120° + 60° = 180°
Q.41
A straight 100 m long raw water gravity main is to carry water from intake to the jackwell of a water treatment plant. The required flow of water is 0.25 m3/s. Allowable velocity through main is 0.75 m/s. Assume f = 0.01, g = 9.81. The minimum gradient (in cm/100 length) required to be given to this main so that water flow without any difficulty should be ________ .
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Sol. Q = 0.25 m3/s Allowable velocity = 0.75 m/s f = 0.01 g = 9.81 Q 0.25 1 2 πd 2 = = m = V 0.75 3 4
d = 0.6515 m
⇒ ⇒
2 flv 2 0.01 × 100 × ( 0.75 ) = hf = m 2gd 2 × 9.81 × 0.6515
= 0.044 m = 4.4 cm ⇒ Minimum gradient =
hf 4.4 cm = 100 m l
Hence answer is 4.4.
Q.42
For a beam cross section W = 230 mm, effective depth = 500 mm, the number of reinforcement bars of 12 mm diameter required to satisfy minimum tension reinforcement requirement specified by IS-456-2000 (assume grade of steel is Fe500) is __________.
Sol. A st min bd
=
A st = n=
0.85 fy 0.85 × 230 × 500 mm 2 500 A st πd 4
2
=
0.85 × 230 π (12 )2 4
= 1.729 = 2 bars
Q.43
The perception - reaction time for a vehicle travelling at 90 km/h, given the coefficient of longitudinal friction of 0.35 and the stopping sight distance of 170 m (assume g = 9.81 m/s2) is ________ seconds.
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Sol. SSD =
Q.44
⇒
170 =
⇒
tr =
0.278 vt r
2 0.278 v ) ( +
2gf
0.278 × 90 × tr +
(0.278 × 90)2
2 × 9.81 × 0.35
3.1510 sec.
A traffic office impose on an average 5 number of penalties daily on traffic violators. Assume that the number of penalties on different day is independent and follows a Poisson distribution. The probability that there will be less than 4 penalties in a day is _________.
Sol. Mean λ = 5 P (x < 4) = p (x = 0) + p (x = 1) + p (x = 2) + p (x = 3) =
e −5s 0 e −5 51 e −5 52 e −5 53 + + + 0! 1! 1! 3!
25 125 ⎤ ⎛ 118 ⎞ −5 ⎡ + = e −5 ⎜ = 0.265 = e ⎢1 + 5 + ⎝ 3 ⎟⎠ 2 6 ⎥⎦ ⎣
Q.45
Ans.
The speed-density (v-k) relationship on a single lane road with unidirectional flow is v = 70 – 0.7 K, where v is in km/hr and k is in veh/km. The capacity of the road (veh/hr) is (a) Capacity = Velocity × Density ⇒
C = V × K = 70 K – 0.7 K2
Now,
dC = 70 – 1.4 K = 0 dK
⇒
K = 50
⇒ Capacity,
C = 70 × 50 – 0.7(50)2 = 1750 veh/hr
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GATE-2014 Exam Solutions Civil Engineering (Morning Session) Q.46
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Page 25
A particle moves along a curve whose parametric equation are x = t3 + 2t, y = –3e-2t and z = 2 sin (5t), where x, y and z show variation of the distance covered by the particles in (cm) with time (t) (in second). The magnitude of the acceleration of the particle (in cm/s2) at t = 0 is __________.
Sol. x = t3 + 2t y = –3 e–2t z = 2 sin (5t) dx = 3 t2 + 2 dt
ax =
⇒
d 2x
= 6t
dt 2
dy = – 3 e–2t × (–2) = 6 e–2t dt
ay =
⇒ ⇒
d 2y
= −12 e −2t
dt 2
dz = –10 × 5 sin (5t) = –50 sin5t dt
az =
⇒
d 2z
= −50 sin 5t
dt 2
a = a x iˆ + a y ˆj + a z kˆ a at t = 0 = 0 iˆ − 12 ˆj + 0 kˆ a = − 12 ˆj
⇒
Q.47
Magnitude of acceleration at t = 0 = 12 cm/s2
For a cantilever beam of a span 3m as shown a concentrated load of 20 kN applied to the free end causes a vertical displacement of 2 mm at a section located at a distance of 1 m from the fixed end (with no other load on the beam) the maximum vertical displacement in the same (in mm) is ___________. 20 kN
2 mm
1m
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2m
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Sol. 20 kN
Δ12
1m
2m
10 kN 1m
2m
Δ21
From Betti’s law
P1 × Δ12 = P2 × Δ21 10 × 2 = 20 × Δ21
⇒
Δ21 = 1 mm
⇒
Q.48
An isolated three-phase traffic signal is designed by webster’s method. The critical flow ratio for three phase are 0.2, 0.3 and 0.25 respectively and lost time per phase is 4 second. The optimum cycle length (in sec.) is ________.
Sol. Sum of the flow,
y = y1 + y2 + y3 = 0.2 + 0.3 + 0.25 = 0.75
Total lost time in a cycle L = 4 × 3 = 12 sec. Optimum cycle length,
C0 =
1.5L + 5 1−y
1.5 × 12 + 5 = 92 sec. 1 − 0.75
Q.49
Mathematical idealization of a crane has three bar with their vertices arranged as shown with load of 80 kN hanging vertically. The coordinate of the vertices are given in parenthesis. The force in member QR is ______.
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Page 27
P(0,4)
22 .8
80 kN
4°
10
y
4 .0
Q(1,0)
x
3°
55.13°
R(3,0)
55.13°
R(3,0)
Sol. P(0,4) 22.84° φ 80 kN
θ
4m
10
4 .0
Q(1,0)
3°
VQ
VR
1m 3m
VQ + VR = 80
...(i)
ΣM R = 0 ⇒
80 × 3 = VQ × 2 VQ = 120 kN
⇒
V R = –40 kN tanφ =
⇒
⇒
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From eq. (i)
1 4
1 4 , cos φ = 17 17
sinφ = tanθ =
3 4
cosθ =
4 5
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Page 28
Consider joint Q F PQ α F QR VQ
α = 104.03° – 90° = 14.03° ΣFy = 0 FPQ cosα = +VQ = 0
⇒
FPQcos14.03° + 120 = 0
⇒
FPQ = –123.6897 kN
⇒
ΣFx = 0 FPQ sinα = FQR
⇒
FQR = –29.986 kN ≈ 30 kNm
Q.50
The flow net constructed for a dam is shown in the figure below. Taking coefficient of permeability as 3.8 × 10–6 m/s, the quantity of flow (in cm3/sec) under the dam per m is _________. 50m
6.3 m 1.6 m
17.2 m
9.4 m
Sol. Quantity of flow,
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Q = KH
Nf Nd
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Page 29
Nf = No. of flow channels = 3 Nd =
No. of equipotential drops = 10
Given,
K = 3.8 × 10–6 m/s
and
H = 6.3 m −6 Q = 3.8 × 10 × 6.3 ×
∴
3 10
= 7.182 × 10–6 m3/s/m = 7.182 × 10–6 × 106 cm3/s/m Q = 7.182 cm3/s/m
Q.51
The full data are given for laboratory sample σ′0 = 175 kPa, e0 = 1.1 σ′0 + Δσ′0 = 300 kPa, e = 0.9. If thickness of the clay specimen is 25 mm, the value of coefficient of volume compressibility is ________ × 10–4 m2/kN.
Sol.
Δe av = Δσ mv = 1 + e0 1 + e0 =
(1.1 − 0.9) 125 × 2.1
= 7.619 × 10–4 m2/kN
Q.52
Ans.
The reinforced concrete section, the stress at extreme fibre in compression is 5.8 MPa. The depth of Neutral Axis in the section is 58 mm and grade of concrete is M25. Assuming Linear elastic behavior of the concrete, the effective curvature of the section (in per mm) is (a) 2 × 10–6 (b) 3 × 10–6 –6 (c) 4 × 10 (d) 5 × 10–6 (c) 5.8 MPa
B Xu = 58 mm d
M25 conrature
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Modulus of elasticity of concrete E = 5000 25 = 25000 N/mm2 ∴
σ E M = = y R I
⇒
σ 5.8 5.8 1 = = = Ey EX u 58 × 25000 R
= 4 × 10–6 Per mm ⇒
Q.53
Curvature = 4 × 10–6 per mm
A venturimeter having diameter of 7.5 cm at the throat and 15 cm at the enlarged end is installed in a horizontal pipeline of 15 cm diameter. The pipe carries incompressible fluid at steady rate of 30 l/s. The difference of pressure head measured in terms of the moving fluid in between the enlarged and the throat of the vent is observed to be 2.45 m. Taking the g = 9.8 m/s2, the coefficient of discharge of venturimeter (correct upto 2 decimal) is _________.
Sol. 1
2
15 cm φ
7.5 cm φ
1
2
Q = 30 l/s ⎛ P1 ⎞ ⎛P ⎞ + Z1 ⎟ − ⎜ 2 + Z 2 ⎟ = 2.45 m = h ⎜⎝ ⎠ ⎝w ⎠ w
g = 9.81 Q = Cd
Cd =
A1 A 2 A12 − A 22
Q A1 A 2 A12 − A 22
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2gh
2gh
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30 × 30 −3 m 3 /s π (0.15)2 × (0.075)2 4 × 2 × 9.81 × 2.45 2 2 0.15 − 0.075 ( ) ( )
Cd = 0.95
Q.54
A traffic surveying conducted on a road yield an average daily traffic count of 5000 vehicle. The axle load distribution on the same road is given in the following table. Axle load (tones) Frequency of traffic (f) 18
10
14
20
10
35
8
15
6
20
The design period of the road is 15 years. The yearly Traffic growth rate is 7.5% the load safety factor (LSF) is 1.3. If the vehicle damage factor (VDF) is calculated from the above data, the design traffic (In million standard axle load MSA) is _______ . Sol. Calculation of vehicle damage factor 4
VDF =
y
4
4
⎛W ⎞ ⎛W ⎞ ⎛W ⎞ ⎛W ⎞ ⎛W ⎞ V1 ⎜ 1 ⎟ + V2 ⎜ 2 ⎟ + V3 ⎜ 3 ⎟ + V4 ⎜ 4 ⎟ + V5 ⎜ 5 ⎟ ⎝ Ws ⎠ ⎝ W3 ⎠ ⎝ Ws ⎠ ⎝ Ws ⎠ ⎝ Ws ⎠ V1 + V2 + V3 + V4 + V5
4
where Ws = standard axle load = 80 kN = 8.2 tonn 4
4
4
4
⎛ 18 ⎞ ⎛ 14 ⎞ ⎛ 10 ⎞ ⎛ 8 ⎞ ⎛ 6 ⎞ + 20 ⎜ + 35 ⎜ + 15 × ⎜ + 20 × ⎜ 10 ⎜ ⎝ 8.2 ⎟⎠ ⎝ 8.2 ⎟⎠ ⎝ 8.2 ⎟⎠ ⎝ 8.2 ⎟⎠ ⎝ 8.2 ⎟⎠ ⇒ VDF = 10 + 20 + 35 + 15 + 20
4
= 4.989
⇒
N =
365 × 5000 ⎡⎣(1.075)15 − 1⎤⎦ × 4.989 0.075
= 237.806 MSA
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GATE-2014 Exam Solutions Civil Engineering (Morning Session) Q.55
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Page 32
An incompressible fluid is flown at steady rate in horizontal pipe. From a section the pipe divides into two horizontal parallel pipes of diameter (d1 and d2) that run, for a distance of L each and then again join back to a pipe of the original size. For both the pipes, assume the head loss due to friction only and the Darcy-weisbach friction factor to be same. The velocity ratio between bigger and smaller branched pipe is _________.
Sol. d1
C Q1 B
A
Q2 d2
D L
d 1 = 4d2
flv12 flv 22 = 2gd1 2gd 2 ⇒
V12 V22 = d1 d2 V12 V22
=
d1 =4 d2
v1 = 2 v2
Section - II (General Aptitude) One Mark Questions Q.56
Rajan was not happy that Sajan decided to do the project on his own on observing his unhappiness, sajan explained to Rajan that he preferred to work independently. Which one of the statement below is logically valid and can be inferred from the above sentences? (a) Rajan has decided to work only in group. (b) Rajan and Sajan were formed into a group against their wishes. (c) Sajan decided to give into Rajan’s request to work with him. (d) Rajan had believed that Sajan and he would be working together.
Ans.
(d)
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GATE-2014 Exam Solutions Civil Engineering (Morning Session) Q.57
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Page 33
A boundary has a fixed daily cost of Rs 50,000 whenever it operates and variable cost of Rs. 8000 Q, where Q is the daily production in tonnes. What is the cost of production in Rs. per tonne for a daily production of 100 tonnes.
Sol. Total cost for
100 tonne = 8000 × 100 + 50000 = 850000
Cost per tonne =
Q.58
Ans.
Q.59
850000 = Rs. 8500/tonne. 100
Choose the most appropriate word from the option given below to complete the following sentences, one of his biggest _______ was his ability to forgive. (a) Vice (b) Virtues (c) Choices (d) Strength (b)
A student is required to demonstrate a high level of comprehension for the subject, especially in the social sciences. The word closes in meaning to comprehension is (a) Understanding (b) Meaning (c) Concentration (d) Stability
Ans.
Q.60
Ans.
(a)
Find the odd one in the following group ALRVX, EPVZB, ITZDF, OYEIX (a) ALRVX (b) EPVZB (c) ITZDF (d) OYEIX (d)
Two Marks Questions Q.61
One percent of the people of country X are taller than 6 ft, 2 percent of the people of country Y are taller than 6 ft. There are thrice as many people in country X as in country Y. Taking both countries together. What % of people are taller than 6 ft? (a) 3 (b) 2.5 (c) 1.5 (d) 1.25
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Page 34
(d) Let the population of county Y is P ∴ Population of country X is 3P 3P × 1 P × 2 + 100 100 % of people taken than 6 ft = 3P + P
= 1.25
Q.62
Ans.
With reference to the conventional certesion (X, Y) the vertices of a triangle have x1, y1 = 1, 0, x2, y2 = 2, 2, and x3, y3 = 4, 3, the area of triangle is (a)
3 2
(b)
3 4
(c)
4 5
(d)
5 2
(a) y C(4,3)
Area of triangle is p ( p − a )( p − b )( p − c )
A=
a+b+c when P = 2
B(2,2)
c
a
b
a=
( 4 − 2 )2 + ( 2 − 1)2
b=
( 4 − 1 ) 2 + (3 ) 2
=3 2
c =
(2 − 1)2 + (2 )2
= 5
p =
5 + 5 +3 2 3 = 5+ 2 2
A=
3 ⎞⎛ 3 3 3 ⎛ ⎞⎛ ⎞⎛ ⎞ − 3 2⎟ ⎜ 5 + − 3 2⎟ ⎜ 5 + − 5⎟ ⎜⎝ 5 + ⎟⎠ ⎜⎝ 5 + ⎠ ⎝ ⎠ ⎝ ⎠ 2 2 2 2
=
= 5
A(1,0)
3 2
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