GATE CE 2013: Civil Engineering
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2013 CIVIL ENGINEERING - CE
CE:CIVIL ENGINEERING
Duration: Three Hours Maximum Marks:100
Please read the following instructions carefully:
General Instructions:
1. Total duration of examination is 180 minutes (3 hours).
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multiple choice type questions will not be shown.
CE 1/16
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2013 CIVIL ENGINEERING - CE
Answering a Question
6. Procedure for answering a multiple choice type question:
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e. To mark the question for review, click on the Mark for Review and Next button. If an
answer is selected for a question that is Marked for Review, that answer will be considered
in the evaluation.
7. Procedure for answering a numerical answer type question:
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e. To mark the question for review, click on the Mark for Review and Next button. If an
answer is entered for a question that is Marked for Review, that answer will be considered
in the evaluation.
8. To change your answer to a question that has already been answered, first select that question for
answering and then follow the procedure for answering that type of question.
9. Note that ONLY Questions for which answers are saved or marked for review after answering will be
considered for evaluation.
CE 2/16
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2013 CIVIL ENGINEERING - CE
Paper specific instructions:
1. There are a total of 65 questions carrying 100 marks. Questions are of multiple choice type or
numerical answer type. A multiple choice type question will have four choices for the answer with
only one correct choice. For numerical answer type questions, the answer is a number and no choices
will be given. A number as the answer should be entered using the virtual keyboard on the monitor.
2. Questions Q.1 – Q.25 carry 1mark each. Questions Q.26 – Q.55 carry 2marks each. The 2marks
questions include two pairs of common data questions and two pairs of linked answer questions. The
answer to the second question of the linked answer questions depends on the answer to the first
question of the pair. If the first question in the linked pair is wrongly answered or is not attempted,
then the answer to the second question in the pair will not be evaluated.
3. Questions Q.56 – Q.65 belong to General Aptitude (GA) section and carry a total of 15 marks.
Questions Q.56 – Q.60 carry 1mark each, and questions Q.61 – Q.65 carry 2marks each.
4. Questions not attempted will result in zero mark. Wrong answers for multiple choice type questions
will result in NEGATIVE marks. For all 1 mark questions, ⅓ mark will be deducted for each wrong
answer. For all 2 marks questions, ⅔ mark will be deducted for each wrong answer. However, in the
case of the linked answer question pair, there will be negative marks only for wrong answer to the
first question and no negative marks for wrong answer to the second question. There is no negative
marking for questions of numerical answer type.
5. Calculator is allowed. Charts, graph sheets or tables are NOT allowed in the examination hall.
6. Do the rough work in the Scribble Pad provided.
CE 3/16
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2013 CIVIL ENGINEERING - CE
Q. 1 – Q. 25carries one mark each.
Q.1 There is no value of x that can simultaneously satisfy both the given equations.Therefore, find the
‘least squares error’ solution to the two equations, i.e., find the value of that minimizes the sum of
squares of the errors in the two equations. __________
2 3
4 1
Q.2 What is the minimum number of multiplications involved in computing the matrix product PQR?
Matrix has 4 rows and 2 columns, matrix has 2 rows and 4 columns, and matrix has 4 rows and
1 column. __________
Q.3 A 1-h rainfall of 10 cm magnitude at a station has a return period of 50 years. The probability that
a 1-h rainfall of magnitude 10 cm or more will occur in each oftwo successive years is:
(A) 0.04 (B) 0.2 (C)0.02 (D) 0.0004
Q.4 Maximum possible value of Compacting Factor for fresh (green) concrete is:
(A) 0.5 (B) 1.0 (C) 1.5 (D) 2.0
Q.5 As per IS 800:2007, the cross-section in which the extreme fiber can reach the yield stress, but
cannot develop the plastic moment of resistance due to failure by local buckling is classified as
(A) plastic section (B) compact section
(C) semi-compact section (D) slender section
Q.6 The creep strains are
(A) caused due to dead loads only
(B) caused due to live loads only
(C) caused due to cyclic loads only
(D) independent of loads
Q.7 As per IS 456:2000 for M20 grade concrete and plain barsin tension the design bond stress
1.2 .Further, IS 456:2000 permits this design bond stress value to be increased by 60 %
for HSD bars. The stress in theHSDreinforcing steel barsin tension, 360 . Find the
required development length, , for HSD barsin terms of the bar diameter, . __________
Q.8 The ‘plane section remains plane’ assumption in bending theory implies:
(A) strain profile is linear
(B) stress profile is linear
(C) both strain and stress profiles are linear
(D)shear deformations are neglected
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2013 CIVIL ENGINEERING - CE
Q.9 Two steel columns P (length and yield strength 250 ) and Q (length 2 and yield
strength 500 ) have the same cross-sections and end-conditions. The ratio of buckling
load of column P to that of column Q is:
(A) 0.5 (B) 1.0 (C) 2.0 (D) 4.0
Q.10 The pin-jointed 2-D truss is loaded with a horizontal force of 15 at joint S and another 15
vertical force at joint U, as shown.Find the force in member RS (in ) and report your answer
taking tension as positive and compression as negative. __________
4m 4m 4m
R S
15
4m
Q V U T
4m
15
W
Q.11 A symmetric I-section (with width of each flange 50 , thickness of each flange 10 ,
depth of web = 100 mm, and thickness of web 10 ) of steel is subjected to a shear force of
100 . Find the magnitude of the shear stress(in / in the web at its junction with the top
flange. __________
Q.12 In its natural condition, a soil sample has a mass of 1.980 and a volume of0.001 . After
being completely dried in an oven, the mass of the sample is 1.800 .Specific gravity is 2.7.
Unit weight of water is 10 / . The degree of saturation of the soil is:
(A) 0.65 (B) 0.70 (C) 0.54 (D) 0.61
Q.13 The ratio Nf/Nd is known as shape factor, where Nf is the number of flow lines and Nd is the
number of equipotential drops. Flow net is always drawn with a constant b/a ratio, where b and a
are distances between two consecutive flow lines and equipotential lines, respectively. Assuming
that b/a ratio remains the same, the shape factor of aflow net will change if the
(A) upstream and downstream heads are interchanged
(B) soil in the flow space is changed
(C) dimensions of the flow space are changed
(D) head difference causing the flow is changed
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2013 CIVIL ENGINEERING - CE
Q.14 Following statementsare made on compacted soils, wherein DS stands forthe soils compacted on
dry side of optimum moisture content and WS stands for thesoils compacted on wet side of
optimum moisture content. Identify the incorrect statement.
(A) Soil structure is flocculated onDS and dispersed on WS.
(B) Construction pore water pressure is low on DS and high on WS.
(C)On drying, shrinkage is high on DS and low on WS.
(D)On access to water, swelling is high on DS and low on WS.
Q.15 Four columns of a building are to be located within a plot size of 10 m x 10 m. The expected load
on each column is 4000 kN. Allowable bearing capacity of the soil deposit is 100 kN/m2. The type
of foundation best suited is
(A) isolated footing (B) raft foundation
(C) pile foundation (D)combined footing
Q.16 For subcritical flow in an open channel, the control section for gradually varied flow profiles is
(A) at the downstream end (B) at the upstream end
(C) at both upstream and downstream ends (D) at any intermediate section
Q.17 Group-I contains dimensionless parameters and Group- II contains the ratios.
Group-I Group -II
P. Mach Number 1. Ratio of inertial force and gravitational force
Q. Reynolds Number 2. Ratio of fluid velocity and velocity of sound
R. Weber Number 3. Ratio of inertial force and viscous force
S. Froude Number 4. Ratio of inertial force and surface tension force
The correct match of dimensionless parameters in Group- I with ratios in Group-II is:
(A) P-3, Q-2, R-4, S-1 (B) P-3, Q-4, R-2, S-1
(C) P-2, Q-3, R-4, S-1 (D) P-1, Q-3, R-2, S-4
Q.18
For a two dimensional flow field, the stream function is given as
3 2
2
y x 2 . The
magnitude of discharge occurring between the stream lines passing through points (0,3) and (3,4)
is:
(A) 6 (B) 3 (C) 1.5 (D) 2
Q.19 An isohyet is a line joining points of
(A) equal temperature (B) equal humidity
(C) equal rainfall depth (D) equal evaporation
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2013 CIVIL ENGINEERING - CE
Q.20 Some of the water quality parameters are measured by titrating a water sample with a titrant.
Group-I gives a list of parameters and Group-IIgives the list of titrants.
Group-I Group-II
P.Alkalinity 1. N/35.5 AgNO3
Q. Hardness 2. N/40 Na2S2O3
R. Chloride 3. N/50 H2SO4
S. Dissolved oxygen 4. N/50 EDTA
The correct match of water quality parameters in Group-I with titrants in Group-II is:
(A) P-1, Q-2, R-3, S-4 (B)P-3, Q-4, R-1, S-2
(C)P-2, Q-1, R-4, S-3 (D) P-4, Q-3, R-2, S-1
Q.21 A water treatment plant is designed to treat 1 m3/s of raw water. It has 14 sand filters. Surface area
of each filter is 50 m2. What is the loading rate (in ) with two filters out of service for routine
∙
backwashing? __________
Q.22 Selectthe strength parameter of concrete usedindesign of plain jointed cement concrete pavements
from the following choices:
(A) Tensile strength
(B) Compressive strength
(C) Flexural strength
(D) Shear strength
Q.23 It was observed that 150 vehicles crossed a particular location of a highway ina duration of 30
minutes. Assuming that vehicle arrival follows a negative exponential distribution, find out the
number of time headways greater than 5 seconds in the above observation? __________
Q.24 For two major roads with divided carriageway crossing at right angle,a full clover leaf interchange
with four indirect ramps is provided. Following statements are made on turning movements of
vehiclesto all directions from both roads. Identify the correct statement:
(A) Merging from left is possible,butdiverging to left is notpossible.
(B) Both merging from left and diverging to left arepossible.
(C) Merging from left is not possible,butdiverging to left is possible.
(D) Neithermergingfrom left nordivergingto leftispossible.
Q.25 The latitude and departure of a line AB are +78 m and -45.1 m, respectively. The whole circle
bearing of the line AB is:
(A) 30° (B) 150° (C) 210° (D) 330°
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Q. 26 to Q. 55 carry two marks each.
Q.26 The state of 2D-stress at a point is given by the following matrix of stresses:
100 30
30 20
What is the magnitude of maximum shear stressin MPa?
(A) 50 (B) 75 (C) 100 (D) 110
Q.27 Find the magnitude of the error (correct to two decimal places) in the estimation of following
1
integral using Simpson’s Rule. Take the step length as 1. __________
3
4
x 10dx
4
0
Q.28 6
cos 3 sin 6 d is:
4 3
The solution for
0
1 8
(A) 0 (B) (C) 1 (D)
15 3
Q.29 Find the value of λ such that the function f (x ) is a valid probability density function. __________
f ( x) ( x 1)(2 x) for 1 x 2
0 otherwise
Q.30 Laplace equation for water flow in soils is given below.
2H 2H 2H
0
x 2 y 2 z 2
Head H does not vary in y and z directions.
dH
Boundary conditions are: at x = 0, H = 5;and 1 .
dx
What is the value of H at x = 1.2? __________
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Q.31 All members in the rigid-jointed frame shown are prismatic and have the same flexural stiffness .
Find the magnitude of the bending moment at Q (in ) due to the given loading. __________
3m 4m
S
2m
P T R
100 kNm
2m
Q
Q.32 A uniform beam in the form of a quarter-circle of radius is fixed at end
and free at the end , where a load is applied as shown. The vertical downward displacement,
, at the loaded point is given by: . Find the value of (correct to 4-decimal
places). __________
Q
W
R
P
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2013 CIVIL ENGINEERING - CE
Q.33 A uniform beam weighing 1800 is supported at E and F by cable ABCD. Determine the tension
(in in segment AB of this cable (correct to 1-decimal place). Assume the cables ABCD, BE and
CF to be weightless. __________
Q.34 Beam has internal hinges in spans and as shown. The beammay be subjected to a
moving distributed vertical load of maximum intensity 4 ⁄ of any length anywhere on the
beam. The maximum absolute value of the shear force (in ) that can occur due to this loading
just to the right of support Q shall be:
P Q R S
5m 5m 20 m 5m 5m
(A) 30 (B) 40 (C) 45 (D) 55
Q.35 A rectangular concrete beam 250 wide and 600 deep is pre-stressed by means of 16 high
tensile wires, each of 7 mm diameter, located at200 from the bottom face of the beamat a
given section. If the effective pre-stress in the wires is700 , what is the maximum sagging
bending moment (in ) (correct to 1-decimal place) due to live loadthat this sectionof the beam
can withstand without causing tensile stress at the bottom face of the beam? Neglect the effect of
dead load of beam. __________
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Q.36 The soil profile below a lake with water level at elevation 0 m and lake bottom at elevation
10 m is shown in the figure, where k is the permeability coefficient. A piezometer (stand pipe)
installed in the sand layer shows a reading of +10 m elevation. Assume that thepiezometric headis
uniform in the sand layer. The quantity of water (in m3/s) flowing into the lake from the sand layer
through the silt layer per unit area of the lake bed is:
Stand pipe
+10
0
Lake Lake bottom
-10
Silt (k = 10-6 m/s)
-30
Sand
(under artesian pressure)
-40
Rock
(A) 1.5 x 10-6 (B) 2.0 x 10-6
(C) 1.0 x 10-6 (D) 0.5 x 10-6
Q.37 The soil profile above the rock surface for a 25oinfinite slope is shown in the figure, where su is the
undrained shear strength and t is total unit weight. The slip will occur at a depth of
(A) 8.83 m (B) 9.79 m (C) 7.83 m (D) 6.53 m
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Q.38 Two different soil types (Soil 1 and Soil 2) are used as backfill behind a retaining wall as shown in
the figure, where t is total unit weight, and c' and ' are effective cohesion and effective angle of
shearing resistance. The resultant active earth forceper unit length (in kN/m) acting on the wall is:
Retaining wall
Soil 1:
2m t = 15 kN/m3; c' = 0; ' = 30o
Soil 2:
2m t = 20 kN/m3; c' = 0; ' = 40o
(A) 31.7 (B) 35.2 (C) 51.8 (D) 57.0
Q.39 A 2 km long pipe of 0.2 m diameter connects two reservoirs. The difference between water levels
in the reservoirs is 8 m. The Darcy-Weisbachfriction factor of the pipe is 0.04. Accounting for
frictional, entry and exit losses, the velocity in the pipe (in m/s) is:
(A) 0.63 (B)0.35 (C) 2.52 (D) 1.25
Q.40 The normal depth in a wide rectangular channel is increased by 10%. The percentage increase in
the discharge in the channel is:
(A) 20.1 (B) 15.4 (C) 10.5 (D) 17.2
Q.41 The transplantation of rice requires 10 days and total depth of water required during transplantation
is 48 cm. During transplantation, there is an effective rainfall (useful for irrigation) of 8 cm. The
duty of irrigation water (in hectares/cumec) is:
(A) 612 (B) 216 (C)300 (D) 108
Q.42 A settling tank in a water treatment plant is designed for a surface overflow rate of30 .
∙
Assumespecific gravity of sedimentparticles = 2.65, density of water (ρ) = 1000 kg/m3, dynamic
viscosity of water (µ)=0.001 N.s/m2,and Stokes’ lawisvalid.The approximate minimum size of
particles that would be completely removed is:
(A) 0.01mm (B) 0.02 mm(C) 0.03 mm(D) 0.04 mm
Q.43 A student began experiment for determination of 5-day, 20°C BOD on Monday. Since the 5thday
fell on Saturday, the final DO readings were taken on next Monday. On calculation, BOD (i.e. 7
day, 20°C) was found to be 150 mg/L. What would be the5-day, 20°C BOD (in mg/L)? Assume
value of BOD rate constant (k) at standard temperature of 20°C as 0.23/day (base e). __________
CE 12/16
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Q.44 Elevation and temperature data for a place are tabulated below:
Elevation, m Temperature, °C
4 21.25
444 15.70
Based on the above data, lapse rate can be referred as:
(A) Super-adiabatic (B) Neutral (C) Sub-adiabatic (D) Inversion
Q.45 The percent voids in mineral aggregate (VMA) and percent air voids (Vv) in a compacted
cylindrical bituminous mix specimen are 15 and 4.5respectively. The percent voids filled with
bitumen (VFB) for this specimen is:
(A) 24 (B) 30 (C) 54 (D) 70
Q.46 Following bearings are observed while traversing with a compass.
Line Fore Bearing Back Bearing
AB 126°45´ 308°00´
BC 49°15´ 227°30´
CD 340°30´ 161°45´
DE 258°30´ 78°30´
EA 212°30´ 31°45´
After applying the correction due to local attraction, the corrected fore bearing of line BC will be:
(A) 48°15´ (B)50°15´ (C) 49°45´ (D) 48°45´
Q.47 A theodolite is set up at station A and a 3 m long staff is held vertically at station B. The depression
angle reading at 2.5 m marking on the staffis 6°10´. The horizontal distance between A and B is
2200 m. Height of instrument at station A is 1.1 m and R.L. of A is 880.88 m.Apply the curvature
and refraction correction, and determine the R.L. of B (in m). __________
Common Data Questions
Common Data for Questions 48 and 49:
A propped cantilever made of a prismatic steel beam is subjected to a concentrated load P at mid span as
shown. P
R
1.5m 1.5m
Q.48 If load 80 ,find the reaction (in ) (correct to 1-decimal place)using elastic analysis.
__________
Q.49 If the magnitude of load is increased till collapse and the plastic moment carrying capacity of steel
beam section is 90 , determine reaction (in )(correct to 1-decimal place) using plastic
analysis. __________
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Common Data for Questions 50 and 51:
For a portion of national highway where a descending gradient of 1 in 25 meets with an ascending gradient
of 1 in 20, a valley curve needs to be designed for a vehicle travelling at 90 kmphbased on the following
conditions.
(i) headlight sight distance equalto the stopping sight distance (SSD) of a level terrain
consideringlength of valley curve> SSD.
(ii) 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 Loose silt
Basement
4m
Foundation slab
6m
Dense sand
Q.52 Using factor of safety = 3, the net safe bearing capacity (in kN/m2) of the foundation is:
(A) 610 (B) 320 (C) 983 (D) 693
Q.53 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 (B) 111 mm (C) 126 mm (D) 179 mm
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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 (B)1.0 (C)1.6 (D) 1.4
Q.55 The intensity of storm II (in cm/h) is:
(A) 2.00 (B)1.75 (C)1.50 (D)2.25
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 (B) 93 (C) 89 (D) 96
Q.57 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 (B) II (C) III (D) IV
Q.58 Which of the following options is the closest in meaning to the word given below:
Primeval
(A) Modern (B) Historic
(C) Primitive (D) Antique
Q.59 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 (B) Wealth: Peace
(C) Education: Knowledge (D) Money: Happiness
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Q. 61 to Q. 65 carry two marks each.
Q.61 X and Y are two positive real numbers such that 2 6 and 2 8. For which of the
following values of , the function , 3 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| 5 then the values of 2 | | | | is:
(A) 2, 1/3 (B) 1/2, 3 (C) 3/2, 9 (D) 2/3, 9
Q.63 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 (B) 10 (C) 15 (D) 30
Q.65 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
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Source: GATE. Question paper published by GATE.