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Office: F-126, (Lower Basement), Katwaria Sarai, New Delhi-110 016
Phone: 011-26522064 Mobile: 81309 09220, 97118 53908
Email: [email protected], [email protected]
Web: iesmasterpublications.com, iesmaster.org
GATE SOLUTIONSCIVIL ENGINEERING
1987-2019
First Edition : 2016
Second Edition : 2017
Third Edition : 2018
Fourth Edition : 2019
Typeset at : IES Master Publication, New Delhi-110016
IES MASTER PUBLICATIONF-126, (Lower Basement), Katwaria Sarai, New Delhi-110016
Phone : 011-26522064, Mobile : 8130909220, 9711853908
E-mail : [email protected]
Web : iesmasterpublications.com
All rights reserved.
Copyright © 2019, by IES MASTER Publication. No part of this booklet may bereproduced, or distributed in any form or by any means, electronic, mechanical,photocopying, recording, or otherwise or stored in a database or retrieval system withoutthe prior permission of IES MASTER Publication, New Delhi. Violates are liable to belegally prosecuted.
The Graduate Aptitude Test in Engineering (GATE) is an All-India examination administered and conductedin eight zones across the country by the GATE Committee comprising of Faculty members from IISc,Bangalore and other seven IITs on behalf of the National Coordinating Board, Department of Education,Ministry of Human Resources Development.
The GATE score/rank is used for admissions to Post Graduate Programmes (ME, M.Tech, MS, direct PhD)in institutes like IIT and IISc, etc. with financial assistance offered by the Ministry of Human ResourceDevelopment. PSUs too use the GATE scores for recruiting candidates for various prestigious jobs withattractive remuneration.
The door to GATE exam is through previous year question papers. If you are able to solve question papersin access of 10 years, you are sure to clear the GATE exam, and open new vistas of career and learning.
The Civil Engineering GATE 2020 book from IES Master offers detailed topic-wise solutions for the past33 years question papers. The emphasis is clearly on the understanding of concepts and building upona holistic picture. So as you finish a topic, for instance, Strength of Materials, you will find all the previousyears’ question papers with detailed explanation under that particular topic.
The approach has been to provide explanation in such a way that just by going through the solutions,students will be able to understand the basic concepts and will apply these concepts in solving otherquestions that might be asked in future exams.
Every care has been taken to bring an error-free book. However, comments, suggestions, and feedbackfor improvement in the future editions are most welcome.
IES Master PublicationNew Delhi
PREFACE
1. Engineering Mechanics .......................................................................................... 01–03
2. Strength of Materials ............................................................................................... 04–74
3. Structural Analysis ................................................................................................. 75–144
4. Construction Materials and Management ............................................................. 145–150
5. RCC Structure and Pre-Stress Concrete ............................................................. 151–215
6. Design of Steel Structure ..................................................................................... 216–265
7. Soil Mechanics .................................................................................................... 266–424
8. Fluid Mechanics................................................................................................... 425–529
9. Engineering Hydrology ......................................................................................... 530–563
10. Irrigation Engineering ........................................................................................... 564–588
11. Environmental Engineering .................................................................................. 589–672
12. Transportation Engineering .................................................................................. 673–744
13. Geomatics Engineering ....................................................................................... 745–772
14. Engineering Mathematics .................................................................................... 773–850
15. General Aptitude .................................................................................................. 851–872
16. English ................................................................................................................873–881
CONTENT
UNIT-1 ENGINEERING MECHANICS
SYLLABUS
System of forces, free-body diagrams, equilibrium equations; Internal forces in structures; Friction and itsapplications; Kinematics of point mass and rigid body; Centre of mass; Euler’s equations of motion; Impulse-momentum; Energy methods; Principles of virtual work.
CONTENTS
1. Engineering Mechanics ................................................................................. 01-03
2 GATE SOLVED PAPER 1987-2019 Civil Engineering
1– Mark1. A simple mass-spring oscillatory system consists
of a mass m, suspended from a spring of stiffnessk. Considering z as the displacement of thesystem at any time t, the equation of motion forthe free vibration of the system is mz kz 0 .The natural frequency of the system is
(a)km
(b)mk
(c)km
(d)mk
[GATE-2019 SHIFT-I ]
2. An assembly made of a rigid arm A-B-C at endA and supported by an elastic rope C-D at end Cis shown in the figure. The members may beassumed to be weightless and the lengths of therespective members are as shown in the figure.
PRigid arm
A D
Rope
B C
L
L L
Under the action of a concentrated load P at Cas shown, the magnitude of tension developed inthe rope is
(a)3P
2 (b)P2
(c)3P8
(d) 2P[GATE-2016 SHIFT-II ]
1 ENGINEERING MECHANICS
2– Marks3. A cylinder of radius 250 mm and weight, W = 10
kN is rolled up an obstacle of height 50 mm byapplying a horizontal force P at its centre asshown in the figure.
P
W 50 mm
All interfaces are assumed frictionless. Theminimum value of P is
(a) 4.5 kN (b) 5.0 kN
(c) 6.0 kN (d) 7.5 kN[GATE–2018 SHIFT-I ]
4. Two rigid bodies of mass 5 kg and 4 kgare at rest on a frictionless surface until actedupon by a force of 36 N as shown in the figure.The contact force generated between the twobodies is
5 kg 4 kg36 N
(a) 4.0 N (b) 7.2 N(c) 9.0 N (d) 16.0 N
[GATE–2018 SHIFT-II ]
5. A particle of mass 2 kg is travelling at a velocityof 1.5 m/s. A force f(t) = 3t2 (in N) is applied toit in the direction of motion for a duration of 2seconds. Where t denotes time in seconds. Thevelocity (in m/s up to one decimal place) of theparticle immediately after the removal of the forceis ______.
[GATE-2017 SHIFT-I]
IES MASTER Publication
ENGINEERING MECHANICS 3Civil Engineering
ANSWER KEY
1 Mark : –
1. (a)
2. (b)
:––: 2 Marks : –
3. (d)
4. (d)
5. (5.5 m/s)
EXPLANATIONS
1– Mark1. (a) For simple harmonic motion
mz kz = 0
kz zm
= 0
Standard equation is 2
22
d x w xdt
= 0
w2 =km
w =km
2. (b)P2
45°
A
L
B L C
P T
Taking moment about A
PL =T TL L 2T P2 2
PT2
2– Marks
3. (d) P
WD
50 mm
W = 10 kN
DM = 0
For rolling, the normal reaction should be zerowhen the cylinder just starts to roll.
A
B D
C50 mm
N = 0
BD = 2 2AD AB 2 2(250) (200)
= BD = 150 mm
P × 200 – W × 150 = 0
P =10 150
200
= 7.5 kN
4. (d)
5 kg 4 kg36 N
Net force = Net mass × acceleration 36 = 9 × a a = 4 ms–2
Now, considering 5 kg weight onlyforce on 5 kg = 5 × 4 N = 20 N
36N F
36N – F = 20N
F = 16N
5. (5.5 m/s)f(t) = 3t2ma = 3t2
dvmdt = 3t2
v
1.52 dv =
2 20
3t dt2(v – 1.5) = 8
v = 5.5 m/s
