GATE CE format:nat PYQs & Answers — Page 27

Questions 261–270 of 495. Imported answers require independent review unless marked reviewed.

Topic practice 495 questionsPage 27 of 50

A square plate O-P-Q-R of a linear elastic material with sides 1.0 m is loaded in a state of plane stress. Under a given stress condition, the plate deforms to a new configuration O′-P′-Q′-R′ as shown in the figure (not to scale). Under the given deformation, the edges of the plate remain straight.

Diagram for Civil Engineering question 42

The horizontal displacement of the point (0.5 m, 0.5 m) in the plate O-P-Q-R (in mm, round off to one decimal place) is

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The activity details for a small project are given in the Table.

Activity	Duration (days)	Depends on
A	6	-
B	10	A
C	14	A
D	8	B
E	12	C
F	8	C
G	16	D, E
H	8	F, G
K	2	B
L	5	G, K

The total time (in days, in integer) for project completion is

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A small project has 12 activities – N, P, Q, R, S, T, U, V, W, X, Y, and Z. The relationship among these activities and the duration of these activities are given in the Table.

Activity	Duration (in weeks)	Depends upon
N	2	-
P	5	N
Q	3	N
R	4	P
S	5	Q
T	8	R
U	7	R, S
V	2	U
W	3	U
X	5	T, V
Y	1	W
Z	3	X, Y

The total float of the activity “V” (in weeks, in integer) is

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An equipment has been purchased at an initial cost of ₹16000 and has an estimated salvage value of ₹1000. The equipment has an estimated life of 5 years. The difference between the book values (in ₹, in integer) obtained at the end of 4th year using straight line method and sum of years digit method of depreciation is

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The soil profile at a construction site is shown in the figure (not to scale). Ground water table (GWT) is at 5 m below the ground level at present. An old well data shows that the ground water table was as low as 10 m below the ground level in the past. Take unit weight of water,

Diagram for Civil Engineering question 44

The overconsolidation ratio (OCR) (round off to two decimal places) at the mid-point of the clay layer is

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A rectangular footing of size 2.8 m × 3.5 m is embedded in a clay layer and a vertical load is placed with an eccentricity of 0.8 m as shown in the figure (not to scale). Take Bearing capacity factors:

, and

; Shape factors:

and

; Depth factors:

and

; and Inclination factors:

and

. Using Meyerhoff’s method, the load (in kN, round off to two decimal places) that can be applied on the footing with a factor of safety of 2.5 is

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A retaining wall of height 10 m with clay backfill is shown in the figure (not to scale). Weight of the retaining wall is 5000 kN per m acting at 3.3 m from the toe of the retaining wall. The interface friction angle between base of the retaining wall and the base soil is 20°. The depth of clay in front of the retaining wall is 2.0 m. The properties of the clay backfill and the clay placed in front of the retaining wall are the same. Assume that the tension crack is filled with water. Use Rankine’s earth pressure theory. Take unit weight of water,

Diagram for Civil Engineering question 45

The factor of safety (round off to two decimal places) against sliding failure of the retaining wall after ignoring the passive earth pressure will be

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The soil profile at a road construction site is as shown in figure (not to scale). A large embankment is to be constructed at the site. The ground water table (GWT) is located at the surface of the clay layer, and the capillary rise in the sandy soil is negligible. The effective stress at the middle of the clay layer after the application of the embankment loading is 180 kN/m

. Take unit weight of water,

kN/m

The primary consolidation settlement (in m, round off to two decimal places) of the clay layer resulting from this loading will be

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A combined trapezoidal footing of length

supports two identical square columns (

and

) of size 0.5 m × 0.5 m, as shown in the figure

Diagram for Civil Engineering question 46

. The columns

and

carry loads of 200 kN and 150 kN, respectively. If the stress beneath the footing is uniform, the length of the combined footing

(in m, round off to two decimal places) is

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Numerically integrate,

from lower limit

to upper limit

. Use Trapezoidal rule with five equal subdivisions. The value (in units, round off to two decimal places) obtained is

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GATE CE format:nat PYQs

Question 42

Question 42

Question 43

Question 43

Question 44

Question 44

Question 45

Question 45

Question 46

Question 46