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# GATE 2022 Rapid Revision Weekly Quiz 3

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Question 1

The saturated unit weight of sand in the bed of a pond 20m deep is 20 kN/m3. Unit weight of water is 10 kN/m3. The effective stress at 4m below bed level of pond is

Question 2

The loading diagram and bending moment of a beam are shown in the following figure.

The shear-force at ‘B’ would be ……. kN. (Round off to two decimal places)

Question 3Multiple Correct Options

The plastic limit of a solid is 24% and its plasticity index is 8%. When the soil is dried from its state of plastic limit, the volume change is 26% of its volume at plastic limit. The corresponding volume change from the liquid limit to dry state is 35% of its volume at liquid limit.

Question 4Multiple Correct Options

For the stepped bar AC as shown having fixed ends at A & C

A1 = 100mm2

A2 = 400 mm2

AB = BC = 500mm

E = 2 × 105 MPa

α = 12 × 10-6/oC

If the temperature increase is 50oC

Which of the following statements are correct

Question 5

The shear force diagram for a beam is shown in the figure below

Question 6

A vertical rod PQ of length L is fixed at its top end P and has a flange fixed to the bottom end Q. A weight W is dropped vertically from a height h (< L) on to the flame. The axial stress in the rod can be reduced by

Question 7

A sand layer found at a river bed (near the sea) under 12m water depth is characterized with porosity 0.5 and gravity of soil solids = 2.65 .Assume the specific gravity of river water to be 1.02 and the unit weight of fresh water to be 9.81 .

What would be the effective stress () at 20m depth from surface of the water?

Question 8

Constant head permeability tests were performed on two soil specimens, S1 and S2. The ratio of height of the two specimens (LS1: LS2) is 1.5, the ratio of the diameter of specimens (DS1:DS2) is 0.5, and the ratio of the constant head (hs1:hs2) applied on the specimens is 2.0. If the discharge from both the specimens is equal, the ratio of the permeability of the soil specimens (ks1:ks2) is ________

Question 9

The stress at a point in a material under plane stress condition is equi-biaxial tension with a magnitude of 10 MPa. If one unit on the σ-τ plane is 1 MPa, the Mohr’s circle representation of the state of stress is given by

Question 10

Height of instrument is 1.460m and vertical angle is 3̊ 30’. Staff reading, taken with the tacheometer are 0.645m, 0.998m and 1.351m. If RL. of ‘P’ is 150.4m then determine distance between the instrument station P & staff Q and RL. of Q. (K=100, C=0)

Question 11

For a rectangular rosette as shown in figure what is the value of shear strain?

ϵ0 = 10x10-4 , ϵ45 = 25x10-4 and ϵ90 = 15x10-4

Question 12

Two beams are connected by a linear spring as shown in the following figure. For a load P as shown in the figure, the percentage of the applied load P carried by the spring is __________.
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