**Quiz: Civil Engineering **

**Exam: GATE**

**Topic: Miscellaneous**

**Each question carries 2 mark**

**Negative marking: 1/3 mark**

**Time: 12 Minutes**

Q1. The state of stresses on an element is shown in the given figure. The values of stresses are σ_x (=32MPa):σ_y (=-10MPa) and major principal stress σ_1 (=40 MPa). The minor principal stress ‘σ_2’ is

(a) -22 MPa

(b) -18 MPa

(c) 22 MPa

(d) Indeterminable due to insufficient data

Q2. What is the limiting principle tensile stress in prestress uncracked concrete member of M25 grade?

(a) 1.2 MPa

(b) 1.5 MPa

(c) 2 MPa

(d) 2.5 MPa

Q3. A steady, two-dimensional, incompressible flow field is represented by u = x + 3y + 3 and V = 2x – y – 8 in this flow field, the stagnation point is

(a) (3, 2)

(b) (-3, 2.5)

(c) (-3, -2)

(d) (3, -2)

Q4. Which one of the following represents relative density of saturated sand deposited having moisture content of 25%, if maximum and minimum void ratio of sand are 0.95 and 0.45 respectively and specific gravity of sand particles is 2.6?

(a) 40%

(b) 50%

(c) 60%

(d) 70%

Q5. The kinematic indeterminacy of the structure shown in the figure is equal to

(a) 14

(b) 15

(c) 16

(d) 17

Solutions

S1. Ans.(b)

Sol. σ_x+σ_y=σ_1+σ_2

32+(-10)=40+σ_2

▭(σ_2= -18 MPa)

S2. Ans.(a)

Sol. As per IS

Maximum principal tensile stress in prestressed concrete member = 0.24 √fck

=0.24√25

=0.24×5

=1.20 MPa

S3. Ans.(d)

Sol. Given,

u = x + 3y + 3

v = 2x – y – 8

For stagnation point u = 0 & v = 0

x+3y+3=0—-(1)

2x-y-8=0—-(2)

By solving equation (1) & (2)

▭(■(x=3@y= -2))⇒(3,-2)

S4. Ans.(c)

Sol. Given, S = 1 (Saturated sand)

e_max=0.95

e_min=0.45

w=25%=0.25

G=2.6

I_D=?

We know,

Se=WG

1×e=0.25×2.6

▭(e=0.65)

Now,

I_D=(e_max-e)/(e_max-e_min )

■(0.95-0.65 @0.95-0.45)×100

▭(I_D=60%)

S5. Ans.(a)

Sol. No.of inextensible members (m) =15

No.of external reactions (r_e) =7

No.of joints (j) =12

Internal hinged reactions (r_r) =0

Kinematic indeterminacy (D_k) =3j-r_e-m+r_r

=(3×12)-7-15+0

=36-22

▭(D_k=14)