Question

19. Case Study 3 :

The tunnels are defined as the underground passages that are used for the transportation purposes. These permit the

transmission of passengers and freights, or it may be for the transportation of utilities like water, sewage or gas etc.

The tunnel engineering is one of the most interesting disciplines in engineering. The work is complex and difficult

throughout its course, even though it is interesting.

Earth is excavated to make a road tunnel. The tunnel is a cylinder of radius 7 m and length 450 m. A level surface is laid

inside the tunnel to make road. The Diagram 1 shows the circular cross - section of the tunnel. The level surface is

represented by AB , the centre of the circle is O and ∠ = 90°. The space below AB is filled with rubble (debris

from the demolition buildings).

Steel girders are erected above the tracks to strengthen the tunnel. Some of these are shown in Diagram 2. The girders

are erected at 6 m intervals along the length of the tunnel, with one at each end. On the basis of the above

information, answer any four of the following questions:

a. What is the cross section area of tunnel before filling debris on ground plane ?

(a) 154m² b. 140m2

c. 155m² d. 145m²

b. What is the area of cross section of tunnel after filling debris on ground plane?

(a) 138m2 b. 140m²

c. 152m² d. 145m²

c. What is the length of each girder ?

(a) 11 m b. 22 m c. 33 m d. 44 m

d. How many girders are erected ?

(a) 76 b. 75 c. 74 d. 73
e. If the weight of 1 meter girder is 25 kg, how much steel is required ?

(a) 2508 quintals (b) 627 quintals (c) 2246 quintals (d) 1646 quintals​

Answer 1

Given :  The tunnel is a cylinder of radius 7 m and length 450 m.  

the centre of the circle is O and ∠OAB = 90°.  

To Find :

cross section area of tunnel before filling debris on ground plane

cross section area of tunnel after filling debris on ground plane

How many girders are erected

Solution:

Cross section area  of tunnel before filling debris on ground plane

= πR²

= (22/7)*7²

= 154   m²

area of cross section of tunnel after filling debris on ground plane

= 154 - (90/360) 154  + (1/2) * 7 * 7  

= 154 - 38.5 + 24.5

= 154  - 14

= 140  m²

Tunnel length 450 m

girders erected at 6 m intervals along the length of the tunnel, with one at     each end

= 450/6  + 1

= 75 + 1

= 76

Learn More:

The tunnel is a cylinder of radius 7 m and length 450 m.

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