Question

19. 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 7m and
length 450m.
A level surface is laid inside the tunnel to make road. The Diagram I shows the
circular cross section of the tunnel. The level surface is represented by AB, the
centre of the circle is O and LAOB = 900. The space below AB is filled with
rubble ( debris from the demolition buildings). what is the cross section area of tunnel after filling debris on ground plane?​

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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