Area Calculation of Horseshoe Shape tunnel with CBS factor by C B Singh

 For calculating the cross-sectional area, most of the time we depend on AutoCAD, as well as various hectic calculations.

From my past experiences and as per knowledge, the short-cut calculation has been developed, called the AREA CBS FACTOR. The calculation has been shown below. …..

C/S AREA OF HORSE SHOE SHAPE TUNNEL =  d2 X CBS FACTOR

Where,

d = Dia. Of horse shoe shape tunnel

CBS FACTOR = 0.829323611

From above formula, we can calculate Area instantly with simple multiplication.

For example….

For a 6mt. dia tunnel, the Area has been calculated…

Area = d² x 0.829323611

             6² x 0.829323611 ->   29.85 m²

The above calculation can be verified using Auto-Cad or any mathematical technique

How to calculate Cement and Water quantity for cement grouting with CBS Factor by Er. C B Singh.

How to calculate the cement and water quantity for cement grout

If the proportion of grout is given, the shortcut calculation has been developed, called the CBS FACTOR; the calculation has been shown below…….

 

Cement Quantity= Grout in Litres/CBSFACTOR (Cement Qty. in                                                                                                                         Bags) Water Quantity = Cement Quantity X proportion of water (Water Qty. in litres)

 

Where,

CBS FACTOR = 65.66 for 1:1 (one cement and one water)

                        = 60.66 for 1:0.9 (one cement and 0.9 water)

                        =55.66 for 1:0.8 (one cement and 0.8 water)

                        =45.66 for 1:0.6 (one cement and 0.6 water)

                        =40.66 for 1:0.5 (one cement and 0.5 water)

                         

From the above formula, we can calculate the quantity of cement bags and water in litres instantly with simple division or multiplication.

 

For example….

For a proportion of grout of 1:0.5 for 1000 litres of grout, the quantity of cement and water has been calculated…

Cement Qty. = 1000/40.66 = 24.59 bags X 50 = 1229.71 kgs

Water Qty. = 1229.71X0.5 = 614.85 Litres

The above calculation can be verified using mathematical techniques.

 

Note- These formulas are for plane grout; no chemicals and additives are added.

 

How to calculate the Area of Segment of Tunnel/Circle

How to calculate the area of a segment of a tunnel (circle)

If the length of the chord and height of the segment are given, the shortcut calculation has been developed, called the CBS Factor. The calculation has been shown below. …..

Area of Segment of Tunnel/Circle = ((Angle of Sector θ/360) - (Sin θ/2π)) X CBS FACTOR

Where,

CBS FACTOR = 78.53981632

θ = 2X (cos^-1 (1-h/r))

where h = height of segment

r = radius of circle

          θ=Angle of sector

r=(c²/8h)+(h/2)

where c = length of chord

           h=height of segment.

          From the above formula, we can calculate the area of a segment of a circle instantly with simple multiplication.

For example….

For 6 mtrs. Chord length and 1 mtr. height of segment, the area of the segment has been calculated.

Area = ((73˚44’23.26’’/360˚)-(Sin73˚44’23.26’’/2π)) X78.53981632

=4.0875 m²

The above calculation can be verified using AutoCAD or any mathematical technique

How to calculate the Area of Ellipse, by Er. C B Singh with CBS FACTOR

How to Calculate the Area of an Ellipse

From my past experiences and as per knowledge, the shortcut calculation has been developed, called CBS FACTOR; the calculation has been shown below…….

Area of Ellipse = Major axis X Minor axis X CBS FACTOR

Where,

Major axis = longest length of ellipse

Minor axis = Shortest length of ellipse

CBS FACTOR = 0.7854

From the above formula, we can calculate the area of an ellipse instantly with simple multiplication.

For example….

For 12 metres' longest length and a shortest length of 1.5 metres of ellipse, the area of the ellipse has been calculated…

Area = 12 x 1.5 x 0.7854

             12 x 1.5  x 0.7854 ->   14.1372 m²

The above calculation can be verified using AutoCAD or any mathematical technique

How to calculate the Area of circle inside a square

INVERT ARCH LENGTH OF HORSE SHOE SHAPE TUNNEL

For calculating the invert arch length of horse shoe shape tunnel , most of the time we depend on Auto Cad, as well as various hectic calculations.

From my past experiences and as per knowledge, the short-cut calculation has been developed, called as CBS  FACTOR, the calculation has been shown below……..

INVERT ARCH LENGTH OF HORSE SHOE SHAPE TUNNEL =  d X CBS FACTOR

Where,

d = Dia. Of horse shoe shape tunnel

CBS FACTOR = 0.8481

From above formula, we can calculate Ivert Arch length instantly with simple multiplication.

For example….

For a 6mt. dia tunnel, the Arch length has been calculated…

Invert Arch length = d x 0.8481

             6 x 0.8481 ->   5.0886 m

The above calculation can be verified using Auto-Cad or any mathematical technique

       

PERIMETER OF HORSE SHOE SHAPE TUNNEL (Excluding Invert Arch)

For calculating the cross-sectional Perimeter of Horse Shoe Shape, most of the time we depend on Auto Cad, as well as various hectic calculations.

From my past experiences and as per knowledge, the short-cut calculation has been developed, called as CBS FACTOR, the calculation has been shown below……..

PERIMETER OF HORSE SHOE SHAPE TUNNEL =  d X CBS FACTOR                     (Excluding Invert Arch)

Where,

d = Dia. Of horse shoe shape tunnel

CBS FACTOR = 2.41880624

From above formula, we can calculate Perimeter instantly with simple multiplication and division.

For example….

For a 6mt. dia tunnel, the Perimeter has been calculated…

Perimeter = d X 2.41880624

            6 X 2.41880624 ->  14.512  mtrs

The above calculation can be verified using Auto-Cad or any mathematical technique

     

PERIMETER CALCULATION FORMULA OF HORSE SHOE SHAPE TUNNEL

For calculating the cross-sectional Perimeter of Horse Shoe Shape, most of the time we depend on Auto Cad, as well as various hectic calculations.

From my past experiences and as per knowledge, the short-cut calculation has been developed, called as CBS FACTOR, the calculation has been shown below……..

PERIMETER OF HORSE SHOE SHAPE TUNNEL =  (2d)/ CBS FACTOR

Where,

d = Dia. Of horse shoe shape tunnel

CBS FACTOR = 0.6122

From above formula, we can calculate Perimeter instantly with simple multiplication and division.

For example….

For a 6mt. dia tunnel, the Perimeter has been calculated…

Perimeter = (2d)/ 0.6122

            (2X 6)/ 0.6122 ->   19.60 mtrs

The above calculation can be verified using Auto-Cad or any mathematical technique

We found geological cracks at bottom during Head Race Tunnel excavation in Dikchu- 96 MW, Hydro Electric Project in Sikkim, India. Expert team has decided to apply treatment by trench cutting followed by RCC application. Further we appreciate your helpful suggestions to over come such phenomenon in future for safe and successful construction practices.

D-SHAPE TUNNEL CROSS-SECTION AREA CALCULATION TECHNIQUE

As presented earlier, the short-cut technique for Area calculation of tunnels cross-section, the calculation for Area of D-Shape tunnels has been specified this time.

For calculating the cross-sectional area, most of the time we depend on Auto Cad, as well as various hectic calculations.

From my past experiences and as per knowledge, the short-cut calculation has been developed, called as AREA CBS FACTOR, the calculation has been shown below……..

C/S AREA OF D-SHAPE TUNNEL =  d2 X CBS FACTOR

Where,

d = Dia. Of D-Shape tunnel

CBS FACTOR = 0.8927

From above formula, we can calculate Area instantly with simple multiplication.

For example….

For a 6mt. dia tunnel, the Area has been calculated…

Area = d² X 0.8927

   6² x 0.8927  ->   32.13 m²

The above calculation can be verified using Auto-Cad or any mathematical technique

area   32.1372 m2          perimeter   21.4248 m

Horse shoe shape tunnel Cross-section Area with CBS Factor by Er. C B Singh : For calculating the cross-sectional area, most of...

Please go through www.cbsinghhydro.blogspot.in for Horse shoe-shaped tunnel cross-section:
For calculating the cross-sectional area, most of... For calculating the cross-sectional area, most of the time we depend on AutoCAD, as well as various hectic calculations. From my past... https://www.youtube.com/watch?v=nO9D-ub84BY

Area Calculation of Horse Shoe Shape Tunnel with CBS Factor by Er. C B Singh

For calculating the cross-sectional area, most of the time we depend on AutoCAD, as well as various hectic calculations.

From my past experiences and as per knowledge, the shortcut calculation has been developed, called the AREA CBS FACTOR; the calculation has been shown below…….

C/S AREA OF HORSE SHOE SHAPE TUNNEL =  d2 X CBS FACTOR

Where,

d = Dia. Of horse-shoe-shaped tunnels

CBS FACTOR = 0.829323611

From the above formula, we can calculate the area instantly with simple multiplication.

For example….

For a 6 m dia tunnel, the area has been calculated…

Area = d² x 0.829323611

             6² x 0.829323611 ->   29.85 m²

The above calculation can be verified using AutoCAD or any mathematical technique

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