How to calculate the correction for slope in surveying?/ How to make tape correction for slope in surveying?

 Eg:

The slope distance between the two points measures 265m. The difference in the elevation between the two points is 8m. Determine the horizontal length by using the slope correction formula.

To find:

The horizontal distance = D =?

Calculation:

Correction for slope 

 Cs = - [ h²  ÷ 2L]

Where,

L = measured distance between two points = 265m.

h = Vertical difference in elevation between two points = 8m.

     Cs  = [8² ÷ (2 х 265) ]

            = [ 64  ÷ 530]

            = 0.1207m.

The horizontal distance between two points

D = [ Measured distance - slope correction]

    = [ 265m - 0.1207m.]

   = 264.879m.

Note:

1. The slope correction is always negative as the horizontal distance will be shorter than the measured slope distance.

2. The correction is applied when there is a difference in elevation between the two points.

To know:

The slope correction formula is derived by applying Pythagoras theorem in the equation.

Let us find the horizontal distance by the Pythagoras theorem.

L² = [D² + h²]

265² = [D² + 8²]

D² = [265² - 8²]

D² = 70,161

D = √ 70,161

    = 264.879m. ✔

To understand A to Z of surveying, click here.

Thank you for going through these calculation steps❤. Have a good day 😄.

 

Share:

Read More

How to make tape corrections for a pull at survey measurements?/ How to calculate true measurement by pull correction of a tape?

 Eg:

A 760m. distance is measured by applying a pulling force of  90N over the 30m. tape. The tape was made at 50N tensile force. Find the true length of the line if the cross-sectional area of the tape is 0.04cm². Modulus of elasticity = 21х 10⁶ N/cm².

To find:

The true distance between the points. = L =?

Calculation:

The true length 

 L = [ Measured length + pull correction.]

 L = [ L1 + Cp ]

Now,

The pull correction is calculated by the formula

Cp = [{( Pm - Po ) ÷ A х E } х L1]

Where,

Cp = Correction for pull = ?

Pm = Applied force over tape for pulling = 90N.

Po = Std. pulling force of tape = 50N.

A = Cross-sectional area of tape. = 0.04cm²

E = Modulus of elasticity of tape material =  21х 10⁶ N/cm².

L1 = Measured distance between the points = 760m.

Cp = [{( 90 - 50 ) ÷ 0.04 х  21х 10⁶ } х 760]

     = [{ 40 ÷ 0.84 х 10⁶ } х 760]

Cp = 0.0362m.

The true length 

 L = [ L1 + Cp ]

    = [ 760m. + 0.0362m.]

  L = 760.0362m.

To understand A to Z of surveying, click here.

Thank you for going through these calculation steps❤. Have a good day 😄.

Share:

Read More

How to make temperature correction for a steel tape in surveying? / How to calculate true length for temperature correction?

 Eg:

A 30m. surveyor's steel tape is correct at 21°C. The distance measured by using this tape on a day when the temperature is 32°C is 230m. Calculate the true distance between the points by applying temperature correction. Coefficient of thermal expansion ∝ = 1.4 х 10⁻⁵ per ° C.

To find:

The true distance between the points.

Calculation:

The true length 

 L = [ Measured length + temp. correction.]

 L = [ L1 + Ct ]

Now,

The temperature correction is calculated by the formula

Ct = [ ∝ х ( Tm - To ) х L1 ]

   Where,

∝ = Coefficient of thermal expansion =  1.4 х 10⁻⁵

Tm = Field temp. = 32°C

To = Standard temp. = 21°C

L1 = Measured distance = 230m.

Ct = [  1.4 х 10⁻⁵ х ( 32°C - 21°C ) х 230m. ]

     = 0.0354m.

The true length between the points

   L  = [ L1 + Ct ]

       = [230m. + 0.0354m.]

    L = 230.0354m.

To understand A to Z of surveying, click here.

Thank you for going through these calculation steps❤. Have a good day 😄.

Share:

Read More

What should be the maximum distance between two columns?

 Let us go through the answer to the FAQ "What should be the maximum distance between two columns?"

There is nothing as such a fixed measurement between two columns as it depends upon several factors.

Some of the factors that decide the distance between two columns are,

1. Total load ( LL + DL ) acting over the column.

2. Type of structural design.

3. Size of the column.

4. Size of the beams resting over the column.

5. Whether the column comes in a seismic zone or not.

6. Type of footing & SBC of soil.

7. No. of storeys in the structure.

Considering all these points & safety factors, a structural engineer provides the most economical structural drawing for the construction.

If you are residing in an urban area, the best way is to hire a consultant for your construction work.

 In rural areas, where a local contractor or workers design the structures, the following are some of the points to be known by the house owners.

Let us discuss the general requirement for the column size & its spacing in a single-storeyed residential building.

1. The minimum required size of the column should be 9"х 9".

2. When you provide a 9"х 9" column to the building, the distance between the two columns should be ≤ 4m or 13'.

3. The standard or most common size of the column for the single-storeyed residential building is 9"х 12"

4. When you provide a 9"х 12" column to the building, the distance between the two columns should be ≤ 5m or 16'.

5. In any condition the dia. of reinforcement should not be less than 12mm. - 4nos.

6. The dia. of lateral ties should be 8mm. as shown in the below drawing.

7. The minimum size of the beam should be  9"х 12" for the safe transfer of the loads.

8. For G +1 residential buildings, you should avoid 9"х 9" size columns in the structure. The general size adopted for the columns are 9"х 12" & 9"х 15".

To go through all types of structural design articles, click here.

Thank you for going through this article❤. Have a good day 😄.

Share:

Read More

How to calculate the volume of earthwork from a contour map? / Finding the volume of earthwork in contour surveying.

 Eg:

Following are the different contours at 3m. intervals for a hill with their respective areas. 

Sl. No.	Contour	Area in m²
1	450	375
2	447	620
3	443	945
4	441	1365
5	438	1880
6	435	2570

 

 

 

Calculate the volume of the earth contained in the hill.

To find:

The volume of earth contained in the hill.

Calculation:

The volume of the earth is calculated by using the trapezoidal & prismoidal formulas for contour maps. The answer will be nearer to accurate & they differ from each other.

Now, let us calculate the volume of the earth by using both of them to observe the difference.

1. Trapezoidal formula:

The volume of earth in the hill

V = D х [{(A0 + An) ➗2} + (A1 + A2 + A3 + ---- + An - 1)]

Here,

 D = Interval between the successive contours 

 D = {450 - 447} = 3

A0 = area of 1st contour line = 375m²

A1 = area of 2nd contour line = 620m²

Similarly,

    A2 = 945m²

     A3= 1365m²

       An  👉 The area of the last contour = 2570m²

(An - 1) 👉 Prior to last contour = A4 = 1880m²

Now,

The volume of earth in the hill

V = D х  [{(A0 + An) ➗2} + {A1 + A2 + A3 + A4}]

    = 3 х [{(375 + 2570) ➗2} + {620 + 945 + 1365 + 1880}]

    = 3 х [{1472.5} + {4810}]

     = 3 х [6282.5]

 V  = 18,847.5m³

2. Prismoidal formula:

The volume of earth in the hill

V = D/3 [ 1st area + last area + 4 Σ even area + 2 Σ odd area ]

V =  (D ➗ 3)  х [{ (A0 + An) + 4  х ( A1 + A3 ) + 2  х ( A2 + A4)}]

   =  (3 ➗ 3)  х [{ (375 + 2570) + 4  х ( 620 + 1365 ) + 2  х ( 945 + 1880)}]

   = 1 х [{ ( 2945 ) + 4  х ( 1985 ) + 2 х ( 2825)}]

  = 1 х [{ 2945  + 7940 + 5650 }]

  = 1 х [16,535 ]

V = 16,535 m³

Note:

For the larger no. of contour data, having minimum intervals between the two contour lines, the prismoidal formula works better. 

For the lesser no. of contour data having maximum contour intervals, the trapezoidal formula works better.

Go through the article 👇

👀. How to calculate the volume of water in a pond by a contour map?

Remember:

 Often there is confusion in selecting the areas in the prismoidal formulas. Some points to be known in selecting them are,

1. Each area is taken only once in the formula. No area is repeated twice.

2. The even area starts from the second area leaving the 1st one (A0). 👉 2nd, 4th, 6th, ...... so on. 

3. The odd area starts from the third area and leaves the last one (An). 👉 3rd, 5th, 7th,  ..... so on.

4. If you have only 3 contour data, the formula does not contain any odd areas.

      V = [ (D ➗ 3)  х { (A0 + An) + 4  х ( A1 ) + 2 х (0)}]

         = [ (D ➗ 3)  х { (A0 + An) + 4  х ( A1 )]

Note:

When we do earthwork filling, we can calculate the volume by using this method.

To understand A to Z of surveying, click here.

Thank you for going through these calculation steps❤. Have a good day 😄.

Share:

Read More

How to calculate superelevation for a circular road? / Finding superelevation for a curved road.

 Eg:

Calculate superelevation for a road having a radius of a curve as 150m. The design speed is 60km/hr. The coefficient of lateral friction is 0.15.

To find :

Superelevation=e =?

Calculation:

The formula to calculate the superelevation of the road is

[e + f ] = [V² / 127R]

Where,

e = rate of superelevation =?

f = lateral friction factor =  0.15

V = Velocity of vehicle in km / hr. = 60km/hr

R = Radius of a circular curve in meters.= 150m.

[e + f ]=  [V² / 127R]

[e + 0.15] = [60² ÷ 127 х 150 ]

[e + 0.15] = [3600 ÷ 19,050]

[e + 0.15] = 0.189

e = [0.189 - 0.15]

   = 0.0389

 Required slope = 1/0.0389

                            = 1 in 25.70

  Superelevation in %

   = [0.0389  х 100]

    = 3.89%

According to IRC, the maximum allowable superelevations for mixed traffic over hills & terrains is 7%.

e = 3.89% < 7% hence safe.

Thank you for going through these calculation steps❤. Have a good day 😄.

Share:

Read More

How to calculate the volume of water in a pond by a contour map?/ Finding volume of a contour lines.

 Eg:

Following are the different contours at 2m. intervals in a pond up to a water level with their respective areas. 

Sl. No.	Contour	Area in m²
1	550	775
2	552	920
3	554	1145
4	556	1565
5	558	1980
6	560	2650
7	562	3425

 

 

Calculate the volume of water in the pond.

To find:

The volume of water in the pond.

Calculation:

The volume of water is calculated by using the trapezoidal & prismoidal formulas for contour maps. The answer will be nearer to accuracy & slightly differ from each other.

Now, let us calculate the volume of water by using both of them to observe the difference.

1. Trapezoidal formula:

The volume of water in the pond

V = D х [{(A0 + An) ➗2} + (A1 + A2 + A3 + ---- + An - 1)]

Here,

 D = Interval between the successive contours 

 D = {562 - 560} = 2

A0 = area of 1st contour line = 775m²

A1 = area of 2nd contour line = 920m²

Similarly,

A2 = 1145m², A3= 1565m², A4 = 1980m², 

       An  👉 The area of the last contour = A6 =3425m²

(An - 1) 👉 Prior to last contour = A5 = 2650m²

Now,

The volume of water in a pond

V = D х  [{(A0 + A6) ➗2} + {A1 + A2 + A3 + A4 + A5}]

    = 2 х [{(775 + 3425) ➗2} + {920 + 1145 + 1565 + 1980 + 2650}]

    = 2 х [{2100} + {8260}]

     = 2 х [10,360]

 V  = 20,720m³

2. Prismoidal formula:

The volume of water in the pond

V = D/3 [ 1st area + last area + 4 Σ even area + 2 Σ odd area ]

V = [ (D ➗ 3)  х { (A0 + An) + 4  х ( A1 + A3 + A5 ) + 2  х ( A2 + A4)}]

   = [ (2 ➗ 3)  х { (775 + 3425) + 4  х ( 920 + 1565 + 2650 ) + 2  х ( 1145 + 1980)}]

   = [0.6667 х { ( 4200 ) +  4  х ( 5135 ) + 2 х ( 3125)}]

  = [0.6667 х { 4200  + 20540 + 6250 }]

  = [0.6667  х 30,990 ]

V = 20, 660 m³

To understand A to Z of surveying, click here.

Thank you for going through these calculation steps❤. Have a good day 😄.

Share:

Read More

How to calculate the volume of earthwork for embankment?/ Earthwork calculation of embankment by mean area method.

 Eg:

Calculate the volume of earthwork for the embankment 75m. long having 4m. width at the top. Depth of embankment at every 15m. interval is 1.45m., 1.70m., 1.95m., 2.25m., 2.55m., &2.80m. The side slope on both sides is 1:2.

To find:

We have to calculate the total volume of earthwork in the embankment by using the mean area method.

Procedure:

Consider an embankment section having 15m. length = L1 as shown in the above drawing. 

1. First, you have to calculate the sectional area A1 for the initial depth d1.

The formula for calculating A1 = [ bd1 + d1²S]

Before proceeding further, Go through the article 👇

👀.  How to calculate the sectional area of an embankment?

To understand the formula derivation &  clear concept of calculation.

2. Similarly, the sectional area A2 should be calculated for the given depth d2 after a 15m. interval.

The volume of earthwork for an embankment for the 1st. 15m. length

        = V15 = [ Am ✖ L1]

Where the mean area 

            Am  = [(A1 +A2) ➗ 2]

3. In a similar way, the volume of earthwork for every 15m. embankment section should be calculated.

4. The total volume of earthwork for embankment 

    V = [V15 + V30 +V45 + V60 + V75]

Calculation:

1. Volume V15:

     A1 = [ bd1 + d1²S]

          =  [ (4m. ✖ 1.45m.) + (1.45² ✖ 2)]

           = [5.8m² + 4.205m²]

     A1 = 10.005m².

    A2 = [ bd2 + d2²S]

          =  [ (4m. ✖ 1.70m.) + (1.70² ✖ 2)]

          = [6.8m² + 5.78m²]

    A2 = 12.58m².

     V15 = [{(A1 +A2) ➗ 2} ✖ L1]   

             = [{(10.005 + 12.58) ➗ 2} ✖ 15]   

     V15 = 169.39m³.

2. Volume V30:

     A3 = [ bd3 + d3²S]

          =  [ (4m. ✖ 1.95m.) + (1.95² ✖ 2)]

           = [7.8m² + 7.605m²]

     A3 = 15.405m².

   V30 = [{(A2 +A3) ➗ 2} ✖ L2]   

           = [{(12.58 + 15.405) ➗ 2} ✖ 15]   

   V30 = 209.88m³.

  NOTE: Area A2 becomes the surface sectional area for the next 15m. length of the embankment.

3. Volume V45:

     A4 = [ bd4 + d4²S]

          =  [ (4m. ✖ 2.25m.) + (2.25² ✖ 2)]

           = [9.0m² + 10.125m²]

     A4 = 19.125m².

   V45 = [{(A3 +A4) ➗ 2} ✖ L3]   

           = [{(15.405 + 19.125) ➗ 2} ✖ 15]   

   V45 = 258.975m³.

4. Volume V60:

     A5 = [ bd5 + d5²S]

          =  [ (4m. ✖ 2.55m.) + (2.55² ✖ 2)]

           = [10.20m² + 13.005m²]

     A5 = 23.205m².

   V60 = [{(A4 +A5) ➗ 2} ✖ L4]   

           = [{(19.125 + 23.205) ➗ 2} ✖ 15]   

   V60 = 317.475m³.

5. Volume V75:

     A6 = [ bd6 + d6²S]

          =  [ (4m. ✖ 2.80m.) + (2.80² ✖ 2)]

           = [11.20m² + 15.68m²]

     A6 = 26.88m².

   V75 = [{(A5 +A6) ➗ 2} ✖ L4]   

           = [{(23.205 + 26.88) ➗ 2} ✖ 15]   

   V75 = 375.637m³.

 The total volume of earthwork for embankment 

    V = [V15 + V30 +V45 + V60 + V75]

       = [169.39m³ + 209.88m³ + 258.975m³ + 317.475m³ + 375.637m³]

       = 1331.357m³

Note: 

The calculation is done in an elaborate way to understand the concept clearly. Once known, the calculation should be done in a table format as shown below.

Thank you for going through these calculation steps❤. Have a good day 😄.

Share:

Read More