Numerical Examples for Chain Surveying | Errors in Surveying

Numerical Examples for Errors in Chain Surveying

We will now move on with different numerical problems on the concept of Errors in Chain Surveying. Going through these numericals will actually give you an idea as to how the calculations are done inspite of errors occurring in the Chain Surveying.

Correction due to incorrect length of chain

This is like a formula list which is to be kept in mind while making Calculations:

True distance = L’/L*measured distance

True area = (L’/L)2*measured area

True Volume = (L’/L)3 * measured volume

Where, L’ = incorrect length of chain

L = correct length of chain

The length of a line measured with 20m chain was found to be 500m. It was subsequently found that the chain was 0.04m too long. What is the length of line?

Correct length of chain, L’ = 20 + 0.04 = 20.04m

Length, L = 20m

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Errors in Chaining | Guide to Surveying and Levelling

Types of Errors occurring in Chain Surveying

There are two types of Errors that are commonly seen to occur in Chain Surveying. For students studying the concept of Chain Surveying, study of the occurrence of different types of Errors in Chain Surveying is important. In this article, we will briefly discuss different types of Errors in Chain Surveying and the situations in which they occur.

Types of Errors:

  1. Cumulative error
  2. Compensative error

Cumulative error

These errors always accumulate in one direction and are serious in nature. They affect the survey work considerably.

They make measurements too long or too short.

These errors are of two types and are known as systematic errors.

They are classified as follows:

  1. Positive error
  2. Negative error

Positive error

These errors make the measured length more than the actual length which results into wrong calculations by the Surveyor.

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Methods for Calculation of Areas in Surveying | Average Ordinate Rule

Calculation of Areas in Surveying | Average Ordinate Rule

In one of my previous articles, I discussed Midpoint Ordinate Rule in detail with an example and listed out various important methods used for the calculation of areas in Surveying. In this article, we will deal with the next important method (rule) used for the calculation of areas in the field of Surveying.

Here are the five important rules (Methods) used for the calculation of areas in Surveying:

  1. Midpoint ordinate rule
  2. Average ordinate rule
  3. Simpson’s rule
  4. Trapezoidal rule
  5. Graphical rule

Average Ordinate Rule

The rule states that (to the average of all the ordinates taken at each of the division of equal length multiplies by baseline length divided by number of ordinates).

Average Ordinate Rule
Average Ordinate Rule

O1, O2, O3, O4….On ordinate taken at each of division.

L = length of baseline

n = number of equal parts (the baseline divided)

d = common distance

Area = [(O1+ O2+ O3+ …. + On)*L]/(n+1)

Here is an example of a numerical problem regarding the calculation of areas using Average Ordinate Rule

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Different Methods for the Calculation of Areas in Surveying

Different methods for the calculation of Areas in the field of Surveying

In this article, we will list out different methods to calculate the areas in Surveying and also study each of the method in depth… We will also explain each method with a suitable example for your better understanding…

Here are the five important rules (Methods) used for the calculation of areas in Surveying:

  1. Midpoint ordinate rule
  2. Average ordinate rule
  3. Simpson’s rule
  4. Trapezoidal rule
  5. Graphical rule

We will now move on with our discussion on the first rule “Midpoint ordinate rule” with a suitable example.

Midpoint-ordinate rule

The rule states that if the sum of all the ordinates taken at midpoints of each division multiplied by the length of the base line having the ordinates (9 divided by number of equal parts).

Midpoint ordinate rule | Method for calculating area in Surveying
Midpoint ordinate rule | Method for calculating area in Surveying

In this, base line AB is divided into equal parts and the ordinates are measured in the midpoints of each division.

Area = ([O1 +O2 + O3 + …..+ On]*L)/n

L = length of baseline

n = number of equal parts, the baseline is divided

d = common distance between the ordinates

Example of the area calculation by midpoint ordinate rule

The following perpendicular offsets were taken at 10m interval from a survey line to an irregular boundary line. The ordinates are measured at midpoint of the division are 10, 13, 17, 16, 19, 21, 20 and 18m. Calculate the are enclosed by the midpoint ordinate rule.

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Stitching Cracks in the Walls | Design of RCC Structures

How to stitch the cracks in the plastering of the wall and prevent further cracking?

Occurrence of cracks in a building is a common problem to deal with. The intensity of the problem of the occurrence of cracks increases with the increased depth of the cracks.

The cracks are generally classified into two major categories:

  1. Minor Cracks or Surface cracks
  2. Major cracks or Structural Cracks

Minor cracks or Surface Cracks

In one of my earlier articles, I discussed various reasons for the occurrence of minor cracks or Surface cracks. Surface cracks do not result in making the structure unsound. The structural stability is intact incase of minor cracks. The aesthetics are affected due to the occurrence of minor cracks.

Major Cracks or Structural cracks

Major cracks or Structural cracks as the name suggests are responsible for making the structure unsound in nature. When deeper cracks are seen to develop on structural components such as columns, beams, foundations, these cracks are termed as Structural cracks since they cause structural damage.

Now we will go ahead with discussing how the cracks occurring on the plastered surface can be stitched and prevented from further deepening…

Stitching cracks
Stitching cracks

The small diagonal grooves are made across the crack.

16mm diameter steel rods are embedded in the grooves and are then covered with cement concrete.

If there are too many cracks occurring on the plastered surface, remove the entire plaster and plaster it again.