Engineering Surveying - II CE313

Surveying Drafting and Computations

Muhammad Noman

IntroductionCourse Book: Surveying and Levelling Part-II by T. P. Kanetker and S.V. KulkarniReference Books: 1. Thomas, M. Lillesand & Ralph W. Kiefer Remote Sensing and Images Interpretation, 5th edition, John Wiley & Sons, Inc. (2005)2. Surveying principles and Application by “Barry F. Kavanagh”, 7th Edition3. Wolf P. R. & Ghilani C. D., Elementary Surveying – An introduction to Geometrics, 11th Edition, Prentice Hall, USA, 2004.Lectures will also be uploaded on: nomank123.wordpress.comEmail: Muhammad.noman@abasyn.edu.pk

Surveying (Definition)

Definition: Surveying is the technique for determining the relative positions of different features on, above or beneath the surface of the earth by means of direct or indirect measurements and finally representingthem on a sheet of paper called Plan or Map.

Uses of Surveying

1. To prepare a topographical map which shows hills, valleys, rivers, forests, villages, towns etc.

Uses of Surveying

2. To prepare a cadastral map which shows the boundaries of fields, plots, houses and other properties..

Uses of Surveying3. To prepare an engineering map which shows the position of engineering works such as buildings, roads, railways, dams, canals.

4. To prepare a contour map to know the topography of the area to find out the best possible site for roads, railways, bridges, reservoirs, canals, etc.

Uses of Surveying

5. Surveying is also used to prepare military map, geological map, archaeological map etc.

6. For setting out work and transferring details from the map on the ground.

Computation of Area

The main objective of the surveying is to compute the areas and volumes. Generally, the lands will be of irregular shaped polygons. There are formulae readily available for regular polygons like, triangle, rectangle, square and other polygons. But for determining the areas of irregular polygons, different methods are used.

Earthwork computation is involved in the excavation of channels, digging of trenches for laying underground pipelines, formation of bunds, earthen embankments, digging farm ponds, land levelling and smoothening. In most of the computation the cross sectional areas at different interval along the length of the channels and embankments are first calculated and the volume of the prismoids are obtained between successive cross section either by trapezoidal or prismoidal formula.

Calculation of area is carried out by any one of the following methods:

a) Mean-ordinate method

c) Trapezoidal rule

d) Simpson’s rule

Mean Ordinate Rule

Consider The following Picture:

A = 𝑛−1

𝑛x [𝑦1 + 𝑦2+𝑦3 . . . . . 𝑦𝑛 ] x d

Where :

n = number of offsets

d = division of each length

𝑦1, 𝑦2, 𝑦3 . . . . . 𝑦𝑛 are lengths of offsets

Trapezoidal Rule

• 𝐴 = [(𝑦1+𝑦𝑛

2) + 𝑦2 + 𝑦3 + 𝑦4. . . . . . . . 𝑦𝑛−1] x d

Simpson’s Rule

A = d/3 (X + 2O + 4E)

Where:

X = y1 + yn

O = Sum of odd numbers i.e. y3 + y5 +y7 …..

E = Sum of Even Numbers i.e. y2 + y4 +y6 …..

Note: Simpson’s rule work only for odd numbers. If our data is in even numbers, we will make it odd by removing the last ordinate and adding its area in the end.

Comparison between Simpsons Rule and Trapezoidal Rule

Trapezoidal Rule Simpson’s Rule

The boundary between the ordinates is considered to be straight

The boundary between the ordinates is considered to be an arc of a parabola

There is no limitation. It can be applied for any number of ordinates

To apply this rule, the number of ordinates must be odd

It gives an approximate result It gives a more accurate result.

Computation of Volume

• For computation of area, we must compute volume of the cross sectional area.

• There can be two types of area sections:

a) Level Section [ A = h (b+nh) ]

b) Two Level Section [ A = 𝑛 ℎ1ℎ2 +𝑏

2ℎ1 + ℎ2 ]

Where:

h = height

b = base

n = slope (horizontal to vertical slope)

Computation of Volume

• Trapezoidal Rule

𝑉 = [(𝐴1+𝐴𝑛

2) + 𝐴2 + 𝐴3 + 𝐴4. . . . . . . . 𝐴𝑛−1] x d

• Prismoidal RuleV = d/3 (X + 2O + 4E)

Where:

X = A1 + An

O = Sum of odd numbers i.e. A3 + A5 +A7 …..

E = Sum of Even Numbers i.e. A2 + A4 + A6 …..

Thank you