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8/22/2019 Handout 1.pdf
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8/14/20
Engineering Graphics & Models
Part 1: Surveying
Part 2: Engineering Graphics & Models
Lecture overview
Part 1: Surveying
Introduction to surveying
Introduction to Height Measurement
Angle & Distance measurement
Detail survey
Lecture overview
Part 2: Engineering Graphics & Models Introduction to Graphics Communication
Sketching
Engineering Geometry
Modeling Fundamentals
Multiviews and visualization
Auxiliary Views
Pictorial projections
Section Views
Dimensioning and Tolerancing
Working Drawings and Assemblies
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Introduction to Surveying
What is surveying?
What do surveyors do?
Why is surveying important?
What is Surveying?
Acquisition, analysis and
presentation of spatial data
Positioning features on and
below the surface of the Earthand representing these
features on a map
Position determined by
measurement of angles,
distances and heights
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What do surveyors do?
Acquirespatial
data using a wide
range of equipmentand techniques
Visualise 2D and
3D data using
AutoCAD, GIS, 3DStudio Max, Maya
etc
Process and analyse
measurements
Total Stations
Taping
Levelling
GPS
Laser Scanning
Coordinate Geometry
Trigonometry
Statistics
GIS
Excel
StarNet
Leica GeoOffice
THE PLOWMAN'SCRAVEN HOUSEFREE
Surveyors in Civil Engineering... Produce accurate, up-to-date plans for the project design process
Map topography to assess the best locations for the construction of tunnels,
bridges, roads etc. (i.e. Detailing)
Set out a site so that structures are built in the correct location and with the
correct building dimensions
Provide stations and benchmarks s to control and monitor the construction
process
Record final as-built positions
Establish control networks for monitoring future movement of structures such as
dams and bridges (deformation monitoring)
Other types of Surveying
Hydrographic Surveying
Photogrammetry
Remote Sensing
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Deformation Monitoring
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What skills does a good surveyor have?
good spatial awareness
trigonometry and coordinate geometrystatistical analysis
computer-aided drawing
project management
using digi tal Geomatics resources
using a wide range of specialist equipment
data acquisition by a range of methods
cartography
Geographic Information Systems (GIS)
www.rics.org
1nd Year Surveying Curriculum
Lecture: Introduction to Surveying & Mapping Science
Lecture: Introduction to Height Measurement Levelling
Lecture: Introduction to Angle and Distance Measurement
Lecture: Detail Survey
Practical: Levelling
Practical: Total Stations
Computer Class: AutoCAD
Computer Class: ArcMap GIS
Map Scales
Ratio of map distance to
ground distance
e.g. 1:10,000 scale implies that 1
unit on the map represents 10,000
units on the ground
The smaller the scale, the
less detail will be shown
small scale > 1:50000medium scale 1:500 to 1:50000
large scale < 1: 500
The smallest distance discernable on a map is 0.2mm (i.e. the thinnest line width
that can be seen by the human eye)
For a 1:500m survey, what level of detail should be recorded?
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Accuracy and Precision
Inaccurate
Precise
Accurate
Imprecise
Accurate
Precise
Types of Error
1. Gross
2. Systematic
3. Random
Plane Surveying
VS
Geodetic Surveying
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Rectangular Coordinate Systems
P
X
Y
x
y
Location of P defined as (x, y)
SOURCE: Bostock and Chandler (1990, p. 75)
Describe the location of London here -
Fundamental Surveying Problem
A
B
N
E
E?
N?
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Trigonometry
A
B
Opposite (b)
Adjacent (c)
sin = opposite/hypotenuse
cos = adjacent/hypotenuse
tan = opposite/adjacent
Polar to Rectangular Conversions
If the coordinates of A (EA, NA) are known, the coordinates of B (EB,
NB) are obtained from A as follows:
EB = EA + EAB= EA + DABsinAB
NB = NA+ NAB = NA + DABcosAB
DAB= the horizontal distance from A to B
AB= the whole circle bearing from A to B
Polar Coordinate Systems
P
rq
N
O
Location of P defined as (r,q)
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SOURCE: Bostock and Chandler (1990, p. 75)
Describe the location of London here -
Polar to Rectangular Conversions
EB = EA + EAB = EA + DABsinAB
NB = NA+ NAB = NA + DABcosAB
Horizontal Distance
BearingKnown coordinates
BearingsThe bearing () is the direction of a line between two points, measured
as a clockwise angle from Grid North.
2S
1S
q
q
180
N
N
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Polar to Rectangular Conversions: Example
The coordinates of A are 311.617m E, 447.245m N.
Calculate the coordinates of B, where:
DAB = 57.916m and AB = 371120.
SOURCE: UREN & PRICE (2006, p. 189)
Rectangular to Polar Conversions: Example
The coordinates of two points A and B are known as
EA = 469.721m, NA = 338.466m and
EB= 501.035m, NB = 310.617m.
Calculate the horizontal distance DAB and whole-circle bearing
AB of line AB.
Pythagoras Theorem: Distance
The distance formula for Cartesian coordinates is derived from the
Pythagorean theorem. If (x0, y0) and (x1, y1) are points in the plane, then
the distance between them is given by
D = (E2 + N2)
D =1
2
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Quadrants
SOURCE: UREN & PRICE (2006, p. 191)
If the change in E and change in N are both positive, your line
lies in Quadrant I
If the change in E is positive and your change in N is negative
your line lies in Quadrant II
If the change in E and change in N are both negative, your line
lies in Quadrant III
If the change in E is negative and your change in N is positive
your line lies in Quadrant IV
Principle of Radiation
A
r
r = horizontal distance
= horizontal angle subtended from line AB to the detail point
P
(known
coords)
B
(known
coords)
Calculate bearing
from coords of A and B
Calculate bearing
from bearing AB and Hz angle
Calculate coords of P
using bearing and
distance
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Control Points
All survey work is based on a series of control points
Located throughout a site at fixed positions within a
coordinate system
q Starting points for detail survey (topographic mapping) projects
q Dimensional control for setting out
qMeasured repeatedly in deformation monitoring
Final Map
Control Points
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Detail Points
Control Surveys
SOURCE: UREN & PRICE (2006, p. 242)
Baselines, traverses, networks: all require measurement ofangles and distances.
Extended by Intersection and
Resectiontechniques
Definitions of North
Arbitrary North
Common method used on siteto define bearings andcoordinates
Magnetic North
Defined using a prismaticcompass
Grid North
This is the direction defined bythe axes of a coordinate systemand its grid.
True North
Based on the spin-axis of theEarth. Used only in specialconstruction projects.
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Defining a 2D coordinate system
Parameters Position (2), Orientation & Scale
i) define coordinates of one point forposition
ii) define the bearing of one line for orientation
iii) incorporate distances in the survey for scale
(237,155)(237,155)
315
BUILDING 3
BUILDING 1BUILDING 2
1S
4S 3S
2S
Boundary
Establishing control on site
BUILDING 3
BUILDING 1
BUILDING 21S
4S 3S
2S
1000 E
2000 N
Arbitrary Bearing
Arbitrary
Coordinates
Key
____ Measured Horizontal Distances
____ Measured Horizontal AnglesBy traversing
Boundary
[Arbitrary]
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Tying into an existing system
Parameters Position (2), Orientation & Scale
a) start at one known point forposition
b) observe an angle from a 2ndknown point (RO) fororientation
c) incorporate distances in thesurvey for scale
BUILDING 3
BUILDING 1BUILDING 2
1S
4S 3S
2S Boundary
RO
Key
____ Measured Horizontal Distances
____ Measured Horizontal AnglesBy traversing
Known
Coordinates
Known
Coordinates
Tying into existing grid
Determine forward bearings of all the traverse lines
If the internal angles have been measured:
forward bearing = back bearing -clockwise angle (Hz Angle)
If the external angles have been measured:
forward bearing = back bearing + clockwise angle (Hz Angle)
The forward bearings are then used in polar to rectangular
conversions along with the measured horizontal distances to
calculate E and N from one control point to the next
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Bearing is computed using the opening bearing
(either arbitrary or calculated from two known
points) and the horizontal angle measured by
the Total Station
Polar to Rectangular Conversions
EB = EA + EAB = EA + DABsinAB
NB = NA+ NAB = NA + DABcosAB
Horizontal Distance
measured by total station
Known coordinates
(either arbitrary, existing or
computed)
Intersection
Method of coordinating a point without setting up on it
Establish coordinates for landmarks around a site, e.g. church spires and
tall buildings
Fixing the framework of building structure surveys from ground level
baselines
Used often in setting out, particularly during construction projects with
tall structures
d
gb
A
C
B
D NBC
D EBC
N
D NBC
DEBC
qBC
Elevated point
of unknown coords
Geometry for horizontal observations and computation by
intersection-from-a-baseline
Baseline established from STN A to STN B
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VABC
hi
datum
hB
hC
DhBC
dBC
B
C
hihi
hB
hC
DhBC
HzDistBC
Geometry for vertical observations and computation by
intersection-from-a-baseline
hC=hB +hiB+DhBC
Calculation
Step 1: Calculate the bearing BC
Step 2: Distance BC cannot be measured directly so use the Sine Rule to compute it
Step 3: Calculate the Eand N from B to C
Step 4: Apply Eand N to coordinates of B to c alculate Eastings and Northing of C
Step 5: Calculate the height of Point C use the trigonometric height method, hC= hB +hiB +DhBC
The Sine Rule
^^^
sinsinsin A
BC
B
AC
C
AB==
^
^sin.
sin
A
C
ABBC=
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Intersection: Measurements
To calculate Eastings and Northings of the elevated point, Hz
Angles [b and g] at each station, along the baseline to the elevated
point need to be observed
To calculate the height of the elevated point, the V Angle [V] from
one station to the point needs to be observed
The height of the instrument above the ground mark [h i] must also
be recorded for the trigonometric method for computing height.
Weak observation geometries for intersection-from-
a-baseline
A B
C
A B
C
B
C
qBC
A B
C
A B
C
A B
C
B
C
qBC
Example
The image partwith relationship ID rId2was not found in the file.
A baseline has been established between
Point A and Point B.
A third point, C, is located at the top of anearby church spire.
Calculate the horizontal coordinates and
height of point C.
Instrument height at B = 1.560 m
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Recap
After this introductory lecture you should begin to understand:
Modern definitions of surveying, the importance of surveying and
the role and activities of surveyors within civil engineering
The structure of the surveying curriculum how it relates to the
learning outcomes
The importance of control to all survey projects
How to define a 2D coordinate system
The mathematics behind plane surveying