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  • INTRODUCTION OF SURVEYING
    • INTRODUCTION
    • REFERENCE ELLIPSOID
    • BASIC MEASUREMENTS
    • The geoid
    • PROTECTION AND REFERENCING
    • CONTROL NETWORKS
    • The ellipsoid
    • BASIC SETTING-OUT PROCEDURES USING COORDINATES
    • LOCATING POSITION
    • COORDINATE SYSTEMS
    • USE OF GRIDS
    • PLOTTING DETAIL
    • Geodetic coordinates
    • SETTING OUT BUILDINGS
    • Computer-aided design (CAD)
    • Cartesian coordinates
    • Error and uncertainty
    • Plane rectangular coordinates
    • SIGNIFICANT FIGURES
    • Height
    • ERRORS IN MEASUREMENT
    • WEIGHT MATRIX
    • LOCAL SYSTEMS
    • Probability
    • ERROR ANALYSIS
    • Deviation of the vertical
    • INDICES OF PRECISION
    • VARIANCE-COVARIANCE MATRIX OF THE PARAMETERS
    • COMPUTATION ON THE ELLIPSOID
    • COMBINATION OF ERRORS
    • Uncertainty of addition or subtraction
    • Eigenvalues, eigenvectors and error ellipses
    • BLUNDER DETECTION
    • RELIABILITY OF THE OBSERVATIONS
    • PRACTICAL CONSIDERATIONS
    • ESTIMATION IN THREE DIMENSIONS

  • LEVELLING
    • LEVELLING
    • OPTICAL METHODS
    • CURVATURE AND REFRACTION
    • MECHANICAL METHODS
    • EQUIPMENT
    • Weiss quadrilateral
    • INSTRUMENT ADJUSTMENT
    • PARAMETER VECTOR
    • Single wires in two shafts
    • Automatic level
    • DESIGN MATRIX AND OBSERVATIONS VECTOR
    • GYRO-THEODOLITE
    • PRINCIPLE OF LEVELLING
    • Plan network
    • SOURCES OF ERROR
    • Distance equation
    • LEVELLING APPLICATIONS
    • Direction & Angle equation
    • Direct and Indirect contouring
    • Controlling earthworks
    • RECIPROCAL LEVELLING
    • PRECISE LEVELLING
    • Parallel plate micrometer
    • ERROR ELLIPSES
    • Field procedure
    • Booking and computing
    • DIGITAL LEVELLING
    • Factors affecting the measuring procedure
    • TRIGONOMETRICAL LEVELLING

  • CONTOURING
    • TAPES
    • Introduction of Satellite positioning
    • FIELD WORK
    • GPS SEGMENTS
    • Measuring in catenary
    • GPS
    • DISTANCE ADJUSTMENT
    • SATELLITE ORBITS
    • Sag
    • BASIC PRINCIPLE OF POSITION FIXING
    • ERRORS IN TAPING
    • DIFFERENCING DATA
    • Tension,Sag and Slope
    • GPS OBSERVING METHODS
    • ELECTROMAGNETIC DISTANCE MEASUREMENT (EDM)
    • Kinematic positioning
    • ERROR SOURCES
    • Global datums
    • GPS SYSTEM FUTURE
    • DATUM TRANSFORMATIONS
    • GALILEO
    • ORTHOMORPHIC PROJECTION
    • APPLICATIONS
    • ORDNANCE SURVEY NATIONAL GRID
    • (t – T) correction
    • PRACTICAL APPLICATIONS
    • Contouring
    • HEIGHTING WITH GPS

  • Theodolite Surveying
    • PLANE RECTANGULAR COORDINATES
    • PRINCIPLE OF LEAST SQUARES
    • PRINCIPLE OF LEAST SQUARES
    • TRAVERSING
    • LINEARIZATION
    • LEAST SQUARES APPLIED TO SURVEYING
    • Reconnaissance
    • NETWORKS
    • LINEARIZATION
    • Sources of error
    • Traverse computation
    • TRIANGULATION
    • Resection and intersection
    • Resection
    • NETWORKS
    • INSTRUMENT ADJUSTMENT
    • FIELD PROCEDURE
    • Setting up using the optical plumb-bob
    • MEASURING ANGLES
    • Measurement by directions
    • SOURCES OF ERROR

  • Simple Curves
    • CIRCULAR CURVES
    • Plotted areas
    • RESPONSIBILITY ON SITE
    • PHOTOGRAMMETRY
    • SETTING OUT CURVES
    • PARTITION OF LAND
    • COMPOUND AND REVERSE CURVES
    • CROSS-SECTIONS
    • SHORT AND/OR SMALL-RADIUS CURVES
    • VOLUMES
    • TRANSITION CURVES
    • Effect of curvature on volumes
    • Centrifugal ratio
    • MASS-HAUL DIAGRAMS
    • CONTROLLING VERTICALITY
    • The equation of motion
    • Coefficient of friction
    • CONTROLLING GRADING EXCAVATION
    • Sources of error
    • SETTING-OUT DATA
    • ROUTE LOCATION
    • LINE AND LEVEL
    • Highway transition curve tables (metric)
    • THE OSCULATING CIRCLE
    • Transitions joining arcs of different radii (compound curves)
    • Coordinates on the transition spiral
    • VERTICAL CURVES
    • Vertical curve design
    • Sight distances
    • Permissible approximations in vertical curve computation

Branch : Civil Engineering
Subject : Surveying-I
Unit : Simple Curves

SETTING-OUT DATA


Figure  indicates the usual situation of two straights projected forward to intersect at I with a clothoid transition curve commencing from tangent point T1 and joining the circular arc at t1. The second equal transition commences at t2 and joins at T2. Thus the composite curve from T1 to T2 consists of a circular arc with transitions at entry and exit.

(1) Fixing the tangent points T1 and T2:

In order to fix T1 and T2 the tangent lengths T1I and T2I are measured from I back down the straights, or they are set out direct by coordinates.

Transition and circular curves

The values of S and C are abstracted from the Highway Transition Curve Tables (Metric) .


(2) Setting out the transitions:
Referring to;


The theodolite is set at T1 and oriented to I with the horizontal circle reading zero. The transition is then pegged out using deflection angles (θ) and chords (Rankine’s method) in exactly the same way as for a simple curve.


The data are calculated as follows:


(a) The length of transition L is calculated (see design factors in Section 10.5.5 and 10.5.6), assume L = 100 m.
(b) It is then spliinto, say, 10 arcs, each 10 m in length (ignoring through chainage), the equivalent chord lengths being obtained from:

Setting out the transitions

(c) The setting-out angles θ1, θ2, . . . , θn are obtained as follows:
Basic formula for clothoid: l

(l is any distance along the transition other than total distance L)

Note that:
(a) The values for l1, l2, etc., are accumulative.
(b) Thus the values obtained for θ1, θ2, etc., are the final setting-out angles and are obviously not to be summed.
(c) Although the chord length used is accumulative, the method of setting out is still the same as for the simple curve.

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