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Topic 7: Setting out

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Page 1: Setting Out

Topic 7: Setting out

Page 2: Setting Out

Aims

-Understand the roles of the various different types of personnel who are involved

in the setting out process

-Understand the aims of setting out

-Refer to the different types of plans that may be used in the setting out process

-Appreciate the good working practices that should be undertaken in order that

the aims of setting out can be achieved

-Understand the procedures required to ensure that the horizontal and vertical

control requirements of setting out operations can be met

-Set out design points on site by a number of methods

-Apply horizontal and vertical control techniques to second-stage setting out

operations

-Appreciate the application of laser instruments in surveying and setting out

Page 3: Setting Out

What is setting out?

A definition of setting out, often used, is that it is the reverse of surveying.

Whereas surveying is a process for forming maps and plans of a particular site or

area, setting out begins with plans and ends with the various elements of a

particular plan correctly positioned on site.

However most techniques and equipment used in surveying are also used in

setting out i.e. while surveying may be the opposite of setting out, the processes

and instruments are almost identical.

The International Organisation for Standardisation (ISO) define setting out as:

Setting out is the establishment of the marks and lines to define the position and

level of the elements for the construction work so that works may proceed with

reference to them. This process may be contrasted with the purpose of

surveying which is to determine by measurement the position of existing features.

Page 4: Setting Out

-Setting out is one application of surveying

-Most of the techniques and equipment used in surveying are also used in setting

out

-Mistakes in setting out can be costly

-For setting out to be undertaken successfully good work practices should be

employed

-There are three parties involved in the construction procedures: the employer,

the engineer and the contractor

-Although the engineer checks the work, the setting out is the responsibility of the

contractor

-The cost of correcting any errors in the setting out has to be paid for by the

Contractor, provided the engineer has supplies reliable information in writing

Page 5: Setting Out

The aims of setting out

There are two main aims when undertaking setting out operations:

-The various elements of the scheme must be correct in all three dimensions

both relatively and absolutely, that is each must be its correct size, in its correct

plan position and correct reduced level

-Once setting out begins it must proceed quickly with little or no delay in order

that the works can proceed smoothly and the cost can be minimised. It must

always be remembered that the contractors main commercial purpose is to make

a profit – therefore setting out needs to be done efficiently.

Page 6: Setting Out

Principles of setting out

The main aim of setting out is to ensure that the various elements of the scheme

are positioned correctly in all three dimensions.

Horizontal control techniques

In order that the design of the scheme can be correctly fixed in position, it is

necessary to establish points on the site which the E, N coordinates are known.

These are horizontal control points and, once they have been located they can

be used with a positioning technique to set out E, N coordinates of the design

points.

Two factors need to be taken into account when establishing horizontal control

points.

1. The control points should be located throughout the site in order that all the

design points can be fixed from at least two or three of them so that the work can

be independently checked.

2. The design points must be set out to the accuracy stated in the specifications

Page 7: Setting Out

The accuracy must be obtained throughout the whole network and this can be

achieved by establishing different levels of control based on one of the

fundamental tenets of surveying: working from the whole to the part.

In practice, this normally involves starting with a small number of very accurately

measured control points (known as first level or primary control) which enclose

the area in question and then using these to establish second level or secondary

control points near the site.

When establishing the control network care needs to be taken that the tolerances

specified are met.

An example if working from the whole to the part using two different levels of

control are shown in the next diagram. In this, the first level of control is provided

by a traverse which is run through the site in question to provide a number of well

positioned primary control points.

These in turn are used to establish a second level of control, in this case

secondary site points at each of a series of baselines which define important

elements of the scheme.

Page 8: Setting Out

On some schemes the same control points that were used in the production of

the site plan prior to design work are used for setting out. These muse be re-

measured before setting out – as positions may have changed for a number of

reasons.

Horizontal control points should be located as near as possible to the site in open

positions for ease of working, but well away from the construction area and traffic

routes to avoid them being disturbed.

Page 9: Setting Out

The construction and protection of control points is very important. Wooden pegs

are often used for non-permanent stations.

For permanent control points it is recommended that they be constructed with

concrete – as shown below.

Page 10: Setting Out

Baselines

A baseline is a line running between two points of a known position. Any

baselines required to set out a project should be specified on the setting out plan

by the designer and included in the contract.

Baselines can take many forms: they can be simply two specified points joined,

they can run between two buildings, they can mark the boundary with an existing

building/development or they can mark the centre line for a new road.

Baselines can be used in a number of different ways:

- Where a baseline is specified to run between two points then once the points

have been established on site, the design points can be set out from the baseline

by offsetting using tapes (as seen below).

Page 11: Setting Out

A design point D is to be set out at right angles to a baseline AB from point C

which lies at a distance y from point A. The required offset distance from C to D

is x. Distances x and y will be given by the designer and will usually be

horizontal distances.

- Primary site control points, such as traverse stations E & F in the figure below

can be use to establish a baseline AB by angle α and distance l values.

Page 12: Setting Out

Subsidiary offset lines can then be set off at right angles from each end of the

baseline to fix two corners R and S of building Z. Once R and S have been

pegged out, the horizontal length of RS is measured and checked against its

designed value. If it is within the required tolerance, points R and S can be used

as a baseline to set out the corners T and U.

- Design points can be set out by taping known as distances from each end of a

baseline as shown below.

Page 13: Setting Out

At point A on building X is set out by taping dimensions 1 and 2 from the baseline

and point B by taping dimensions 3 and 4. As before, the set out lengths of AB is

then checked against its designed value and within tolerance, it can be used as a

baseline to set out corners C and D.

-In some cases, the designer may specify a baseline that runs between points on

two existing buildings. Design points are then set out from this line either by

offsetting at right angles or by measuring distances from points on the line. The

accuracy of this method depends upon how well the baseline can be established

and how the dimensions required to set out the design points are known.

The accuracy of the baselines method increases if two baselines at right angles

to each other are used.

Design points can be established either by measuring and offsetting from both

lines, or a grid system can be set up to provide additional control points in the

area enclosed by the baselines.

Page 14: Setting Out

Reference grids

A control grid enables points to be set over a large area. Several different grids

can be used in setting out

-Survey grid: is drawn on the survey plan from the original traverse or network.

The grid points have known eastings and northings related either to some

arbitrary origin or to the national grid.

-Site grid: is used by the designer. It is usually related in some way to the

survey grid and should, if possible, actually be the survey grid, the advantage of

this being that if the original control stations have been permanently marked then

the design points will be on the same coordinate system and setting out is greatly

simplified.

Page 15: Setting Out

- The structural grid is established around a particular building or structure which

contains much detail such as columns, which cannot be set out with sufficient

accuracy from the grid site.

-The secondary grid is established inside the structure from the structural grid

when it is no longer possible to use the structural grid to establish internal

features of the building – as the vision becomes obscured.

Offset pegs

Whether used in the form of a baseline or a grid, the horizontal control points are

used to establish design points on the proposed structure.

Once excavations for foundations begin, the corner pegs will be lost. To avoid

this extra pegs called offset pegs are used

Page 16: Setting Out

Vertical control techniques

In order that design points on the works can be positioned at their correct levels,

vertical control points of known elevation relative to some specified vertical datum

are established. To ordnance datum is commonly used and levels on the site are

reduced to a nearby OS benchmark.

Transferred or temporary benchmarks

The positions of TBMs should be fixed during the initial reconnaissance so that

their construction can be completed in good time and they can be allowed to

settle before levelling them in. In practice, 20mm diameter steel bolts and 100mm

long, driven into existing steps, ledges, footpaths etc are ideal.

Page 17: Setting Out

If TBM are constructed at ground level on site, a design to that shown below

should be used.

There should never be more that 80m between TBMs on site and the accuracy of

levelling should be within the following limits:

Site TBM relative to the MBM ± 0.005m

Spot levels on soft surfaces relative to a TMB ± 0.010m

Spot levels on hard surfaces relative to a TBM ± 0.005m

Page 18: Setting Out

Sight Rails

These consist of a horizontal timber cross piece nailed to a single upright or a

pair of uprights driven into the ground (see below)

The upper edge of the cross piece is set to a convenient height above the

required plane of the structure, usually to the nearest 100mm, and should be a

height above ground to ensure convenient alignment by eye with the upper edge.

Page 19: Setting Out

Sight rails are usually offset 2 or 3 metres at right angles to construction lines to

avoid them being damaged as excavations proceed.

Travellers and boning rods

A traveller is similar in appearance to a sight rail on a single support and is

portable. The length of the upper edge to its base should be a convenient

dimension to the nearest half metre.

Travellers are used in conjunction with sight rails. The sight rails are set some

convenient value above the required plane and the travellers are constructed so

that their length is equal to this value.

Page 20: Setting Out

As excavation works proceeds, the traveller is sighted in between the sight rails

and used to monitor the cutting and filling.

Slope rails or batter boards

For controlling side slopes on embankments and cuttings slope rails are used.

For an embankment the slope rails usually define a plane parallel to the slope of

the embankment offset by a convenient distance:

Page 21: Setting Out

For a cutting the slope rails can either be used to define the actual plane of the

slope or an offset plane as shown below:

Page 22: Setting Out

The advantage of the above method being that additional slope rails may be

added as excavation proceeds.

The advantage of this method being that the slope rail can be lower in height

and may make it easier to sight along than the example above.

Page 23: Setting Out

Positioning Slope Rails

In order to position slope rails we must first locate the toe of the embankment.

Consider the embankment below, which runs from A to B with a width of 12m.

Point C is on the existing ground level. The sides of the embankment are to

slope at 1 in s. the procedure is as follows:

Page 24: Setting Out

1.From the Road Design / Plans obtain the reduced level of A.

2. Peg out point C by measuring a distance 6m horizontally from F at right

angles to the centreline.

3.Peg out points at 5m intervals from point C towards and beyond T.

4. Measure the reduced level on the ground surface at the first 5m peg

5.Calculate the proposed reduced level of on the embankment slope above this

point from:

6. Compare the measure and calculated values at the 5m point, if the ground

level measured is lower than the calculated slope level, the toe is located a

further 5m away from C.

7. Repeat the procedure for the 10m peg, the calculation becomes:

Page 25: Setting Out

Once the Toe has been located the wooden uprights of the slope rails can be

hammered in at some offset from the embankment/cutting. The next stage is

to calculate the required reduced levels at which the tope edges of the slope

rails must be fixed to the wooden uprights.

Page 26: Setting Out

For an embankment, assuming that a 1.5m traveller is to be used as shown, the

reduced levels of P and Q should be obtained using (it is assumed that the

RL at the toe is known):

For a cutting the reduced levels of R and S should be obtained using (it is

assumed that the RL at edge of the embankment is known):

Page 27: Setting Out

Profile boards

These are similar to sight rails but are used to determine the corners and sides

of buildings. Offset pegs are normally used to enable building corners to be

relocated after foundation excavation. Profile boards are normally erected near

each offset peg and used in the same way as a sight rail.

Page 28: Setting Out

A variation on corner profiles is to use a continuous profile all around the

building ser to a particular level above the required structural plane.

The advantage of a continuous profile is that the lines of the internal walls can

be marked on the profile and strung across to guide construction.

Page 29: Setting Out

Coordinate positioning techniques

For setting out by coordinates to be possible, a control network consisting of

coordinated points (with heights) must be established on site. These are

obtained by using theodolites, tapes, GPS and total station.

Setting out using a theodolite and tape

To set out using coordinates by theodolite and tape, one of the following

procedures is used:

1. Angle and distance from two control points e.g. from point A below, can be

set out from a control point S using one of two methods:

Using the inverse calculation, determine the horizontal length l (SA) and the

whole circle bearings of ST and SA.

Page 30: Setting Out

With the theodolite set up at S, sight T and set the horizontal circle to read zero

along this direction. Then the telescope is rotated through angle α to fix the

direction to A and measure l along this direction to fix the position of A. This is

known as setting out by angle and distance.

An alternative method would be to: compute l, WCB (ST) and WCB(SA) as per

the first method. Sight T from S and set the horizontal circle of the theodolite to

read the WCB of ST. Rotate the telescope towards point A until the WCB of SA

is read on the horizontal circle.

The telescope line of sight is no defining the direction of A and the exact

position of A can be fixed by measuring a horizontal distance l along this

direction. This is setting out by bearing and distance.

Page 31: Setting Out

2. Intersection with two theodolites, from four control points using angles or

bearings only. Intersection is shown below.

When setting out using coordinate-based methods with theodolites and tapes,

the situation may arise where there are no nearby control points available for

this. This is overcome by establishing a free station at any convenient place for

setting out. This is shown in the next FIG and it is essentially a resection.

Free station points are particularly applicable to large sites where the

coordinates of prominent features and targets on nearby buildings or parts of

the construction are known.

Page 32: Setting Out

The following steps are used when setting up a free station point:

-The theodolite is set up at some suitable place in the vicinity of the points

which are to be set out – hence the title free station as the choice of the

instrument position is arbitrary.

-Any angular resection is carried out to fix the position of the free station point.

-The coordinates of the free station are calculated

Following this, setting out continues as before and the required design points

are ser out using the theodolite at the free station point.

Page 33: Setting Out

Although setting out can be conducted using theodolites, tapes (and levels) in

what might be sometimes called traditional methods, a lot of work on site is

done using total stations and GPS equipment.

When setting out by so-called traditional methods, direct methods of angle and

distance are taken to position structures and other works from nearby control

points or from baselines.

Following this, offsets and profiles are put in place to define the main lines of a

building and provide vertical control for second stage setting out.

Despite their popularity on site, these well-established methods have the

disadvantages that the horizontal and vertical components of setting out have to

be done separately (levelling must be used for any heighting), they can be time

consuming if a lot of points have to be set out, and they require at least two

people to do the setting out.

Page 34: Setting Out

Setting out by total station

To use a total station for setting out, it must be levelled and then centred over a

control point in the same way as for a theodolite. As before this must be done

correctly otherwise the subsequent readings taken with the instrument will not

give the correct results.

Having set up the total station, it has to be orientated horizontally to the site

coordinate system and it may also have to be orientated vertically. For

horizontal orientation, the coordinates of the control point at which the

instrument is set up are entered into the total station.

An adjacent control point is then chosen as a reference point (reference object)

and the coordinates for this site are also keyed in. To orientate the total station,

the RO is sighted and the horizontal circle orientation programme automatically

computes the bearing from the total station to the RO.

For vertical orientation, the height of collimation of the total station has to be

determined. If the height of the control point at which the total station is known,

this is entered into the instrument or is already stored in the control point data.

Page 35: Setting Out

Once the total station has been orientated it can be used for setting out

horizontal positions either using the coordinates of the points to be set out

directly or using bearing and distance values calculated from these coordinates.

Two approaches can be used.

-When the coordinates of the point to be set out are used, these are usually

contained in the file together with the coordinates of the control points for the

project, and this is downloaded to the total station before work commences.

-If the bearing and distance to be set out are known, these can also be used for

setting out. They are entered into the total station and, as soon as the

appropriate key(s) are pressed to activate this is setting out mode, the

instrument once again displays the difference between the entered and

measured bearing values.

Page 36: Setting Out

Setting out by GPS

For setting out by GPS, an RTK system is required consisting of two geodetic

receivers working in precise relative mode.

One of these will be permanently located at a base station and the other (the

rover) will move around the site and take the measurements needed for

positioning design points.

In common with all other setting out methods, GPS is based on a control

network, which must be in place before any work can start.

Control points with positions defined on the site grid are needed for base

stations, for determining transformation parameters when deriving site

coordinates from GPS coordinates.

Depending on the site, control can be local and based on an arbitrary

coordinate system or it can be connected to a national system.

Page 37: Setting Out

For small local sites a control network consisting of at least three but preferably

five points with known site coordinates and heights is required for determining

transformation parameters.

This can be surveyed using a total station and traverse methods.

On large sites, whether they cover an extensive area or are long linear sites

such as those occurring on road and railway projects, site control is often based

on national control.

Page 38: Setting Out

Applying the principles of setting out

Stages in setting out

As the works proceed, the setting out falls into two broad stages.

First stage setting out

In practice, first stage setting out involves the use of many of the horizontal and

vertical control methods and positioning techniques . The purpose of this stage

is to locate the boundaries of the works in their correct position on the ground

surface and to define the major elements. In order to do this, horizontal and

vertical control points must be established on or near the site.

Second stage setting out

Second stage setting out continues on from the first stage, beginning at the

ground floor slab, road sub-base level etc. Up to this point, all the control will be

outside the main construction, for example, the pegs defining building corners,

centre lines and so on will have been knocked out during the earthmoving work

and only the original control will be undisturbed.

Page 39: Setting Out

Examples of setting out

Setting out a pipeline

This operation falls into the first category of setting out.

General considerations: sewers normally follow the natural fall in the land and

are laid at gradients which induce self-cleansing velocity. The figure below

shows a sight rail offset at right angles to a pipe line laid in a granular bedding

trench.

Page 40: Setting Out

Horizontal control: the working drawings will show the directions of the sewer

pipes and the positions of the manholes. The line of the sewer is normally

pegged at 20 to 30m intervals using coordinate methods of positioning from

reference points or in relation to existing detail. The direction of the line can be

sighted using a theodolite and pegs.

Vertical control: involves the erection of sight rails some convenient height

above the invert level of the pipe.

Erection and use of sight rails: the sight rail uprights are hammered firmly into

the ground, usually offset from the line rather than straddling it. Using a nearby

TBM and levelling equipment, the reduced levels of the tops of the uprights.

Where the natural slope of the ground is not approximately parallel to the

proposed pipe gradient, double sight rails can be used as shown in the next fig.

Often it is required to lay storm water and foul water sewers in adjacent

trenches. Since the storm water pipe is usually at a higher level than the foul

water pipe, it is common to dig one trench to two different levels – as shown in

fig 2 on the next slide.

Page 41: Setting Out
Page 42: Setting Out

Both pipe runs are then controlled using different sight rails nailed to the same

uprights.

Pipe laying: on completion of the excavation, the sight rail control is transferred

to pegs in the bottom of the trench as shown below

Page 43: Setting Out

Setting out a building to ground-floor level

This process falls into the first category of setting out. It must be remembered

when setting out that, since dimensions, whether scaled or designed, are

almost always horizontal, slope must be allowed for in surface taping on sloping

ground. The steps involved in setting out a building are as follows:

-Two corners of the building are ser out from a baseline, site grid or control

points

-From these two corners, the two other corners are ser out using a theodolite to

turn off the right angels as shown below

-Diagonals are checked

-Profile boards are placed at each corner

Page 44: Setting Out

Setting out bridge abutments

Structures such as bridge abutments can be set out by a combination of

horizontal control methods and coordinate positioning. The following procedure

should be used:

-The centre line of the two roads are set out

-The bridge is set out in advance of the road construction

-The bridge is set out in advance of the road construction. If GPS techniques

are to be used, the abutment points A, B, C and D can be set out directly.

-However, if total stations or theodolites and tapes are to be used then it will be

necessary to establish secondary site control points around the area containing

the abutments. These secondary points could either be in the form of a

structural grid

-TBMs are set up as separate levelled points or a control point can be levelled

and used as a TBM.

Page 45: Setting Out

If a structural grid in used (as in a), the distances from the secondary site

control points to abutment design points A, B, C and D must first be calculated.

They are then set out either using a theodolite to establish the directions and

steel tapes to measure the distances or by using a total station.

Page 46: Setting Out

-If coordinates are used as shown (b), the bearings and distances from the

secondary site control points to A, B, C and D are calculated from their

respective coordinates such that each design point can be established from at

least two control points.

-Once points A, B, C and D have been set out, their positions should be

checked by measuring between them and also measuring to them from control

points not used to establish them initially.

-Offset pegs are established for each of A, B, C and D to allow excavation and

foundation work to proceed and to enable the points to be relocated as and

when required.

-Once the foundations are established, the formwork, steel or precast units can

be positioned with reference to the offset pegs.

Page 47: Setting Out

Controlling vertically

One of the most important second stage setting out operations is to ensure that

those elements of the scheme which are designed to be vertical are actually

constructed be so, and there are a number of techniques available by which this

can be achieved.

Particular emphasis is placed on the control verticality in multi-storey structures.

In order to avoid repeating information earlier in this chapter, the following

assumptions have been made.

- Offset pegs have been established to enable the sides of the building to be

located as necessary.

-The structure being controlled has already had its ground floor slab constructed

and the horizontal control lines have already been transferred.

Plumb-bob methods The traditional method of controlling verticality is to use plumb-bobs, suspended

on piano wire or nylon. A range of weights is available (from 3 kg to 20 kg) and

two plumb-bobs are needed in order to provide a reference line from which the

upper floors may be controlled.

Page 48: Setting Out

In an ideal situation, the bob is suspended from an upper floor and moved until

it hangs over a datum reference mark on the ground floor slab.

If it is impossible or Inconvenient to hang the plumb-bob down the outside of the

structure, holes and openings must be provided in the floors to allow the plumb-

bob to hang through, and some form of centring frame will be necessary to

cover the opening to enable the exact point to be fixed.

Page 49: Setting Out

Theodolite methods

These methods assume that the theodolite is in perfect adjustment so that its

line of sight will describe a vertical plane when rotated about its tilting axis.

Controlling a multi -storey structure using a theodolite and targets

A and B are offset pegs. The procedure is as follows.

- The theodolite is set over offset peg A, carefully levelled and aligned on the

reference line marked on the side of the slab

- The line of sight is transferred to the higher floor and a target accurately

positioned at point C.

- A three-tripod traverse system is used and the target and theodolite are

interchanged. The theodolite, now at C, is sighted onto the target at A, transited

and used to line in a second target at D. Both faces must be used and the mean

position adopted for D.

- A three-tripod traverse system is again used between C and D and the

theodolite checks the line by sighting down from D to the reference mark at B,

again using both faces.

- It may be necessary to repeat the process if a slight discrepancy is found.

- The procedure is repeated along other sides of the building.

Page 50: Setting Out
Page 51: Setting Out

Transferring height from floor to floor

Reduced levels must be transferred several times during the second stage

setting out operations as the construction proceeds from floor to floor. One

method by which this can be done is to use a weighted steel tape to measure

from a datum in the base of the structure as shown in FIG A.

The base datum levels should be set in the bottom of lift wells, service ducts

and so on, such that an unrestricted taping line to roof level is provided. The

levels should be transferred to each new floor by always measuring from the

datum rather than from the previous floor.

Each floor is then provided with TBMs in key positions from which normal

levelling methods can be used to transfer levels on each floor. Alternatively, if

there are cast-in situ stairs present, a level and staff can be used to level up and

down the stairs, as shown in FIG B. Note that both up and down levelling must

be done as a check.

Page 52: Setting Out
Page 53: Setting Out

Setting Out Example 1 : Setting Out a pipeline using sight rails and a

Traveller

An existing sewer at P is to be continued to Q and R on a falling gradient of 1 in

150 for plan distances of 27.12m and 54.11m consecutively, where the position

of P, Q and R are defined by wooden uprights.

Level reading to staff on TBM (RL 89.52m) = 0.39m

Level reading to staff on top of upright at P = 0.16m

Level reading to staff on top of upright at Q = 0.35m

Level reading to staff on top of upright at R = 1.17m

Level reading to staff on invert of existing sewer at P = 2.84m

All readings are taken at the same instrument position.

Page 54: Setting Out

Solution

Height of collimation of instrument = 89.52 + 0.39 = 89.91m

Invert level at P = 89.91-2.84 = 87.07m

This gives:

Sight rail top edge level at P = 87.07 +2.5 = 89.57m

Level of top of upright at P = 89.91 – 0.16 = 89.75

Hence

Upright level – sight rail level = 89.75 – 89.57 = +0.18m

Therefore the top edge of the sight rail at P must be fixed 0.18m below the top

of the upright.

Fall of sewer from P to Q = -27.12 x (1/150) = -0.18m

Invert level at Q = 87.07 – 0.18 = 86.89m

Page 55: Setting Out

Sight rail top edge level at Q = 86.89 +2.50 = 89.39m

Level of top of upright at Q = 89.91-0.35=89.56m

Upright level – sight rail level = 89.56 – 89.39 = 0.17m

Therefore the top edge of the sight rail must be fixed 0.17m below the top

upright at Q.

Fall of sewer from P to R =

Invert level at R = 87.07 - 0.54 = 86.53m

Sight rail level at R = 86.53 + 2.50 = 89.03m

Level of top of upright at R = 89.91 -1.17 = 88.74m

Upright – sight rail = 88.74 - 89.03 = -0.29m

Therefore the top edge of the sight rail must be fixed 0.29m above to the top of

the upright at R, i.e. the upright must be extended.

m54.0150

11.5412.27−=

+−

Page 56: Setting Out

Setting Out Example 2 : Setting Out by intersection

A rectangular buildings having plan sides of 75.36 and 23.24m was set out with

its major axis aligned precisely east-west. The design of the coordinates of the

SE corner were (348.92, 591.76) and this corner was fixed by theodolite

intersection from two stations P and Q whose respective coordinate were

(296.51, 540.32) and (371.30, 522.22). The other corners were set out by

similar methods.

When setting out was completed, the sides and the diagonals of the building

were measured as a check. To help with this the existing ground levels at the

four corners of the proposed structure were determined by levelling:

SE(152.86m) SW(149.73m) NE(151.45m) NW(146.53m)

Page 57: Setting Out

Calculate the respective horizontal angles (to the nearest 20”) that were set off

P relative to PQ and at Q relative to QP in order to intersect position SE.

Calculate the surface check measurements that should have been obtained for

the four sides and two diagonals (assuming even gradients along the surface).

Calculation of α and β

Let the corner SE of the building be X:

Easting of X 348.92 Northing of X 591.76

Easting of P 296.51 Northing of P 540.32

∆EPX +52.41 ∆NPX +51.44

Therefore by rectangular to polar conversion:

Bearing PX = 45o32’07”

Easting of X 348.92 Northing of X 591.76

Easting of Q 371.30 Northing of Q 522.22

∆EQX -22.38 ∆NQX +69.54

Page 58: Setting Out

Therefore by rectangular to polar conversion:

Bearing QX = 342o09’37”

Easting of Q 371.30 Northing of Q 522.22

Easting of P 296.51 Northing of P 540.32

∆EQP +74.79 ∆NQP -18.10

Therefore by rectangular to polar conversion:

Bearing PX = 103o36’17”

This gives:

Angle α = bearing PQ – bearing PX = 58o04’10”

Clockwise angle to be set off P relative to PQ = 360o - 58o04’10” = 301o56’00”

Angle β = bearing QX – bearing QP = 58o33’20”

Clockwise angle to be set off P relative to PQ = 360o - 58o04’10” = 301o56’00”

(angles rounded to nearest 20” as specified)

Page 59: Setting Out

Calculation of surface checks

Recall that slope correction = + (∆h2/2L):

From SE to SW, ∆h = 156.82 – 149.73 = 7.09 ∆h2 = 50.27

From NE to NW, ∆h = 151.42 – 146.53 = 4.92 ∆h2 = 24.21

From SE to NE, ∆h = 156.82 – 151.42 = 5.37 ∆h2 = 28.84

From SW to NW, ∆h = 149.73 – 146.53 = 3.20 ∆h2 = 10.24

Hence the slope distances for all four sides should have been:

SE to SW =

NE to NW =

SE to NE =

SW to NW =

m59.7533.036.7536.752

27.5036.75 =+=

×

+

m52.7516.036.7536.752

21.2436.75 =+=

×

+

m86.2362.024.2324.232

24.2824.23 =+=

×

+

m46.2322.024.2324.232

24.1024.23 =+=

×

+

Page 60: Setting Out

For the diagonals:

Horizontal diagonals = m

From SE to NW, ∆h = 156.82 – 146.53 = 10.29 ∆h2 = 105.88

From SW to NE, ∆h = 151.45 – 149.73 = 1.72 ∆h2 = 2.96

Slope distances:

SE to NW =

SW to NE =

86.78)24.23()36.75(22

=+

m53.7967.086.7886.782

88.10586.78 =+=

×

+

m88.7802.086.7886.782

96.286.78 =+=

×

+

Page 61: Setting Out

Setting Out Example 3 : Using Site Rails

The six corners of a proposed L shaped excavation shown below have been set

out on site and offset pegs haven been established to help define the sides of

the excavation.

The proposed formation level of the surface of the excavation at point R is

95.72m. The surface is to fall at 1 in 150 from R to W and is to rise at a slope of

1 in 100 at right angle to the line RW.

To help with excavation sight rails are to be erected above the offset pegs for

use with a 2m traveller.

Page 62: Setting Out

Given the reduced levels of the offset pegs calculate the heights of the sight

rails to be used at P1, P2, P3 and P4.

Solution: for line P1RWP2

Formation level at P1 = 95.72 + (3/150) = 95.74m

Formation level at P2 = 95.72 – (48/150) = 95.40m

For offset peg P1

Required top of sight rail level = 95.74 + 2.00 = 97.74m

Actual to of peg level = 96.95m

Therefore, distance above P1 = 0.79m

Page 63: Setting Out

For offset peg P2

Required top of sight rail level = 95.40 + 2.00 = 97.40m

Actual to of peg level = 96.45m

Therefore, distance above P1 = 0.95m

Solution: for line P4UTP3

Page 64: Setting Out

Formation level at Z = 95.72 - (15/150) = 95.62m

Formation level at P3 = 95.62 – (28/100) = 95.90m

Formation level at P4 = 95.62 - (3/100) = 95.59m

For offset peg P3

Required top of sight rail level = 95.90 + 2.00 = 97.90m

Actual to of peg level = 97.12m

Therefore, distance above P1 = 0.78m

For offset peg P4

Required top of sight rail level = 95.59 + 2.00 = 97.59m

Actual to of peg level = 96.75m

Therefore, distance above P1 = 0.84m

Page 65: Setting Out

Setting Out Example 4: Using Slope Rails

An embankment was constructed with a formation width of 36m and a formation

level of 103.59m. The traverse slope at right angle to the centre line was 1 in 12

and the side slopes 1 in 2. Slope rails were used with a 1.50m traveller held

vertically to monitor the formation of the embankment.

Page 66: Setting Out

The point R (ground level at CL) had a level of 85.08m. the slope rails on either

side of the embankment were attached to verticals A and B on the left and C

and D on the right. These were positioned as shown above. The tops of the

vertical stakes A, B, C and D were levelled as 80.54m, 80.81m, 90.59m and

89.89m respectively.

Using this information calculate the slope that were set out along the ground

surface from point P at right angle to the centre line to establish the centres of

stakes A, B , C and D.

Calculate the Vertical distances that were set out from the tops of the stakes A,

B, C and D to fix the top edges of the sight rails in their correct positions.

Solution

The parameters of the embankment are : h = (103.59 - 85.08+ = 18.51m; n = 2

S = 12; b = 18m

For a two level cross section :

Page 67: Setting Out

Wg = greater side width

WL = lesser side width

h = depth of cut on the centre line from the existing to the proposed levels

1 in n = side slope

1 in s = ground on the traverse slope

b = formation width

The slope distances set out were:

For stake A = WG + 1.0 + 1.0 = 68.02m

For stake B = WG + 1.0 = 67.02m

For stake C = WL + 1.0 = 48.16

For Stake D = WL + 1.0 + 1.0 = 49.16m

mns

nhbsW

G02.66

212

)51.18)2(18(12

)(

)(=

+=

+=

mns

nhbsW

L16.47

212

)51.18)2(18(12

)(

)(=

+

+=

+

+=

Page 68: Setting Out

But the transverse slope = 1 in 12 hence:

Transverse slope =

Therefore to the centre of stake A =

To the centre of stake B =

To the centre of stake C = 48.33m and centre of stake D = 49.33m

Vertical distances:

For stake B:

RL of the top of the rail = RLP + 1.50 – 0.50

RLP = existing RL on the centreline – (WG/12)

RL of the top of rail = 85.08 – (66.02/12) + 1.50 – 0.50 = 80.58m

RL of the top of the stake was given as 80.81m

''49'4504cos12

1tan

1 o=

mo

26.68''49'4504cos

02.68=

mo

25.67''49'4504cos

02.67=

Page 69: Setting Out

vertical distance = (80.58 - 80.81) = -0.23m.

the top edge of the slope rail must be set 0.23m below the top of the vertical

stake B.

For Stake A:

The top of the rail is 0.50m below the top of the rail at stake B, hence:

RL of the top of the rail = 80.58 – 0.50 = 80.08m

Vertical distance = (80.08 – 80.54(given)) = -0.46m

Therefore the top edge of the slope rail at A must be fixed 0.46m below the top

of the stake.

For stake C:

RL of the top of the rail = RLQ +1.50 – 0.50

RLQ = existing RL at R + (WL/12)

85.08 + (47.16/12) + 1.50 – 0.50 = 90.01m

Vertical distance = (90.01 – 90.59(given)) = -0.58m

Therefore the edge of the slope rail at C must be fixed 0.58m below the top of

the stake.

Page 70: Setting Out

For Stake D:

The top of the rail is 0.50m below the top of the rail at stake C, hence:

RL of top of the rail = 90.01 – 0.50 = 89.51m

Vertical distance = (90.01 – 90.59) = -0.38m