ENGINEERING SURVEYING 2.

Lecture Notes for the BSc course BMEEOAFASI1

Szabolcs Rózsa

Budapest, 2009

1. The importance of geodetic control in the construction process

The purpose of construction guidance observations Geodetic observations are quite often required during the construction of the engineering structures. The purpose of these observations is either the geometric guidance of the construction or the control of the geometrical quality of the built structures. In both cases surveyors are required to compare the ’as built’ status of the structure with the geometric position and dimensions of the structures on the plans. Construction guidance observations are a part of the construction activities. These observations are carried out continuously during the construction process. The purpose of these observations is to quantify the discrepancies between the built structures and the planned positions and dimensions, thus these discrepancies can be corrected for by applying ’construction/assembly corrections’. Continuous guidance observations are required for example in the case of the construction of reinforced concrete structures using sliding formworks. Let’s imagine that the chimney is being constructed, that has a circular cross‐section. The purpose of the construction guidance observations is to determine the radius and the center of the cross‐section of the built part. The discrepancies between the ’constructed’ cross‐sections and the planned cross‐sections provide the geometrical correction for the placement of the sliding formwork. These corrections show not only the correction of the center line, but also the correction of the radius of the structure. Thus both the position of the sliding formwork and the dimension of the formwork can be corrected based on the construction guidance observations. In many cases the purpose of construction guidance observations is to adjust the position and the orientation of structural elements (for example: pillars). These adjustments are done with an iterative procedure. Firstly the structural element is placed approximately to the correct place and it is oriented approximately in the correct direction. Afterwards surveyors measure the exact position and orientation of the element and compute the required corrections to meet the planned position and orientation values. Based on these corrections, construction workers can adjust the placement and the orientation of the structural element. Unfortunately – mainly due to the large size and weight of these structures, this adjustment can not be done in a single step. Thus the new discrepancies in position and orientation must be quantified by the surveyor again, and new correction values are computed. Usually the correction values have a decreasing trend, thus the position and the orientation of the structure should converge to its planned position and orientation. This iterative process is done until the computed correction values are below the given tolerance. Construction control observations are done after the construction process is finished. In this case the purpose of the observations is the determination of the geometric error of the construction.

The final approval of the construction usually depends on the results of these construction control observations. In some cases, when the construction process is separated into different individual steps, the results of the construction control observations are taken into consideration during the planning of the next construction step. Such an example can be the construction of the nuclear power plant in Paks, when the small geometric error of the construction of the buildings was taken into consideration in the planning of the technological facilities. In some cases the documentation of geometric construction error helps to determine the cause of malfunctioning structures. It is also important to mention that the positioning observations of the entire structures are usually distinguished from the positioning and dimensional observations of the structural elements. This is because of the fact that – in most cases – a lower accuracy is required for the positioning and the orientation of the entire structure compared to the positioning and the orientation of the structural elements. Imagine that a large hall can be misplaced by several centimeters without any serious consequences, but the misplacement of pillars inside the building by the same amount would lead to the failure of the structure. The accuracy requirements of the construction guidance and control observations The accuracy requirements of the construction guidance and control observations are usually defined separately for the structural and positional guidance and controls. Structural requirements define the guidance and control accuracies for the positioning and orientation of structural elements, while positioning requirements define the accuracies applied for the positioning and orientation of the entire structure/building. The requirements of the structural guidance and control observations are usually defined by the chosen construction method and the type of the structure. The numerical definition of the accuracies of the geodetic observations is usually based on the largest acceptable discrepancy, which can be defined as a function of the construction tolerance. In exceptional cases the construction tolerance or the mean error can be used as accuracy requirements. During the definition of the accuracy requirements one must bear in mind that these observations are carried out on built structures. Thus the first task is the definition of the observed (sample) points on the structure. On some of the structural elements it is easy to localize points, which can be undoubtedly observed by geodetic methods. For example the head of the screws on steel structures can be used as precise marking for the points. In other cases the marking of the observational points is not so unambiguous, thus the marking of the points might increase the error of the observations. Such an example can be the control of the horizontality of reinforced concrete walls. The accuracy

requirements of the construction guidance and control observations are usually computed using the acceptable construction discrepancy: ctzt ⋅= , where t is the accuracy requirement, tc is the largest acceptable construction discrepancy and z is the scale factor between the two aforementioned quantities. According to the Hungarian regulations z=0.15‐0.30, when the observed points are marked precisely. A usual values of z=0.25. In case of non‐precise marking z=0.25‐0.60, with a usual value of 0.40. The Hungarian Guide for Engineering Surveying defines the accuracy of construction control and guidance observations are a function of the structural discrepancy and the distance between the control points and the observed structure (Table 1.) Acceptable structural observation discrepancy Distance [m] 10 20 40 80 100 5 mm 2 3 6 12 15 5‐10 mm 4 6 11 18 22 10‐20 mm 5 8 14 24 30 20 mm 8 12 19 30 40

Table 1-1. The accuracy of construction control as a function of acceptable structural observation discrepancy and distance to the control points

2. The preparation of Construction guidance and control observations

The reconnaissance The purpose of reconnaissance is to get acquainted with the construction site, to understand the requirements related to surveys and to discuss the schedule of construction activities with the client(s). Office preparations The office preparations can be classified into three steps, which affect each other: a) scheduling the observations; b) localization of observational points; c) planning the observational technology. Scheduling the observation The scheduling of the observations highly depends on the scheduling of the construction activities. This can be checked in the project plan. However a continuous negotiation and contact is necessary with the client. Based on the applied construction technology guidance observations are needed for some activities (for example when pillars are erected and set to a vertical position) or continuously during the whole construction (application of sliding formworks). The scheduling of as‐built surveys depends on the scheduling of the forthcoming construction activities as well as the further application of the surveying data. When the results of the as‐built surveys are used is input data for the forthcoming planning phases then the as‐built surveys must be created as soon as the previous phase of construction has been finished. The as‐built surveys – when possible – should be carried out before the next construction phase begins, since continuing construction activities cause worse observation conditions due to the vibration and the obstructing objects, vehicles, etc. The localization of observational points The localization and the number of observational points are determined by taking geometrical, observational, economical aspects as well as the duration of the observations into account. The number of observational points should enable us to determine the structure geometrically. Since only points can be measured, some simplification must also be made. These simplifications rely on the geometrical properties of some structural elements. For instance when the verticality of high rise buildings is controlled then the

number of the observational points depends on the assumed geometrical properties of the walls: Assumption Minimal number of points

The wall is a vertical plane 2 (not on the same vertical) Arbitrary plane 3 (not on the same line)

Arbitrary parabolic surface 10 In order to provide redundant observations, the number of points always exceeds the minimal values. The characteristics of the applied observation technology must also be taken into account. It means that the location of the points should provide an optimal configuration for the observations. The duration of the observations might also have an impact on the determination of the number of points (mainly in construction guidance observations). The number of points should be chosen so, that the duration should not cause significant delays in the construction processes. Economical considerations mean that the more observational point should be measured, the more expensive the observations are. Due to this, the number of points should be increased until the level, where the geometrical assumptions and accuracy requirements are fulfilled. It is extremely important to have a good cooperation between the Surveyor, the Residential Engineer and the Constructor to determine the appropriate number of the observational points and their locations. This continuous discussion can be avoided, when the observations are done routinely.

Planning the observational technology The planning of the observational technology includes the selection of the • selection of the control points used; • selection of the the applied observation technology; • selection of the the instruments; • and the accuracy optimization (planning). Building guidance and control observations usually rely on the horizontal set‐out network and the vertical control network. In case of unique, large buildings it might be

necessary to create a unique control network assisting the construction. The accuracy requirements of the control networks must be determined so, that the foreseen damages of control points are also taken into account. Thus the guidance and control observations must provide the required accuracy when some of the control points are missing. Accuracy optimization (planning) of the observations should prove that the chosen technology and observational points could provide suitable accuracy for the control or guidance. The planning is usually done be comparing the acceptable mean error of the control measurements (µ) with the “a priori” mean error of the observational technology and instrumentation (m). The chosen technology and instrumentation should fulfill the following requirement: . The m acceptable mean error can be computed from the structural or positioning tolerance (t) with the following equation: . The m ‘a priori’ mean error consists of three parts. The first is the mean error describing the observational technology (m1). The m1 value can be determined using the formulae derived for the different setting out technologies. The deformations of the examined structures induced by the external conditions have an impact on the overall mean error, too. In case of tall and thin structures one has to take into account the effect of wind load and the temperature change. The uncertainty stemming from these effects can be described by the m2 mean error. The level of m2 can be determined with the help of the structural engineers. The processing of construction guidance and control observations are usually done by applying some simplifications. Due to these simplifications and assumptions we have to take into account another uncertainty, which is quantified with the m3 mean error. Let’s suppose that our task is to check whether the observed points are on the same line, or not. In this case the equation of the line is determined by the xi, yi coordinates of the points. The equation of lines can be determined using different criteria, like: , or | | .

In both cases the determined parameters (a0, a1) have uncertainties, which are described by the m3 mean error. The m3 can be determined with the application of error theory and error propagation. The overall mean error can be computed using the m1, m2 and m3 mean error values with the following equation: .

Preparations on site The preparation on the construction site consists of three parts. The first one is to establish the control network. In case of an existing control network one should locate the control points, temporarily mark them (erect tripods, etc.) and check their relative positions. When no control network exists, then either the densification of the network should be made, or a totally new control network should be established. The second step of the preparations is to choose the final location of the observational points. The final locations should be chosen based on the requirements determined during the office preparations. The observational points are usually marked. A permanent marking is especially important when the points are used for guidance and control observations many times. The third part of the preparations is the establishment of structures, which are necessary for the observations or for working safety (pillars, barriers, etc.).

3. Observational technologies for construction guidance and control

Construction guidance and control observations of building with vertical or near‐vertical walls can be done with the technology of plumbing. The plumbing can be done with theodolites, zenitlots (plummets), or plumb bobs. The application of building guidance and control observations are explained in some case studies. Case 1. The exercise is a building guidance observation for the vertical alignment of pillars. The observations are done with two theodolites, which are placed orthogonally from the pillar. Now the observations of the first theodolite are explained only, but the second one follows the same procedure, too. The steps of the alignment are the following: 1. Before the erection of the pillar, the centerline of the pillar should be marked on the bottom as well as on the top of the pillar. Afterwards the pillar is lifted and set to an approximately vertical position. 2. Sight the mark on the bottom of the pillar with the theodolite. (The vertical plane of the line of sight should be approximately perpendicular to the surface of the pillar.) 3. Tilt the telescope around the trunnion axis until the mark on the top of the pillar becomes visible. Due to the tilting of the pillar, the mark is not sighted correctly (not aligned with the vertical crosshair). 4. Instruct the constructor to adjust the pillar till the mark is aligned with the vertical crosshair. 5. As a check, the lower mark should be sighted again. When it is necessary to rotate the alidade of the instrument to do this, then step 3 and 4 should be repeated. Case 2. Let’s suppose that a construction of a cooling tower with a hyperboloid surface should be guided continuously, since it is made with the sliding formwork technology. The task can be solved with the instrumentation seen on Figure 3‐1. The most important parts of the instrumentation are the laser‐theodolite – set up in the geometrical center of the tower – providing a horizontal laser beam, and an adjustable prism, which reflects the laser beam to the appropriate position. The prism ensures that the reflected laser beam has the inclination of α. The distance between the laser theodolite and the prism is denoted with s. When the geometry of the structure should be controlled at the level of Hi above the ground, then the horizontal distance between the wall of the structure and the laser

beam should be measured with a rod. Thus the radius of the tower at the level of Hi can be computed using the formula below: . Finally the observed radius should be compared to the values given in the plans. The discrepancy between the two values would provide us the error, or the correction in case of guidance observations.

lasertheodolite

α

Prism

staff

ai

Ri

Cent

erlin

e

S Figure 3-1. Guidance of a hyperboloid shape cooling tower constructed with sliding formworks Due to practical reasons, usually not the radii are compared, but the ai is computed for a certain α angle: . With this approach, the geometry of the cooling tower can be checked in various cross‐sections.

Case 3. The task is to control the verticality of the wall edges of a high rise building. The measurements are done using a theodolite. During the control observations, the yi

distances of the points are determined from a vertical plane, which is approximately parallel with the wall. The vertical plane is created by the standing plane of the theodolite. The principle of the observation can be seen on Figure 3‐2. The yi values are computed from the observed αi angles and the distance d, which is measured by a tape: . The deviations from the vertical position can be determined from the changes of the yi values. When the surface of the examined structure is not parallel with the standing plane of the theodolite, then the observations should be made from two orthogonal directions. yi

H i

Pi

Stan

ding

pla

ne

Frontal view Top view

Pi

yi

Stan

ding

pla

ne

α

d

4. Construction guidance and control observations of straight‐axis structures Very often some structural elements of the large structures can be characterized with a straight axis. In most cases the guidance of such constructions are mandatory. Such a structures are: roads, railways, tunnels, crane rails, axis of large industrial machinery. Straight axis or center lines can be set out by two points. After marking these two points, a wire can be stretched between the points. This method is used for example to guide pavers in road construction. The appropriate setting out of the points enables the horizontal as well as the vertical guidance of the pavers. Such a configuration can be seen on Figure 4‐1. paver

road

elevationsensor elevation

sensor

alignmentsensor

stakes

wire

wire

View of the stakes

Figure 4‐1. Guidance of a road paver with wires Laser theodolites (Fig 4‐2.) are also very useful to set out straight lines. After an orientation, the laser theodolites can set out the WCB of the straight axis, or a line with an offset from the centerline. In many cases the road pavers are equipped with a sensor, which detects the laser beam, thus the paver can move automatically along the straight line.

paver

road

orientation δ

las e

r b e

a mlaser theodolite

Figure 4-2. Guidance of road paver with the laser theodolite Another solution is the application of inductive guidance devices. In this case the straight lines are set out with two points. Afterwards a cable is stretched between the points. The paver senses the electric field around the cables. Thus by ensuring that the detected signal has a maximum the paver follows the right direction. These solutions can be modified to be appropriate for the guidance along curves, too. Alignment observations Structures with straight axis can be geometrically controlled with the alignment observations. In this case a line approximately parallel with the straight axis of the structure is set out with two points. The positions of the monitoring points are observed as chainage (xi) and offset (yi) values relative to the reference line. The principle of the observation can be seen on Figure 4‐3.

A B

examined structure

x1

y1 x ‐iyi x ‐n

yn

control point

observation point Figure 4-3. The principle of alignment observations During alignment observations the xi coordinates are usually set out according to the requirements of the observations. In case of the examination of crane rails the xi coordinates are 0,1,2,… meters (thus we have one point in every meter). During the location of the monitoring points, it must be ensured that a point is placed to each break in the straight axis. The chainage values are usually measured with tapes. In order to measure the yi offsets, many approaches and technologies can be used. One of them is to use a theodolite set up on point A and a target mark set up at point B. After sighting the mark at point B, the yi offsets are measured with a tape (or yardstick) with the precision of 1mm.

AB

examined structure

yi

theodolite markyardstick

Figure 4-4. Alignment observations with theodolite and yardstick

When the monitoring points are not accessible, then instead of measuring the yi values, the angle αi is measured (Fig. 4‐5.). The yi offset is computed from the equation: , or .

AB

examined structure

yi

theodolite mark

Oixi

s i

αi

Pi

Figure 4-5. Alignment observations based on angular observations In case of the guidance or control observations of industrial machinery, the aforementioned approaches cannot provide the sufficient accuracy. In such cases special devices are used, which utilize the phenomena of optical interference, or apply a collimator telescope. These instruments are called ‘microgeodetic’ instruments.

Alignment with interferometric observations The structure of such a device can be seen on Figure 4‐6. The instrument contains the following elements: • a transmitter, which contains a light emitter and a slit in front of it (0,2‐0,5mm); • a whiteboard with two slits (0,2‐0,5mm) on the monitoring points; • the receiver, which is a telescope with crosshairs.

The principle of the observation is that a symmetric interference can be achieved only, when the three elements of the instrument are aligned. The whiteboard (A2) can be adjusted very finely. According to references, up to 50 meters the accuracy of 0.010‐0.015mm can be achieved.

A1A2 A3

a1

a2

a’2β

View of the receiver

Light emitter with a single slit Whiteboard with telescope(receiver)Whiteboardwith double slits

Figure 4‐6. Alignment observation based on the interference of light

Collimator telescopes In practice the application of collimator telescopes are more popular. A possible set up can be seen on Figure 4‐7. The figure shows the telescope (2) with the micrometer screw (1) and the collimator (3) with the light emitter. The diaphragm (4) is located in the focal distance of the objective of the collimator. The collimator can be mounted to the structure with the help of two mount points (5 and 5’) in the distance of b. Telescope Collimator Light emitter43

85 5’

b θ

θ

1 2

q

Figure 4-7. Allignment observation with collimator During the observation, the collimator is mounted to the structure and the telescope is tilted with a micrometer screw, until both of the lines of sight becomes parallel. In this case the two crosshairs (in the collimator and in the telescope) are aligned. The angular

rotation of the micrometer screw can be read on the screw. Let’s denote this angular rotation with n. Since the amount of tilting is a linear function of the rotation, it can be computed by: =n∙υ'', where u’’ is a constant given by the operation manuals. Since q’’ is usually small, therefore the offset difference of the two mountpoints of the collimator (q) can be computed using the following equation: θ · . Since b and u’’ are constant for a specific instrument, therefore q can be written in the following form: · · . The mean error of one q observation can be computed by applying the law of error propagation: . Since q is relatively small and the value of s and b can be accurately determined in calibration laboratories, the second part of the sum can be neglected. Thus: . It must be noted that the mean error of q does not depend on the distance between the collimator and the telescope (see the above equation). During the control observations of a structure, the reference line is created by the telescope and a mark. The collimator is moved along the structure so, that the chainage values of the close mountpoint should be b, 2b,…. kb consecutively. The offset of point k is: ∑ .

Telescope Collimator Mark

Figure 4-8. Setting the reference line with a telescope and a mark for alignment observations with collimator The mean error of yk can be computed from the mean error of the quantities q: ∑ . Experience shows that up to 200 meters the mean error of the tilting angles can supposed to be constant: , thus: √ √ .

5. Observing deformations General information on deformation observations Engineers measure the displacement or the changes in the shape (deformation) of various structures using geodetic, photogrammetric or other techniques. The purpose of the deformation observations can be different depending on the specific task, such as: • The prediction of the expected displacement of the structure. This task is usually important for structures, which have high loads, such as dams, bridges, embankments of large rivers. The prediction of displacements is important to avoid the failure of the structure, which could lead to a catastrophic situation. In many cases the studies of a new category of structures starts after a real failure experiences in an already built structure. For example the systematic deformation observation of dams started in the 1920s after a dam was torn down in Italy, or the deformation analysis of the bridges in Vienna started after the damage of the Reichsbrücke. • The deformation observations can help to understand the cause of an experienced displacement. These types of observations are carried out after the visible occurrence of structural damages. An example could be the deformation analysis of the river walls in Dunaújváros, where the observations were started after a landslide. • Deformation observations may help to improve the design and planning of building and other structures, when the observations are made on existing buildings or on laboratory models. In this case the observed displacements and deformations are used for further planning processes. For example the Conder storage structures were studied in laboratories, before the first ones were built in Hungary. On the other hand deformation observations of existing high‐rise buildings helped to predict the displacements of the further buildings. • In many cases the aim of the deformation observation is to provide information for the technical approval of the structure. For example bridges are approved when they pass a load test, during which the deformation of the bridge is measured. • Deformation analysis may serve the scientific research as well. Deformation observations are used in the field of technical sciences, physics, biology and medical sciences. • Finally the purpose of the deformation analysis can be to help legal processes, too. In case of damages or accidents, deformation observations are helpful to judge the responsibility for the damage.

Application fields of deformation observations Geodetic and photogrammetic deformation observations are used a wide variety of branches of the economy. In the following list we have given some branches of applications: • The most important field of application is the construction industry. Deformation observations are made in case of thin and tall structures (chimneys, TV towers), large structures (multi‐storey buildings, skyscrapers), or during the application of some industrial construction technologies (like the application of sliding formworks). In the construction industry the primary cause of the deformations is usually the weak soil. • Transportation: many structures used by the transportation are studied by the method of deformation observations, such as: bridges, railway embankments, underground railways. • Water management and water resources: deformation analysis of dams and river embankments. • Industry: deformation analysis is carried out in mining (quantifying the depression caused by mining), during the establishment and maintenance of nuclear power stations, or in some structures of the mechanical industry (ships, airplanes, etc.) • Non‐profit branches and research: deformation analysis of natural structures (for example tectonic plates) or historical structures.

The principle of deformation analysis The displacement and the deformation of object are very complicated processes. In order to be able to measure these processes and to mathematically model them, some assumptions (simplifications) should be made. The first simplification is that the structure is substituted by some points only. The positions of the points are measured and the displacement of the structure is modeled with the quantified displacement of these points. The second – general – assumption is that we have some fixed control points, which are not subject to any displacements. By using these control points, the observed coordinate changes of the points on the structure shows the displacement of the structure itself. The third assumption is that the observed structure is stable during the observation. Due to this the observations are identified by an observation epoch (time of observation) instead of an observation interval. Let’s see the simplest example: a beam with two supports. According to the first assumption, some points must be chosen on the beam. The number and the location of

the points depend on the fact whether the beam is a rigid or a deformable body. A possible solution for the observational points could be found on Fig. 5‐1.

Figure 5-1. Deformation observation of a beam with two supports According to the second assumption, fixed control points should be established in the vicinity of the structure. These points are points A and B on Fig. 5‐2. (Of course the stability of the control points must be checked regularly using some additional observations to other points.) Finally observations are made from the fixed control points to the observational points on the structure. According to the third assumption the observations (and the coordinate solutions) refer to a certain time epoch. On Figure 5‐2 the observations at epoch t1 and t2 are displayed (the figure is not to scale).

P

P’

t1

t2

AB

κ

Ω

ϑ+X

+Z

+Y

ZP1

Yp1

Xp1

Xp2Yp2

Zp2

Figure 5-2. The position of the beam at epochs t1 and t2

The coordinates referring to the aforementioned epochs can be computed from the respective observations. Using the coordinates of the observational points in the various epochs the parameters of the displacements or deformations can be computed. When the beam is rigid the elements of the translation and rotation vectors must be computed. In this case the elements of the translation vector between the epoch t1 and t2 are the following: ∆ , ∆ , ∆ , where XP1, YP1, ZP1 are the coordinates of point P at the epoch t1, and XP2, YP2 and ZP2 are the coordinates at the epoch t2. The rotational angles can also be computed from the same coordinates. Let’s suppose that the rotation of the beam along the Y axis should be determined (ω). In this case the X and Z coordinates of the points S and U (Figure 5‐3.) at the epoch t1 and t2 should be used for the computations:

In some cases the deformation parameters (angular deformation and linear deformation) must also be computed among the displacements of the bodies. In this case the same coordinates should be used as before. Let’s suppose that the linear deformation (extension) of the beam should be computed. In this case the change of the distance between points U and S should be computed from the coordinates.

S

t1

t2

κ

Ω

ϑ+X

+Z

+Y

Zs1

Ys1

Xs1 Xs2

Ys2

Zs2

S’

U

U’

Zu1

Yu1

Xu1 Xu2

Yu2

Zu2

Figure 5-3. Observing the expansion of a beam

The distance between point U and S at the epoch t1 is: , at the epoch t2 it is: . The change of the length of the beam is: ∆ . Summarizing this chapter, it can be stated that geodetic deformation observations are carried out from stable fixed control points, to a suitable number of observational points which substitute the studied body. The coordinates of the observational points are computed, and finally the parameters of displacements and deformations are computed using these coordinates.

6. Planning deformation observations The planning of deformation observations is a process of the following steps: 1. The exact definition of the task. 2. Acquiring information related to the displacements and/or deformations. 3. The determination of accuracy requirements. 4. The determination of observation epochs. 5. The determination of the duration of the observations. 6. The determination of the location and marking of the observational points. 7. The selection of the applied observation technology and instrumentation. The listed steps are not independent from each other. Usually the steps must be revisited and renegotiated before the final decisions are made. The planning process is concluded, when all of the aforementioned steps were done and an appropriate solution has been found for each of them. 1. The exact definition of the task The exact definition of the task helps us to define the purpose of the observations. The definition must contain the exact definition of the structure, the description of the characteristics of the expected displacements and the required time interval between the epochs. 2. Acquiring information related to the displacements and/or deformations The information on the displacements and/or deformation has a big impact on the required accuracy and duration of observations as well as on the appropriate selection of observation epochs. The most important information is the following: the amount and location of the highest and lowest displacement, the amount of the critical displacement, the displacement rates (speed) and the characteristics of the additional displacements must also be known, which are not subject to the observations, but must be taken into account. For example: In case of the deformation observation of chimneys due to the wind loads, the deformation of the chimney due to the solar radiation must also be taken into account, because only the sum of the two effects can be observed, but during the processing the two parts must be separated. The main characteristics of displacements can be obtained from the client or the designer of the structure. When this fails, related literature should be checked for reference values.

3. The determination of accuracy requirements In case of deformation observations the accuracy requirements highly depend on the purpose and requirements of the observations. The accuracy requirements are usually defined as a function of the highest expected displacement (Dmax) or the critical displacement (Dcrit). During the determination of the accuracy requirements either homogeneous requirements can be defined for the whole structure or stringent requirements can also be defined for the critical parts of the structure. Until now there is not a general rule for the definition of accuracy requirements. When the highest expected displacement (Dmax) is given, then the mean error of the parameter stemming from a single observation must fulfill the following criteria: 0,03 0,1 . When the critical displacement is given, then the following formula can be used: 0,1 0,2 . During the determination of the accuracy of the deformation observations the opinion of the experts of the client or the designer of the structure must also be obtained. 4. The determination of observation epochs During the planning phase, the observation epoch must also be chosen. In case of continuously acting forces (e.g. quantification of subsidence of buildings) the problem is solved so, that a certain number of observation epochs (depending on technical and economical considerations) should be distributed during the expected lifetime of displacements. When no prior information exists on the evolution of displacements then the observations should be distributed homogeneously over the lifetime of the displacements. However when some prior information exist (e.g. soil consolidation in the case of the subsidence of buildings) then it is wiser to have more frequent observations when the displacement rates are higher compared to the time when the displacement rates become smaller and smaller. An example can be seen on Figure 6‐1. When the evolution of the displacements is known, then it is also possible to define the observation epochs by solving an optimization problem.

Observation epochs

Expected displacement function

Z

Time

Figure 6-1. The determination of observation epochs It is extremely important to have a repeated reference observation (also known as null observation). It is necessary because of the fact that all of the further observations would be referred to the first null observation, therefore it must have a higher accuracy and reliability. During the planning phase only the expected evolution of the displacement might be known. In the real situation, the displacements and deformations may occur in a different way. Therefore it is important to compare the observed displacements with the expected ones. In case of significant discrepancies the planning of the observation epochs should be revised. In most cases additional requirements of the clients should also be taken into consideration in the determination of the observation epochs. When the deformation observations are carried out as a part of a complex investigation (such as bridge load testing), the observation epochs should be aligned with the epochs of other observations. 5. The determination of the duration of observations The acceptable duration of the observations depend on the amount of the displacement rates as well as on some external conditions. One of the principal assumptions of the deformation observations was that the observed structure is supposed to be stable during the observation. Under real conditions, structures suffer some displacements or deformations continuously, thus they have some displacements or deformations during the duration of the deformation observations, too. The duration of the observations should be chosen so, that the amount of displacement or deformation of the structure during the observations should not decrease the accuracy of the observations significantly. When the displacement rate is v

and the accepted mean error of the observations (µi) are known, then is can be prescribed that the total amount of displacement should not exceed a certain level of the mean error. Thus: · · , where v is the displacement rate, t is the duration of the observations, k is the coefficient of acceptable displacement and µ is the accepted mean error of the coordinates. K has the usual value of 0.2‐0.5. The maximal duration of the observations can be computed by reformatting the previous equation: . This duration is the duration of the observations only, and excludes the duration of the preparations for the observation (transportation, set up, etc.) and the processing of the observations. In case of high displacement rates, or large structures it might occur that the it is not possible to carry out the observations within the maximal accepted duration (t) computed with the aforementioned formula. One solution of the problem could be to find an appropriate time for the observations, when the displacement rates are lower. For example steel structures can be measured during the night, when the large deformations due to the solar radiation can be eliminated from the observations. In case of large structures sometimes we can not assume that the structures are stable during the observations. In this case a more complicated mathematical model should be applied for the analysis of the observations, which handles the observations as a function of time, too. Such a model can be used for the studies of recent tectonic displacements. External conditions have an impact on the duration of the observations, when the geodetic observations are made in combination with other observations, or other operations. In this case the duration of the geodetic observations should have similar to the duration of other observations. However it must be taken into account that the duration of the observations can be shortened till it does not affect the accuracy of observations significantly. 6. The determination of location and marking of the observational points The number and the location of observational points on the examined structure depend on many factors. A general rule is that the number of points and their location should enable us to quantify all of the parameters of the displacements (translation, rotation) and deformations.

In order to find the appropriate location of the observational points, a few simplifications should be made. The simplifications rely on the physical properties of the structure (rigid or non‐rigid) and on the characteristics of the displacements (direction, maximal displacement, etc.). During the determination of the number of the required points one should take into account the fact that some of the points might be destroyed during the observations (usually deformation observations last for a long time, sometimes for decades as well). Therefore some spare points should also be used for the observations. Moreover the economical and time observational time limitations should also be taken into account. The more observational points should be measured, the longer the observations are, and more expensive the whole deformation analysis becomes. When the number of points is determined, then the appropriate locations should be chosen. The locations should reveal the displacements and deformations. For example a point should be placed on the place of the highest and lowest displacement. When the number of points is fixes then the locations could also be found by mathematical optimization. After defining the number and the location of the points, the appropriate way of marking must also be determined. The marking depends on the material of the surface of the structure, on the accuracy requirements, on the applied measurement technology and the total lifetime of the deformation observations. An appropriate marking must fulfill two criteria: the points must show the displacement of the structure and they must not damage due to natural phenomena (wind, rain, snow, ice, etc.) during the observations.

7. Methods of continuous deformation observations In many cases the structures can not supposed to be stable during a normal geodetic or photogrammetric deformation observation. In such a case the deformations or the displacements of the structure must be observed continuously. This is usually done with some built‐in sensors, but some of the geodetic observations can also be automated and thus a continuous monitoring of the structures can also be solved by geodetic tools, like robotic total stations or GNSS instruments. Continuous observations are usually used in the following cases: a.) The displacement or deformation rate of the observed structure is high, thus it is not possible to sight the points manually. An example for this could be the loading test of bridges. b.) A large number of observational points should be measured, and the structure can not supposed to be stable during the long duration of observations. An example for this is the deformation observations of steel structures, which are exposed to solar radiation. c.) In many cases the observations should be repeated in a very short time, like in the case of thin and tall structures, which deform due to the temperature change and wind loads. In these cases it is useful to build some sensors into the structure. Of course before the final decision of the installation of such sensors a technical and economical analysis should also be made.

The principles of continuous deformation observations In case of continuous deformation observations some observational points are established in or on the structure, where the changes of some physical parameters (length, angle, bearing, inclination, etc) can be measured. These changes are directly related to the displacements or deformations of the structure. The sensors sometimes have a display directly showing the observable, but in most cases the observations are transformed to an electronic signal, which is transmitted to a centralized data processing facility, where the signals are transformed to real observations. Due to the fact that many sensors are present on or in the structure, therefore a switch is also installed between the sensor and the data processing facility, in order to be able to process the sensors individually. The switch can be a manual switch when only a few sensors are used, or can be a fully automatic one, which can handle a large number of sensors. An automatic switch is capable to switch between all of the sensors, and reads

the data of the sensors consecutively. Programmable switches are also capable to read only a certain set of the applied sensors in one step. With these switches it is easy to monitor the whole structure in one step as well as to have a detailed view of a certain part of structure by reading the appropriate sensors more frequently. Since the distance between the sensors and the data processing facility is usually large, therefore a signal amplifier is also needed in the system. The results can be displayed in a digital display or the data can be sent to a data logger or to a computer directly. The most efficient way to visualize and analyze the observations is to feed the sensors to a central computer, which can process and analyze the data in real time. In some cases, when the accuracy requirements are lower, an analogue graphical visualization is done. In most cases the observations are stored digitally either on a hard drive or on some other data storage material. Various types of sensors The sensors used for the continuous deformation observations are the following based on the observed quantity: Observed physical quantity Sensor Length inductive position detector

position sensitive diode Extension sensor based on oscillating chords

strain gage pendulum

Tilting electronic level tiltmeter

Continuous observation of lengths Lengths are measured continuously with the application of inductive position detectors and position sensitive diodes. There are many versions of inductive position detectors. These detectors convert the observed length to inductivity. The inductivity of a cylindrical coil (L) depends – among others ‐ on the number of turns (N) and the magnetic permeability (µ0): , where µ0 is the magnetic permeability, µr is the relative permeability, while A is the area of the cross‐section of the coil. When the inductivity is expressed as a function of the

number of turns (N), the permeability (µ=µ0µr) and a variable, which describes the geometry of the coil (G), then the inductivity can be written as: . According to this, the inductivity of a coil may change due to the: a) change of the number of turns; b) change in the geometry; c) change in the permeability. The principle of inductive position detectors is that these devices convert the observable – usually displacement – to a change of any of the aforementioned 3 variables. The most widely used equipments are the linear variable differential transformator (LVDT) and the inductive position transducers. Inductive position transducers The inductive position transducers have a very simple structure. It contains a coil and a movable permeable core within the coil. The principle of the operation is that the inductivity depends on the position of the core within the coil. This function is shown on Fig. 7‐1. It can be seen that the maximal inductivity occurs, when the core is totally inside the coil. When the core is moved from the coil outward, then the inductivity reduces. The inductivity is a non‐linear function of the position of the core and decreases its value until the core is driven out of the coil. In this case the inductivity reaches the level of the inductivity of a coil with air core (L0). The function of inductivity can be approximated by:

, where x is the distance between the center of the coil and the center of the core; l is the length of the coil (which is similar to the total length of the core) and k is a sensor specific constant (a usual value is 4).

L

L0

core

coil

x

c

Figure 7-1. The inductivity of the coil as a function of core’s position This simple transducer is linear in a very small interval around the inflection point of the inductivity curve. In order to extend this interval either more coils are used, or the shape of the inductivity curve (characteristic curve) is determined, and the displacements are computed using the characteristic curve of the sensor. The characteristic curve can be approximated by polynomials or Fourier‐series or any other appropriate mathematical methods. The inductive transducers have an operational interval of 0.5mm‐200mm. The accuracy of the observations is usually in the order of 0,1% of the observed displacement.

Position sensitive diodes The basis of the position sensitive diode is a semi‐conductor block (made of silicon), on which a thin layer of gold (approx. 15 nm) is placed. The silicon is artificially polluted, thus the atoms of the polluting material create some free electrons in the silicon block. When the silicon block is voltage free, then the free electrons enter to the golden layer, thus in the semiconductor block an electron‐poor zone is created. When a the block is put under voltage, then the size of this zone increases, which disables any current to flow through the semiconductor block.

U

Golden layer

Light

Electron‐poor zone

Silicon semiconductor

X

l/2 l/2

l

Figure 7-2. The semiconductor block of position sensitive diods When some light is emitted by the golden layer, then additional electrons free up in the electron‐poor zone, thus an electric current flows through the semiconductor block. The current I1 and I2 observed at both ends of the semiconductor blocks must fulfill the following equation according to the 2nd law of Kirchoff: , where R1 and R2 are the respective resistances and U is the voltage. Let x denote the distance of light from the center of the diode. In this case x can be expressed as a function of the two currents with the following equation: . Thus the location of the ray of light (x) can be determined. The observation of x can be carried out by the application of the Wheatstone‐bridge (Fig. 7‐3.) When the Wheatstone bridge is balanced (UD=0) then the following equation is fulfilled: , thus the value of x can be expressed: . In case of real observations the amplification of the signals must also be solved regardless of the way of the determination of x (current measurement or the application of the Wheatstone bridge).

V

positionsensitivediode

U

R3R4

I2I1

x

Figure 7-3. Measurement of displacement with PSD and the Wheatstone bridge Position sensitive diodes usually have an observational interval of less than 10 cm. The resolution of these devices is usually better than 1% of the measurement interval. Lowest limit of the resolution is 2.5×10‐3 mm.

8. Strain and tilting (deflection) measurements One of the most important purposes of deformation observations is the determination of the stress accumulated in the investigated structures. Since the stress cannot be measured, therefore the strain should be measured and the stress can be computed by the Hooke law – considering its limitations. Thus strain observations are unavoidable for the determination of stress. In the next sections the electrical resistance strain gages and the vibrating‐wire strain gages are introduced. It must be noted that strain observations can be done using the inductive position transducers, too.

Electrical resistance strain gages The physical background of the electrical resistance strain gages is the fact that the resistance of a wire depends on its length (l), area of cross‐section (A) and the electrical resistivity (ρ): . When the length of the wire changes with ∆l, then the electrical resistance changes as well (∆R). The ratiod between the relative change in the length (strain) and the relative change in the resistance can be described by the following equations: ∆ ∆ , where k is the so called gage factor. The gage factor is a function of the gage material and can be looked up in the manuals. A usual value is around 2. In the application of the electrical resistance strain gages, the changes of electrical resistance are measured, and the strain is computed from the observations. Since the k is not constant for the whole operational interval, therefore the strain is not a totally linear function of the relative change of the electrical resistance. Two types of electrical resistance strain gages can be distinguished: • Wire strain gage • Foil strain gage • Strain gages with special carrier materials (like asbestos for high temperature observations) Electrical resistance strain gages have the observational interval of 0.3mm to 100mm. The accuracy is usually 0.5% of the observed displacement.

Figure 8-1. Electrical resistance strain gauge

Vibrating‐wire strain gages The body of the strain gauge is a steel tube with flanges at either end. Inside the body, a steel wire held in tension between the two flanges. Strain in the concrete causes the flanges to move relative to one another, increasing or decreasing the tension in the wire. The tension in the wire is measured by plucking the wire with electromagnetic coils and measuring the frequency of the resulting vibration. The resonant frequency of the wire can be described with the following formula: , where f is the resonant frequency, l is the length of the wire, ρ is the density of the wire, σ is the stress in the wire due to the tension, n is the order of the harmonics. Usually the higher order harmonics are fast damped, therefore usually the 1st order harmonic is measured. This damping can be accelerated when wire is plucked in the middle. The frequency equation of the vibrating wire shows that the observed frequency changes due to the change in the length of the wire and the stress occurring due to the tension of the wire. The strain observations are done by the observation of the resonant frequency. Strain in the wire is calculated by squaring the frequency reading and multiplying a gauge factor and a batch calibration factor.

Figure 8-2. The structure of the vibrating wire strain gauge The material of the vibrating wire is usually steel. The accuracy and the resolution of the observations is 1 microstrain. When the vibrating‐wire is used for measuring strain in non‐steel materials, then the effect of the temperature change must also be taken into account. Since the different materials have different thermal expansion coefficients, it causes an extra stress in the vibrating‐wire. This must be corrected in order to determine the strain caused by the deformation of the structure only.

A major advantage of the vibrating‐wire is its long lifetime. Therefore it is very advantageous to use this type of gages in places, which are not accessible after finishing the construction (interior of reinforced concrete dams, etc.)

Tiltmeters The geodetic tiltmeters are instruments, which were originally capable to measure tilting angles and were improved to be able to provide the observations continuously. Tilting angles in surveying are measured with tools, which are capable to detect the direction of the gravity vector. Such instruments are: levels, pendulums and the free surface of liquids. All of the instruments can be equipped with an electronic reader, thus the changes in the tilting angles can be recorded continuously. There are many types of electronic levels in practice. One solution is shown on Figure 8‐3. Electronic levels have a high sensitivity, it can reach the level of 0.1”. They consist of a bubble tube filled with an electrolytic solution and three electrodes. As the sensor tilts, the excitation electrodes ont he top of the tube move across the meniscus of the bubble, linearly changing the electronical resistance between the pick‐up electrode on the bottom of the tube and each excitation electrode. By measuring the resistance change, the tiltmeter electronics determine angular movement with great precision. The total angular range of a sensor is a function of the length of its excitation electrodes and the sensor's radius of curvature.

Figure 8-3. Electronic tiltmeters The tiltmeters based on pendulums usually contain some inductive transducers. Such an instrument is the Talyvel made by the Rank‐Taylor‐Hobson company (Figure …). The pendulum is a high permeability iron core (K), which can swing between two coils (L1 and L2). The oscillator generated the alternating circuit, while the resistors (R1 and R2) and the coils form a Wheatstone bridge, on which the amplified (A) voltage is measured with a galvanometer. Placing the instrument on a tilted surface, the pendulum K is moved toward one of the coils, thus a current is flowing on the Wheatstone bridge. With the adjustment of the R1

resistor the bridge can be balanced. Thus the amount of tilting can be determined by the measurement of the resistance of the R1 resistor. The Thalyvel 5 tiltmeter has the measurement range of ±10’ and the accuracy of 0.2” or ±3% of the reading. pendulum unit

KL1 L2

R1 R2

EO G

measuring unit

instrument base

Figure 8-4. The structure of the Thalyvel tiltmeter

9‐10. Vertical Deformation observations

Practical Observe the leveling polygons shown on Fig. 9‐1 using precise levels! Inside the building the Wild N3 precise tilting level is used, while outside the building electronic precise levels are used. Follow the rules of precise leveling during the observations. After the observations compute the height of the observed points by adjusting the observations using the least squares method.

The computational adjustment of the Deformation Analysis Observations of the Central Building of BME Altogether 7 leveling lines have been observed in and around the Central building of BME. Out of these lines, six sections can be formed (4 inside the building and 2 outside the building). The seventh line is the link to the stable benchmark located in the rock of the Gellert‐hill (2915). In order to compute the vertical coordinates of the observational points, the observed elevation differences in the network (Fig. 9‐1.) must be adjusted. Since the elevation differences were observed, one should realize that the sum of the elevations differences in the various loops should be zero. Let’s denote the observed elevation differences with L and the respective corrections v. Please also note that the direction of leveling is denoted with red arrows on Fig. 9‐1. Thus: 0 for the loop of L1, L4 and L3, 0 for the loop of L5, L6 and L2, 0 for the loop of L3 and L5, 0 for the loop of L4 and L6.

Figure 9-1. The levelling polygons of the network The vi corrections should be determined so, that the above equations are fulfilled for all of the loops. In order to compute these corrections (and the adjusted elevations of the nodes), the least‐squares method could be used. In this solution the parametric least‐squares method is used.

Parametric least squares method The parametric least squares method uses observation equations, where the observables are expressed as the function of parameters.: , , … . , in order to linearize the problem, an approximate value of the parameters should be defined (X10, X20, ….Xn0). , , … . , , , … . , where (x1, x2, …, xn) are the changes of the approximate parameters. After the linearization, the above equation has the form of: , , … . , where A is the so called design matrix containing the partial derivatives of the functions (Jacobian‐matrix) and x is the vector of the changes of the approximate parameters. By reordering the above equation to the corrections, one gets:

where X is the vector of the approximate values of the parameters and l is the vector of the approximate residual. By minimizing the weighted square of the corrections: one gets the solution of the parameter changes by: Please note that AT is the transpose of the design matrix and PLL is the weight matrix: where QLL is the variance‐covariance matrix of the observations, which is assumed to be known. After the computation of the parameter changes (x) the adjusted parameters can be computed: The adjusted observation residuals can be computed by the direct method: Finally the variance‐covariance matrix of the parameters is:

The application of least-squares method for the adjustment of the leveling network In our case the elevation differences (observables) are expressed as the functions of vertical coordinates (parameters):

Let’s define the approximate values of the vertical coordinates: H22_0=0, H9_0=L1 and H1005_0=L3 Since one station in the network should be fixed (and the elevation of the other nodes are computed relative to this one), the elevation of point 22 should be fixed to the value of 0. Thus the set of correction equations are: Let’s see the contents of the design matrix:

1 01 00 11 10 11 1

and the approximate residual vector is: __ __ ___ _

In the next step the weight matrix (PLL) should be created. Please note that the weight matrix is the inverse of the variance‐covariance matrix of the observations. When the observations are statistically independent, then the variance‐covariance matrix as well as the weight matrix have a diagonal form. The variances can be approximated by the square of the ’a priori’ mean error of the observations. The ’a priori’ mean error of leveling is given by the following formulae:

∆ √ for one way levelling and ∆ for two‐way levelling, where α is the mean oscillation of the line of sight of the level, S is the length of the leveling line and d is the instrument‐staff distance.

Thus the weights can be defined inverse proportionally with the length of the leveling lines: 1 0 0 0 0 00 1 0 0 0 00 0 1 0 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1

In the next step the changes of the parameters can be computed: and the adjusted value of the parameters can be obtained by: Since the parameters are in this case the elevations of the nodes, therefore the adjusted values of the elevations of point 9, 22 and 1005 are determined. Please note that these elevations are relative to the elevation of point 22.

11. Verticality check of the wall of shafts It is a frequent task in the construction practice to check the verticality of the wall of shafts. Before the assembly of the elevators (the placement of the leader rails) it is necessary to carry out the exact survey of the geometry of the built walls. Checking the verticality of surfaces, straights lines or edges in a shaft can be done using a plumb bob or an optical plummet. The application of the plumb bob is more difficult, since it swings when the hanging wire is long. In this case an appropriate damping should be achieved. To eliminate this disadvantage the optical plummet instruments were developed. The most important part of the precise optical plummets is the standing geodetic telescope, which can be turned around the central vertical axis that is fixed in the tribrach. An automatic compensator or a precise level is used to make the line of sight of the telescope vertical.

Figure 11-1. PZL precise compensator plummet Such a precise compensator plummet is the Zeiss’s PZL (Präzisions‐Zenitlot) instrument.

Figure 11-2. PZL schematic optical equipment and his beam procession Because of the fact that the standing axis and the line of sight are not parallel due to small misalignments, it is necessary to make two measurements in diametral positions. The observations are started with the setting out of the station points. Afterwards a sketch of the layout of the staircase is prepared. The station points are marked on the sketch and the observation of their positions are taken relative to the walls. In the next step the vertical section is defined (the interval of the section points is defined relatively to the level of the basement). After setting up the instrument, the horizontal distance between the walls and the vertical line of sight should be measured. In order to do this, a yardstick (or a horizontally placed leveling staff) can be placed to the section points. Afterwards the readings are taken in two diametral positions (the instrument must be revolved around the standing axis by 180°. Based on these measurements the vertical section of the wall can be created and the winding of the shaft can be plot on graphs as well.

12‐13. Controlling measurement of crane rails

15030-58 MSz is the valid standard for the building and assembling of the crane rails in Hungary. This standard includes the regulations that must be followed of design, -build and technical approval. The main rules which relate to surveying works:

- the winding tolerance of the theoretical center line of the ground-plan is ±10 mm, - the tolerance of the middle distance of the rail is ± 5 mm, - the tolerance of the altitude in the direction of the axis of the support of the crane rail

from the theoretical level is ±20 mm, but the maximal slant of the rail is 1 per thousand,

- the altitude difference of the rails in one cross-section is max. 1 per thousand of the distance of the rails,

- the eccentricity of the rail centre line compared to the middle of the support of the crane rail is: at a steel support ±l0 mm, at a reinforced concrete support ±30 mm.

The controlling measurement justifies that the rail was being built according to a plan and it kept its planned geometry during its use.

The geometry of the actual state of the crane rails are computed based on geodetic surveys. The supports of the crane rails and the crane rails themselves describe a winding line compared to the planned theoretical axis (both in the horizontal and the vertical sense). The deteriorations from these planes are called horizontal- and altitude winding. The most frequent task is the definition of the windings, but it is also necessary to make the following checks:

- The examination of the verticality of supports, - The examination of the theoretical axis of the rail and the theoretical axis of the crane-

bridge (crane-bridges), - Checking the size of the bridge wheels and the rail lines, - Checking the placement of the bumpers.

In the industry there are many kinds of crane rails. The most precise construction is required by the - so called - travelling crane. That’s why we introduce the control measurements and related computation of this kind of cranes. Of course this method can also be used for simpler kinds of cranes.

The determination of horizontal winding needs different kind of equipments and measurement techniques compared to the vertical winding. Due to this, the problem is solved in the following way:

- the determination of the horizontal winding and the span of crane rails, - the determination of the position of the supports of the crane rails and the

determination of the axis of the crane rails compared to each other, - the determination of the altitude winding of the crane rails.

The determination of the horizontal winding and the span of the crane rails

Before starting the controlling measurements it is necessary to compute:

n = ±z e

where

n: permitted measurement difference of the structure

e: permitted size difference due to building and assembling

z: scale factor

According to MSz 15030-58 standard z = 0.4 (usual value)

n = ±0.4×5 = ±2mm.

Due to the fact that we are not allowed to exceed this permitted measurement difference (n) at any point, we should use a 1” theodolite, invartape and a staff with a correct mm graduation.

The horizontal winding of the crane rails is determined with offset surveying using a theodolite. The first step of the work is to create the horizontal geodetic network.

Usually a rectangular quadrangle network (or chain) is used for this purpose, but the two opposite sides of the network must be nearly parallel with the rails. We may set the points of reference according to their spatial situation:

– on the floor level, – near the altitude of the crane rails, or – in different altitudes.

We may set out the control points:

– outside the crane rails, – between the crane rails, – partly outside the crane rails, partly between the crane rails.

On Figure 1 a rectangular quadrangle network is shown, which consist of four points. For the determination of the horizontal winding we have to measure the offsets of the axis of the rails to a straight line from the control points 1-2 and 3-4 in two faces.

It is necessary to fix the section of the examination points (see the bi values on Fig. 12-1) for the determination of both the horizontal winding, and the span.

Figure 12-1. Rectangular quadrangle network

Figure 12-2. The theoretical axis of the crane rail

The situation of the theoretical axis of the crane rail can be computed according to the notations of Fig. 12-2. The horizontal winding is defined as the discrepancy between the true axis and a vertical plane coinciding with the theoretical rail axis.

The coordinate of the points of the theoretical axis:

thus the horizontal winding of rail “A” can be computed:

The horizontal winding of rail “B” is:

It must be noted that the values of the horizontal winding has a sign. The positive sign means that the rail axis point lies outside the theoretical rail axis, while the negative sign means that it lies inside the theoretical rail axis.

Please note that in the previous formulae f is the planned span and T is the horizontal distance between the baselines. T can be measured directly, or it can be computed from the network observations.

The adjustment of the network observations can be done using the techniques learned in other courses. All the methods of the adjustment of direct and indirect observations can be used for this purpose. In some cases only the angular misclosures are computed, and the distances, which have not been observed, are computed using the corrected angles and the measured distances.

The definition of the position of the supports of crane rails and the situation of the axis of crane rails relative to each other

The crane rail standard prescribes the maximal eccentricity of the support of crane rail and the axis of the rail. It is necessary to refer the observation of the winding of the rails to a common vertical plane. Let’s discuss the principles of computing the horizontal winding of the supports in a case, when the baseline is located between the supports of the crane rails.

The position of the baselines can be seen on Fig. 3. In order to determine the horizontal windings, firstly the ordinate values of the points of the theoretical axis are computed. Using the notation of Fig. 3.:

The values of the horizontal winding of the examination points:

Figure 12-3. The position of the baseline

The determination of the altitude winding of the crane rails

According to the crane rail standard the altitude winding of the crane rails must be determined, too. It is necessary to make the determination of the relative altitude differences based on two independent leveling. In the industry it is necessary to use a hanging tape for the determination of the absolute altitude. During this practice a leveling staff is used instead.

Both automatic and tilting levels can be used for the observations. Since it is usually hard to find a vibration-free environment on industrial sites, therefore the application of a tilting level is strongly encouraged.

It is necessary to calibrate the level before the controlling observation, since it is hard to ensure the equal instrument-staff distance during the observations. When the level is not adjusted, then the tilting of the line-of-sight can be calculated, and the observations are corrected for this effect.

References

Detrekői Á.-Ódor K.: Ipari geodézia II. rész. Műegyetemi kiadó, Budapest, 1998. California Department of Transportation: Surveys Manual (http://www.dot.ca.gov/hq/row/landsurveys/SurveysManual/Manual_TOC.html) Fernsteuergeraete: Linear Displacement Transmitters, Technical Specification, Berlin, 2009 Department of the Army: Construction Surveying, p. 238, Washington D.C., 1985 DiBiagio, E.: A Case Study of Vibrating Wire Sensors That Have Vibrated Continuously for 27 Years, Proceedings of the 6th International Symposium on Field Measurements in Geomechanics, Oslo, September 15-18, 2003, pp 445-459. Gage Technic International Ltd: The theory of vibrating wire transducers. p 5, 2009 LCM Systems: PD13 Linear Displacement Transducer, Technical Specifications, 2008 Slope Indicator Inc.: VW Embedment Strain Gauge, White Paper, Mukilteo, 2009 Slope Indicator Inc: VW Spotweld Strain Gauge, White Paper, Mukilteo, 2004 Smith L.M, Brodt G.L, Stafford B.: Performance Assessment and Reinstatement of Vibrating Wire Strain Gauges in Nuclear Power Plant Structures. Transactions SMiRT 16, Washington D.C., 2001 Vishay Micro Measurements: Strain Gauge Rosettes: Selection, Application and Data reduction. Technical Note TN-515, http://www.vishaymg.com, 2009