Methods for breaking down structures. Linear serif method
The method of polar coordinates is widely used when laying out the axes of buildings, structures and structures from the points of theodolite or polygonometric traverses, when these points are located relatively close to the points to be staked out.
In this method, the position of the point to be determined WITH(Fig. 16) are found on the ground by deposition from the direction AB design angle β and distance S. Design angle β is found as the difference in directional angles a AB and α AC, computed as the distance S from the solution of inverse problems on the coordinates of points A, B and WITH. To control the position of the fixed point WITH can be checked by measuring at point V injection β ׳ ’ and comparing it with the value obtained as the difference in directional angles a B A and αCA .
Rice. 16. Chart of stakeout by polar coordinates method
The root mean square error of the stakeout of point C is determined by the formula
The error of the actual splitting in the polar way depends on the error m β building an angle β and mistakes t S design distance deposits S
. (56)
Influence of initial data errors at t A = t B = t A B is expressed by the formula
, (57)
and centering errors
. (58)
Formulas (57) and (58) are similar. It follows from these formulas that in order to reduce the influence of errors in the initial data and centering, it is necessary that the angle β and the ratio were minimal, the polar angle would be less than the right angle, and the design distance would be less than the stakeout basis, i.e. β < 90°, S< b.
For approximate calculations, taking β = 90° and S=b, we get
; , (59)
and for the total error in the position of a point divided by the method of polar coordinates,
. (60)
For example, let's evaluate the accuracy of the breakdown of the design position "points C with points of polygonometry moves, for which b= 250 m tAB= 10 mm. Accept S=100 m, , β = 45° m β= 10", e= 1 mm and m f= 1 mm.
The design line deposition error will be
mm;
linear value of the error in constructing the design angle -
mm,
quantities t β and ρ expressed in seconds;
impact of initial data errors -
From the ratio of the obtained values, it can be seen that the centering and fixation errors can be neglected. In this way,
The calculation shows that for these conditions, a decrease in the error in the position of the point to be set out in nature is possible only with a significant decrease in the error in deposition of the design distance, at least twice.
Rice. 17. Scheme of stakeout by the design landfill method
If the point to be staked is located at a considerable distance from the starting point, then the design angles and distances have to be set aside several times by the polar method, laying the design course (Fig. 17). With line of sight from a point WITH point V for control, adjacent angles are measured γ 1 and γ 2 , forming a closed corner polygon. Therefore, this method is called the design polygon method. . With accurate marking work, the corners of the polygon are equalized, the coordinates of the point are calculated from them and the design distances WITH, compare them with the design ones and, if necessary, reduce them to the design position.
With a sparse stakeout basis, the design polygon method can be used to stake out all points of intersection of the main axes of the structure from one starting point. In this case, the design course with design angles and distances is laid completely.
Work on the breakdown of artificial structures located on the axis of the existing railway. paths and on the designed bypass, have almost no difference.
In both cases, it is necessary first of all to check and restore the correct position of the track axis.
In the case when the structure is located on a straight path, they act as follows.
At a distance of at least 200 m from the structure in one direction and the other, sections of a well-aligned path are selected and a theodolite is installed on the axis of the path of one section, and on the axis of the path of another section - milestone.
Then the theodolite is pointed at the milestone and the axis of the track is hung along the vertical thread, setting the milestones “on itself”, i.e. bringing their installation gradually from the initial milestone to the theodolite.
Two of these milestones must be placed near the artificial structure on both sides of it so that any point on the surface of the earth can be seen from them within the location of the structure designated by the project.
The reference points for laying out the structure on the straight section of the bypass should be the points of the angles of rotation.
In order to break and fix the axis of the structure, coinciding with the axis of the track, in the lowered places of its location, i.e. to design it on the ground, it is necessary to transfer the theodolite to the installation site of one of these milestones and, orienting it to a remote milestone on the axis of the path, then mark the position of the axis of the structure along the entire lower part with milestones.
If the shore closest to the theodolite is not visible, then the theodolite must be rearrange milestones, located on the opposite bank, and repeat the breakdown described above.
After breaking down the longitudinal axis of the structure, the position of the transverse axis is broken down. It determines the location of the structure on the railway line.
This provision is indicated in the construction project:
if the structure is being erected on a haul, then its position is indicated by the stationing of the line;
if it is constructed on station tracks, then most often its position is indicated relative to the axis of the station.
According to these data, with the help of a steel tape, lay distance from nearest picket or another firmly fixed point specified in the project and hammer a stake.
At this point, an ekker or theodolite is installed, centered, oriented along the axis of the path and a right angle is beaten off on both sides of the axis of the path. The direction of the axis is indicated by milestones.
If the angle in the project is not 90 °, then the ekker cannot be used and the desired angle is set aside with a theodolite or goniometer. This completes the breakdown of the axes of the structure.
The axes are usually fixed with piles with a diameter of 10-12 cm, hammered into the ground with a hand-made woman to a depth of about 0.7 m or poles dug in to a depth of about 1 m. Such poles are installed one or two at each end of the longitudinal and transverse axis.
One of these pillars can be made high-altitude benchmark. At the same time, if the construction of the bridge will last more than a year or the breakdown is done in the fall for the work of the next year, then the benchmark must be buried 0.25 - 0.50 m below the freezing depth of the soil.
In addition, at the lower end of the benchmark, two mutually perpendicular strips must be cut and nailed to prevent the benchmark from sticking out of the ground when the upper layers of the soil freeze.
Axis
In order to more accurately fix the position of the latter on the pillars fixing the axis, you should first, instead of the milestones indicating the direction of the axes, hammer in small pegs or stick studs from the tape into the ground.
Then, at a distance of 2 m from these studs, four pegs should be driven into the ground, located at the ends of two straight lines crossing the stud, and a wire should be drawn between them in pairs through hairpin and fix the position of the wires either with nails or notches on the stakes.
Then, having removed the wires and the hairpin, instead of the last one they hammer in a pile or dig a hole to install a pole.
When the pile is driven or the post is installed, the wires are pulled through the notches on the stakes again and at the point of their intersection, a nail is driven into the post or a notch is made.
We can also recommend driving flush with the ground near each pillar at a distance of 1 m towards the structure (or away from it, depending on the conditions of preservation) in the direction of the axis of the structure of more pieces of iron pipe with a diameter of 2-2.5 cm, a length of 0.5- 0.7 m for control in case of damage to poles during construction work.
In order to protect against damage, the poles should be painted white or red and fenced. If the soil is rocky, then instead of installing pillars, the surface of the rock is cleared and leveled at the axis point, two grooves intersecting on the point are cut with a chisel, and sometimes a circle with a diameter of 10-20 cm is also around the point.
The grooves and the circle are painted over with oil paint.
If the structure is located on a curve
If the structure is located on a curve, then first of all check the curve by re-laying it out.
To do this, you need to make a measurement, calculation and straightening of the curve, if the structure to be broken will be built on the existing track.
If the structure is designed on a site located along a curve, where there is no rail track at the time of breakdown, then it is necessary to break the curve from tangents using the ordinate method or the angle method.
For this, first of all, check the directions of the straight lines, adjacent to the curve, find their intersection point and measure the angle of rotation with a theodolite.
Then, according to the radius of the curve specified in the project and the lengths of the transition curves, make the main and detailed breakdown of the curve after 10 m.
After that, by measuring with a tape along the axis of the curve, a point is assigned WITH(Fig. 101) the location of the transverse axis of the bridge in accordance with the project.
From this point, two more points are broken at exactly the same distance from it. A and V so that they are out of scope. between points A and V draw a straight line and find its midpoint WITH 1 .
If now at this point the perpendicular is restored with an acker or theodolite, then it must pass through the previously set point WITH, and this perpendicular will be the transverse axis of the bridge.
The transverse axis is continued in both directions from the longitudinal axis of the bridge and is indicated by milestones or pins at the points D and E outside of work.
Then all four points A, V,D and E on the rectilinear axis of the bridge, they are fixed with pillars, piles or notches on the rock.
A detailed breakdown of the bridge supports is usually made from a straight axis AB. If local conditions require it, you can also split the auxiliary straight axle A 1 B 1 outside the scope of work and a detailed breakdown should also be carried out with respect to it.
The position of the centers of the individual supports of the small bridge on the curve is set from the rectilinear axis by the coordinate method. If all the spans are the same, then they stand with a theodolite in the center O each support (Fig. 102):
measure the angle between the three centers of the supports and, dividing this angle in half, get the direction on the axis of the support or hang the chord rs(see Fig. 102), connecting the centers of the supports adjacent to this support O, find the middle of this chord and restore the perpendicular to it with an ecker nm, which gives the desired direction of the support axis.
If the supports are located at unequal distances, then it is necessary to split on the curve symmetrically with respect to each support the auxiliary points used to split the direction of the axes of the supports, as described above.
The breakdown of the main axes AB and DE (see Fig. 101) should be checked.
To do this, determine the picket position of the middle WITH(Fig. 103):
broken bridge and the beginning of the curve NK distance to the axle of the bridge from the beginning of the curve NK.
According to the length of the curve (twice the distance) and its radius, the corresponding values of the tangent are found from the tables T, bisectors B and angle of rotation a.
After that, on the ground, the found length is measured from the beginning of the curve T.
Here at the point F they put the theodolite and break the bisector of the angle, for which they set aside with the help of the theodolite from the tangent line an angle equal to 90-(α / 2) The direction of the axis of the pipe, with the correct breakdown, will indicate the previously broken points WITH,D and indicating the direction of the transverse axis of the bridge.
Length FC must be equal to the bisector B. The position of the points A and V can be checked by splitting them using tables in the way of ordinates relative to the beginning of the curve NK.
All of the above actions assume that the stakeout is in dry land or the width of the watercourse does not exceed 1 m.
If the river is wider, then in all places where stakes and piles are installed, the simplest scaffolding should first be arranged on piles or goats.
In the second case, when it is necessary to break the axis of the place on the bypass routed and fixed by the stationing, work also begins with the restoration of the longitudinal axis of the structure.
To do this, you need to find on the ground the corner posts installed during tracing at the corners of rotation.
The axis of the bridge is defined by two vertices of the angles of rotation behind opposite ends of the bridge.
Between these two points hang the axis of the bridge, as described above in the first case. Just as described there, they break and fix the transverse axis of the bridge.
The breakdown of the axes of the structure on the bypass, located on the curve, is no different from the case of the location of the bridge on the curve of the main path.
The following methods are used to perform layout work: polar and rectangular coordinates, angular, linear and alignment serifs.
Angle notch method used to stake out inaccessible points located at a considerable distance from the starting points.
Distinguish between direct and reverse angular serifs.
In the method of direct angular serif, the position on the ground of the design point WITH(Fig. 10) are found by deposits at the starting points A and V design angles in 1 and in 2. The basis of the notch is either a specially measured side, or the side of the grid network. The design angles at 1 and at 2 are calculated as the difference between the directional angles of the sides. Directional angles are found from the solution of the inverse geodetic problem according to the design coordinates of the point being determined and the known coordinates of the starting points.
Rice. 10.
The accuracy of staking by the method of direct angular serif is influenced by errors: the direct serif itself, the initial data, theodolite centering and sighting targets , fixing the stakeout point. During stakeout work, the centering of the theodolite and sighting targets using optical plummets, as well as fixing the point to be set out, can be performed relatively accurately. Therefore, the main errors that determine the accuracy of the method of direct angular serif are the errors of the serif itself and the initial data. The total value of these errors can be significant, which will require the performance of an angular notch with increased accuracy.
The required staking accuracy in this case can be achieved as follows. Having set aside with possible accuracy the angles in l AND in 2, determine in nature the position of the point WITH. Then, at the control points, the exact value of the pending angles is measured by the appropriate number of steps. For the given example, when using the 2T30 theodolite, at least four steps must be performed. Angle r is also measured at the point WITH. Having distributed the discrepancy in the triangle equally to all three corners, determine the coordinates of the point WITH. Comparing them with the design values, they find corrections (reductions), by which in nature they shift (reduce) an approximately placed point WITH. This method is called closed triangle method.
On the principle of reduction, the use of the reverse angle resection method for staking is also based. On the ground, find an approximate position O" staked design point O(Fig. 11). At this point, a theodolite is installed and, with the required accuracy, angles are measured for at least three starting points with known coordinates. According to the resection formulas, the coordinates of an approximately defined point are calculated and compared with the design values. By the difference in coordinates, the reduction values are calculated (angular and linear elements) and the point is shifted to the design position.
![](https://i2.wp.com/studwood.ru/imag_/32/102964/image012.png)
Rice. eleven.
For control, angles are measured at this point, its coordinates are recalculated and compared with the design ones. In case of unacceptable discrepancies, all actions are repeated.
In the method of linear resection, the position of the point to be staked out WITH(see Fig. 10) are determined at the intersection of the design distances S 1 and S 2, laid off from the starting points A and V. This method is usually used to lay out the axes of building structures in the case when the design distances do not exceed the length of the measuring device.
It is most convenient to break down using two tape measures. from point A distance S 1 is plotted along the tape measure, and from the point V on the second roulette - S 2 . By moving both roulettes with the zeros aligned with the centers of the points A and V, at the intersection of the ends of the segments S 1 and S 2 find the position of the point to be determined WITH. geodetic breakdown road construction site
Polar coordinate method are widely used when laying out the axes of buildings, structures and structures from the points of theodolite or polygonometric passages, when these points are located relatively close to the points taken out in nature.
In this method, the position of the point to be determined WITH(Fig. 12) are found on the ground by deposition from the direction AB design angle in and distance S. The design angle in is found as the difference in directional angles b AB and b AC , computed as well as the distance S from the solution of inverse problems on the coordinates of points A, B and C. To control the position of the fixed point WITH can be checked by measuring at point V angle in "and comparing it with the value obtained as the difference in directional angles b VA and b Sun " .
![](https://i1.wp.com/studwood.ru/imag_/32/102964/image013.png)
Rice. 12.
The error of the actual stakeout by the polar method depends on the error of constructing the angle β and the error of deposition of the design distance S. The calculation shows that for these conditions, a decrease in the error in the position of the point to be set out in nature is possible only with a significant decrease in the error of deposition of the design distance - at least twice.
If the point to be staked is located at a considerable distance from the starting point, then it is necessary to postpone the design angles and distances several times in the polar way, laying the design course.
Ways of leading and leading-linear serifs are widely used for setting out the alignment axes of buildings and structures, as well as the mounting axes of structures and process equipment.
Design point position WITH in the way of the alignment notch, it is determined at the intersection of two alignments, set between the starting points 1-1 "and 2-2" (Fig. 13). The target is usually set with a theodolite, which is centered over the starting point (for example, 1), and the telescope is oriented along the sighting target, centered on another starting point (in this case, 1 "). Point position WITH fixed in a given alignment.
The root mean square error of the alignment depends on the errors in the construction of the first and second alignments, as well as the error in fixing the reference points.
![](https://i0.wp.com/studwood.ru/imag_/32/102964/image014.png)
Rice. thirteen. a- sash serifs; b- sash-linear notch
Sash-linear method allows you to determine the design position of the point to be staked out WITH(see Fig. 13) by plotting the design distance d along the line AB.
Rectangular coordinate method are used mainly when available on site or in the workshop industrial enterprise construction grid, in the coordinate system of which the position of all main points and axes of the project is specified.
Staking out a design point WITH(Fig. 14) are produced according to the calculated values of increments of its coordinates D X and D Y from the nearest grid point. Larger increment (in Figure D Y) set aside along the grid points AB. At the received point D install a theodolite and build a right angle from the side of the grid. A smaller increment is laid along the perpendicular and the resulting point is fixed WITH. To control the position of the point WITH can be determined from another point in the construction grid. The scheme of the method of rectangular coordinates, in essence, combines the scheme of the linear and polar methods.
Rice. 14. Staking scheme by the method of rectangular coordinates
A house project, developed in electronic format or on paper, is a virtual image that gives a complete picture of its structure. Usually floor plans are performed at a scale of 1:100, if this does not cause problems with the dimensions of the paper carrier and it is common for individual houses. The general plan adopted the ratio of 1 unit of measurement of the drawing to 500 units on the ground.
This is due to the display of a larger area and the relatively low detail of the drawing. Results are shown on the same scale. topographic survey for building, containing symbols of the appropriate size, easily readable on the drawing.
The real construction of a house begins with the transfer of dimensions from the drawing to the area and the marking of the foundation of the house. This part of the work is called "taking the project to nature." It uses the specified dimensions or coordinates, if the drawing does not contain any values that turned out to be necessary, then they are removed from the scaled plan and, after magnification by 100 or 500 times, are deposited on the ground. It is much more convenient and reliable to stake out using surveying equipment, such as a laser electronic total station, which provides the highest level of accuracy.
Callout with a tape measure
You need to start it with drawing up a layout scheme developed on the basis of the master plan. It defines the baseline and the reference point. For example, on the one hand, the site is fenced with a fence made of canvases fixed on racks, and this situation is reflected in the master plan.
The straight section of the fence is taken as the base line, and the center of the post at its beginning is taken as the reference point. The dimensions are laid out on the layout plan parallel or perpendicular to this line, and the distances are calculated from the starting point.
To transfer the project to nature, it is enough to mark the longitudinal and transverse, or alphabetic and digital axes. Further distances are plotted from them for positioning all other points.
The construction of perpendicular lines is main problem with this method. No artisanal techniques give the necessary accuracy. This may not be critical for the placement of the building relative to the baseline, but perpendicularity is absolutely essential when anchoring the axes. They try to achieve it by aligning the diagonals of the rectangle at four corner points.
Having determined the difference, one or two points are corrected, after which all sides and diagonals are again measured. The difference in readings cannot exceed one centimeter, which is practically impossible to do with a tape measure and other hand tools, since the error appears due to uneven tension or sagging of the tape. Having achieved a satisfactory result, the corner points are fixed with marks from reinforcing bars with a diameter of 8-10 millimeters.
Setting out axes with an electronic total station
The best results are achieved with the use of surveying instruments. In this case, the work is done by offsetting coordinates or by constructing lines parallel and perpendicular to the baseline.
To work on coordinates, it is desirable to have a master plan drawing in vector format or inserted into such a file. The coordinates of the points are taken out by a total station equipped with a laser rangefinder with an accuracy of 5 millimeters and are immediately fixed on the ground.
In the same way, axial lines are set directly on the cast-off. For a coordinate callout, the complexity of the plan configuration and the angles between the axes do not matter, ideal results are still achieved. The error of fixing with a steel rod will exceed the inaccuracy of positioning a point with a total station. Therefore, it is recommended that the axes be taken out immediately on a cast-off, fixed with a nail or drawn with a thin line, this will increase the accuracy of the dimensions.
Wear, what is it, how is it installed
This term refers to a structure that allows, if necessary, to restore to construction site center lines of the building. Points fixed on the ground cannot be used in the process of work, since the ground is moving, equipment and people are moving, and it is unrealistic to ensure the safety of such a leader. The axes should not interfere with work, but it is required to be able to get their position at any time.
To do this, the center lines are transferred to a solid planed board, fixed horizontally at a height of about one and a half meters on two supports, securely installed in the ground. If necessary, a building cord is stretched over these points, indicating the position of the axis. The more thoroughly the wear is done, the less risk that it will shift, leading to errors in the position of the axes with all the ensuing problems.
It is desirable that the upper cut of the crossbars be at the same level, which will simplify the removal of corner points in the future. Two structures are made on one line, consisting of a pair of supports with a crossbar. To secure four axes, which is the minimum number for a building, eight such structures will need to be installed.
Considering that free space is required between the building and the cast-off for the movement of equipment, the construction of slopes of the pit, and the like, it is placed at a distance of three to five meters from the building.
When working with a total station, the removal of lines on horizontal jumpers is not difficult. Acting on the basis of the corner points broken by the tape measure, a cord is stretched between the corresponding pair of cast-offs. Its position is controlled by a plumb line, aimed directly at the clogged rod with a sinker, shifting the thread to the required distance, achieving full compliance with the line of the rods.
This method is cheap, and if you have a lot of free time, you can use it, but it is better to spend some money and invite a surveyor who has the necessary equipment. Despite the cost, this guarantees confidence in the correct alignment of the axes of the building and saves you from long work that does not provide the desired accuracy.
Breakdown of the foundation of the house
At the stage of excavation, great accuracy is not needed. Previously fixed points or stretched axes can be used as the contour of the pit. The bottom of the sample is made half a meter wider than the contour of the building and the soil is selected taking into account its natural slope and depth. If a trench is dug under strip foundation, act in a similar way, laying the width of the bottom 20–30 centimeters more than the size of the supporting part. On device columnar foundations, it is recommended to mark their axes for control with four pegs spaced from the edges by two meters, since due to the small area of \u200b\u200bthe base, the bottom of the pit sometimes turns out to be outside the design position.
Having completed this stage of earthworks, they stretch the cord along the marks of the cast-off and restore the position of the axes and corner points at their intersections. When crossing threads in a horizontal plane, you need to make sure that they do not displace each other. From the corner points, a plumb line is lowered to the surface level and a steel rod or wooden peg is hammered. By lowering all the corner points in this way, the position of the axes is recreated at the level of the bottom of the pit, which allows you to start work on the formwork or installation of prefabricated foundation blocks.
Conclusion
The marking of the foundation for the house begins with the removal of the project in nature, for which it is recommended to use the services of a surveyor with an electronic total station equipped with a laser rangefinder. Don't neglect the scrap device and try to save money on it by using junk material, it will end up costing more due to accuracy issues. The foundation is broken along the bottom of the pit or trench, so you must first complete the necessary excavation and move the axes to the bottom level with a plumb line.
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