CN108332725A - Sharp central angle is without center of circle circular arc plane rise setting out method - Google Patents
Sharp central angle is without center of circle circular arc plane rise setting out method Download PDFInfo
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- CN108332725A CN108332725A CN201711404301.0A CN201711404301A CN108332725A CN 108332725 A CN108332725 A CN 108332725A CN 201711404301 A CN201711404301 A CN 201711404301A CN 108332725 A CN108332725 A CN 108332725A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C15/00—Surveying instruments or accessories not provided for in groups G01C1/00 - G01C13/00
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Abstract
A kind of sharp central angle is without center of circle circular arc plane rise setting out method, and built construction object M, arc-shaped planar buildings N yet to be built, center of circle O are the center of circle of building N, and the center of circle O is fallen in the building M, and central angle is 2 α, and outer arc radius is R, the method includes：Quadrangle angle point A, B, C, D of the building N are taken, string AB is connected, takes midpoint E, connection OE to hand over circular arc in string ABIn F, OF friendships AB is rise in E, EF=h, and h=EF=R (1 cos α) can be derived from correspondence：Rise h can accurately calculate out according to known conditions h=R (1 cos α), angle point A and angle point B it is known that withRise h again, camber line is determined according to the string relationship of dividing equally vertical with riseEach cut-point carry out picture arc setting-out.The present invention is using sharp central angle without center of circle circular arc plane rise setting out method, and according to string with rise, the vertical relationship of dividing equally determines each cut-point of camber line and carries out picture arc setting-out, can direct cable measure measurement, achieve the purpose that camber line setting-out.
Description
Technical field
The present invention relates to a kind of plane setting out method more particularly to a kind of when the centre point of building yet to be built is fallen built
It builds on object plane or massif slope, in paleocurrent, the sharp central angle in the case where that can not establish and fix center location is justified without the center of circle
Arc plane rise setting out method.
Background technology
Circular arc plane setting-out is common in engineering construction, in the construction site of spacious sky, as long as measuring center location by plan view
It can directly draw arc according to the radius of arc with four angle points of house plane and release plane full-page proof afterwards.But when centre point is fallen
On built building object plane or massif slope, in paleocurrent, center location can not be being established and fix, it is fixed just to use at this time
The point center of circle and fixed length radius release planar arc.
Invention content
The object of the present invention is to provide a kind of sharp central angles without center of circle circular arc plane rise setting out method, to solve existing skill
When building centre point yet to be built is fallen on built building object plane or massif slope, in paleocurrent in art, can not establish and
In the case of fixed center location, the problem of pinpointing the center of circle and fixed length radius releasing planar arc can not be used.Therefore, the present invention uses
Following technical scheme.
Sharp central angle is without center of circle circular arc plane rise setting out method, built construction object M, arc-shaped planar buildings N yet to be built,
Center of circle O is the center of circle of building N, and the center of circle O is fallen in the building M, and central angle is 2 α, and outer arc radius is R, the side
Method includes：Quadrangle angle point A, B, C, D of the building N are taken, string AB is connected, takes midpoint E, connection OE to hand over circular arc in string AB
In F, OF ⊥ AB, OF hands over AB in E, and getsIf arc lengthEF=h is rise, ∠ AOE=
∠ BOE=α, can obtain：H=EF=R (1-cos α)；
Cos α are carried out to the expansion of Taylor series：
Cos α are approximatively substituted by first two of Taylor series,By cos α
Formula h=R (1-cos α) is substituted into, then is hadIt willIt substitutes into：It enablesThen there is h=Kl2；That is rise h and corresponding arc length l2Direct proportionality；Arc length is pressedMultiple is split, arc lengthString AF is connected, then G points are taken at the midpoints AF, OG is connected, hands over arcIn I, then GI is rise h1, and set
ArcIt is sequentially connected string AI, takes midpoint K, connection OK to hand over arc in string AIIn Q points, ifThen QK is rise h2,
It can similarly obtain,
Substitute into formulaFinallyI.e.：Substitute into formulaFinallyI.e.：The midpoint for continuing to take string AK, can be derived from corresponding pass successively
System：
Rise h can accurately calculate out according to known conditions h=R (1-cos α), angle point A and angle point B it is known that withTimes
Rise h determines camber line according to the string relationship of dividing equally vertical with riseEach cut-point carry out picture arc setting-out.
Preferably, the rise h ' after being adjusted is adjusted to rise h initial values, wherein h '=β h, β be adjustment because
Son.
The beneficial effects of the invention are as follows：Centre point is fallen on built building object plane or massif slope, in paleocurrent, just
The fixed point center of circle and fixed length radius can not be used to release planar arc, the present invention is using sharp central angle without center of circle circular arc plane rise setting-out
Method, according to string with rise, the vertical relationship of dividing equally determines each cut-point of camber line and carries out picture arc setting-out, can direct cable zhang
It is fixed to measure, and achievees the purpose that camber line setting-out.
Description of the drawings
Fig. 1 is that the center of circle of arc-plane building yet to be built in the present invention falls the schematic diagram in built construction object.
Fig. 2 is schematic diagram of the sharp central angle without center of circle circular arc plane rise setting out method in the present invention.
Specific implementation mode
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation describes, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
Circular arc plane setting-out is common in engineering construction, in the construction site of spacious sky, as long as measuring center location by plan view
It can directly draw arc according to the radius of arc with four angle points of house plane and release plane full-page proof afterwards.But when centre point is fallen
On built building object plane or massif slope, (as shown in Figure 1) in paleocurrent, just can not with fixed point the center of circle and fixed length radius put
Go out planar arc.A kind of sharp central angle of present invention offer is without center of circle circular arc plane rise setting out method, to solve in the prior art
When centre point is fallen on built building object plane or massif slope, in paleocurrent, the fixed point center of circle and fixed length radius can not be just used
The problem of releasing planar arc.
As shown in Fig. 2, a kind of sharp central angle is without center of circle circular arc plane rise setting out method, built construction object M, circular arc yet to be built
Tetra- jiaos of shape planar buildings N, building N has determined angle point A, B, C, D, and for center of circle O in the building M, central angle is 2 α, outer arc
Radius is R, circular arcAnd circular arcAll using O points as the center of circle, string AB is connected, takes midpoint E, connection OE to hand over circular arc in string AB
In F, if arc lengthIt can demonstrate,prove：OF ⊥ AB hand over AB in E, and getIf EF=h is arrow
Height, while understanding ∠ AOE=∠ BOE=α；According to known α and R, can directly obtain：H=EF=R (1-cos α)；
Cos α are carried out to the expansion of Taylor series：
Cos α are approximatively substituted by first two of Taylor series,By cos α
Formula h=R (1-cos α) is substituted into, then is hadIt willIt substitutes into：It enablesThen there is h=Kl2；That is rise h and corresponding arc length l2Direct proportionality；Arc length is pressedMultiple is split, arc
It is longString AF is connected, then G points are taken at the midpoints AF, OG is connected, hands over arcIn I, then GI is rise h1, and
If arcIt is sequentially connected string AI, takes midpoint K, connection OK to hand over arc in string AIIn Q points, ifThen QK is rise
h2, it can similarly obtain,
Substitute into formulaFinallyI.e.：Substitute into formulaFinallyI.e.：Continue arc length l being divided into
It can be derived from following correspondence successively, as shown in table 1.
The correspondence of table 1 arc length and rise
Therefore, the rise h at each cut-point can be obtainednCorrespondence between initial rise hRise
H can accurately calculate out according to known conditions h=R (1-cos α), angle point A and angle point B it is known that withRise h again, according to string
The relationship of dividing equally vertical with rise determines camber lineEach cut-point carry out picture arc setting-out.According to the value of string AB and rise h,
And vertical relation between the two can determine camber lineCut-point F；According to string AF and rise h1Value and the two
Between vertical relation can determine camber lineCut-point I；Therefore camber line can be obtained successivelyCut-point, to carry out
Arc setting-out is drawn, camber line is worked asCut-point take it is more when, draw arc setting-out result it is more accurate.Due in Taylor series expansion
When, the cos α values that approximation takes first two to substitute are adjusted rise h initial values so to make the precision higher of result
Rise h ' after to adjustment, wherein h '=β h, β is Dynamic gene.
Take arc radius R be 116 meters, camber line to 2 α of central angle be 80 °, Dynamic gene β be 1.03.Result of calculation is such as
Under：
H=R (1-cos α)=116 × (40 ° of 1-cos)=27.1394, then 1.03h=27.1394 × 1.03=
28.035。
WhenWhen,The rise at place isWhenWhen,The rise at place isWhenWhen,The rise at place isWhenWhen,The rise at place is
It now calculates and accurately calculates value：h1=R (1-cos α1)=116 × (20 ° of 1-cos)=7.006, h2=R (1-cos
α2)=116 × (10 ° of 1-cos)=1.7622, h3=R (1-cos α3)=116 × (5 ° of 1-cos)=0.442, h4=R (1-
cosα4)=116 × (2.5 ° of 1-cos)=0.111.
By above-mentioned result of calculation it is found that sharp central angle according to the present invention is obtained without center of circle circular arc plane rise setting out method
Required precision of setting-out result when meeting construction lofting.
Architectural engineering arc-plane institute to when central angle is 2 α of acute angle, circular arc rise laying off can be used and measure camber line,
Its basic skills is：Initial rise h=R (1-cos α) value is calculated first multiplied by with regulation coefficient 1.03 then to divide
Arc length l is not divided intoIt corresponds to string midpoint rise and can be used respectivelyIt calculates and determines, i.e., when arc length is divided intoWhen, corresponding string midpoint rise is
Camber line is determined according to the string relationship of dividing equally vertical with riseEach cut-point carry out picture arc setting-out, the method can directly draw
Line measures measurement, achievees the purpose that camber line setting-out.
The above-described embodiments merely illustrate the principles and effects of the present invention, and is not intended to limit the present invention.It is any ripe
The personage for knowing this technology can all carry out modifications and changes to above-described embodiment without violating the spirit and scope of the present invention.Cause
This, institute is complete without departing from the spirit and technical ideas disclosed in the present invention by those of ordinary skill in the art such as
At all equivalent modifications or change, should by the present invention claim be covered.
Claims (2)
1. sharp central angle is without center of circle circular arc plane rise setting out method, built construction object M, arc-shaped planar buildings N yet to be built, circle
Heart O is the center of circle of building N, and the center of circle O is fallen in the building M, and central angle is 2 α, and outer arc radius is R, and feature exists
In, the method includes：Quadrangle angle point A, B, C, D of the building N are taken, string AB is connected, midpoint E is taken in string AB, connects OE
Hand over circular arcIn F, OF ⊥ AB, OF hands over AB in E, and getsIf arc lengthEF=h is arrow
Height, ∠ AOE=∠ BOE=α, can obtain：H=EF=R (1-cos α)；
Cos α are carried out to the expansion of Taylor series：
Cos α are approximatively substituted by first two of Taylor series,Cos α are substituted into
Formula h=R (1-cos α), then haveIt willIt substitutes into：It enablesThen
There is h=Kl2；That is rise h and corresponding arc length l2Direct proportionality；Arc length is pressedMultiple is split, arc lengthString AF is connected, then G points are taken at the midpoints AF, OG is connected, hands over arcIn I, then GI is rise h1, and set
ArcIt is sequentially connected string AI, takes midpoint K, connection OK to hand over arc in string AIIn Q points, ifThen QK is rise h2,
It can similarly obtain,
Substitute into formulaFinallyI.e.：Substitute into formulaFinallyI.e.：The midpoint for continuing to take string AK, can be derived from corresponding pass successively
System：
Rise h can accurately calculate out according to known conditions h=R (1-cos α), angle point A and angle point B it is known that withRise again
H determines camber line according to the string relationship of dividing equally vertical with riseEach cut-point carry out picture arc setting-out.
2. sharp central angle according to claim 1 is without center of circle circular arc plane rise setting out method, which is characterized in that rise
H initial values are adjusted the rise h ' after being adjusted, wherein h '=β h, β is Dynamic gene.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201711404301.0A CN108332725A (en) | 2017-12-22 | 2017-12-22 | Sharp central angle is without center of circle circular arc plane rise setting out method |
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| CN201711404301.0A CN108332725A (en) | 2017-12-22 | 2017-12-22 | Sharp central angle is without center of circle circular arc plane rise setting out method |
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111765875A (en) * | 2020-07-13 | 2020-10-13 | 江苏东交智控科技集团股份有限公司 | Circular curve measuring and paying-off method |
| CN111927118A (en) * | 2020-08-05 | 2020-11-13 | 深圳市维业装饰集团股份有限公司 | Circular arc wall surface line laying method |
| CN112648982A (en) * | 2020-12-07 | 2021-04-13 | 北京建工四建工程建设有限公司 | Simple arc line laying construction method for equal division of rise |
| CN113152224A (en) * | 2021-04-27 | 2021-07-23 | 上海奥建道路设施技术有限公司 | Method for making curved surface of steel mould for paving of integral crossing |
| CN113202181A (en) * | 2021-06-16 | 2021-08-03 | 中建八局第四建设有限公司 | Simple and accurate manufacturing method of arc-shaped edge-sealing template |
-
2017
- 2017-12-22 CN CN201711404301.0A patent/CN108332725A/en not_active Withdrawn
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111765875A (en) * | 2020-07-13 | 2020-10-13 | 江苏东交智控科技集团股份有限公司 | Circular curve measuring and paying-off method |
| CN111927118A (en) * | 2020-08-05 | 2020-11-13 | 深圳市维业装饰集团股份有限公司 | Circular arc wall surface line laying method |
| CN112648982A (en) * | 2020-12-07 | 2021-04-13 | 北京建工四建工程建设有限公司 | Simple arc line laying construction method for equal division of rise |
| CN113152224A (en) * | 2021-04-27 | 2021-07-23 | 上海奥建道路设施技术有限公司 | Method for making curved surface of steel mould for paving of integral crossing |
| CN113202181A (en) * | 2021-06-16 | 2021-08-03 | 中建八局第四建设有限公司 | Simple and accurate manufacturing method of arc-shaped edge-sealing template |
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Application publication date: 20180727 |