CN111400805A - Computer aided design method for tie bars of concrete bridge plate - Google Patents

Computer aided design method for tie bars of concrete bridge plate Download PDF

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CN111400805A
CN111400805A CN202010218574.1A CN202010218574A CN111400805A CN 111400805 A CN111400805 A CN 111400805A CN 202010218574 A CN202010218574 A CN 202010218574A CN 111400805 A CN111400805 A CN 111400805A
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steel bar
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tie
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CN111400805B (en
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胡方健
周良
陆元春
顾颖
陈龙
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Shanghai Urban Construction Design Research Institute Group Co Ltd
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Abstract

The invention discloses a computer aided design method of a tie bar of a concrete bridge plate; the method comprises the following steps: a. selecting a concrete member; b. preparing a graph; c. generating a control point; d. generating tie bar information; e. and modeling the center line of the tie bar. The invention can quickly establish the tie bar model group in the concrete bridge plate type member or plate without manually establishing an initial bar model, has high automation degree, can establish the hook sections of various types of tie bar models according to the requirement, can adjust the angle and the length of the hook, and has wide application range.

Description

Computer aided design method for tie bars of concrete bridge plate
Technical Field
The invention relates to the technical field of computer-aided design of bridges, in particular to a computer-aided design method of tie bars of concrete bridge plates.
Background
In the current BIM design software, a steel bar modeling function aiming at a concrete member appears in the fields of civil buildings and hydraulic structures, and a steel bar model can be generated aiming at a conventional member. However, since the bridge structure is significantly different from the above-mentioned fields in design methods and habits, the related steel bar modeling function is not applicable.
In 2018 to 2019, a series of modeling methods based on CATIA software reinforcing steel bars are proposed by Shanghai city City construction design research institute (group) Limited company, but related methods do not mention modeling of tie reinforcing steel bars between two reinforcing steel bar nets in a concrete member, and related technologies are still insufficient.
Therefore, how to model the tie bars between two layers of reinforcing meshes inside the concrete member becomes a technical problem which needs to be solved urgently by the technical personnel in the field.
Disclosure of Invention
In view of the above-mentioned defects of the prior art, the invention provides a computer aided design method for a tie bar of a concrete bridge slab, which aims to quickly establish a tie bar model group in a concrete bridge slab member or slab without manually establishing an initial bar model, has high automation degree, can establish hook sections of various types of tie bar models according to requirements, can adjust hook angles and lengths, and has wide application range.
In order to achieve the purpose, the invention discloses a computer aided design method of a tie bar of a concrete bridge plate; the method comprises the following steps:
a. selecting a concrete member; selecting a plate with an established concrete appearance model and a concrete surface corresponding to the steel bar net model, wherein the plate is used as an implementation main body of the tie steel bar modeling;
the steel bar net model is completely composed of three-dimensional curve segments or three-dimensional straight segments;
b. preparing a graph;
b1, selecting the first surface and the second surface of the plate as a main reference surface and a secondary reference surface for establishing the tie bar model; the main reference surface and the auxiliary reference surface are parallel to each other or intersect with each other;
b2, selecting two groups of reinforcing meshes respectively corresponding to the main reference surface and the auxiliary reference surface as a main reinforcing mesh and an auxiliary reinforcing mesh;
the main reinforcing mesh and the auxiliary reinforcing mesh are similar in shape;
the shape similarity means that the projections of the outer layer main steel bar array group and the inner layer main steel bar array group of the main steel bar mesh and the projections of the outer layer auxiliary steel bar array group and the inner layer auxiliary steel bar array group of the auxiliary steel bar mesh on the main reference surface in the corresponding array directions are parallel to each other, and the projections of the corresponding steel bar axial directions on the main reference surface are parallel to each other;
b3, extracting control information in the main reinforcing meshes and the auxiliary reinforcing meshes;
the control information includes the diameter of each bar array group in the main reinforcing mesh and the auxiliary reinforcing mesh
Figure BDA0002425271400000027
The absolute value of the distance d from the center line of each steel bar to the reference surface, the distance s between every two steel bar arrays and the total number n of the steel bars of each steel bar array;
namely, the two control information arrays of the steel bar array group of the main steel bar mesh are named as an outer main steel bar array group control information array RAPIFO and an inner main steel bar array group control information array RAPIFI respectively, and the included control information is
Figure BDA0002425271400000021
dpO、spOAnd npOAnd an
Figure BDA0002425271400000022
dpI、spIAnd npI；
The auxiliary reinforcing steel bar mesh comprises two groups of control information of reinforcing steel bar array groups, namely an outer auxiliary reinforcing steel bar array group control information array RADIFO and an inner auxiliary reinforcing steel bar array group control information array RADIFO, wherein the included control information is
Figure BDA0002425271400000023
ddO、sdOAnd ndOAnd an
Figure BDA0002425271400000024
ddI、sdIAnd ndI；
c. Generating a control point;
c1, selecting the outer layer main steel bar array group and the outer layer auxiliary steel bar array group from the main steel bar mesh and the auxiliary steel bar mesh as main reference bodies for modeling the tie steel bar control points;
c2, selecting the main reference surface and the auxiliary reference surface, and utilizing the RAPIFO and RADIFO of the outer layer main steel bar array group and the outer layer auxiliary steel bar array group to respectively offset the distance to the interior of the concrete member based on the main reference surface and the auxiliary reference surface
Figure BDA0002425271400000025
And
Figure BDA0002425271400000026
then, generating a main reference surface of the control point of the drawknot reinforcing mesh and a control point auxiliary reference surface;
c3, projecting the outer layer main steel bar array group and the inner layer main steel bar array group of the main steel bar mesh to the main reference surface of the control point, and obtaining an outer layer main steel bar projection line group, an inner layer main steel bar projection line group and a main intersection point array group of the outer layer main steel bar array group and the inner layer main steel bar array group on the main reference surface of the control point;
the number of the main intersection point array groups in the direction along the central line of the steel bars of the outer layer main steel bar array group is npIThe number of the main intersection point array groups in the direction along the central line of the steel bars of the inner-layer main steel bar array group is npO；
c4, projecting the outer layer auxiliary steel bar array group and the inner layer auxiliary steel bar array group of the auxiliary steel bar mesh to the control point auxiliary reference surface to obtain the outer layer auxiliary steel bar array group and the inner layer auxiliary steel bar array groupThe array group is arranged on the outer layer auxiliary steel bar projection line group, the inner layer auxiliary steel bar projection line group and the auxiliary intersection point array group on the control point auxiliary reference surface, and the number of the auxiliary intersection point array groups in the direction along the central line of the steel bars of the outer layer auxiliary steel bar array group is ndIThe number of the auxiliary intersection point array groups in the direction along the central line of the reinforcing steel bar of the inner-layer auxiliary reinforcing steel bar array group is ndO；
c5, taking the main intersection array group as a starting point for generating subsequent tie bars;
d. generating tie bar information; arranging the tie bars in the direction of the center line of the steel bar of any one steel bar array group of the corresponding steel bar mesh;
d1, dividing any steel bar central line of the outer layer main steel bar projection line group into a plurality of line segments by the inner layer main steel bar projection line group, and recording the number of the line segments as the total grid number GO of the outer layer main steel bar projection line group; when the total grid number GO is equal to the number of the main intersection point array groups in the direction along the central line of the steel bars of the outer-layer main steel bar array group minus 1, namely: GO ═ npI-1；
d2, dividing the total grid number GO by a modulus MD and solving for a remainder, recording the obtained divisor as DIV and the obtained remainder as MOD;
d3, setting a grid distance array ADGI, wherein the grid distance array ADGI is a one-dimensional array and is used for storing information of a plurality of line segment groups obtained after the outer main reinforcement projection line group is divided by the tie reinforcement, the length L GI of the grid distance array ADGI is the number of the line segment groups, and the quantity value of each element in the grid distance array ADGI is equal to the number of the line segments of each line segment group in the corresponding line segment groups;
d4, for the grid distance array ADGI, if the modulus MD is equal to or greater than the total grid number GO, no tie bars need to be arranged in the direction of the central line of the steel bars of the outer layer main steel bar array group, at this time, the length L GI of the grid distance array ADGI is equal to 1, and the element value of the grid distance array ADGI is equal to the total grid number GO;
d5, if the modulus MD is smaller than the total grid number GO and the remainder MOD is equal to 0, then the length L GI of the grid distance array ADGI is equal to the divisor DIV and the initial value of each element of the grid distance array ADGI is equal to the modulus MD;
if the modulus MD is smaller than the total grid number GO and the remainder MOD is not equal to 0, making the length L GI of the grid distance array ADGI equal to a divisor DIV plus 1, making an initial value of each element of the grid distance array ADGI equal to the modulus MD;
d6, information about arrangement of the tie bars in the direction of the center line of the bars of the inner-layer main bar array group of the bar mat: total grid number GI ═ npO-1, a grid distance array ADGI, a length L GI of the grid distance array ADGI;
d7, specifying the extension direction of the tie bar, selecting a reference surface as the extension reference surface of the main line segment of the tie bar, and extracting the normal vector of the extension reference surface; the extended reference surface is a plane or a curved surface;
e. modeling the center line of the tie bar;
e1, if the length L GI of the grid distance array ADGI is 1, or the length L GI of the grid distance array ADGI is 1, it is not necessary to establish a model of the tie bars in the direction of the center line of the bars of the outer layer main bar array group and the inner layer main bar array group;
e2, if the length L GI >1 of the grid distance array ADGI and the length L GI >1 of the grid distance array ADGI are needed to establish a model of the tie bar;
e2.1, establishing information required to be utilized when the model of the tie bar is established, wherein the information comprises the grid distance array ADGI, the main intersection point array group and the auxiliary intersection point array group, the main reference surface of the control point of the tie bar mesh and the auxiliary reference surface of the control point, the outer-layer main bar array group, the inner-layer main bar array group, the outer-layer auxiliary bar array group, the inner-layer auxiliary bar array group and the extension reference surface;
e2.2, establishing a pointer array PT with the length of 2, wherein 2 elements in the pointer array PT are used for recording the intersection point position of the intersection point array group; the 1 st element PTA of the pointer array records the intersection point sequence number along the direction of the central line of the steel bar of the outer-layer main steel bar array group, and the 2 nd element PTB of the pointer array records the intersection point sequence number along the direction of the central line of the steel bar of the inner-layer auxiliary steel bar array group;
e2.3, establishing a variable S L K for storing the total length of the tie bar;
e3.4, establishing a circulation action, wherein the circulation execution frequency formula is L GI-1 ×L GI-1, the circulation priority is that the number of the circulation action is L GI-1 along the direction of the central line of the steel bars of the outer layer main steel bar array group in the j direction or the row direction, and the number of the circulation action is L GI-1 along the direction of the central line of the steel bars of the inner layer auxiliary steel bar array group in the i direction or the row direction;
e3.5, when the execution loop number nj is 1 and ni is 1:
e3.5a, let the magnitude of pointer array element PTA equal the magnitude of the 1 st element of the grid distance array ADGI or the correction value a1 plus 1, i.e.: PTA 1+ a1, let the magnitude of the pointer array element PTB equal the magnitude of the 1 st element of the grid distance array ADGI or the correction value b1 plus 1, i.e.: PTB ═ 1+ b 1;
e3.5b, using the first PTA row of the intersection point array group to follow the direction of the central line of the steel bar of the outer layer main steel bar array group, using the second PTB row to follow the direction of the central line of the steel bar of the inner layer main steel bar array group, and using the intersection point of the rows as a starting point to serve as a1 st to 1 st main segment of the tied steel bar;
the 1 st-1 st main segment of the tie bar is perpendicular to the extension reference surface, and the 1 st-1 st main segment of the tie bar starts from the starting point and extends to the control point and the auxiliary reference surface to intersect to form an end point; the end point does not necessarily coincide with the set of secondary intersection arrays;
e3.5c, correcting the 1 st to 1 st main segment of the tie bar;
making a working plane, wherein the working plane passes through the 1 st to 1 st main segment of the tie bar and is perpendicular to the central line of the bar closest to the starting point in the inner main bar array group;
the starting point edge and the outer layer main steel bar arrayMoving the end point along the extending direction of the central line of the steel bars of the outer layer auxiliary steel bar array group, keeping the 1 st-1 st main segment of the tie steel bar rotating on the working plane, and enabling the distances between the 1 st-1 st main segment of the tie steel bar and the initial positions of the starting point and the end point to be equal
Figure BDA0002425271400000051
Figure BDA0002425271400000052
e3.5d, based on the corrected starting point, making a main hook line segment at the tail end of the 1 st to 1 st tie bar along the main reference surface of the control point;
the main hook line segment at the tail end of the 1 st-1 st drawknot steel bar is parallel to the steel bar central line closest to the starting point in the outer layer main steel bar array group, and the extending direction of the main hook line segment at the tail end of the 1 st-1 st drawknot steel bar is the extending direction of the steel bar central line of the outer layer main steel bar array group;
e3.5e, based on the corrected end point, making an auxiliary hook line segment at the tail end of the 1 st to 1 st tie steel bar along the auxiliary reference surface of the control point;
the auxiliary hook line segment at the tail end of the 1 st-1 st drawknot steel bar is parallel to the central line of the steel bar closest to the starting point in the outer layer auxiliary steel bar array group, and the extending direction of the auxiliary hook line segment at the tail end of the 1 st-1 st drawknot steel bar is opposite to the extending direction of the central line of the steel bar of the outer layer auxiliary steel bar array group;
e3.5f, intersecting the working plane with the central line of the steel bar closest to the starting point in the inner-layer main steel bar array group to obtain a main datum point;
taking the main datum point as a rotation point, enabling the main hook line segment at the tail end of the 1 st-1 st tie bar to rotate on the working plane, enabling the rotation direction to face the interior of the concrete member, and enabling the included angle between the main hook line segment at the tail end of the 1 st-1 st tie bar and the main line segment of the 1 st-1 st tie bar to be 45 degrees;
e3.5g, intersecting the working plane with the central line of the steel bar closest to the starting point in the inner-layer auxiliary steel bar array group to obtain an auxiliary reference point;
taking the auxiliary datum point as a rotation point, enabling the auxiliary hook line segment at the tail end of the 1 st-1 st tie bar to rotate on the working plane, enabling the rotation direction to face the interior of the concrete member, and enabling the included angle between the auxiliary hook line segment at the tail end of the 1 st-1 st tie bar and the main line segment of the 1 st-1 st tie bar to be 45 degrees;
e3.5h, rounding on a working plane by taking the main hook line segment at the tail end of the 1 st to 1 st tie bar and the main line segment of the 1 st to 1 st tie bar as reference line segments;
the fillet radius is the sum of the radius of the inner layer main steel bar array group and the radius of the tie steel bar, namely:
Figure BDA0002425271400000061
the length of the main hook line segment at the tail end of the 1 st-1 st drawknot steel bar is set to be 5 times to 10 times of the diameter of the drawknot steel bar, namely:
Figure BDA0002425271400000062
to
Figure BDA0002425271400000063
e3.5i, using the auxiliary hook line segment at the tail end of the 1 st to 1 st tie bar and the main line segment of the 1 st to 1 st tie bar as reference line segments, and performing rounding treatment on a working plane;
the fillet radius is the sum of the radius of the inner layer auxiliary steel bar array group and the radius of the tie steel bar, namely:
Figure BDA0002425271400000064
the length of the auxiliary hook line segment at the tail end of the 1 st-1 st drawknot steel bar is set to be 5 times to 10 times of the diameter of the drawknot steel bar, namely:
Figure BDA0002425271400000065
to
Figure BDA0002425271400000066
So far, the modeling of the center line of the 1 st-1 st tie bar is completed;
e3.5j, moving the center line of the 1 st to 1 st tie steel bar along the center line of the steel bar closest to the starting point in the inner-layer main steel bar array group;
the moving distance is the sum of the radius of the outer layer main steel bar array group and the radius of the tie steel bar, namely
Figure BDA0002425271400000071
e3.5k, and enabling the total length variable S L K of the tie steel bar to be equal to the total length of the center line of the 1 st to 1 st tie steel bar;
e3.6, when the number of executions nj>1，ni>1, time:
e3.6a, making the magnitude of the pointer array element PTA equal to the 1 st to nth of the grid distance array ADGIjSum of magnitude or correction value of individual elements Σ anjAdding 1, namely: PTA 1+ Σ anjThe magnitude of the pointer array element PTB is equal to the 1 st to nth of the grid distance array ADGIiSum of individual element magnitudes or correction values Σ bniAdding 1, namely: PTB 1+ Σ bni；
e3.6b, taking the PTA row of the intersection point array group 11 along the direction of the central line of the steel bar of the outer-layer main steel bar array group, the PTB row and the central line of the steel bar of the inner-layer main steel bar array group, and taking the intersection point of the rows as a starting point to serve as the nth rowj-niA steel bar main body line segment is tied;
the n-thj-niThe main line segment of the root tie steel bar is vertical to the extension reference surface, and the nthj-niThe segment of the main body of the steel bar is extended from the starting point to the auxiliary reference surface of the control point and intersects with the auxiliary reference surface to form an end point; the end point is not necessarily intersected with the sideOverlapping the point array groups;
e3.6c, modified nthj-niA steel bar main body line segment is tied;
making a new working plane, said working plane passing through said nth planeiA steel bar main line segment is tied, and the steel bar main line segment is perpendicular to the steel bar central line closest to the starting point in the inner layer main steel bar array group;
moving the starting point along the direction opposite to the extending direction of the central line of the steel bars of the outer layer main steel bar array group, moving the terminal point along the extending direction of the central line of the steel bars of the outer layer auxiliary steel bar array group, and keeping the nthj-niThe main line segment of the root tie steel bar rotates on the working plane to make the nthj-niThe distances between the main line segment of the root tie steel bar and the initial positions of the starting point and the end point are all
Figure BDA0002425271400000072
Figure BDA0002425271400000073
e3.6d, based on the corrected starting point, making the nth reference plane along the control point main reference planej-niA main hook line segment at the tail end of the root tie bar;
the n-thj-niThe main hook line segment at the tail end of the root tie steel bar is parallel to the central line of the steel bar closest to the starting point in the outer layer main steel bar array group, and the nth line segmentj-niThe extending direction of the main hook line segment at the tail end of the root tie steel bar is the extending direction of the steel bar central line of the outer layer main steel bar array group;
e3.6e, based on the corrected end point, making the nth datum plane along the control point sub-datum planej-niA secondary hook line segment at the tail end of the root tie bar;
the n-thj-niThe secondary hook line segment at the tail end of the root tie steel bar is parallel to the central line of the steel bar closest to the starting point in the outer layer secondary steel bar array group, and the secondary hook line segment is parallel to the central line of the steel bar closest to the starting point in the outer layer secondary steel bar array groupN thj-niThe extending direction of the auxiliary hook line segment at the tail end of the root tie steel bar is opposite to the extending direction of the steel bar central line of the outer layer auxiliary steel bar array group;
e3.6f, intersecting the working plane with the central line of the steel bar closest to the starting point in the inner-layer main steel bar array group to obtain a main datum point;
using the main reference point as a rotation point to make the nth pointj-niThe main hook line segment at the tail end of the root tie steel bar rotates on the working plane, and the rotating direction faces the interior of the concrete member, so that the nth hook line segmentj-niThe included angle between the main hook line segment at the tail end of the root tie steel bar and the main line segment of the 1 st tie steel bar is 45 degrees;
e3.6g, intersecting the working plane with the central line of the steel bar closest to the starting point in the inner-layer secondary steel bar array group to obtain a secondary reference point;
using the auxiliary reference point as a rotation point to make the nth pointj-niThe auxiliary hook line segment at the tail end of the root tie steel bar rotates on the working plane, and the rotating direction faces the interior of the concrete member, so that the nth hook line segmentj-niAn auxiliary hook line segment at the tail end of the root tie bar and the nthj-niThe included angle of the main line segment of the root tie steel bar is 45 degrees;
e3.6h, and the nj-niA main hook line segment at the tail end of the root tie bar, the n-thj-niThe main line segment of the root tie steel bar is a reference line segment, and rounding treatment is carried out on a working plane;
the fillet radius is the sum of the radius of the inner layer main steel bar array group and the radius of the tie steel bar, namely:
Figure BDA0002425271400000081
the n-thj-niThe length of the main hook line segment at the end of the root tie bar is set to be 5 to 10 times the diameter of the tie bar, namely:
Figure BDA0002425271400000082
to
Figure BDA0002425271400000083
e3.6i, as defined above for the n-thj-niAn auxiliary hook line segment at the tail end of the root tie bar, the n-thj-niThe main line segment of the root tie steel bar is a reference line segment, and rounding treatment is carried out on a working plane;
the fillet radius is the sum of the radius of the inner layer auxiliary steel bar array group and the radius of the tie steel bar, namely:
Figure BDA0002425271400000084
the n-thj-niThe length of the secondary hook line segment at the end of the root tie bar is set to be 5 to 10 times the diameter of the tie bar, namely:
Figure BDA0002425271400000091
to
Figure BDA0002425271400000092
So far, the modeling of the center line of the nj-ni tie bars is completed;
e3.6j, adding the n-th elementj-niThe central line of the root tie steel bar moves along the central line of the steel bar closest to the starting point in the inner layer main steel bar array group;
the moving distance is the sum of the radius of the outer layer main steel bar array group and the radius of the tie steel bar, namely
Figure BDA0002425271400000093
e3.6k, and making the total length variable S L K of the tie bar equal to the nthj-niThe sum of the total length of the central line of the root tie bar and the magnitude of the variable S L K of the total length of the tie bar in the last circulation.
Preferably, in the step d5, for the conventional case of bridge engineering, the magnitude of the modulus MD is 2 to 5, and the calculation method of the correction value of each element of the grid distance array ADG is as follows:
① when the modulus MD is equal to 2:
when the divisor DIV is 0, the grid distance array ADGI is not corrected;
when the divisor DIV is not equal to 0 and the remainder MOD is 0, the grid distance array ADGI is not corrected;
when the divisor DIV is not equal to 0 and the remainder MOD is 1, correcting the grid distance array ADGI to reduce the value of the 1 st element by 1;
② when the modulus MD equals 3:
when the divisor DIV is 0, the grid distance array ADGI is not corrected;
when the divisor DIV is not equal to 0 and the remainder MOD is 0, the grid distance array ADGI is not corrected;
when the divisor DIV is not equal to 0 and the remainder MOD is 1, correcting the grid distance array ADGI to reduce the magnitude of the 1 st element and the magnitude of the last 1 element by 1;
when the divisor DIV is not equal to 0 and the remainder MOD is 2, correcting the grid distance array ADGI to reduce the value of the 1 st element by 1;
③ when the modulus MD equals 4:
when the divisor DIV is 0, the grid distance array ADGI is not corrected;
when the divisor DIV is not equal to 0 and the remainder MOD is 0, the grid distance array ADGI is not corrected;
when the divisor DIV is not equal to 0, the remainder MOD is not equal to 1, and the length L GI of the grid distance array ADGI is not equal to 2, correcting the grid distance array ADGI to reduce the magnitude of the 1 st element, the 2 nd element and the last 1 element by 1;
when the divisor DIV is not equal to 0, the remainder MOD is 1, and the length L GI of the grid distance array ADGI is 2, modifying the grid distance array ADGI to reduce the magnitude of the 1 st element by 1 and reduce the magnitude of the last 1 element by 2;
when the divisor DIV is not equal to 0 and the remainder MOD is 2, correcting the grid distance array ADGI to reduce the magnitude of the 1 st element and the magnitude of the last 1 element by 1;
when the divisor DIV is not equal to 0 and the remainder MOD is 3, correcting the grid distance array ADGI to reduce the value of the 1 st element by 1;
④ when the modulus MD equals 5:
when the divisor DIV is 0, the grid distance array ADGI is not corrected;
when the divisor DIV is not equal to 0 and the remainder MOD is 0, the grid distance array ADGI is not corrected;
when the divisor DIV is not equal to 0, the remainder MOD is not equal to 1, and the length L GI of the grid distance array ADGI is not equal to 2, correcting the grid distance array ADGI to enable the magnitude of the 1 st element and the magnitude of the 2 nd element to be reduced by 1 and the magnitude of the last 1 element to be reduced by 2;
when the divisor DIV is not equal to 0, the remainder MOD is 1, and the length L GI of the grid distance array ADGI is 2, modifying the grid distance array ADGI to reduce the magnitude of the 1 st element and the magnitude of the last 1 element by 2;
when the divisor DIV is not equal to 0, the remainder MOD is not equal to 2, and the length L GI of the grid distance array ADGI is not equal to 2, correcting the grid distance array ADGI to reduce the magnitude of the 1 st element, the 2 nd element and the last 1 element by 1;
when the divisor DIV is not equal to 0, the remainder MOD is 2, and the length L GI of the grid distance array ADGI is 2, modifying the grid distance array ADGI to reduce the magnitude of the 1 st element by 1 and reduce the magnitude of the last 1 element by 2;
when the divisor DIV is not equal to 0 and the remainder MOD is 3, correcting the grid distance array ADGI to reduce the magnitude of the 1 st element and the magnitude of the last 1 element by 1;
when the divisor DIV ≠ 0 and the remainder MOD ═ 4, the grid distance array ADGI is modified to reduce the magnitude of the 1 st element by 1.
The invention has the beneficial effects that:
the application of the invention can realize the rapid establishment of the tie steel bar model group in the concrete bridge plate member or plate without manually establishing the initial steel bar model, and the degree of automation is high.
The invention can establish the hook section of various types of tie bar models according to the requirements, can adjust the angle and the length of the hook, and has wide application range.
The application of the invention can obtain the length of each tie steel bar model and the total length of the tie steel bar model group, and can be completely measured in the statistics of the quantity of engineering materials.
The method can be applied to the modeling of the tie steel bar group of the concrete bridge plate type member or plate, and can also adapt to the modeling of the tie steel bar group of the variable-thickness plate type member or plate.
The method can be popularized to the modeling of the tie bar group of other concrete solid members such as bar-shaped members and special-shaped members.
The conception, the specific structure and the technical effects of the present invention will be further described with reference to the accompanying drawings to fully understand the objects, the features and the effects of the present invention.
Drawings
Fig. 1 is a schematic view of a concrete bridge deck member or plate and a reinforcing mesh module according to an embodiment of the present invention.
Fig. 2 shows a schematic diagram of an auxiliary surface and an auxiliary line in an embodiment of the invention.
Fig. 3 is a schematic diagram of the master rebar grid control point generation in accordance with one embodiment of the present invention.
Fig. 4 is a schematic diagram of the generation of the control points of the sub-reinforcing mesh in one embodiment of the present invention.
Fig. 5 is a schematic diagram illustrating the generation of information of tie bars according to an embodiment of the present invention.
Fig. 6 is a schematic diagram illustrating modeling of a center line of a tie bar in an embodiment of the present invention.
Fig. 7 is a schematic diagram showing the relationship between a body segment and a distal hook segment of a tie bar in an embodiment of the invention.
Detailed Description
Examples
As shown in fig. 1 to 7, a computer aided design method of tie bars of a concrete bridge slab; the method comprises the following steps:
a. selecting a concrete member; selecting a built concrete appearance model 4 and a plate of a concrete surface corresponding to the steel bar net model, wherein the plate is used as an implementation main body of the tie steel bar modeling;
the steel bar net model is completely composed of three-dimensional curve segments or three-dimensional straight segments;
b. preparing a graph;
b1, selecting the first surface and the second surface of the plate as a main reference surface 31 and a secondary reference surface 32 for establishing the tie bar model; the main reference surface 31 and the sub-reference surface 32 are parallel to or intersect with each other;
b2, selecting two groups of reinforcing meshes corresponding to the main reference surface 31 and the auxiliary reference surface 32 respectively as the main reinforcing mesh 21 and the auxiliary reinforcing meshes 22;
the main reinforcing mesh 21 and the auxiliary reinforcing mesh 22 are similar in shape;
the similar shape means that the projections of the outer layer main steel bar array group 211 and the inner layer main steel bar array group 212 of the main steel bar mesh 21 and the projections of the outer layer auxiliary steel bar array group 221 and the inner layer auxiliary steel bar array group 222 of the auxiliary steel bar mesh 22 on the main reference surface 31 in the corresponding array directions are parallel to each other, and the projections on the main reference surface 31 in the corresponding steel bar axial directions are parallel to each other;
b3, extracting control information in the main reinforcing mesh 21 and the auxiliary reinforcing mesh 22;
the control information includes the diameter of each bar belonging to each bar array group in the main mesh 21 and the sub mesh 22
Figure BDA0002425271400000127
The absolute value of the distance d from the center line of each steel bar to the reference surface, the distance s between every two steel bar arrays and the total number n of the steel bars of each steel bar array;
namely, the two control information arrays of the steel bar array group of the main steel bar mesh 21 are named as an outer main steel bar array group control information array RAPIFO and an inner main steel bar array group control information array RAPIFI respectively, and the included control information is
Figure BDA0002425271400000121
dpO、spOAnd npOAnd an
Figure BDA0002425271400000122
dpI、spIAnd npI；
The two sets of control information of the auxiliary reinforcing steel bar mesh 22 including the reinforcing steel bar array set are named as an outer auxiliary reinforcing steel bar array set control information array RADAFO and an inner auxiliary reinforcing steel bar array set control information array RADAFO respectively, and the included control information is
Figure BDA0002425271400000123
ddO、sdOAnd ndOAnd an
Figure BDA0002425271400000124
ddI、sdIAnd ndI；
c. Generating a control point;
c1, selecting an outer layer main steel bar array group 211 and an outer layer auxiliary steel bar array group 221 from the main steel bar mesh 21 and the auxiliary steel bar mesh 22 as main reference bodies for modeling of the tie steel bar control points;
c2, selecting the main reference surface 31 and the auxiliary reference surface 32, and respectively offsetting the offset distance to the interior of the concrete member based on the main reference surface 31 and the auxiliary reference surface 32 by using the RAPIFO and RAIFO of the outer layer main steel bar array group 211 and the outer layer auxiliary steel bar array group 221
Figure BDA0002425271400000125
And
Figure BDA0002425271400000126
then, generating a main reference surface 311 and a control point auxiliary reference surface 321 of the control point of the tie bar mesh;
c3, projecting the outer layer main steel bar array group 211 and the inner layer main steel bar array group 212 of the main steel bar mesh 21 to the control point main reference surface 311, and obtaining an outer layer main steel bar projection line group 2111, an inner layer main steel bar projection line group 2121 and a main intersection point array group 11 of the outer layer main steel bar array group 211 and the inner layer main steel bar array group 212 on the control point main reference surface 311;
the number of the main intersection array groups 11 in the direction along the central line of the steel bars of the outer layer main steel bar array group 211 is npIThe number of the main intersection array groups 11 in the direction along the central line of the steel bars of the inner-layer main steel bar array group 212 is npO；
c4, projecting the outer layer auxiliary steel bar array group 221 and the inner layer auxiliary steel bar array group 222 of the auxiliary steel bar net 22 to the control point auxiliary reference surface 321, obtaining the outer layer auxiliary steel bar projection line group 2211, the inner layer auxiliary steel bar projection line group 2221 and the auxiliary intersection point array group 12 of the outer layer auxiliary steel bar array group 221 and the inner layer auxiliary steel bar array group 222 on the control point auxiliary reference surface 321, wherein the number of the auxiliary intersection point array groups 12 in the direction along the central line of the steel bars of the outer layer auxiliary steel bar array group 221 is ndIThe number of the auxiliary intersection array groups 12 in the direction along the central line of the reinforcing steel bar of the auxiliary reinforcing steel bar array group 222 at the inner layer is ndO；
c5, taking the main intersection array group 11 as a starting point for generating subsequent tie bars;
d. generating tie bar information; arranging the tie bars in the direction of the center line of the steel bar of any one steel bar array group of the corresponding steel bar mesh;
d1, dividing any steel bar central line of the outer layer main steel bar projection line group 2111 into a plurality of line segments by the inner layer main steel bar projection line group 2121, and recording the number of the line segments as the total grid number GO of the outer layer main steel bar projection line group 2111; when the total grid number GO is equal to the number of the main intersection array groups 11 in the direction along the central line of the steel bars of the outer-layer main steel bar array group 211 minus 1, that is: GO ═ npI-1；
d2, dividing the total grid number GO by the modulus MD and solving for the remainder, recording the obtained divisor as DIV and the obtained remainder as MOD;
in engineering design, the tied steel bars arranged in the same direction are arranged at a certain interval, and the interval of the tied steel bars arranged along the central line direction of the outer-layer main steel bar array group is the interval s of the inner-layer main steel bar array grouppIIs defined as the modulus MD.
d3, setting a grid distance array ADGI, wherein the grid distance array ADGI is a one-dimensional array and is used for storing information of a plurality of line segment groups after the outer layer main reinforcement projection line group 2111 is divided by the tie reinforcement, the length L GI of the grid distance array ADGI is the number of the line segment groups, and the quantity value of each element in the grid distance array ADGI is equal to the number of the line segments of each line segment group in the corresponding line segment groups;
d4, for the grid distance array ADGI, if the modulus MD is equal to or greater than the total grid number GO, no tie bars need to be arranged in the direction of the central line of the steel bars of the outer layer main steel bar array group 211, at this time, the length L GI of the grid distance array ADGI is equal to 1, and the element value of the grid distance array ADGI is equal to the total grid number GO;
d5, for the grid distance array ADGI, if the modulus MD is smaller than the total grid number GO and the remainder MOD is equal to 0, the length L GI of the grid distance array ADGI is equal to the divisor DIV, and the initial value of each element of the grid distance array ADGI is equal to the modulus MD;
if the modulus MD is smaller than the total grid number GO and the remainder MOD is not equal to 0, making the length L GI of the grid distance array ADGI equal to the divisor DIV plus 1 and making the initial value of each element of the grid distance array ADGI equal to the modulus MD;
d6, information about arrangement of the tie bars in the direction of the central line of the bars of the inner-layer main bar array group 212 of the steel bar mesh: total grid number GI ═ npO-1, grid distance array ADGI, length of grid distance array ADGI L GI;
d7, specifying the extension direction of the tie bar, selecting a reference surface as the extension reference surface 30 of the main line segment of the tie bar, and extracting the normal vector of the extension reference surface 30; the extended reference surface 30 is a plane or curved surface;
e. modeling the center line of the tie bar;
e1, if the length L GI of the grid distance array ADGI is 1, or the length L GI of the grid distance array ADGI is 1, it is not necessary to establish a model of tie bars in the direction of the central lines of the bars of the outer layer main bar array group 211 and the inner layer main bar array group 212;
e2, if the length L GI of the grid distance array ADGI is more than 1 and the length L GI of the grid distance array ADGI is more than 1, a model of the tie bar needs to be established;
e2.1, establishing information required to be utilized when the tie bar model is established, wherein the information comprises grid distance arrays (ADGI and ADGI), a main intersection point array group (11) and an auxiliary intersection point array group (12), a control point main reference surface (311) and a control point auxiliary reference surface (321) of the tie bar mesh, an outer layer main bar array group (211), an inner layer main bar array group (212), an outer layer auxiliary bar array group (221), an inner layer auxiliary bar array group (222) and an extension reference surface (30);
e2.2, establishing a pointer array PT with the length of 2, wherein 2 elements in the pointer array PT are used for recording the intersection point position of the intersection point array group 11; the 1 st element PTA of the pointer array records the intersection point sequence number along the direction of the central line of the steel bar of the outer-layer main steel bar array group 211, and the 2 nd element PTB of the pointer array records the intersection point sequence number along the direction of the central line of the steel bar of the inner-layer auxiliary steel bar array group 222;
e2.3, establishing a variable S L K for storing the total length of the tie bar;
e3.4, establishing a circulation action, wherein the circulation execution frequency formula is L GI-1 ×L GI-1, the circulation priority is that the number of the circulation action is L GI-1 along the direction of the central line of the steel bars of the outer-layer main steel bar array group 211, i direction or row direction, and the number of the circulation action is L GI-1 along the direction of the central line of the steel bars of the inner-layer auxiliary steel bar array group 222, i direction or row direction;
e3.5, when the execution loop number nj is 1 and ni is 1:
e3.5a, let the magnitude of pointer array element PTA equal the magnitude of the 1 st element of grid distance array ADGI or the correction value a1 plus 1, i.e.: PTA is 1+ a1, the magnitude of pointer array element PTB is equal to the magnitude of the 1 st element of the grid distance array ADGI or the correction value b1 plus 1, i.e.: PTB ═ 1+ b 1;
e3.5b, taking the PTA row of the intersection array group 11 along the direction of the central line of the steel bar of the outer-layer main steel bar array group 211, taking the intersection of the rows as the starting point 101 and taking the intersection of the rows as the 1 st to 1 st main line segment 231 of the tie steel bar along the direction of the central line of the steel bar of the inner-layer main steel bar array group 212 and the PTB row;
the 1-1 st main segment 231 of the tie bar is perpendicular to the extension reference surface 30, and the 1-1 st main segment 231 of the tie bar starts from the starting point 101 and extends to the control point secondary reference surface 321 to intersect to form an end point 102; the end point 102 does not necessarily coincide with the sub intersection array group 12;
e3.5c, and correcting the 1 st to 1 st main segment 231 of the tie bar;
a working plane 33 is made, the working plane 33 passes through the 1 st to 1 st main segment 231 of the tie bar and is perpendicular to the central line of the bar closest to the starting point 101 in the inner layer main bar array group 212;
moving the starting point 101 along the direction opposite to the extending direction of the central line of the steel bar of the outer layer main steel bar array group 211, moving the end point 102 along the extending direction of the central line of the steel bar of the outer layer auxiliary steel bar array group 221, and keeping the 1 st-1 st main segment 231 of the tie steel bar to rotate on the working plane 33, so that the distances between the 1 st-1 st main segment 231 of the tie steel bar and the initial positions of the starting point 101 and the end point 102 are all the same
Figure BDA0002425271400000151
Figure BDA0002425271400000152
e3.5d, based on the corrected starting point 1011, making a main hook line segment 232 at the tail end of the 1 st to 1 st drawknot steel bar along the main control point reference surface 311;
the main hook line segment 232 at the tail end of the 1 st to 1 st drawknot steel bar is parallel to the steel bar central line closest to the starting point in the outer layer main steel bar array group 211, and the extending direction of the main hook line segment 232 at the tail end of the 1 st to 1 st drawknot steel bar is the extending direction of the steel bar central line of the outer layer main steel bar array group 211;
e3.5e, based on the corrected end point 1021, making an auxiliary hook line segment 233 of the tail end of the 1 st to 1 st drawknot steel bar along the auxiliary reference surface 321 of the control point;
the auxiliary hook line segment 233 at the tail end of the 1 st-1 st drawknot steel bar is parallel to the steel bar central line closest to the starting point in the outer-layer auxiliary steel bar array group 221, and the extending direction of the auxiliary hook line segment 233 at the tail end of the 1 st-1 st drawknot steel bar is opposite to the extending direction of the steel bar central line of the outer-layer auxiliary steel bar array group 221;
e3.5f, intersecting the working plane 33 with the central line of the steel bar closest to the starting point in the inner-layer main steel bar array group 212 to obtain a main reference point 103;
taking the main reference point 103 as a rotation point, rotating the main hook line segment 232 at the tail end of the 1 st-1 st tie bar on the working plane 33, wherein the rotation direction faces towards the interior of the concrete member, and making the included angle between the main hook line segment 232 at the tail end of the 1 st-1 st tie bar and the main line segment 231 of the 1 st-1 st tie bar be 45 degrees;
e3.5g, intersecting the working plane 33 with the central line of the steel bar closest to the starting point in the inner-layer auxiliary steel bar array group 222 to obtain an auxiliary reference point 104;
taking the auxiliary reference point 104 as a rotation point, enabling the auxiliary hook line segment 233 at the tail end of the 1 st-1 st tie bar to rotate on the working plane 33, wherein the rotation direction faces towards the interior of the concrete member, and enabling the included angle between the auxiliary hook line segment 233 at the tail end of the 1 st-1 st tie bar and the main line segment 231 of the 1 st-1 st tie bar to be 45 degrees;
e3.5h, taking a main hook line segment 232 at the tail end of the 1 st to 1 st tie bar and a main line segment 231 of the 1 st to 1 st tie bar as reference line segments, and rounding on the working plane 33;
the fillet radius is the sum of the radius of the inner layer main steel bar array group 212 and the radius of the tie steel bar, namely:
Figure BDA0002425271400000161
Figure BDA0002425271400000162
the length of the main hook line segment 232 at the end of the 1 st-1 st rebar is set to be 5 to 10 times the diameter of the rebar, namely:
Figure BDA0002425271400000163
to
Figure BDA0002425271400000164
e3.5i, taking the auxiliary hook line segment 233 at the tail end of the 1 st to 1 st tie bar and the main line segment of the 1 st to 1 st tie bar as reference line segments, and rounding on the working plane 33;
fillet radius is vice reinforcing bar array group 2 of inlayer22 and the sum of the radius of the tie bar, namely:
Figure BDA0002425271400000165
Figure BDA0002425271400000166
the length of the secondary hook line segment 233 at the end of the 1-1 st lashing bar is set to be 5 to 10 times the diameter of the lashing bar, i.e.:
Figure BDA0002425271400000171
to
Figure BDA0002425271400000172
So far, the modeling of the center line of the 1 st-1 st tie bar is completed;
e3.5j, moving the center line of the 1 st to 1 st tie steel bar along the center line of the steel bar closest to the starting point in the inner-layer main steel bar array group 212;
the distance of movement is the sum of the radius of the outer main steel bar array group 211 and the radius of the tie steel bar, i.e. the distance of movement is
Figure BDA0002425271400000173
Figure BDA0002425271400000174
e3.5k, and enabling the total length variable S L K of the tie steel bar to be equal to the total length of the center line of the 1 st to 1 st tie steel bar;
e3.6, when the number of executions nj>1，ni>1, time:
e3.6a, the magnitude of the pointer array element PTA is equal to the 1 st to nth of the grid distance array ADGIjSum of magnitude or correction value of individual elements Σ anjAdding 1, namely: PTA 1+ Σ anjThe magnitude of the pointer array element PTB is equal to the 1 st to the n th of the grid distance array ADGIiSum of individual element magnitudes or correction values Σ bniAdding 1, namely: PTB 1+ Σ bni；
e3.6b, in a cross-point arrayThe PTA row of the column group 11 is along the direction of the central line of the steel bar of the outer layer main steel bar array group 211, the PTB row is along the direction of the central line of the steel bar of the inner layer main steel bar array group 212, and the intersection point of the rows is taken as the nth row with the starting point 101j-niA root tie bar body segment 231;
n thj-niThe main line segment of the root tie bar is vertical to the extension reference surface 30, the nthj-niThe segment of the main body of the steel bar is extended from the starting point 101 to the control point and the auxiliary reference surface 321 to form an end point 102; the end point 102 does not necessarily coincide with the sub intersection array group 12;
e3.6c, modified nthj-niA root tie bar body segment 231;
as a new working plane 33, the working plane 33 passes through the nthiA steel bar main line segment is tied and is perpendicular to the central line of the steel bar closest to the starting point in the inner-layer main steel bar array group 212;
moving the start point 101 in the direction opposite to the direction in which the center line of the steel bar of the outer-layer main steel bar array group 211 extends, moving the end point 102 in the direction in which the center line of the steel bar of the outer-layer sub-steel bar array group 221 extends, and holding the nthj-niThe main body segment 231 of the steel tie bar is rotated on the working plane 33 to rotate the nth segmentj-niThe distances between the root tie bar body line segment 231 and the initial positions of the starting point 101 and the end point 102 are all the same
Figure BDA0002425271400000175
Figure BDA0002425271400000176
e3.6d, based on the corrected starting point 1011, making the nth reference point along the control point main reference plane 311j-niA main hook line segment 232 at the end of the root tie bar;
n thj-niThe main hook line 232 at the end of the root tie bar is parallel to the central line of the bar closest to the starting point in the outer layer main bar array group 211, the nth barj-niExtension of the main hook segment 232 at the end of the root tie barThe extending direction is the extending direction of the central line of the steel bars of the outer layer main steel bar array group 211;
e3.6e, making the nth reference plane 321 along the control point sub-reference plane based on the corrected end point 1021j-niA secondary hook segment 233 at the end of the root tie bar;
n thj-niThe secondary hook line segment 233 at the end of the root tie bar is parallel to the central line of the bar closest to the starting point in the outer secondary bar array group 221, the nth barj-niThe extension direction of the auxiliary hook line segment 233 at the tail end of the root tie steel bar is opposite to the extension direction of the steel bar central line of the outer-layer auxiliary steel bar array group 221;
e3.6f, intersecting the working plane 33 with the central line of the steel bar closest to the starting point in the inner-layer main steel bar array group 212 to obtain a main reference point 103;
using the main reference point 103 as the rotation point, let the nthj-niThe main hook line segment 232 at the end of the root tie bar rotates in the working plane 33 in the direction toward the interior of the concrete member to make the nthj-niThe included angle between the main hook line segment 232 at the tail end of the steel bar and the main line segment 231 of the 1 st steel bar is 45 degrees;
e3.6g, intersecting the working plane 33 with the central line of the steel bar closest to the starting point in the inner-layer secondary steel bar array group 222 to obtain a secondary reference point 104;
let the nth datum point 104 be the rotation pointj-niThe secondary hook wire 233 at the end of the steel bar rotates on the working plane 33 in the direction of the concrete member to make the nthj-ni Secondary hook segment 233 and nth at the end of the root tie barj-niThe included angle of the main line segment 231 of the root tie bar is 45 degrees;
e3.6h, and nj-ni Main hook line 232, nth of the end of the root tie barj-niThe root tie bar main body line segment 231 is a reference line segment, and rounding processing is carried out on the working plane 33;
the fillet radius is the sum of the radius of the inner layer main steel bar array group 212 and the radius of the tie steel bar, namely:
Figure BDA0002425271400000181
Figure BDA0002425271400000182
n thj-niThe length of the main hook line segment at the tail end of the root tie bar is set to be 5 to 10 times of the diameter of the tie bar, namely:
Figure BDA0002425271400000183
to
Figure BDA0002425271400000184
e3.6i, and (n)j-niSubsidiary hook line section 233, n-th at the end of root tie barj-niThe root tie bar main body line segment 231 is a reference line segment, and rounding processing is carried out on the working plane 33;
the fillet radius is the sum of the radius of the inner-layer secondary steel bar array group 222 and the radius of the tie steel bar, namely:
Figure BDA0002425271400000185
Figure BDA0002425271400000191
n thj-niThe length of the secondary hook segment 233 at the end of the root tie bar is set to be 5 to 10 times the diameter of the tie bar, i.e.:
Figure BDA0002425271400000192
to
Figure BDA0002425271400000193
So far, the modeling of the center line of the nj-ni tie bars is completed;
e3.6j, will nj-niThe central line of the root tie steel bar moves along the central line of the steel bar closest to the starting point in the inner-layer main steel bar array group 212;
the distance of movement is the sum of the radius of the outer main steel bar array group 211 and the radius of the tie steel bar, i.e. the distance of movement is
Figure BDA0002425271400000194
Figure BDA0002425271400000195
e3.6k, and the total length variable S L K of the tie bar is equal to the nthj-niThe sum of the total length of the central line of the root tie bar and the magnitude of the variable S L K of the total length of the tie bar in the last circulation.
The principle of the method is that based on the information of the concrete member model and the information of the concrete member surface layer steel bar net model, the steel bar model is quickly established through a programmed method according to engineering design rules.
In some embodiments, in step d5, for the conventional case of bridge engineering, where the magnitude of the modulus MD is 2 to 5, the correction values for each element of the grid distance array ADG are calculated as follows:
① modulus MD equals 2:
when the divisor DIV is equal to 0, the grid distance array ADGI is not corrected;
when the divisor DIV is not equal to 0 and the remainder MOD is 0, the grid distance array ADGI is not corrected;
when the divisor DIV is not equal to 0 and the remainder MOD is 1, correcting the grid distance array ADGI, and reducing the value of the 1 st element by 1;
② modulus MD equals 3:
when the divisor DIV is equal to 0, the grid distance array ADGI is not corrected;
when the divisor DIV is not equal to 0 and the remainder MOD is 0, the grid distance array ADGI is not corrected;
when the divisor DIV is not equal to 0 and the remainder MOD is 1, correcting the grid distance array ADGI, and subtracting 1 from the magnitude of the 1 st element and the magnitude of the last 1 element;
when the divisor DIV is not equal to 0 and the remainder MOD is 2, correcting the grid distance array ADGI, and reducing the value of the 1 st element by 1;
③ modulus MD equals 4:
when the divisor DIV is equal to 0, the grid distance array ADGI is not corrected;
when the divisor DIV is not equal to 0 and the remainder MOD is 0, the grid distance array ADGI is not corrected;
when the divisor DIV is not equal to 0, the remainder MOD is not equal to 1, and the length L GI of the grid distance array ADGI is not equal to 2, correcting the grid distance array ADGI to reduce the magnitude of the 1 st element, the 2 nd element and the last 1 element by 1;
when the divisor DIV is not equal to 0, the remainder MOD is 1, and the length L GI of the grid distance array ADGI is 2, the grid distance array ADGI is modified, so that the magnitude of the 1 st element is decreased by 1, and the magnitude of the last 1 element is decreased by 2;
when the divisor DIV is not equal to 0 and the remainder MOD is 2, correcting the grid distance array ADGI, and subtracting 1 from the magnitude of the 1 st element and the magnitude of the last 1 element;
when the divisor DIV is not equal to 0 and the remainder MOD is 3, correcting the grid distance array ADGI, and reducing the value of the 1 st element by 1;
④ modulus MD equals 5:
when the divisor DIV is equal to 0, the grid distance array ADGI is not corrected;
when the divisor DIV is not equal to 0 and the remainder MOD is 0, the grid distance array ADGI is not corrected;
when the divisor DIV is not equal to 0, the remainder MOD is not equal to 1, and the length L GI of the grid distance array ADGI is not equal to 2, correcting the grid distance array ADGI, and subtracting 1 from the magnitude of the 1 st element and the magnitude of the 2 nd element and subtracting 2 from the magnitude of the last 1 element;
when the divisor DIV is not equal to 0, the remainder MOD is 1, and the length L GI of the grid distance array ADGI is 2, modifying the grid distance array ADGI to reduce the magnitudes of the 1 st element and the last 1 element by 2;
when the divisor DIV is not equal to 0, the remainder MOD is not equal to 2, and the length L GI of the grid distance array ADGI is not equal to 2, correcting the grid distance array ADGI to reduce the magnitude of the 1 st element, the 2 nd element and the last 1 element by 1;
when the divisor DIV is not equal to 0, the remainder MOD is 2, and the length L GI of the grid distance array ADGI is 2, the grid distance array ADGI is modified to reduce the magnitude of the 1 st element by 1 and reduce the magnitude of the last 1 element by 2;
when the divisor DIV is not equal to 0 and the remainder MOD is 3, correcting the grid distance array ADGI, and subtracting 1 from the magnitude of the 1 st element and the magnitude of the last 1 element;
when the divisor DIV is not equal to 0 and the remainder MOD is 4, the grid distance array ADGI is modified to decrease the magnitude of the 1 st element by 1.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.

Claims (2)

1. A computer aided design method of the tie bars of the concrete bridge slab; the method comprises the following steps:
a. selecting a concrete member; selecting a built concrete appearance model (4) and a plate of a concrete surface corresponding to the steel bar net model, wherein the plate is used as an implementation main body of the tie steel bar modeling;
the steel bar net model is completely composed of three-dimensional curve segments or three-dimensional straight segments;
b. preparing a graph;
b1, selecting the first surface and the second surface of the plate as a main reference surface (31) and a secondary reference surface (32) for establishing the tie bar model; the main reference surface (31) and the auxiliary reference surface (32) are parallel to each other or intersect each other;
b2, selecting two groups of reinforcing meshes corresponding to the main reference surface (31) and the auxiliary reference surface (32) respectively as a main reinforcing mesh (21) and an auxiliary reinforcing mesh (22);
the main reinforcing mesh (21) and the auxiliary reinforcing mesh (22) are similar in shape;
the shape similarity means that the outer layer main steel bar array group (211) and the inner layer main steel bar array group (212) of the main steel bar mesh (21) and the outer layer auxiliary steel bar array group (221) and the inner layer auxiliary steel bar array group (222) of the auxiliary steel bar mesh (22) are parallel to each other in projection on the main reference surface (31) in the corresponding array direction, and the projection on the main reference surface (31) in the corresponding steel bar axial direction is parallel to each other;
b3, extracting control information in the main reinforcing mesh (21) and the auxiliary reinforcing meshes (22);
the control information comprises the diameter of each steel bar array group in the main steel bar mesh (21) and the auxiliary steel bar mesh (22)
Figure FDA0002425271390000011
The absolute value of the distance d from the center line of each steel bar to the reference surface, the distance s between every two steel bar arrays and the total number n of the steel bars of each steel bar array;
namely, two groups of control information arrays of the steel bar array group of the main steel bar net (21) are named as an outer main steel bar array group control information array RAPIFO and an inner main steel bar array group control information array RAPIFI respectively, and the included control information is
Figure FDA0002425271390000012
dpO、spOAnd npOAnd an
Figure FDA0002425271390000013
dpI、spIAnd npI；
The auxiliary reinforcing steel bar net (22) comprises two groups of control information of reinforcing steel bar array groups which are named as an outer auxiliary reinforcing steel bar array group control information array RADIFO and an inner auxiliary reinforcing steel bar array group control information array RADIFO respectively, and the included control information is
Figure FDA0002425271390000014
ddO、sdOAnd ndOAnd an
Figure FDA0002425271390000015
ddI、sdIAnd ndI；
c. Generating a control point;
c1, selecting the outer layer main steel bar array group (211) and the outer layer auxiliary steel bar array group (221) from the main steel bar mesh (21) and the auxiliary steel bar mesh (22) as main reference bodies for modeling the tie steel bar control points;
c2, selecting the main reference surface (31) and the auxiliary reference surface (32), and utilizing RAPIFO and RADIFO of the outer layer main steel bar array group (211) and the outer layer auxiliary steel bar array group (221) to respectively offset the distance to the interior of the concrete member based on the main reference surface (31) and the auxiliary reference surface (32)
Figure FDA0002425271390000021
And
Figure FDA0002425271390000022
then, generating a main reference surface (311) of the control point of the tie bar mesh and a control point auxiliary reference surface (321);
c3, projecting the outer layer main steel bar array group (211) and the inner layer main steel bar array group (212) of the main steel bar mesh (21) to the control point main reference surface (311), and obtaining an outer layer main steel bar projection line group (2111), an inner layer main steel bar projection line group (2121) and a main intersection point array group (11) of the outer layer main steel bar array group (211) and the inner layer main steel bar array group (212) on the control point main reference surface (311);
the number of the main intersection point array groups (11) in the direction along the central line of the steel bars of the outer layer main steel bar array group (211) is npIThe number of the main intersection point array groups (11) in the direction along the central line of the steel bars of the inner layer main steel bar array group (212) is npO；
c4, projecting the outer layer auxiliary steel bar array group (221) and the inner layer auxiliary steel bar array group (222) of the auxiliary steel bar net (22) to the control point auxiliary reference surface (321), obtaining the outer layer auxiliary steel bar array group (2211), the inner layer auxiliary steel bar projection group (2221) and the auxiliary intersection point array group (12) of the outer layer auxiliary steel bar array group (221) and the inner layer auxiliary steel bar array group (222) on the control point auxiliary reference surface (321), wherein the auxiliary intersection point array group (12) is along the steel bar projection line group (2211) of the outer layer auxiliary steel bar array group (221)The number of the center line directions is ndIThe number of the auxiliary intersection point array groups (12) in the direction along the central line of the reinforcing steel bar of the inner-layer auxiliary reinforcing steel bar array group (222) is ndO；
c5, using the main intersection array group (11) as a starting point for generating subsequent tie bars;
d. generating tie bar information; arranging the tie bars in the direction of the center line of the steel bar of any one steel bar array group of the corresponding steel bar mesh;
d1, dividing any steel bar center line of the outer layer main steel bar projection line group (2111) into a plurality of line segments by the inner layer main steel bar projection line group (2121), wherein the number of the line segments is recorded as the total grid number GO of the outer layer main steel bar projection line group (2111); when the total grid number GO is equal to the number of the main intersection array groups (11) in the direction along the central line of the steel bars of the outer-layer main steel bar array group (211) minus 1, namely: GO ═ npI-1；
d2, dividing the total grid number GO by a modulus MD and solving for a remainder, recording the obtained divisor as DIV and the obtained remainder as MOD;
d3, setting a grid distance array ADGI, wherein the grid distance array ADGI is a one-dimensional array and is used for storing information of a plurality of line segment groups obtained by dividing the outer layer main reinforcement projection line group (2111) by the tie reinforcement, the length L GI of the grid distance array ADGI is the number of the line segment groups, and the quantity value of each element in the grid distance array ADGI is equal to the number of the line segments of each line segment group in the corresponding line segment groups;
d4, for the grid distance array ADGI, if the modulus MD is equal to or greater than the total grid number GO, no tie bars need to be arranged in the direction of the central line of the steel bars of the outer layer main steel bar array group (211), at this time, the length L GI of the grid distance array ADGI is equal to 1, and the element value of the grid distance array ADGI is equal to the total grid number GO;
d5, if the modulus MD is smaller than the total grid number GO and the remainder MOD is equal to 0, then the length L GI of the grid distance array ADGI is equal to the divisor DIV and the initial value of each element of the grid distance array ADGI is equal to the modulus MD;
if the modulus MD is smaller than the total grid number GO and the remainder MOD is not equal to 0, making the length L GI of the grid distance array ADGI equal to a divisor DIV plus 1, making an initial value of each element of the grid distance array ADGI equal to the modulus MD;
d6, information about arrangement of the tie bars in the direction of the center line of the bars of the inner-layer main bar array group (212) of the mesh reinforcement: total grid number GI ═ npO-1, a grid distance array ADGI, a length L GI of the grid distance array ADGI;
d7, specifying the extending direction of the tie bar, selecting a reference surface as the extending reference surface (30) of the main line segment of the tie bar, and extracting the normal vector of the extending reference surface (30); the extended reference surface (30) is a plane or a curved surface;
e. modeling the center line of the tie bar;
e1, if the length L GI of the grid distance array ADGI is 1, or the length L GI of the grid distance array ADGI is 1, it is not necessary to establish a model of the tie bars in the direction of the bar center lines of the outer layer main bar array group (211) and the inner layer main bar array group (212);
e2, if the length L GI >1 of the grid distance array ADGI and the length L GI >1 of the grid distance array ADGI are needed to establish a model of the tie bar;
e2.1, establishing information needed to be utilized when the model of the tie bar is established, wherein the information comprises the grid distance array ADGI and ADGI, the main intersection point array group (11) and the auxiliary intersection point array group (12), the control point main reference surface (311) and the control point auxiliary reference surface (321) of the tie bar mesh, the outer layer main bar array group (211), the inner layer main bar array group (212), the outer layer auxiliary bar array group (221), the inner layer auxiliary bar array group (222) and the extension reference surface (30);
e2.2, establishing a pointer array PT with the length of 2, wherein 2 elements in the pointer array PT are used for recording the intersection point position of the intersection point array group (11); the 1 st element PTA of the pointer array records the intersection point sequence number along the direction of the central line of the steel bar of the outer-layer main steel bar array group (211), and the 2 nd element PTB of the pointer array records the intersection point sequence number along the direction of the central line of the steel bar of the inner-layer auxiliary steel bar array group (222);
e2.3, establishing a variable S L K for storing the total length of the tie bar;
e3.4, establishing a circulation action, wherein the circulation execution frequency formula is L GI-1 ×L GI-1, the circulation priority is that the quantity is L GI-1 along the direction of the central line of the steel bars of the outer layer main steel bar array group (211), the direction j or the row direction, and the quantity is L GI-1 along the direction of the central line of the steel bars of the inner layer auxiliary steel bar array group (222), the direction i or the row direction;
e3.5, when the execution loop number nj is 1 and ni is 1:
e3.5a, let the magnitude of pointer array element PTA equal the magnitude of the 1 st element of the grid distance array ADGI or the correction value a1 plus 1, i.e.: PTA 1+ a1, let the magnitude of the pointer array element PTB equal the magnitude of the 1 st element of the grid distance array ADGI or the correction value b1 plus 1, i.e.: PTB ═ 1+ b 1;
e3.5b, taking the PTA row of the intersection point array group (11) along the direction of the central line of the steel bar of the outer layer main steel bar array group (211), taking the intersection point of the first PTB row as a starting point (101) to be a main line segment (231) of the 1 st-1 st tie steel bar along the direction of the central line of the steel bar of the inner layer main steel bar array group (212);
the 1-1 main segment (231) of the tie bar is perpendicular to the extension reference surface (30), and the 1-1 main segment (231) of the tie bar begins from the starting point (101) and extends to the control point and the secondary reference surface (321) to intersect to form an end point (102); the end point (102) not necessarily coinciding with the set of secondary intersection arrays (12);
e3.5c, and correcting the 1 st to 1 st main segment (231) of the tie bar;
making a working plane (33), wherein the working plane (33) passes through the 1 st-1 st main steel bar line segment (231) and is perpendicular to the steel bar central line closest to the starting point (101) in the inner-layer main steel bar array group (212);
aligning the starting point (101) with the outer layer main reinforcement arrayMoving the end point (102) along the direction opposite to the direction of the extension of the central line of the steel bar of the outer layer auxiliary steel bar array group (221), and keeping the 1 st-1 st main segment (231) of the tie steel bar to rotate on the working plane (33), so that the distances between the 1 st-1 st main segment (231) of the tie steel bar and the initial positions of the starting point (101) and the end point (102) are both the same
Figure FDA0002425271390000051
e3.5d, based on the corrected starting point (1011), and making a main hook line segment (232) at the tail end of the 1 st to 1 st tie bar along the control point main reference surface (311);
the main hook line segment (232) at the tail end of the 1 st-1 st drawknot steel bar is parallel to the steel bar central line closest to the starting point in the outer layer main steel bar array group (211), and the extending direction of the main hook line segment (232) at the tail end of the 1 st-1 st drawknot steel bar is the steel bar central line extending direction of the outer layer main steel bar array group (211);
e3.5e, based on the corrected end point (1021), making an auxiliary hook line segment (233) at the tail end of the 1 st to 1 st tie bar along the auxiliary reference surface (321) of the control point;
the auxiliary hook line segment (233) at the tail end of the 1 st-1 st drawknot steel bar is parallel to the steel bar central line closest to the starting point in the outer layer auxiliary steel bar array group (221), and the extending direction of the auxiliary hook line segment (233) at the tail end of the 1 st-1 st drawknot steel bar is opposite to the extending direction of the steel bar central line of the outer layer auxiliary steel bar array group (221);
e3.5f, intersecting the working plane (33) with the central line of the steel bar in the inner layer main steel bar array group (212) which is closest to the starting point to obtain a main datum point (103);
taking the main datum point (103) as a rotation point, enabling the main hook line segment (232) at the tail end of the 1 st to 1 st tie bar to rotate on the working plane (33), enabling the rotation direction to face towards the interior of the concrete member, and enabling the included angle between the main hook line segment (232) at the tail end of the 1 st to 1 st tie bar and the main line segment (231) of the 1 st to 1 st tie bar to be 45 degrees;
e3.5g, intersecting the working plane (33) with the central line of the steel bar in the secondary steel bar array group (222) of the inner layer, which is closest to the starting point, to obtain a secondary reference point (104);
taking the auxiliary reference point (104) as a rotation point, enabling the auxiliary hook line segment (233) at the tail end of the 1 st to 1 st tie bar to rotate on the working plane (33), enabling the rotation direction to face towards the interior of the concrete member, and enabling the included angle between the auxiliary hook line segment (233) at the tail end of the 1 st to 1 st tie bar and the main line segment (231) of the 1 st to 1 st tie bar to be 45 degrees;
e3.5h, using the main hook line segment (232) at the tail end of the 1 st to 1 st tie bar and the main line segment (231) of the 1 st to 1 st tie bar as reference line segments, and rounding on a working plane (33);
the fillet radius is the sum of the radius of the inner layer main steel bar array group (212) and the radius of the tie steel bar, namely:
Figure FDA0002425271390000061
the length of the main hook line segment (232) at the tail end of the 1 st-1 st drawknot steel bar is set to be 5 times to 10 times of the diameter of the drawknot steel bar, namely:
Figure FDA0002425271390000062
to
Figure FDA0002425271390000063
e3.5i, using the auxiliary hook line segment (233) at the tail end of the 1 st to 1 st tie bar and the main line segment of the 1 st to 1 st tie bar as reference line segments, and performing rounding treatment on a working plane (33);
the fillet radius is the sum of the radius of the inner layer secondary steel bar array group (222) and the radius of the tie steel bar, namely:
Figure FDA0002425271390000064
the 1 st to 1 st drawknotThe length of the secondary hook line segment (233) at the end of the bar is set to be 5 to 10 times the diameter of the tie bar, namely:
Figure FDA0002425271390000065
to
Figure FDA0002425271390000066
So far, the modeling of the center line of the 1 st-1 st tie bar is completed;
e3.5j, moving the center line of the 1 st to 1 st tie bar along the center line of the bar closest to the starting point in the inner layer main bar array group (212);
the moving distance is the sum of the radius of the outer layer main steel bar array group (211) and the radius of the tie steel bar, namely
Figure FDA0002425271390000067
e3.5k, and enabling the total length variable S L K of the tie steel bar to be equal to the total length of the center line of the 1 st to 1 st tie steel bar;
e3.6, when the number of executions nj>1，ni>1, time:
e3.6a, making the magnitude of the pointer array element PTA equal to the 1 st to nth of the grid distance array ADGIjSum of magnitude or correction value of individual elements Σ anjAdding 1, namely: PTA 1+ Σ anjThe magnitude of the pointer array element PTB is equal to the 1 st to nth of the grid distance array ADGIiSum of individual element magnitudes or correction values Σ bniAdding 1, namely: PTB 1+ Σ bni；
e3.6b, the PTA row of the intersection point array group 11 is taken as the n-th row by taking the intersection point of the first PTA row as the starting point (101) along the direction of the steel bar central line of the outer layer main steel bar array group (211), the PTB row and the steel bar central line of the inner layer main steel bar array group (212)j-niA steel tie body segment (231);
the n-thj-niThe main line segment of the root tie steel bar is vertical to the extension reference surface(30) The n-thj-niThe segment of the main body of the tie bar starts from the starting point (101) and extends to the control point and the secondary reference surface (321) to form an end point (102) by intersection; the end point (102) not necessarily coinciding with the set of secondary intersection arrays (12);
e3.6c, modified nthj-niA steel tie body segment (231);
making a new working plane (33), said working plane (33) passing through said nth planeiA steel bar main line segment is tied, and the steel bar main line segment is perpendicular to the steel bar central line closest to the starting point in the inner layer main steel bar array group (212);
moving the starting point (101) in the direction opposite to the direction in which the center line of the steel bar of the outer layer main steel bar array group (211) extends, moving the ending point (102) in the direction in which the center line of the steel bar of the outer layer auxiliary steel bar array group (221) extends, and keeping the nthj-niThe main line segment (231) of the root tie bar rotates on the working plane (33) to enable the nth barj-niThe distances between the root tie bar main body line segment (231) and the initial positions of the starting point (101) and the end point (102) are all the same
Figure FDA0002425271390000071
Figure FDA0002425271390000072
e3.6d, based on the corrected starting point (1011), making the nth reference point along the control point main reference plane (311)j-niA main hook line segment (232) at the end of the root tie bar;
the n-thj-niThe main hook line segment (232) at the tail end of the root tie steel bar is parallel to the central line of the steel bar in the outer layer main steel bar array group (211) which is closest to the starting point, and the nth steel barj-niThe extending direction of a main hook line segment (232) at the tail end of each tie bar is the extending direction of the central line of the bar of the outer layer main bar array group (211);
e3.6e, endpoint based on said correction(1021) Making the nth reference plane along the control point minor reference plane (321)j-niA secondary hook line segment (233) at the end of the root tie bar;
the n-thj-niThe secondary hook line segment (233) at the tail end of the root tie steel bar is parallel to the central line of the steel bar in the outer secondary steel bar array group (221) which is closest to the starting point, and the nthj-niThe extending direction of the secondary hook line segment (233) at the tail end of the root tie steel bar is opposite to the extending direction of the steel bar central line of the outer layer secondary steel bar array group (221);
e3.6f, and the working plane (33) intersects with the central line of the steel bar closest to the starting point in the inner-layer main steel bar array group (212) to obtain a main reference point (103);
the nth reference point (103) is used as a rotation pointj-niThe main hook line segment (232) at the tail end of the root tie bar rotates on the working plane (33) in the direction towards the interior of the concrete member, so that the nth hook line segmentj-niThe included angle between the main hook line segment (232) at the tail end of the steel bar and the 1 st main line segment (231) of the steel bar is 45 degrees;
e3.6g, and the working plane (33) intersects with the central line of the steel bar closest to the starting point in the inner-layer secondary steel bar array group (222) to obtain a secondary reference point (104);
the nth reference point (104) is used as a rotation pointj-niThe auxiliary hook line segment (233) at the tail end of the root tie bar rotates on the working plane (33) in the direction towards the interior of the concrete member to enable the nthj-niThe auxiliary hook line segment (233) at the tail end of the root tie steel bar and the nthj-niThe included angle of the main line segment (231) of the root tie steel bar is 45 degrees;
e3.6h, and the nj-niA main hook line segment (232) at the tail end of the root tie bar, the nthj-niThe main line segment (231) of the root tie steel bar is a reference line segment, and rounding processing is carried out on the working plane (33);
the radius of the fillet is the radius of the inner layer main steel bar array group (212)The sum of the radius of the tie bar, namely:
Figure FDA0002425271390000081
the n-thj-niThe length of the main hook line segment at the end of the root tie bar is set to be 5 to 10 times the diameter of the tie bar, namely:
Figure FDA0002425271390000082
to
Figure FDA0002425271390000083
e3.6i, as defined above for the n-thj-niA secondary hook line segment (233) at the end of the root tie bar, the nthj-niThe main line segment (231) of the root tie steel bar is a reference line segment, and rounding processing is carried out on the working plane (33);
the fillet radius is the sum of the radius of the inner layer secondary steel bar array group (222) and the radius of the tie steel bar, namely:
Figure FDA0002425271390000084
the n-thj-niThe length of the secondary hook line segment (233) at the end of the root tie bar is set to be 5 to 10 times the diameter of the tie bar, namely:
Figure FDA0002425271390000085
to
Figure FDA0002425271390000086
So far, the modeling of the center line of the nj-ni tie bars is completed;
e3.6j, adding the n-th elementj-niThe center line of the tie bar moves along the center line of the bar closest to the starting point in the inner layer main bar array group (212);
the moving distance is the outer layer main steelThe sum of the radius of the bar array set (211) and the radius of the tie bar, i.e.
Figure FDA0002425271390000091
e3.6k, and making the total length variable S L K of the tie bar equal to the nthj-niThe sum of the total length of the central line of the root tie bar and the magnitude of the variable S L K of the total length of the tie bar in the last circulation.
2. The computer-aided design method of tie bars for concrete bridge slab according to claim 1, characterized in that in said step d5, the magnitude of said modulus MD is between 2 and 5 for the conventional case of bridge works, and the calculation of the correction values for each element of said grid distance array ADG is as follows:
① when the modulus MD is equal to 2:
when the divisor DIV is 0, the grid distance array ADGI is not corrected;
when the divisor DIV is not equal to 0 and the remainder MOD is 0, the grid distance array ADGI is not corrected;
when the divisor DIV is not equal to 0 and the remainder MOD is 1, correcting the grid distance array ADGI to reduce the value of the 1 st element by 1;
② when the modulus MD equals 3:
when the divisor DIV is 0, the grid distance array ADGI is not corrected;
when the divisor DIV is not equal to 0 and the remainder MOD is 0, the grid distance array ADGI is not corrected;
when the divisor DIV is not equal to 0 and the remainder MOD is 1, correcting the grid distance array ADGI to reduce the magnitude of the 1 st element and the magnitude of the last 1 element by 1;
when the divisor DIV is not equal to 0 and the remainder MOD is 2, correcting the grid distance array ADGI to reduce the value of the 1 st element by 1;
③ when the modulus MD equals 4:
when the divisor DIV is 0, the grid distance array ADGI is not corrected;
when the divisor DIV is not equal to 0 and the remainder MOD is 0, the grid distance array ADGI is not corrected;
when the divisor DIV is not equal to 0, the remainder MOD is not equal to 1, and the length L GI of the grid distance array ADGI is not equal to 2, correcting the grid distance array ADGI to reduce the magnitude of the 1 st element, the 2 nd element and the last 1 element by 1;
when the divisor DIV is not equal to 0, the remainder MOD is 1, and the length L GI of the grid distance array ADGI is 2, modifying the grid distance array ADGI to reduce the magnitude of the 1 st element by 1 and reduce the magnitude of the last 1 element by 2;
when the divisor DIV is not equal to 0 and the remainder MOD is 2, correcting the grid distance array ADGI to reduce the magnitude of the 1 st element and the magnitude of the last 1 element by 1;
when the divisor DIV is not equal to 0 and the remainder MOD is 3, correcting the grid distance array ADGI to reduce the value of the 1 st element by 1;
④ when the modulus MD equals 5:
when the divisor DIV is 0, the grid distance array ADGI is not corrected;
when the divisor DIV is not equal to 0 and the remainder MOD is 0, the grid distance array ADGI is not corrected;
when the divisor DIV is not equal to 0, the remainder MOD is not equal to 1, and the length L GI of the grid distance array ADGI is not equal to 2, correcting the grid distance array ADGI to enable the magnitude of the 1 st element and the magnitude of the 2 nd element to be reduced by 1 and the magnitude of the last 1 element to be reduced by 2;
when the divisor DIV is not equal to 0, the remainder MOD is 1, and the length L GI of the grid distance array ADGI is 2, modifying the grid distance array ADGI to reduce the magnitude of the 1 st element and the magnitude of the last 1 element by 2;
when the divisor DIV is not equal to 0, the remainder MOD is not equal to 2, and the length L GI of the grid distance array ADGI is not equal to 2, correcting the grid distance array ADGI to reduce the magnitude of the 1 st element, the 2 nd element and the last 1 element by 1;
when the divisor DIV is not equal to 0, the remainder MOD is 2, and the length L GI of the grid distance array ADGI is 2, modifying the grid distance array ADGI to reduce the magnitude of the 1 st element by 1 and reduce the magnitude of the last 1 element by 2;
when the divisor DIV is not equal to 0 and the remainder MOD is 3, correcting the grid distance array ADGI to reduce the magnitude of the 1 st element and the magnitude of the last 1 element by 1;
when the divisor DIV ≠ 0 and the remainder MOD ═ 4, the grid distance array ADGI is modified to reduce the magnitude of the 1 st element by 1.
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