BIM (Building Information Modeling)-based double-layer reinforcing mesh tie bar arrangement method

Abstract

The invention discloses a BIM (Building Information Modeling)-based double-layer reinforcing mesh lacing wire arrangement method. The method comprises the following steps: acquiring a BIM three-dimensional model of a component; arranging a double-layer reinforcing mesh on the reinforcement surface of the model; and grid intersection points in the double-layer reinforcing mesh are calculated, and tie bars are positioned and arranged based on the calculated grid intersection points. The method is based on BIM forward design, the tie bars are positioned in the mode of calculating the grid intersection points in the steel bar meshes, the irregular characteristics of the special-shaped steel bar meshes, especially complex special-shaped components, are fully considered, and the positioning accuracy and applicability are improved. Besides, an algorithm for solving the shortest distance between the spatial steel bars is introduced, the problem that the tie bars are difficult to position when the two steel bars do not intersect at the grid is effectively solved, various tie bar arrangement working conditions are comprehensively covered, the method is closer to actual engineering requirements, the vacancy of the members for tie bar three-dimensional arrangement is filled, manual processing after drawing is reduced, and the construction efficiency is improved. And the working efficiency is improved, and good application prospects are achieved.

Description

Technical Field

[0001] The invention belongs to the technical field of three-dimensional reinforcement design and BIM (Building Information Modeling) application, and particularly relates to a double-layer steel mesh reinforcement arrangement method based on BIM. Background Art

[0002] With the continuous development of engineering design technology, BIM forward design has become an important trend in the industry. It not only includes the creation of three-dimensional models of engineering components, but also covers key links such as structural analysis and reinforcement design.

[0003] In terms of reinforcement design, accurate arrangement of reinforcement not only ensures the safety and stability of the structure, but also brings many advantages. First, it can enhance the intuitive display of the 3D model, improve the quality of the drawing, and reduce the need for later adjustments. Second, accurate arrangement of reinforcement can significantly improve design efficiency and reduce the chance of human error and rework.

[0004] In the face of increasingly mature 3D modeling technology, existing technology still has certain limitations in the design of reinforcement. This is because the design of reinforcement on most current BIM design platforms is based on standard building forms, and it is difficult to achieve the expected effect for complex and irregular building forms. Summary of the invention

[0005] The purpose of the present invention is to provide a double-layer steel mesh reinforcement arrangement method based on BIM, which solves the problem of difficulty in calculating the reinforcement position of a concrete component with a double-layer steel mesh reinforcement.

[0006] The technical solution adopted by the present invention is: a double-layer steel mesh reinforcement arrangement method based on BIM, comprising the following steps: Step 1: Obtain component BIM 3D model; Step 2, arranging a double-layer steel mesh on the reinforcement surface of the model obtained in step 1; Step 3: Calculate the grid intersections in the double-layer steel mesh obtained in step 2, and locate and arrange the reinforcement based on the calculated grid intersections.

[0007] The present invention is also characterized in that: In step 1, select OpenCASCADE based on the open source modeling engine to build a BIM platform, and create or import a concrete component model.

[0008] Step 2 specifically includes the following steps: Step 2.1, select the model surface where the steel mesh is to be installed as the reinforcement surface; Step 2.2, offset the reinforcement surface to obtain the surface where the reinforcement is located; Step 2.3, construct the cutting plane; Step 2.4, calculate the intersection lines between the surface where the steel bars are located and all the cutting surfaces, obtain the three-dimensional steel bar positioning line, i.e., the steel bar line, and group the steel bars in two directions of a single layer into a layer of steel mesh; Step 2.5: Repeat steps 2.1 to 2.4 to obtain another layer of steel mesh, thus completing the arrangement of the double-layer steel mesh.

[0009] The offset distance in step 2.2 Use the following formula to calculate:

[0010] Where: is the distance from the outer surface of the steel bar to the reinforcement surface; is the diameter of the steel bar.

[0011] Step 2.3 specifically includes the following steps: Step 2.3.1, select the continuous edge of the model as the guide line; Step 2.3.2, set array parameters; Step 2.3.3, based on the array parameters, arrange the distribution points along the guide line in sequence; Step 2.3.4, at each distribution point, use the tangent vector of the guide line as the normal vector and create a cutting plane passing through the distribution point; Step 2.3.5: Repeat step 2.3.4 until the cutting planes are created at all distribution points.

[0012] The array parameters in step 2.3.2 include the starting distance, array spacing, and end distance.

[0013] Step 3 specifically includes the following steps: Step 3.1, select four steel bar groups of the double-layer steel mesh, and set the number of intervals for the reinforcement arrangement for each group of steel bars; Step 3.2, based on the four steel bar groups selected in step 3.1 and the corresponding number of reinforcement arrangement intervals, screen out the steel bars actually involved in arranging the reinforcement in each steel bar group; Step 3.3: Nest and traverse the inner reinforcement of one layer and outer reinforcement , calculate the shortest distance between two spatial steel bars and the coordinates of their corresponding points , ; Step 3.4: Repeat step 3.3 to calculate the shortest distance between the two inner and outer sides of another layer and the coordinates of their corresponding points. , ; Step 3.5: Combine steps 3.3 and 3.4 to obtain a point set consisting of four coordinate points in the corresponding order, and calculate the two hook positioning points by the following formula: , :

[0014]

[0015]

[0016] In the formula, is the spatial midpoint of the two layers of steel mesh; is a function for calculating the distance between two points in space; Step 3.6: Determine the plane where the reinforcement is located by using the two directions of one layer of reinforcement wire at the corresponding point obtained in step 3.3 or step 3.4 and the hook positioning point obtained in step 3.5:

[0017] In the formula, Indicates the direction in which the hook bends; Indicates that the reinforcement line is at point The direction unit vector at Indicates that the reinforcement line is at point The direction unit vector at ; , At the same time, take the , Or take the , ; , is the directional coefficient;

[0018] In the formula, is the normal vector of the plane where the reinforcement is located, is the reinforcement direction vector; Step 3.7: Locate the hook obtained in step 3.5 , Bend the hook along the direction obtained in step 3.6 Offset the corresponding distance to get the main positioning point of the reinforcement , , is the offset direction coefficient; Step 3.8: The main positioning point of the reinforcement obtained from step 3.7 , Construct a straight line as the main body of the reinforcement; Step 3.9: Construct the curved segments and straight segments of the tie hooks at both ends of the tie rod body obtained in step 3.8. The normal vector of the plane where the hook is located is the same as the normal vector of the tie rod plane obtained in step 3.6. Same direction.

[0019] The offset distance in step 3.7 is the sum of the radius of the corresponding layer of reinforcement and the radius of the tie bar.

[0020] The beneficial effects of the present invention are as follows: the present invention is based on the BIM-based double-layer steel mesh reinforcement arrangement method, based on BIM forward design, and uses the method of calculating the grid intersection points in the steel mesh to locate the reinforcement, which fully considers the irregular characteristics of the special-shaped steel mesh, especially the complex special-shaped components, such as curved walls, branch holes, branch pipes, etc., and improves the accuracy and applicability of positioning. In addition, the present invention introduces an algorithm for obtaining the shortest distance between spatial steel bars, which effectively solves the problem of difficulty in locating the reinforcement when two steel bars do not intersect at the grid, comprehensively covers various reinforcement arrangement working conditions, is closer to actual engineering needs, fills the gap in the three-dimensional arrangement of reinforcement for such components, reduces the manual processing after drawing, improves work efficiency, and has good application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 It is a schematic flow chart of a method for arranging reinforcement bars of a double-layer steel mesh based on BIM of the present invention; Figure 2 is a schematic diagram of a vault model in an embodiment of the present invention; Figure 3 Schematic diagram of a double-layer steel mesh for a vault according to an embodiment of the present invention; Figure 4 It is a schematic diagram of the shortest distance between two spatial steel bars and their corresponding points in the double-layer steel mesh reinforcement arrangement method based on BIM of the present invention; Figure 5 It is a schematic diagram of the bending direction of the tie hooks of two space steel bars in the double-layer steel mesh tie bar arrangement method based on BIM of the present invention; Figure 6 It is a schematic diagram of the reinforcement arrangement effect of the double-layer steel mesh of the vault in an embodiment of the present invention. DETAILED DESCRIPTION

[0022] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0023] Example 1 The present invention provides a double-layer steel mesh reinforcement arrangement method based on BIM, such as Figure 1 As shown in the figure, a BIM platform with modeling and rendering capabilities is used as the integrated environment. Based on the existing BIM model, the reinforcement line is generated by translating the reinforcement surface and making it tangent to the auxiliary surface. This method of generating reinforcement lines can be completed step by step. Figure 3 The double-layer steel mesh arrangement shown in the figure. Starting from the idea of ​​using the grid intersection of the steel mesh to determine the location point of the tie hook, considering that there is no precise intersection at the grid intersection due to different steel bar overlap and layout methods in practice, the method of finding the shortest distance between two steel bars at the grid intersection and the corresponding point on the steel bar line is used to obtain the location point of the tie hook. Finally, determine the bending direction of the hook and the plane where the tie bar is located, and arrange the straight and curved sections of the tie bar according to business needs. This method is flexible and effective, and has no requirements on the shape of the model. It can not only meet the tie bar arrangement of conventional model components, but also support the tie bar arrangement of special-shaped and complex components.

[0024] Example 2 The present invention provides a double-layer steel mesh reinforcement arrangement method based on BIM, comprising the following steps: Step 1: Create or import a BIM 3D model based on BIM forward design ideas; Step 2: Based on the model obtained in step 1, create a double-layer steel mesh at relevant locations; Step 3: Based on the double-layer steel mesh reinforcement model obtained in step 2, arrange the reinforcement.

[0025] Example 3 The present invention provides a double-layer steel mesh reinforcement arrangement method based on BIM. Based on Example 2, in step 1, a BIM platform can be selected according to business scenarios and technical needs. The platform needs to support modeling capabilities such as creating points, lines, surfaces, bodies, and Boolean operations. Then, according to the selected BIM platform and the data format it supports, a component three-dimensional model is created or imported.

[0026] Example 4 The present invention provides a double-layer steel mesh reinforcement arrangement method based on BIM. Based on Example 2, step 2 preferably includes the following steps: Step 2.1. Because the steel mesh is usually attached to the model surface, select the model surface where the steel mesh is to be installed as the reinforcement surface.

[0027] Step 2.2, offset the reinforcement surface to get the surface where the reinforcement is located, and calculate the offset distance using the following formula:

[0028] Where: is the offset distance; It is the distance from the outer surface of the steel bar to the reinforcement surface. If it is an outer steel bar, it is the thickness of the protective layer. If it is an inner steel bar, its value can be taken as the sum of the thickness of the protective layer and the diameter of the outer steel bar. is the diameter of the steel bar.

[0029] Step 2.3, constructing a cutting plane; specifically comprising the following steps: Step 2.3.1. Select continuous edges as guide lines.

[0030] Step 2.3.2: Set the array parameters, including the starting distance, array spacing, and end distance.

[0031] Step 2.3.3: Based on the array parameters, arrange the distribution points along the guide line.

[0032] Step 2.3.4: At each distribution point, use the tangent vector of the guide line as the normal vector and create a cutting plane passing through the point.

[0033] Step 2.3.5: Repeat step 2.3.4 until the cutting planes are created at all distribution points.

[0034] Step 2.4: Use the geometric algorithm provided by the platform to calculate the intersection lines between the surface where the steel bars are located and all the cutting surfaces. These lines are the three-dimensional steel bar positioning lines (referred to as "steel bar lines"), which form a steel bar group.

[0035] Step 2.5: Repeat steps 2.1 to 2.4 to complete the arrangement of the double-layer steel mesh.

[0036] Example 5 The present invention provides a double-layer steel mesh reinforcement arrangement method based on BIM. Based on Example 2, step 3 preferably comprises the following steps: Step 3.1, select four steel bar groups in two directions of the double layer, and set the number of intervals for the tie bar arrangement for each group of steel bars.

[0037] Step 3.2: Based on the four steel bar groups selected in step 3.1 and the corresponding number of reinforcement arrangement intervals, select the steel bars in each group that are actually involved in the reinforcement arrangement.

[0038] Step 3.3: nest and traverse two groups of steel bars in the horizontal and vertical directions of one layer. and outer reinforcement , calculate the shortest distance between two spatial steel bars and the coordinates of their corresponding points , .

[0039] Step 3.4: Repeat step 3.3 to calculate the shortest distance between two spatial steel bars in another layer and the coordinates of the corresponding points on the steel bars. , .

[0040] Step 3.5: Based on the principle that the hook positioning point should be on the outer steel bar at the intersection of the grid, a point set consisting of four points is obtained in the corresponding order in combination with steps 3.3 and 3.4, and two hook positioning points are calculated by the following formula:

[0041]

[0042]

[0043] In the formula, is the spatial midpoint of the two layers of steel mesh; , They are the positioning points of the bending hooks of the two layers of steel mesh; is a function that calculates the distance between two points in space.

[0044] Step 3.6: Determine the plane where the reinforcement is located by using the two directions of one layer of reinforcement wire at the corresponding point obtained in step 3.3 or step 3.4 and the hook positioning point obtained in step 3.5:

[0045] In the formula, Indicates the direction in which the hook bends; Indicates that the reinforcement line is at point The direction unit vector at Indicates that the reinforcement line is at point The direction unit vector at the point; because the hooks at both ends of the tie rod are in the same plane, , You can also take the steps mentioned in step 3.3 , Or take the steps mentioned in step 3.4 at the same time , . , is the direction coefficient.

[0046]

[0047] In the formula, is the normal vector of the plane where the reinforcement is located, is the reinforcement direction vector.

[0048] Step 3.7: Locate the hook obtained in step 3.5 , Bend the hook along the direction obtained in step 3.6 Offset the corresponding distance to get , The offset distance is the sum of the corresponding layer reinforcement radius and the tension radius, and the offset direction coefficient is Determined by the shape of the reinforcement.

[0049] Step 3.8: Obtained from step 3.7 , The two-point straight line is used as the main body of the reinforcement.

[0050] Step 3.9: According to business needs, construct the curved segments and straight segments of the tie hook at both ends of the tie body obtained in step 3.8. The normal vector of the plane where the hook is located should be consistent with the normal vector of the tie plane obtained in step 3.6. Same direction.

[0051] Example 6 The present invention provides a double-layer steel mesh reinforcement arrangement method based on BIM, which can be implemented according to the following steps: S1: Select a BIM platform based on the open source modeling engine OpenCASCADE (hereinafter referred to as "Occ") as the modeling engine, and choose to create or import a Figure 2 The concrete vault model shown is used as an example, and the model parameters are shown in Table 1.

[0052] Table 1 Vault model parameters (unit: m)

[0053] Reinforcement parameters are shown in Table 2: Table 2 Reinforcement parameters of the vault model (unit: mm)

[0054] S2: First, create the outer reinforcements on the soffit and back surfaces, select the two as reinforcement surfaces, and use the member function PerformByJoin of the tool class BRepOffsetAPI_MakeOffsetShape provided by Occ to pass in the offset value to obtain the TopoDS_Shape (the base class of all boundary representation (BoundaryRepresentation, B-Rep) geometric shapes in Occ) objects O-1 and O-2 where the reinforcement is located. The offset value is the thickness of the protective layer plus half the diameter of the outer steel bar.

[0055] S3: Figure 2 As shown in the figure, the edge of the arch foot is selected as the guide line, and the selected guide line is passed to the tool class BRepAdaptor_Curve provided by Occ (adapting the geometric edge in the topology to a parametric curve), and the object is constructed and recorded as CurveA. According to the settings of the starting distance, array spacing and end distance of 5cm, 20cm, and 5cm respectively, the distribution points are evenly arranged on the guide line. Then, the tangent vector of the guide line at the distribution point is used as the normal vector to construct the cutting plane Geom_Plane objects CO-1, CO-2, CO-3, ... passing through the point.

[0056] S4: Take the two mesh outer steel bars O-1 and O-2 obtained by S2, and the cutting planes CO-1, CO-2, CO-3, ... obtained by S3 as parameters, respectively, to construct a BRepAlgoAPI_Section (a tool class provided by Occ to calculate the intersection between two geometric objects) object, and then call its SectionEdges member function to obtain the intersection line, which is the steel bar line. All steel bars generated by O-1 and the cutting plane are recorded as steel bar group GO-1, and all steel bars generated by O-2 and the cutting plane are recorded as steel bar group GO-2.

[0057] S5: Create the inner reinforcements on the soffit and back surfaces, and select the two as reinforcement surfaces. Use the method described in S2 to offset the reinforcement surfaces TopoDS_Shape objects I-1 and I-2. The offset value is the thickness of the protective layer plus the outer reinforcement diameter and half of the inner reinforcement diameter.

[0058] S6: Figure 2 As shown, the spandrel is selected as the guide line, and the cutting plane Geom_Plane objects CI-1, CI-2, CI-3, ... are constructed by the method described in S3.

[0059] S7: By the method described in S4, I-1, I-2 and cutting planes CI-1, CI-2, CI-3, ... are used to cut each other to generate steel bar lines. All steel bars generated by I-1 and the cutting plane are recorded as steel bar group GI-1, and all steel bars generated by I-2 and the cutting plane are recorded as steel bar group GI-2.

[0060] S8: Figure 3 As shown, based on the four steel bar groups obtained by S4 and S7, the inner and outer steel bars GI-1 and GO-1 form the steel mesh of the arch back; the inner and outer steel bars GI-2 and GO-2 form the steel mesh of the arch soffits. The number of intervals for arranging the steel bars of each group is set to 2, and then the steel bars of each group that actually participate in the arrangement of the steel bars are selected.

[0061] S9: Nested traversal of the inner and outer reinforcement groups GI-1 and GO-1 at the arch back. i Root steel bar and the first j Root steel bar , use the tool class BRepExtrema_DistShapeShape provided by Occ to calculate the minimum distance between two geometric shapes, pass in and TopoDS_Shape object, calculate and obtain the corresponding points of the shortest distance between two spatial reinforcement lines through the member functions GetPointOnShape1 and GetPointOnShape2 of BRepExtrema_DistShapeShape , , see the schematic diagram Figure 4 (In the figure , It refers to the corresponding point with the shortest distance between two steel bars inside and outside any steel mesh layer). and The TopoDS_Shape constructs BRepAdaptor_CompCurve (a tool class provided by Occ that adapts the composite curve in the topology to a parameterized curve) object, and then uses the member function D1 of BRepAdaptor_CompCurve to obtain At the point The unit tangent vector at and At the point The unit tangent vector at .

[0062] S10: Nested traversal of the reinforcement groups GI-2 and GO-2 on both sides of the arch. i Root steel bar and the first j Root steel bar , calculated using the method described in S9 , , , .

[0063] S11: The same sequence of bits obtained from S9 and S10 , , , (The same order can be simplified to: , , , ) and the unit tangent vector , , , (The same order can be simplified to: , , , ) are combined together as the positioning conditions for constructing a single tie rod.

[0064] The hook positioning point is obtained by the following formula , , in this embodiment, = , = .

[0065]

[0066]

[0067]

[0068] S12: Figure 5 As shown, the bending direction of the reinforcement is obtained by the following formula, where the directional coefficient , According to business needs and the direction of the steel bar itself, in order to ensure that the hooks at both ends of the tie bar are in the same plane, and Can be taken at the same time , .

[0069]

[0070] S13: Substituting S11 for , The bending direction of the hook obtained along S12 The sum of the outer reinforcement radius and the reinforcement radius is offset to obtain the reinforcement main body positioning point , .

[0071] S14: Incoming parameters , Construct a BRepBuilderAPI_MakeEdge (a tool class provided by Occ for creating geometric edges) object, and obtain the TopoDS_Shape of the reinforcement body through its member function Shape.

[0072] S15: The normal vector of the plane where the reinforcement is located is obtained according to the following formula :

[0073]

[0074] Create tie hooks (including the curved and straight segments at both ends of the body) according to business requirements (hook angle, hook length), provided that the normal vectors of the planes where the two hooks are located are parallel to In this embodiment, the hook angle is 180 degrees, the hook length is 6.25d (d is the diameter of the reinforcement), and the arrangement effect is as follows: Figure 6 shown.

Claims

1. A double-layer steel mesh reinforcement arrangement method based on BIM, characterized in that: The following steps are involved: Step 1: Obtain component BIM 3D model; Step 2, arranging a double-layer steel mesh on the reinforcement surface of the model obtained in step 1; Step 3: Calculate the grid intersections in the double-layer steel mesh obtained in step 2, and locate and arrange the reinforcement based on the calculated grid intersections.

2. The method for arranging double-layer steel mesh reinforcement based on BIM according to claim 1, characterized in that: In the step 1, OpenCASCADE based on the open source modeling engine is selected to build a BIM platform, and a concrete component model is newly created or imported.

3. The method for arranging double-layer steel mesh reinforcement based on BIM according to claim 1, characterized in that: The step 2 specifically includes the following steps: Step 2.1, select the model surface where the steel mesh is to be installed as the reinforcement surface; Step 2.2, offset the reinforcement surface to obtain the surface where the reinforcement is located; Step 2.3, construct the cutting plane; Step 2.4, calculate the intersection lines between the surface where the steel bars are located and all the cutting surfaces, obtain the three-dimensional steel bar positioning line, i.e., the steel bar line, and group the steel bars in two directions of a single layer into a layer of steel mesh; Step 2.5: Repeat steps 2.1 to 2.4 to obtain another layer of steel mesh, thus completing the arrangement of the double-layer steel mesh.

4. The method for arranging double-layer steel mesh reinforcement based on BIM as claimed in claim 3, characterized in that: The offset distance in step 2.2 Use the following formula to calculate: Where: is the distance from the outer surface of the steel bar to the reinforcement surface; is the steel bar diameter.

5. The method for arranging double-layer steel mesh reinforcement based on BIM as claimed in claim 3, characterized in that: The step 2.3 specifically includes the following steps: Step 2.3.1, select the continuous edge of the model as the guide line; Step 2.3.2, set array parameters; Step 2.3.3, based on the array parameters, arrange the distribution points along the guide line in sequence; Step 2.3.4, at each distribution point, use the tangent vector of the guide line as the normal vector and create a cutting plane passing through the distribution point; Step 2.3.5: Repeat step 2.3.4 until the cutting planes are created at all distribution points.

6. The method for arranging double-layer steel mesh reinforcement based on BIM as claimed in claim 5, characterized in that: The array parameters in step 2.3.2 include the starting point distance, array spacing and end point distance.

7. The method for arranging double-layer steel mesh reinforcement based on BIM as claimed in claim 3, characterized in that: The step 3 specifically comprises the following steps: Step 3.1, select four steel bar groups of the double-layer steel mesh, and set the number of intervals for the reinforcement arrangement for each group of steel bars; Step 3.2, based on the four steel bar groups selected in step 3.1 and the corresponding number of reinforcement arrangement intervals, screen out the steel bars actually involved in arranging the reinforcement in each steel bar group; Step 3.3: Nest and traverse the inner reinforcement of one layer and outer reinforcement , calculate the shortest distance between two spatial steel bars and the coordinates of their corresponding points , ; Step 3.4: Repeat step 3.3 to calculate the shortest distance between the two inner and outer sides of another layer and the coordinates of their corresponding points. , ; Step 3.5: Combine steps 3.3 and 3.4 to obtain a point set consisting of four coordinate points in the corresponding order, and calculate the two hook positioning points by the following formula: , : In the formula, is the spatial midpoint of the two layers of steel mesh; is a function for calculating the distance between two points in space; Step 3.6: Determine the plane where the reinforcement is located by using the two directions of one layer of reinforcement wire at the corresponding point obtained in step 3.3 or step 3.4 and the hook positioning point obtained in step 3.5: In the formula, Indicates the direction in which the hook bends; Indicates that the reinforcement line is at point The direction unit vector at Indicates that the reinforcement line is at point The direction unit vector at ; , At the same time, take the , Or take the , ; , is the direction coefficient; In the formula, is the normal vector of the plane where the reinforcement is located, is the reinforcement direction vector; Step 3.7: Locate the hook obtained in step 3.5 , Bend the hook along the direction obtained in step 3.6 Offset the corresponding distance to get the main positioning point of the reinforcement , , is the offset direction coefficient; Step 3.8: The main positioning point of the reinforcement obtained from step 3.7 , Construct a straight line as the main body of the reinforcement; Step 3.9: Construct the curved segments and straight segments of the tie hooks at both ends of the tie rod body obtained in step 3.

8. The normal vector of the plane where the hook is located is the same as the normal vector of the tie rod plane obtained in step 3.

6. Same direction.

8. The method for arranging double-layer steel mesh reinforcement based on BIM as claimed in claim 7, characterized in that: The offset distance in step 3.7 is the sum of the radius of the corresponding layer of reinforcement and the radius of the tension reinforcement.

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