The WinTess3 works with objects. There are several types of objects, each one of them has its own properties. Some of them are used continuously, while others are only used in some state or phase of the program.
Objects that are used at any time:
- Nodes: A point in space.
- Bars: A line in space that goes from one node to another node.
- Elements: A triangle in space of which vertices are nodes.
Objects that are used in the state of calculation of the structure:
- Tubes: Bars formed by a steel tube of hollow circular cross-section.
- Cables: Bar or set of adjacent bars formed by a steel cable.
- Membrane: Isotropic (film) or orthotropic (fabric) material that form elements.
- Foundations: Reinforced concrete footings in prismatic shape.
Objects that are used in the stage of patterning:
- Geodesic: Lines that run along the surface of the membrane and are used for the design of patterns.
- Patterns: Each one of the pieces of membrane which, once cut and assembled, form the warped surface of the structure.
Helper objects for the design:
- Auxiliaries: Lines, arcs, points, etc. , which serve as a reference in designing a structure. They are not part of the structure itself.
A node is an object that can be defined as a point in space. It is characterized by the following properties:
- Class: The classification of nodes in the program. This WinTess3 recognizes if a node is on the ground and carries Foundation, if it is the end of a cable, etc. The class 0 nodes are those who have no any specific function.
The nodes of class 1-Vertex are those that define the cables at perimeter (boltrope) of a membrane.
The nodes of class 2-Geodesic are belong to a geodesic line and normally are not part of the structure.
The nodes of class 3-Foundation.
The nodes of class 4-Auxiliary.
The nodes of class 5-Apex
- Coordinates X,Y,Z: They can be initial (before displacement) or final (after displacement)
- No displacement: If a node can be moved in X,Y,Z, then it is a free node. If it cannot move in any direction, then it is a fixed node. Of course, there are cases in which it can be moved only in any of the axis X,Y,Z. If this is an end node of a rigid bar, it is also necessary to define the displacement in terms of rotation. That is to say, it needs to be defined if the node can be rotated according to the axes X,Y,Z
- Displacements: Difference between the initial and final coordinates.
- External loads: External loads applied directly at the nodes: a lamp, a speaker, etc.
- Cp: Wind coefficient corresponding to the normal to the surface at the node.
A node has no dimensions and therefore it doesn’t have any material. It is present in all the states of the program: form finding, analysis and patterning.
A bar is an object that can be defined as a straight segment going from one node to another node. It is characterized by the following properties:
- Type: According to that object material, the bar can be one of these 6 different types:
- 0 = Tube. It refers to a hollow circular section steel tube. Therefore it can bear tension and compression. Bending is not supported.
- 1 = Membrane. This type of bar simulates a piece the membrane (#). However, if we deal with a steel cable net that form a warped surface, each piece of the net, ranging from node to node, will be of this type.
- 2 = Rigid bar. It is a hollow circular section steel tube, like type 0 (tube), but it is also capable of supporting shear, bending and torsion forces.
- 3 = Fixed length. (This option is not operational at this time)
- 4 = Diagonal of quad. This is a type of bar useful only in cases where there is a square mesh of bar type 1 (membrane) (#). To avoid the excessive deformations of the grid with respect to the diagonal, WinTess3 automatically creates this type of diagonal bars at the time generating elements of a square mesh. We’ll see later how to parameterize this type of bar.
- 5 = Boltrope. Bar at the perimeter of membrane. It is usually a steel cable, load belt, etc. going from one vertex to another vertex of the membrane perimeter.
- 6 = Guyrope. External Bar. It usually connects the ground or other fixed support to the membrane, masts, etc.
(#) Membrane type bars (1 and 4) may have different properties as they are situated in a position parallel to the warp or parallel to the weft of the fabric used.
- Group: A bar can belong to one (or more) group. A group doesn’t serve any other interest than editing several bars with same properties at the same time. Perimeter cables are a case of automatic groups of bars, since generally each perimeter cable brings a group of bars on perimeter together.
These are the basic data of the bars. In the sections devoted to calculation, we will comment on other properties.
An element is a triangle. Therefore it is delimited by three nodes. The only limitation is that none of these three nodes matches any of the other two, that is to say, the area of the triangle is greater than zero.
The elements have orientation. This means that the two sides of the triangle (as viewed from top or bottom) are different. Orientation of an element is determined by the order of the nodes. An element defined by the knots 1, 4 and 7 has different top and bottom sides as opposed to the element defined by the nodes 1, 7 and 4. To verify that there are no errors in orientation of the elements, WinTess3 colors the topside face (blue) different than the underside (yellow).
In the image above, we can see how an element of the membrane is incorrectly oriented. The program has a menu to invert the elements incorrectly oriented.
WinTess3 can calculate structures using hollow (or massive) tubes of circular cross-section. To do this, it has a database with a set of tubes to choose from.
It is very likely that the user of the program needs to use tubes that are not found in this database provided by the program. WinTess3 menu Tubes | Database allows you to modify this database and add all those the user needs for the projects.
The database of the tubes is located in the file tubs.txt file as seen in the title of the window that opens with the menu given above. It is important to make a backup of this file from time to time in case for some reason it is lost or corrupted. If this file is damaged, all the pipes added by the user will be lost and only the default ones provided by the program will be available.
To add a new tube into the database, we only need to add a new text line (it doesn’t matter where, at the end or in the Middle).
In this text line:
- Name (tube). This is a string of text (without spaces) where we define the tube in the way that we want.
- Outer diameter in mm
- Wall thickness of the pipe in mm. If thickness is equal to half the diameter, it means that it’s a solid tube.
- Material type. In principle you can use any of these types: S235, S275, S355 and S450 (#)
- E (modulus of elasticity of the material) in kN/mm2
- Density (relative = kg/dm3 = t/m3)
(#) These steel denominations represent materials with the following characteristics:
S235: Elastic limit = 235 N/mm² (thickness < 16 mm), 225 N/mm² (thickness < 40 mm), 215 N/mm² (thickness > 40 mm)
S275: Elastic limit = 275 N/mm² (thickness < 16 mm), 265 N/mm² (thickness < 40 mm), 255 N/mm² (thickness > 40 mm)
S355: Elastic limit = 355 N/mm² (thickness < 16 mm), 345 N/mm² (thickness < 40 mm), 335 N/mm² (thickness > 40 mm)
S450: Elastic limit = 450 N/mm² (thickness < 16 mm), 430 N/mm² (thickness < 40 mm), 410 N/mm² (thickness > 40 mm)
However, any material can be used. To do this, we use a text type “Mxxx”, where
- “M” is a letter that defines the material (for example for aluminum, see the last tube of the database in the previous image)
- “xxx” is the elastic limit of the material in N/mm²
If the letter “S” is used, it means steel. If the thickness of the tube exceeds 16 mm the elastic limit is taken 10 N/mm² less, and if it exceeds 40 mm take 20 N/mm² less.
WinTess3 can calculate structures that use steel cables (or other similar material). For this, it has a database with a set of cables to choose from.
It is very likely that the user of the program may need to use cables that are not in this database provided by the program. For this reason, WinTess3 has a menu Cables | Database that allows you to modify this database and add all those that the user might need for their projects.
The database of the cables is located in the file cables.txt file as seen in the title of the window that opens with the menu given above. It is important to make a backup of this file from time to time, in case for some reason it is lost, all the cables added by the user and only the default ones provided by the program will be available.
To add a new cable in the database, we only need to add a new text line (it doesn’t matter, at the end or in the middle).
In this line of text we find:
- Diameter outside of the cable in mm
- Section solid in mm²
- Breaking load of cable in kN
- Name of cable. Text without spaces.
- Modulus of elasticity of the cable material in kN/mm²
- Density. Relative value or T/m³
The membrane is the material forming elements. It is possible that a tensile structure has no elements and therefore we do not need to define any membrane. In the majority of such cases, an open-mesh of cables form the structures, like an aviary, support for vegetation (warped pergola), etc.
WinTess has a database with a set of membranes to choose from. It is very likely that the user of the program may need to use membranes that are not in this default database provided by the program. For this reason, WinTess3 has a menu Membrane | Database that allows you to modify this database and add all those membranes that the user might need for their projects.
The database of the membranes is located in the file membranes.txt file as seen in the title of the window that opens with the menu given above. It is important to make a backup of this file from time to time, in case if for some reason it is lost, all the membranes added by the user will be lost and only the default membranes provided by the program will be available.
The geodesic lines are lines formed by a set of segments of which ends are always on the surface of the membrane, i.e. in one of the elements that form the surface.
In geometry, the geodesics line is defined as the line of minimal length that joins two points in a given area, and is contained in this area. At any point, the osculador plane of the geodesics is perpendicular to the plane tangent to the surface. Geodesic of a surface are the “straightest” possible lines (with lesser curvature) fixed point and a given direction on said surface.
The term “geodesic” comes from the word geodesy, the science of measuring the size and shape of the planet Earth; in the original sense, it was the shortest route between two points on the surface of the Earth, specifically, the segment of a great circle.
In 3D space in architecture, any straight line is a geodesic. In an area any maximum circle obtained by intersection of the spherical surface with a plane passing through its center, is also a geodesic. In particular, the equator and the meridian of a sphere are geodesic lines. Using spherical coordinates for a sphere of radius R, the equations of the geodesic are simply:
The osculador plane is the plane containing its tangent vector and the normal vector in each point of the curve. For a particle moving in the space the osculating plane coincides with the plane containing in each instant acceleration and speed. This plane equation is given by:
, the point of the trajectory.
, the velocity vector at the point considered.
, the coordinates of a generic point of the osculador plane.
Patterns are the cut pieces of fabric that once (with their margins) joined form the warped surface of the membrane. As we shall see, they are often delimited by geodesic lines and edges of the membrane. A pattern, in fact, is a set of triangles (they do not have to or tend to coincide with elements which are also triangles) on the membrane, laid down on a flat plane.
The auxiliaries (points, lines, arcs, etc. ) are objects used mostly during the task of form finding. They help us to define some coordinates in space which we will then use to generate a given form. These lines do not, in any way, affect the calculation of the structure.
For an explanation of how to create auxiliary see Using WinTess | Menu: Auxiliaries.
See also an example of the use of auxiliary in the Form finding | Using auxiliary.