Article > How to design the SpaceFrame structures?

header image from: novumstructures.com

1-About the "Spaceframe"

Spaceframes are designed with members that extend in all three dimensions of space, (as opposed to building structures that typically utilize perpendicular plane frames). The most commonly used spaceframe system is the double-layered roof with Mero (KK-Ball) connections. These connections feature a perforated central drilled ball made of high-strength steel, to which structural members are attached using sheathed bolts.

The complete design process for a spaceframe consists of 5 essential steps, which are as follows:

1. Wired Model Design
2. Structural Analysis and Member Selection
3. Connection and Support Design
4. Shop Drawing and Fabrication Tables
5. GA Plans for Installation

1-1- The advantages/disadvantages of spaceframes from architectural point of view:?

• The possibility of covering large spans (up to 36 meters for a flat two-layer roof with a module of 3 meters for an area with semi-heavy snow) and more for multi-layered, arched roofs, or roofs implemented in areas with less snow.
• The flexibility of the structure's form is directly related to the ratio of overall dimensions to the length of its constituent elements. The greater the ratio, the greater the flexibility of the forming.
• The possibility of implementing various forms of flat, dome, semi-cylindrical, sinusoidal, pyramidal, etc.
• The appearance of the spaceframes (due to the regular repetition of a pattern) is beautiful.
• The possibility of uniform/designed?coloring for members and nodes
• Possibility of installing lighting, equipment, hangers etc. with the help of existing nodes.
• Providing sufficient space for installation of air-went pipelines or other equipment between the structural elements.
• The relatively high thickness of the two-layer spaceframe roof (approximately 70% of the length of the constituent elements), makes restrictions for creating more complex forms on smaller spans. Although this thickness can be reduced by using variable modules in the middle layer, it leads to a variety of node types and an increase in implementation costs.

1-2- The structural advantages that spaceframe provides:?

• The three-dimensional structure brings the behavior of the roof assembly closer to the rigid diaphragm against lateral loads. Therefore, placing the brace in a part of the skeleton can provide the stability of a large area of the whole structure to which the roof is connected. Unlike the 2D portal frames, in order to overcome this weakness, cross cables must be implemented along their entire length, which, of course, does not create cohesion in the vertical direction.
• The elimination of bending tensions in the design of members and the use of thin-crust tubular sections causes minimal consumption of materials, especially in tensile members.
• The ratio of the steel weight used to the roof area in spaceframes is much lower than competing systems.
• The seismic behavior of spaceframes is very good and interesting due to their low weight (and low earthquake force absorption) and at the same time three-dimensional and braced structure. Especially, this type of structure is used to cover large areas and the heavy weight of structural components is usually the cause of absorbing more seismic forces.
• The reliability of the spaceframe is very high in the stages of modeling, analysis results, production and implementation of the structure. That is, what is modeled and analyzed in the software with very high accuracy is the one that is implemented and behaves real. The required welding are mainly done in the factory in a mechanized manner and there is a possibility of quality control. Other connections and installation of the structure are in the form of bolts and nuts, and the reliability and accuracy of its implementation is more than welding.
• The most important reason is the removal of bending tensions in force distribution. The presence of bending in members introduces many parameters into the analysis: > Local buckling of cross-sectional components. > Relatively more complex design of connections. > The effects of semi-rigidity of connections and the effect of stiffeners of elements on the degree of end-rigidity > Second-order effects caused by deformation and intensification of the existing bends in the member. > Effects of material nonlinearity and geometrical nonlinearity in structural analysis. > The effect of changing the section and stiffness of a member on the validity of the analysis results of other members in bending frames.

1-3- The parameters that are mentioned in the optimization and design with minimum consumption of materials in spaceframes are as follows:

• Optimized Loading
• Design method
• Selection of profile sections
• Column spacing and setting span length in the correct way.
• Incorporating purlins into the structural analysis considering the method of connecting purlins to the spaceframe
• considering the result of waste of steel in the determination of element length
• Usage of local strengthening methods of the structure
• Discontinuity seam or roller support for amortization of thermal loads
• Choosing the right location and quantity of peripheral supports
• Using columns with tree branches
• Use optimized thickness for the spaceframe

1-4- The complete design of a spaceframe includes the following five main steps:

1. Geometric modeling:
2. Analysis and overall design of the structure in the software
3. Design of connections (bolts, sleeves, balls) for ultimate loads and complete design of supports.
4. Typing of spheres and elements, preparation of production tables and shop drawings, and fabrication tables.
5. Preparation of GA plans for installation and addressing each element type in the specific location.

• In modeling, the connection of elements is assumed as a joint. Although there is a certain amount of resistance for the period of the structural member, but due to the three-dimensional structure of the spaceframe and the absence of bending tensions in the analysis results, the joint assumption of the connection does not make the analysis results unrealistic. At the same time, it is reliable in calculating the effective length of buckling. Secondly, due to the presence of slack between the conical hole and the screw body, this assumption is completely true for the range of small deformations
• Determining the length of the structural elements considering that minimizing the variation in the length of the members makes the production and installation of the structure easier
• Determining the length of the members so that the net cut length of the pipes has a minimum deviation compared to the 6-meter branch of the profile.
• The configuration of the members should be set in relation to each other so that the nodes used have the minimum variety of types in terms of drilling angles.
• The thickness of the three-dimensional roof truss should be proportional to its overall span.
• In the parts where the members of the spaceframe approach each other with a relatively small angle in a plane, the interference of the body of screws or pipes should be controlled, increasing the diameter of the ball or modifying the geometric model is the solution to this problem.

2- Principles of "Wired Model" preparation for the Spaceframe

2-1- To Be Engineered

"Wired model" engineering plays a crucial role in making significant decisions during the structural design phase. It encompasses choices such as determining the roof thickness and element lengths.

This stage determines the level of uncertainty associated with the structure and aims to prevent a design that may lead to progressive failures.

Optimizing the tension and pressure distribution in the elements is achieved by selecting the appropriate amount of protrusion for arched roofs without the need to over-strengthen the size of the elements.

Designing a suitable wire model helps to control deformation & rainwater direction.

In this stage, the interference of the members or bolts must be correctly predicted. In cases where two members are placed in the same plane or close to it, reducing the angle between them can cause their extruded shape to interfere.

Also, in the center of the domes and near the poles, the density of the members increases, leading to reduction in length of members and being too close to each other. In this situation, combining two or more members together and pruning the structure in the Wired Model is one of the solutions.

2-2- To Be Accurate

Maintaining accuracy in creating a wired model for the spaceframe is of utmost importance. While some tolerance may be acceptable in structural analysis and design, the wire model prepared for the structure is used throughout all stages, including shop drawing and member production. Therefore, the deviation from the wire model to the actual implemented should be minimized.

The wired model comprises discrete points and lines which connect these points. Each point must be precisely located in spatial coordinates to serve as the center for future calculations, such as drilling angles. The lines in the wire model are assumed to represent the central axes of the structural elements. In the case of supports, it is crucial to accurately predict the elevation of the ball's center with respect to the column's axis and also the extent of deviation.

Failure to achieve convergence of lines leading to a single point in the wireframe may be challenging to detect visually. Such discrepancies can lead to unrealistic results in structural analysis results.

2-3- To Be Optimized

The wired model design stage contributes to the overall optimization of the project in two primary aspects:

• Structural Optimization: Accurate determination of element lengths, arch protrusions, support distances, and removal of unnecessary members helps optimize material consumption in the structural system.
• Fabrication Optimization: Precise determination of point distances enables the most efficient cutting plan for profiles. Minimizing the variety of element production types is also important. Furthermore, achieving the correct three-dimensional configuration of the wire model is essential to reduce the variety of drilling types for spheres.

2-4- Aesthetic aspects

Depending on their use and appearance, spaceframes can serve as visually valuable elements rather than just functional supports for architectural components. Therefore, form design plays a crucial role. There are numerous forms that can be implemented, each offering specific visual and functional features. These geometric forms can be developed manually or with the assistance of three-dimensional geometric drawing software such as Formian. Alternatively, a newer approach and software allow for parametric design. However, it is essential that the output of this step fulfills all the requirements established in the previous stages.

3- Modeling, loading, analysis, and member Design of Spaceframes

After completing the initial wired model , the next step involves modeling, loading, analyzing, and designing the structural members within software tools such as Sap2000. This stage follows a standard process common to structural design. However, there are a few specific points that warrant attention during this process:

• Structural members should be modeled as joint ends due to the slight play between the screw and the hole's cones.
• Coverage can also be modeled in the software, but its hardness is usually assumed to be negligible during loading to avoid impacting structural analysis results.
• Purlins need not be modeled if they're perpendicular to the axis of the transverse trusses and don't hinder structural deformation. Using slotted holes for joint connections with purlins is advisable. Detailed purlin design can be done manually later.
• The point where purlins connect to the roof is where load transfer occurs. Careful consideration is needed when assigning cover panels to this area.
• While deformation control criteria don't specify a particular value (sometimes referred to as L/150), any shape change should not raise doubts about analysis accuracy or assumptions. Additionally, it shouldn't compromise roof serviceability or proper rainwater drainage. Thin roofs might necessitate assessing the potential for buckling collapse.
• Effective pipe length under pressure is slightly less than its ax-to-ax length. While this can be factored into unbraced length calculations, it's often recommended to overlook this for certainty.
• Members with KL/r factors around 200 are highly susceptible to buckling. Though analysis and design might not reveal problems, construction and installation forces could induce buckling.
• Each ball's weight and associated connections typically range from 5 to 10 kg. For diameters exceeding 11 cm, the weight could be significantly higher. This weight can be applied as a concentrated dead load.
• Thermal stresses due to material expansion and contraction should be factored into loading, especially for larger structures. For expansive and integrated structures, accommodating the release of thermal stresses at supports might be prudent.
• The effects of bearing settlement, underlying structure deformation, and significant concentrated loads are crucial for structures with high importance and low uncertainty.
• Structural members are typically designed using pipe profiles due to their optimal buckling performance in all directions, ease of installation, and aesthetic appeal.
• Determining the Seismic behavior factor (R) for spaceframes is complex and is better addressed through reference to scientific articles.
• Ensure to account for the vertical component of seismic loads as well ;)
• Connections, bolts, and spheres are not designed in this phase; these will be the focus of the upcoming post.

4- Design of connections

After finalizing the structural design for members, it is time to design connections. The connector explained in this article is known as the KK-BALL NODE system by “MERO”.

Design of connections means determining the Node's diameter, determining angular digits for drilling, size of bolt and sleeve, controlling weld lines, designing supports, and the final stage (which is the next article about) categorizing nodes and elements in the most efficient way for the production line and display them on GA drawings.

First of all, gears that are connecting members to nodes should be checked against transferred axial loads. The bolts are subjected to tension, and sleeves transfer compression between member and node. We should collect critical loads from the PUSH load combination. So maximum values (positive) are design tensions and minimums (negative values) are the compression amounts to be used.

4-1- BOLT

To determine a bolt's appropriate size, we consider the maximum tension load in connecting members in all load combinations that could be obtained from PUSH. There is a slight hole in the middle of the screws which is used to turn and fasten it with a pin.

Is it necessary to consider it and reduce the effective cross-section in calculations? If the hole is in the threaded zone the answer is yes but if not, we can ignore it. There is a factor that reduces nominal strength to actual strength for bolts (usually 0.75) due to the reduction of cross section in the threaded zone and the mentioned hole is not usually there. If the reduction in cross-section due to the hole is less than 25% (where the mentioned factor is 0.75) it is possible to neglect the hole. How about considering it anyway for sure? It leads to an increase in the quantity of upper-size bolts and as a result more variety in element and node types!

The bolt’s length depends on the thickness of the connected cone and height of the sleeve and also the minimum length of involving threats into the sphere. As mentioned in the related criteria a minimum length of 0.9*D for H.R 8.8. and 1.1*D for H.R 10.9. bolts are required to be involved in the sphere. Generally, we exceed this a few for sure and make bolts typical in length. It is necessary to use high-resistant bolts but grade 12.10. is not allowed.

Generally, we choose a minimum bolt size considering executive aspects. For example, it is possible to design bolts with diameters under 20mm but it probably creates trouble in drilling or variety in element types.

It is better to use only one of the grades for each blot size. If not, it may cause an increase in the number of element types and also difficulty in distinction, which is not preferred.

Finally, each bolt is defined by its Size, Length, and Grade. For example “M20x80 H.R 8.8.”

4-2- Sleeve

Sleeves are similar to nuts in shape but there is a hole in them (as it is on the bolt) to pass a pin through. Turning the sleeve results in tightening the bolt. The sleeve is also transferring compression between the member to the spherical node and should be resistant to it.

In fact, the Sleeve is a compressive object that does not matter to buckling because of its short length. But it is important to check for crushing (Not to neglect the hole on it).

Better to use the same material as its corresponding screw, also it is possible to use highly resistant steel grades such as CK45.

Similar to any other component it is good to minimize the variety of sizes to keep the final element types minimal in quantity.

Better to use the same material as its corresponding screw, also it is possible to use highly resistant steel grades such as CK45.

Similar to any other component it is good to minimize the variety of sizes to keep the final element types minimal in quantity.

4-3- Cone

As you know a sudden change in dimension results concentration of tension so it is good to reduce a member’s diameter radiantly by a cone shape of steel. As the diameters get down the thickness comes up and a thick end-cap transfers the axial force to the sleeve or bolt.

The cone's perimeter should be completely welded to the pipe. A full penetration groove welding.

It is important to use an oversized hole (not too much!) on cones. It allows the bolt to have a few angles to make the installation process much easier and also certain us that the connections are behaving completely as a joint.

4-4-Spherical Node

Spherical nodes are at the center of integrated forces transferred from each member and because of that usually made by high-resistant steel like CK45. However, in a statical stayed condition net sum of forces is zero (in the center) but when it comes to edges the tensions might be high in value. It is difficult to calculate the exact tension values without numerical analysis software.

We should choose bigger spheres for larger members. Not only to control the tensions also it is necessary to provide enough involved length of threaded blots or to prevent interference between holes in tight angles. However, variety in node size results in variety in element types. Better to use 3 different sphere sizes: Small, Medium, and Large.

There are drilled and threatened holes on spheres. Each one is addressed by 3 digits: α,β,M

Where:

“α” is an angular value that shows the angle between the origin and the hole’s shadow on a horizontal surface.

“β” is an angular value that shows the angle between the radius points to the hole and its shadow on a horizontal surface.

“M” is the size of the bolt connected in place.

It could be up to 12 holes on a spherical node (or even more). while carving and drilling each hole, a determined amount of surface is eliminated to provide a settlement for the sleeve.

4-5- Supports

Supports are the points where loads are transferred into the sub-structure. It is important to be designed accurately. Supports are also connections and are designed manually. Just take support reactions or transferring forces from the software analysis. Generally, there are no moment forces on them (because of being hinges) but considering the eccentricity between the center of the support node and the weld line or anchors to the basement, there would be a considerable amount of bending forces to be checked.

5- Grouping the Nodes and Elements

The spaceframe consists of pipes, bolts, cones, sleeves, and spherical nodes, which are grouped together as elements, and the elements are connected by nodes.

In the 4th stage, the elements and nodes are classified into types or groups, where all components in each “element type” are similar in dimension and size, and all the nodes in each type are similar in diameter and holes.

It is good to mention that firstly all the figures and images in this article are taken from the software that I provided to design the KK-ball connected spaceframes. And are not necessarily of the same project.

5-1-Element types

An element contains a straight pipe that has two similar joints at both ends. Each joint is a combination of bolt, Welded Cone, and Sleeve.

We should collect similar elements from the whole structure and group them into countable element types.

Certainly, it is best to keep the rows of the table as few as possible. There are some solutions to achieve this:

• Try to have a simple wired model with minimal variety in lengths.
• Try to minimize the number of pipe sizes in your design selection list. Also, avoid using similar diameters with different thicknesses that are difficult to distinguish.
• Different bolt sizes lead to differences in node sizes which affect the elements and cause new element types. Minimize this.
• Choosing a consistent sleeve size for each bolt size and a similar sleeve length for all leads to simplification and no significant increase in material consumption. Certainly, by checking the compression.
• Remember to round up the length digits to an acceptable value. Otherwise, every millimeter of difference in length will lead to an unnecessary increase in the number of element types which is not important to be considered in many projects. It is at the discretion of the engineer how to round the digits. (e.g. 1 , 2.5 or 5 millimetres to be rounded). Note that even a millimeter of carelessness can cause problems for large or rounded geometries.

5-2-Node Types

The Node is a spherical high-resistant steel that is drilled with several holes in it. When two nodes are assigned to a particular node type, it means that they are the same in the parameters of material, diameter, number, and angle of the holes.

In general, all the nodes are equal in material and all are CK45 usually.

The diameter is a design parameter. as already mentioned, it depends on the geometry of the holes and the stresses applied.

The number of holes can be up to 12 (or even more!). However, one of them is usually at the bottom of the sphere to form a fixed point on the drilling table. It can be useful later on the roof for hangers or purlin mounting.

As with the element table, keeping the number of node types as low as possible is good, but it is much more complicated to do!

The solutions to achieve this are as follows:

• The most important thing is to know how to rotate a node in space to connect members with minimal changes compared to the other nodes. It is easy to use similar nodes for whole the flat roofs, but when it comes to curved or freeform structures where the surface rotates, it is necessary to rotate the nodes as well to continue using similar nodes. Finding the normal vectors for each point is the solution.
• If you have avoided using different bolt sizes to keep the number of element types to a minimum, you now also have much less variety in node types.
• As mentioned earlier, you should avoid using different node diameters. Good to have a maximum of three different sizes: Small, medium, and large. At the beginning of the node dimensioning run, it is recommended to have a wide variety of node sizes to check the node size distribution. Depending on this, then it makes sense to pick out only the node sizes with the largest number of elements for the final node dimensioning.

• Keep in mind the difference between the text and the physical reality in computer programming. The order of the holes is not important in geometry, but if you try to find and write them down for each node, the results may be different in order, which is not a good reason to consider them as different.
• The digital accuracy in determining angular digits is effective on the number of types. Sometimes it is not possible to have rounded and similar values for holes, but they are very close to each other. For example, there are 44.8 – 45 - 45.5 in three different nodes for a given angle value. Given the manufacturing constraints, they are indeed the same in fact and it depends on your technical expectations on how you round up or down the digital values. At least, it is good to be more sensitive with multiples of 15 and leave the other values as they are. Also, as mentioned earlier, there is a clearance between the bolt and its hole on the cone, so there is no need to worry about geometrical effects.
• As mentioned earlier, there is a hole under each node as a fixed point for drilling. If you rotate the nodes of the TOP layer by 180 degrees, it would make sense to connect the purlin. ?At the same time, the MID layer members are connected by positive β-values! A great effect on minimizing node types!
• One of the reasons that led to an increase in the number of types is the absence of some holes in particular places of the roof, edges, or corners. On the other hand, they would be useful to connect the side cover, or at least it is not harmful to have them even if they are not used. Consider that, may have 2 different types for each side of the roof and 2 different types for each corner!
• Why do we say 2 types and not 8? (In a double-layered roof there are 8 corners). This is due to a complicated geometric issue. In 3D modeling, it is possible to obtain a 3D shape by simply mirroring a component, not needing to modify and rename it. But in the physical reality, this possibility of mirroring does not exist. It is only possible to "rotate" the solids. If we rotate a certain corner node by 180 degrees, it is not useful for the corner on the other side, the same line and layer. But if we rotate it again vertically by 180 degrees, or shift it to the other side of the roof, the node type would be useful for other corners as well.
• We rotate the nodes around the space corresponding to the surface curve (as mentioned in “a”). But when it comes to supports, a problem arises in locating rotated nodes on a horizontal surface. The best solution is to leave them as separate types, without spatial rotation. No worry about the increase in type quantity, it arises anyway from the upper hole size under the sphere, which is usually needed to transmit support reactions.

6-Generating the Erection Plans

The Erection Plans or General Arrangement Drawings should show the Element and Node Types in their specific positions for each layer. In a typical double-layered spaceframe, there are 3 layers! These are the BOT, MID, and TOP layers.

There are many other points in the field of production, painting, loading, and installation of the structure and the coverage and drainage, but since our focus was on structural design, it was not covered. What was written may not be free of errors and defects, but expressing opinions and suggestions will help to complete it. Also, it is not a substitute for the national standards and regulations that are the responsibility of engineering.

Written by: Mehran Komeili - 2023