the technical and feasibility selection of space truss ...3.2 structural analysis and design of the...

The technical and feasibility selection of space truss construction systems

M. F. A. Elfawal CG Point Civil Engineering Consulting Services, Egypt

Abstract

This study proposes a space truss system called Pin Node Space Truss (PNST) which depends on pin connection between members (hollow pipe) and nodes (perpendicular welded plates) with one degree of freedom – rotation perpendicular to the member axis-in a limited angle that it can produce using an allen bolt connection with special casted item. Structural analyses have been carried out on PNST in order to check the system stability and the stresses, also technical and economical comparisons between PNST and MERO systems were carried out through a case study of two layer grids space truss system. Using PNST of variable depth in two layer grids space systems is the best solution to cover a certain area, which can be achieved to figure out the optimum locations of lower layer nodes that result in maximum allowable stresses in members and the shortest lengths of them. PNST – without special nodes just only change the length of the members – it can give infinite forms and shapes of double grid system or multi-grid systems and it also can change supporting points easily, providing more flexibility in architecture design and easy to fabricate, manufacturing and erection. Keywords: Pin Node Space Truss, PNST, space truss, nodes, two layer grid system, minimum cost, feasibility study, new double grid system.

1 Introduction

A space truss is a structural system assembled of linear elements which are arranged so that the loads are transferred in a three dimensional manner. It can be

Mobile and Rapidly Assembled Structures IV 293

doi:10.2495/MAR140241

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defined also as a structural system in the form of a network of elements or (lattice structural system) in which the load carrying mechanism is three-dimensional in nature.

2 Space structure systems

A space structure system called the ‘piece-small’ systems is the most widely used and has different jointing methods. Most use circular or square hollow tube members because of their better performance in resisting the forces present in space trusses (normally pure axial tension or compression, with only secondary bending effects). Tubular members are also considered to have a superior aesthetic appearance. To architects this is especially important, as space grids are normally left exposed to view so that the building’s users can appreciate the pattern of the regular grid geometry. The main difference between tubular members in the alternative systems is the detailing of their ends for connection to the nodes. The following subsections describe the most common nodes:

2.1 The MERO Node System

MERO Node (Figure 1) by Max Mengeringhausen Rohrbauweise is a casted ‘ball’ joint that connects circular tube members with a single concealed bolt for each tube [1].

Figure 1: MERO Node System.

2.2 The NODUS Node System

The NODUS Node System, Figure 2, was developed during the late 1960s by the Tubes Division of the British Steel Corporation and introduced commercially in the early 1970s [2].

294 Mobile and Rapidly Assembled Structures IV


Figure 2: NODUS Node System.

2.3 The TUBALL Node System

The TUBALL Node System (Figure 3) was developed by Eekhout [3].

Figure 3: TUBALL Node System.

2.4 The TRIODETIC Node System

The TRIODETIC Node System (Figure 4) was developed by Fentiman [3].

Figure 4: TRIODETIC Node System.



2.5 The OCTATUBE Node System

The OCTATUBE Node System (Figure 5) was developed by Prof. Mick Eekhout [3].

Figure 5: OCTATUBE Node System.

2.6 Continuous Chord Systems (Nodeless System)

Continuous Chord Systems are the halfway stage between the piece-small systems (Node Systems) and Modular Systems. They have no separated node but depend only on connecting members together through continuous chords (upper and lower). One of the widely known continuous chord systems called (CATRUS) (Figure 6), which was developed by El-Sheikh, at Dundee University and which uses cold-formed channel section members that are bent to shape and have bolt holes punched at the ends [2].

Figure 6: CATRUS System (Nodeless).



2.7 Modular space truss systems

Modular space truss systems, simply consist of members and nodes which are prefabricated in units to form pyramids. The square based pyramid is the most common modular unit, however, other modular systems may form rigid-jointed space frames.

3 PNST (Pin Node Space Truss System)

The PNST (Pin Node Space Truss System) [3] is a space truss system with infinite and unlimited configurations and shapes and depends only on the length of members (Not the NODES). So, PNST Node is a universal node for the system that has a capability to achieve any configuration or shape of the Space Truss System, which produce an unlimited horizon for geometry of Space Truss Systems.

3.1 Description of the PNST Node

The PNST node, (Figure 7) is an open spherical outlined shape; it consists of a circular plate, welded to its lower and upper surfaces with two semi-circle plates such that the angle between each other’s is 45º to form the final shape of the proposed node.

Figure 7: Node of PNST (all views).



The four members of upper/lower chord of a double-layer space truss are connected to the upper/lower semi-circle orthogonal plate using special casted iron connections and four bolts; one for each member (Figure 8).

Figure 8: Node and members before assembly.

The diagonal members are then connected (Figure 9) to the lower/upper semi-circle orthogonal plates by another special casted iron connection and four bolts

Figure 9: Node and members after assembly.

The use of special casted iron member ends (Figure 10) make pin joined between nodes and members (free connection) of PNST and that is the spirit of system generation.



Figure 10: Special casted conical connection.

By choosing the lengths of the connected members only, the PNST can form the needed configuration and shape. On the other hand the system can be modified using a double layer node to form a multilayer space truss system (Figure 11).

Figure 11: Multilayer Pin Node Space Truss (NODE).

The connected members can rotate freely so that the depth of the double-layer grid space truss can be changed.

3.2 Structural analysis and design of the proposed node

A structural analysis is carried out initially to calculate the internal forces in the members of a space truss system. From these forces a detailed analysis are then carried out to calculate the dimensions and thicknesses of the plates comprising the node in addition to the weld lengths and sizes, required to connect the node plates (Figure 12).



Figure 12: Stress distribution in the components of the Node.

Furthermore, PNST Node Dimensions (Figure 13) can be generated through structural design using steel (St37) as shown in Table 1.

Table 1: PNST Node dimensions.

Pipe Pipe Bolt max Node Node Node Node Node

Diameter thicknes

s Diameter Force Diameter thickness leaf Hole Edge

Height Diameter distance

Dp tp Dn tn Hn dn D/2 D (D-t)/2 d 1.5d mm mm mm t mm mm mm mm mm

42.164 1.651 8 1.8 86 5 40.5 9 13.5 48.26 1.651 10 2.56 98 5 46.5 11 16.5

60.325 2.769 12 4.08 122 5 58.5 13 19.5 73.025 3.048 14 5.61 148 6 71 15 22.5

88.9 3.048 16 7.6 178 8 85 17 25.5 101.6 5.74 18 9.29 204 9 97.5 19 28.5 114.3 6.02 20 11.81 230 10 110 21 31.5 141.3 6.553 22 14.63 284 12 136 23 34.5

168.275 7.112 24 16.94 338 14 162 25 37.5

3.3 Pan/depth ratios of double-layer space truss systems

The Optimum Span/Depth Ratio for space truss structures is difficult to be generalized, as it is influenced by the method of support, type of loading and, to a large extent, on the system being considered. Makowski [5] finds that the Span/Depth Ratios may vary from 20 to 40 depending on the rigidity of the Space Truss System. However, the ratio can be reduced to be 15 to 20 when the Space Truss System is only supported at corners or near the corners [2]. Furthermore, René Motro concluded that the optimum grid depth is approximately 1/15th of the clear span [2].



Node connection parameters. Figure 13:

Using the possibility of the depth variation of space truss when using the PNST, the Span/Depth Ratio must be followed by another term when as a function of depth variation which can be expressed also as the shape of surface.

Span/depth ratio (S/d) = f (Span, Space Truss Shape) The flexibility of depth variation of a space truss leads to different surfaces such as pyramids or curved surfaces or parts of spheres. In following case study, (Figure 14) giving 13 different cases with various shapes of the lower grid through changing the nodes location. After applying the dead loads and live loads of an inaccessible roof as a comparison loading case and using the Finite Element Analysis Package “Sap2000” [4] to calculate the maximum and minimum axial forces acting in space truss members. The following observations can be obtained: The smaller distance between the centres of the upper grid and the lower grid,

the maximum of compressive and tensile axial forces in the space truss members.

The parallel double-layer grid system leads to the smallest compressive and tensile axial forces.



The 0-curve case generates the maximum compressive and tensile axial forces which represent about 150% of parallel case.

The deflection of the studied cases is within the maximum allowable deflections with a percentage of 33%.

The parallel double-layer grid system generates the smallest deflection. The 0-curve case gives the smallest member lengths compared with the other

studied cases, on the other hand parallel case gives the greatest required member lengths with a percentage of 107.7% compared with 0-curve case.

Figure 14: Different cases of variable depth.

4 Feasibility of PNST

A relative measuring of space truss systems can be done to adapt an economical visibility study by choosing the most known space truss system (MERO Node System) and PNST Pin Node Space Truss system. Analytical Hierarchy Process (AHP) [5] can be carried out through the phases of space truss life time. Evaluation is done using Availability, Cost, Quality and Time which results in the following:

1. Availability in market in all phases of construction is with ratio 1 MERO: 3.5 PNST.

2. Proposed System is the most accepted cost with ratio 1 MERO: 2 PNST.



3. MERO System has a better expected quality compared with the proposed system; with ratio 1.5 MERO: 1 PNST.

4. Time is weighted equally for the two systems.

5 Conclusion

From the technical and economic studies of PNST, it can be concluded that: The proposed node has proved to be structurally efficient. It can be simply manufactured locally, to save the large cost of the imported

similar nodes. It can be produced easily for any space truss configuration. It can be used for any depth/grid ratio which is not available in the other

available nodes in the market. Generally, it saves the time of execution compared to other space truss

systems. PNST is an economical space truss system to cover a certain area.

References


[1] Mero, “node system”, 31 Jan 2001. [Online]. Available: http://www.mero-structures.com/history.html. [Accessed 20 Aug 2009].

[2] J. C. Chilton, Space Grid Structures, England: Architectural Press, 2000. [3] G. S. Ramaswamy, Analysis, design and construction of steel space frames,

Chennai, India: Thomas Telford, 2002. [4] M. F. A. Elfawal, “PNST (Pin Node Space Truss)”. EGYPT Patent

WO/2013/079078, 29 11 2011. [5] Z. S. Makowski, “Development of Jointing Systems for Modular

Prefabricated Steel Space Structures”, in Lightweight Structures in Civil Engineering, Warsaw, Poland, 2002.

[6] csiberkeley, http://www.csiberkeley.com/products_SAP.html, CSI, 14 May 2007. [Online]. Available: http://www.csiberkeley.com/support_downloads.html. [Accessed 3 April 2009].

[7] M. Anson, J. M. Ko, L. S. S. Lam, Advances of Building Technology, London, UK: Elsevier Science Ltd, 2002.


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