A truss is essentially a triangulated system of straight interconnected structural elements. The most common use of trusses is in buildings, where support to roofs, the floors and internal loading such as services and suspended ceilings, are readily provided. The main reasons for using trusses are:
- Long span
- Controlled deflection
- Opportunity to support considerable loads.
The penalty, however, is increased fabrication costs .
The article describes alternative forms of truss, proposes where and why different forms might be appropriate and introduces design considerations. Primarily, pin connected trusses are discussed, however consideration is given to rigid jointed Vierendeel trusses.
Definition of a truss
A truss is essentially a triangulated system of (usually) straight interconnected structural elements; it is sometimes also referred to as an open web girder. The individual elements are connected at nodes; the connections are often assumed to be nominally pinned. The external forces applied to the system and the reactions at the supports are generally applied at the nodes. When all the members and applied forces are in a same plane, the system is a plane or 2D truss.
The principal force in each element in a truss is axial tension or compression. When the connections at the nodes are stiff, secondary bending is introduced. See figure right.
Overview of trusses
Use of trusses in buildings
Trusses are used in a broad range of buildings, mainly where there is a requirement for very long spans such as in airport terminals, aircraft hangers, sports stadia roofs, auditoriums and other leisure buildings, etc., or to carry heavy loads, i.e. trusses are often used as transfer structures. However, this article focuses on typical single storey industrial buildings where trusses are widely used to serve two main functions.
- To carry the roof load:
- To provide horizontal stability:
Two types of general arrangement of the structure of a typical single storey building are shown in the figure below.
In the first case (above left) the lateral stability of the structure is provided by a series of portal trusses: the connections between the truss and the columns provide resistance to a global bending moment. Loads are applied to the portal structure by purlins and side rails.
In the second case, (above right) each vertical truss and the two columns between which it spans, constitute a simple beam structure: the connection between the truss and a column does not resist the global bending moment, and the two column bases are pinned. Transverse restraint is necessary at the top level of the simple structure; it is achieved by means of a longitudinal wind girder carries the transverse forces due to wind on the side walls to the braced gable walls.
Types of trusses
Trusses comprise assemblies of tension and compression elements. The top and bottom chords of the truss provide the compression and tension resistance to overall bending, and the bracing resists the shear forces. A wide range of truss forms can be created. Each can vary in overall geometry and in the choice of the individual elements. Some of the commonly used types are shown below.
Pratt truss ('N' truss)
Pratt trusses are commonly used in long span buildings ranging from 20 to 100 m in length. In a conventional Pratt truss, diagonal members are in tension for gravity loads. This type of truss is used where gravity loads are predominant (see below left). An alternative Pratt truss is shown (below right) where the diagonal members are in tension for uplift loads. This type of truss is used where uplift loads are predominant, such as open buildings.
It is possible to add secondary members (as illustrated below left) to:
- Create intermediate loading points
- Limit the buckling length of members in compression (without influencing the global structural behaviour).
For the Pratt truss and any of the types of truss mentioned below, it is possible to provide either a single or a double slope to the upper chord of a roof supporting truss. An example of a double (duo-pitch) Pratt truss is shown (below right).
In this type of truss, diagonal members are alternatively in tension and in compression. The Warren truss has equal length compression and tension web members, and fewer members than a Pratt truss. For larger spans the modified Warren truss may be adopted where additional restraint to the internal members is required (this also reduces secondary stresses).
Warren trusses are commonly used in long span buildings ranging from 20 to 100 m in length.
This type of truss is also used for the horizontal truss of gantry/crane girders.
North light truss
North light trusses are traditionally used for short spans in industrial workshop-type buildings. They allow maximum benefit to be gained from natural lighting by the use of glazing on the steeper pitch which generally faces north or north-east to reduce solar gain. On the steeper sloping portion of the truss, it is typical to have a truss running perpendicular to the plane of the North Light truss shown.
The use of north lights to increase natural daylighting can reduce the operational carbon emissions of buildings although their impact should be explored using dynamic thermal modelling. Although north lights reduce the requirement for artificial lighting and can reduce the risk of overheating, by increasing the volume of the building they can also increase the demand for space heating. Further guidance is given in the Target Zero Warehouse buildings design guide .
A variation of the North light truss is the saw-tooth truss which is used in multi-bay buildings. Similar to the North light truss, it is typical to include a truss of the vertical face running perpendicular to the plane of the saw-tooth truss shown.
There are two different types of X truss :
- If the diagonal members are designed to resist compression, the X truss is the superposition of two Warren trusses.
- If the resistance of the diagonal members in compression is ignored, the behaviour is the same as a Pratt truss.
This type of truss is more commonly used for wind girders, where the diagonal members are very long.
The Fink truss offers greater economy in terms of steel weight for short-span high-pitched roofs as the members are subdivided into shorter elements. There are many ways of arranging and subdividing the chords and internal members.
This type of truss is commonly used to construct roofs in houses.
Aspects of truss design for roofs
Truss or I beam
For the same steel weight, it is possible to get better performance in terms of resistance and stiffness, with a truss than an I-beam. This difference is more sensitive for long spans and/or heavy loads. The full use of this advantage is achievable if the height of the truss is not limited by criteria other than the structural efficiency, e.g. a limit on total height of the building. However, fabrication of a truss is generally more time consuming than for an I beam, even considering that the modernisation of fabrication equipment allows the optimisation of fabrication times.
The balance between minimum weight and minimum cost depends on many conditions: the equipment of the fabrication factory, the local cost of manufacturing; the steel unit cost, etc. Trusses generally give an economic solution for spans over 20 or 25 m.
An advantage of the truss design for roofs is that ducts and pipes that are required for operation of the buildings services can be installed through the truss web, i.e. service integration.
In order to get a good structural performance, the ratio of span to truss depth should be chosen in the range 10 to 15. The architectural design of the building determines its external geometry and governs the slope(s) given to the top chord of the truss. The intended use of the internal space can lead either to the choice of a horizontal bottom chord, e.g. where conveyors must be hung under the chord, or to an inclined internal chord, to allow maximum space to be provided.
To get an efficient layout of the truss members between the chords, the following is advisable:
- The inclination of the diagonal members in relation to the chords should be between 35° and 55°
- Point loads should only be applied at nodes
- The orientation of the diagonal members should be such that the longest members are subject to tension (the shorter ones being subject to compression).
Types of truss member sections
Many solutions are available. The main criteria are:
- Sections should be symmetrical for bending out of the vertical plane of the truss
- For members in compression, the buckling resistance in the vertical plane of the truss should be similar to that out of the plane.
A popular solution, especially for industrial buildings, is to use sections composed of two angles bolted on vertical gusset plates and intermediately battened, for both chords and internal members. It is a very simple and efficient solution.
For large member forces, a good solution to use is:
- Chords having UKB and UKC sections, or a section made up of two channels
- Diagonals formed from two battened angles.
The web of the UKB/UKC chord section is oriented either vertically or horizontally. As it is easier to increase the resistance to in-plane buckling of the chords (by adding secondary diagonal members) than to increase their to out-of-plane resistance, it is more efficient to have the web horizontal, for chords in compression. On the other hand, it is easier to connect purlins to the top chord if it has a vertical web. A solution could be to have the top chord with a vertical web, and the bottom chord with a horizontal web.
Another range of solutions is given by the use of hollow sections, for chords and/or for internals. Structural hollow sections are popular due to their efficiency in compression and their neat and pleasing appearance in the case of exposed trusses. Structural hollow sections, however, have higher fabrication costs and are only suited to welded construction.
Types of connections
For all the types of member sections, it is possible to design either bolted or welded connections. Generally in steelwork construction, bolted site splices are preferred to welded splices for economy and speed of erection. Where bolted connections are used with bolts loaded perpendicular to their shank, it is necessary to evaluate the consequences of 'slack' in connections. In order to reduce these consequences (typically, the increase of the deflections), solutions are available such as use of preloaded bolts, or limiting the hole size.
Hollow sections are typically connected by welding whilst open sections are connected by bolting or welding, which will usually involve the use of gusset plates. Guidance on the design of welded joints for Celsius®355 and Hybox®355 hollow sections is available from Tata Steel.
Small trusses which can be transported whole from the fabrication factory to the site, can be entirely welded. In the case of large roof trusses which cannot be transported whole, welded sub-assemblies are delivered to site and are either bolted or welded together on site.
In light roof trusses entirely bolted connections are less favoured than welded connections due to the requirement for gusset plates and their increased fabrication costs.
Profile shaping of tubular sections for joint fabrication
It is necessary to design the chords in compression against the out-of-plane buckling. For simply supported trusses, the upper chord is in compression for gravity loading, and the bottom chord is in compression for uplift loading. For portal trusses, each chord is partly in compression and partly in tension.
Lateral restraint of the upper chord is generally given by the purlins and the transverse roof wind girder.
For the restraint of the bottom chord, additional bracing may be necessary, as shown in the figure below. Such bracing allows the buckling length of the bottom chord to be limited out of the plane of the truss to the distance between points laterally restrained: they serve to transfer the restraint forces to the level of the top chord, the level at which the general roof bracing is provided. This type of bracing is also used when a horizontal load is applied to the bottom chord, for example, forces due to braking from a suspended conveyor.
Thick black dashes - two consecutive trusses
Blue - The purlin which completes the bracing in the upper region
Green - The longitudinal element which closes the bracing in the lower region
Red - Vertical roof bracing
The roof purlins often serve as part of the bracing at the top chord. Introduction of longitudinal members at the lower chord allows the trusses to be stabilised by the same vertical bracing.
It is possible to create a horizontal wind girder at the level of the bottom chords, with longitudinal elements to stabilize all the trusses.
Design of wind girders
Transverse wind girder
In general, the form of a transverse wind girder is as follows:
- The wind girder is arranged as an X truss, parallel to the roof plane
- The chords of the wind girder are the upper chords of two adjacent vertical trusses. This means that the axial forces in these members due to loading on the vertical truss and those due to loads on the wind girder loading must be added together (for an appropriate combination of actions)
- The posts of the wind girder are generally the roof purlins. This means that the purlins are subject to a compression, in addition to the bending due to the roof loading
- It is also possible, for large spans of the wind girder, to have separate posts (generally tubular section) that do not act as purlins
- The diagonal members are connected in the plane of the posts. If the posts are the purlins, the diagonal members are connected at the bottom level of the purlins. In a large X truss, diagonals are only considered in tension and it is possible to use single angles or cables.
It is convenient to arrange a transverse wind girder at each end of the building, but it is then important to be careful about the effects of thermal expansion which can cause significant forces if longitudinal elements are attached between the two bracing systems, especially for buildings which are longer than about 60 m.
In order to release the expansion of the longitudinal elements, the transverse wind girder can be placed in the centre of the building, but then it is necessary to ensure that wind loads are transmitted from the gables to the central wind bracing.
Transverse wind girders are sometimes placed in the second and penultimate spans of the roof because, if the roof purlins are used as the wind girder posts, these spans are less subject to bending by roof loads.
The purlins which serve as wind girder posts and are subject to compression must sometimes be reinforced:
- To reinforce UKB purlins: use welded angles or channels (UKPFC)
- To reinforce cold formed purlins: increase of the thickness in the relevant span, or, if that is not sufficient, double the purlin sections (with fitting for the Zed, back to back for the Sigma).
Longitudinal wind girder
It is necessary to provide a longitudinal wind girder (between braced gable ends) in buildings where the roof trusses are not 'portalized'.
The general arrangement is similar to that described for a transverse wind girder:
- X truss
- The chords are two lines of purlins in small buildings, or additional elements (usually tubular sections)
- The posts are the upper chords of the consecutive stabilized roof trusses.
Guidance on global analysis
In reality, truss structures deviate from theoretical behaviour and their global analysis involves consideration of these deviations. In particular, the deviations include the occurrence of bending in the members, in addition to the axial forces. These bending moments, known as 'secondary moments', can cause significant additional stresses in the members which make up the truss.
The deviations in design take various forms:
- All the members which make up the structure are not usually articulated at their original node and their end node. Truss chords, in particular, are usually fabricated in one length only, over several truss purlins: the continuous chord members are then connected rigidly to their original and end nodes. Rotation of the nodes, resulting from general deformation of the truss beam then causes bending moments in the rigidly connected members; the more rigid the chord members, the bigger the moments .
- The members are not always strictly aligned on their original and end nodes. Bending moments which result from a misalignment of axes increase in proportion to the size of the eccentricity and the stiffness of the members.
- Loads are not always strictly applied to the nodes and, if care is not taken to introduce secondary members to triangulate the point of application of the loads between nodes, this results in bending moments.
Careful consideration must also be given to the out-of-plane stability of the truss and resistance to lateral loads such as wind loads or eccentric loads causing torsion about their longitudinal axis. An individual truss is very inefficient, and generally sufficient bracing must be provided between trusses to prevent instability.
Consideration should also be given to load reversal acting on the truss and allow for provision of out of plane restraints to the reversed compression chord, if needed.
Several questions arise in respect of the modelling of a truss.
It is always convenient to work on restricted models. For example, for a standard building, it is common and usually justified to work with 2D models (portal, wind girder, vertical bracing) rather than a unique and global 3D model. A truss can even be modelled without its supporting columns when it is articulated to the columns.
Nonetheless, it is important to note that:
- If separate models are used, it may be necessary, in order to verify the resistance of certain elements, to combine the results of several analyses; example: the upper chord of a truss also serves as chord of the wind girder.
- If a global 3D model is used, 'parasitic' bending can be observed, which often only creates an illusory precision of the structural behaviour process. That is why 2D models are generally preferable.
Once the scope of the model has been decided and adapted according to use to be made of the results, it is important to consider the nature of the internal connections. In current modelling of member structures, the selection is made between 'a pin-jointed member at a node' and 'a member rigidly connected to a node'; the possibility offered by BS EN 1993 to model connections as semi-rigid is rarely used for truss structures.
For trusses, the model is commonly represented as either:
- Continuous chords (and therefore chord members rigidly connected at both ends)
- Truss members (diagonals and verticals) pin jointed to the chords.
Influence of chord rigidity
Chord members in trusses which are used in construction are rarely pinned at the nodes and are more often rigidly connected; this means that members connected to the same node have to keep their respective angles. During deformation of the structure under load, the ends of the members all rotate at the same angle around the node. In these conditions, bending loads (bending moments and shear forces) called secondary forces are added to the axial loads in the members calculated assuming the nodes are pinned (primary forces).
It is routine in design to use continuous chord members and to pin the truss members.
In fact, transforming pinned connections into rigid nodes hardly leads to any modification to the axial forces in the members, because the shear transmitted by the members has little influence on the equilibrium equation of nodal forces and, on the other hand, bending of the member due to secondary bending moments only causes a slight variation in the distance between the ends of this member compared to the difference in length due to axial force.
Nevertheless, it is essential that the triangulated structures be designed properly so that the members are adequately arranged to withstand bending stresses, but not too slender so as to avoid buckling. Note that the greater the stiffness of the chords (which are usually continuous), compared to the global stiffness of the truss beam, the bigger the moments developed in the chords. For instance, for a wind girder in a roof, the stiffness of the chords is relatively small and the secondary moments remain small as well.
For a stocky truss, i.e. when the flexural stiffness of the individual chords is not significantly lower than the global stiffness of the truss, it can be necessary to take into account the secondary moments. Then the members and the connections must be designed accordingly.
Effect of clearance of deflection
When the connections between elements which make up a truss beam are bolted connections, with bolts in shear (category A in BS EN 1993-1-8 ), the clearance introduced into these connections can have a significant effect on displacement of the nodes.
In order to facilitate erection, the bolts are in fact inserted in holes which are larger than the bolts themselves. For standard bolt sizes, holes more than 2 mm bigger than the bolt are usually made (usually referred to as a 2mm clearance).
In order for a connection with clearance to transmit to the node the load required by the attached member, the bolt must come into contact with one or other of the connected parts: this is called often referred to as 'taking up slack'. For a connected tension member, this slack can be assimilated as an additional extension that is added to the elastic elongation of the member in tension. Likewise, for a connected compression member, the slack is assimilated as a reduction in length that is added to the elastic shortening of the compressed member.
The total slack in the many different connections of a truss structure can lead to a significant increase in displacements, which can have various and more or less serious consequences. Amongst these, note:
- In most of the cases, the visual effect is the worst consequence
- Increased deflection can lead to a reduction of free height under the bottom chord, which might prevent or upset the anticipated usage. For example, the additional deflection of a truss holding doors suspended in a gable of an aeroplane hangar could prevent the passage of the aeroplane
- Increase in the deflection can result in reduction in the slope of the supported roof and even, if the nominal slope were small, to a slope inversion; a risk of water accumulation is therefore associated with an inversion in pitch
- If the truss structure is not a statically determinate system, this may lead to unexpected internal forces.
It is therefore essential, where truss structures are concerned, to control the effect of connection slack on the displacements. In order to do this, it is often necessary:
- Either to limit slack in category A connections: drilling at +1 mm, even +0,5 mm and using shear bolts on a smooth bolt shank (to limit the increase in slack by deformation) of the threads and pieces; or
- To use 'fit bolts'; or
- To use preloaded bolts (category C connections); or
- To use welded connections instead of bolted connections.
Detailed design considerations for elements
Truss members are subjected to axial force, but in many cases members are also subject to stress by bending moments, i.e. secondary moments.
Verification of members under compression
The resistance of a member to compression is evaluated by taking into account the different modes of instability:
- Local buckling of the section is controlled using section classification
- Buckling of the member is controlled by applying a reduction coefficient in the calculation of resistance.
For a compression member, several buckling modes must be considered. In most truss members, only flexural buckling of the compressed members in the plane of the truss structure and out of the plane of the truss structure need be evaluated.
For each buckling mode, the buckling resistance is obtained from BS EN 1993-1-1 by applying a reduction to the resistance of the cross-section. This reduction factor is obtained from the slenderness of the member, which depends on the elastic critical force.
For the diagonals and the verticals stressed in uniform compression the elastic critical force is determined from the buckling length of the member in accordance with BS EN 1993-1-1 Section 22.214.171.124 and according to Annex BB of BS EN 1993-1-1 :
- For buckling in the plane of the truss beam: the buckling length is taken equal to 90% of the system length (distance between nodes), when the truss member is connected at each end with at least two bolts, or by welding.
- For buckling out of plane of the truss beam, the buckling length is taken equal to the system length.
For buckling in the plane of the truss of the chord members in uniform compression, the buckling length may be taken as 90% of its system length (distance between nodes).
For buckling out of plane of the truss, it can be more difficult to determine the elastic critical force for the following reasons:
- There is not necessarily a lateral support at each node of the truss
- The lateral support points are not necessarily effectively rigid.
When there is no lateral support at each node along the chord, the segment located between support points is subject to variable compression between bays. In these circumstances:
- A conservative approach would be to use the normal compression force at its maximum value and to take the buckling length as the distance between supports but this can lead to an under-estimate of the chord resistance.
- Refined methods can be adopted by investigating an equivalent buckling length under constant compression.
- All the purlins connected to a roof bracing can be considered as lateral rigid support points.
- Intermediate purlins can also be considered as a rigid point of support. Insofar as a diaphragm role has been attributed to the roof (class 2 construction according to BS EN 1993-1-3).
- With regard to the lower chord, these lateral support points are provided by additional vertical bracing elements between trusses.
Another point to note, which is very common, concerning determination of the compression resistance, is the case of pairs of members. It is quite common, as was stated, to make up members from a truss structure using two angles, or two channels.
Verification of members in tension
The resistance of tension members is based on the net cross section of the member.
Use of Vierendeel trusses
Vierendeel trusses are rigidly-jointed trusses having only vertical members between the top and bottom chords. The chords are normally parallel or near parallel.
Elements in Vierendeel trusses are subjected to bending, axial force and shear , unlike conventional trusses with diagonal web members where the members are primarily designed for axial loads.
Vierendeel trusses are usually more expensive than conventional trusses and their use limited to instances where diagonal web members are either obtrusive or undesirable.
Vierendeel trusses are moment resisting. Vertical members near the supports are subject to the highest moments and therefore require larger sections to be used than those at mid-span. Considerable bending moments must therefore be transferred between the verticals and the chords, which can result in expensive stiffened details.
As Vierendeel trusses are statically indeterminate structures, computer analysis software packages are used to obtain the most accurate and efficient structural analysis solution.
Plastic theory may be applied to the design of Vierendeel trusses in a similar way to its application to other rigid frames such as portal frames. Software is available for the plastic analysis of plane frameworks including Vierendeel trusses.
Vierendeel trusses have rigid joints with full fixity and so the connections must be of a type which prevents rotation or slip of the incoming members, such as welded. Welded connections are the most efficient and compact although undesirable if the connections are required to be made on site. Normally site splices are bolted for economy. For large Vierendeel trusses delivered and erected piecemeal, fully bolted connections are normally used. For member and joint efficiency the ends of the verticals are often splayed. This is of advantage in heavily-loaded trusses as the high concentrated local stresses are reduced thus avoiding the need for heavy stiffening. Some typical joint examples are shown below.
- ^ BS EN 1993 Eurocode 3: Design of steel structures. Various parts, BSI
- ^ BS EN 1993-1-8:2005. Eurocode 3: Design of steel structures. Design of joints, BSI
- ^ 3.0 3.1 3.2 BS EN 1993-1-1: 2005, Eurocode 3: Design of steel structures. General rules and rules for buildings, BSI
- ^ BS EN 1993-1-3:2006 Eurocode 3. Design of steel structures. General rules. Supplementary rules for cold-formed members and sheeting, BSI
- Steel Designers' Manual 7th Edition. Editors B Davison & G W Owens. The Steel Construction Institute 2012, Chapter 20
- Architectural Design in Steel – Trebilcock P and Lawson R M published by Spon, 2004
- Target Zero: Guidance on the design and construction of sustainable, low carbon warehouse buildings
- SCI P167 Architectural Teaching Resource. Studio Guide. SCI and Corus, 2003
- NCCI: Design of roof trusses SN027a-EN-EU
- Scheme Development: Conceptual design of truss and column solutions SS050a-EN-EU
- Example: Single span truss and post frame for a low pitch roof using battened section chords SX017a-EN-EU
- Single-Storey Steel Buildings Part 5: Joint design, The Steel Alliance
- Design of welded joints - Celsius®355 and Hybox®355, 2011, Tata Steel
- Single storey industrial buildings
- Cost of structural steelwork
- Operational carbon
- Target Zero
- Preloaded bolting
- Steel construction products
- Simple connections
- Moment resisting connections
- Modelling and analysis
- Member design