Trusses are structures that comprises of members that are joined together such that they resist external loads in axial tension and compression. They generally consist of top chords, bottom chords, and triangulated internal web elements. They are used to support roofs, floors, bridge decks, and can also be used as transfer members. They can also be incorporated in buildings as bracings to stabilize against lateral loads, as well as also provide temporary support during erection of structures.

Lightly loaded truss members are mostly dominated by hot-rolled angles, especially the web elements, The top and bottom chords can also be hot-rolled angles, however Tee sections are often preferred because of ease of connection. Heavily loaded truss can compose any of UB, UC, CHS, RHS, and SHS which are generally connected together by gusset plates.

Classification of trusses

In this article trusses shall be generally classified into two based on the slope of their top chords:

1. Pitched roof truss

Pitched roof truss are generally used in supporting building roofs. The top chord of the truss has a slope that enhances natural drainage of water to avoid ponding on the roof.

     2. Lattice girders

Lattice girders are trusses with parallel top and bottom chords. They are often used in supporting floors where slope is not necessary for drainage.  They are also used as booms in heavy lifting cranes.

Types of Trusses

• Pratt Truss
• Howe Truss
• Fink Truss
• Mansard truss

Advantages of Trusses

• Lattice girders and trusses are effective for accommodating services within their depth through the web openings
• Lattice girders are more efficient in spanning large space than plated girders as they weigh lesser and also use less materials. Although they are often of greater depth than equivalent plate girder of same strength.
• Owing to the use of less material, trusses are more economical and cost-effective
• Trusses can speed up delivery speed as they can be pre-fabricated and conveyed to site to be installed
• Because they can be pre-fabricated under more controlled conditions, truss elements are often of better quality.

Assumptions in Truss design and Practical limit of assumptions

Trusses are idealized as structures that comprises members that are joined together such that they resist external loads in axial tension and compression. Before a structure can be considered as a truss, it is presumed that it satisfies the following assumptions

Assumptions

1. Truss members are connected together at their ends only.
2. Truss members are connected together by frictionless pins
3. The truss structure is loaded only at the joints.

Practical Validity of assumptions

The assumptions in the foregoing sections are often violated on-site due to practical constraints. A designer must know these constraints, their extent of deviation from ideal assumptions, limits they impose on these assumptions, and their consequence as related to member resistance and stability. Some of these practical constraints are discussed below.

• Continuity of top and bottom chords rather than been discrete members that are connected at joints:

In practice, the top and bottom chords are normally continuous, spanning several joints. For lightly loaded truss where significant bending moments is not induced in the chords, this assumption in the analysis is acceptable. However, for heavily loaded truss where the bending moment are significant, the top chord may have to be designed for the bending moment.

• Loading of top and bottom chord within span rather than at joints:

The span of a roof truss, and the weight of the sheet cladding are two major factors that dictates the spacing of purlins, which are often according to manufacturer’s data. Often times the location of the purlins does not coincide with node points of the truss and are required to be supported on the span of the chords.

• Stiffness at Connections

Connections in trusses are assumed to be frictionless pins which implies that the centroidal axis of all members meeting at a connection are coincident. In practice, this is often not the case as connections between members possesses some rigidity and eccentricity due to practical constraints. These induced secondary bending stresses in the members connected at the node points that should be accounted for during member and connection design.

The use of gusset plate is encouraged to make the connections between members to be concentric as much as possible, particularly in heavily-loaded truss where the secondary stress significantly affects the member sizing disproportionately to the primary axial forces.

Critical issues to be factored during design

• Transportation: Ease of transportation of the truss system from fabrication point to erection location should be considered during design
• Connection: Prior to settling for a cross-section for chords or internal web bracings, the ease and method of connection should also be considered. It should be considered what part of the member would be connected, would the connection be welded or bolted, would there be need for gusset plate or not, would the connection require additional stiffening, etc.
• Repetition: The designer should work towards achieving repetitive structural configuration for the truss as well as repetitive connection details. These can massively reduce the cost of labour and fabrication.
• Availability: It is required for the designer to ensure that the sections used are easily accessible
• Constructability: The ease of executing the design should also be considered.

 

Analysis of Trusses and Verification of Members

Trusses are likely to be supported by columns or beams where the support conditions in the vertical direction are restrained but are neither released nor restrained in the horizontal direction. However, majority of trusses can be isolated from the main structure and analyse as a planar structure. In such cases, one end of the truss must be restrained in the horizontal direction while the other end is released in the horizontal direction. This type of determinate trusses can be analysed by hand using traditional methods such as joint resolution methods, method of sections, and graphical methods.

For indeterminate planar truss or space truss that cannot be correctly rendered as an assemblage of 2d trusses, adopting computer programmes for comprehensive 3D analysis of the whole structure becomes indispensable. Advanced computer software enables different types of trusses with different complexities to be modelled and analysed. Sometimes, to beat deadlines in design offices, determinate planar trusses which are amenable to hand computation can also be analysed using computer programmes. The advantage of these computer programmes includes:

• This software enables engineers to be able to model accurately the connection between different truss members thereby generating the primary stresses and secondary stresses in those members
• They also enable engineers to load the chords accurately within their spans thereby generating the secondary moment withing continuous chord members
• They also assist in efficient connection design

 

Modelling of Trusses with computer programmes

Trusses can be modelled using computer programmes as one of the followings:

1. Pin-jointed Frames

 

This perfectly model the assumption in truss systems but fail to acknowledge the limit of these assumptions in actual practice.

2. Continuous Chords with Pin-jointed Web Members

This is the most preferred model as it finds a balance between truss idealization and practical constraints. The continuous top and bottom chord would resist minimal secondary moment even though the dominant stress in them is axial compression or tension.

3. Rigid Frames.

This is majorly employed in Vierendeel truss. This truss always has all its members, including web elements, rigidly connected and also resists loads through bending.

 Example of Truss Modelling and Analysis using ETABS Software  

This section presents the modelling of Pratt and Howe truss using ETABS software. Trusses with different span-to-depth ratio are analysed, with both Pratt and Howe truss configurations modeled for each ratio. The comparative analysis results are then discussed.

Modelling Philosophy

The trusses are modelled using continuous top and bottom chords, while the web members are pin-jointed by releasing moments at both ends in ETABS. Additionally, the bottom chord members connected to supporting columns are released to simulate typical truss behaviour, ensuring adequate tension in the bottom chord and creating a determinate planar truss.

Span and Depth Considered

The span and depth considered for each truss is listed below

1. Span/depth = 4.2 | Span = 6 | depth = 1.4

2. Span/depth = 4.4 | Span = 12 | depth = 2.7

3. Span/depth = 7 | Span = 15 |    depth = 2.1

4. Span/depth = 7 | Span = 30 |    depth = 4.3

Loads on truss

Weight of roofing sheet = 0.5KN/m2 (Assumed to be taken from manufactures data sheet)

Weight of ceiling = 0.25KN/m2 (Assumed to be taken from manufactures data sheet)

Live load on roof = 1KN/m2 (Table 6.1 EN 1991-1-1)

Spacing of truss = 2m

Although the loads ideally would be distributed on the roof truss as point load via purlins, however in this example, the loads shall be distributed directly on the truss ignoring the purlins.

Total Load on top chord = (1.35 x 0.5 + 1.5 x 1) 2/2 = 2.175KNm

Total load on bottom chord = 1.35 x 0.25 x 2/2 = 0.338KNm

Members

The top and bottom chord elements are: UKA 150 x 75 x 15

The web elements are: UKT 210 x 267 x 61

Analysis Results

Below are the axial stress diagrams of each truss

 

Comment on Analysis Results

• It is noticed that for 6m span truss the longer web elements of the Pratt truss are in tension while the longer elements in Howe truss are in compression. Additionally, the top-chord members of the Howe truss are generally subjected to more compressive stress than those of the Pratt truss. Against the background that steel members are much efficient under tensile stress where they are not vulnerable to buckling, the Pratt truss is more efficient for short span roof.

 

• As the truss span increases to 12m and then 15m, more and more diagonal members of Pratt truss are under compressive stress while otherwise is for Howe truss. In fact, for 15m span trusses, more diagonal members of Pratt truss are in compression only that the compressive stress is very low, the maximum being 13.11KN while the maximum compressive force in diagonal member of Howe truss is 26.47KN.

 

• On getting to a very large span of 30m, although the Howe truss as the highest compressive stress overall in one of the top chord members, its web members are reasonably under compressive stress. In fact, two of the diagonal members of the Pratt truss have the highest compressive force in a web member which is 69.24KN. Additionally, the howe truss distributes its load efficiently so that none of its bottom chord member is subjected to compressive stress. At large span of 30m, the Howe truss can be said to be as efficient as the Pratt truss

 

• Another scenario where howe truss might be more desired especially for short spans is in the case of uplift probably due to wind load on roofs. If wind load is more critical than gravity loads, there would be stress reversal in a truss, the diagonal members of a howe truss for a short span would be subjected to tensile stress and vertical members would be subjected to compressive stress just like in the case of Pratt truss under gravity load. This stress reversal is also true for pratt truss under wind uplift.

 

Verification of Members

After analysis, each of the member can be verified to ensure its reliability to withstand the internal stresses. The top and bottom chords are to be designed as members subjected to combined bending moment and axial force. The internal web members are to be designed as members subjected to pure axial tension and compression. Click here to study a worked example of the design of a steel section subjected to combined bending and axial force. A separate post shall be made on the design of web members of the 32m span Pratt truss as members subjected to pure axial compression and tension.