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CLOSE THIS BOOKRoof Truss Guide - Design and construction of standard timber and steel trusses (BASIN - SKAT, 1999, 187 p.)
2 PRINCIPLES OF ROOF TRUSS DESIGN
VIEW THE DOCUMENT2.1 What is a roof truss?
VIEW THE DOCUMENT2.2 When to use a roof truss
VIEW THE DOCUMENT2.3 Roof shapes suitable for the truss
VIEW THE DOCUMENT2.4 Loads on trusses
VIEW THE DOCUMENT2.5 Load combinations
VIEW THE DOCUMENT2.6 Truss spacing
VIEW THE DOCUMENT2.7 Structural analysis
VIEW THE DOCUMENT2.8 Roof truss selection step-by-step
VIEW THE DOCUMENT2.9 Stability of the Truss

Roof Truss Guide - Design and construction of standard timber and steel trusses (BASIN - SKAT, 1999, 187 p.)

2 PRINCIPLES OF ROOF TRUSS DESIGN

2.1 What is a roof truss?

A truss is a structure with straight pieces forming triangles to support a load. The members of the triangles are placed under tension and compression but do not bend.


Figure

2.2 When to use a roof truss

Roof trusses are characterised by an economic use of construction materials (timber, steel). Composed of individual lightweight pieces, a truss can also provide considerable advantage in transport and assembly as compared to conventional roof structures. On the other hand, trusses are more labour-intensive and require connection devices. However, if a greater number of identical trusses can be manufactured, then considerable economies of scale can be achieved.

The structural height of a truss is usually larger than the height of similar structures using solid beams. For roofs, however, this is usually no disadvantage as roofs must often - depending on roof cover material used - be higher at the ridge and lower at the eaves to facilitate roof drainage and ensure water tightness.

Competitors of the Truss

While the use of steel for roof structures almost invariably calls for a truss, it is with timber structures where the truss has strong competitors. These are the purlin and the rafter roofs.

The purlin roof

The purlin roof consists of both rafters and purlins. The ridge purlin is supported by posts. The rafters act as simple supported beams between the purlins, either with or without cantilever.


Figure

The rafter roof

The rafter roof originates from tent construction. It consists of two rafters and a tie beam, which form a triangle. The simplest form of the rafter roof is thus identical with the basic element of the truss. Stiffness of the rafters can be increased with a collar beam near the ridge. A bevel shoulder traditionally made the connection between the rafters and the tie beam. This had the disadvantage that the slope of the roof was not uniform but became flatter at the rafter foot to accommodate the bevel shoulder. Today, steel connectors are often used and roof slopes remain uniform. The rafters can also rest on a concrete slab, which then replaces the tie beam.


Figure

The following table presents the main features, and the pros and cons of the three basic design options for roof structures. It can assist designers in selecting the most appropriate roof structure for a specific application.

Note, large hangars and halls are not considered.

Selection criteria

Table 1: Selection criteria for roof structures

Selection criteria

Truss

Purlin roof

Rafter roof

Span

6 - 30 m

up to 4 m between purlins, but needs intermediate support (concrete slab, girder for posts)

up to 9 m

Distance between trusses / rafters

0.75 - 1.25 m (with battens only)
up to 4 m with timber and steel purlins

0.75 - 1.25 m (with battens only)

0.75 - 1.25 m

Slope

any slope (but most economically up to 35°)

25° - 35°

35° - 60°

Use of loft

restricted by diagonals and braces of truss

slightly restricted by posts and struts

free

Roof cover material

any

any

mainly for heavy tiles

Material input

low, but requires connectors, fasteners

high (requires rafters, posts, struts, purlins and battens)

less material input than for purlin roof

Labour input

high (considerable reduction potential if properly planned ahead)

medium

low

Complexity / engineering input

low for standard truss and regular roof shapes; high for non-standard trusses

low

medium

Disadvantage of truss

One of the main disadvantage of the truss is that the strength and stability of its elements is to be designed by an engineer while the other roof structures, especially the purlin roof, can be built by carpenters and steel workshops themselves. It is one of the aims of this guide to eliminate this drawback by providing a number of fully detailed trusses ready for fabrication.

2.3 Roof shapes suitable for the truss

Trusses are suitable for a number of roof shapes

Roof type

Suitability

Flat

high

Gable or saddle

high

Single pitch

high

Hipped

medium

Pyramid

low

2.4 Loads on trusses

Two categories of loads on trusses can be distinguished: dead load and life load.

Dead load (G)

Dead loads for roof structures are basically the own weight of the materials used. These forces act vertically.

own weight of truss:

· for timber typically (per area covered) 0.25 kN/m2

· for steel: use the following formula:

where L = span in metre

typical weight of steel truss: 0.10 kN/m2

weight of purlins / battens

· for timber trusses with battens: negligible (since truss spacing is small, battens are mere laths)
· for steel trusses with steel purlins: 0.09 kN/m2

weight of roof cover

0.27 kN/m2 for MCR tiles


0.12 kN/m2 for steel roofing


0.47 kN/m2 for clay tiles (double depression, interlocking tiles)

weight of under-roof, timber 24 mm thick, 0.14 kN/m2

Note: Dead load per horizontal surface area of roof cover materials increases with the slope of the roof: multiply with 1/cosa where a is the roof pitch or slope. For a typical slope of 30°, the increase in load per horizontal surface area is 15%; hence, an MCR roof would weigh 0.31 kN/m2 of area covered.

Life load (Q)

Wind load: the magnitude of the wind load depends on the roof shape, wind direction and location of the building (see figures below). For lightweight roof structures and cover materials, the wind load is the most important load. Wind can also create suction forces and whole roof sections can be blown off. Appropriate fasteners and holding down bolts or anchors must be used (see manuals of roof cover manufacturer).

Snow load (according to climatic zones, typically 0.03 kN/m2 for each 10 mm of snow)

Concentrated load ("man load") due to foot traffic for fixing and maintenance, typically 0.8 kN. The man load is usually disregarded when analysing the truss as a whole. However, for sizing battens, the man load is the most important life load (see Annex 3.1 of the FCR/MCR Toolkit No. 24).

Wind loads increase with the elevation above ground level and the degree of exposure (open fields, coastal strips, mountain tops). The following assumptions have been used:

· max. wind speed: 100 km/h
· max. elevation above ground level: 8 m

The wind loads indicated below act perpendicular to the roof or wall surface.


Figure

2.5 Load combinations

Life loads need not be assumed as acting simultaneously in full magnitude. Maximum wind loads do not occur together with snow. It is also unlikely that somebody would step onto the roof at highest snow depth or during gale winds. In areas where snow occurs, a combination of wind, snow and dead load is taken as the design condition. Two cases need to be examined, one with the snow as the leading impact and one with the wind as the decisive life load.

Case (1): Total load S'1 = 1.0 G + 0.9 Qsnow + 0.7 Qwind

Case (2): Total load S'2 = 1.0 G + 0.9 Qwind + 0.7 Qsnow

It must also be checked whether dead load and either of the life loads (at 100 %, without reduction) exceeds any of the total loads of the above two cases.

Total vertical load of a typical truss for a 22° roof slope covered with MCR tiles in a tropical area (no snow) is:

S' = 1.00 kN/m2.

2.6 Truss spacing

The factors governing the spacing of individual roof trusses are different for steel and timber structures:

Timber: The sizes of sawn timber boards and beams are limited to widths / heights of 150 to 200 mm. With the given loading capacity of timber, the most economical spacing of timber trusses is around 1.5 to 2.0 m.

Steel: Small roof trusses are usually put in place without the use of cranes. The limiting factor for the spacing of steel trusses is therefore the weight of the individual truss (or portions of it, if it is assembled on site). The steel truss samples presented in this manual are not heavier than 3 kN (300 kg) per individual truss. The other factor to be considered is the size of the purlins. Purlins used for small roofs covered with MCR or steel roofing consist of equal angle bars or C-sections (where available). Spacing of purlins for MCR roofing system is 400 mm. Even for small buildings (8 × 15 m) the total length of purlins required is often several hundred meters of steel sections. Purlins should preferably be light sections to make an economic roof structure.

Considering the above, typical steel truss spacing is 2.5 m to 3.0 m for spans below 15 m.

2.7 Structural analysis

For an introduction into structural analysis please refer to the FCR / MCR Toolkit No. 25, Chapter 2.

With the structural analysis it must be shown that the truss is safe from:

· failure of any of its members (strength and stability) including the connections
· failure of the truss as a whole (stability)
· developing excessive deflection.

Working principle

A roof truss will slightly deflect under a vertical load. The upper chord will be under compression while the lower chord is under tension. Diagonals can either be compression or tension members depending on their inclination.


Figure

The convention for the presentation of tension and compression members in drawings is as follows:

· Arrow towards panel point = compression
· Arrow away from panel point = tension

The members of flat roof trusses will change sign under extreme wind loading. Suction forces may exceed dead load and the lower chord will be under compression and the upper chord will be under tension.

Buckling of members

While tensile forces in roof truss members can be handled by very slender timber or steel sections, it is the compression members that require most attention by the designer. Compression members tend to buckle under load and need to be restrained laterally. Instead of using simple timber boards or flat steel sections, either composite or stiffened compression members must be used.


Figure

Assumptions for structural analysis of trusses

Analyses of trusses assume pin jointed connections regardless of the actual type of connector used. The loads are applied exclusively through the panel points even though in reality this will not normally be the case.


Figure

Ideally, the system lines (centre lines) of truss members should precisely meet at the panel points. In practice, this can hardly be achieved. Trusses almost invariably have eccentric connections, which exert additional stresses on members and connectors. Adequate margins to stress limits need to be allowed for. Rule of thumb: If system lines of three truss members cannot meet in one point (e.g. with nail plates), the system lines of diagonals should meet at least within the chord member.


Figure

2.8 Roof truss selection step-by-step

The sample trusses of chapters 4 and 6 will not cover all the different spans and loads that may occur in practice. The philosophy is to maintain the basic design of the truss as per the samples given in chapter 4 and 6 and then adjust the span of the truss and the distance between individual trusses to suit the design of the building and the load of the roof.

Proceed as follows:

1. Determine the shape of your roof, the span of the truss and the loads (S') using the recommendations in chapter 2.5 above or consult your National Standards (Loading Code).

2. Select the desired truss from the samples given in chapters 4 and 6 considering the span that comes closest to your design.

3. Compare your design span with the span of the chosen sample. If the span differs, adjust the distance between the trusses (A’) to suit your design span:

4. Compare the load of your roof with the load of the sample. If the loads differ, adjust the distance between the trusses (A') to suit your load:


Figure

Note: For the sizing of battens and purlins FCR / MCR Toolkit No. 24 can be used (Appendix 3.1 and 3.3).

A combination of steps 3 and 4 is possible!

Example:

Standard distance A (as per given sample)

= 1.50 m

Span of standard truss (as per given sample)

= 6.00 m

Standard total load (as per given sample)

= 1.00 kN/m2

Design span

= 5.40 m

Design load

= 0.95 kN/m2

2.9 Stability of the Truss

By using the sample trusses of Chapters 4 and 6, the structure will carry the vertical loads it was designed for. However, the stability of the truss against lateral movement is not yet ensured. Compression chords tend to buckle in a direction perpendicular to the plane of the truss. In addition, wind loads on gables are also exerting forces perpendicular to the plane of the truss. A lateral restraining or bracing system is therefore required.

Purlins and battens may form part of this lateral bracing system. It is important that at least each panel point is braced against out-of-plane movement. X-bracing in the plane of the roof is added to form a structurally sound system.


Figure

The eaves must take up the wind forces on gables and must lead these safely into the foundations either through solid walling or braces.

Lateral restraining systems including wind braces consist of minimum two braces in the plane of the upper chord. Alternatively, special bracing trusses in the upper chord plane may be used.


Figure

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