Roof trusses become necessary when sloping roofs have to be provided. At places of heavy rainfall or heavy snowfall sloping roofs are necessary which have to be supported by roof trusses. Workshops warehouses, industrial buildings etc. also need sloping roofs and hence roof trusses. For many single storey buildings sloping roofs on trusses are common. When a roof is to be provided for a building which does not have interior supports and the exterior walls are more than 12 m apart, a roof truss will be a convenient arrangement to support the roof.
Components of a Steel Roof Truss:
A roof truss consists essentially of the following components:
(i) Upper chord members.
(ii) Bottom chord members.
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(iii) Web members.
The upper most line of members which extend from one support to the other through the apex is called the upper chord, where as the bottom chord consists of the lowermost line of members extending from one support to the other.
In trusses simply supported at the ends, the members in the top chord are subjected to compression and the members of the bottom chord are subjected to tension. But in cantilever trusses, the top chord members will be in tension and the bottom chord members will be in compression. Usually in simply supported trusses, for the normal loadings, the top and bottom chord members near the support carry greater forces.
The top and the bottom chord members are connected by vertical or diagonal members called web members. The joints at which the web members are connected to the chords are called panel points. The joint at the support is called the heel joint while the joint at the ridge is called the peak joint.
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Tension members are called ties while compression members are called struts.
The truss provides an easy means to transmit the loads through the reactions to the walls or supporting columns.
The distance between the supporting end joints of a truss is called its span. When supported on walls, the distance between the centres of bearings is considered as the span. When framed into columns the distance between the column faces is regarded as the span.
The rise of the truss is the vertical distance between the apex and the line joining the supports.
ADVERTISEMENTS:
The ratio of the rise to the span is called the pitch.
The pitch and slope for various inclinations of roofs are given below:
When the rise is not more than 1 vertical to 6 horizontal the roof is called a flat roof. If the rise exceeds the above limit the roof is called a pitched roof. As far as possible steep pitches are to be avoided since they will have to resist greater wind pressure. Moreover truss members become longer, particularly the compression members, if made longer can carry only low stresses depending on their slenderness ratio. Thus compression members will have to be of heavy sections.
The portion of the truss lying between two consecutive joints is called a panel. The portion of the roof contained between successive trusses is called a bay. The member spanning from truss to truss which is meant to carry the load of the roofing material and to transfer it on the panel points is called a purlin. Hence the length of the purlin is equal to the width of the bay, i.e., the spacing of the trusses.
The various components of the truss are shown in Fig. 12.1.
Types of Trusses:
The king post truss is mainly adopted for short spans (less than 6 m). It is usually built of wood completely or of wood combined with steel. Steel rods are used as tension members.
ADVERTISEMENTS:
The Queen post truss is found suitable for spans 6 m to 9 m. For ordinary buildings the fink type truss is found to be very satisfactory. These trusses are convenient for spans 12 m to 18 m.
For small spans flat roofs may be supported on beams. But for larger spans flat trusses are to be used. In this case the upper chord will be inclined sufficiently to provide just the required slope for proper drainage.
In factory buildings where considerably more light is desirable the saw tooth truss is used. In this type the steep sides of the trusses will be glazed. The glazed panels are usually faced towards North to avoid the direct glare of the sun and are hence called North light roof trusses. For long spans and where more head room is required the crescent truss is adopted. For such conditions the scissors truss, the curb truss, the shed truss, the three hinged arched truss, the Hammer beam truss are also used.
Loads on Roof Trusses:
1. Dead Loads:
These consist of weights of trusses, roof coverings, purlins and bracings. Usually the dead load on the truss is expressed as the load per unit horizontal area.
Weight of Roof Covering:
The following table shows the weights of roof covering commonly provided.
Pitch of Trusses:
The slope of the top chord members or the ratio of rise to span of a truss is called the pitch of the truss. The pitch of the truss is an important factor in the selection of a truss. Slope for roof is necessary to drain off rain water falling on the roof. If roof slopes are not provided, i.e., if the roofs are flat, then it may be very difficult to provide sheet roofing without the use of effective mastic sealing of the sheet joints.
When G.I. sheets are used the pitch may be 1/6 of the span. When A.C. sheets are provided the pitch may be 1/10 to 1/12 of the span. Where snow loads and wind loads exist, a pitch of 1/4 the span is found convenient. In regions where snowfall is absent, a pitch of 1/6 is reasonable. In trusses of low pitch there is the advantage of reduced wind pressure.
Purlins:
Purlins are beams of light sections spanning between trusses carrying dead load of roof, live load and wind load. Purlins transmit these loads to the trusses. Generally the purlins are so spaced that they are supported over the top chord joints of the truss.
In the case of trusses of large spans it may become necessary to support the purlins over the top chord members between panel points. In such cases the top chord members will be subjected to bending moment in addition to axial load. Purlins may be angles, channels, I-sections, tube sections etc.
Spacing of Trusses:
The spacing of trusses is determined by the spacing of the columns. The spacing of the trusses may be such as to minimize the cost of roofing. The spacing of trusses may be about 1/3 to 1/5 of the span. Where snow loads and superimposed loads are practically absent larger spacing may be provided.
Reasonable spacing of trusses based on spans are given below:
Lateral Bracings:
Wind forces parallel to the ridge acting on the gable ends are liable to produce displacements and deformation of the roof trusses, unless a thick gable masonry wall is provided at each end. When such end gable walls are not provided, it is necessary to provide lateral bracings connecting the last two trusses. These bracings consist of two systems of lacings-One system of lacing connects the bottom chord joints of the last two trusses. The second system of lacing connects the top chord joints of the last two trusses (Fig. 12.3).
Weight of Purlins:
The size of purlins depends on the nature of roof covering supported, wind and other loads and the spacing of the trusses.
Generally the following figures may be adopted:
i. Purlins supporting slate roof = 120 N/m2
ii. Purlins supporting glazed roof = 100 N/m2
iii. Purlins supporting corrugated sheeting = 80 N/m2
Weight of Trusses:
Assuming that the roof covering is of corrugated sheeting and the trusses are spaced at 4 metres and that the trusses are provided with a rise of one-fourth to one-fifth the span, the weight of a truss expressed in N/square metre of plan area may be taken as-
Weight of Wind Bracing:
This may be assumed as 12 to 13 N/metre2 of plan area.
2. Live Loads on Roof Trusses:
(i) For sloping or flat roof with slopes up to and including 10 degrees.
The live load shall be taken as follows:
(a) When access is provided – 1500 N/m2
(b) When access is not provided – 750 N/m2 (except for maintenance)
(ii) Sloping roof with slope greater than 10 degrees.
The live load to be taken in this case is 750 N/m2 less 20 N/m2 for every degree increase in slope over 10 degrees.
Note:
The live load shall not be taken less than 400 N/m2.
Snow Load:
If a roof is subjected to snow load it should be designed for the actual loads due to snow or for the live loads specified above, whichever is more severe. Actual load due to snow will depend upon the shape of the roof and its capacity to retain the snow and each case shall be treated on its own merits. In the absence of any specific information, the loading due to the collection of snow may be assumed to be 2.5 N/m2 per mm depth of snow.
The possibility of total or partial snow load should be considered, that is, one half of the roof fully loaded with the design snow load and the other half loaded with half the design snow load. In the ease of roofs with slopes greater than 50°, snow load may be disregarded; where, however, there are possibilities of formation of snow pockets, these should be taken into account.
Economic Spacing of Trusses:
The economic spacing of trusses means the spacing at which the overall cost of trusses, purlins, roof cover, columns etc. is the minimum. For large spacing of trusses purlins will work out to be heavy and costly. For small spacing of trusses, while the purlins become light and less costly, the trusses will work out to be costly. The trusses may be spaced such that the overall cost of the roof structure is a minimum.
Hence, for economic spacing of trusses, the cost of the trusses should be equal to double the cost of the purlins plus the cost of the roofing material.
Wind Load:
Wind means air in motion with respect to the surface of the earth. The rotation of the earth and variations in terrestrial radiation cause the wind. Upward and downward convection of wind are due to radiation effects. In general wind blows horizontally at high speeds. Anemometers or anemographs are the aids used for estimating wind speeds. These are installed in meteorological observatories at a height of 10 m to 30 m above the ground level.
Winds of speed over 80 km/h are referred to as very strong winds and are usually associated with cyclonic storms, dust storms, thunder storms or active monsoons. Cyclonic storms crossing the coasts in India are observed to quickly get weakened and move inwards in the form of depressions or lows. Sometimes we notice hurricanes of very high velocities for short durations in the summer months over North East India.
The observed wind speeds at any place vary in a large range. How a high wind pressure affects a building depends upon the presence of near by obstruction to air flow, the geographical location of the building, and on the characteristics of the building itself. We determine the effect of wind on the structure as a whole by considering the combined action of external as well as internal pressures acting upon it. We always assume that the wind loads act normal to be surface on which it acts.
Wind Speed and Pressure:
The wind speed is practically zero at ground level and increases to a maximum value at a height called the gradient height. The terrain condition at a site is responsible for the variation of wind speeds with height. At any height the wind speed does not really remain constant and so it is found convenient to arrive at an average value and a fluctuating component, fluctuating from the average value. The fluctuating component is called gust.
Basic Wind Speed:
Fig. 12.4 shows the basic wind speeds applicable at 10 m height above ground level for various zones of India. The basic wind speed shown is based on peak gust velocity averaged over a short interval of 3 seconds. These basic wind speeds have been determined for a 50 year return period. The Table 12.1 shows the basic wind speeds for some important cities of India.
Design Wind Speed VZ:
The basic wind speed Vb for any site shall be obtained from the map or table above and shall be modified to include the following effects to get the design wind velocity at any height (VZ) for the chosen structure:
(a) Risk level;
(b) Terrain roughness, height and size of structure; and
(c) Local topography.
The design wind speed VZ is given by-
VZ = Vb k1 k2 k3
where,
VZ = Design wind speed at any height Z, in m/s.
k1 = Probability factor (risk co-efficient)
k2 = Terrain, height and structure height factor
k3 = Topography factor.
Note:
Design wind speed up to 10 m height from mean ground level shall be considered constant.
Risk Coefficient (k1 Factor):
The suggested life period to be assumed in design and the corresponding k1 factors for different class of structures for the purpose of design is given in Table 12.2. In the design of all buildings and structures a regional basic wind speed having a mean return period of 50 years shall be used except as specified in the note of Table 12.2.
Note:
The factor k1 is based on statistical concepts which take account of the degree of reliability required and period of time in years during which these will be exposed to wind, that is life of the structure. Whatever wind speed is adopted for design purposes, there is always a probability (however small) that it may be exceeded in a storm of exceptional violence; the greater the period of years over which these will be exposed to the wind, the greater is the probability.
Higher return periods ranging from 100 to 1000 years (implying lower risk level) in association with greater periods of exposure may have to be selected for exceptionally important structures, such as, nuclear power reactors and satellite communication towers.
Equation given below may be used in such cases to estimate k1 factors for different periods of exposure and chosen probability of exceedance (risk level). The probability level of 0.63 is normally considered sufficient for design of buildings and structures against wind effects and the values of k1 corresponding to this risk level are given above.
where,
N = mean probable design life of structure in years;
PN = risk level in N consecutive years (probability that the design wind speed is exceeded at least once in N successive years), nominal value = 0.63;
XN, P = extreme wind speed for given values of N and PN; and
X50, 0.63 = extreme wind speed for N = 50 years and PN = 0.63.
A and B are coefficients having the following values for different basic wind speed zones:
Terrain, Height and Structure Size Factor (k2 Factor):
Terrain Selection of terrain categories shall be made with due regard to the effect of obstructions which constitute the ground surface roughness. The terrain category used in the design of a structure may vary depending on the direction of wind under consideration. Whenever sufficient meteorological information is available about the nature of the wind direction the orientation of any building or structure may be suitably planned.
Terrain in which a specific structure stands shall be assessed as being one of the following terrain categories:
(a) Category 1:
Exposed open terrain with few or no obstruction and in which the average height of any object surrounding the structure is less than 1.50 m.
Note:
This category includes open sea coasts and flat treeless plains.
(b) Category 2:
Open terrain with well scattered obstructions having height generally between 1.50 m and 10 m.
Note:
This is the criterion for measurement of regional basic wind speeds and includes airfields, open park lands and undeveloped sparsely built-up outskirts of towns and suburbs. Open land adjacent to sea coast may also be classified as category 2 due to roughness of large sea waves at high winds.
(c) Category 3:
Terrain with numerous closely spaced obstructions having the size of building structures up to 10 m in height with or without a few isolated tall structures.
Note 1:
This category includes well wooded areas, and shrubs, towns and industrial areas full or partially developed.
Note 2:
It is likely that the next higher category than this will not exist in most design situations and that selection of a more severe category will be deliberate.
Note 3:
Particular attention must be given to performance of obstructions in areas affected by fully developed tropical cyclones, vegetation which is likely to be blown down on defoliated cannot be relied upon to maintain category 3 conditions. Where such situation may exist, either an intermediate category with velocity multipliers midway between the values for category 2 and 3 given in Table 12.3 or category 2 should be selected having due regard to local conditions.
(d) Category 4:
Terrain with numerous large high closely spaced obstructions.
Note:
This category includes large city centres, generally with obstructions above 25 m and well developed industrial complexes.
Variation of Wind Speed with height for different terrains (k2 factor). Table 12.3 gives multiplying factors (k2) by which the basic wind speed given in the map shall be multiplied to obtain the wind speed at different heights, in each terrain category for different sizes of buildings/structures.
The buildings/structures are classified into the following classes:
Class A – Structures of size less than 20 m.
Class B – Structures of size between 20 m and 50 m.
Class C – Structures of size greater than 50 in.
Note:
Intermediate values may be obtained by linear interpolation, if desired. It is permissible to assume constant wind speed between 2 heights for simplicity.
Terrain Categories in Relation to the Direction of Wind:
The terrain category used in the design of a structure may vary depending on the direction of wind under consideration. Where sufficient meteorological information is available the basic wind speed may be varied for specific wind direction.
Changes in Terrain Categories:
The velocity profile for a given terrain category does not develop to full height immediately with the commencement of that terrain category but develop gradually to height (hx) which increases with the fetch on upwind distance (x).
Fetch and Developed Height Relationship:
The relation between the developed height (hx) and the fetch (x) for wind flow over each of the four terrain categories may be taken as given in Table 12.4.
Topography (k3 Factor):
The basic wind speed k6 given in the map takes account of the general level of site above sea level. This does not allow for local topographic features such as hills, valleys, cliffs, escarpments or ridges which can significantly affect wind speed in their vicinity. The effect of topography is to accelerate wind near summits of hills, or ridges and decelerate the wind in valleys or near the foot of cliffs, steep escarpments, or ridges.
The effect of topography will be significant at a site when the up wind slope (θ) is greater than 3°, and below that, the value of may be taken to be equal to 1.0. The value of k3 is confined in the range of 1.0 to 1.36 for slopes greater than 3°. The value of k3 varies with height above ground level, at a maximum near the ground and reducing to 1.0 at higher levels.
For a hill or ridge the k3 factor can be determined from the relation k3 = 1 + Cs, where C shall be taken as given in the table below.
where, l = Horizontal length covered by the upwind slope in the wind direction
s = Factor depending on the height H above the mean ground level
x = Horizontal distance from the summit or crest relative to the effective length Le.
The factor s should be determined from-
(a) Fig. 12.5 (b) for cliffs and escarpments, and
(b) Fig. 12.5 (c) for hills and ridges.
Any structure which lies in the affected zone (1.5 Le on the wind ward side and 2.5 Le on the leeward side) must be designed for this co-efficient. Note that the location of the structure is measured with respect to the crest.
In the above figures-
H = Height of the crest above ground level
X = Distance from the summit to the effective length
Le = Effective horizontal length of the hill.
Design Wind Pressure:
The design wind pressure at any height is given by-
3. Erection Load:
All loads required to be carried by the structure or any part of it due to placing or storage of construction materials and erection equipment including all loads due to operation of such equipment, shall be considered as ‘erection loads’. Proper provision shall be made to take care of all the stresses due to such loads.
Load Combinations on Roof Trusses:
A judicious combination of the working loads keeping in view of the probability of- (a) their acting together and (b) their disposition in relation to their loads and the severity of stresses or deformations caused by the combination of the various loads, is necessary to ensure the required safety and economy in the design of a structure.
The various loads specified above should therefore be combined in accordance with the stipulation in the relevant design codes.
In the absence of such recommendations, however, the following load combinations, given for general guidance, may be adopted:
(a) Dead load alone.
(b) Dead load + partial or full live load whichever causes the most critical condition in the structure.
(c) Dead load + wind or seismic loads.
(d) Dead load + such part of or whole of the specified live load whichever is most likely to occur in combination with the specified wind or seismic loads + wind or seismic loads.
(c) Dead loads + such parts of live load would be imposed on the structure during the period of erection + wind or seismic load + erection loads.
Note:
For design purposes, wind load and seismic forces shall be assumed not to act simultaneously. Both forces shall, however, be investigated separately and adequately provided for.
Purlins:
These are members spanning on the roof frames to support the roof coverings. Obviously, the spacing of the trusses is the span of the purlin.
Purlins consist of angles, channels, or I-sections. When angles and channels are used, the connections of the purlin to the rafters are made by using cleat angles. But, when I-sections are used, they are bolted directly to the rafters.
Loading on the Purlin:
Let W be the vertical load transmitted to a purlin. This is due to the dead load of the purlin, roofing, snow and live load.
Let We be the wind load on the purlin acting normal to the rafter.
Let θ be the inclination of the rafter with the horizontal.
Total load on the purlin normal to the rafter-
= we + w cos θ
Total load on the purlin parallel to the rafter-
= W sin θ
The purlin is thus subjected to biaxial bending. The bending stresses about both axes of bending are determined. The resultant stress shall not exceed the permissible value. When wind load is also considered it is usual to adopt a safe stress, 33⅓% in excess of the usual safe stress.
In the case of roofs whose slopes are less than 30° the purlin may be designed as follows:
(i) Width of the angle leg in a plane at right angles to the roof covering shall not be less than L/45.
(ii) Width of the angle leg parallel to the roof covering shall not be less than L/60
where, L = Span of purlin
= Spacing of the trusses
(iii) The maximum bending moment for the purlin
= WL/10
where, W = Total load on the purlin including the wind load. The loading on the purlin may be assumed as acting normal to the roof. Bending about the minor axis may be ignored.
Roof and Side Covering:
Corrugated Galvanised Iron sheets (G.I. sheets) and Asbestos Cement Sheets (A.C. sheets) are usually used as the covering material.
The G.I. sheets are available in curved condition also to a radius not less than 375 mm.
The two usual sizes of G.I. sheets are:
(i) 8 corrugations 75 mm wide, 19 mm deep
Overall width = 660 mm
(ii) 10 corrugations 75 mm wide, 19 mm deep overall width
Overall width =810 mm
In order to make the joints waterproof side laps of 1.5 to 2 corrugations are usually given. Where the slopes exceed 20° an overlap of at least 150 mm shall be provided.
The G.I. sheets mentioned above are available in different lengths ranging from 1.20 metres to 3 metres increasing by 0.15 m.
These sheets are connected to the purlins.
A.C. sheets are weaker in strength than G.I. sheets. But A.C. sheets are better insulators. These are usually available in two shapes (Fig. 12.14).
These are available in lengths of 1.50. 1.80, 2.10, 2.4. 2.7 and 3 metres. These sheets may be spanned safely up to a span of 1.68 m. For a good arrangement a longitudinal overlap of at least 150 mm and a side overlap of at least 1 corrugation may be provided. The Trafford sheets are available with a width of 1 metre (actually 1.02 m) between centres of end corrugations. The corrugated sheets are available with a width of 1 metre (actually 1.07 m).
For calculating the wind load on individual structural elements like roofs and walls and individual cladding units, it is essential to take account of the pressure difference between opposite faces of such elements. For clad structures, it is necessary to know the internal as well as external pressures.
The wind load F acting normal to the individual structural element or cladding unit is given by-
F = (Cpe – Cpi)Apd
where,
F = Net wind force on the element
Cpe = External pressure coefficient
Cpi = Internal pressure coefficient
A = Surface area of the structural element or cladding unit and
and P = Design wind pressure
Note:
Positive wind load indicates the force acting towards the structural element and negative wind load indicates the force acting away from the structural element.
Fig. 12.40 shows an elevation and plan of a building with pitched roof. Four zones E, F, G and H are shown. The external pressure coefficient for the various zones are shown in the Table 12.7.
Internal Pressure Co-Efficient (Cpj):
The internal air pressure in a building depends upon the degree of permeability of cladding to the flow of air. The internal pressure may be positive or negative depending on the duration of flow of air in relation to the openings in the buildings.
In the case of building where more than 20% of wall area is open the internal pressure coefficients shall be taken as indicate is Fig. 12.36.
Advantages of Steel Roof Trusses:
Steel trusses have the following advantages:
(i) Steel trusses have good strength and may be economical to beams for large spans
(ii) They can be fabricated easily
(iii) They are most suitable for long spans
(iv) Angles, channels etc. can be easily transported from place to place
(v) They are free from attack by white ants and dry rot
(vi) Steel members are fire resistive, and
(vii) Steel trusses can be erected fast and easily.