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CHAPTER 5
TRUSSES
5.1 Introduction
A truss is an arrangement of bars or members connected at joints. It is essentially a
triangulated system of (usually) straight interconnected structural elements. In many
cases, such as roof trusses and lattice girders, it is assumed that, for design purposes, no
significant moments are generated at the connections-the connections are often assumed
to be nominally pinned.
Truss can be fabricated from various steel sections available and joined by welding or
bolting. Truss can be used in Bridge, roof structure, members supporting heavy loads
and members with long span. There are 2 types of truss; planar truss and space truss as
shown in Figure 5.1 and 5.2 respectively. A frame which has all its members ad applied
forces are in one plane is called a plane frame or 2D truss, while a three-dimensional
frame is called a space frame.
Figure 5.1
Figure 5.2
5.2 Typical members
Truss, lattice girder and bracing members for buildings are selected from:
Open sections, primarily angles, channels, tees and joints.
Compound sections, i.e. double angle and channels.
Closed sections, in practice structural hollow sections.
a. Open sections
b. Compound sections
c. Closed sections
Figure 5.3
Terminology that used in truss system is shown in Figure 5.4. In order to facilitate weld
connection for truss system, can be achieved by limiting the number of members at a node to
the main chord member and at most two subsidiary web members and limiting the minimum
angle between members to 30o.
Figure 5.4: Design of Roof Truss System
Under the action of the loading system, the frame tends to take the form in dotted lines, i.e. A
and B move outwards putting member AB in tension, and C moves downwards putting
members AC and BC in compression. AC and BC are termed struts and AB a tie.
Figure 5.5
5.3 Different shapes of trusses
A large range is available for the general shapes of the trusses. Some of the commonly used
shapes are shown in Table 5.1.
Tie
Table 5.1
5.4 General procedure in simple roof truss design
Figure 5.6
5.5 Aspects of truss design for roof structure
In order to get a good structural performance, the ratio of span to truss depth should be chosen
in the range 10 to 15. 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).
Joints in structural steelwork are invariably bolted or welded, and although such joints will in
fact transmit some moments from member to member, these moments are usually ignored in
the determination of the forces acting in the frame. Thus when a triangulated frame is loaded at
the joints, the internal forces developed in its members are axial tension or compression. If a
local load is applied to a member between its end joints, however, bending moments and shear
forces are induced in that member and the effects of these must be considered in the design of
that member. The resulting joint forces are assumed as simple reactions applied to the frame at
the joints. In general when truss is subjected to a given loading, the force developed in each
member is either tensile or compressive and in certain cases even bending.
Trusses support purlins, the member being secondary members lay longitudinally along the
rafter, which support the roof covering (Fig. 5.7). The roof load is transferred to the truss at
joints by a series of purlins (members running between the trusses). The purlins may also
provide lateral support to the top chord.
Truss may either supported by columns or walls. The distance between trussed is termed as
bays. For roof truss bays are economically spaced between at about 4.5m to 6m. The internal
bracing members of a truss should be so arranged that, under vertical loading, the longer
members are in tension and the shorter members in compression. The arrangement of the
internal bracing depends on its span. Rafters are normally divided into equal panel lengths and,
ideally, the purlins should be supported at the node points, so that the rafters are subjected only
to axial forces (Fig. 5.8). However, in some cases purlins may have to be supported between
node points (Fig. 5.9) the rafters then have to be designed for bending and shear in addition to
axial forces as in sub topic 5.3
Figure 5.7
Figure 5.8
Figure 5.9
5.6 Loads on trusses
In the normal design in practice there are three basic loads:
Permanent Actions: cladding, insulation, ceiling, self weight of trusses and purlins
Variable Actions: May be taken from any relevant codes. For roofs the action may be
summarized as follow;
• 0.75 kN/m2 – only access to the roof for maintenance and repair
• 1.5 kN/m2 – where there is access in addition to that in above
Wind Actions: The guide to estimate these actions are given by BS 6399: part 2 or
CP3:Ch V: Part 2. Wind action depends on the location of buildings, its dimension as
well as slope. The wind actions acts normal to the roof surfaces. Wind may cause the
uplift on the roof, which may cause load reversal in truss member.
There are four combinations of the above loads:
Dead load alone
Dead load plus imposed load
Dead load plus imposed load plus wind load
Dead load plus wind load
Combination 2 (dead load plus imposed load) is normally assumed to be the design criterion,
because in most ‘normal’ roof truss designs this is the case. However, in practice all the above
combinations must be considered, particularly if the wind load is high. If the force due to the
wind is greater than that due to the dead load, then combination 4 (dead load plus wind load)
above becomes important, because stress reversal occurs, i.e. a member that was a tie under a
dead load condition now becomes a strut and vice versa. Combination 4 should always be
checked when a lightweight roof cladding is used. It should also be noted that any services load
applied to the truss should not be taken into account when considering uplift as there is no
guarantee that it will be present during high wind (this is a requirement of BS 6399: Part 1).
Purlins are those members in a truss system which carries the roof sheets and transfer the load
to the rafters. The analysis of truss is carried out to determine the axial forces in the members
and in certain cases the bending moment due to the applied loads.
5.7 Analysis of trusses
5.7.1 Primary forces
The primary forces in all members are calculated by applying loads at the nodes and
assuming the truss is pin-jointed and statically determinate. Several manual methods
analysis is available such as joint resolution, force diagram and method of sections. The
axial forces in members may be of tensile or compressive.
5.7.2 Secondary Stresses
In many cases in the design of trusses, it is not necessary to consider secondary stresses.
These stresses should however, be calculated for heavy trusse used in industrial
buildings and bridges.
These secondary stresses are caused by:
a. Load applied between the nodes of the truss.
b. Eccentricity at connections
c. Moments resulting from rigid jointed and deflection of trusses.
Eccentricity at connections
Trusses should be detailed so that either the centroidal axes of the members or the bolt
gauge lines meet at a point at the nodes. Otherwise, members and connections should be
designed to resist the moments due to eccentricity. These moments should be divided
between members meeting at joint in proportion to their rational stiffnesses. Stresses
due to small eccentricities are often neglected.
Load applied between the nodes of the truss.
This solution often occurs to the rafter of the trusses where the purlins are not
positioned at the nodes. Bending moment induced by this situation should be calculated
and combined to those due to the primary axial loads and included in design.
In most cases it is not necessary to consider secondary stresses in the design of trusses
and lattice girder. However for heavy trusses used in bridges and industrial buildings,
secondary stresses ought to be calculated and considered. The calculation may be
carried out by moment redistribution or computer analysis. Alternatively bending
moment for the top chord where the purlins are not positioned at nodes may be
conservatively taken as wL2/6 (clause 4.10 BS 5950) where w is the total load per unit
length applied perpendicular to the rafter and L is the length between nodes.
The top chord in this case is designed for axial load and bending. The calculation is first
to analyses the truss for the loads applied at the nodes which gives the axial forces in
the members. Then a separate analysis is made for bending in the top chord which is
considered as a continuous beam.
Figure 5.10: Loads applied between truss nodes
For the design of members in trusses where secondary bending stresses are insignificant, the
following assumptions are made:
For the purpose of analysis, the joints are taken as pinned.
For calculating effective lengths, the fixity of connections and rigidity of adjacent
members may be taken into account.
Where the exact position of point loads on the rafter relative to the connection of the
web members is not known, the local bending moment may be taken as WL/6.
In accordance with Clause 5.8.2 of Part 1.1 of Eurocode 3 [2], the buckling length of
chord members may be taken as the distance between connections to web members in
the plane and the distance between purlins or ties out of plane of the truss.
Two common internal truss members are the single angle discontinuous strut connected to a
gusset or another member and the double angle discontinuous strut connected to both sides of
a gusset or another member. These should be connected by at least two bolts or the equivalent
in welding. Eurocode 3: Part 1.1: Clause 5.8.3 states that the end eccentricity may be ignored
and the struts designed as axially loaded members in accordance with that clause [1].
5.8 Design of purlins
They may be design as beams especially for flat roof where the slope of the rood is less
than 10o. Alternatively empirical method is applied if the condition suggested in clauses
4.12.4.2 and 4.12.4.3 in BS 5950 are met.
Purlins are those members in truss system which carries the roof sheets and transfer the
load to the rafters. It is normally placed perpendicular to the rafters and sag rod may be
added to reduce bending moment of purlins.
Clause 4.12.4.3
Purlins must satisfy:
The slope of the roof should be less than 30% from the horizontal
Loading on purlins should be uniformly distributed
Limitation of section modulus Z about its axis, member dimension D and B are given in
Table 27 BS5950.
Table 27 BS5950
Design condition for purlins
1. Minimum steel grade of S275
2. Unfactored load should be used
3. Uniform loading
4. The slope of the roof should not exceed 30o from the horizontal
5. Section modulus Z, and dimension B and D should not be less than the respective values
given in Table 2.7 BS 5950: part 1: 2000.
Example 5.1: Analysis of Truss
Given:
◦ Imposed load on plan, Qk = 0.75 kN/m2
◦ Dead load on plan, Gk = 3 kN/m2
◦ Spacing between trusses St = 5m
◦ Purlin spacing Sp = 2m
Determine the loading transfer to the node.
Solution:
Design load per unit area,
q = 1.4Gk + 1.6Qk
= 1.4(3kN/m2) + 1.6(0.75kN/m2)
= 4.2 + 1.2 = 5.4 kN/m2
Area of load transferred to intermediate node, A = Sp St = 5m 2m = 10m2
Point load, P = q A = 5.4kN/m2 10 m2 = 54 kN
Example 5.2 : purlin design
Loading summary of the truss
Example 5.2:
Design the purlins using single angle sections for the sloping truss given. Using the following
data:
Slope = 1:25
Spacing between trusses = 5.5 m
Distance between purlins = 1.6 m
Permanent actions = 0.3 kN/m2 (on slope)
Variable actions = 0.75 kN/m2 (on plan)
Design by empirical method (no sag rod at the middle)
From Table 2.7: BS 5950: Part 1: 2000
Therefore, use single angle;
Design by beam method (Clause 6.2.5 En 1993-1-1: 2005)
Section should at least be Class 3 section
Therefore, use single angle
Check the deflection:
Allowable deflection (Table 8: BS 5950: Part 1: 2000)