1

TRUSS DESIGN

DR NORWATI
JAMALUDDIN
2
 3

1. A truss is an arrangement of bars or

members connected at joints.
2. It is essentially a triangulated system of
(usually) straight interconnected structural
elements.
 4

INTRODUCTION

1. Truss can be fabricated from various steel sections

I. Open sections, primarily angles, channels, tees and
joints.
II. Compound sections, i.e. double angle and
channels.
III. Closed sections, in practice structural hollow
sections.
 5

•Open sections

•Closed sections

•Compound sections
 6

INTRODUCTION

2. Generally, the trusses act in one plane called

planar truss and usually designed as pin-jointed
frames (although some main members may be
designed as continuous.
3. Members lie is 3-dimensions truss the truss is known
as a space frame.
 7

Planar truss
8
9
 10

Terminology
Terminology 11
Terminology 12
Terminology 13
 14
Basic fundamental

1. 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.
 15
Design Consideration

1. In order to get a good structural performance, the

ratio of span to truss depth should be chosen in the
range 10 to 15.
2. 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
(IDEAL!! But commonly not always possible)
•
 16
Design Consideration

• The orientation of the diagonal members should be

such that the longest members are subject to tension
(the shorter ones being subject to compression).
2. 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.
3. Vierendeel trusses- could not assuming for pin-
jointed during analysis.
17
18
 19

Design Consideration

4. 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.
5. 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.
 20

Design Consideration

6. 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.
7. However, in some cases purlins may have to be
supported between node points the rafters then
have to be designed for bending and shear in
addition to axial forces.
 21
Analysis : Internal Force

1. Thus when a triangulated frame is loaded at the joints,

the internal forces developed in its members are axial
tension or compression.
2. 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.
3. 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.
 22

figure 1 figure 2 figure 3

truss method of section method of joint
23
 24

Purlin Design
 25

Purlin Design

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.
 26
Purlin Design

2. Trusses support purlins, the member

being secondary members lay
longitudinally along the rafter, which
support the roof covering.
3. The roof load is transferred to the truss
at joints by a series of purlins (members
running between the trusses).
4. The purlins may also provide lateral
support to the top chord.
 27

Truss - Loads

1. In the normal design in practice there are three basic

loads:
i. Permanent Actions: cladding, insulation, ceiling,
self weight of trusses and purlins
ii. 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
Truss - Loads 28

1. 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.
2. EN 1991-1-4: Eurocode 1 - Wind actions
 29

Truss - Loads

1. There are four combinations of the above loads:

i. Dead load alone
ii. Dead load + imposed load
iii. Dead load + imposed load + wind load
iv. Dead load + wind load

2. 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.
 30
Design of purlins

1. 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.
31
 32

Design of purlins

2. 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 must satisfy:
i. The slope of the roof should be less than 30%
from the horizontal
ii. Loading on purlins should be uniformly
distributed
iii. Limitation of section modulus Z about its axis,
member dimension D and B are given in Table
27 BS5950.
 33

BS 5950
 34

Design of purlins

Design condition for purlins

Minimum steel grade of S275

Unfactored load should be used
Uniform loading
The slope of the roof should not exceed 30o from
the horizontal
Section modulus Z, and dimension B and D should
not be less than the respective values given in
Table 27 BS 5950: part 1: 2000.
 35

Design of purlins
Design of purlins 36

Example 5.1: Analysis of Purlins load

Given:
Imposed load , Qk =0.75kN/m2
Dead load , Gk = 3 kN/m2
Spacing between trusses St = 5m
Purlin spacing Sp = 2m
Determine the loading transfer to the node.
 37

Design of purlins

a
b
c
d

Purlin

Apex Apex
a

b St
Purlin
spacing, Sp Sp

c
Truss
d

Truss PLAN
spacing, St St VIEW
 38
Design of purlins

Solution:
Design load per unit area,
q = 1.35Gk + 1.5Qk
= 1.0(3kN/m2) + 1.0(0.75kN/m2)
= 3.75 kN/m2
Area of load transferred to intermediate node,
A = Sp  St = 5m  2m = 10m2
Point load, P = q  A = 3.75kN/m2  10 m2 = 37.5 kN
 39

kN
kN kN
kN kN
kN kN

b
c
d
 40
Example 5.2 : purlin design
 41
Example 5.2 : purlin design
 42

1.35Gk+1.5Qk
P=19.1 kN
 43

P=19.1 kN
P=19.1/2 =9.55 kN
44
 45

Analysis of internal forces

Primary forces
1. The primary forces in all members are
calculated by applying loads at the
nodes and assuming the truss is pin-
jointed and statically determinate.
2. 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.
 46
Analysis of internal forces

Secondary Stresses
1. In many cases in the design of trusses, it is not
necessary to consider secondary stresses.
These stresses should however, be calculated
for heavy trusses used in industrial buildings
and bridges.
2. These secondary stresses are caused by:
1. Load applied between the nodes of the truss.
2. Eccentricity at connections
3. Moments resulting from rigid jointed and deflection
of trusses.
 47

Eccentricity at connections

1. 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.
2. Stresses due to small eccentricities are often
neglected.
 48

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.
 49

Load applied between the nodes of the truss

1. 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.
2. The calculation may be carried out by moment
redistribution or computer analysis.
 50

Load applied between the nodes of the truss

3. The top chord in this case is designed for axial

load and bending.

4. 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.
 51

Load applied between the nodes of the truss

5. Alternatively bending moment for the top chord

where the purlins are not positioned at nodes may
be conservatively taken as wL 2 /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.
 52
General procedure in simple roof truss design
 53

Load applied between the nodes of the truss

 54
Design of truss members - tension

1. Steel tension member are probably the most

common and efficient member. This is due to the
entire cross section is subjected to almost
uniform stress.
2. As the tensile force increases on a member it will
straighten out as the load is increased.
3. For a member that is purely in tension, we do not
need to worry about the section classification
since it will not buckle locally.
 55

Design of truss members - tension

4. Tension members are generally designed using

rolled section, bars or flats.

5. Flats are higher in flexibility and their slenderness

should be limited.

6. In general, rolled sections are preferred and the

use of compound sections is reserved for larger
loads or to resist bending moments in addition to
tension.
 56

7. In reference to Cl. 6.2.3, EN 1993-1-1:2005, the

design value of tension force, at each cross
section shall satisfy;
 57

8. The tensile resistance is limited by the lesser of:

- Design Plastic Resistance Npl,Rd

- Design Ultimate Resistance Nu,Rd

Nu,Rd is the design ultimate resistance of the net

cross-section, and is concerns with the ultimate
fracture of the net cross-section, which will
normally occur at fastener holes.
 58

 Partial Factors γM

Net section
A tension member is often connected to
main or other member by bolt or welds. For
bolts connection, the members with bolt
holes, the net area should be taken into
consideration. Holes in the member will
cause stress concentration.
 59
 Characteristic Strengths fy and fu
The UK National Annex says you should get
the values of fy and fu from the product
standards. For hot-rolled sections you can use
the table below. Or Table 3.1
 60
Anet for fasteners holes
 61
Anet for non-staggered fasteners

Anet = A – Σd0t
 62
Anet for staggered fasteners
 63
 Anet for Non staggered fasteners
clause 6.2.2.2 (4)
 64

 The total area to be deducted should be taken as

the greater of:
a) The maximum sum of the sectional areas of the
holes on any line perpendicular to the member
axis
b)

where:
 t is the thickness of the plate
 p is the spacing of the centres of the same two holes measured perpendicular
to the member axis
 s is the staggered pitch of the two consecutive holes
 n is the number of holes extending in any diagonal or zig-zag line progressively
across the section
 d0 is the diameter of the hole
 65

Tension members: Single Angles

For angles connected by 1 leg and other

unsyammetrically connected members in
tension (i.e. T or channel sections), the
eccentricity in joints and the effects of the
spacing and edge distances of the bolts
should be taken into account in determining
the design resistance (Cl. 3.10.3, EN 1993-1-8:
2005)
 66

 A single angle in tension connected by a single row of

bolts in one leg may be treated as concentrically
loaded over an effective net section. The design
ultimate resistance should be determined as follows;
Refer to EN 1993-1-8 (clause 3.10.3)

With 1 bolt
 67

With 2 bolts

With 3 bolts
 68

Values of reduction factors β2 and β3 can be found in Table 3.8

BS EN 1993-1-8
Tension Member Design Steps Summary
69

1. Determine the design axial load NEd

2. Choose a section
3. Find fy and fu from the product standards
4. Get the gross area A and the net area Anet
5. Substitute the values into the equations to work out Npl,Rd and Nu,Rd
For angles connected by a single row of bolts, use the required
equation to work out Nu,Rd from EN 1993-1-8 which will depend on
the number of bolts.
The design tensile Resistance is the lesser of the values of Npl,Rd and
Nu,Rd
7. Carry out the tension check:
 70

Design resistance of the cross section

For a compression member, several buckling

modes must be considered.

For each buckling mode, the buckling

resistance is obtained from EN 1993-1-1[3] 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.
 71

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.
According to Annex BB §BB.1 of EN 1993-1-1: 72

• 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 (EN 1993-1-1 §BB.1.1 (4)).

(An exception is made by Annex BB for angle truss members,

for which a different evaluation is given; it is not specified in
this annex if the particular rule also concerns members
made up to two pairs of angles: by way of simplification, it is
recommended that a buckling length of 0.9 times the
length of the axis be retained.)
 73

According to Annex BB §BB.1 of EN 1993-1-1:

• For buckling out of plane of the truss beam,

the buckling length is taken equal to the
system length.
 74

Design resistance of the cross section

In reference to Cl. 6.2.4: EN 1993-1-1:2005,

the design value of compression force, at
each cross section shall satisfy:
 75

Buckling resistance

In reference to Cl. 6.3: EN 1993-1-1:2005, a

compression member should be verified
against buckling as follows;
Detailing requirement for connection
truss structure using two angles, or two channels 76

to ensure that such built-up members will behave as

sole members in the flexural buckling mode, the two
components are connected by small battens.

Since the role of these members is to prevent relative

slip of one component compared with the other,
they must be connected without slack. The gap
between the angles, and the thickness of the battens,
should be the same as the thickness of the gusset to
which the built-up member is connected.
 77

Members composed of two angles

 Detailing requirement for connection
78

The maximum spacing of the connections

between members is limited by EN 1993-1-1 to
15 times the minimum radius of gyration of the
isolated component.
79
80
81
82
83
84
85
86
87
88
89
90
91
92