Ch8 Truss Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally Abu-Hamd)

Chapter 8: Truss Bridges
CHAPTER8
______________________________________________________________
TRUSS BRIDGES

Steel Bridges
CHAPTER8
TRUSS BRIDGES
8.1 TRUSS TYPES & CHARACTERISTICS
8.1.1 GENERAL
A truss is essentially a triangulated assembly of straight members. A planar
truss may be regarded as a deep girder, where the girder flanges are replaced
by the truss chords and the web plate is formed by an open system of web
members. A truss may be used to replace a girder in several cases: as a
simply supported or continuous girder; as an arch; or in the deck of a
suspension or a cable-stayed bridge; see Fig. 8.1 and Fig. 8.2.
In a typical truss, the centroidal axes of all members are straight and
concurrent at the joints. Because the truss is loaded only at the joints; applied
loads are resisted primarily by axial forces induced in the truss members.
Bending moments are generally small and have a minor effect on the axial
forces. Ideally, all member bending moments should be close to zero, a
condition that can only be achieved by using frictionless pins at the joints. In
practice, however, most members are rigidly connected at the joints, resulting
in small moments which are usually neglected, except in some few special
cases.
A truss bridge has thus two major structural advantages:
(a) the primary member forces are axial loads,
(b) the open web system allows a greater overall depth than in an
equivalent solid web girder. This increased depth gives more rigidity to
the bridge and results in reduced deflections.

Chapter 8: Truss Bridges 313
Fig. 8.1 Applications of Trusses in Bridges

Steel Bridges
Fig. 8.2 Examples of Truss Bridges

8.1.2 TRUSS BRIDGE COMPONENTS
A truss bridge of conventional design consists of the following parts; see
Fig. 8.3;
(a) a deck slab or similar structural system,
(b) longitudinal stringers directly supporting the deck slab,
(c) cross beams at truss panel points carrying the load from the
longitudinal stringers,
(d) the two main truss systems,
(e) lateral bracing systems in the planes of the upper and lower
chords,
(f) end sway frames transmitting the reactions of the lateral bracing
systems to the bridge supports,
(g) additional intermediate sway frames distributing the transverse
wind loads to the lateral systems and keeping the system stable
during erection.
For through trusses, a system of upper wind bracings is always provided.
This upper bracing provides rigidity, stabilizes the compression chord, and
carries the main part of the wind loads to the bridge end sway frames, called
portal frames. These end frames are designed as rigid frames to transmit the
load from the upper bracing to the bridge supports.
Fig. 8.3 Components of a Through Truss Bridge

Steel Bridges
8.1.3 TRUSS FORMS
The most common forms of bridge trusses are:
(1) Pratt or N-Truss (Fig. 8.4 a):
In this system the diagonals are always subjected to tension while the
verticals carry the shear in compression only. This case can represent an
advantage since the shorter members carry the compression.
(2) Warren Truss (Fig. 8.4 b):
Where the chords carry the bending in tension and compression and the
diagonals carry the shears, also in tension and compression. The vertical
members carry only panel loads.
(3) Trusses with Curved chords (Fig. 8.4 c)
Truss Chords may be placed on a curved alignment to carry part of the
shear and to reduce the forces in the diagonals. This alignment results in a
slight increase in the fabrication cost which is offset by material savings.
(4) Subdivided Panels ( Fig. 8.4 d):
The economic height-span ratio is about one-sixth to one-eighth, according
to loading and span length. With increasing span lengths, truss height also
increases. Thus, both the warren and Pratt trusses will result in long panel
length if the diagonal inclination remains about 45P
o
P. An alternative is to
subdivide these trusses as shown in Fig. 8.4 d.
(5) K – Truss (Fig. 8.4 e:)
Subdivided trusses develop high secondary stresses. A better solution may
be obtained by using K-trusses to keep the desired inclinations, accommodate
the required truss depth, and also limit the strength span.

d =
span
7
(0.5-0.7) d
"d" Subdivided Truss
"e" K-Truss
"a" N-Truss
"b" Warren Truss
"c" Truss with Curved Chord
Fig. 8.4 Common Forms of Trusses used in Bridges
8.1.4 SPECIAL CHARACTERISTICS
8.1.4.1 Truss Depth
For simple span trusses, experience has shown that a depth-span ratio of
1 : 6 to 1 : 8 yields economical designs. For continuous trusses a depth-span
ratio of 1 : 12 should be satisfactory. Because of the lighter live loads for

Steel Bridges
roadway bridges, trusses are rarely used. If trusses are used for roadway
bridges, somewhat shallower truss depths may be used.
The truss depth shall be sufficient to limit the elastic deflections due to live
load without impact to L/600 for roadway bridges and L/800 for railway
bridges and L/300, where L = bridge span.
8.1.4.2 Economic Truss Spans
Truss bridges are generally comparatively easy to erect because light
equipment often can by used. Assembly of bolted joints in the field is
relatively costly, which may offset some of the savings in steel.
Consequently, trusses seldom can be economical for roadway bridges with
spans less than about 130 m. Railway bridges, however, involve different
factors, because of the heavier loading. Trusses generally are economical for
railway bridges with spans greater than 45 m.
8.2 DESIGN OF TRUSS MEMBERS
8.2.1 Determination of Member Forces:
Structural analysis techniques may be applied to the bridge system to find
the effect of applied loads and forces acting on the truss members. The
following assumptions are usually made:
1- Members are connected at their ends by hinges,
2- Loads are applied at the truss joints,
3- In case of a curved member, the additional bending moment induced
due to member curvature should be calculated,
4- Secondary stresses due to joint rigidity and bending moments due to
own weight are neglected expect in trusses with subdivided panels,
trusses with loads acting between joints, and trusses with member
height more than one tenth of the member length.
Load cases that yield maximum straining actions should be considered
carefully. The resulting forces in the truss members are axial compression
and tension. Members are then designed using the allowable stress method.
Special design considerations are outlined next.

8.2.2 Cross Section Shapes for Truss Members:
Members for bridge trusses generally consist of; see Fig. 8.5:
(a) Box sections made of plates or rolled sctions by welding;
(b) l-sections, either rolled or built up.
Box sections are usually used for chord members and heavy web members.
I-sections are usually used for light web members. Box sections present some
difficulties in their connection with gusset plates. Bolted connections with
gusset plate shall require the existence of temporary erection openings in the
box section to allow for bolt tightening. These openings shall be closed after
the truss erection. If design permits, use of I-sections for chord members
results in much easier connections.
Top Chord Bottom Chord
Diagonals and Verticals
b
b
b b
Fig. 8.5 Common Shapes of Bridge Truss Members

Steel Bridges
8.3 GENERAL DESIGN PRINCIPLES
8.3.1 Geometry
For short and medium spans, it will generally be found economic to use
parallel chords to keep fabrication and erection costs down. However, for
long continuous spans, a greater depth is often required at the piers.
Secondary stresses should be avoided as far as possible by ensuring that the
neutral axes of all intersecting members meet at a single point, in both
vertical and horizontal planes. This will not always be possible, e.g. cross
girders will be deeper than the bottom chord and bracing members may be
attached to only one flange of the chords.
8.3.2 Compression Chord Members
These members should be kept as short as possible and consideration given
to additional bracing if economical. The effective length for buckling in the
plane of the truss is normally not the same as that for buckling out of the
plane of the truss, depending on the arrangement of upper bracings. This
effect can be further complicated in through trusses where horizontal bracing
may be provided at mid panel points as well as at the main nodes. When
making up the section for the compression chord, the ideal disposition of
material will be one that produces a section with radii of gyration such that
the ratio of effective length to radius of gyration is the same in both planes. In
other words, the member is just as likely to buckle horizontally as vertically.
8.3.3 Tension Chord Members
Tension members should be as compact as possible, but depths have to be
large enough to provide adequate space for bolts at the gusset positions. The
width out of the plane of the truss should be the same as that of the verticals
and diagonals so that simple lapping gussets can be provided without the
need for packing.
It should be possible to achieve a net section about 85% of the gross section
by careful arrangement of the bolts in the splices. This means that fracture at
the net section will not govern for common steel grades.
As with compression members, box sections would be preferable for ease
of maintenance but open sections may well prove cheaper.

8.3.4 Vertical and Diagonal Members
These members should be all the same width normal to the plane of the
truss to permit them to fit flush with or to be slotted inside the top chord
(where the top-hat section is used) and to fit flush with the bottom chord.
However, the width of the diagonals in the plane of the truss should be
reduced away from the supports by about 75 mm per panel. This reduction
may mean that some members are understressed. It is often possible to use
rolled sections, particularly for the lightly loaded members, but packs will
probably be required to take up the rolling margins. This fact can make
welded members more economic, particularly on the longer trusses where the
packing operation might add a significant amount to the erection cost.
Aesthetically, it is desirable to keep all diagonals at the same angle, even if
the chords are not parallel. This arrangement prevents the truss looking over-
complex when viewed from an angle. In practice, however, this is usually
overruled by the economies of the deck structure where a constant panel
length is to be preferred.
8.3.5 Wind Bracings
Truss bridges should be provided with top and bottom lateral bracing
systems as shown in Fig. 8.3 to carry wind and other lateral loads acting on
the bridge. These lateral bracing systems are also effective in providing
lateral supports to the main truss compression chords. In addition, transversal
bracing should be provided at truss ends to transmit lateral loads from lateral
bracing systems to the bridge supports. These transversal bracings take the
form of portal frames for through bridges and cross frames for deck bridges.
Similar intermediate portal or cross frames are used to provide space rigidity
to the bridge and help in distributing lateral loads.
Forces to be considered in bracing design include wind, seismic loads, and
centrifugal forces. The bridge truss chords act as the chords of the lateral
system. In general, the design of these members is governed by slenderness
ratio conditions. Because of the long unbraced lengths of these members, it is
often advantageous to consider the cross bracing acting in tension only and
the neglect its resistance to compression.

Steel Bridges
8.4 DESIGN OF TRUSS MEMBERS
8.4.1 Selection of Member Dimensions:
1. Member height “h” and distance between gussets “b” can be selected as
follows:
h)
4
5
4
3
(b
10
LengthPanel
1512
LengthPanel
h
−=
≤
−
=
“b” should be constant for all members.
“h” is usually the same for top and bottom chord members.
2. Top chord is symmetrical about y-axis, Bottom chord is usually
symmetrical about x and y axes.
3. Start the design with the members with maximum forces.
8.4.2 Slenderness Ratios:
The maximum allowable slenderness ratios “L/i”, as per the Egyptian Code
of Practice are as follows:
Railway Roadway Bracing Hanger
Compression 90 110 140 ---
Tension 160 180 200 300
8.4.3 Minimum Plate Thickness:
The minimum plate thickness to be used is as follows:
)ElementStiffened(
F
64
t
w
&)ElementdUnstiffene(
F
21
t
w
YY
≤≤
where w is the plate width from the points of fixation (welds or bolts)

8.4.4 Allowable Stresses:
According to the Egyptian Code of Practice for the allowable stresses of
Tension and Compression Members:
Grade of Steel Allowable Stresses (t/cmP
2
P)
0BTension
Member
1BCompression Member
100〉
i
L
100〈
i
L
St. 37
1.4
2
7500






i
L
2
000065.04.1 





−
i
L
St. 44
1.6 2
000085.06.1 





−
i
L
St. 52
2.1 2
000135.01.2 





−
i
L
8.4.5 Buckling Length of Truss Bridge Members:
i) According to the Egyptian Code of Practice for determination of the
buckling length of truss bridge members:

Steel Bridges
Buckling Length of Truss Bridge Members
Member Effective Buckling Length LR
e
3BIn-Plane 2BOut-of-Plane
Compression
Chord Laterally
Braced
Compression
Chord Unbraced
Chord
Members
0.85 The
Member Length
0.85 The distance
between lateral
bracing members
1.25 the distance
between U
frames or 0.75
Truss Span
WebSystem
Single
Web
System
0.7 The Member
Length
0.85 The
Member Length
1.0 The Member
Length
Multiple
Web
System
0.85 The
Member Length
0.7 The distance
between
intersection with
Main Chords
0.85 The distance
between
intersection with
Main Chords
ii) For Pony Trusses:
For a bridge truss where the compression chord is laterally restrained by
U-frames composed of the cross girders and verticals of the trusses, the
effective buckling length of the compression chord (ℓR
bR) is

ℓR
bR aaIE5.2 4
y ≥δ⋅⋅⋅⋅=
Where,
E = The Young’s modulus (t/cm2).
Iy = The moment of inertia of the chord member about the Y-Y axis
shown in Figure 4.2 (cmP
4
P).
a = The distance between the U-frames (cm).
δ = The flexibility of the U-frame: the lateral deflection near the mid-
span at the level of the considered chord’s centroid due to a unit
load acting laterally at each chord connected to the U-frame. The
unit load is applied only at the point at which δ is being calculated.
The direction of each unit load shall produce a maximum value for δ
(cm).
Force
Unit
Force
Unit
Y
11
2
2d1d
Y
Figure 8.6 Lateral Restraint of Pony Truss Chords by U-Frame
The U-frame is considered to be free and unconnected at all points except
at each point of intersection between cross girder and vertical of the truss
where this joint is considered to be rigidly connected.
In case of symmetrical U-frame with constant moment of inertia for each
of the cross girder and the verticals through their own length, δ may be taken
from:
2
2
2
1
3
1
EI2
Bd
EI3
d
+=δ

Steel Bridges
Where:
d = The distance from the centroid of the compression chord to the
nearest face of the cross girder of the U-frame.
d = The distance from the centroid of the compression chord to the
centroidal axis of the cross girder of the U-frame.
IR
1 = The second moment of area of the vertical member forming the arm
of the U-frame about the axis of bending.
IR
2 = The second moment of area of the cross girder about the axis of
bending .
B = The distance between centres of consecutive main girders connected
by the U-frame.
The verticals of the pony truss are designed to carry a bending moment
in addition to the normal forces induced due to regular loads. The bending
moment is estimated as:
H
100
C
M = ,
where C is the average compression force in the top chord members
intersecting the vertical member, and H is the distance between the top chord
and the top of the cross girder at the vertical member.
8.4 DESIGN EXAMPLE:
8.4.1 Design a top chord member for a roadway bridge for the
following data:
Design Force = -1250 Tons (Compression)
Member Length = 1000 cm
Buckling Length LR
xR = LR
yR = 0.85 × 1000 = 850 cm
Steel Grade St. 52
Selection of Member Dimensions: (Assume member stress = 1.8 t/cmP
2
P)
2
.req cm695
8.1
1250
A
cm708752h
4
5
4
3
b
cm806683
1512
Panel
h
≅=
−⇒−=





−=
−⇒−=
−
=

Min Thickness :
Flange : cm2.2Choose,cm075.2
7.33
70
tf =≥
Web : cm4.2Choose,cm255.2
7.33
75
tw =≥
Try the following section:
Area (cmP
2
P)
Top Flange Pl. 800 × 22 176
Web 2 Pl. 800 × 24 384
Bottom
Flange
Pl. 652 × 22 143.44
703.44
Section Properties and Stress Check:
SafeFcm/t777.1
44.703
1250
f
cm/t976.1)4.30(000135.01.2F
1004.30
28
850
i
L
cm28a4.0i
cm32h4.0i
buck
2
act
22
buck
y
y
y
x
⇒<==
=−=
<==
=×≈
=×≈
−
8.4.2 Design a bottom chord member for a roadway bridge for the
following data:
Design Force = + 1250 Tons (Tension)
Buckling Length LR
xR = LR
yR = 0.85 × 1000 = 850 cm
Use section similar to top chord:
22
act
net
cm/t1.2cm/t091.2
44.703x85.0
1250
f
Agross85.0A
〈==
≈
800
700

Steel Bridges
Fatigue Check :
.k.ocm/t80.1Fsr
BClassDetail
10x5cyclesof.No:for
cm/t588.1
44.703x85.0
950
f
t950F
t300F
2
2
2
sr
lLL
DL
=





=
=
==





=
=
+
8.4.3 Design a diagonal member for a roadway bridge for the following
data:
Design Force = - 180 Tons (Compression)
Buckling Length LR
xR = 0.7 × 700 = 490 cm
LR
yR = 0.85 × 700 = 595 cm
Total member depth = b = 70 cm
Trial Section :
Web 660 x 20 = 132
Flange 2x300 x 20 = 120
Total Area = 252 cmP
2
.k.of2cm/t714.0252/180f
cm/t772.017.99*000135.01.2f
.k.o11017.99
6
595
i
L
cm630x2.0i
7.17
28
495
i
L
28~i
pbact
22
pb
y
y
y
x
x
x
〈==
=−=
〈==
=≅










==

8.4.4 Design a diagonal member for a roadway bridge for the following
data:
Design Force = + 250 Tons (Tension)
Buckling Length LR
xR = 0.7 × 700 = 490 cm
LR
yR = 0.85 × 700 = 595 cm
Trial Section :
Web 676 x 12 = 81.12
Flange 2x300 x 12 = 72.00
Total Area = 153.12 cmP
2
P
( )
.k.o1.22cm/t92.1152.130/250f
cm152.13012.153x85.0A
.k.o1802.9930x2.0/595
i
l
act
2
net
y
y
〈==
=≈
〈==
8.5 DESIGN OF TRUSS CONNECTIONS
8.5.1 Truss Joints
Members of bridge trusses are usually connected by gusset plates at the
joints where members meet. Connections are usually made by bolting the
members to gusset plates on both sides of the cross section as shown in Fig.
8.7.
Fig. 8.7 Bolted Truss Joints

Steel Bridges
The usual gusset plate thickness is 14-20 mm. At every truss joint, working
lines of the intersecting members should meet at one point to avoid eccentric
loading. Force transmission through the gusset plates at a truss joint may be
achieved in one of the following two ways:
(a) If the chord member runs continuous through the joint, the main portion
of the force is transferred directly within the chord, and only the difference of
the chord forces is carried through the gusset. This arrangement if often used
to relieve the gusset plate of any excessive load. In this case, chord members
are usually spliced outside the joints, see Fig. 8.8.
Fig. 8.8 Bolted Truss Joints with Splice outside Joint
(b) If the chord members are spliced at the joint, the gusset plates at this
location will be subjected to heavy stresses because it transmits the entire
amount of the chord forces.
At the nodes of a truss where the web members are connected to the chords,
there is a change in load in the chord which necessitates a change in its cross-
section area. The node is, therefore, the point at which there is a joint in the
chord as well as being the connection point of the web members.
The web members are connected to the chords by vertical gusset plates.
They are usually bolted to the chord webs and the web members fit between
them (Figure 8.9a).
The chord joint is effected by providing cover plates. They should be so
disposed, with respect to the cross-section of the member, as to transfer the
load in proportion to the respective parts of the section (Figure 8.9b).

Fig. 8.9 Bolted Truss Bridge Connections
The gusset plates form the external web cover plates. Since they work in
the dual capacity of cover plate and web connector, their thickness takes this
into account. The joint is designed to carry the coexistent load in the lesser
loaded chord plus the horizontal component of the load in the adjacent
diagonal. The load from the other diagonal is transferred to the more heavily
loaded chord through the gussets alone. In compression chords which have

Steel Bridges
fitting abutting ends in contact, design codes allow up to 75% of the
compressive load to be carried through the abutting ends.
Sometimes the gusset is formed by shop-welding a thicker shaped plate to
the chord in place of the chord web. The web members are then all narrower
than the chords and the chord splice is offset from the node. An advantage
occurs in erection as the web connections can be made before the next chord
is erected.
At the connections of all tension members and elements, care has to be
taken in the arrangement of bolt holes to ensure that the critical net section
area of the section is not so small that fracture will govern. If necessary
remember that the critical net section is usually at the ends of the section or
the centre of the cover plates, and that elsewhere some of the load has been
transferred to the other parts of the joint and more bolt holes can be tolerated.
Connections of web members to gussets are quite straightforward and
special treatment such as the use of lug angles is rarely required. In
connecting rectangular hollow sections the method shown in Figure 8.9d is
preferable to that of Figure 8.9c.
Unsupported edges of gussets should be such that the distance between
connections does not exceed about 50 times the gusset plate thickness (Fig.
8.9a). If this is unavoidable, the edge should be stiffened.
8.5.2 Cross Girder Connections
They are quite straightforward. The 2 or 4 rows of bolts in the cross girder
end plate are made to correspond with the equivalent central rows of bolts in
the gusset. Packing plates may be required to accommodate the difference in
height of gussets and cross girders (Figure 8.9e).
8.5.3 Lateral Bracing Connections
The axes of the lateral systems should be in the same planes as those of the
truss chords. This requirement is met in 2 of the 3 types of lateral members
and connections described below:
i. For long and medium spans, the lateral members are frequently made from
two rolled channel sections connected by lacing to give an overall depth the
same as the chords. They are connected to the chords by gussets bolted to the
chord flanges exactly as the main web members are connected to the main
joint gussets.

ii. For medium spans, laterals consisting of two rolled angles arranged toe to
toe in "star" formation and with intermediate battens are often ideal. They are
connected to the chords by gussets positioned at the chord axis (Figure 8.9f).
Note, angles "back-to-back", but separated by a small gap should never be
used because of maintenance problems.
iii. On short spans single laterals often suffice. They can be connected by a
gusset to the upper or lower chord flange, as the moments due to eccentricity
are small.
8.5.4 MEMBER SPLICES
Splices of bridge truss members are needed because of the limitations
imposed by:
(a) the available length of plates and shapes;
(b) length limits imposed by the transportation facilities; and
(c) capacity of the erecting cranes.
Splices made in the shop are dictated by the available plate lengths. Full
penetration butt welding of the V or X type is usually used for shop splices.
Splices made in the field are preferably made using high strength bolts.
Splices are usually designed to carry the maximum strength of the spliced
parts computed from:
SR
maxR = AR
netR x FR
tR (Tension)
= AR
gross Rx FR
cR (Comp.)
Member splices made with shear plates require a complete design of load
transfer from the spliced parts through splice plates. On the other hand, for
compression members bearing against each other at the splice location, the
bearing surfaces may be milled for full contact and direct load transfer.

Ch8 Truss Bridges (Steel Bridges تصميم الكباري المعدنية & Prof. Dr. Metwally Abu-Hamd)

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