In
architecture and
structural engineering, a
truss is a
structure comprising one or more
triangular units constructed with straight slender members whose
ends are connected at joints referred to as
nodes. External forces and reactions to
those forces are considered to act only at the nodes and result in
forces in the members which are either
tensile or
compressive forces. Moments (torsional
forces) are explicitly excluded because, and only because, all the
joints in a truss are treated as
revolutes.
A planar truss is one where all the members and nodes lie within a
two dimensional plane, while a space truss has members and nodes
extending into three dimensions.
Characteristics of trusses
A truss is composed of triangles because of the structural
stability of that shape and design. A triangle is the simplest
geometric figure that will not change shape when the lengths of the
sides are fixed. In comparison, both the angles and the lengths of
a four-sided figure must be fixed for it to retain its shape.
The simplest form of a truss is one single triangle. This type of
truss is seen in a
framed
roof consisting of
rafters and a ceiling
joist. Because of the stability of this shape
and the methods of analysis used to calculate the forces within it,
a truss composed entirely of triangles is known as a simple
truss.
A planar truss lies in a single
plane. Planar trusses are typically used
in parallel to form roofs and bridges. A space truss is a
three-dimensional framework of members pinned at their ends. A
tetrahedron shape is the simplest space
truss, consisting of six members which meet at four joints.
The depth of a truss, or the height between the upper and lower
chords, is what makes it
an efficient structural form. A solid
girder
or
beam of equal strength would have
substantial weight and material cost as compared to a truss. For a
given span length, a deeper truss will require less material in the
chords and greater material in the verticals and diagonals. An
optimum depth of the truss will maximize the efficiency.
== Truss types
- For a more truss types, see List of truss types or Truss
Bridge.
There are two basic types of truss:
- The pitched truss, or common truss, is
characterized by its triangular shape. It is most often used for
roof construction. Some common trusses are named according to their
web configuration. The chord size and web configuration
are determined by span, load and
spacing.
- The parallel chord truss, or flat truss, gets
its name from its parallel top and bottom chords. It is often used
for floor construction.
A combination of the two is a truncated truss, used in
hip roof construction. A metal plate-connected
wood truss is a roof or floor truss whose wood members are
connected with
metal connector
plates.
Pratt truss
The Pratt truss was patented
in 1844 by two Boston railway
engineers; Caleb Pratt and his son Thomas Willis Pratt. The design
uses vertical beams for
compression and horizontal beams to
respond to
tension. What is
remarkable about this style is that it remained popular even as
wood gave way to iron, and even still as iron gave way to
steel.
The
Southern Pacific Railroad
bridge in Tempe, Arizona is a 393
meter (1291 foot) long truss bridge built in 1912. The
structure is composed of nine Pratt truss spans of varying lengths.
The bridge is still in use today.
Bow string roof truss
Named for its vicissitudal shape, thousands of bow strings were
used during
World War II for aircraft
hangars and other military buildings.
King post truss
One of the simplest truss styles to
implement, the
king post consists of two angled
supports leaning into a common vertical support.
The
queen post truss,
sometimes
queenpost or
queenspost, is similar to
a king post truss in that the outer supports are angled towards the
center of the structure. The primary difference is the horizontal
extension at the centre which relies on
beam action to provide mechanical
stability. This truss style is only suitable for relatively short
spans.
Lenticular Truss
American Lenticular Truss Bridges have the top and bottom chords of
the truss arched forming a lens shape. Patented in 1878 by William
Douglas.
Town's lattice truss
American
architect Ithiel Town
designed
Town's Lattice Truss as an alternative to
heavy-timber bridges. His design,
patented
in 1820 and 1835, uses easy-to-handle planks arranged diagonally
with short spaces in between them.
Vierendeel truss
The
Vierendeel truss is a truss where the members
are not
triangulated but form
rectangular openings, and is a
frame
with fixed joints that are capable of transferring and resisting
bending moments. Regular trusses
comprise members that are commonly assumed to have pinned joints
with the implication that no moments exist at the jointed ends.
This style
of truss was named after the Belgian engineer
Arthur Vierendeel, who developed
the design in 1896. Its use for bridges is rare due to
higher costs compared to a triangulated truss.
The utility of this type of truss in buildings is that there is no
diagonal bracing, the creation of rectangular openings for windows
and doors is simplified and in cases the need for compensating
shear walls is reduced or eliminated.
After
being damaged by the impact of a plane hitting the building, parts
of the framed curtain walls of the Twin Towers of the World Trade
Center resisted collapse by Vierendeel action displayed by
the remaining portions of the frame.
Statics of trusses
A truss that is assumed to comprise members that are connected by
means of pin joints, and which is supported at both ends by means
of hinged joints or rollers, is described as being statically
determinate. Newton's Laws apply to the structure as a whole, as
well as to each node or joint. In order for any node that may be
subject to an external load or force to remain static in space, the
following conditions must hold: the sums of all horizontal forces,
all vertical forces, as well as all moments acting about the node
equal zero. Analysis of these conditions at each node yields the
magnitude of the forces in each member of the truss. These may be
compression or tension forces.
Trusses that are supported at more than two positions are said to
be statically indeterminate, and the application of Newton's Laws
alone is not sufficient to determine the member forces.
In order for a truss with pin-connected members to be stable, it
must be entirely composed of triangles. In mathematical terms, we
have the following necessary condition for
stability:
- m \ge 2j - r \qquad \qquad \mathrm{(a)}
where
m is the total number of truss members,
j
is the total number of joints and
r is the number of
reactions (equal to 3 generally) in a 2-dimensional
structure.
When m=2j - 3, the truss is said to be
statically
determinate, because the (
m+3) internal member forces
and support reactions can then be completely determined by
2
j equilibrium
equations, once we know the external
loads and the geometry of the truss. Given a
certain number of joints, this is the minimum number of members, in
the sense that if any member is taken out (or fails), then the
truss as a whole fails. While the relation (a) is necessary, it is
not sufficient for stability, which also depends on the truss
geometry, support conditions and the load carrying capacity of the
members.
Some structures are built with more than this minimum number of
truss members. Those structures may survive even when some of the
members fail. They are called
statically indeterminate
structures, because their member forces depend on the relative
stiffness of the members, in addition to
the equilibrium condition described.
Analysis of trusses
Because the forces in each of its two main girders are essentially
planar, a truss is usually modelled as a two-dimensional plane
frame. If there are significant out-of-plane forces, the structure
must be modelled as a three-dimensional space.
The analysis of trusses often assumes that loads are applied to
joints only and not at intermediate points along the members. The
weight of the members is often insignificant compared to the
applied loads and so is often omitted. If required, half of the
weight of each member may be applied to its two end joints.
Provided the members are long and slender, the
moments transmitted through the joints are
negligible and they can be treated as "
hinges"
or 'pin-joints'. Every member of the truss is then in pure
compression or pure tension – shear, bending moment, and other more
complex
stresses are all
practically zero. This makes trusses easier to analyze. This also
makes trusses physically stronger than other ways of arranging
material – because nearly every material can hold a much larger
load in tension and compression than in shear, bending, torsion, or
other kinds of force.
Structural analysis of trusses
of any type can readily be carried out using a matrix method such
as the
direct stiffness
method, the
flexibility
method or the
finite element
method.
Forces in members
On the right is a simple,
statically determinate flat truss
with 9 joints and (2 x 9) − 3 = 15 members. External loads are
concentrated in the outer joints. Since this is a
symmetrical truss with symmetrical vertical loads,
it is clear to see that the reactions at A and B are equal,
vertical and half the total l
The internal
forces in the members of the
truss can be calculated in a variety of ways including the
graphical methods:
Design of members
A truss can be thought of as a
beam
where the web consists of a series of separate members instead of a
continuous plate. In the truss, the lower horizontal member (the
bottom chord) and the upper horizontal member (the
top chord) carry
tension and
compression, fulfilling the same
function as the
flanges of an
I-beam. Which chord carries tension and which carries
compression depends on the overall direction of
bending. In the truss pictured above right, the
bottom chord is in tension, and the top chord in compression.
The diagonal and vertical members form the
truss
web, and carry the
shear
force. Individually, they are also in tension and compression, the
exact arrangement of forces depending on the type of truss and
again on the direction of bending. In the truss shown above right,
the vertical members are in tension, and the diagonals are in
compression.
In addition to carrying the static forces, the members serve
additional functions of stabilizing each other, preventing
buckling. In the picture to the right, the top
chord is prevented from buckling by the presence of bracing and by
the stiffness of the web members.
The inclusion of the elements shown is largely an engineering
decision based upon economics, being a balance between the costs of
raw materials, off-site fabrication, component transportation,
on-site erection, the availability of machinery and the cost of
labor. In other cases the appearance of the structure may take on
greater importance and so influence the design decisions beyond
mere matters of economics. Modern materials such as
prestressed concrete and fabrication
methods, such as automated
welding, have
significantly influenced the design of modern
bridges.
Once the force on each member is known,the next step is to
determine the
cross section
of the individual truss members. For members under tension the
cross-sectional area
A can be found using
A =
F × γ / σ
_{y}, where
F is the
force in the member, γ is a
safety
factor (typically 1.5 but depending on
building codes) and σ
_{y} is the
yield tensile
strength of the steel used.
The members under compression also have to be designed to be safe
against buckling.
The weight of a truss member depends directly on its cross section
-- that weight partially determines how strong the other members of
the truss need to be.Giving one member a larger cross section than
on a previous iteration requires giving other members a larger
cross section as well, to hold the greater weight of the first
member -- one needs to go through another iteration to find exactly
how much greater the other members need to be.Sometimes the
designer goes through several iterations of the design process to
converge on the "right" cross section for each member. On the other
hand, reducing the size of one member from the previous iteration
merely makes the other members have a larger (and more expensive)
safety factor than is technically necessary, but doesn't
require another iteration to find a buildable truss.
The effect of the weight of the individual truss members in a large
truss, such as a bridge, is usually insignificant compared to the
force of the external loads.
Design of joints
After determining the minimum cross section of the members, the
last step in the design of a truss would be detailing of the
bolted joints, e.g., involving shear of
the bolt connections used in the joints, see also
shear stress.
Applications
Post Frame Structures
Component connections are critical to the structural integrity of a
framing system. In buildings with large, clearspan wood trusses,
the most critical connections are those between the truss and its
supports. In addition to gravity-induced forces (a.k.a. bearing
loads), these connections must resist shear forces acting
perpendicular to the plane of the truss and uplift forces due to
wind. Depending upon overall building design, the connections may
also be required to transfer bending moment.
Wood posts enable the fabrication of strong, direct, yet
inexpensive connections between large trusses and walls. Exact
details for post-to-truss connections vary from designer to
designer, and may be influenced by post type. Solid-sawn timber and
glulam posts are generally notched to form a truss bearing surface.
The truss is rested on the notches and bolted into place. A special
plate/bracket may be added to increase connection load transfer
capabilities. With mechanically-laminated posts, the truss may rest
on a shortened outer-ply or on a shortened inner-ply. The later
scenario, places the bolts in double shear and is a very effective
connection.
Gallery
Image:80ft Double Chorded Heavy Timber Truss.JPG|Double chorded
heavy timber truss with 80 foot clear span.
Image:HK_Bank_of_China_Tower_View.jpg|The
Hong Kong
Bank of China Tower 中銀大廈 (香港) has an externally visible truss
structure.Image:HK_HSBC_Main_Building_2008.jpg|The
HSBC Main
Building, Hong Kong has an externally visible truss
structure.Image:Below Auckland Harbour Bridge
Hossen27.jpg|Support structure under the Auckland Harbour
Bridge.Image:Auckland Harbour Bridge
Watchman.jpg|The Auckland Harbour Bridge from Watchman Island, west of it.Image:The Little Belt Bridge
(1935).jpeg|Little
Belt: a truss bridge in DenmarkImage:Bow-string-truss.jpg|
Pre-fabricated steel bow string roof trusses
built in 1942 for war department properties in Northern
Australia.
Image:Truss Dachstuhl.jpg|Roof truss in a
side building of Cluny
Abbey, France.File:Queen-post-truss.png|A section through
a Queen post roof truss, see
Timber
roof trussesFile:Woodlands mall3 texas.jpg|A space truss
carrying a floor in
The Woodlands
Mall.File:Elledningsstolpe2_lund.jpg|
Electricity pylon
See also
References
- page 199
- page 221
- Bethanga Bridge at the NSW Heritage
Office; retrieved 2008-Feb-06
- A Brief History of Covered Bridges in Tennessee
at the Tenessee Department of Transportation; retrieved
2008-Feb-06
- The Pratt Truss courtesy of the Maryland Department of
Transportation; retrieved 2008-Feb-6
- Tempe Historic Property Survey at the
Tempe
Historical Museum; retrieved 2008-Feb-06
- Covered Bridge's Truss Types
- Vierendeel bruggen
External links
2egcd