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University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
What is a truss
a truss is an assembly of linear members
connected together to form a triangle or
triangles that convert all external forces into
axial compression or tension in its members
Single or number of trianglesa triangle is the simplest stable shape
Joints assumed frictionless hinges
1/27
loads placed at joints
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
Primitive dwelling
heavy timber trusses
Rafter pair - Joistsimple roof construction
loading along rafters - bending
Simple Truss
2/27
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
Depth
or Rise
Panel
Span
Flat Truss or Parallel Chord Truss
Vertical Diagonal
Web
Members(verticals & diagonals)
Top Chord
Bottom Chord
Joint,
Panel point
or Node
3/27
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
BowstringFlat Pratt Triangular Howe
Flat Howe Inverted Bowstring Simple Fink
Warren Fink
Camelback Triangular Pratt Cambered Fink
Scissors Shed
Lenticular
4/27
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
A truss provides depth with less material than a
beam
It can use small pieces
Light open appearance (if seen)
Many shapes possible
Pyrmont Bridge
5/27
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
Multipanel Trusses
Sainsbury Centre
Norwich, England
Foster & Partners
Anthony Hunt Associates
Warren Trusses
Centre Georges Pompidou
Paris
Piano & Rogers
Ove Arup & Partners
Shaping Structures: Statics, W. Zalewski and E. Allen (1998)
6/27
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
Shaping Structures: Statics, W. Zalewski and E. Allen (1998)
3-Hinged Truss Arches
Waterloo Terminal for Chunnel Trains
Nicholas Grimshaw & Partners
Anthony Hunt Associates
7/27
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
Stadium Australia
Homebush, Sydney, 1999
Bligh Lobb Sports Architects
Sinclair Knight Merz (SKM)
Modus Consulting Engineers
8/27
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
Much more labour in the
joints
More fussy appearance, beams have cleaner lines
Less suitable for heavy loads
Needs more lateral support
Triangular-section steel truss
(for lateral stability)9/27
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
Domestic roofing, where the space is available
anyway
Longspan flooring, lighter and stiffer than a beam
Bracing systems are usually big trusses
Longspan
floor
trusses
10/27
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
Span-to-depth ratios are commonly between 5 and 10
This is at least twice as deep as a similar beam
Depth of roof trusses to suit roof pitch
Beam, depth = span/20
Truss, depth = span/4
Truss, depth = span/10
Typical proportions
11/27
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
Gangnail joints in light timber
Gusset plates (steel or timber)
Nailplate joint
Riveted steel
gusset plates
12/27
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
Welded joints in steel
Various special concealed joints in timber
Steel gussets concealed
in slots in timber members
13/27
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
The members should form triangles
Each member is in tension or compression
Loads should be applied at panel points
Loads between panel points cause bending
Supports must be at panel points
Load causes
bending Extra member
14/27
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
C C CC
CC C C
C
T T TT
T T T T
Only tension & compression forces are developed in pin-connected
truss members if loads applied at panel points
15/27
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
Basic truss assemblies
Imagine diagonals removed
Look at deformation that would occur
Look at role of diagonal in preventing
deformation
Final force distribution in members
Analogy to ‘cable’ or ‘arch’ action
T
c c
0 0
00 0
T0
c
0
c
c cTT c
16/27
A B
D
C
F E
Truss A Truss B
A B
D
C
F E
B
BDF
A C
B
DF
cA C
E
c c
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
The top and bottom chord resist the bending
moment
The web members resist the shear forces
In a triangular truss, the top chord also resists
shear
Top chord
Bottom chord
Web members
17/27
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
For detailed design, forces in each member
For feasibility design, maximum values only
are needed
Maximum bottom chord
Maximum top chordMaximum web members
18/27
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
Find all the loads and reactions (like a beam)
Then use ‘freebody’ concept to isolate one piece
at a time
Isolate a joint, or part of the truss
This joint in
equilibrium
19/27
This piece
of truss in
equilibrium
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
Three methods
1. Method of Joints
2. Method of Sections
3. Graphical Method
20/27
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
Have to start at a reaction
Move from joint to joint
Time-consuming for a large truss
Start at reaction (joint F)
Then go to joint A
Then to joint E
Then to joint B ...
generally there is only
one unknown at a time
21/27
A B C
DEF
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
Resolve each force into horizontal and
vertical components
A
AF
AB
AE
Angle
Vertically:
AF + AE sin = 0
If you don’t know otherwise,
assume all forces are tensile
(away from the joint)
Horizontally:
AB + AE cos = 0
22/27
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
Quick for just a few members
x1
x2
W1
W2
W3
R1
A
T1
T3
T2
H
23/27
taking moments about A
W1 * x1 + W2 * x2 + T1 x H = R1 * x1
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
useful to find maximum chord forces in
long trusses
24/27
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
Uses drafting skills
Quick for a complete truss
g, h, o
a
b
c
d
e
f
i
j , m
k
l
n
Scal e
for
for ces
0
1
2
3
4
Maxwell diagramBow’s Notation
4 bays @ 3m
1 2 2 2 1
4 4
3m a
b c d e
f
g
h
i
j
k l
mn
o
25/27
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
The chords form a couple to resist bending
moment
This is a good approximation for long trusses
C
Td
First find the Bending Moment
as if it was a beam
A shallower truss produces larger forces
Resistance Moment
= Cd = Td
therefore C = T = M / d
26/27
University of Sydney –Building Principles
Trusses
Peter Smith 1998/Mike Rosenman 2000
The maximum forces occur at the support
First find the reactions
A shallower truss produces
larger forcesR
C
T
Then the chord forces are:
C = R / sin
T = R / tan
27/27