What is a truss - Angelo Filomeno mech 7 -trusses.pdf · Peter Smith 1998/Mike Rosenman 2000...

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

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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

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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

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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

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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)

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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

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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

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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

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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

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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

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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