university of sydney –building principles trusses peter smith 1998/mike rosenman 2000 l what is a...

University of Sydney –Building Principles Trusses

Peter Smith 1998/Mike Rosenman 2000

What is a trussa 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 triangles

a triangle is the simplest stable shape

Joints assumed frictionless hinges

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loads placed at joints



Primitive dwelling

heavy timber trusses

Rafter pair - Joistsimple roof constructionloading along rafters - bending

Simple Truss

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Depthor Rise

Panel

Span

Flat Truss or Parallel Chord Truss

Vertical Diagonal

WebMembers

(verticals & diagonals)

Top Chord

Bottom ChordJoint,Panel pointor Node

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BowstringFlat Pratt Triangular Howe

Flat Howe Inverted Bowstring Simple Fink

Warren Fink

Camelback Triangular Pratt Cambered Fink

Scissors Shed

Lenticular

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A truss provides depth with less material than a

beam It can use small pieces Light open appearance (if seen) Many shapes possible

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Multipanel TrussesSainsbury Centre

Norwich, England

Foster & PartnersAnthony Hunt Associates

Warren TrussesCentre Georges Pompidou

Paris

Piano & RogersOve Arup & Partners

Shaping Structures: Statics, W. Zalewski and E. Allen (1998)6/27



Shaping Structures: Statics, W. Zalewski and E. Allen (1998)

3-Hinged Truss ArchesWaterloo Terminal for Chunnel Trains

Nicholas Grimshaw & PartnersAnthony Hunt Associates

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Stadium AustraliaHomebush, Sydney, 1999

Bligh Lobb Sports ArchitectsSinclair Knight Merz (SKM) Modus Consulting Engineers

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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)

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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

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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

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Gangnail joints in light timber

Gusset plates (steel or timber)

Nailplate joint

Riveted steel gusset plates

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Welded joints in steel

Various special concealed joints in timber

Steel gussets concealed in slots in timber members

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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

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C C C C

CC C C C

T T TT

T T T T

Only tension & compression forces are developed in pin-connectedtruss members if loads applied at panel points

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Basic truss assemblies

Imagine diagonals removedLook at deformation that would occurLook at role of diagonal in preventingdeformation

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

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Truss A Truss B

B

DF

cA C

E

c c



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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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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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



Three methods

1. Method of Joints

2. Method of Sections

3. Graphical Method

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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 AThen to joint EThen to joint B ...

generally there is only one unknown at a time

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A B C

DEF



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

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Quick for just a few members

d1

d2

W1

W2

W3

R1

A

T1

T3

T2

H

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taking moments about AW1 * d1 + W2 * d2 + T1 x H = R1 * d1



useful to find maximum chord forces in long trusses

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Uses drafting skills Quick for a complete truss

g,h,o

a

b

c

d

e

f

i

j ,mk

l

n

Scaleforfor 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

ij

k lm

no

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The chords form a couple to resist bending moment

This is a good approximation for long trusses

C

Td

First find the Bending Momentas if it was a beam

A shallower truss produces larger forces

Resistance Moment= Cd = Td

therefore C = T = M / d

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The maximum forces occur at the support

First find the reactions

A shallower truss produceslarger forcesR

C

T

Then the chord forces are:C = R / sin T = R / tan

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university of sydney –building principles trusses peter smith 1998/mike rosenman 2000 l what is a...

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