graphic truss analysis - pc\|macimages.pcmac.org/.../documents/09-truss-analysis.pdf · oakland bay...

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Graphic truss analysis Copyright Prof Schierle 2011 1

Graphic truss analysis


Truss examples

Oakland Bay Bridge

Truss joists


Stadium roof Milan Airport terminal HamburgPrismatic trusses providelateral & rotational stability

Vertical compression bars: thickDiagonal tension bars: thin


Truss concepts• Replace beams for long spans• Replace bulk by triangulation

• Triangle is the only stable polygon

• Square is an unstable polygon

• All other polygons are unstable

Truss

Beam


Common trusses1 Pratt truss

2 Howe truss

3 X-truss

4 K-truss

5 Warren truss

6 Warren truss with vertical bars

7 Fink truss

8 Belgian truss

9 Scissor truss

10 Bowstring truss

11 Bowstring truss (alternate)

12 Bowstring K-truss


Note:Prismatic and folded trusses resist buckling and rotation

Unique trusses

1 Prismatic truss

2 Prismatic truss frame

3 Prismatic truss arch

4 Folded truss

5 Folded truss frame

6 Folded truss vault


Graphic Truss Analysis

1 Truss diagram2 Force polygon for loads and reactions

Force polygon for joint ABHGEquilibrium arrows on bars

3 Truss with tension & compression arrows 4 Equilibrium polygons for left half of truss

(right half is equal due to symmetry)5 Bar force list (+ tension, - compression)


Truss Analysis steps• Draw truss diagram to scale• Add tributary joint loads• Compute reactions• Add letters between loads and reactions• Add letters between truss bars• Draw load / reactions polygon• Draw equilibrium polygon for joints

Select joint sequence to limit unknown bar forces (max. 2 per joint)

• Draw equilibrium arrows on bars• Measure bar forces at force scale• Define bar tension / compression:

arrow pulling from joint = tension (+)arrow pushing joint = compression (-)

• Record bar forces


Graphic Truss Analysis

1 Joint ABHG2 Joint ABHG equilibrium polygon

3 Joint BCJH4 Joint BCJH equilibrium polygon

5 Joint HJKG6 Joint HJKG equilibrium polygon


Parallel chord truss1 Truss diagram2 Equilibrium force polygon3 Bar force table4 Intuitive analysis

Top chord shortens in compressionBottom chord elongates in tensionInward sloping bars elongate in tensionOutward sloping bars shorten in compressionVertical bars shorten in compression

Note:Diagonal bars in tension are preferredsince they are the longest bars and thuswould tend to buckle in compression.Buckling increases quadratic with length !!!


Truss analysis examples

1 Warren truss2 Warren truss equilibrium polygons

3 Pratt truss4 Pratt truss equilibrium polygons

5 Braced frame6 Braced frame equilibrium polygon


Wood truss

1 Truss with gusset plate joints

2 Gusset plate for nails, both sides

3 Gang nail gusset plate

4 Truss with bolt and split ring joints

5 Split ring joint

A Split ring resists shear stress

B Bolt


Wood truss

Timber truss with steel rods anddiagonal wood bars in compression(wood tension joints are difficult)

7 Truss joist with steel web bars8 Truss with gusset plates9 Truss with twin chord and single

web bars


Steel truss joints

1 Truss

2 Twin angles with gusset plate

3 Channels with gusset plate

4 Pipe with gusset plate

5 Welded tube joint


Steel truss joints

1 Twin angles with gusset plate

2 Welded tube joint

3 Welded pipe jointNote: Concentric truss joints avoid bending stressEccentric joints caused collapse in the past


Steel truss joist

Glas

s wall

supp

orted

with

trus

s jois

ts

Roof / floor


Space truss joint Mero

The popular Mero joint provides concentric connectionsfor space truss bars in any direction. Mero is an abbreviation of:The first 2 letters of Dr. Meneringhausen, the inventorand the first 2 letters of Rohr, German for pipe.

A NodeB Web barC Chord barD Roof supportE Wall supportF Joint support


trusses are cool