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Tree Stability in WindsTree Stability in WindsKen James,

School of Resource ManagementUniversity of Melbourne

Australia

Introduction

• A structural analysis to assess tree stability• How wind loads on trees are measured• Static and Dynamic Methods• Wind Loads on trees – measured values• Wind loads on branches

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Tree stability assessment

Current methods• VTA (Mattheck)• QTRA• Visual and experience• Data ?Tendency if a weakness or hazard

is detected in a tree, to recommend removal.

“If in doubt, take it out!”

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Urban tree failure

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•Causes injury and property damage

Arborists face issues of LIABILITY

How to assess tree stability?

Can a structural analysis of a tree help?

Structural Analysis of trees

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Structural Analysis based on these assumptions;

• Plants, like all other types of organisms cannot violate the laws of physics. (Niklas 1992)

• As trees grow in size and height, the added biomass develops greater self-loading, and also exposes the upper reaches of the tree to higher wind speeds, which develop larger bending moments at its base, (Niklas and Spatz 2000).

• Moments Unit (kNm) – Wind Load

Stability and FailureTrees are stable if they are

stronger than the loads they experience.

If LOAD exceeds STRENGTH

FAILURE OCCURS

Biggest load is WIND

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Current methods of structural analysisSTATIC• Tree pull (Germany)

DYNAMIC• Forestry modelling• Urban trees – very little.• Wind loads – need data

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Dynamic wind loading

Complex dynamic motionDynamic interaction of branches

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Tree shapes – branch are important

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Trees in this studyDifferent branching forms

Palm Italian cypress Araucaria (Hoop pine) Eucalyptus teretecornus

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Urban trees – branch sway dominates

Melbourne, River Walks

A tree is a collection of branches (Shigo 1991)

Melbourne, River Walks

A tree is a collection of branches (Shigo 1991)

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Measuring wind loadswith strain meters

• Measure trunk flexure near the base, as trunk bends under wind loading.

• New instruments connect to computer, record at 20Hz.

• Dynamic wind loads

Research Project (2005-2009)• Ken James, Australia• Brain Kane, USA

Sponsor - Tree Fund

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Measuring wind loads on trees- Strategy “Make the tree the sensor”

Strain meters record bending in winds

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Wind Loads – Static analysisMattheck and Bethge (2000)

Simple STATIC approach to tree biomechanics

Calculated (no measurements)

Max overturning force 1219 kN m.

•Estimate from wood fibre strength, very, very big number!!

Canopy is lumped mass, no branches

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Strainmeter• Attaches to base of tree

• Measures strain (stretch)

• CONVERT to WIND LOAD (kNm)

• Accurate to 2 parts per million (1 micron)

• Dynamic data (20 Hz)

• Weather proof, storm monitoring

• 2 sensors, N/S, E/W strain, wind , temp, humidity

• Monitors for weeks under field conditions,24 hours a day

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Calibrate the tree – Static Pull Test

Calibration so instruments measure bending moments in

wind

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Measuring wind loads on treesMeasuring wind loads on trees

•• As wind bends trunkAs wind bends trunk•• Outer fibers expand or contractOuter fibers expand or contract•• StrainmeterStrainmeter measures measures fibrefibre length length

changechange

•• White pine, Virginia, USAWhite pine, Virginia, USA

•• Dr Brian Kane, U Dr Brian Kane, U MassechusettsMassechusetts•• Ken James, U Ken James, U MelbMelb..

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Sample graph of tree motion in wind from one sensor

Sensor1- linearSensor 2 – linear (at right

angles)Resultant XY graph

Gives motion for wind from any angle

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Dynamic sensors on treesN/S & E/W directions

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Wind Loads – Hoop pine

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Wind Loads – Hoop pine

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Wind Load data (kNm) – Hoop pine

Maximum along wind load 175 kNmMaximum across wind load 58 kNm

Values can be used to measure

Wind load on trunk

Wind loads on rootsNote significant side loading on roots

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Wind Loads – Hoop pine

Use data to;

•Assess wind load•For design data on other similar trees•Estimate stability

•Failure? (need higher wind data).

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Tree response spectrumHoop pine

•Provides data on tree dynamics, frequency, drag, damping•Shows trees do NOT have a harmonic sway•Spread of tree frequencies shows branch sway prevents harmonic sway•Branches detune the tree

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Palm

• Height 18.1 m• dbh 0.436 mLocation• Burnley Campus• Melbourne• Victoria• Australia

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Palm with strain meters

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Wind Load - palm

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Palm video

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Palm

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Palm

Nat Frequ. = 0.27 hz, Period = 1/.27 = 3.7s

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Palms asstructures

•Flexible

•Survive winds with flexible response

Man –made crane

•Rigid

•Survives winds with strength in structure

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Palms – Survive wind loads?

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Wind Load - palm

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Spotted GumWind dir

Biggest gust in 3 months

Win

d di

r

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Spotted gum, Monash Uni

Wind dir

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Results – Monash

• Wind load and wind speed• Design data for similar trees

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Tree dynamics, E. grandis, wind loads

Wind Dir

Zero pt

Wind load summary

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Wind load (logarithmic)

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7. Branches

Branches can dominate an urban trees structureMelbourne, Botanic Gardens

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Branch dynamics

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Branch sway - Eucalyptus salignaWind direction

Branch sway left and UPWARDS

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Wind forces on branches!up or down?

Burnley, Melbourne, April 2008

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Branch movement upwards?Shigo (1991)• Suggested upward

breaking of branches occurs

• observed broken fibresat end of branch

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Tree motion

Harmonic motion?

Do trees sway back and forth?

Is there a natural frequency?

What are the dynamic forces on trees?

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Harmonic motion

Oscillating response with a natural frequency

SpectrumPeak showsNatural frequency

Time domain Frequency domain

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Tree motion – harmonic?

Oscillating response.Is there a natural frequency?

SpectrumPeak showsNatural frequency

Time domain Frequency domain

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8. Tree Models• Dominated by Greenhill (1880) concept• Trunk analysed, no branches• Conventional dynamic mathematics

•Natural frequency ???

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Current dynamic tree models

Woods, C.J. 1995Oscillating response with a natural frequency

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Current dynamic tree models

Sanderson, et al.1999

Mass of canopy - rigid

Nield & Wood, 1998

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New Dynamic Tree Model

- with dynamic branches

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Mass Damping minimises sway

The dynamic interaction of masses (branches) that prevent large oscillations occurring

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Features of the new dynamic modelAll components of a tree’s dynamic system can be included in

the model - a 3D matrix equation of motion

• Mass, of trunk, and all branches (matrix)• Material (k) –Young’s modulus• Damping (complex

- aerodynamic (known)- viscoelastic (known)- mass damping (not previously identified)

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9. Examples of mass damping

Tuned mass damped StructureBuildingsPolesBridges

| Mass damper

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Taipei 101 – tallest building

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Tuned mass damper

730 tonnesReduces movement

40%

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Tuned mass damper

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Real tree sway is complex

Branch masses sway “out of tune”

No regular harmonic motion, but complex interaction of branches (damping – aerodynamic, viscoelastic, mass damping)

No movement upwind from zero point

Normal speed x3 speed

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No branches – no mass damping

Removing tree crown• Branches removed• no mass damping• Energy from top not

dissipated• Arborist becomes the

dynamic mass• SAFETY???• Learn how the tree

uses dynamics to minimise energy transfer

• New methods???

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No mass damping, US - style

Static Pull test - Method

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Static Pull test

• Rope and controlled pull.Measure • Pull• Trunk strain• Root plate angle

(Max 0.25°)• How good is it?

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Static pull test - limitations• does not really simulate wind loading because there is no allowance

for dynamic sway (Oliver and Mayhead 1974, Gardiner et al. 1997)• direction of pull is usually in one direction only which may or may

not represent the direction from which the wind blows and loads the tree.

• may overestimate the critical wind speed that is predicted to cause tree failure (Hassinen et al. 1998).

• conditions of the test may also be different from the conditions at failure, especially if soil moisture has changed due to rain. A test performed under dry soil conditions may be very different from a test when the soil in the tree root plate is wet.

• Not suited to all trees, eg. Multi-limbed trees such as cypress

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Static pull test - Advantages• Measures strength of trunk and root plate• Provides data to assist decision making on the tree stability• Can prove a tree is weak and needs to be removed (good

for Heritage listed trees, native vegetation regulations)• Data can be used in court , thus limits liability due to

opinion• Gives some loading data (base bending moment in kNm)

for comparison to other trees and wind load data.• Not a guarantee of stability for the future as a tree is a

biological structure and strength may change.

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Static pull test - Summary• Useful for assessing tree stability (at that date)• Provides verifiable data which may help with decisions

about the tree• Data reduces Liability of arborist• Good for assessing root plate strength (though soil

moisture may vary)• Costs need to be considered• Does not predict failure• Statics does not account for wind dynamics (branches are

not considered).

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Tree characteristics that influence dynamic effects

1. Tree HEIGHT2. DIAMETER (DBH)3. SLENDERNESS RATIO (HEIGHT/DBH)4. BRANCHESThese properties influence DYNAMICS

IMPORTANTSmall trees are not mini versions of large trees

IMPORTANTSmall trees are not mini versions of large trees

Tree Height is important

For Urban trees• 10 – 15 m height, wind loads become large• Trees of this height need special care• Above 20 m,• Winds loads are very large• Special care is needed because any failure

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AN example of tree stabilityTrees – largest living thing on earthRedwood, General Grant, USA, California•Sequoiadendron giganteum•Height 275 ft (83.9m)•Basal girth 82.3 ft (25.1m)•Dbh = 26 ftWeight (diff estimates)•Trunk - 5.46 x 105 kg (~600 tons)•Total - 12.7 x 105 kg (~ 1300 tons)

Niklas (1992)

Slenderness h/d = 275/26= 10.5

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The King of trees

• Eucalyptus regnans• Mountain Ash• Tallest flowering plant• 101 m, Tas. (Oct 2008)

Distribution

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Tree heights

The range of tree heights

Plantation treesUrban trees30

20

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Height and diameter or

Slenderness – h/dA measure of stability

Example - E. Tereticornis

Height = 14 mDiameter at breast height

(dbh = 0.886m)

Slenderness = height/dbh= 14 / 0.886= 15

Slenderness 15:1

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Tree height – convert to slenderness plot

Plantation treesUrban trees

Danger15m

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Slenderness (Stability?)

Plantation treesUrban trees

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Plantation trees

• Height 15m• Slenderness - 160 max• Dynamic solution like a

vibration pole(Rudniki et al. 2001)

• Quite a lot of dynamic analysis of tree response in winds

• NOTE- very small branch mass

• Are urban trees the same?

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Allometry – tree size and shapeBIG TREES are NOT

scaled up versionsof small trees

Wind tunnel Plantation Urban trees Forest giants

Effect of BRANCHES is important in wind (dynamics)

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Allometry – size and shapeHuman size ratio changes with age

OLD is not a scaled up

version of YOUNG

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Wind tunnel tests on trees

Constant wind

Wind TunnelSmall treesConstant wind speedNo gusts???Minimal branch dynamicsLarge drag due to large proportion of leavescompared to branch mass

(Rudnicki et al. 2007)Can results be used for urban trees?

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Wind tunnel – scale modelSmall modelTwo dimensionalHoles approximate

canopyConstant windNo branch dynamics(Sanz 2003)

Can results be scaled up?

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Wind loads – plantation trees

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Tree Structural analysisStatics versus Dynamics What is the difference?

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Statics - Tree Pull Test

•Rope pull simulates the wind force

•One result (How accurate?)

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Dynamics – two massesTwo masses

Two solutions

1. Masses move together 2. Masses move apart

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Dynamics – two branchesTwo branchesTwo solutions

1. Branches move together 2. Branches move apart

Many masses, many solutions, as in trees with many branches

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Dynamic solutions• Complex• Several possibilities for the same structure• Different tree shapes will behave differently• Dynamic outcomes different for different treesDynamic groups of trees1. Small trees, drag dominates because leaves (drag) has a

significant effect2. Medium tree, damping dominates because flexible branches

sway (mass damping)3. Large trees, inertia dominates, (mass of trunk) so dynamic

effects less

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Removing branches may not be good!

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Pruning farm trees

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Lower branches removed

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Remove branches more sway occurs

• Branch mass damping removed• Sway increases• Dynamics magnifies response of tree• May need to rethink some pruning options

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Pruning limbs

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Pruning - comment

James Urban 2008 Up by roots.

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Brudi (2002)Maximum force 505 kN m

Calculated - statics

Max overturning force 505 kN m.

•Estimate from computer model,very big number!!

Canopy is lumped mass, no branches

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Fatality Melbourne Thur Jun 28, 2007

Tree –Mountain Ash, E regnans

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Wind storm fells tree, kills residentThu Jun 28, 2007

• Jim Jewell was killed instantly when a tree fell on his house at Mt Macedon. (The Herald Sun)

• Police say Jim Jewell was killed instantly at about 11pm AEST yesterday, when a 30-metre tall gum tree weighing several tons crashed through his bedroom roof.

• Neighbour Grant Ford says the wind resembled a hurricane. • "It was pretty persistent, it wasn't the one gust of wind," he said.

"Basically it went all night from 9 (pm) to the early hours of this morning."

• Inspector Mario Fiorentino says it took three hours to reach the deceased man. Police say that the back third of the house has been sheared away by the force of the impact.

• Neighbours say last night's gale force winds were like being in the middle of a hurricane and with more bad weather predicted tonight many have opted to stay away.

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Failure is “not all at once”

Nelson, New Zealand, storm

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What really happened?

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Wind damage to tree – Burnley3 April 2008

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Spotted GumSpotted GumMonashMonash UniversityUniversity

Case studyCase studyFeb 2008Feb 2008

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Location – Monash Campus

Building 3A, Vice-Chancellor’s Office, Clayton. Left side tree

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Roots severed on left sideRoots cut by contractor.Is damage enough to cause instability?Performance

in high winds?Risk to people?Should the tree be

- removed or- retained?

Roots cut on left

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Root plate

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PicturecourtesyTreeLogic

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PicturecourtesyTreeLogic

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PicturecourtesyTreeLogic

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PicturecourtesyTreeLogic

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PicturecourtesyTreeLogic

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Problem – Keep or remove?Conventional Method• Three written arborist reports submitted• Two recommended removal, one to keep tree• Recommendations based on observation by

experienced and qualified arborists.

AlternativeMeasure the stability of the tree and collect structural Measure the stability of the tree and collect structural

information.information.This is done in two stagesThis is done in two stages1.1. Static Pull Test and Static Pull Test and 2.2. Monitor wind loads over a period (2 months)Monitor wind loads over a period (2 months)

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MonashMonashSpotted GumSpotted GumApril 2008April 2008

Wind sensor on roof

H=25mDbh=0.716Slenderness = 34.9

Tree sensors on trunkAt 3 meters (for security)

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Strainmeters on trunk

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Static Pull Test

Static pull East

Static Pull North

Static Pull Results

Static Pull North

Static Pull East

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Static Pull Results

Pull East

50 kN.m

Pull North

56 kN.m

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Wind measurement

Action photo of Ross Payne and Monash security guard.

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Wind sensor and tree

Cup anemometer• Measures wind speed

and direction• 1 sec average• Units m s-1

• Links to computer• Calibrated in wind

tunnel up to 30 m s-1

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Compare wind load to pull test

Wind direction180o

SOUTHERLY

22FEB 1532hrs

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Spotted Gum - Biggest gustWind dir

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Spotted gum, Monash UniWind dir

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Wind loads - dynamic

Static Pull North

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MonashMonash University, Wind Storm University, Wind Storm -- 2 April 20082 April 2008

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North WindNorth WindForceForce

MonashMonash University, Wind Storm University, Wind Storm -- 2 April 20082 April 2008

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North WindNorth WindForceForce

MonashMonash University, Wind Storm University, Wind Storm -- 2 April 20082 April 2008

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MonashMonash University, Wind Storm University, Wind Storm -- 2 April 20082 April 2008

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Peak moment during stormStatic pull

Static forces

Dynamic forces

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Monash wind storm datafile1411

Peak force 400 kN.m, but no significant wind gust

Large wind gust but no peak force on tree???

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Case study 2Trees and Wind loading on pipes

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Existing trees

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20 m Pin Oak

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Site Plan

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Pin Oak over concrete pipe

Wind load on canopy transferred to underground pipe.

An extreme wind would cause pipe failure when tree is mature (20 y)

Liability to council who decided to go ahead

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Tree shapes or structuresand motion

Is the dynamic motion the same as wind blows on trees?Can all trees be treated the same way?What are the differences?

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Discussion – Statics and Dynamics• Static approach misses dynamic interaction of branches• Wind not constant, changes velocity and direction• Must measure tree movement continuously during

storms (at least 10 hz, better 20 hz)• Branches on trees are dynamic and create complex

motion (minimises sway)• Trees are “de-tuned” by branch masses swaying out of

phase with each other. This may be a survival mechanism to prevent excess sway

• Tree species (canopy shapes) may need to be considered individually (eg for pruning recommendations).

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Future ProgramTree Dynamics Research

• Measure wind loads on trees in storms, in Australia, USA, other???

• Understand tree dynamics(a tree without branches is not a tree – Shigo)

• Effect of pruning on tree dynamics and wind loading• Use data to correlate with tree failure• Measure all loads, (torsion, internal stress)• Theory (new dynamic models, mass damping, wind

speed, drag coefficients, design guides)

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The End

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Italian cypress

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Tree - Cupressus sempervirens

WIND

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Cypress - gust

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Cypress – dynamic motion

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E E teretecornisteretecornis #1#1

Summary Summary –– windloadwindload v wind speedv wind speedSite Site –– SALE, AustraliaSALE, Australia

Ken JamesKen JamesJan 2006Jan 2006

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Red gum - unpruned

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Red gum – 20% pruned

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Red gum - gust

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13dec05 - b2310

Three similar gusts – different response of tree. Why?

E teretecornus #1 Sale, Vic. – pre-pruned

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Comparison – pre/post pruning

Wind speed (m/s)

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Comparison – pre/post pruning

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Comparison – pre/post pruning

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Storm front : 21dec05 - e1451E teretecornus #1 Sale, Vic. – pre-pruned

Mild wind

Strong gusts

Front

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1jan06 - k1419

Post-pruned 20%

E teretecornus #1 Sale, Vic. – after pruning 20%

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Wind forces compared Overturning moments (kN m)

MonashApr08

563

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Wind Speeds

Windthrow &BreakageCullen (2002)Spatz (2000)Sanderson et al (1999)

HurricaneHedden(1995)Dennis(2005) 185 kph

Hurricane max gustHedden(1995)