Ken James, School of Resource Management University of ... · School of Resource Management...
Transcript of Ken James, School of Resource Management University of ... · School of Resource Management...
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Tree Stability in WindsTree Stability in WindsKen James,
School of Resource ManagementUniversity of Melbourne
Australia
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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?
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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
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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
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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
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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
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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
KJ ISAAC 2010 64
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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.
KJ ISAAC 2010 65
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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).
KJ ISAAC 2010 66
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KJ ISA 2009 67
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
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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
may cause severe damage.KJ ISAAC 2010 68
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KJ ISAAC 2010 69
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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KJ 70
The King of trees
• Eucalyptus regnans• Mountain Ash• Tallest flowering plant• 101 m, Tas. (Oct 2008)
Distribution
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KJ ISAAC 2010 71
Tree heights
The range of tree heights
Plantation treesUrban trees30
20
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KJ ISAAC 2010 72
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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KJ ISAAC 2010 73
Tree height – convert to slenderness plot
Plantation treesUrban trees
Danger15m
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KJ ISAAC 2010 74
Slenderness (Stability?)
Plantation treesUrban trees
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KJ ISAAC 2010 75
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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KJ ISA 2009 76
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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KJ ISA 2009 77
Allometry – size and shapeHuman size ratio changes with age
OLD is not a scaled up
version of YOUNG
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KJ ISAAC 2010 78
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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KJ ISAAC 2010 79
Wind tunnel – scale modelSmall modelTwo dimensionalHoles approximate
canopyConstant windNo branch dynamics(Sanz 2003)
Can results be scaled up?
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KJ ISAAC 2010 80
Wind loads – plantation trees
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KJ ISAAC 2010 81
Tree Structural analysisStatics versus Dynamics What is the difference?
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KJ ISA 2009 82
Statics - Tree Pull Test
•Rope pull simulates the wind force
•One result (How accurate?)
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KJ ISA 2009 83
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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KJ ISA 2009 86
Removing branches may not be good!
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KJ ISA 2009 87
Pruning farm trees
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KJ ISA 2009 88
Lower branches removed
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KJ ISA 2009 89
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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KJ ISA 2009 90
Pruning limbs
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KJ ISA 2009 91
Pruning - comment
James Urban 2008 Up by roots.
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KJ ISA 2009 92
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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KJ ISA 2009 93
Fatality Melbourne Thur Jun 28, 2007
Tree –Mountain Ash, E regnans
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KJ ISAAC 2010 94
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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KJ ISAAC 2010 95
Failure is “not all at once”
Nelson, New Zealand, storm
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KJ ISAAC 2010 96
What really happened?
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KJ ISAAC 2010 97
Wind damage to tree – Burnley3 April 2008
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KJ ISA 2009 98
Spotted GumSpotted GumMonashMonash UniversityUniversity
Case studyCase studyFeb 2008Feb 2008
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KJ ISA 2009 99
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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KJ ISA 2009 101
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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KJ ISA 2009 107
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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KJ ISA 2009 108
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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KJ ISA 2009 109
Strainmeters on trunk
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KJ ISA 2009 110
Static Pull Test
Static pull East
Static Pull North
Static Pull Results
Static Pull North
Static Pull East
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KJ ISA 2009 111
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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KJ ISA 2009 113
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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KJ ISA 2009 114
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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KJ ISA 2009 119
Wind loads - dynamic
Static Pull North
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KJ ISA 2009 120
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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KJ ISA 2009 123
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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KJ ISA 2009 126
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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KJ ISA 2009 127
Case study 2Trees and Wind loading on pipes
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KJ ISA 2009 128
Existing trees
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KJ ISA 2009 129
20 m Pin Oak
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KJ ISA 2009 130
Site Plan
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KJ ISA 2009 131
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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KJ ISA 2009 132
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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KJ ISA 2009 133
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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KJ ISA 2009 134
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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KJ ISA 2009 135
The End
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KJ ISA 2009 136
Italian cypress
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KJ ISA 2009 137
Tree - Cupressus sempervirens
WIND
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KJ ISA 2009 138
Cypress - gust
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KJ ISA 2009 139
Cypress – dynamic motion
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APR08 Wind & Trees Seminar KJ 140
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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APR08 Wind & Trees Seminar KJ 141
Red gum - unpruned
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APR08 Wind & Trees Seminar KJ 142
Red gum – 20% pruned
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APR08 Wind & Trees Seminar KJ 143
Red gum - gust
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APR08 Wind & Trees Seminar KJ 144
13dec05 - b2310
Three similar gusts – different response of tree. Why?
E teretecornus #1 Sale, Vic. – pre-pruned
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APR08 Wind & Trees Seminar KJ 145
Comparison – pre/post pruning
Wind speed (m/s)
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APR08 Wind & Trees Seminar KJ 146
Comparison – pre/post pruning
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APR08 Wind & Trees Seminar KJ 147
Comparison – pre/post pruning
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APR08 Wind & Trees Seminar KJ 148
Storm front : 21dec05 - e1451E teretecornus #1 Sale, Vic. – pre-pruned
Mild wind
Strong gusts
Front
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APR08 Wind & Trees Seminar KJ 149
1jan06 - k1419
Post-pruned 20%
E teretecornus #1 Sale, Vic. – after pruning 20%
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APR08 Wind & Trees Seminar KJ 150
Wind forces compared Overturning moments (kN m)
MonashApr08
563
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APR08 Wind & Trees Seminar KJ 151
Wind Speeds
Windthrow &BreakageCullen (2002)Spatz (2000)Sanderson et al (1999)
HurricaneHedden(1995)Dennis(2005) 185 kph
Hurricane max gustHedden(1995)