WIND - SAG Baumstatik eV

Tree Stability in Winds 

Ken James, 

School of Resource Management 

University of Melbourne 

Australia 

KJ 1

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 

KJ ISA AC 2010 2

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!” 

KJ ISAAC 2010 3

Urban tree failure 

•Causes injury and 

property damage 

Arborists face issues 

of LIABILITY 

How to assess tree 

stability 

Can a structural 

analysis of a tree help 

KJ ISAAC 2010 4

Structural Analysis of trees 

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 

KJ ISAAC 2010 5

Stability and Failure 

Trees are stable if they are 

stronger than the loads they 

experience. 

If 

LOAD exceeds STRENGTH 

FAILURE OCCURS 

Biggest load is WIND 

KJ ISAAC 2010 6

STATIC 

Current methods of structural analysis 

• Tree pull (Germany) 

DYNAMIC 

• Forestry modelling 

• Urban trees – very little. 

• Wind loads – need data 

KJ ISAAC 2010 7

Dynamic wind loading 

Complex dynamic motion 

Dynamic interaction of branches 

KJ ISAAC 2010 8

Tree shapes – branch are important 

KJ ISAAC 2010 9

Trees in this study 

Different branching forms 

Palm Italian cypress Araucaria (Hoop pine) 

Eucalyptus teretecornus 

KJ ISAAC 2010 10

Urban trees – branch sway dominates 

Melbourne, River Walks 

A tree is a collection of branches (Shigo 1991) 

KJ ISAAC 2010 11

Measuring wind loads 

with 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 

KJ ISAAC 2010 12

Measuring wind loads on trees- Strategy 

“Make the tree the sensor” 

Strain meters record bending in winds 

KJ ISAAC 2010 13

Wind Loads – Static analysis 

Mattheck 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 

KJ ISA 2009 14

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 

KJ ISAAC 2010 15

Calibrate the tree – Static Pull Test 

Calibration so 

instruments measure 

bending moments in 

wind 

KJ 16

Measuring wind loads on trees 

• As wind bends trunk 

• Outer fibers expand or contract 

• Strainmeter measures fibre length 

change 

• White pine, Virginia, USA 

• Dr Brian Kane, U Massechusetts 

• Ken James, U Melb. 

KJ 17

Sample graph of tree motion in 

wind from one sensor 

Sensor1- linear 

Sensor 2 – linear (at right 

angles) 

Resultant XY graph 

Gives motion for wind 

from any angle 

KJ 18

Dynamic sensors on trees 

N/S & E/W directions 

KJ 19

Wind Loads – Hoop pine 

KJ 20


KJ 21

Wind Load data (kNm) – Hoop pine 

Maximum along wind load 175 kNm 

Maximum across wind load 58 kNm 

Values can be used to measure 

Wind load on trunk 

Wind loads on roots 

Note significant side loading on roots 

KJ 22


Use data to; 

•Assess wind load 

•For design data on 

other similar trees 

•Estimate stability 

•Failure (need 

higher wind data). 

KJ 23

Tree response spectrum 

Hoop 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 

KJ 24

Palm 

• Height 18.1 m 

• dbh 0.436 m 

Location 

• Burnley Campus 

• Melbourne 

•Victoria 

• Australia 

KJ ISA 2009 25

Palm with 

strain meters 

KJ ISA 2009 26

Wind Load - palm 

KJ 27

Palm video 

KJ ISA 2009 28

Palm 

KJ ISA 2009 29

Palm 

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

KJ ISA 2009 30

Palms as 

structures 

•Flexible 

•Survive winds with 

flexible response 

Man –made crane 

•Rigid 

•Survives winds with 

strength in structure 

KJ ISA 2009 31

Palms – Survive wind loads 

KJ ISA 2009 32

Wind Load - palm 

KJ 33

Wind dir 

Wind dir 

Spotted Gum 

Biggest gust in 3 months 

KJ 34

Wind dir 

Spotted gum, 

Monash Uni 

KJ 35

Results – Monash 

• Wind load and wind speed 

• Design data for similar trees 

KJ 36

Tree dynamics, E. grandis, wind loads 

Wind Dir 

Zero pt 

KJ 37

Wind load summary 

KJ ISA 2009 38

Wind load (logarithmic) 

KJ ISA 2009 39

7. Branches 

Branches can dominate an urban trees structure 

Melbourne, Botanic Gardens 

KJ 40

Branch dynamics 

KJ 41

Branch sway - Eucalyptus saligna 

Wind direction 

Branch sway left and UPWARDS 

KJ 42

Wind forces on branches! 

up or down 

Burnley, Melbourne, April 2008 

KJ 43

Branch movement upwards 

Shigo (1991) 

• Suggested upward 

breaking of branches 

occurs 

• observed broken fibres 

at end of branch 

KJ 44

Tree motion 

Harmonic motion 

Do trees sway back and forth 

Is there a natural frequency 

What are the dynamic forces 

on trees 

KJ 45

Harmonic motion 

Spectrum 

Peak shows 

Natural frequency 

Oscillating response 

with a natural frequency 

Time domain 

Frequency domain 

KJ 46

Tree motion – harmonic 

Spectrum 

Peak shows 

Natural frequency 

Time domain 

Oscillating response. 

Is there a natural frequency 

Frequency domain 

KJ 47

8. Tree Models 

• Dominated by Greenhill (1880) concept 

• Trunk analysed, no branches 

• Conventional dynamic mathematics 

•Natural frequency 

KJ 48

Current dynamic tree models 

Woods, C.J. 1995 

Oscillating response 

with a natural frequency 

KJ 49

Current dynamic tree models 

Nield & Wood, 1998 

Sanderson, et al.1999 

Mass of canopy - rigid 

KJ 50

New Dynamic Tree Model 

- with dynamic branches 

KJ 51

Mass Damping minimises sway 

The dynamic interaction 

of masses (branches) that 

prevent large oscillations 

occurring 

KJ 52

Features of the new dynamic model 

All 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) 

KJ 53

9. Examples of mass damping 

KJ 54

Tuned mass damped Structure 

Buildings 

Poles 

Bridges 

| Mass damper

Taipei 101 – tallest building 

KJ 56

Tuned mass damper 

730 tonnes 

Reduces movement 

40% 

KJ 57

Tuned mass damper 

KJ 58

Real tree sway is complex 

Normal speed 

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 

x3 speed 

KJ 59

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 

KJ 60

No mass damping, US - style 

KJ 61

Static Pull test - Method 

KJ ISAAC 2010 62

Static Pull test 

• Rope and controlled pull. 

Measure 

•Pull 

• Trunk strain 

• Root plate angle 

(Max 0.25°) 

• How good is it 

KJ ISAAC 2010 63

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

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

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

Tree characteristics that 

influence dynamic effects 

1. Tree HEIGHT 

2. DIAMETER (DBH) 

3. SLENDERNESS RATIO (HEIGHT/DBH) 

4. BRANCHES 

These properties influence DYNAMICS 

IMPORTANT 

Small trees are not mini versions of large trees 

KJ ISA 2009 67

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

AN example of tree stability 

Trees – largest living thing on earth 

Redwood, General Grant, USA, 

California 

•Sequoiadendron giganteum 

•Height 275 ft (83.9m) 

•Basal girth 82.3 ft (25.1m) 

•Dbh = 26 ft 

Weight (diff estimates) 

•Trunk - 5.46 x 10 5 kg (~600 tons) 

•Total - 12.7 x 10 5 kg (~ 1300 tons) 

Slenderness h/d = 275/26 

= 10.5 

Niklas (1992) 

KJ ISAAC 2010 69

The King of 

trees 

• Eucalyptus regnans 

• Mountain Ash 

• Tallest flowering plant 

• 101 m, Tas. (Oct 2008) 

Distribution 

KJ 70

Tree heights 

30 

20 

Urban trees 

Plantation trees 

The range of tree heights 

KJ ISAAC 2010 71

Height and diameter 

or 

Slenderness – h/d 

A measure of stability 

Example - E. Tereticornis 

Height = 14 m 

Diameter at breast height 

(dbh = 0.886m) 

Slenderness = height/dbh 

= 14 / 0.886 

= 15 

Slenderness 15:1 

KJ ISAAC 2010 72

Tree height – convert to slenderness plot 

Urban trees 


Danger 

15m 

KJ ISAAC 2010 73

Slenderness (Stability) 

Urban trees 


KJ ISAAC 2010 74

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 

KJ ISAAC 2010 75

Allometry – tree size and shape 

BIG TREES are NOT 

scaled up versions 

of small trees 

Effect of BRANCHES is important 

in wind (dynamics) 

Wind tunnel Plantation Urban trees Forest giants 

KJ ISA 2009 76

Allometry – size and shape 

Human size ratio 

changes with age 

OLD 

is not a scaled up 

version of 

YOUNG 

KJ ISA 2009 77

Wind tunnel tests on trees 

Constant wind 

Wind Tunnel 

Small trees 

Constant wind speed 

No gusts 

Minimal branch dynamics 

Large drag due to 

large proportion of leaves 

compared to branch mass 

(Rudnicki et al. 2007) 

Can results be used for urban trees 

KJ ISAAC 2010 78

Wind tunnel – scale model 

Small model 

Two dimensional 

Holes approximate 

canopy 

Constant wind 

No branch dynamics 

(Sanz 2003) 

Can results be scaled up 

KJ ISAAC 2010 79

Wind loads – plantation trees 

KJ ISAAC 2010 80

Tree Structural analysis 

Statics versus Dynamics 

What is the difference 

KJ ISAAC 2010 81

Statics - Tree Pull Test 

•Rope pull simulates the wind force 

•One result (How accurate) 

KJ ISA 2009 82

Dynamics – two masses 

Two masses 

Two solutions 

1. Masses move together 2. Masses move apart 

KJ ISA 2009 83

Dynamics – two branches 

Two branches 

Two solutions 

1. Branches move together 2. Branches move apart 

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

KJ ISA 2009 84

Dynamic solutions 

• Complex 

• Several possibilities for the same structure 

• Different tree shapes will behave differently 

• Dynamic outcomes different for different trees 

Dynamic groups of trees 

1. Small trees, drag dominates because leaves (drag) has a 

significant effect 

2. Medium tree, damping dominates because flexible branches 

sway (mass damping) 

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

effects less 

KJ ISAAC 2010 85

Removing branches may not be 

good! 

KJ ISA 2009 86

Pruning farm trees 

KJ ISA 2009 87

Lower branches removed 

KJ ISA 2009 88

Remove branches more sway occurs 

• Branch mass damping removed 

• Sway increases 

• Dynamics magnifies response of tree 

• May need to rethink some pruning options 

KJ ISA 2009 89

Pruning limbs 

KJ ISA 2009 90

Pruning - comment 

James Urban 2008 Up by roots. 

KJ ISA 2009 91

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 

KJ ISA 2009 92

Fatality Melbourne Thur Jun 28, 2007 

Tree –Mountain Ash, E regnans 

KJ ISA 2009 93

Wind storm fells tree, kills resident 

Thu 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. 

KJ ISAAC 2010 94

Failure is “not all at once” 

Nelson, New Zealand, storm 

KJ ISAAC 2010 95

What really happened 

KJ ISAAC 2010 96

Wind damage to tree – Burnley 

3 April 2008 

KJ ISAAC 2010 97

Spotted Gum 

Monash University 

Case study 

Feb 2008 

KJ ISA 2009 98

Location – Monash Campus 

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

KJ ISA 2009 99

Roots severed on left side 

Roots 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 

KJ ISA 2009 100

Root plate 

KJ ISA 2009 101

Picture 

courtesy 

TreeLogic 

KJ ISA 2009 102

Picture 

courtesy 

TreeLogic 

KJ ISA 2009 103

Picture 

courtesy 

TreeLogic 

KJ ISA 2009 104

Picture 

courtesy 

TreeLogic 

KJ ISA 2009 105

Picture 

courtesy 

TreeLogic 

KJ ISA 2009 106

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. 

Alternative 

Measure the stability of the tree and collect structural 

information. 

This is done in two stages 

1. Static Pull Test and 

2. Monitor wind loads over a period (2 months) 

KJ ISA 2009 107

Monash 

Spotted Gum 

April 2008 

Wind sensor on roof 

H=25m 

Dbh=0.716 

Slenderness = 34.9 

Tree sensors on trunk 

At 3 meters (for security) 

KJ ISA 2009 108

Strainmeters on trunk 

KJ ISA 2009 109

Static Pull Test 

Static Pull Results 

Static Pull 

North 

Static 

Pull 

North 

Static pull East 

Static 

Pull 

East 

KJ ISA 2009 110

Static Pull Results 

Pull North 

56 kN.m 

Pull East 

50 kN.m 

KJ ISA 2009 111

Wind measurement 

Action photo of Ross Payne and Monash security guard. 

KJ ISA 2009 112

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 

KJ ISA 2009 113

Compare wind load to pull test 

Wind direction 

180 o 

SOUTHERLY 

22FEB 1532hrs 

KJ ISA 2009 114

KJ ISA 2009 115

KJ ISA 2009 116

Spotted Gum - Biggest gust 

Wind dir 

KJ ISA 2009 117

Spotted gum, Monash Uni 

Wind dir 

KJ ISA 2009 118

Wind loads - dynamic 

Static Pull 

North 

KJ ISA 2009 119

Monash University, Wind Storm - 2 April 2008 

KJ ISA 2009 120

North Wind 

Force 


KJ ISA 2009 121

North Wind 

Force 


KJ ISA 2009 122


KJ ISA 2009 123

KJ ISA 2009 124

Peak moment during storm 

Static pull 

Static forces 

Dynamic forces 

KJ ISA 2009 125

Monash wind storm data 

file1411 

Large wind gust but no 

peak force on tree 

Peak force 400 kN.m, but 

no significant wind gust 

KJ ISA 2009 126

Case study 2 

Trees and Wind loading on pipes 

KJ ISA 2009 127

Existing trees 

KJ ISA 2009 128

20 m Pin Oak 

KJ ISA 2009 129

Site Plan 

KJ ISA 2009 130

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 

KJ ISA 2009 131

Tree shapes or structures 

and motion 

Is the dynamic motion the same as wind blows on trees 

Can all trees be treated the same way 

What are the differences 

KJ ISA 2009 132

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). 

KJ ISA 2009 133

Future Program 

Tree 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) 

KJ ISA 2009 134

The End 

KJ ISA 2009 135

Italian cypress 

KJ ISA 2009 136

Tree - Cupressus sempervirens 

WIND 

KJ ISA 2009 137

Cypress - gust 

KJ ISA 2009 138

Cypress – dynamic motion 

KJ ISA 2009 139

E teretecornis #1 

Summary – windload v wind speed 

Site – SALE, Australia 

Ken James 

Jan 2006 

APR08 Wind & Trees Seminar KJ 140

Red gum - unpruned 


Red gum – 20% pruned 


Red gum - gust 


13dec05 - b2310 

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

Three similar gusts – different response of tree. Why 


Comparison – pre/post pruning 

Wind speed (m/s) 






Storm front : 21dec05 - e1451 

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

Mild wind 

Strong gusts 

Front 


1jan06 - k1419 

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

Post-pruned 20% 


Wind forces compared 

Overturning moments (kN m) 

Monash 

Apr08 

563 


Wind Speeds 

Windthrow & 

Breakage 

Cullen (2002) 

Spatz (2000) 

Sanderson et al 

(1999) 

Hurricane 

Hedden(1995) 

Dennis(2005) 

185 kph 

Hurricane 

max gust 

Hedden(1995)

WIND - SAG Baumstatik eV

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