Tree Structure - Dynamics Ken James University of Melbourne, Australia

Tree Structure Statics & Dynamics Trees are optimised structures Statics well covered in last 10 years Dynamics - difficult Wind creates largest loads Total loads on trees consist of STATICS & DYNAMICS

Loads on Trees - Research Statics Trees growth responds to loads Axiom of Uniform stress (Mattheck ) Static approach good in still air Dynamics Wind is dynamic, creates large loads Tree dynamic response is not known Research Strategy Measure wind loads Measure tree response

Tree Structures and their loads Structure must be stronger than the loads applied. Failure occurs when Applied stress at point > strength of material Load > strength Need data to assess structure - Research Data on strengths of trunks and limbs Data on loads on trunks and limbs in high winds

Tree structures Auracaria with branches, STABLE, - without branches, UNSTABLE

Loads on trees Tension Compression Bending Shear Torsion Growth

Static and Dynamic Loads Loads applied as Static weight of branch, snow, ice Dynamic wind -------------------- Static and Dynamic loads ADD Biggest loads occur during high winds Difficult to measure actual loads during wind storms, but need data on this!

Tree Structure 1. Data on strengths of trunks and limbs Strength of a trunk/limb depends on 1. Size (area of cross section) 2. Shape (where material is positioned) 3. Material strength (k) - Young s modulus

Strength depends on 1. Size Trees largest sections are the oldest and stiffest Taper, gradually matches section to loads Base trunks/branches stiffest Ends smallest, most flexible Bigger sections hold more load, but also approach the limit of strength Imperfections in wood reduce strength so as trees get bigger they get nearer to failure. Q. Must know what loads on section to assess how close to failure!

Strength depends on 1. Size

Strength depend on 2. Shape Bending compression and tension forces on opposite sides of section Bending I beam shape Torsion twisting (may be significant in small flexible sections) - circular shape best Load history of tree/branch seen in growth rings and thickness variations

Loads on branches and trees Bending - tree weaker in compression than tension

Strength depend on 2. Shape Howarth, 18 th Century Mattheck, 1994

Strength depend on 2. Shape Response to loads Bending - tension, top & compression, bottom Growth is not uniform from the centre

Strength depends on 3. Material Strength of wood varies greatly Tensile strength about twice compressive strength Measured by Young s modulus Young wood flexible (7 year old Scot s pine (Pinus sylvestris)1.7 GN m -2 Old wood stiffer (27 year old Scot s Pine 7.9 GN m -2 (Mencuccini, 1997) Tree - base stiff, strong, - tips flexible, not as strong

Strength depends on 3. Material Material elasticity measured by (k) Young s modulus Shows as slope of line k 1 stiff k 2 flexible Strength is different k 2 flexible and strong

Dynamic Loads on trees 1. Static loads weight of limbs, foliage, snow, ice 2. Dynamic loads (wind) greatest (Mattheck 1994) bending (tension and compression) shear torsion Wind comes in gusts and pushes on tree canopy. Gusts occur with period of 20 to 40 seconds Complex sway motion of branches and tree Pendulum? How do trees sway?

Current dynamic tree models Woods, C.J. 1995

Current dynamic tree models Nield & Wood, 1998 Sanderson, et al.1999 Mass of canopy - rigid

Dynamic model Mass and spring oscillator Cyclic period Damping reduces motion

Dynamic model Mass and spring oscillator 1. Mass (m) 2. Spring (k) 3. Damping (d) Cyclic period defined

Tree sway motion Complex sway motion of tree and limbs. Dynamic model considers 1. Mass of trunk, branches and leaves 2. Spring wood Young s Modulus 3. Damping has three components aerodynamic drag leaves in wind viscoelastic damping stem/root/earth mass damping limb sway interaction

A dynamic model of trees A mass (m) oscillates on a spring (k) and motion is damped (d) Model Tree Oscillation

Mass damping effect of one branch A small mass (m) oscillates on a spring and damper and detunes the structure The amplitude is greatly reduced Model Tree Oscillation

Tuned mass damped Structure Buildings Poles Bridges

Tuned mass damped Structure First building using TMD, tuned mass damping 1987, Centrepoint Tower, Sydney Soong, 1997

Mass damping 2 nd order branch further small branch (mass) oscillates on larger branch and adds another mass damper Structure is detuned even more The amplitude is greatly reduced Model Tree Oscillation

Mass damping 5th order branch further small branch (mass) oscillates on larger branch and adds another mass damper Structure is detuned even more The amplitude is greatly reduced Model Tree Oscillation

A dynamic model of trees Structure of trunk is damped by leaves, internal & branches 1. Branches mass damping Large branches are first order mass dampers 2 nd, 3 rd, 4 th, 5 th & 6 th order branches 2. Damping (d) combination of leaves and viscoelastic Mass (m) and stiffness (k) of each branch in model Model Tree

A dynamic model for urban trees

Spectrum data Kerzenmacher & Gardiner, 1997

Spectrum data Saunderson, et al. 1999.

Tree Structure - Urban trees

Tree Structure Wind effects

Measuring wind loads in trees and branches Wind map of Australia AS 1170.2:2000

Wind Speeds Tree Windthrow Break Comment mph m s -1 mph m s -1 Cullen, 2002 55-63 25-28 55-63 26-28 Wind scales and vel comparison Hedden, R.L. 1995 46 69 Winch tests, Sth Carolina, hurricane 165 (max 249) km/h Spatz, 2000 20-30 Norway spruce, 56 y. 27 m high Sanderson et al. 1999 28 20 Mathematical model, values seem high (his comment) Coutts 1986 3-17 Ref from Sanderson AS1170.2. 2000 48-60 m s -1. Code values for return period of 100 years

Measuring wind loads - instrumentation

Wind Loads on Branches - Shigo

Branches in wind Deflection sideways and upwards Wind pushes branch Some sway but not back towards wind direction Branch does not sway like a pendulum

Analysis of Tree Structures 1. Wind throw whole tree 2. Limb/trunk failure parts of the tree

Wind throw whole tree analysis Overturning moment of wind resisted by tree roots in soil

Wind throw TREE PULL TEST Pull tree to measure resistance to overturning Determine wind loads (difficult) Verify strength of tree in ground to resist measured wind loads

Overturning forces Tree Eucalypt -200mm dia. Erica Eucalypt - 500 mm dia. Burnley Sitka spruce, 20 m high NZ trees, 7 sites x 13 trees, 9-39 years old, 28-35 m high Calculated -Plane trees 18m high Parkville Calculated from max wood fibre stress kn.m 6 60 10-52 300 600 1219 Bell et al., 1991 Comment Winch test in forest, Aust. - failed still stable though noticeable movement Max from winch tree pulls, Moore, 2000 PhD. Australian Wind Code (AS 1170.2) - very high Mattheck & Bethge, 2000

200mm Eucalypt (Erica) 6 kn.m failed Tree Pulls

Tree Pull - Burnley, 2002 400 mm Eucalypt Burnley - 60 kn.m still stable though noticeable movement

Overturning Force - calculated University of Melbourne Parkville 18 m plane trees - calculated at 600 kn.m (AS 1170.2) very high

Tree Pull Test 4 directions

Pull Test Burnley Pull test in 4 directions Gives measure of resistance to overturning Need accurate wind load data (project to measure overturning moments in wind storms) Provides data for decisions

Modes of vibration

Dismantling trees

Examples

Conclusions Wind is dynamic, creates largest loads Static and Dynamic loads ADD Biggest loads occur during high winds Complex sway motion of limbs modified by damping Damping has three components aerodynamic drag leaves in wind viscoelastic damping stem/root/earth mass damping limb sway interaction Mass damping minimises sway response

Further Work Difficult to measure actual loads during wind storms, but need data on this! Measure wind loads Measure tree response Develop strength testing such as pull tests Develop removal techniques to use natural damping of tree to advantage.