Tree Structure - Dynamics Ken James University of Melbourne, Australia

Transcription

1 Tree Structure - Dynamics Ken James University of Melbourne, Australia

2 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

3 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

4 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

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

6 Loads on trees Tension Compression Bending Shear Torsion Growth

7 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!

8 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

9 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!

10 Strength depends on 1. Size

11 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

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

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

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

15 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

16 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

17 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?

18 Current dynamic tree models Woods, C.J. 1995

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

20 Dynamic model Mass and spring oscillator Cyclic period Damping reduces motion

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

22 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

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

24 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

25 Tuned mass damped Structure Buildings Poles Bridges

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

27 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

28 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

29 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

30 A dynamic model for urban trees

31 Spectrum data Kerzenmacher & Gardiner, 1997

32 Spectrum data Kerzenmacher & Gardiner, 1997

33 Spectrum data Saunderson, et al

34 Tree Structure - Urban trees

35 Tree Structure Wind effects

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

37 Wind Speeds Tree Windthrow Break Comment mph m s -1 mph m s -1 Cullen, Wind scales and vel comparison Hedden, R.L Winch tests, Sth Carolina, hurricane 165 (max 249) km/h Spatz, Norway spruce, 56 y. 27 m high Sanderson et al Mathematical model, values seem high (his comment) Coutts Ref from Sanderson AS m s -1. Code values for return period of 100 years

38 Measuring wind loads - instrumentation

39 Wind Loads on Branches - Shigo

40 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

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

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

43 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

44 Overturning forces Tree Eucalypt -200mm dia. Erica Eucalypt mm dia. Burnley Sitka spruce, 20 m high NZ trees, 7 sites x 13 trees, 9-39 years old, m high Calculated -Plane trees 18m high Parkville Calculated from max wood fibre stress kn.m 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 ) - very high Mattheck & Bethge, 2000

45 200mm Eucalypt (Erica) 6 kn.m failed Tree Pulls

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

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

48 Tree Pull Test 4 directions

49 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

50 Modes of vibration

51 Dismantling trees

52 Examples

53 Examples

54 Examples

55 Examples

56 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

57 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.