Tree Biomechanics and Risk Assessment

Tree Biomechanics and Risk
Assessment
Texas Tree Conference, Texas Chapter of the ISA
Waco, Texas
October 2, 2013
Frank W. Telewski, Ph.D.
W.J. Beal Botanical Garden and Campus Arboretum
Department of Plant Biology
Michigan State University
Outline
Tree structure and anatomy
Intro to tree biomechanics
•
•
•
Primary vs. Secondary Growth
Wood (xylem)
– Stress v. strain
– Tension, compression, torsion
– Volume v. material properties
– Conifers
– Angiosperms
•
•
•
•
• Diffuse porous
• Ring porous
•
Tropisms
– Gravitropism
• Compression wood
• Tension wood
– Phototropism
•
•
Crown architecture
BREAK
Basic terms
•
•
•
•
2 moment of area
Elastic modulus
Density
brashness
Bending and buckling
Sway and damping
Fracture mechanics
Root plate stability
– Soil
– Roots
•
BREAK
Outline
Why trees Fail
Hollow trees- detecting
Branch and canopy failure
Root failure
Cradle to the Grave
• Tree care
Primary vs. Secondary Growth
• Primary Growth- from the apical meristem,
provides for tree height growth, and initial
diameter growth
• Secondary Growth- from the vascular and
cork cambia, provides radial growth or
increase in girth (diameter)
Primary vs. Secondary Growth
http://www.moodlesite.info/files/BiologyExploringLife04/0-13-115075-8/text/chapter20/concept20.4.html
Primary vs. Secondary Growth
http://www.moodlesite.info/files/BiologyExploringLife04/0-13-115075-8/text/chapter20/concept20.4.html
MATURE PHLOEM
DIFFERENTIATING
PHLOEM
MATURING PHLOEM
RADIALLY
ENLARGING PHLOEM
DIVIDING PHLOEM
(Phloem mother cells)
CAMBIUM
DIFFERENTIATING
XYLEM
CAMBIAL INITIAL
(dividing)
CAMBIAL
ZONE
DIVIDING XYLEM
(Xylem mother cells)
RADIALLY
ENLARGING XYLEM
MATURING XYLEM (Secondary cell wall formation)
MATURE XYLEM
Wood (Secondary Xylem)
• Functions:
– Conduct water up the stem
– Storage of photosynthate
• Carbohydrates (sugar, starch)
• Proteins
• Lipids (fat)
– Mechanical Strength
Types of Wood
•
•
•
•
•
•
Juvenile wood vs. mature wood
Sapwood vs. heart wood
Earlywood vs. latewood
Non-porous wood vs. porous wood
Ring porous wood vs. diffuse porous wood
‘Normal wood’ vs. reaction wood
Juvenile wood vs. Mature wood
• Juvenile wood is the first wood formed in a stem or branch
and will continue to be formed for a few years.
–
–
–
–
–
Large cells
Thin cell walls
Low wood density (weak, but fast to produce)
Short cells
Cellulose Microfibrils have a larger fiber angle in cells
• Mature wood is formed as the cambium and tree ages.
–
–
–
–
–
Smaller cells
Thicker cell walls
Higher wood density (stronger, but slower to produce)
Longer cells
Cellulose Microfibrils have a smaller fiber angle in cells
What are cellulose microfibrils?
The arrangement of cellulose microfibrils in
wood cells are important to mechanical
properties
http://www.metriguard.com/fiber.php
Sapwood vs. Heartwood
• Sapwood:
–
–
–
–
–
Water conducting elements are dead (tracheids and vessels)
Parenchyma are alive
Usually light or white in color
Capable of responding to injury- barrier formation
But less resistant to decay
• Heartwood:
–
–
–
–
–
No longer conducts water, conducting elements can be blocked
Parenchyma are dead
Usually a darker color, more prized by wood workers
Can no longer respond to injury
More decay resistant due to secondary products
Juvenile wood vs. Mature wood
Sap wood vs. Heart wood
Heart Wood
Sap Wood
http://ifbholz.ethz.ch/natureofwood/pc/jr/jr2.html
Heartwood vessels of oak are sealed by parenchyma cells
which grow into the lumen space. These ingrowths are
known as tyloses.
Earlywood vs. Latewood
• Non-porous wood
– Wood of conifers
• Tracheids
– Conduct water
– Provide mechanical
support
– Earlywood- tracheids
• Cells thin walled
• Large lumens
• Low density
– Latewood- tracheids
• Cells thick walled
• Small lumens
• High density
• Porous wood
– Wood of most angiosperms
• Vessels
– Conduct water
• Fibers
– Provide mechanical
Support
– Earlywood and Latewood
depend if diffuse porous or
ring porous. See
subsequent slides.
Non-Porous wood (conifers)
Conifers: radial files of cells (for most species)
Note: colors are inverted!
This is an x-ray!
Conifers: radial files of cells (for most species)
Non-porous (vessel-less) wood
Tracheids
Tracheids
Resin ducts
Resin ducts
Horizontal rays
Horizontal rays
Porous Wood (angiosperms)
Ring Porous vs. Diffuse Porous
Ring porous: large earlywood vessels
Vessels
Fibers
Rays
Diffuse porous: small vessels throughout
Vessels
Fibers
Rays
Reaction wood
• Compression wood (conifers)
– Round shaped tracheids
– Higher lignin content
– Cellulose microfibrils with steeper angle (perpendicular to the long
axis of the cell
• Tension wood (porous wood angiosperms)
– Gelatinous fibers (more cellulose)
– Fewer vessels
– Cellulose microfibrils approaching vertical (parallel to long axis of the
cell
• Flexure wood (both in conifers and angiosperms)
– Less lignin
– Cellulose microfibrils intermediate between tension wood and normal
wood
Maintaining trees in equilibrium with
their mechanical environment
Normal Angiosperm Wood
Tension Wood
Compression Wood
Opposite
wood
Tension wood
Opposite
wood
White Oak (Quercus alba)
Compression
wood
Eastern White Pine (Pinus strobus)
What’s in a cell wall?
• Normal wood and Tension
wood gelatinous fiber
• Normal wood and Compression
wood tracheid
Kwon et al. 2001. Phytochemistry 57:847-857
Land slipping and
snow load on slopes
can cause trees to
tilt, resulting in a
sweeping stem with
reaction wood.
In order to reorientate limbs and
trucks, reaction
wood creates
internal growth
strains, tension and
compression. When
cut, these strains are
released and can
cause severe splitting
and kickback, a
hazard to the urban
forester and the
forester alike.
Wind Effects in Trees
Flexure wood (below) and ‘normal’ wood
(above) in Fraser fir (Abies fraseri)
Combining the different concepts of
wood together
Different wood formation will induce internal growth strains to
maintain the mechanical equilibrium within the tree to its
mechanical environment.
Bert and Danjon 2006. For Ecol and Man 222:279-295
Types of Tropisms
• Gravitropism (geotropism)- response to
gravity
– Negative gravitropic (shoots)
– Positive gravitropic (roots)
• Phototropism- response to light
Negative Gravitropism
Negative Gravitropism
Gravity
Negative Gravitropism
Gravity
Auxin
Positive
Phototropism
Sun Light
Positive
Phototropism
Auxin
Positive
Phototropism
Tropisms interact within
a tree and by organ:
Branches are neutral
gravitropic and
phototropic, where as
shoots are negatively
gravitropic and
positively phototropic.
Crown Architecture
• Conical- excurrent branching habit
– Common in conifers
– Lombard poplars
– other ‘Fastigate trees’
• Rounded- decurrent or deliquescent
branching habit
– Most temperate deciduous trees
Crown Architecture
Time for a Break
Introduction to Tree Biomechanics
• To make a stronger tree you need one of two
things:
– Stronger Wood (mechanical property)
• Density
• Elastic Modulus
– More Wood (volume)
• Second moment of inertia
Introduction to Tree Biomechanics
• Basic terms
– Wood density g/cc or lbs/cu. Ft.
– Elastic Modulus (Young’s modulus) kg/mm2
– Second Moment of Cross Sectional Area (moment of
inertia of plane area m4)
– Stress
– Strain
– Bending
– Tension
– Compression
– Torsion
– Shear
– Fracture
Wood density
• In green wood (living trees), wood density
scales proportionally with the elastic modulus
• The modulus of rupture scales with the 1.25
power of wood density
Factors influencing Wood Density
• What is wood density?
• Genetic
• Environmental
– Drought
– Nutrients
– Mechanical requirements
• Tropisms
• Wind
Wood Density
(mass/volume; usually reported as kg/m3)
Annual ring of a ‘hard pine’
Low density earlywood
Thin cell wall, large lumen
Annual ring of a ‘soft pine’
High density latewood
Thick cell wall, narrow lumen
What determines density?
• Most important factor: ratio of cell wall
(cellulose, lignin, and hemicellulose) to lumen
space (air)
• Packing density: amount of cell wall material
packed into a cell wall
• Lignin:Cellulose ratio
Importance of Density
• Density (δ ) and Mechanics
– δ = Cell wall:air space + cellulose:lignin + packing
– δ Proportional to “strength”, used in construction
– δ Correlated to Young’s Elastic Modulus- BUT…
reaction wood is an exception
The bending moment:
Applied force
Compression
Side
Tension Side
Stress and Strain relations in plants:
Lessons from the world of mechanics
• Stress- applied force
• Strain- resultant deformation or change
in the object or material being stressed
(response)
• Elastic deform
• Plastic deform
Elastic
Plastic
limit
• Tolerate the stress
deformation
• Avoid the stress Stress
Elastic range
Strain
Strength
• Material property, the Elastic modulus (E) can be
obtained from the slope of the stress-strain
curve. It is a material property
• Amount of material in the cross-section being
loaded (I) is critical to strength or resistance to
bending (stiffness).
– It can be determined from the dimensions of the
object being tested
• (remember how to make a stronger tree?)
• E (material property) X I (amount of material) = stiffness or EI
Strength of Douglas fir Timbers
2 x 8 vs. 2 x 12
2 x 12
2 x 8 Floor Joist
h
E, Elastic modulus of
Douglas fir =
13 x 109 N/m2 (Gpa)
I, Second moment of
cross sectional area =
I = bh3/12
b
h = 8” = 0.2032 m
b = 2” = 0.0508 m
I = 0.0508 x 0.20323/ 12
I = 0.0508 x 0.0084/12
I = 0.0004 /12
I= 3.5518 x 10-5
EI = 46.17 x 104 N/m2
2 x 8 Scaffold Plank
Floor Joist
h
b
EI = 2.89 x 104 N/m2
h
h = 12” = 0.3048 m
b = 2” = 0.0508 m
I = 0.0508 x .20323/ 12
I = 0.0508 x 0.0283 /12
I= 0.0014/12
I= 1.1987x 10-4
EI = 155.83 x 104 N/m2
b
The same principle applies to columns
or cylinders:
For a Douglas Fir Tree
I = πD4/64
D=2m
I = 0.7854 m4
EI = 10.2 x 109 N/m2
D
D
I = πD4/64
D=1m
I = 0.2618 m4
EI = 3.4 x 109 N/m2
D
d
I = π/64 (D4 – d4)
D=2m
d=1m
I = 0.7363 m4
EI = 9.6 x 109 N/m2
Practical Application of the Cylinder
From E. Thomas Smiley, Bartlett Tree Research Laboratories “Hugo Broken Trees”
What about trees with different
densities or values of E?
Northern white cedar compared to cherry bark oak
N. White cedar E = 4.4 x 109 N/m2
D
I = πD4/64
D=2m
I = 0.7854 m4
EI = 3.5 x 109 N/m2
Cherry bark oak E = 12.3 x 109 N/m2
D
Chapter 5: Mechanical Properties of Wood, David E. Kretschmann
In: General Technical Report FPL-GTR-190
http://www.fpl.fs.fed.us/documnts/fplgtr/fplgtr190/chapter_05.pdf
I = πD4/64
D=1m
I = 0.2618 m4
EI = 3.3 x 109 N/m2
The Hazard Beam
Point of
attachment
to trunk
Applied force
Snow, Ice
Tension Side
Compression
Side
Wood is weaker under compression than under tension!
Pine branch as a Hazard Beam
Compression Failure
Types of Mechanical Loads on Trees
The induction of bending moments
Self-Loading: perceiving one’s own weight
Euler’s Buckling-
g
Cell within
vertical stem
F = maximum or critical force
(vertical load on column)
E = modulus of elasticity
I = area moment of inertia
l = unsupported length of
column
K = a constant for one end
fixed and the other end free
to move laterally K = 1/4;
g
Critical Heightρ = density
E = Young's modulus
r = radius vertical column of circular cross section
CA
CB
CA ~ CB
Stem under
compression load
due to acceleration
of Gravity
Stem failure (Euler’s
Buckling) due to
exceeding hcrit
(McMahon 1973)
Euler’s BucklingIn Larix at Strbske
Pleso after
blowdown or
windthrow event.
Self-loading and growth induced internal
pressures (growth strains)
• Circumnutations- correction for self-support?
• Regulation of stem taper (allometry)
• Compressive force induce callus cell differentiation
(Lintilhac & Vesecky, 1981; Barnett & Asante, 2000)
• Maintain organization of the vascular cambium
(Brown & Sax, 1962; Makino et al., 1983)
• Induction of a vascular cambium and 2nd growth in
Arabidopsis (Ko et al., 2004)
Gravitropism: sensing of differential loading on
plasmamembrane?
Static load, or
displacement meeting
requirement of
presentation time
Cell on tension side
of stem
g
Telewski 1993
TA
TB
Cell on compression
side of stem
Tension
side
TA > TB
CA
Compression
side
CB
CA < C B
Pressure Waves: Thigmorphogenesis
• Wind
• Water currents and tides
• Mechanical contact
– Fungal penetration peg
– Animals brushing past vegetation
– Roots or stems pushing through soil
• Sound?
Pressure Waves: Thigmorphogenesis
Buoyancy
g
Currents
Aquatic Algae
Lateral
pressure
Alternating
Return sway
Due to sway (damping) beyond
vertical, presentation time
requirement may not met
g
Wind
Return
Sway
T
C
0
Land Plants
Sway, Damping and Streamlining
• The branches of trees act to counter balance
or damp sway in trees.
• Without damping, a tree could go into
oscillation and fail. Think the Tacoma Narrows
Bridge in a wind.
• Pruning, opening up a crown, will impact a
trees ability to damp.
Streamlining reduces drag in the
canopy and thus in the entire tree
Streamlining of crowns reduce wind
loading by reducing the speed specific
drag. Avoidance of stress by shedding
the load.
Telewski & Jaffe 1986
Fracture Mechanics
Crack in silver
maple that
sealed up,
note included
bark. This is
very
susceptible to
cracking again
Self-splitting tree: Unusual radial fracture pattern in a
Tree of Heaven, note ‘cat face’ growth pushing open
the crack to the lower right
Continued cambial
growth is actually
forcing this crack
open.
Steep Branch Angles
• Steep branch angles tend to be
weak
• Examples:
– Elm
– Bradford pear
• Fracture Mechanics- included bark,
crack propagation (think windshield and stone
chip)
Steep branch angles can lead
to fractures, weak points due
to included bark
Note bark pucker!
Sudden branch drop/summer drop
• Usually observed on wind-still, sunny days
• Observation- more common during drought,
after a rain
• Fatigue?
• Wood brashness?
• Incipient decay?
• Repetitive water loading and unloading
(transpiration)
Tight growth rings in Oak- potential
source of brashness
Time for a Break
WHY TREES FAIL
Frank W. Telewski
Professor and Curator
W. J. Beal Botanical Garden
and Campus Arboretum
Michigan State University
So, why do trees fail?
• The Four Aces–Wood quantity and quality
(branches, stems, & roots)
–Canopy architecture
–Disease
–Soil conditions
Smiley and Fraedrich 1992. Journal of Arboriculture 18:201-204
Most Common Tree Failures at MSU
• Branch Breakage
– Wind
– Ice
– Snow
– Self-pruning/dead
• Trunk Failure (wind snap)
• Root Plat Failure (wind throw)
• Sudden Branch Drop
Tree Assessment
• Evaluate tree for structural
soundness/likelyhood of failure
• Evaluate site for potential damage/liability
Visual Assessment
• Look for defects
–
–
–
–
–
Scars
Hollows
Cracks
Seams (sealed cracks, usually a ‘pucker’)
Fungal fruiting bodies
• Heart rot
• Root rot
–
–
–
–
–
Root Plat lifting or leaning
Dead or broken branches
Old cabling or bolts
Butt swelling, slumping
Girdling roots
Scars worth testing
Scars- bark death in Kentucky Coffee Tree
Don’t get fooled
Large hollows can be revealed by small
openings
Weak crotch in elm with crack and scar
Before
Structural Failure Crackweak branch crotch
Branch
was
removed
to
reduce
weight
on crack,
crack
closed.
After
Structural Failure Crackweak branch crotch
Before
After
Pins to
measure
crack
opening
and
closing
Frost CracksWood still solid, but future cold will reopen these cracks
Accelerated bark growth
in Honey Locust
Check old cables
This Norway spruce
has an unusually
wide base, sharp
taper for this area.
When tested, it was
found to be hollow.
Diseases: Wood rotting fungi
• Root Rots
• Butt Rots
• Heart Rots
–loss of heartwood not critical as
long as the outer third of the stem is
solid
Heart Rot: What appears solid
may not be solid. Central
hollow log, but everything
within the red line is decayed.
10% decay can lead to a loss of
80% strength.
Root Plate Stability
Soil Condition
• Soil Type
• Water saturation
• pH and nutrients
• Soil depth
• Microflora and fauna
The WILD CARD
• Even if all four aces are in
good to excellent conditions,
trees can and will fail due to
wind if a strong wind comes
from the non-prevailing
direction or is extreme i.e.
tornado or hurricane.
Assessment Continued:
• External testing– Least expensive, most effective way to determine if a
tree is hollow is to use a mallet.
• Probing: If a tree is determined to be hollow,
determine the extent of the hollow
– Resistograph or other electric resistance drilling
method
– Increment borer
– Sonic Tomograph
– Inclinometers
Low Tech, non-invasive, highly reliableThe mallet
Resistograph and other resistance
drilling techniques
Sonic Tomography
From the Cradle to the GraveThe importance of proper tree care
When a tree leaves the nursery, and is
subsequently planted its growth
history can and will become an issue
for the arborist
• Planting depth – girdling roots
– In nursery
– In the landscape
• Staking
– In the nursery
– In the landscape
• Soil conditions
– In the nursery
– In the landscape (urban soils)
• Species selection/site selection (right tree, right location)
To Stake or Not to Stake?
Nursery stock?
To stake or not to stake?
Location, Location, Location?
Never say ‘NEVER’
• Never stake a tree
• Never leave a newly
planted tree unstaked
How not to stake or guy a tree...
Just in case gravity fails
Don’t hold back!
Know the Facts:
• Site conditions
–exposure
–soil
• Species selection
• Nursery stock history
Site Conditions:
• Is the site exposed to wind?
• What is the prevailing wind
direction?
– If you select your own material from the
nursery plots, mark the tree to identify
the direction of the prevailing wind and
align the tree in that direction when
planting in the new site.
Site Conditions:
• Check soil type
– Sandy soils may be loose and will allow
the root ball to rotate during strong
winds.
– Heavy soils may hold the ball well, but
inhibit new root growth out of the ball.
– Check the type of soil in the ball. Is the
tree loose within the ball?
Species Selection
• Know what form you want in a mature tree
canopy
– Streamlined
– Non-streamlined
• Select stronger wood varieties for windy
locations
Nursery stock history
• Was the tree staked in the nursery?
• How ‘tightly’ were the trees planted in the
field?
• How exposed was the nursery planting?
• What was the prevailing wind direction at the
nursery?
• What type of soil was the tree grown in?
• Was the tree grown in a poly house or shade
house for any period of time?
Ash and Honey Locust
Bradford Pear and Honey Locust
Prevailing wind
Photos: F.W. Telewski
Bradford Pear
Decision: To Stake
• If conditions require staking to prevent the
root ball from rotating or to keep a weak
nursery stock tree upright, the staking
should be:
– Loose to allow some stem movement to
stimulate radial stem growth and root growth
– Removed as soon as possible, preferably by the
second growing season
Give the tree room to move in
response to wind…
But not enough room so that it is
blown over.
Check periodically for abrasion of
the bark and remove guys as soon
as roots have successfully anchored
the tree.
Photos: F.W. Telewski
Thank You!
Questions?
Acknowledgements
Mark Jaffe – deceased
Michele Pruyn- Biology Dept, Univ. New Hampshire
Lothar Kohler – Plant Biology, MSU
Frank W. Ewers – Cal Poly University
Jameel Al-Haddad – Plant Biology, MSU
Shawn Mansfield – University of British Columbia
Some of the work presented here was supported by the National
Research Initiative of the USDA Cooperative State Research,
Education and Extension Service, grant number 2005-35103-15269