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(American Journal of Botany. 1999;86:465-469.)
© 1999 Botanical Society of America, Inc.

The mechanical role of bark1

Karl J. Niklas

Section of Plant Biology, Cornell University, Ithaca, New York 14853-5908

Received for publication June 29, 1998. Accepted for publication August 21, 1998.


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 LITERATURE CITED
 
The ability of stem bark to resist bending forces was examined by testing in bending segments of Acer saccharum, Fraxinus americana, and Quercus robur branches with and without their bark. For each species, the bark contributed significantly to the ability of stem segments differing in age to resist bending forces, but its contribution was age-dependent and differed among the three species. The importance of the mechanical role of the bark decreased basipetally with increasing age of F. americana and Q. robur stem segments and was superceded by that of the wood for segments >= 6 yr old. A. saccharum bark was as mechanically important as the wood for stem segments 7 yr old but was not a significant stiffening agent for younger or older portions of stems. On average, the stiffness of the bark from all three species was 50% that of the wood. However, the geometric contribution to the flexural rigidity of stems made by the bark (i.e., the bark's second moment of area) was sufficiently large to offset its lower stiffness (Young's modulus) relative to that of the wood. A simple model is presented that shows that the bark must be as mechanically important as the wood when its radial thickness equals 32% that of the wood and its stiffness is 50% that of the wood. Based on this model, which is shown to comply with the data from three species purported to have stiff woods, it is evident that the role of the bark cannot be neglected when considering the mechanical behavior of juvenile woody stems subjected to externally applied bending forces.

Key Words: bark • flexural rigidity • phellem • plant biomechanics • tissue stiffness • woody stems


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 LITERATURE CITED
 
The bark is that portion of the plant body consisting of all tissues external to the vascular cambium (Esau, 1967 , p. 338). It may thus be composed of phloem, cortex, periderm, and remnants (if any) of the epidermis. This complex tissue composition permits the bark to simultaneously perform manifold functions, among which sap conduction, photosynthesis, tissue aeration, and protection from the external environment are well known. By virtue of its location, the bark also has the potential to significantly stiffen and rigidify stems, although comparatively little is known about the extent to which it fulfills this possible function (see, however, Gibson and Ashby, 1988 ; Xu et al., 1997 ). Engineering theory shows that the location of the bark is ideally suited for mechanical support because bending and twisting stresses invariably reach their maximum intensities at the surface of any support member (Wainwright et al., 1976 ; Silk, Wang, and Cleland, 1982 ; Niklas, 1992 ), which is occupied by typically dead cell layers (i.e., the phellem) in old stems capable of secondary growth (Esau, 1967 ). Provided that these layers are composed of sufficiently stiff materials, the bark can serve as the principal stiffening agent in stems, even for those in which comparatively large amounts of wood have accumulated.

I test this hypothesis here by relying on the ease with which the flexural rigidity of stems with and without their bark can be measured and compared. Flexural rigidity EI quantifies the ability of any structure to resist bending forces (Wainwright et al., 1976 ; Niklas, 1992 ). It is the product of Young's modulus E, which measures a material's bulk stiffness, and the axial second moment of area I, which measures the contribution made by the geometry and size of materials to the ability of a support member to resist bending. The experimental protocol, which has been used in modified form elsewhere (see Niklas and Paolillo, 1997 ), is to measure the flexural rigidity of intact stems, remove their bark, and remeasure the flexural rigidity of the remaining portions of the stem, taking note of the reductions in the transverse area resulting from the removal of tissues. The difference between the flexural rigidity of intact and surgically manipulated stems must equal the flexural rigidity of the bark and thus its contribution to the ability of intact stems to resist bending forces. Since measurements of the thickness and geometry of the bark can be used to calculate its second moment of area, the Young's modulus of bark tissues is determined indirectly. Likewise, the flexural rigidity of stems without their bark can be used to calculate the stiffness of the remaining internal tissues (mostly wood in progressively older portions of stems) based on the second moment of area of the specimen. In this way, comparisons can be drawn between the geometric and material stiffness contributions made by the bark and wood to stem rigidity. Since secondary tissues typically accumulate in stems as a function of age, comparisons must be made among conspecific stems differing in age. With the aid of this protocol, it is possible to show that the bark of woody dicot species, many of which are purported to have very stiff and strong wood, nevertheless contributes significantly to stem rigidity.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 LITERATURE CITED
 
Three species, cultivated on the Cornell Campus, were selected for study because of their availability and their reputed wood stiffness and strength: Acer saccharum Marsh. (Aceraceae), Fraxinus americana L. (Oleaceae), and Quercus robur L. (Fagaceae). Three healthy, straight, and horizontally cantilevered branches were selected for mechanical testing from different trees of each species growing in different sites. Each branch was removed with a pruning saw at the point of its attachment to the trunk. Terminal bud scars and annual growth rings were used to determine stem age A. Stem segments were then removed sequentially to obtain specimens differing in age from along the length of each branch. Only straight segments with uniform girth were used in bending tests. Careful selection of branches in the field reduced the number of segments that failed to meet these criteria.

The EI of stem segments was determined by placing the ends of each segment between two vertical supports and applying weights P differing in mass at the midlength {ell}/2 of the segment. The vertical deflection {delta} resulting from each weight was measured by sighting a {Gamma}-shaped needle located at {ell}/2 against a vertical ruler with the aid of a microscope equipped with an ocular micrometer. The flexural rigidity of each segment was calculated using the formula EI = P{ell}3/48{delta} (see Gordon, 1978 ; Niklas, 1992 ). Three to five different weights were used for each segment. Mean values of EI are reported for each segment. In terms of the second moment of area, the orientation of each segment with respect to the bending plane was important. Older segments often had elliptical (or nearly so) transverse cross sections. When tested in bending, the minor axis of these elliptical transections was oriented parallel to the bending plane because the ends of segments were not clamped. The I of each segment was thus computed from the formula I = 0.25{pi}a3b, where a and b are the mean semiminor and semimajor axes of the elliptical stem cross section based on orthogonal measurements of stem radius taken with a microcaliper at {ell}/2 and 1 cm from each end of the segment. The mean E of each stem segment was computed from E = P{ell}3/48{delta}I based on the different bending loads P.

Measurements of bark thickness t and wood radius Ri were obtained by coating the cut ends of segments with HCl-phloroglucinol and determining the radial dimensions of stained tissues under a dissecting microscope equipped with an ocular micrometer. For stem segments A >= 1 yr, the location of the vascular cambium could be determined unambiguously with this protocol such that t and Ri could be measured with confidence. For stem segments A = 0.5 yr (first-year growth), careful visual inspection of transections was required because the recently formed secondary xylem was often nonlignified.

Bark and wood radial thickness were not uniform in many cross sections, although the variances for most segments were <5%. The thickest regions of the bark typically occurred at the opposing ends of the minor axes of elliptical stem cross sections; the thickest portions of individual annual growth rings were located at one end of the major axes of elliptical transections. However, bark and wood thickness were fairly uniform along each side of each stem segment (e.g., longitudinal corrugations in the bark of older branches were not present on the stem segments tested in bending due to their limited age). Values of t and Ri are the means of two sets of measurements taken in the thickest and thinnest regions of these tissues.

After determining the EI of intact specimens, each segment was carefully stripped of its bark with the aid of sandpaper (for young segments) or by peeling the bark off by hand (for older specimens). The former technique undoubtedly resulted in the loss of some tissues beneath the vascular cambium, but visual inspections and cross references to measurements of t and Ri indicated that this was minimal. The EI of de-barked specimens was determined using the previously described experimental protocol and taking careful note of the reduction in I resulting from the removal of tissues. The second moment of area was computed from the formula I = 0.25{pi}a3b, where a and b now denote the mean semiminor and the mean semimajor axes of the elliptical transection of the stem's remaining tissues. Values of a and b were computed based on the means of orthogonal measurements of diameters taken with a microcaliper at {ell}/2 and 1 cm from each end of the segment.


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
LITERATURE CITED
 
The radial thickness of wood and bark varied as a function of the age of stem segments and differed among the three species. For each branch, the radial thickness of the wood increased exponentially with segment age, while the bark thickness increased as a linear function of age (Fig. 1). The second moment of area of the wood thus increased exponentially with segment age for all three species (Fig. 2). With the exception of the youngest A. saccharum stem segments, the second moment of bark area also increased exponentially with respect to age. These trends were remarkably similar for each of the branches removed from different trees of the same species (Fig. 3).



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  		Fig. 1. Mean radial thickness of wood and bark plotted against stem segment age for branches from three species. Solid lines are ordinary least squares regression curves. Wood radial thickness increases exponentially and bark thickness increases linearly with respect to stem segment age for each of the three species.

 


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  		Fig. 2. Second moments of bark and wood area (IB and IW, respectively) plotted against stem segment age for branches from three species. Curved lines are ordinary least squares regression curves.

 


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  		Fig. 3. Second moment of bark area IB plotted against the age of stem segments removed from three branches of Quercus robur.

 
The stiffness of the bark was, on average, ~ 50% that of wood for each of the three species despite an exponential increase in tissue stiffness with respect to age (Fig. 4). The bark contributed significantly to the ability of stem segments to resist bending forces, but this contribution was age-dependent. When the flexural rigidity of the bark (EI)B was plotted against that of the wood (EI)W, data points falling above the isometric relationship (EI)B = (EI)W indicated that the bark's contribution was larger than that of the wood (Fig. 5A). The age dependency of the bark's contribution to overall branch rigidity was evident when (EI)B/(EI)W was plotted against segment age (Fig. 5B). In the case of the Q. robur and F. americana stem segments <=6 yr old, the bark's contribution was unequivocally as much as or more than that of the wood; the reverse was true for older portions of the same branches. In the case of A. saccharum, the bark was as important as the wood for stem segments ~7 yr old, but less important for younger or older portions of the same branches.



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  		Fig. 4. Bark and wood Young's modulus E plotted against stem segment age for branches from three species. Curved lines are ordinary least squares regression curves.

 


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  		Fig. 5. Bark and wood flexural rigidity [(EI)B and (EI)W, respectively]. (A) Log10-transformed (EI)B plotted against similarly transformed (EI)W for stems from three species. Data points falling above the isometric relationship (EI)B = (EI)W (shown by diagonal dashed line) indicate that the bark contributes more to the flexural rigidity of the stem segment than the wood. (B) The quotient (EI)B/(EI)W plotted against stem segment age for three branches. Data points falling above (EI)B/(EI)W = 1 (indicated by horizontal dashed line) indicate the ages of stem segments for which the bark contributes more to the flexural rigidity than the wood. Solid lines indicate ordinary least squares regression curves.

 
Even though the mechanical role of the bark is eclipsed by that of the wood as branches age and accumulate wood, it is clear that bark tissues can rigidify stems, although this varies among species depending on the allometry of bark and wood accumulation and the relative material stiffness of bark tissues and wood. Since the branches tested in bending were in no way atypical of woody dicot shoots nor are the three species (which have stiff and strong wood) unusual dicots, there is good reason to believe that the phenomenology reported here may be widespread.

The bark's location with respect to that of the wood is an important factor because the bark was, on average, 50% less stiff than the wood for the species examined and thus its second moment of area must compensate for its comparatively low stiffness. This is easily demonstrated by comparing the second moments of area of hollow and solid beams that, respectively, mimic the transverse geometry of the bark and wood. Assuming that the biomass allocations to these two regions of the stem equal one another such that both have equivalent transverse areas, it mathematically follows that the second moment of area of the bark must be three times that of the wood (Fig. 6). Equivalent investments in the amount of bark and wood, therefore, reap significantly different dividends in terms of the geometric contributions these tissues make to the stem's ability as a whole to resist bending forces.



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  		Fig. 6. Comparison between the second moment of areas of a solid and hollow beam (IS and IH, respectively) with equivalent solid cross-sectional areas (AS and AH, respectively) that mimic stem bark and wood, respectively. The external radius of the solid (wood) beam Ri equals the inner radius of the hollow (bark) beam with external (overall stem) radius Ro. Assuming that both beams have equivalent transverse areas, it follows that Ro = 1.414 Ri and that the quotient of the second moments of area of the hollow and solid beams equals 3. See Fig. 7 for an extension of this model that accounts for differences in bark and wood stiffness.

 
Extending the logic of this model also shows that the radial thickness of the bark with respect to that of the wood (i.e., t/Ri) must increase dramatically as the stiffness of the bark with respect to that of the wood (i.e., EB/EW) decreases. This follows from the fact that t/Ri must equal [1 + (EW/EB)0.25]- 1 when the second moments of bark and wood area equal one another (Fig. 7A). For the data presented here, on average, EB = 0.5EW, and so t/Ri must equal 0.316 whenever (EI)B/(EI)W equals one, while the role of the bark must exceed that of the wood when t/Ri > 0.32. These predictions hold true for the data at hand (Fig. 7B). Naturally, as wood accumulates in stems, the bark's mechanical role is progressively reduced. But comparatively large amounts of much stiffer wood are required for this tissue to equal or exceed the mechanical importance of the less stiff bark (see Fig. 1).



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  		Fig. 7. Relationships among bark and stem wood differing in thickness (t and Ri, respectively) and stiffness (EB and EW, respectively) based on the assumption that the stem has a circular transverse geometry with external radius Ro such that the second moments of area of the wood and the bark are equal and given by the formulas IW = 0.25{pi}R4i and IB = 0.25{pi}(R4o - R4i), respectively. Assuming that IW = IB, it follows that Ro = 1.414Ri (see Fig. 6 ). (A) Values of t /R predicted to achieve equivalent bark and wood flexural rigidities [i.e., (EI)B = (EI)W] plotted against different values of EB/EW. The solid curved line is the relationship predicted by the formula t/Ri = (1 + E)W/E)B)0.25 - 1, which assumes that (EI)B = (EI)W. This formula predicts that t/Ri {approx} 0.32 when EB/EW = 0.5 (shown by dashed lines). (B) The quotient of bark and wood flexural rigidity (EI)B/(EI)W plotted against the quotient of the bark and wood radial thickness t /Ri for a representative branch from three species tests the prediction that the mechanical role of the bark is equivalent to that of the wood (EI)B/(EI)W = 1 when t/Ri {approx} 0.32 and EB/EW = 0.5. Since the data points falling in the shaded area correspond to the conditions (EI)B/(EI)W < 1 and t/Ri < 0.32, the prediction is confirmed. Solid line is ordinary least squares regression curve (formula shown in lower right of graph). Although (EI)B/(EI)W and t/Ri are auto-correlated (r2 = 0.97) by virtue of the formulas for IB and IW, the point t/Ri {approx} 0.32 when (EI)B/(EI)W = 1 falls well within the 95% confidence intervals (shown by dashed lines).

 
Bark thickness can increase linearly (Ryan, 1982 ; Peterson et al., 1991 ) or curvilinearly with stem diameter (Gill and Ashton, 1968 ; Harmon, 1984 ) depending on phellogen activity, phellem attrition, and the amortization of secondary phloem. Likewise, the stiffness of the bark relative to that of the wood varies among species, while the allometry of wood production is age-dependent and varies within and across species (e.g., Duff and Nolan, 1953 ). Therefore, my model cannot estimate the age of stem segments for which the burden of mechanical support shifts from the bark to the wood for all species, and under any circumstances, the model only applies when the bark is half as stiff as the wood in stems. Yet another factor is that bark exhibits mechanical isotropy, that is, its stiffness is not equal when measured in different directions. Some species produce bark that is far more stiff in the tangential (circumferential) than in the longitudinal direction with respect to stem length (e.g., Prunus serrula; see Xu et al., 1997 ). For these species, the bark may contribute little or nothing at all to the ability of stems to resist bending forces. Indeed, for these species, the bark may enhance stem flexibility and resist stem expansion as secondary vascular tissues accumulate. In contrast, other species produce bark that is more stiff in the longitudinal than in the tangential direction (e.g., Vitus sp.). For these species, the bark can rigidify stems that lack appreciable amounts of wood.

The properties and the amount of bark are likely biologically important, especially when stem diameter is <=2 cm, which is the size range for the branches examined in this study, because stems in this category typically bear the majority of leaves and are elevated well above ground for many trees. These stems are expected to experience high drag forces such that their functional lifetimes will depend on their ability to flex and respond to drag forces (Vogel, 1996 ). The data presented here show that this ability depends in part on the stiffness and amount of bark tissues because these tissues unequivocally serve as the principal stiffening agent in the comparatively young stems that comprise the bulk of leaf-bearing tree stems. Consequently, much more attention should be paid to the mechanical properties of the bark and how these properties vary within species as a result of growth and development and across species as a result of phyletic legacy.


   FOOTNOTES
 
1 The author thanks N. Michele Holbrook (Harvard University) who, as an Associate Editor of the American Journal of Botany, supervised the reviewing process and served as Editor-in-Chief for this manuscript; Mathew V. Thompson (Harvard University); and Dominick J. Paolillo (Cornell University) for offering helpful suggestions to improve the paper; and Mr. Edward D. Cobb (Cornell University) for field and laboratory assistance. This research was supported by Hatch Act Award 185–403. Back


   LITERATURE CITED
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 LITERATURE CITED
 
Duff, G. H., and N. J. Nolan. 1953 Growth and morphogenesis in the Canadian forest species I. The controls of cambial and apical activity in Pinus resinosa Ait. Canadian Journal of Botany 31: 471–513.

Esau, K. 1967 Plant anatomy, 2d ed. John Wiley & Sons, New York, NY.

Gibson, L. J., and M. F. Ashby. 1988 Cellular solids, structure and properties. Pergamon Press, Oxford.

Gill, A. M., and D. H. Ashton. 1968 Role of bark type in relative tolerance to fire of three central Victorian eucalypts. Australian Journal of Botany 16: 491–498.[CrossRef]

Gordon, J. E. 1978 Structures: or, why things don't fall down. Plenum, New York, NY.

Harmon, M. E. 1984 Survival of trees after low-intensity surface fires in Great Smoky Mountains National Park. Ecology 65: 796–802.[CrossRef][ISI]

Niklas, K. J. 1992 Plant biomechanics: an engineering approach to plant form and function. University of Chicago Press, Chicago, IL.

———, and D. J. Paolillo, Jr. 1997 The role of the epidermis as a stiffening agent in Tulipa (Liliaceae) stems. American Journal of Botany 84: 735–744.[Abstract]

Peterson, D. L., M. J. Asbaugh, G. H. Pollock, and L. J. Robinson. 1991 Post-fire growth of Pseudotsuga menziesii and Pinus contorta in the northern Rocky Mountains, USA. International Journal of Wildlife and Fire 1: 63–71.

Ryan, K. C. 1982 Evaluating potential tree mortality from prescribed Burning. In D. M. Baumgartner [ed.], Site preparation and fuels management on steep slopes, 167–174. Symposium Proceedings, Washington State University Press, Pullman, WA.

Silk, M. W. K., L. L. Wang, and R. E. Cleland. 1982 Mechanical properties of the rice panicle. Plant Physiology 70: 460–464.[Abstract/Free Full Text]

Vogel, S. 1996 Blowing in the wind: storm-resisting features of the design of trees. Journal of Arboriculture 22: 92–98.

Wainwright, S. A., W. D. Biggs, J. D. Currey, and J. M. Gosline. 1976 Mechanical design in organisms. Princeton University Press, Princeton, NJ.

Xu, X, E. Schneider, A. T. Chien, and F. Wudl. 1997 Nature's high-strength semitransparent film: the remarkable mechanical properties of Prunus serrula bark. Chemistry of Materials 9: 1906–1908.[CrossRef][ISI]




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