FACTORS AFFECTING STRENGTH IN TIMBER
Many of the variables influencing modulus of elasticity also influence the various strength properties of timber. Once again, these can be regarded as being either material dependent or manifestations of the environment.
Anisotropy and Grain Angle
The marked difference between the longitudinal and transverse planes in both shrinkage and modulus of elasticity has been discussed in previous chapters.
Strength likewise is directionally dependent, and the degree of anisotropy present in both tension and compression is presented in Table 1 for small clear test pieces of Douglas fir. Irrespective of moisture content, the highest degree of anisotropy is in tension (48:1); this reflects the fact that the highest strength of clear, straight-grained timber is in tension along the grain while the lowest is in tension perpendicular to it.
A similar degree of anisotropy is present in the tensile stressing of both glass-reinforced plastics and carbon fibre reinforced plastics when the fibre is laid up in parallel strands. Table 1 also demonstrates that the degree of anisotropy in compression is an order of magnitude less than in tension.
While the compression strengths are markedly affected by moisture content, tensile strength appears to be relatively insensitive, reflecting the exclusion of moisture from the crystalline core of the microfibril; it is this crystalline core that imparts to timber its very high longitudinal tensile strength.
Comparison of the data in Table 1 for tension and compression strengths along the grain reveals that clear, straight-grained timber, unlike most other materials, has a tensile strength considerably greater than its compression strength. In structural timber containing knots and distorted grain, the opposite is the norm.
Anisotropy in strength is due in part to the cellular nature of timber and in part to the structure and orientation of the microfibrils in the wall layers. Bonding along the direction of the microfibrils is covalent, while bonding between microfibrils is by hydrogen bonds.
Consequently, since the majority of the microfibrils are aligned at only a small angle to the longitudinal axis and the timber is cellular, it will be easier to rupture the cell wall if the load is applied perpendicular to than if applied parallel to the fibre axis.
Since timber is an anisotropic material, it follows that the angle at which stress is applied relative to the longitudinal axis of the cells will determine the ultimate strength of the timber. Figure 1 illustrates that over the range 0–45° tensile strength is much more sensitive to grain angle than is compression strength.
However, at angles as high as 60° to the longitudinal axis both tension and compression strengths have fallen to only about 10% of their value in straight-grained timber. The sensitivity of strength to grain angle in clear straight-grained timber is identical to that for fibre orientation in both glass-fibre- and carbon-fibre-reinforced plastics.
It is possible to obtain an approximate value of strength at any angle to the grain from a knowledge of the corresponding values of strength both parallel and perpendicular to the grain using the following formula which, in its original form, was credited to Hankinson:
where fθ is the strength property at angle θ from the fibre direction, fL is the strength parallel to the grain, fT is the strength perpendicular to the grain, and n is an empirically determined constant; in tension n = 1.5–2 while in compression n = 2–2.5. The equation has also been used for the modulus of elasticity, for which a value of n = 2 has been adopted.
Knots are associated with distortion of the grain, and since even slight deviations in grain angle reduce the strength of the timber appreciably, it follows that knots will have a marked influence on strength. The significance of knots, however, will depend on their size and distribution both along the length of a piece of timber and across its section.
Knots in clusters are more important than evenly distributed knots of a similar size, while knots on the top or bottom edge of a beam are more significant than those in the centre; large knots are much more critical than small knots. It is very difficult to quantify the influence of knots; one of the parameters that have been successfully used is the knot-area ratio, which relates the sum of the cross-sectional area of the knots in a cross section to the cross-sectional area of the piece. The loss in bending strength that occurred with increasing knot area ratio in 200 UK grown Douglas fir boards is illustrated in Fig. 2.
The very marked reduction in tensile strength of structural-size timber compared with small clear test pieces is due primarily to the presence and influence of knots in the former.
Density is a function of cell-wall thickness and therefore dependent on the relative proportions of the various cell components and also on the level of cell-wall development of any one component. However, variation in density is not restricted to different species, but can occur to a considerable extent within any one species and even within a single tree. As density increases, so modulus of elasticity and the various strength properties increase.
Density continues to be the best predictor of timber strength, since high correlations between strength and density are a common feature in timber studies. Most of the relations that have been established throughout the world between the various strength properties and timber density take the form of:
f = kgn
where f is any strength property, g is the specific gravity, k is a proportionality constant differing for each strength property, and n is an exponent that defines the shape of the curve.
An example of the use of this expression on the results of over 200 species tested in compression parallel to the grain is presented in Fig. 3; the correlation coefficient between compression strength and density of the timber at 12% moisture content was 0.902. Similar relationships have been found to hold for other strength properties, though in some the degree of correlation is considerably lower.
This is the case in tension parallel to the grain, where the ultra-structure probably plays a more significant role. Over the range of density of most of the timbers used commercially, the relationship between density and strength can safely be assumed to be linear, with the possible exception of shear and cleavage; similarly, within a single species, the range is low and the relationship can again be treated as linear.
Since density is influenced by the rate of growth of the tree it follows that variations in ring width will change the density of the timber and hence the strength. However, the relationship is considerably more complex than it first appears. In the ring-porous timbers such as oak and ash, increasing rate of growth (ring width) results in an increase in the percentage of the latewood, which contains most of the thickwalled fibres; consequently, density will increase and so will strength.
However, there is an upper limit to ring width beyond which density begins to fall owing to the inability of the tree to produce the requisite thickness of wall in every cell. In the diffuse-porous timbers such as beech, birch and khaya, where there is uniformity in structure across the growth ring, increasing rate of growth (ring width) has no effect on density unless, as before, the rate of growth is excessive.
In the softwoods, however, increasing rate of growth results in an increased percentage of the low-density earlywood, consequently both density and strength decrease as ring width increases. Exceptionally, it is found that very narrow rings can also have very low density; this is characteristic of softwoods from the very northern latitudes where latewood development is restricted by the short summer period.
Hence ring width of itself does not affect the strength of the timber, nevertheless, it has a most important indirect effect working through density.
Ratio of Latewood to Earlywood
Since the latewood comprises cells with thicker walls, it follows that increasing the percentage of latewood will increase the density and therefore the strength of the timber. Differences in strength of 150–300% between the late- and earlywood are generally explained in terms of the thicker cell walls of the former.
However, some workers maintain that when strength is expressed in terms of the crosssectional area of the cell wall the latewood cell is still stronger than the earlywood. Various theories have been advanced to account for the higher strength of the latewood wall material; the more likely are couched in terms of the differences in microfibrillar angle in the middle layer of the secondary wall, differences in degree of crystallinity and differences in the proportion of the chemical constituents.
Since the cells overlap one another, it follows that there must be a minimum cell length below which there is insufficient overlap to permit the transfer of stress without failure in shear occurring. Some investigators have gone further and have argued that there must be a high degree of correlation between the length of the cell and the strength of cell wall material, since a fibre with high strength per unit of cross-sectional area would require a larger area of overlap in order to keep constant the overall efficiency of the system.
The angle of the microfibrils in the S2 layer has a most significant effect in determining the strength of wood. Figure 4 illustrates the marked reduction in tensile strength that occurs with increasing angle of the microfibrils; the effect on strength closely parallels that which occurs with changing grain angle.
The structure of the cellulose molecule has the longitudinal plane of covalent bonds both within the glucose units and also linking them together to form filaments containing from 5000 to 10000 units. There is little doubt that the high tensile strength of timber owes much to the existence of this covalent bonding.
Certainly, experiments in which many of the β-1–4 linkages have been ruptured by gamma irradiation, resulting in a decrease in the number of glucose units in the molecule from over 5000 to about 200, resulted in a most marked reduction in tensile strength; it has also been shown that timber with inherently short molecules, e.g. compression wood, has a lower than normal tensile strength. Until the 1970s it had been assumed that the hemicelluloses – which constitute about half of the matrix material – played little or no part in determining the strength of timber.
However, it has now been demonstrated that some of the hemicelluloses are oriented within the cell wall, and it is now thought that these will be load bearing. It is known that lignin is less hydrophilic than either cellulose or hemicellulose and, as indicated earlier, at least part of its function is to protect the more hydrophilic substances from the ingress of water and consequent reduction in strength.
Apart from this indirect effect on strength, lignin is thought to make a not too insignificant direct contribution. Much of the lignin in the cell wall is located in the primary wall and in the middle lamella. Since the tensile strength of a composite with fibres of a definite length will depend on the efficiency of the transfer of stress by shear from one fibre to the next, it will be appreciated that in timber lignin plays a most important role.
Compression strength along the grain has been shown to be affected by the degree of lignification not between the cells, but rather within the cell wall, when all other variables have been held constant. It would appear, therefore, that both the fibre and the matrix components of the timber composite contribute to its strength, as in fact they do in most composites, but the relative significance of the fibre and matrix roles will vary with the mode of stressing.
Compression wood: The chemical and anatomical properties of this abnormal wood, which is found only in the softwoods. When stressed, it is found that the tensile strength and toughness are lower and the compressive strength higher than those of normal timber. Such differences can be explained in terms of the changes in fine structure and chemical composition.
Tension wood: This second form of abnormal wood, which is found only in the hardwoods, has tensile strengths higher and compression strengths lower than normal wood. Again this can be related to changes in fine structure and chemical composition.
Experimentation has indicated the probability that at moisture contents of less than 2% the strength of timber may show a slight decrease rather than the previously accepted continuation of the upward trend.
Confirmatory evidence of the significance of moisture content on strength is forthcoming from Fig. 3, in which the regression line for the compression strength of green timber against density is lower than that for timber at 12% moisture content for over 200 species; strength data for timber are generally presented for these two levels of moisture content (Lavers, 1969).
However, reference to Table 1 indicates that the level of moisture has almost no effect on the tensile strength parallel to the grain. This strength property is determined by the strength of the covalent bonding along the molecule, and since the crystalline core is unaffected by moisture, retention of tensile strength parallel to the grain with increasing moisture content is to be expected.
Within certain limits and excluding tensile strength parallel to the grain, the regression of strength, expressed on a logarithmic basis, and moisture content can be plotted as a straight line. The relationship can be expressed mathematically as:
log10 f = log10 fs + k(µs – µ)
where f is the strength at moisture content µ, fs is the strength at the fibre saturation point, ms is the moisture content at the fibre saturation point, and k is a constant.
It is possible, therefore, to calculate the strength at any moisture content below the fibre saturation point, assuming fs to be the strength of the green timber and ms to be 27%. This formula can also be used to determine the strength changes that occur for a 1% increase in moisture content over certain ranges (Table 2); the table illustrates for small clear test pieces how the change in strength per unit change in moisture content is non-linear.
This relationship between moisture content and strength may not always apply when the timber contains defects, as is the case with structural-size timber. Thus, it has been shown that the effect of moisture content on strength diminishes as the size of knots increases.
The relationship between moisture content and strength presented above, even for knotfree timber, does not always hold for the impact resistance of timber. In some timbers, though certainly not all, impact resistance or toughness of green timber is considerably higher than it is in the dry state; the impact resistances of green ash, cricket bat willow and teak are approximately 10, 30 and 50% higher, respectively, than the values at 12% moisture content.
In the case of structural timber, several types of model have been proposed to represent moisture– property relationships. These models reflect the finding that increases in strength with drying are greater for high-strength structural timber than for low-strength material.
At temperatures within the range -20 to +200°C and at constant moisture content, strength properties are linearly (or almost linearly) related to temperature, decreasing with increasing temperature. However, a distinction must be made between short and long term effects.
When timber is exposed for short periods of time to temperatures below 95°C the changes in strength with temperature are reversible. These reversible effects can be explained in terms of the increased molecular motion and greater lattice spacing at higher temperatures.
For all the strength properties, with the possible exception of tensile parallel to the grain, a good rule of thumb is that an increase in temperature of 1°C produces a 1% reduction in their ultimate values (Gerhards, 1982). At temperatures above 95°C, or at temperatures above 65°C for very long periods of time, there is an irreversible effect of temperature due to thermal degradation of the wood substance, generally taking the form of a marked shortening of the cellulose molecules and chemical changes within the hemicelluloses.
All the strength properties show a marked reduction with temperature, but toughness is particularly sensitive to thermal degradation. Repeated exposure to elevated temperature has a cumulative effect and usually the reduction is greater in the hardwoods than in the softwoods. Even exposure to cyclic changes in temperature over long periods of time has been shown to result in thermal degradation and loss in strength and especially toughness.
The effect of temperature is very dependent on moisture content, sensitivity of strength to temperature increasing appreciably as moisture content increases (Fig. 5), as occurs also with modulus of elasticity; these early results have been confirmed by Gerhards (1982). The relationships between strength, moisture content and temperature appear to be slightly curvilinear over the range 8–20% moisture content and –20 to 60°C.
However, in the case of toughness, while at low moisture content it is found that toughness decreases with increasing temperature, at high moisture contents toughness actually increases with increasing temperature.
Timber is a viscoelastic material and as such its mechanical behaviour will be time dependent. Such dependence will be apparent in terms of its sensitivity to both rate of loading and duration of loading.
Rate of loading: An increase in the rate of load application results in increased strength values, the increase in green timber being some 50% greater than that of timber at 12% moisture content; strain to failure, however, actually decreases. A variety of explanations have been presented to account for this phenomenon, most of which are based on the theory that timber fails when a critical strain has been reached and consequently at lower rates of loading viscous flow or creep is able to occur, resulting in failure at lower loads.
The various standard testing procedures adopted throughout the world set tight limits on the speed of loading in the various tests. Unfortunately, recommended speeds vary throughout the world, thereby introducing errors in the comparison of results from different laboratories; the introduction of European standards (ENs) and the wider use of International standards (ISOs), should give rise to greater uniformity in the future.
Duration of load (DOL): In terms of the practical use of timber, the duration of time over which the load is applied is perhaps the single most important variable. Many investigators have worked in this field and each has recorded a direct relationship between the length of time over which a load can be supported at constant temperature and moisture content and the magnitude of the load. This relationship appears to hold true for all loading modes, but is especially important for bending strength.
The modulus of rupture (maximum bending strength) will decrease in proportion, or nearly in proportion, to the logarithm of the time over which the load is applied; failure in this particular time dependent mode is termed creep rupture or static fatigue.
Wood (1951) indicated that the relationship was slightly different for ramp and constant loading, was slightly curvilinear and that there was a distinct levelling off at loads approaching 20% of the ultimate short-term strength such that a critical load or stress level occurs below which failure is unlikely to occur. The hyperbolic curve that fitted Wood’s data best for both ramp and sustained loading, and which became known as the Madison curve, is illustrated in Fig. 6.
Other workers have reported a linear relation, though a tendency to non-linear behaviour at very high stress levels has been recorded by some of them. Pearson (1972), in reviewing previous work in the field of duration of load and bending strength, plotted on a single graph the results obtained over a 30-year period and found that despite differences in method of loading (ramp or constant), species, specimen size, moisture content, or whether the timber was solid or laminated, the results showed remarkably little scatter from a straight line described by the regression:
f = 91.5 – 7 log10t
where f is the stress level (%), and t is the effective duration of maximum load in hours.
This regression is also plotted in Fig. 6 to allow comparison with Wood’s curvilinear line. Pearson’s findings certainly threw doubt on the existence of a critical stress level below which creep rupture does not occur. These regressions indicate that timber beams that have to withstand a dead load for 50 years can be stressed to only 50% of their ultimate short term strength.
Although this type of log-linear relationship is still employed for the derivation of duration of load factors for wood-based panel products, this is certainly not the case for solid timber. By the early 1970s there was abundant evidence available to indicate that the creep rupture response of structural timber beams differed considerably from the classic case for small clear test pieces described above.
Between 1970 and 1985 an extensive amount of research was carried out in America, Canada and Europe; you can follow the historical development of the new concepts in DOL in comprehensive reviews by Tang (1994) and Barrett (1996). This research confirmed that the DOL effect in structural timber was different to that in small clear test pieces and was also less severe than the Madison curve predicted for loading periods of up to one year.
It also confirmed that high-strength timber possessed a larger DOL effect than lowstrength timber. The above test work clearly indicated that the DOL factors then in current use were conservative and in order to obtain a more realistic prediction of time to failure, attention moved to the possible application of reliability-based design principles for the assessment of the reliability of timber members under in-service loading conditions.
In particular, this approach led to the adoption of the concept of damage accumulation. It should be appreciated that in the application of this concept there does not exist any method for quantifying the actual damage; the development of damage is simply deduced from the time-to-failure data from long-term loading experiments under a given loading history.
These models generally use the stress-level history as the main variable and are thus independent of material strength. In order to calculate time to failure for a given stress history under constant temperature and humidity, the damage rate is integrated from an assumed initial value of 0 to the failure value of 1 (Morlier et al., 1994). Several types of damage accumulation models have been recorded, of which the most important are those listed by Morlier et al. (1994) and Tang (1994).
The dependence of these damage models on the stress ratio results is a logistical problem, since both the short-term and the long-term strength has to be known for the same structural test piece, but the test piece can be tested only once. This problem is usually resolved by using two side-matched test pieces and assuming equal strengths!
A comparison among four of the damage-accumulation models, together with one model based on strain energy (Fridley et al., 1992a), is presented in Fig. 7, from which it will be noted how large is the variability among them. The levels of both moisture content and temperature have a marked effect on time to failure.
Thus, increasing relative humidity results in reduced times to failure when stressed at the same stress ratios (Fridley et al., 1991), while varying levels of humidity have an even greater effect in reducing time to failure (Hoffmeyer, 1990; Fridley et al., 1992b).