# Failure & Strength in Timber

While it is easy to appreciate the concept of deformation primarily because it is something that can be observed, it is much more difficult to define in simple terms what is meant by the strength of a material. Perhaps one of the simpler definitions of strength is that it is a measure of the resistance to failure, providing of course that we are clear in our minds what is meant by failure.

In modes of stressing where a distinct break occurs with the formation of two fracture surfaces, failure is synonymous with rupture of the specimen. However, in certain modes of stressing, fracture does not occur and failure must be defined in some arbitrary way such as the maximum stress that the sample will endure or, in exceptional circumstances such as compression strength perpendicular to the grain, the stress at the limit of proportionality.

Having defined our end point, it is now easier to appreciate our definition of strength as the natural resistance of a material to failure. But how do we quantify this resistance? This may be done by calculating either the stress necessary to produce failure or the amount of energy consumed in producing failure. Under certain modes of testing it is more convenient to use the former method of quantification, as the latter tends to be more limited in application.

## DETERMINATION OF STRENGTH

## Test Piece Size and Selection

Although in theory it should be possible to determine the strength properties of timber independently of size, in practice this is found not to be the case. A definite though small size effect has been established, and in order to compare the strength of a timber sample with recorded data it is necessary to adopt the sizes set out in the standards.

The size of the test piece to be used will be determined by the type of information required. Where tests are required to characterise new timbers or for the strict academic comparison of wood from different trees or different species, small, knot-free, straight-grained, perfect test pieces representing the maximum quality of wood that can be obtained and known as ‘small clears’, should be used. However, where tests are required to determine the strength performance of structural-grade timber with all its imperfections, such as knots and distorted grain, generally large test pieces of structural timber are required. Current testing standards still permit the derivation of structural stresses from small clear test pieces, but it is better to use structural-size test pieces as the effects of strength limiting characteristics are easier to quantify with such pieces.

**Use of Small Clear Test Pieces**

This size of test piece was originally used for the derivation of working stresses for timber, but in the 1970s this was superseded, though not exclusively, by the use of actual structural-size timber. However, the small clear test piece still remains valid for the derivation of structural stresses as well as characterising new timbers and the strict academic comparison of the strength of wood from different trees or different species.

Two standard procedures for testing small clear test pieces have been used internationally; the original was introduced in the USA as early as 1891 using a test sample 2 × 2 inches in cross section; the second, European in origin, employs a test specimen 20 × 20 mm in cross section. Before 1949 the former size was adopted in the UK, but after this date this larger sample was superseded by the smaller, thereby making it possible to obtain an adequate number of test specimens from smaller trees. Because of the difference in size, the results obtained from the two standard procedures are not strictly comparable and a series of conversion values has been determined (Lavers, 1969).

The early work in the UK on species characterisation employed a sampling procedure in which the test samples were removed from the log in accordance with a cruciform pattern. However, this was subsequently abandoned and a method devised applicable to the centre plank removed from a log; 20 × 20 mm sticks, from which the individual test pieces are obtained, are selected at random in such a manner that the probability of obtaining a stick at any distance from the centre of a cross section of a log is proportional to the area of timber at that distance.

Test samples are cut from each stick eliminating knots, defects and sloping grain; this technique is described fully by Lavers (1969). Methods of test for ‘small clears’ are given in BS 3731 (retained as a national standard) for the UK and ASTM D143-52 for the USA. The use of small clears for the derivation of structural stresses is given in BS EN 384. Dinwoodie (2000) describes most of the tests in BS 373.

**Use of Structural-Size Test Pieces**

Use of these larger test pieces reproduces actual service loading conditions, and they are of particular value because they allow directly for defects such as knots, splits and distorted grain rather than indirectly (by applying a series of reduction factors), as is necessary with small clear test pieces.

## Standardised Test Procedures

Europe at the present time is in the final stages of a transition period in which national test procedures have been largely replaced by European procedures. It is interesting to note that many of the European Standards (ENs) on testing have now been adopted as International Standards (ISOs). Methods for the testing of structural timber in Europe are described in BS EN 408, and for small clears in BS EN 384. Some of these tests are described by Dinwoodie (2000).

## STRENGTH VALUES

## Strength Derived Using Small Clear Test Pieces

In Table 1 tensile strength parallel to the grain is listed for certain timbers and it is in this mode that clear timber is at its strongest. Comparison of these values with those for compression strength parallel to the grain indicates that, unlike many other materials, the compression strength is only about one-third that of tensile strength along the grain.

## Strength Derived Using Structural-Size Test Pieces

After the end of October 2008 all structural test work and design within Europe should be carried out according to the new European standards by testing to EN 408 and deriving the characteristic values according to EN 384. Within the European system, the characteristic value for the strength properties is taken as the 5-percentile value; for modulus of elasticity there are two characteristic values, one the 5-percentile, the other the mean or 50-percentile value.

The design of structures must be carried out according to Eurocode 5 (BS EN 1995-1-1). The sample 5-percentile value is determined for each sample by the equation:

f_{0.5} = f_{r}

where f_{0.5} is the sample 5-percentile value, and f_{r }is obtained by ranking all the test values for a sample in ascending order.

The 5-percentile value is the test value for which 5% of the values are lower. If this is not an actual test value (i.e. the number of test values is not divisible by 20) then interpolation between the two adjacent values is permitted.

The characteristic value of strength (f_{k}) is calculated from the equation:

f_{k} = f_{0.5}k_{s}k_{v}

where f_{0.5} is the mean (in MPa) of the adjusted 5-percentile values (f_{0.5}) for each sample (see above) weighted according to the number of pieces in each sample, k_{s }is a factor to adjust for the number of samples and their size, and k_{v} is a factor to allow for the lower variability of f_{0.5} values from machine grades in comparison with visual grades; for visual grades k_{v} = 1.0, and for machine grades k_{v} = 1.12.

In order to permit a comparison between the strength values obtained from structural-size test pieces and small clear specimens, previous data obtained from the testing of structural test pieces to the now withdrawn BS 5820 and the results recorded as mean values are presented in Table 2 for each of the major strength modes.

Not only are these mean values considerably lower than the mean values derived from small clear test pieces (Table 1), but the tensile strengths are now lower than the compression strengths. This is directly related to the presence of knots and associated distorted grain in the structural-size test pieces.

## VARIABILITY IN STRENGTH VALUES

The timber is a very variable material and that for many of its parameters, e.g. density, cell length and microfibrillar angle of the S_{2} layer, distinct patterns of variation could be established within a growth ring, outwards from the pith towards the bark, upwards in the tree, and from tree to tree. The effects of this variation in structure are all too apparent when mechanical tests are performed.

Test data for small clear test pieces are usually found to follow a normal distribution and, we can describe the variability with the sample standard deviation, SD, and, sometimes more usefully, the coefficient of variation, which relates SD to the mean strength value. The coefficient of variation for timber varies considerably, but is frequently under 15%.

For design purposes the two most important properties are the modulus of elasticity and bending strength, which have coefficients of variation typically in the range of 10–30%. As a general rule, a normal distribution curve fits the data from small clear test pieces better than do the data from structural-size test pieces, for which – as noted earlier – the 5 percentile characteristic value is determined simply by ranking the results.

## INTERRELATIONSHIPS BETWEEN STRENGTH PROPERTIES

## Modulus of Rupture (Bending Strength) and Modulus of Elasticity

A high correlation exists between the moduli of rupture and elasticity for a particular species, but it is doubtful whether this represents any causal relationship; rather it is more probable that the correlation arises as a result of the strong correlation that exists between density and each modulus. Whether it is a causal relationship or not, it is nevertheless put to good use, for it forms the basis of the stress grading of timber by machine.

## Impact Bending and Total Work

Good correlations have been established between the height of drop in impact bending tests and both work to maximum load and total work; generally the correlation is higher with the latter property.

## Hardness and Compression Perpendicular to Grain

Correlation coefficients of 0.902 and 0.907 have been established between hardness and compression strength perpendicular to the grain of timber at 12% moisture content and timber in the green state, respectively. It is general practice to predict the compression strength from the hardness result using the following equations:

Y_{12 }= 0.00147x_{12} + 1.103

Y_{g} = 0.00137x_{g} – 0.207

where Y_{g} and Y_{12} are the compression strengths perpendicular to the grain (MPa) for green timber and timber at 12% moisture content, respectively, and x_{g} and x_{12} are hardness in N.