Stress Levels for Solid Timber
2.2 DERIVATION OF BASIC STRESS AND CHARACTERISTIC STRENGTH VALUES
2.2.1 Background
Originally the mean and basic stress values were obtained from the statistical analy- sis of test results from small, clear, green (moisture content above the fibre satu- ration point) specimens. This procedure was replaced with the testing of full-sized, graded pieces of timber, a practice which is continued today. Since the introduc- tion of full size ‘in grade’ testing the only changes have been to the statistical methods of analysis employed.
2.2.2 The UK methods up to 1984
Values were based on the ‘basic stress’, i.e. ‘the stress which could safely be permanently sustained by timber containing no strength-reducing characteristics’.
The basic stress was then modified to allow for the particular grade characteristics and moisture content. The basic stresses were derived from small (20 mm¥20 mm cross-section), clear (no strength-reducing defects), green (moisture content above the fibre saturation point) specimens. Many hundreds of samples of a particular species would be tested. Because of the ‘uniformity’ of the sample, statistical analy- sis was possible assuming a normal, Gaussian distribution.
A well-quoted example of tests on small clear specimens which illustrates this method for deriving basic stresses was carried out at the Forest Products Research Laboratory, Princes Risborough (now incorporated in the Building Research Establishment) to establish the modulus of rupture of ‘green’ Baltic redwood. Two thousand, seven hundred and eight specimens, each 20 mm square ¥300 mm long, were tested in bending under a central point load. (BS 373 detailed the standard test method.) The failure stresses for all specimens were plotted to form a his- togram as shown in Fig. 2.1. This demonstrates the natural variation of the modulus of rupture about the mean value for essentially similar pieces of timber. Superim- posed upon the histogram is the normal (Gaussian) distribution curve and this is seen to give a sufficiently accurate fit to the histogram to justify the use of statis- tical methods related to this distribution to derive basic stresses. In the example shown, the mean modulus of rupture for the green timber is 44.4 N/mm2and the standard deviation is 7.86 N/mm2.
In mathematical terms the standard deviation of a normal distribution is given by
where s =standard deviation x =individual test value
=mean of the test values N=number of tests.
The normal distribution curve extends to infinity in either direction but for practical purposes it may be regarded as terminating at three times the standard deviation on each side of the arithmetic mean. Likewise it is possible to set prob- ability levels below which a certain proportion of the overall sample would be expected to lie. For example, the exclusion value is given by
s =x -kps x
s x x
= N( - ) -
Â
21
Stress Levels for Solid Timber 43
Fig. 2.1 Variability of modulus of rupture of wet Baltic redwood.
where kpis the number of standard deviations. The resulting value, s, is termed the ‘exclusion value’. To determine the appropriate value for kpreference is made to diagrams similar to Fig. 2.2 that give the area under the normal distribution curve for the selected probability level. The area increases from 0.135% of the total area to 50% as kpdecreases from 3 to 0, representing a change in the probability level from 1 in 740 to 1 in 2.
What is not as straightforward is the choice of probability level to take account of the various stress conditions and the appropriate factors of safety to be assigned to these exclusion levels. Where overstress can lead to failure, it was the practice in the UK to take the 1 in 100 exclusion level. In the Codes of Practice before 1984 this applied to bending, tension, shear and compression parallel to the grain. Where overstress would not lead to other than local failure (as with compression perpen- dicular to the grain) the probability level was taken as 1 in 40. Probability levels of 1 in 100 and 1 in 40 have kpvalues of 2.33 and 1.96 respectively.
These statistical basic stress values then had to be further modified to account for the dry condition (at that time 18% moisture content), size (conversion of the 20 mm size to 300 mm) and defects that set the particular grade. To this was added a further ‘safety’ factor by simply rounding the other factors into a practical number.
2.2.3 The methods in BS 5268-2: 1984
The testing of structural size members during the 1970s had shown a more realis- tic assessment of strength than small clear test pieces, therefore in BS 5268-2:1984 the strength values for visual grades were derived from full-sized tests, or, where there was insufficient data, assessments of full size values were made from the data for small clear specimens. Machine grades still relied on the relationship between the modulus of rupture and the modulus of elasticity to arrive at settings for grading machines. For the visual grades the exclusion level (as defined by the probability level) was set at 1 in 20 or the 5th percentile value for all properties. This value was, and still is, termed the characteristicvalue.
The characteristic bending strength and modulus of elasticity values were derived by test on SS grade timber from various common species. Other charac- Fig. 2.2 Areas of normal distribution curve for selected probability levels.
teristic strength properties and other grade values were derived by proportion from these test values. Because the method of sampling produced statistically ‘skewed’
populations, the statistical analysis became complicated to the point where it ceased to be comprehensible to the wider audience to whom the previous normal distri- bution procedure had been fairly straightforward.
The characteristic grade strengths were then further modified for duration of load (converting the relatively short-term test value to a long-term value), for size (con- verting the full-size test value for, say, a 150 mm deep joist to the standard 300 mm depth) and a safety factor that included an allowance for the change from the 1 in 100 exclusion level in the previous Code to 1 in 20 in 1984.
2.2.4 The methods in BS 5268-2: 1996
The 1996 revision of BS 5268-2 brought in the European standards for solid timber.
This included the statistical analytical methods given in BS EN 384. By compar- ison with all previous methods, including the normal distribution, the ranking method described in BS EN 384 for modulus of rupture and density, is simple:
place the results in ascending order with the 5th percentile being the value for which 5% of the test values are lower. Adjustment is then made for size, moisture content and duration of load in a manner similar to the previous editions of CP 112 and BS 5268. The mean value of modulus of elasticity is determined by test. From these three test values the characteristic values for other properties are determined as follows:
tensile strength parallel to grain ft, 0, k =0.6fm, k
compressive strength parallel to grain fc, 0, k =5(fm, k)0.45
shear strength fv, k =0.2(fm, k)0.8
tension strength perpendicular to grain ft, 90, k =0.001rk
compressive strength perpendicular to grain fc, 90, k =0.015rk
modulus of elasticity parallel to grain for softwood E0, 05 =0.67E0, mean
species
modulus of elasticity parallel to grain for hardwood E0, 05 =0.84E0, mean
species
mean modulus of elasticity perpendicular to grain – E90, mean=E0, mean/30 softwoods
mean modulus of elasticity perpendicular to grain – E90, mean=E0, mean/15 hardwoods
shear modulus Gmean =E0, mean/16