Dissemination of IT for the Promotion of Materials Science (DoITPoMS)

# Strength of wood

The strength of wood can also be measured using a three-point bend test. The width (w) and height (h) of wood samples are measured, and the specimens are placed in the three-point bend testing apparatus with the height of the wood orientated vertically in the apparatus. The distance (L) between the two supports is also measured. The wood samples are again loaded in 100 g increments. If the micrometer needle continues to move after a 100 g load has been added to the pan, the reading is allowed to stabilise before further mass is added. The mass on the pan is increased in this way until the sample fails. At this point the load and deflection of the sample before failure are noted.

Video of three-point bend test of greenheart

By following this method and repeating for three samples of balsa, Scots pine and greenheart the following results were obtained:

 Wood tested Greenheart Scots pine Balsa 1 2 3 1 2 3 1 2 3 w (mm) 3.0 3.4 3.0 3.4 3.1 3.6 3.8 3.7 3.7 h (mm) 3.1 3.6 3.4 3.6 3.4 3.4 3.7 3.6 3.6 L (mm) 90 Maximum mass (kg) 4.7 7.9 5.8 2.9 3.3 3.0 2.5 0.8 1.0 Maximum deflection (mm) 6.05 5.75 6.80 3.59 6.06 4.60 2.50 4.10 4.00 Strength (MPa) 215.9 237.4 221.5 87.2 120.4 95.5 63.6 22.1 27.6 Average strength (MPa) 225 101 38

The error in the individual strength results can be calculated using the standard deviation in the strength measurements. The error in the average value of strength is then found by dividing this error by , where N is the number of strength measurements taken.

The errors in measurements are:

 Greenheart Scots pine Balsa Standard deviation (MPa) 11.2 17.3 22.6 Error in average strength (MPa) 6.5 10.0 13.0

To calculate the strength the following equation is used:

Strength =  $$\frac{{3mgL}}{{2w{h^2}}}$$

The results for balsa, Scots pine and greenheart are as follows:

 Greenheart Scots pine Balsa Strength (MPa) 225±7 101±10 38±13 Textbook values (MPa) 181 90 23

The textbook values reflect a wider range of samples. The large differences between our experimental results and the textbook values can also reflect errors in the weights, distance between the supports, and w and h. Three-point bending is not a very accurate method for strength testing, as the force is concentrated at one point in the material. The high error also shows the natural variability of wood within a species, and even within a tree.

Wood performs well under uniaxial tension, due to the high strength of the cellulose microfibrils. Wood is a lot weaker in compression, as the cells can collapse. Buckling of the cell walls occurs first in the vertical cells at the point where they are deflected by the rays (radial cells). This leads to creases, which can act as cracks in the wood when tension is applied. For this reason, diving boards break if turned over. The unseen crease that was in compression on the underside of the board is put in tension when turned over, causing the board to fail. On bending of wood, gradual crushing occurs on the compression side of the beam, transferring load to the tension side (lower side in our three-point bend tests). Trees have evolved to avoid this problem by being in a pre-stressed state. As the outer layers of the tree trunk are in tension normally, on bending the compressive side of the trunk can avoid going into an absolute state of compression.

Compressive failure in wood

The wood samples fail by crack propagation across the lower surface of the samples, which are under tension. A simple way of explaining the high failure stress (strength) of wood is to say a fibre pull-out mechanism occurs on failure. As it is the fibres that must be broken for the sample to fail, the strength of the sample depends mostly on the strength of the fibres within the wood. Cellulose fibres are quite strong, so wood also has reasonable strength, and very high specific strength due to its low density. However, as we will see later, the fibre pull-out mechanism cannot completely explain the high strength of wood.