872 Mr. H. Garrington on Young* s Modulus 



The determination of the elastic properties for a particular 

 species of timber presents some difficulty, for treated — as it 

 should be — as having three planes of elastic symmetry, nine 

 elastic constants are required, completely to define its elastic 

 properties, whereas an isotropic material such as steel 

 requires only two. The problem is further complicated 

 by the fact that the seolotropy of the material is variable, 

 which has to be reckoned with in an investigation on its 

 elasticity. 



Before the advent of the aeroplane a knowledge of the 

 elasticity of timber was seldom required in practical 

 problems. When, however, it began to be used extensively 

 in aeroplane construction, information about its elasticity 

 became both desirable and necessary. A research on the 

 elastic properties of spruce was accordingly undertaken by 

 the author during the war, in the College of Technology, 

 Manchester, for the Air Board and Royal Aircraft Establish- 

 ment, and the following paper gives the results of the 

 investigation to determine values of Young's Modulus and 

 Poisson's Ratio. 



The results were obtained on the assumption that each 

 piece of spruce experimented upon had three planes of elastic 

 symmetry. All the test pieces were accordingly cut so far 

 from the pith of the tree that the annual layers of the 

 portion of each piece over which the strains were measured 

 were sensibly plane surfaces. The portion could thus be 

 considered as having three planes of symmetry of structure, 

 which were treated as planes of elastic symmetry. 



The largest pieces experimented upon were 13 inches long, 

 about 1 in. wide and J in. thick, the dimensions of the smaller 

 pieces being approximately in proportion. The values of: 

 Young's Modulus and Poisson's Ratio were obtained from 

 measurements of the principal curvatures of the neutral sur- 

 faces when the pieces were bent by couples suitably applied 

 to their ends*. Considering the case of a large piece, this 

 rested upon knife-edges 12 inches apart, and the load was 

 applied equally to two other knife-edges, 8 inches apart and 

 symmetrical with respect to the outer knife-edges. The 

 bending moment between the inner knife-edges was thus 

 constant, and the neutral surface was a surface of anti- 

 clastic curvature f . From measurements of the principal 



* Phil. Mag. Feb. 1921. 



f Thomson & Tait, Nat. Phil., Arts. 711-718. 



