38 



and tlK- streugth iu tciisinu. Tims tlic cinsliiii,i; strength of a givcu stitk was fonnd to be 5,820 

 pouuds per square iiicli, while the tensile strength was 15,780 pounds ; the cross-breaking strength 

 was found by this test to be 10,900 pounds. 



The modulus of elasticity is computed from tlie formula— 



WP^ _ WP _W P . . . . (2) 



^ - IS J) I~4l)h¥~ D' 4b ¥ 

 where E = modulus of elasticity, 



and ^^ ' '' ''' '^^^ '' "^ "' ^^^' '^''^ 

 J) = deflection of beam. 



I = moment of inertia of the cross-section = -^ b ¥ for rectangular sections. 



To find this modulus, a tangent line is drawn to the strain diagram at its origin, as A, and 

 the coordinates of any point on this line used as the W and D from which to compute E. 



The modulus is thus seen to vary directly as the load and inversely as tlie deflection, hence it 

 is a true measure of the stiffness of the material. It is the most constant and reliable property of 

 all kinds of engineering materials,* and is a necessary means of computing all deflections or dis- 

 tortions under loads. 



In using the modulus of elasticity of timber for coiiipiiting deflections, it must l)e remembered 

 tliat in this case the time ettcct is very great (it is nearly zero in metals) and tliat this factor can 

 only be used to com])ute the deflection for temporary loads. The deflection of floor or loof timbers, 

 for instance, under constant loads is a very difierent matter, as it increases with time. 



Relation between strength and stiffness. 



In Fig. 6 is shown the relation loiind by Professor Uauschingert between the modulus of 

 elasticity (stiffness) and tlie cross-breaking strength, from tests on pine, larch, and fir timber. 

 Althougli the results show a wide range, there is evidently a general relation between these two 

 quantities, as indicated by the straiglit line ilrawn through llie plotted points. The algebraic 

 expression of the law shown by this line, rendered into pounds per square inch, is, in round 

 numbers — 



Cross-breaking strength — 0.0045 Modulus of Elasticity + 4.">0. (3) 



If it should be found that there is such a law for all kinds of timber, then there may be derived 

 an equation of this form, but with different constants, for each species. 



Relation between sfrenfith ami n-cight. 



In Fig. 7 is shown the relation between the crushing strength and the specific gTavity, when 

 both are reduced to the standard percentage of moisture, which was taken at 15 per cent. 



These results are also taken from Professor Bauschinger's jmblished records of tests on Pine, 

 Larch, and Fir timbers, and they conclusively show that the greater the weight the greater the 

 strength of the timber. The law here is a well-defined one, so far as these timbers are concerned. 

 When rendered into English units (pounds per sq. in.), the equation of this line is: 



Crushing strength = 13S0(» specific gravity — 900. (4) 



when the timber contains but 15 per cent of moisture. This equation would also vary m its 

 constants for each species of timber. 



* Tlie wide raufe of values of tlie modulus of ehistieity of tlie various metals, found in iiublislied records of 

 tests, must be explained by erroueous metliods of testiug. 



t See PI. II, vol. 16, of Professor Bauschinger's Reports of Tests made at Government Testing Laboratory at Munich. 



