10 



cubic inches in the stick between end bearings, the result is the true Relafirc Resilience in Croftif- 

 bnakiny in inch pounds per cubic inch. Tiiis result is independent of the dimensions of the test 

 si)ecimen and is therefore a true measure of the quality of timber which is usually known as 

 toughness. It depends, as toughness in the usual undeistanding does, on both the strength and 

 the deflection; in fact, it is very nearly the halt' product of the strength developed and the detle<' 

 tion produced at this particular point P. It is probably the nearest quantitative measure of tlie 

 toughness that can be arrived at. 



The modulus of rupture is computed by the ordimiry formula — 



•^ jibli'- . . . (^) 



where /=modulus of rupture in pounds jier sijuare inch, 

 ir=load at center in ponnds, 

 /=length of Ijeam in inches, 

 ft=breadth of beam in inches, 

 /t=height of beam in inches. 

 In green timber, where tlie crushing strength is greatly I'cduced by the presence of the sap, 

 the crushing resistance is only about one-third as much as the resistance to tension, so that the 

 stick invariably begins to fail on the compression side. This causes the neutral jd.ane or plane of 

 no stress to be lowered, and at the time of linal rnptnre.this plane may be from one fourth to one- 

 sixth the depth from the bottom side of the beam. The value of/ computed by this I'ormula from 

 a cross-breaking test, therefore, will always be intermediate between the crushing strength and 

 the strength in tension. Thus the crashing strength of a given stick was found to be 5,820 jiounds 

 per square inch, wJule tlie tensile strength was l.'»,7S() jiounds; the cross-breaking strength was 

 found by this test to be 10,900 i)ounds. 



The modulus of strength at the elastic limit is found in tlie same manner as the above, except 

 that for l)reaking load is taken the load at tlie i)oint 7', d(>scribed abov(% this being called the 

 "elastic limit," although strictly speaking tindjer is not perfectly elastic for any load if left on any 

 great length of time. 



The modulus of elasticifi/ is computed from the formula — 



,,_ 117' _ WP _ W I' ■ 



" 4H 1) I 4l)bh^ l)-4b¥ . . . . \) 



where E = modulus of elasticity, 



and ^^^' '' ''' '^"^^ ''■ "^ '" ^'^- (-^^ 

 D = detlection of beam. 



1 = moment of inertia of the cross-section = ^^b h^ for rectangular sections. 



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

 the cocinlinates of any point on this line used as the IT and /> (.V(>'n 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 ot 

 all kinds of engineering materials* an<l is a necessaiy means of computing all deflections or dis- 

 tortions under loads. 



In using the modulus of elasticity of timber for computing deflections, it must be remembered 

 tliat in this case the time effect is very great (it is nearly zero in nu'tals) and that this factor can 

 (udy be used to comi)ute the detlectioii for temporary loads. The deflection of floor or roof timbers, 

 for instance, under constant loads is a very difterent matter, as it increa.ses with time. 



baxjschingee's relations. 



Relation between strength and stiffness. 



In Fig. 7 is shown the relation found by Professor Banschingert betM'een the modulus of 

 elasticity (stift'ness) and the cross-breaking strength, from tests on ])ine, larch, and flr timber. 

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



• The wide range of values of the modulus of elasticity of the various metals, found in i>nblic resoids of tests, 

 must be exjilained liy erroneous methods of testing. 



t See PI. II, vol. 16, of Professor Bauschinger's Reports of Testo made at Govermnent Testing Laboratory at 

 Munich. 



