;^7 



The obseivod data arc given in the cohiinns headed "Time," "Load," and "Scale Reading." 

 These results are recorded on this slieet in ink as they are observed. Tlie icsult in the " l)et1(!C- 

 tiou" coliunn is coniimted from tlie scale reading, [t is placed next to the column of " Loads" for 

 convenience in i)]otting the strain diagram, which is done ou the ruled .sciuares at the bottom of 

 each sheet. These i)lotted results fall in all cases ou a true curve, similar to the one shown on )). 36. 

 The total area of this curve, 0. D. JJ., properly evaluated by the scales used, represents the total 

 mtniber of foot pounds or inch-iiounds of work doue upon the stick before rui)ture occurred. This 

 is called the Total Vronn-birakiixj licniUence of the stick, and when dixided by the volume of the 

 stick in cubic inches it gives approximately the total cross- breaking resilience of the stick in inch- 

 pounds ]>er cubic inch of timber. 



A better criterion of toughness, or resistance to shock, is some delinite portion of this strain 

 diagram area, as P K, for example. This amount of resilience or sprmg can be used over and 

 over again, and is a true measure of the toughness of the timber as a working (|uality. To locate 

 the point P, the following arbitrary rule has been followed: 



Draw a tangent to the curve at the origin, as A. Lay off A C=hB A, and draw G. 

 Draw m n parallel to C and tangent to the curve. Take the point of tangency as the point /', 

 and draw P K. The area P K is then called the Relatii-c Elantic KeaUicnvc* 



There is no " elastic limit" in timber as there is in rolled metals. In this respect it is like cast 

 iron. The point P is the point where the rate of deflection is 50 per cent more than it is at first, 

 and usually falls on that jiart of the curve where it begins to change rapidly into a horizontal 

 directi(m or where the deflection liegins to increase rapidly. The areas of these curves are meas- 

 ured with a planimeter and reduced to inch-pounds. Thus, if 1 inch vertically represents .'>,()()() 

 pounds, and 1 inch horizontally represents 1 inch deflection, then 1 square inch represents ."),0(M»x 

 1=5,000 inch pounds. If the area I' K is 1.73 squaic inches, then the corresponding resilience 

 is 8,<)50 inch-pounds. This means that a weight of 100 pounds, falling St;.5 inches, or 1,000 pounds 

 falling 8.G5 inches, would have strained the beam up to the point P or it would have deflected it 

 l.(!(i inches, and the beam would have been then resisting with a force of 10,000 pounds, since /' 

 falls on the 10,000-pound line. If this result — !S,(i.")0 iucli-i)ounds — be divided by the number of 

 cubic inches in the stick between end l)earings, the result is the true Relatire Resilience in Cross- 

 hrcal-infi in inch-pounds per cubic inch. This result is independent of the dimensions of the test 

 specimen, and is therefore a true measure of the (puility of timber which is usually known as 

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

 the deflection; in fact, it is very nearly the half-product of the strength developed and the deflec- 

 tion produced at this particidar point P. It is i>robably the nearest ipuintitative measure of the 

 tonghness that can l>e arrived at. 



The strength of the extreme fibre is computed by the ordinary formula — 



where / = stress on extreme fibre in pounds per square inch, 



W = load at center in itounds, 



I = length of beam in inches, 



h =: breadth of beam in inches, 



/( = height of beam in in<-hes. 

 At the time of flnal rupture this formula by no means represents the actual facts. It assumes 

 that the neutral plane remains at the center of the beam till rujiture occurs, which is far from 

 correct. In green timber, where the crushing strength is greatly retluced by the presence of the 

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

 the stick invariabl.N' begins to fail on the compiession side. This causes the neutral |ilane or plane 

 of no stress to be htwered, and at the time of final rujiture this ])lane may be from one-fourth to 

 one-sixth the depth from the bottom side of the beam. The value of /<-om])uted by this formida 

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



'Tliis term h;is been roiued to <l(^finl■ tliis ]>;irlii'iilar ]niiti(>ii (if tlic ivsilieinH- wliirli will Ik- used t'cji i'iiiii|i:iriii)f 

 tlie relative elasticity or tougliuess of UiUerout limlnrs. 



