STRENGTH OF WOOD 



119 



from the formula D 



PxW 



:, where Z= length, in feet, W=the 



greatest weight in pounds which the beam can bear without losing 

 its elasticity or acquiring a permanent set, 6 = breadth in inches, 

 6?= depth in inches, and 5= deflection in inches. From this it 

 obviously f oUows that 



PxW 

 ~ 6 X # X D" 

 It is found in practical engineering that the deflection of timber 

 beams (5) should not exceed :j-|7yth of their length. 



Bauschinger employed, for testing tensile strength, rods 18 inches 

 long and 1 or 2|- inches square for 5 J inches at each end, reducing to 

 J or If inch in the middle. He does not, however, consider these, 

 or his experiments on bending (in which the individual variation of 

 the large beams employed, as to knots, etc., produces wide difler- 

 ences in the results), so instructive as to the relative values of 

 timbers as are crushing experiments. For such experiments he 

 used blocks 6 inches high and 3| inches square, protected at the 

 ends with metal plates. 



Eesults wiU be affected by so many circumstances that it is 

 most important that the history of logs experimented with should 

 be known. The nature of the locahty in which the timber is 

 grown, the age of the tree, the part of the tree from which the 

 timber is taken, and the extent to which it has been seasoned, will 

 all modify the results. Thus Bauschinger showed that strength 

 varies according to the proportion of summer to spring wood, and 

 that the centre of a tree is therefore weaker ; whilst the following 

 table of the range of variation in 2Q trees of Pinus paHstris, quoted 

 by Professor Unwln from a Eeport of the U.S. Department of 

 Agriculture, shows how butt, middle, and top logs differ in strength, 

 largely no doubt for the reason, which we explained in a previous 

 chapter, that the annual increments of wood forming cones do 

 not extend uniformly from end to end of a log. [See p. 66 and 

 Fig. 40.] 



Butt, 



Middle, 



Top, 



Heaviness 



m lbs. 



per 



cubic foot. 



28-64*8 

 36-53-5 

 32-56*5 



Coefficient of 

 Elasticity 



from 

 Bending 



Test. 



500-1380 

 510-1369 

 375-1200 



Crushing' 

 strength,. 



Coefficient 



of 

 Bending 

 Strength. 



3 -84-14 -4 

 2 -82-13 -4 

 1-85-10 -8 



All in tons per square inch 

 2-13-4-40 



2-25-415 

 2 "04-4-06 



2 -12-7 -25 

 3 40-7-65 

 1-90-7 -00 



Shearing 

 strength. 



•21- -58 

 •24- -55 

 •22- -52 



