STIFFNESS OF WOOD. 39 



reduces the stiffness eightfold. Stiffness then decreases as the cube of 

 the length. 



Cutting out a piece 2 by 4 inches and 4 feet long, placing it flatwise 

 so that it is double the width of the former stick and loading it with 

 100 pounds, we find it bending only one-sixteenth inch; doubling the 

 width doubles the stiffness. 



Setting the same 2 by 4 inch piece on edge, so that it is 2 inches wide 

 and 4 inches deep, the load of 100 pounds bends it only about one 

 sixty-fourth inch : doubling the thickness increases the stiffness about 

 eightfold. 



It follows that if we double the length and wish to retain the same 

 stiffness we must also double the thickness of the piece. 



A piece of wood is usually stiffer with the annual rings set vertically 

 than if the rings are placed horizontally to the load. 



Crossgrained and knotty wood, to be sure, is not as stiff as clear 

 lumber; a knot on the upper side of a joist, which must resist in com- 

 pression, is, however, not so detri- 

 mental as a knot on the lower side, / '-— , """* — i rf • " ' — ' "_^-~ '\ 



where it is tried in tension. "f'r---- -._." ~_ ~-----"''F 



Every large timber which comes J|r— - _„,— . -«"-"""J| k 



from the central part of the tree con- 



. . . , . „ .. , . Fig. 25. — Bending a beam. 



tarns knots, and much of its wood is 



cut more or less obliquely across the grain, both conditions rendering 



such material comparatively less stiff than small clear pieces. 



The same stick of pine, green or wet, is only about two-thirds as 

 stiff as when dry. A heavy piece of longleaf pine is stiffer than a light 

 piece; heavy pine in general is stiffer than light pine, but a piece of 

 hickory, although heavier tban the pine, may not be as stiff as the 

 piece of longleaf pine, and a good piece of larch exceeds in stiffness 

 any oak of the same weight. 



In the same tree stiffness varies with the weight, the heavier wood 

 being the stiffer; thus the heavier wood of the butt log is stiffer tban 

 that of the top; timber with much of the heavy summer wood is stiffer 

 than timber of the same kind with less summer wood. In old trees (of 

 pine) the center of the tree and the sap are the least stiff; in thrifty 

 young pine the center is the least stiff, but in young second growth 

 hard woods it is the stiff'est. 



Since it is desirable, and for many purposes essential, to know before 

 hand that a given piece with a given load will bend only a given 

 amount, the stiffness of wood is usually stated in a uniform manner 

 and under the term " modulus (measure) of elasticity." 



If AB, fig. 25, is a piece of wood, and d the deflection produced by a 



weight or load, the elasticity of the wood, as usually stated, is found 



by the formula : 



W I 3 

 Modulus of elasticity = — , ^ , , — 



J 4 D bd 3 



