TIMBER PHYBICS RELATION OF CRUSHING TO BENDING. 



373 



as the increments of load in the test machine vary. Therefore, the distribution of stresses on the compression side 

 of the neutral plane will be shown by an ordinary strain diagram for compression, and on the tension side by a 

 similar tension-strain diagram. Unfortunately there are no reliable diagrams of these kinds now on record. The 

 compression pieces tested have usually been too short to afford reliable measurements of distortion, and, owing to 

 structural and mechanical difficulties, satisfactory tension tests seem to be impossible. 



STRESSES /A/ £000 LBS. 

 a / 2 3 4 5 ' 6 



,, STRESSES /A/ WOO IBS. 

 U / 2 3 4- 5 6 7 8 9 /O // 



Fig 98.— Relation of fiber stresses and distortions. 



S 1 - / 2 3 4-5678 & f /0^// 



Fig. 99 .—Distribution of internal stresses in a beam at rupture 



Experience in testing, however, has taught that when a piece of green wood is tested in compression it will 

 undergo a great distortion after the maximum load has been applied without actually breaking down — in fact, while 

 sustaining the same load. A piece tested in tension, on the other hand, breaks suddenlv as ?oon as the maximum 

 load is applied. A beam in failing may, therefore, sustain an increasing load long after the extreme compression 

 fiber Ms been loaded to its ultimate strength; the fibers on the compression side continue to be mashed down, 

 while the neutral plane its lowered and the stress in the tension fiber increases until, very oftenin practice, the beam 

 " fails in tension." With these facts and 



/ 2_3 4 S 



//I/ 

 6 7 

 T 



WOO „ 

 8 9 /O. 



T 



LBS 

 // /2 



observations before us it is possible to con- 

 struct a diagram so that it will represent, 

 approximately, at least, the distribution of 

 internal stresses in a beam at rupture. (See 

 fig. 100.) 



In this figure OA represents the position 

 of neutral plane at time of rupture, OU the 

 distortion in the extreme compression fiber, 

 UC the stress on same fiber, OL the distor- 

 tion in extreme tension fiber, and LT the 

 stress on that fiber. 



It can readily be seen that the manner 

 of breaking will influence slightly the form 

 of this diagram. If the beam fails in com- 

 pression before the tension fiber reaches its 

 elastic limit the line OT will be straight as 

 shown, otherwise the line will assume some 

 such position as O^T, (diagram 99), in which 

 I, is the elastic limit in tension. 



From the approximate distribution of 

 internal stresses their relation to the external 

 load may be determined. The two funda- 

 mental equations— (1) that the sum of inter- 

 nal stresses on the tension side equals the sum 



of internal stresses on the compression side, and (2) that the sum of the external moments equals the sum of the inter- 

 nal moments— apply at the time of rupture as well as at the elastic limit. From (1) it follows that area OUCZ= area 

 OLT, and the position of the neutral plane at rupture is thereby fixed. If now the line LU be assumed to represent 

 the depth of the beam in inches instead of indicating the distortion of the fibers, the sum of the internal moments 

 about the point O is found by multiplying the area of either the compression or tension diagram by the sum of the 

 distances of their respective centers of gravity from the neutral plane. By putting tlrigj §u,m. equal to the monien^ 

 Of tlie external loa4 about t{|e s§m§ uqjnti fbf firgt relation is established, 



# u / 2 3 4 & 6 7 8 9 fO // /B 



Fig. 100.— Position of neutral axis and internal stresses at rupture of beam. 



