TiMi-.r.i; iMLYsirs KKLATION OF CRUSHING TO RENDING. 



373 



as the increments of load in the tesl 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, anil 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 dit'licnlties, satisfactory tension tests seem to be impossible. 



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I''ni. 08. -Uelnlion <f liber .stresses mid distortions. 



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 U. / 2 3 4 



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ff 



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 78 9 /O // 



NEUTRAL AX/S 



FIG. 99. Distribution of internal stresses in a beam at rupture. 



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

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

 sustaining the same load. A piece tested in tension, on the other hand, breaks suddenly as soon is the maximum 

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

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

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

 " fails iu tension." With those facts and 



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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 iu 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 OUC7 = area 

 OLT, and the position of the neutral plane at rupture is thereby fixed. If now the lino LU bo 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. Ky putting this sum equal to the moment 

 of the external load about the same point O the first relation is established. 



8 

 FIG. 100. Position of neutral axis and internal stresses at rupture (if beam. 



