Report upon the forestry investigations of the of agriculture1877-1898 . it in tension. From the approximate distribution ofinternal stresses their relation to the externalload 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 := areaOLT, and the position of the neutral plane at rupt
Report upon the forestry investigations of the of agriculture1877-1898 . it in tension. From the approximate distribution ofinternal stresses their relation to the externalload 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 := areaOLT, and the position of the neutral plane at rupture is thereby fixed. If now the line LU be assumed to representthe depth of the beam in inches instead of indicating the distortion of the fibers, the sum of the internal momentsabout the point O is found by multiplying the area of either the compression or tension diagram by the sum of thedistances of their respective centers of gravity from the neutral plane. By putting this sum equal to the momentof the external load about the same point O the first relation is ^-Z 2 3 ^ S 6 7 8 9 JD // /2 Tig. 100.—Position of neutral axis and internal stresses at rupture of beam. 374 ? FORESTRY INVESTIGATIONS U. S. DEPARTMENT OF AGRICULTURE. RELATION OF CRDSHING-ENDWISE STKBNGTH. The second relation (that of crushing-endwise strength to internal stresses) -was touched upon in discussing thefirst, when it was stated: (1) That the true elastic limit of the beam is proljably reached at the same instant thatthe extreme fibers on the compression side reach their elastic limit in compression. (2) That this latter limit liesclose to the ultimate compression-c-ndwise strength (so close that former experimenters have been unable satisfactorilyto separate them). (3) That a piece of green wood will stand a great deal of distortion after the ultimate load isapplied before actually failing. And to these statements may be added the evident fact (4) that the stress on anyfiber on the
Size: 1901px × 1314px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, bookdecade1890, booksubjectforestsandforestry
