to Transverse Strain in Beams. 409 



points measured, which had been increased $% units by the 

 load, was reduced on its removal only 73 units. Similarly a 

 load of 1(3,000 lb. caused an extension of 102 units, and its 

 removal a contraction of only 89 units. 



Now it is manifest that when a beam is transversely strained 

 the amount of strain in any part of a given section will vary 

 directly as the distance from the neutral axis. The stress, 

 tensile or compressive, will, however, not necessarily vary in 

 the same proportion, but will be that due to the strain, being 

 nearly proportionate to it until the maximum stress — that 

 which will ultimately cause rupture — is approached, but 

 increasing no further than the breaking stress and maintaining 

 practically the same amount until actual rupture commences. 



And if the point A, in the last diagram, represent the 

 position of the neutral axis of a beam undergoing transverse 

 strain, and the distance below it AB on a vertical line repre- 

 sent the depth below it of any part of the section, if a horizontal 

 line B C represent the tensile strain at that depth, then B D 



will likewise represent, on a scale =^ of that used in measuring 



the strain, the tensile stress at the same depth. 



It follows then that, when the limit of 

 elasticity has not been exceeded, if the 

 line D (fig. 6) , being the lower side of 

 any section ABCD of a rectangular 

 beam, subjected to transverse strain 

 only"*, be taken to represent the stress 

 per inch at that line, then the same line 

 measured in units E times the length of 

 those in which it measures the stress will 

 represent the longitudinal elongation 

 per unit of length of the filaments of the 

 beam, or the strain at that line. Join * 7 9 ® ' 



AD B C : then Gr, the intersection of 



those lines, is the centre of gravity of the section, and also 

 under the same condition the position of the neutral axis. 

 And the length of any horizontal lines ah or cd between those 

 lines win represent in similar units the stress per inch either 

 compressive or tensile, as well as the contraction or elongation 

 at such line. 



Moreover, the areas of the triangles AGB, CGD, multiplied 



* That is to say, the sum of the longitudinal stresses at that section 

 reckoned positive or negative according as they are tensile or compressive 

 amounting to zero. Should the beam in addition to the transverse strain 

 be subjected also to longitudinal strain, the conditions will be altered and 

 the position of the neutral axis changed. 



