to Transverse Strain in Beams. 405 



For the 2nd Beam, with a load of 



8.000 lb. the maximum elongation was -000858 or -000107 per 1000 lb. 

 16/)00 „ „ „ "00223 „ -000139 „ „ 



In the four experiments on solid rectangular beams 1 inch 

 wide by 2 inches deep and 5 feet long, the mean initial de- 

 flexion was '00035 inch per lb. of load, and the mean ultimate 

 deflexion '000524 inch per added lb., or half as much again, 

 showing a diminished resistance as the curvature increased. 



This fact is of the highest importance for the determination 

 of the causes of the amount of transverse strength. If there 

 were a resistance to flexure this should rather increase with the 

 curvature. The consequence would be that the ratio of the 

 elongation of the lower fibres, and of the deflexion, to the 

 load should diminish as the curvature increases. It is found 

 on the contrary to increase, and the fact of its doing so is 

 fatal to Mr. Barlow's hypothesis. 



Another material feature observable in these experiments, 

 but not particularly noticed by Mr. Barlow, is that in all 

 cases when the loads were removed the measured lengths did 

 not return to their original dimensions but retained a per- 

 manent set. The amount of set shown is given in the last 

 columns of the preceding tables, and will be hereafter again 

 referred to. 



Mr. Barlow assumes (1) that the resistance which he ascribes 

 to flexure has the same effect as an addition to the tensile stress, 

 and (2) that the amount of this addition varies with the 

 degree of flexure, and also with the depth of the beam. But 

 when he comes to determine the amount of this resistance in 

 solid rectangular beams at the moment of rupture, he makes 

 this addition, due to the resistance to flexure, a constant quan- 

 tity, bearing a proportion to the tensile resistance of 1 to * 78 ! 

 (Well may a doubt be expressed whether lateral action alone 

 is sufficient to account for such an addition to the tensile 

 resistance.) For a beam of different pattern he assumes that 

 this constant is multiplied by the depth of metal and by the 

 deflexion, and divided by the depth and deflexion of the solid 

 beam. 



In effect this is simply to treat the question as though 

 the tensile strength were so much greater than it really is, the 

 amount of the excess being taken at an arbitrary quantity, 

 determined from the excess of transverse strength required to 

 be accounted for, and modified to suit the case of beams of a 

 different form in an equally arbitrary manner. 



And no satisfactoiy account or explanation is given of this 

 assumed enormous addition to the tensile resistance. It is 

 clear that the relative lateral displacement of the fibres must 



