﻿of Ductile Material* under Combined Stress. 54 7 



There is no sign of a regular increase or decrease of the 

 maximum shear corresponding to an increase of the tensile 

 stress across the plane of shear. The present tests have a 

 rough indication of increase of maximum shear stress with 

 increase of bending moment, and therefore of both ten-ion 

 and compression, but it is by no means conclusive. It is 

 opposed to the idea of either positive or negative friction. 

 The true reason of the variation in the maximum shear 

 stress, after allowing for errors in measurement, appears to 

 be that the shearing resistance varies in different directions. 

 Bauschinger tested the shear strength of various specimen- in 

 six different directions. For annealed puddled plate it varied 

 from 8*89 to 19*68 tons/in. 2 , for rolled iron bar from 10*15 

 to 2255 tons/in. 2 With steel the variation was less, for 

 Bessemer plate from 21*45 to 27*35 tons/in. 2 , and for another 

 specimen of the same from 25*05 to 2 ( .**2 tons/in. 2 Remem- 

 bering these results, assuming the maximum shear stress to 

 be the criterion determining yield, and also that with tension 

 and torsion the planes of shear are different, it cannot be 

 expected that the tensile strength of steel will be exactlv 

 twice the shear strength. The fact that sometimes it appears 

 to be more, and at others less, points to this being the true 

 explanation of the variation of the maximum shear stress at 

 the yield-point under combined loading. The relation noticed 

 above between the stresses in the present tests is just tin 

 kind of connexion that would be expected if the assumption 

 is correct, remembering that different specimens were used, 

 no doubt differing slightly in properties and strength. 



14. Final Conclusions. 



It must be concluded that the maximum shear stress 

 determines when yield takes place, but this will vary slightly 

 on account of the difference in the shearing resistance in 

 various directions, and any idea of a force analogous to 

 friction must be abandoned. For the common case of com- 

 bined bending and twisting either the circular or elliptic 

 formula may be safely used, or to approximate to the elliptic 

 formula \/M 2 + T 2 may be equated to the equivalent moment, 

 taken as being of the same kind as the larger which is actually 

 operating, and the corresponding true working stress used. 

 It is not admissible to extend the conclusions to brittle 

 materials until further evidence is available, and the author 

 hopes to make experiments in this direction shortly. The 

 writer wishes to acknowledge his debt to Mr. Guest for the 

 results borrowed from his paper, and to thank Lord Biyths- 

 wood for affording the opportunity of making the test>. 



