THE MECHANICAL INTERPRETATION OF JOINTS 719 



Each "fan" consists of a gently curved "master-joint," marked 

 t and t' , from which start, at a very acute angle, a number of minor 

 joints, 5 and s\ which unmistakably tend to be 

 straight and parallel to each other. 



The clue to this peculiar fan-structure of 

 fractures we find in Hartmann's experiments 

 with rectangular strips of soft steel.' Under 

 torsion, two systems of Liiders' lines appeared 

 on them, each parallel to one of the sides 

 of the test piece, intersecting practically at 

 right angles. This indicates that the direc- 

 tion of greatest tension traverses the surface 

 obliquely, forming an angle near 45° with 

 the axis of torsion.^ When the deformation 

 was carried farther additional lines of defor- 

 mation appeared in the vicinity of the longer 

 edges, bisecting the angles formed by the 

 first set of lines. 



When a plate is subjected to simple 

 torsion, each element of the upper surface 

 suffers simultaneously tension in one direction 

 and compression at right angles to it. The 

 same is true of the lower surface, but with 

 the directions of tension and compression 

 reversed.^ 



At any point on either surface, therefore, Fig. 5. — The fractures 

 the position of the shearing planes is sharply forming two characteristic 



^ . . fans on one of the glass 



defined through the combined action of tension pktes used in Daubree's 

 and compression as shown diagrammatically experiments on fractures 



'■ produced by torsion. 



in Figure 6. In case tension fractures are 



formed in addition, they bisect the acute angle of the shearing 



planes. This is what happened in Hartmann's experiment with 



' Hartmann, loc. cit., p. 175 and Fig. 173. 



2 This can be verified readily by drawing a circle on the flat side of a rubber 

 eraser and twisting it. G. F. Becker, "The Torsional Theory of Joints," Trans. 

 Amer. Inst. Meek. Engineers, Vol. XXIV (1895), p. 136. 



3 For the purposes of the following discussion it is important to remember that 

 essentially horizontal tensional stresses arise in surfaces made convex, and similar 

 compressive stresses in surfaces made concave through the process of bending. 



