THE MECHANICS OF GEOLOGIC STRUCTURES 



519 



sheet, illustrated in Figures 6 and 7. In this experiment constant 

 distance between the clamps was maintained and compression 

 along the center line thus prevented. The tension cracks are 

 evidently due to a combination of cross-bending and stretching 

 and are in accord with the conclusions indicated in Figure loC. 



Depending on the relative intensity of the stresses due to 

 change in area and those due to cross-bending, the curvature of 

 the cracks would vary from 

 the position in Figure loA, 

 due only to change in area, 

 to the position shown in Fig- 

 ure loB, due only to cross- 

 bending. 



Relative intensity of stresses 

 due to cross-bending and those 

 due to change in area. — ^With a 

 given length of torsional axis 

 the amount of cross-bending 

 is a function of the angular 

 displacement by torsion and 

 is independent of the width 

 of the warped sheet. The 

 change in area (and therefore 

 the tensional and compres- 

 sional stresses), however, is a 

 function of the width of the 

 sheet as well as of the angle 

 of torsion. It follows, there- 

 fore, that in narrow strips 

 deformed by torsion, cross- 

 bending stresses may be domi- 

 nant while in wide areas a 

 small angle of torsion with a 

 small amount of resultant 



cross-bending may develop relatively large tensional and com- 

 pressional stresses. Cross-bending stresses also increase with the 

 thickness of the individual beds. 



Fig. 12. — Vertical view of reproduction 

 in plaster of Paris of folds produced by 

 shearing deformation. The direction of 

 movement is indicated by arrows and the 

 amount of deformation is shown by the 

 shape of the block. 



