5i8 WARREN J. MEAD 



side just as in the case of a simple beam under load, in which com- 

 pression is developed on the concave side and tension on the 

 convex side. 



Resolution of stresses due to change in area and to cross-bending — • 

 The stress condition at any point is the resultant of all of the 

 stresses acting at that point. To determine conditions at a given 

 point on the surface of a warped sheet it is necessary, therefore, to 

 resolve the stresses due to cross-bending and the stresses due to 

 areal change. In Figure loA the stresses due to change of area 

 caused by torsional warping are indicated in direction and relative 



Fig. II. — -Plaster of Paris positive of folds produced by compression or shortening 



magnitude by arrows. These represent the stresses occurring along 

 any transverse line of the warped sheet. In Figure loB the stresses 

 due to cross-bending occurring along any transverse line of the 

 warped sheet are shown by arrows in a similar fashion. In Figure 

 loC the resultants of the stresses in Figures loA and loB are 

 shown. In Figure loC typical cracks developed by tension and 

 compression are shown at a, b, and c. The tension cracks a and c 

 should begin at nearly 90° with the edge at the margin, and gradu- 

 ally curve to an angle of 45° at the neutral line. The curved 

 line b indicates the strike of inclined thrust fractures which would 

 be developed by compression. It is of interest to compare these 

 curves with the tension cracks developed in paraffin on a rubber 



