5i6 



WARREN J. MEAD 



which has been deformed by warping and then flattened out for 

 comparison with the original area. 



Cross-bending stresses resulting from torsional warping. — We 

 have so far considered only the stresses resulting from change in 

 area, and now turn to a consideration of the stresses due to warping 

 or cross-bending. In Figure 9 a warped surface is represented in 

 isometric projection. In one set of diagonals the lines curve 

 downward toward their centers forming a synclinal depression. 

 In the other set of diagonals the lines curve upward toward their 

 centers and form an anticlinal elevation. 



Fig. 9. — An isometric representation of a warped surface 



If we consider a sheet of finite thickness to be thus deformed it 

 is evident that on the upper surface compressional stresses will be 

 developed at right angles to the axis of the synclinal depression 

 and that tensional stresses will be developed at right angles to the 

 axis of arching. At every point on the upper surface of this 

 warped sheet there is a tensional stress and a compressional stress 

 acting at right angles, each of them at an angle of 45° to the axis 

 of torsion. On the lower surface it is evident that similar stress 

 conditions exist but the tensional and compressional stresses are 

 acting at angles of 90° to the similar stresses at the upper surface. 

 These stresses are caused by cross-bending, and tensional condi- 

 tions on one side mean compressional conditions on the opposite 



