ELASTIC PKOPERTIES OF MATERIALS 



That component of the stress which lies in the plane of the face 

 tends to slide this face past the adjoining portion of the body, and 

 for this reason is called the shear, since its action resembles that of a 

 pair of scissors or shears. 



5. Unit stress. If the total stress acting on any cross section of 

 a body is divided by the area of the cross section, the result is the 

 stress per unit of area, or unit stress. In what follows p will be used 

 to denote the unit normal stress and q to denote the unit shear. 

 Thus if a bar 2 in. square is stretched by a force of 800 lb., the 

 unit normal stress is 



If a rod is subjected to tension, it is customary to assume that the 

 stress is uniformly distributed over any cross section of the rod. 

 This assumption, however, is only approximately correct ; for if two 

 parallel lines are drawn near the center of a 

 rubber test piece, as ab and cd in Fig. 1, A, it 

 is found that when the test piece is subjected 

 to tension these two lines become convex 

 toward one another, as indicated in Fig. 1, B, 

 showing that the tensile stress is greater_near I 

 the ed^es of the }>HMT than at the center. In 

 such a case of nonuniform distril mtion of 

 stress, the smaller the area considered the 

 nearer the unit stress approaches its true 

 value. That is to say, if AP is the stress acting on a small area 



, then, in the notation of the calculus, 



AP dP 



FIG. 1 



Problem 1. A post 1 ft. in diameter supports a load of one ton. f Assuming 

 that the stress is uniformly distributed over any cross section, find the unit 

 normal stress. 



Problem 2. A shearing force of 50 lb. is uniformly distributed over an area 

 4 in. square. Find the unit shear. 



* For the sake of brevity and clearness all dimensions in this book will be expressed 

 as above ; that is, " lb. per sq. in." will be written " lb. /in. 2 ," etc. 



t Throughout this book the word "ton" is used to denote the net ton of 2000 lb. 



