14 



HOW SHEARING STRESSES OCCUR 



Art. 17' 



shrars arc not resisted by sit earing stresses, but by tension or 

 compression in the diagonal members. The diagonals of the end 

 pa nrls are in tension, because the shear tends to distort the rect- 

 angles so as to elongate these diagonals. In this case, as in the 

 cases of Figs. 9 and 10, there is also bending; in fact, shear 

 strictly never occurs except in combination with bending. 



17. How Shearing Stresses Occur. In Fig. 5 it was shown 

 how shearing stresses occur in connection with tensile stresses; 

 in like manner, shearing stresses occur with compressive stresses. 

 If, as in Fig. 12, we have a combination of 

 tensile and compressive stresses of equal 

 intensities, acting at right angles to each 

 other, and investigate the stresses on planes 

 making angles of 45 degrees with the direc- 

 tions of these stresses, we shall find simple 

 shearing stresses; on other planes there 

 will be both shearing and normal stresses. 

 Fig. 12 shows how, on both sides of the 

 plane AC, the normal components of the tensile and compressive 

 forces neutralize each other, and how the tangential components 

 are added together : the same result will, of course, obtain for the 

 plane ED. The cube may be conveniently considered as a unit 

 cube so that the stresses on the faces AB, EC, CD, and DA will 

 be unit stresses. 



AVe have, then, under the above conditions, simple shearing 

 stresses, of equal intensity, at right angles to each other. Con- 

 versely, if we have shearing stresses of equal intensities acting 

 at right angles to each other, there will be tensile and compressive 

 stresses of equal intensity on planes making angles of 45 degrees 

 with the planes of the shearing stresses. This 

 is shown in Fig. 13, which is the same as Fig. 

 12, except that the directions of the stresses 

 have been turned through an angle of 45 de- 

 grees, and that the diagonal planes are the 

 pin nes on which simple tensile and compres- 

 sive stresses act. The figure shows how the 

 Compressive stress on plane EG is produced. 

 On FH there will be tensile stresses. 



Fig. 13. 



The above investigation shows that shearing stresses occur 



