ANALYSIS OF STRESS IX BEAMS 59 



therefore also pass through B. For any other point of MN it is 

 approximately correct to assume that the direction of the stress also 

 passes through B. 



Therefore, in order to determine the direction and intensity of the 

 shear at any point of a circular cross section, a chord is drawn through 

 the point perpendicular to the direction of the shear and tangents 

 drawn at its extremities, thus determining a point such as B in 

 14. Assuming the axes as in Fig. 44, the vertical shear acting 

 at the point is then calculated by formula (28), where, in the present 

 case, b is the length of the chord and the integral is extended over 

 the segment above the chord. The horizontal component of the shear 

 is then determined by the condition that the resultant of these two 

 components must pass through B. 



The amount of the component and resultant shears acting at any 

 point can be calculated as foil 



a strip parallel to the Z-axis, dF = zdy, and z = Vr 2 y 2 . 

 Then 



The vertical component of the shear is, therefore, 



Let KB and A'.V, Fig. 44. iv]ri's<*nt in magnitude and direction 

 the vertical and horizontal components of the shear acting at N. Then, 

 from the similar triangles KNB and KNO, 



KN 

 KB 



b 



Since BN* = BK* + KN* t the resultant shear at N is 



