Art. 12. KINDS OF STRESS. 



Solving equations (a) and (6) we get 



s s =840 Ibs. per sq. in. 

 840 



9 



35 



=24 Ibs. per sq. in. 



12. Kinds of Stress. The fundamental idea of a stress is 

 that of two equal, opposite forces acting in any direction on the 

 opposite sides of a plane section, taken in any direction, through 

 any point of a body at which the stress is desired. It is usually 

 desired to find that section for which the intensity of stress is a 

 maximum, since this is the stress to which the working unit 

 stresses are applied to determine the required area of the section. 



It may be shown that, in general, there are three stresses, of 

 tension or compression, acting at right angles to each other, 

 which are called principal stresses; these simple principal stresses 

 occur in any body under stress no matter how produced. Since 

 we usually have to deal with forces assumed to act in a plane, we 

 consider only two principal stresses; the intensity of stress in the 

 direction of one of these is greater, and of the 

 other is less, than in any other direction. 1 In the 

 case of simple tension, Fig. 5, the maximum 

 principal stress is equal to P acting on the sec- 

 tion CD. On any inclined section, AB, there will 

 be a normal component N (tension) and a tan- 

 gential component S, called a SHEARING STRESS. 

 If the material is homogeneous (isotropic), CD 

 is the critical section ; but if it were timber, for 

 example, with the grain running in the direction 

 AB, the critical section would be AB. 



It is evident, then, that wherever there are tensile or com- 

 pressive stresses there will also ~be shearing stresses, except on 

 particular planes perpendicular to the principal stresses. It is 

 evident too that a tensile (or compressive) stress may be the 

 resultant of a shearing stress and a tensile (or compressive) 

 stress. Tensile and compressive stresses may also result from 





\ 



j?ig. 5. 



*See Merriman's Mechanics of Materials, Greene's Structural Me- 

 chanic* Alexander and Thompson's Applied Mechanics or Rankine's Ap- 

 plied Mechanics. 



