LAWS OF BONE ARCHITECTURE 197 



S2. Regardless of the intensity and direction of these unknown 

 stresses, let each be resolved into its horizontal and vertical 

 components. The horizontal components will be applied at 

 various points in the cross section, some in one direction and 

 some in the other: that is, some of the horizontal stresses will 

 be tensile and some will be compressive. But by the first con- 

 dition above their algebraic sum is zero. The vertical forces 

 will be added and form a resultant force F, which by the second 

 condition equals the algebraic sum of the vertical forces on the 

 left of the section. This vertical force V acts in opposite direc- 

 tions upon the two parts into which the beam is assumed to be 

 separated, hence it is in the form of a shear. 



33. Laws of internal stress. From a consideration of the fore- 

 going, the following laws concerning the internal stresses in any 

 section of any beam may be given: 



1. The algebraic sum of the horizontal stresses is zero; the 

 sum of the horizontal tensile forces is equal to the sum of the 

 horizontal compressive stresses. 



2. The algebraic sum of the vertical stresses forms a result- 

 ant shear which is equal to the algebraic sum of the external 

 forces on either side of the section. 



3. The algebraic sum of the moments of the internal stresses 

 is equal to the algebraic sum of the moments of the external 

 forces on either side of the section. 



34. These laws are the foundation of the theory of the flexure 

 of beams. Resisting moment is the term given the algebraic 

 siun of the moments of the internal horizontal stresses with 

 reference to a point in the section; 'bending moment' is the 

 term for the algebraic sum of the moments of the external forces 

 on either side of the section with reference to the same point 

 (as for resisting moment). 



35. 'Resisting shear' is the term applied to the algebraic sum 

 of the internal vertical stresses in any section, and 'vertical 

 shear' is the term for the algebraic sum of the external vertical 

 forces on one side of the section. 



36. Laws of beams. The foregoing principle may be summa- 

 rized into the following three laws for any section of any beam : 



