STRESSES IN SOLID BEAMS. 



Art. 67. 



67. General Consideration of Stresses in Solid Beams. 



In the most general case of forces acting in any direction and in 

 any position on a bar, there will be produced, on any section, 

 tensile or compressive stresses (normal), shearing stresses (tan- 

 gential, bending stresses (normal), and torsional stresses (tan- 

 gential ) . In special cases, any one of these stresses, or any com- 

 bination of two or three of them may occur. According to the 

 usual assumption, these stresses may be investigated independ- 

 ently and the results of like kind, for any point, may be added. 

 In Chapter IX combinations of bending and tensile or compres- 

 sive stresses are treated. In this chapter only the usual cases of 

 simple bending and shearing stresses are treated. When these 

 two are combined, it is seldom necessary to find the resultant 

 principal stress (12) ; a method of doing this is, however, given 

 in Art. 76 and the lines of principal stress, for a certain case, are 

 shown in Art. 77. 



Ordinarily, beams have loads acting perpendicular to their 

 axes; they may be spoken of as vertical loads and horizontal 

 beams. When the loads are inclined to the axis of a beam, there 

 will be a combination of bending, shearing, and tensile or com- 

 pressive stresses the horizontal components producing the lat- 

 ter. Stresses are investigated upon sections perpendicular to 

 the axis of a beam. In arches the shearing stress acts in a radial 

 direction, and, in general, there will be shearing, bending, and 

 compressive stresses upon the radial sections. In beams with 

 straight axes, provision must ordinarily be made to resist the 

 shear and the bending moment (57), and these are treated in- 

 dependently although, in general, both shearing and bending 

 stresses act upon each particle. Like provision must be made in 

 trusses, but in this case the shear is not resisted by shearing 

 stresses, but by tensile or compressive stresses in the web mem- 

 bers and inclined chord members (58). 



68. Bending Stress in Solid Beams. Theory of Flexure. 

 In the special case shown in 



Afomcnfo 



Shear 'O 



Fig. 65, the shear between 



loads is zero, and in this part 



of the beam there is only 



bending stress. Stresses in 



solid beams are investigated pig. 55. 



on planes perpendicular to the axis of the beam by the method 



of sections, as explained in Art. 57. It was there shown that the 



