TJXI-:S ()I< IXTKRXAL vSTRESS IN BKAMS. 



Ahslracl of l;ilk before the Iiislilute, 

 U\ C. M. I?KOOMAI,L. 



Imagine a horizontal beam supported at the ends and car- 

 rying a uniformly distributed load. The investigation of the 

 amount and direction of the maximum stresses in such a beam 

 is so essentially mathematical that most persons are deterred 

 from taking up the study. The theory of the subject will be 

 found fully set forth in Merriman's " Mechanics of Materials," 

 Tenth Edition, Chapter XI. Here also will be found a dia- 

 gram illustrating the lines of stress for a portion of the beam. 

 More or less similar diagrams are given in many works, but 

 nowhere has the writer seen a complete diagram showing both 

 direct stress and shear lines for the whole beam. If such dia- 

 grams exist they are not common. 



By the aid of a complete diagram such as is referred to it is 

 possible to make clear to the non-technical reader the results of 

 mathematical investigation. It is with this object in view 

 that the accompanying figure has been prepared. It shows, 

 in a general way, the lines of maximum stress, tension, com- 

 pression and shear, for the whole beam, supposed to be uni- 

 formly' loaded. In case of a load other than uniform the 

 curves would be of different shape, but would retain, never- 

 theless, their constant relationship to each other. 



The equations for plotting such curves are general static 

 equations l)ased upon the supposition of a rigid beam sub- 

 jected to "bending moment" and "vertical shear" only. 

 They do not, therefore, take into account the effect due to the 

 direct application of the load to the beam nor the changes pro- 

 duced by varv'ing the method of supporting the ends. To do 

 this the equations would have to be modified for every change 

 in these factors. Again, the equations neglect the fact that in 

 actual practice the beam suffers more or less change of shape 

 under the load and thus certain stresses other than those neces- 

 sary to prodiice external equilibrium are called into play. The 



