STRESS AND DEFORMATION IN THE I BEAM. 



BV C. M. BROOM ALL. 



The internal stresses and deformations in the loaded 

 I Beam differ radically from those in the beam of rectangular 

 cross section. In a previous article* the writer has attempted 

 a short treatment of the stresses and strains in the rectangu- 

 lar beam and called attention to those cases where the 

 Common Theory of Flexure may lead to dangerous results. 

 In the present writing it is intended to treat the I Beam in a 

 somewhat similar manner, and attempt to ascertain wherein 

 the Common Theory differs from the true theory. 



As a preliminary^ to the subject in hand it is well to exam- 

 ine particularly into the mechanics of internal stress in the 

 ordinary rectangular beam. To this end we may classify' the 

 various forces under consideration into : — 



1 . The external forces, vertical loads and vertical reactions, 



2. The forces brought to play by such loads and reactions 

 upon any chosen group of elements of the body, and, 



3. The maximum internal stresses produced in these ele- 

 ments by the external forces. 



The forces of (2) are really the internal resultants of the 

 forces of ( I j and will obviously (since the loads and reac- 

 tions are vertically directed and the beam is horizontal) con- 

 sist of horizontal compressions and tensions, and vertical 

 shear. These horizontal forces and the vertical shear, as 

 stated, are the true resultants of the external forces. The 

 actual maximum stresses produced by these forces in the sub- 

 stance of the elements is found by resolution in the various 

 directions. Of course, stresses exist in these elements in all 

 directions simultaneously, but it is only the maximum values 

 which interest us. 



In general, any element of the body will be acted upon 

 (a) by direct horizontal compression or tension, (b) by verti- 



*Proc. Dei.. Co. IxsT. Sci., VoL VIII, No. i. 



