118 



STRESSES IN GIRDERS. 



Art. 79. 



stress. Having calculated this, as explained below, an equivalent 

 direct stress is used as a working stress. 



Knowing 8 max ., s w E 8 max . 



For the case of Art. 76, 



S' t (max) == s f (max) -- 

 A L m 



S' c (max) = - s' c (max) 



& L m 



Substituting -~ for 8 





-- s t '(min) or s w = 



s\ (min) I 

 J 



s' c (min) I . 

 J 



s c '(nrin) (31) 



At the neutral axis of a beam, the shearing stresses are 

 principal stresses, and their values are-(-s s and S 8 from equa- 

 tion (30), 5 t being 0. 



These values in equation (31) give 



1 m 



-S.Ors.^^ 



SS---SB or s s = 



ST, 



(32) 



that is, theoretically, the working stress in shear should be $ 

 of that in tension, when m 4 or Poisson's ratio is y; it is, 

 however, always taken less than this, and usually low enough 

 so that the shearing stress may be taken as uniformly distributed 

 over a cross section (75) . 



79. Stresses in Girders. All of the preceding general 

 discussion of solid beams applies, of course, to girders. In Fig. 

 66 are shown the forces acting upon a part of a girder to the left 

 of the section win. The shearing stress S=R; this is assumed 

 to be uniformly distributed over the area of the cross section 

 of the web only (75;. Therefore, 



A '=^ = ht (33) 



This equation determines the area of the web; its depth, h, is 

 determined by considerations of economy; its thickness, t, is 

 never made less than %", and for railway bridges seldom less 

 than %". 



Since there are compressive stresses in the web (77), it is 

 usually stiffened, because its ratio of depth to thickness is much 

 greater than for I beams. The unknown influence of the tensi It- 

 stresses acting at right angles to the compressive stresses, makes 

 a calculation of the buckling stresses impossible. 



The bending stress in a girder may be calculated by means 



