162 W. H. WARREN. 



The cracking is more likely to occur with distributed 

 loads than with a load concentrated at the centre as in 

 testing, and it is more likely to occur in deep beams than 

 in shallow beams, as in both cases the shearing forces are 

 greater. In a steel-concrete beam properly designed, a 

 crack should appear on the tension face before the elastic 

 limit of the steel reinforcement is reached. Before a crack 

 has developed, the internal stresses will follow the curved 

 lines shown in the ligure in which the full lines denote 

 compression and the thin lines tension; these lines intersect 

 the neutral axis at an angle of 45 degrees and equilibrium 

 is established among the internal stresses, and no reinforce- 

 ment is needed. AVhen a crack has developed, the thick 

 curved lines should be eliminated below their intersection 

 with the neutral axis, and tangents to the curve at the 

 points where they intersect the neutral axis continued to 

 their intersection with the horizontal reinforcement at the 

 under side of the beam, show the altered directions of the 

 lines denoting the internal stresses. These inclined lines 

 may be resolved horizontally and vertically at the points 

 where they intersect the horizontal reinforcement, into 

 horizontal and vertical components of equal intensity; the 

 former are resisted by the horizontal reinforcement, the 

 latter must be resisted by vertical stirrups or preferably by 

 inclined bars, the sectional area and spacing of which 

 should be made proportional to the shearing stresses 

 developed. 



If the beam is subjected to a uniformly distributed load, 

 the distribution of bending moments along the beam is 

 represented by a parabola, fig. 14, the equation being : — 



Where y = the bending moment at any distance % measured 

 from the origin. 



