86 Notes on Iron At 



ture in the loaded side of the arch, as in Fig. 6, and reduce 

 it in the unloaded ; and the compression endured by the 

 material of the rib will no longer be uniformly distributed, 

 but will be greatly increased on the upper side of the 

 loaded and the under side of the unloaded half of the rib. 

 Hence, bearing in mind that either half of the arch may be 

 the loaded portion, it is evident^ — 1st. That the amount of 

 metal in the rib must be increased. 2nd. That the best 

 section for the rib is like a girder section consisting of two 

 massive flanges united by a comparatively slight web. 3rd. 

 That the rib should be made as deep as practical considera- 

 tions will allow. The formulae to be employed in comput- 

 ing the actual stresses in this case are too complex to be 

 introduced here ; they do not, of course, contain any terms 

 representing change of temperature. 



Let us now consider the beha\dour of a rib hinged at the 

 springing but continuous at the croAvn. When a load is 

 imposed the metal will be compressed longitudinal^, the 

 rib will shorten, its crown will sink, and its radius of curva- 

 tion increase (see dotted lines in Fig. 7), and any yielding of 

 the abutaients will tend to augment this result. The 

 alteration in the radius of curvature implies a cross-bending 

 action tending to increase the compression on the upper part 

 of the rib, and to diminish it on the lower part, and this 

 action will be present no matter how accurately the original 

 form of the arch may have been adapted to the load to be 

 carried. Let us now suppose the temperature to diminish. 

 The crown of the arch will fall still further, the cross-bend- 

 ing action will be intensified, and the increasing inequality 

 in the distribution of stress will produce a corresponding 

 diminution in the available strength of the structure ; the 

 colder it becomes the more liable the bridge is to give way, 

 and when fracture does ensue it will commence by the 

 crushing of the upper part of the rib. We will next assume 

 the temperature to increase. The crown of the arch will 

 rise^ its radius of curvation will be reduced, and the cross- 

 bending action and consequent inequality of stress will 

 diminish and ultimately vanish, and the arch will be 

 stronger — i.e., it will be able safely to bear a greater load 

 than before ; and under these conditions the formulse quoted 

 in the preceding case will apply to this also. A further 

 increase of temperature will cause a further rise of the 

 crown, and a further reduction of the radius of curvation, 

 involving a cross -bending action in an opposite direction 



