389 



and, for many cases, I tliink the following formula may be 

 employed w = C being tbe tensile strength of 



the rod, A its area, and D the depth from the neutral area 

 of the beam, say at | of its depth, to the bolt under the beam 

 over which the trussing rod passes, or to which it may be 

 attached. I think this formula will apply when the strength 

 gained by the rod is greater than the original strength of 

 the beam, or when the trussing rod is attached to a pillar 

 muck deeper than the beam. In the former of these cases 

 it will also be needful to ascertain if the beam be strong 

 enough, as a pillar, to bear the compression of the rod. 



There are cases in which the advantage obtained by 

 trussing a beam with a wrought iron rod would be estimated 

 at very little by the foregoing formula; the advantage is, 

 nevertheless, very decided in practice. For instance, when a 

 very shallow beam is trussed by a rod not extending to a 

 greater depth than that of the beam, the formula would 

 shew very little additional strength. As the case is 

 very different in fir timber and cast iron, as regards the 

 relation between the tensile and compressive strengths, the 

 tensile strength in fir being much greater than the com- 

 pressive, it would appear of little moment to add to the 

 stronger, for the rod appears to add only to that part of the 

 beam exposed to tension. 



The advantage, however, appears to me to arise in that the 

 beam being pressed upwards by the action of the trussing, so 

 as to become somewhat arched upwards, the neutral axis is 

 brought nearer the lower part of the beam, and a greater 

 portion of the area is in a condition to resist the compressive 

 strain ; and also the beam, instead of being exposed to the 

 compressive strain mostly along the upper side, receives the 

 compressive strain in a direction nearly coincident with its 

 axis : and we have seen that a pillar will bear three times 

 more strain in the direction of its axis than along one side. 



F F 2 



