170 _ CONSOLIDATED STEEL CORPORATION _ 



It may be necessary to decrease the distance between tie rods given in the 

 preceding table or found from formula (2), in order to satisfy the second re- 

 quirement that the lateral stress in the beams or channels produced by the 

 thrust of the arches may not be excessive. 



Let /' = moment of inertia of beam or channel, sideways. 

 6 = width of flange of beam or channel, in inches. 

 x = distance, in inches, of neutral axis from back of channel. 

 / = fiber stress produced by thrust of arch, in pounds per square 

 inch. 



The beams or channels may be considered as continuous, in which case the 

 stress produced by flexure and the corresponding spacing of rods are given by 

 the following formulas: 



For Beams, /=|rp' (3); and rf=y'^ (4) 



For Channels, /=, (5); and d=, (6) 



Where the thrusts of adjacent arches are opposed to each other, as in the 

 interior beams of a floor, the thrust / in these formulas may be taken only for 

 the live loads. The sum of the stresses produced by lateral thrust and vertical 

 loading should not exceed 20,000 pounds per square inch. As the vertical load- 

 ing in building construction is usually allowed to produce a fiber stress of 

 16,000 pounds per square inch, the lateral stress must therefore be limited to 

 4,000 pounds per square inch. In such case the fiber stress, /, in formula (4) 

 is to be taken as 4,000. 



For exterior arches along walls, or around openings, the thrust t must be 

 taken for the full live and dead load. 



Channels will be found to require a greater number of tie rods than interior 

 beams, and it may be advisable in some instances to use a beam for a skewback 

 instead of a channel. 



If formulas (4) and (6) give a greater distance between rods than is obtained 

 by the use of formula (2), the value given by the latter is to be used, as the stress 

 on the tie rod itself must not exceed its safe limit. 



Beams must be held laterally at intervals not greater than twenty times 

 the width of their flanges, otherwise their safe loads as given in the tables must 

 be reduced in the proportion given in the table at the bottom of page 77. 



