CAMBRIA STEEL. 



In order that the total resultant intensity of unit stress shall 

 not exceed the allowable limit of 16 000 pounds per square inch, 

 the stress due to vertical loading must be reduced by the amount 

 of the intensity of stress due to the horizontal thrust of the arch, 

 as determined by formula (2). 



If p' represents the intensity of unit stress due to the horizontal 

 thrust of the arch, and p the corresponding allowable intensity 

 of unit stress due to the vertical loading, then 

 *p = 16000 -p' 



Having thus obtained the reduced vertical stress p, the safe 

 vertical load of the tables corresponding to this stress should ac- 

 cordingly be reduced by multiplying it by the ratio ^ and 



J.D UUU 



similarly for other stresses and corresponding loads, thus making 

 proper allowance for the additional stresses produced by the 

 lateral forces. 



If the reduction of the safe loads on this account is a consider- 

 able proportion of the original amount due to vertical loading 

 only, it would be more economical to provide lateral braces or tie 

 rods at shorter intervals, thus avoiding the use of an excessive 

 amount of material in the beam. 



As the etresses due to vertical forces for usual cases of loading are 

 a maximum at the center of the span it will ordinarily be sufficient 

 to space the tie rods or braces at shorter intervals near the center 

 in order to allow for the combined stresses due to vertical loading 

 and horizontal thrusts. 



The above method of calculation is not exact when considering 

 the lateral thrust of arches, or loads from similar materials which 

 do not exert a uniform pressure throughout their surfaces of con- 

 tact with the sustaining beam on account of the friction and bond 

 of their component parts, but this analysis of the stresses may 

 serve as a guide in designing. 



The above formulae should be used in connection with the 

 tables and formula given on pages 82 and 83 relating to the 

 lateral strength of beams, due to compression of the upper flange 

 figured as a column between points of lateral support. 



* This method of treatment gives approximate results which are on the side 

 of safety. 



The correct determination can be secured by the use of the section modulus 

 polygon. (See Transactions of the American Society of Civil Engineers, 

 Vol. LVI, 1906, page 169, et seq.) 



