78 CAMBRIA STEEL. 



LATERAL STRENGTH OF BEAMS TO RESIST 



FLEXURE DUE TO THRUST OF 



ARCHES, ETC. 



In special cases where the thrust of a floor arch is exerted against 

 a beam, channel, angle or other shape without other lateral sup- 

 port than the tie rods, or braces, this will produce lateral flexure 

 and stresses in addition to those caused by the vertical loading. 

 Throughout the body of the floor the thrusts of the adjoining 

 arches, when completed, will usually counterbalance each other, 

 but in the outer beams around shafts or elsewhere, if unsupported 

 sideways, the stresses due to the lateral forces should be considered. 



The total allowable stress per square inch for the extreme fibres 

 of beams has been placed at 16 000 pounds per square inch, and 

 in order that this may not be exceeded owing to lateral stresses, 

 the stress due to vertical loading should be correspondingly 

 reduced so that the resultant intensity shall not exceed the 

 allowable limit. This may be calculated by considering the beam 

 as continuous and laterally supported at intervals by the tie rods, 

 the spans being equal to the spacing of the rods. 



In this case the fibre stress due to the lateral forces is: 



CD 



in which 



p' = fibre stress in pounds per square inch due to lateral forces. 

 w = lateral load or thrust in pounds per lineal foot of section used 



as a beam. 



xi = distance of the extreme fibre from the neutral axis in inches. 

 B = distance between tie rods or lateral supports in feet. 

 I' = moment of inertia about the vertical axis of the section or 



that one at right angles to the line of application of the 



lateral forces. 



For I-Beams with the web placed vertically, as usual, xi 

 becomes equal to > where b is the width of the flange in inches. 



In this case the above formula for intensity of unit stress due to 

 lateral load becomes: 



(2) 



