280 PRACTICAL STRUCTURAL DESIGN 



M = bending moment in inch pounds, 

 c = distance from resultant through section to lee- 

 ward edge, in inches, 

 7 = moment of inertia. 



The quantity c is of importance because the chimney shaft is 

 hollow. With a solid symmetrical section the distance to the 

 most stressed fiber is measured from the center of area, that is, 

 the center of gravity. In a hollow ring or square the pressure 

 varying uniformly from zero on the windward edge to a maxi- 

 mum on the leeward edge is not an average at the neutral axis 

 of the section, but is an average at a point a trifle beyond. The 

 distance from the center of area to the center of pressure will 

 be termed q. 



Let D = outer diameter of a round hollow shaft or outside length 



of a square hollow shaft. 



d = inner diameter of a round hollow shaft or inner length 

 of a square hollow shaft. 



then, for a round hollow shaft q = s ^ 2 > 



D 2 + d* 



and for a square hollow shaft q = TTT^ 



6D 2 



Approximately values of q are for square and \ for round 

 shafts. jy 



c = 2 - 



The chimney for analysis is divided into a number of sections 

 and the horizontal area found at each section. The weight of 

 the chimney above any section is ascertained and divided by the 

 area of the ring to get the direct pressure. The vertical area of 

 the chimney above the section is obtained and multiplied by the 

 factor 0.707 if octagonal and 0.667 if cylindrical. The height to 

 the center of this area, measured from the section, is a moment 

 arm, by which the wind moment is obtained. Then find c and 

 apply the formula. The compressive fiber stress should not ex- 

 ceed the maximum allowed for the material and for good brick 

 in cement mortar there can be some tension on the windward 

 side not exceeding one-tenth the compressive stress, provided 

 the tension is not more than one-fifteenth of the allowable com- 

 pressive stress in the material. With lime mortar tension is not 

 permissible. 



