nS 



STRESSES IN PORTALS 



be H = -- 



To find the vertical reactions proceed as follows: Determine the 

 center of gravity of the columns by taking moments about the base of 

 one of the columns. Now there will be tension in each one of the 

 columns on the windward side and compression in each one of the 

 columns on the leeward side of the center of gravity of the columns. 

 The sum of the moments of the reactions must be equal to the moment 



FIG. 63. 



of the external wind load, R. The reactions at the bases of the columns 

 will vary as the distance from the center of gravity and their moments 

 will vary as the square of the distance from the center of gravity. Now, 

 if a equals the reaction of a column at a units distance from the center 

 of gravity, we will have V^ = a d lf V 2 = a d 2f V z ~- a d 3f 

 V 4 = + a dt, V 5 = + a d 5 , and F 6 - + a d Q 

 and the moment 



M = a (d^ + d* + d, 2 + d? + d^ + rf 6 2 ) = R h 

 a d 2 = R h 



Having found a, the vertical reactions may be found. 



Now having found the external forces H and V, the stresses can 

 be calculated by either algebraic or graphic methods. 



Stresses in a Double Portal. To illustrate the general problem 

 the stresses in a double portal are calculated by graphic resolution in 

 Fig. 64. In this case 



