COLUMNS AND STRUCTURES 259 



shear at each story height is found, precisely as shear is deter- 

 mined for any cantilever beam. 



This shear is distributed across the frame in the direction of 

 the wind by dividing the total shear at any floor by twice the 

 number of panels. (Number of columns less 1 = number of 

 panels.) Each end column carries the amount thus found and 

 each intermediate column carries double this amount, because 

 the end columns support only one-half a panel and each inter- 

 mediate column supports a full panel. 



For the top story the formulas in relating to Fig. 166 or Fig. 

 167 may be used. The direct stress in the column is added to 

 the concentric load in that column, but is not carried to the floor 

 below. The bending moment in the column is treated as a mo- 

 ment due to eccentric loading. 



For each story below the top the moment for each column is 

 equal to the total horizontal shear on that column multiplied 

 by the story height. The wind force is assumed to act at the 

 mid-height and as the column is practically a cantilever with a 

 length equal to hah* the story height the proper length to use for 

 this condition of a column fixed at the bottom and free at the 

 upper end is twice the actual length. 



The bending moment in a girder is in all cases the mean be- 

 tween the bending moments in the column below and above the 

 girder. It is independent of the span. The moments in columns 

 and girders are at the ends, the force in the middle being shear. 

 The bending moments in girders must be provided for by adding 

 haunches to them instead of using simple brackets. Brackets 

 on which girders rest are assumed to resist vertical shear by the 

 rivets which connect them to the columns. They should be de- 

 signed, when possible, so none of the rivets will be in tension. 

 Gusset plates and brackets for connecting wind-bracing girders 

 to columns are in compression below, or above the girder and 

 are in tension above, or below, the girder. It is, therefore, neces- 

 sary to use a very low tensile stress in the rivets, which it is cer- 

 tain they can withstand, .and this it will be found calls for a 

 great number of rivets. A tensile stress of 6000 Ibs. per sq. in. 

 is used in such cases. 



Fig. 168 is a graphical representation of the moments in some 

 of the columns and girders of a frame. The moment is a maxi- 

 mum at the end and varies uniformly, so it is only necessary to 



