84 STRESSES IN A TRANSVERSE BENT 



columns will depend (a) upon whether the bases of the columns are 

 fixed or free to turn, (b) upon whether the columns are rigidly fixed 

 to the truss at the top, and (c) upon the knee brace and truss con- 

 nections. Of the numerous assumptions that might be made, only two, 

 the most probable, will be considered, viz.: (I) columns pin connected 

 (free to turn) at the base and top, and (II) columns fixed at the base 

 and pin connected at the top. 



Columns in mill buildings are usually fixed by means of heavy 

 bases and anchor bolts. Where the columns support heavy loads the 

 dead load stress in the columns will assist somewhat in fixing them. 

 Where the dead load stress plus algebraically the vertical component 

 of the wind stress in the column, multiplied by one-half the width of 

 the base of the column parallel to the direction of the wind, is greater 

 than the bending moment developed at the base of the leeward 

 column when the columns are considered as fixed, the columns will be 

 fixed without anchor bolts (see Chapter XII, Fig. 61). In any case 

 the resultant moment is all that will be taken by the anchor bolts. The 

 dead load stresses in mill buildings are seldom sufficient to give material 

 assistance in fixing the columns. Unless care is used in anchoring 

 columns it is best to design mill buildings for columns hinged at the 

 base. 



The general problem of stresses in a transverse bent for Case I 

 and Case II, in which the stresses and forces are determined by alge- 

 braic methods, will now be considered. The application of the general 

 problem will be further explained by the graphic solution of a par- 

 ticular problem. 



ALGEBRAIC CALCULATION OF STRESSES: Case I. 



Columns Free to Turn at Base and Top. In Fig. 51, H H l 



W 

 = ~~2 = horizontal reaction at the base of the column due to external 



wind force, W. 



W I 

 V = F 1 = 2 s = vertical reaction at base of column due to 



the wind force, W. 



The wind produces bending in the columns, and also the direct 



