Art. 114. 



COLUMNS IN TOWERS. 



193 



B B 



114. Columns in Towers. Fig. 142 shows a two-story 

 tower, composed of- four columns 

 fastened together with bracing. 

 The column being held at the mid- 

 dle, may take on the reverse curva- A 

 ture shown by the dotted line. The , 

 point A being a point of contra- 

 flexure. will be in the condition of 

 a pivoted end; but if the connec- 

 tion of the strut AB is large and 

 rigid, and if the strut itself has 

 considerable stiffness, there will be 

 a tendency to hold the column in a 

 vertical line at A. The two seg- 



Fig. 142. 



incnts of the column are treated as separate columrs witli inde- 

 terminate end conditions ; a safe assumption is that of pivoted 

 ends. The bracing in the vertical planes holds the columns against 

 buckling in two directions only. To prevent buckling in a diago- 

 nal direction the horizontal braces AC ard BD may be used. 



If the column AE, Fig. 143, be held against | 

 sidewise movement (in all directions) at points 

 A 9 B, G, D and E, by means of pivoted connec- 

 tions, then eacli segment is in the condition of a 

 column with pivoted ends. Of course initial 

 bends may interfere considerably with the uni- 

 form bending indicated by the dotted line, but 

 under the most favorable conditions, the seg- 

 ments are in the same condition if the column is 

 of uniform section and divided into equal 

 lengths. 



If the strut connections are not pivoted, the 

 bending will not be so great. 



If the load on the column is ecoentric the 

 effect will be quite different. In this case the 

 small accidental eccentricities are neglected. It 

 is not possible to make an exact solution in a 

 practical case because of the indefinite end con- 

 ditions, but the cases shown in Fig. 144 will fur- 

 nish a guide for the judgement. The column is assumed to be 

 continuous, and except in case (&), to have pivoted ends. Under 

 the assumption of pivoted ends, the lines of the reaction fall in 



Fig. 143. 



