252 



PRACTICAL STRUCTURAL DESIGN 



Fig. 164 illustrates the four conditions affecting the end load- 

 ing of columns. At (a) is shown the column with pin-joints at 

 top and bottom. This is the standard case assumed for all column 

 formulas, a modification being a flat-ended column, the bolts at 

 the ends of which are intended to merely hold it in position and 

 are not strong enough to resist much tension. The I in the for- 

 mulas is the total unsupported length of the column. 



At (6) is a column fixed at the ends to maintain both position 

 and direction. The I to use is one-half the unsupported length. 



At (c) one end is fixed (in 

 position and direction) and 

 the other end is a pin, or 

 hinged, end, fixed in position 

 but not in direction. The I 

 to use is two-thirds the un- 

 supported length. 



. , At (d) the lower end of the 



\ Y jr_ column is fixed in position 



and direction but the upper 

 end is free to move laterally, 

 differing from (a) and (c) in 

 which the upper end of the column is vertically over the lower 

 end. The column shown at (d) bends in a simple curve which is 

 one-half that of a column double the length, as shown by the 

 lower dotted end. Obviously the I to use is twice the actual 

 length of the column. 



The temptation to consider a greater degree of fixity than is 

 actually obtained is great, and all designers must be warned 

 against yielding to it. Probably the only fixed columns in a build- 

 ing are those on the ground floor of a high building with massive 

 foundations. Above the ground floor there is bound to be some 

 vibration and swaying, especially in a wind. 



To Proportion Struts or Compression Members 



Every strut is designed as a column with rounded or hinged 

 ends. Nothing is deducted for rivet holes, as the rivets are assumed 

 to fill them. First select the form of strut from the many illus- 

 trated in Fig. 163, decide on the radius of gyration, and be careful 

 with angles to use two, back to back, even when the computa- 

 tions show one to be amply strong. Steel compression members 



Fig. 164 Methods of Fixing Columns 



