INEXTENSIBILITY AND INCOMPRESSIBILITY 167 



In the ease of radially inflexible compound girders or hollow 

 cylinders, the continuous flange, or wall of the tube, must not be too 

 thin, as otherwise it is liable to collapse under the transverse tensions 

 which result when the structure is subjected to bending stresses ; such 

 a collapse is always preceded by an alteration of the cross-sectional 

 outline of the girder, and even this minor deformation must obviously 

 be avoided as far as possible. The thickness of the wall or continuous 

 flamje must therefore not fall below a certain fraction of the total 

 diameter of the cylinder or compound girder. Schwendener estimates 

 the minimum thickness of the wall which is admissible in such a 

 radial compound girder at about one-seventh or one-eighth of the total 

 diameter. A thinner wall is only permissible where special stiffening 

 arrangements are provided, which help to preserve the cross-sectional 

 outline of the girder. Later on we shall become more intimately 

 acquainted with such special reinforcing devices. 



B. INEXTENSIBILITY. 



The degree of inextensibility of a structure depends entirely upon 

 the cross-sectional area of its resistant elements : the disposition of 

 these elements is therefore theoretically a matter of indifference. The 

 theory, however, assumes that the stretching force is uniformly dis- 

 tributed, a condition which is not likely to be fulfilled unless the area 

 over which the resistant elements are distributed is very small. If, 

 therefore, the resistant elements were scattered, an unequal distribu- 

 tion of tensions would be very liable to occur, and individual strands 

 might break, with the result that the strength of the whole structure 

 would be seriously impaired. The more closely aggregated on the 

 other hand the resistant elements are, the more uniform the distribu- 

 tion of tensions is likely to be ; hence the aggregation of the mechanical 

 cells into a single compact and solid mass is the most advantageous 

 arrangement for an organ which has to withstand longitudinal 

 tension. 



C. INCOMPRESSIBILITY. 



1. Resistance to longitudinal compression. 



If an erect prismatic or cylindrical body, with a longitudinal axis 

 greatly exceeding its transverse diameter, be fixed at its lower extremity 

 and weighted at its upper end, in such a manner that the load acts 

 in the direction of the longitudinal axis, it will suffer longitudinal 

 compression. The middle line of such a body can, however, only 

 remain vertical, if the line of action of the load coincides exactly with 

 the longitudinal axis ; in this event the load will give rise to the same 

 amount of compression at every point within the body, ami thus produce 



