Flexibility factor

In the absence of more direc tly applicable data, the flexibility factor k and stress-intensification factor i shown in Table 10-54 may be used in flexibihty calculations in Eq. (10-101). For piping components or attachments (such as valves, strainers, anchor rings, and bands) not covered in the table, suitable stress-intensification factors may be assumed by comparison of their significant geometry with that of the components shown. 

TABLE 10-54 Flexibility Factor kand Stress-Intensification Factor i ... 

The flexibility factor k applies to bending in any plane. The flexibility factors k and stress intensification factors shall not be less than unity factors for torsion equal unity. Both factors apply over the effective arc length (shown by heavy centerlines in the sketches) for curved and miter bends and to the intersection point for tees. 

Factors shown apply to bending. Flexibility factor for torsion equals 0.9. 

The shaft flexibility factor is directly related to the static deflection of a simply supported shaft, and is therefore a good indicator of the runout attainable during manufacture and the quality of balance that can be achieved and maintained. 

Stress intensification and flexibility factor data in this table are for use in the absence of more directly plicable data (see para. 319.3.6). Their validity has been demonstrated for D/T < 100. 

The concepts behind the analysis are not difficult. The piping system is simply a structure composed of numerous straight and curved sections of pipe. Although, for straight pipe, elementary beam theory is sufficient for the solution of the problem, it is not adequate for curved pipe. However, by the introduction of a flexibility factor, k, to account for increased flexibility of curved pipe over straight pipe, and a stress intensification factor, i, to account for the increase in stress in a curved pipe or any other piping component over that predicted by beam theory, the elementary beam analysis can be used. 

Flexibility and Stress-Intensification Factors. The flexibility factor k (>1.0) is defined as the ratio between the rotation per unit length of the part in question produced by a given moment to the rotation of a straight pipe (of the same size and schedule) produced by the same moment. A close approximation of the flexibility factor that agrees quite well with theory and experiment for bends is as follows ... 

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