94 PRESSURE VESSEL DESIGN HANDBOOK 1

and Fi is the initial bolt load due to pretightening of theibolt nut , lb/bol t . The minimum Fi t o maintain the compression is when Sc = 0: .

or , after simplification, I

Fi A (4MlNd) - (WIN). I

The external moment M in the above equation is the maximum design moment. Actually, it fluctuates from zero t o some maximum value. The maximum force on the bolt due to this moment is given by

Fa = (4MINd) - (WIN). ,

However, since the anchor bolt forms an elastic joint with the skirt base on the concrete pedestal, pretightened by the force F , , only a part of Fa will be carried by the bolt [33] .

The total variable load F per bolt under moment M can be visualized from the diagram in Fig. 4.5. Using the diagram, the following equation can be derived:

c1FC = c'F, - el(F - Fi) Fc = Fi - (F - Fi) e'/c' F = Fa + Fc = Fa + F, - (F - Fi) et/c'

= Fi + [cl/(c' + e ' ) ] Fa = Fi + CFa

and the minimum tensile stress in the bolt is

Substituting the components for Fa we get

where K is the stress concentration factor from Table 4.1 applied t o the variable component only.

The factor C = c1/(c' + e') for hard elastic joints is quite small. The actual value of C would be difficult t o evaluate. However, if for instance c' is one sixth of

DESIGN OF TALL CYLINDRICAL SELF-SUPPORTING PROCESS COLUMNS 95

forcelbolt I bolt-base joint under variable bolt-base joint after pretightening stress range

in bolt

F,

F, I t .

-deflection 0 l I *

bolt elongation 6, separation between concrete foundation and vessel base support contraction 6,

Fi = initial bolt preload, lblbolt Fa = applied operating load, Ib/bolt F = combined total load on a bolt, lb/bolt

F, = compressive load on the vessel support under a bolt; at point a , Fc = F, e' = lb/AbEb, rate of elongation of the bolt, in./lb c' = rate of compression of the combined supports, in./lb. If the concrete foundation is

assumed to be rigid, c' = /b/AsEs, whcre is the bolt length, E b is the modulus of elasticity of the bolt material, As is the support steel area in compression, and E, is the modulus of elasticity of the vessel base

Fa, = CFa/2, steady load component of CF, in bolt Far = +CFa/2, variable load component of CFa in bolt

Fig. 4.5. Force-deflection diagram for anchor bolt and support base.

Table 4.1. Stress Concentration Factor K for Threaded (American Standard) Steel Fasteners Subject to

Tesnile Loads.

ROLLED CUT FASTENER FASTENER

Annealed 2.2 2.8 Quenched and tempered 3.0 3 .8