Allowable Axial Stresses

For the lower portion of tall towers, where the combined axial stress controls the design of the shell, there is the problem of selecting the maximum allowable axial compressive stress. The combined axial tensile stress presents no problem. The tensile stresses produced by internal pressure, bending stress of wind loads or bending stress firom seismic loads may be combined by simple addition of the stresses. The thickness of the shell may be calculated so that the combination of axial tensile stresses is equal or less than the maximum permissible value specified by the ASME Code. 

Thin-walled cylindrical vessels imder axial loads can fail in two manners by column action as in the case of Euler s buckling or by wrinkling between tray supports. The stiffness provided by the internal structures of columns containing trays, tray supports, downcomers, etc., provide additional rigidity. As a result, Euler s buckling, which is produced by bending of the shell as a whole, is seldom a controlling factor in tall vertical vessels. 

One satisfactory procedure for combining the compressive loads is to add together all the compressive stresses. However, the design problem is still one of elastic stability. The elastic stability 

In using this equation, check to assure that the combined compressive stress does not exceed that allowed for simple compression (taken as 1/3 the yield point in tension) and that it is within the safe limits of elastic stability (taken as 1.5 times 10 t/r). 

Tray support plates and circumferential or axial stiffeners provide additional rigidity to the shell against wrinkling. Credit may be taken for this stiffening effect by using the following equations  

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With a 25,000-psi allowed radial stress, the maximum allowable axial stress is 25,000/0.4 = 62,500psi. Substituting the appropriate values into Eq. 4.7-3, but not setting K = 1, we get... 

Fv = vertical seismic force, lb F), = horizontal seismic factor, see Procedure 3-3 F i = allowable axial stress, psi F, = allowable bending stress, psi F( = seismic force applied at top of vessel, lb F(. = Euler stress divided by safety factor, psi f] = miiximum eccentric load, lb = horizontal load on leg, lb F,i = maximum axial load, lb... 

Q = vertical load per lug, lb Qa = axial load on gusset, lb Qi, = bending load on gusset, lb n = number of gussets per lug Fa = allowable axial stress, psi Fb = allowable bending stress, psi fa = axial stress, psi fb = bending stress, psi... 

Fy = vertical seismic force, lb Fh = horizontal seismic force, lb Fa = allowable axial stress, psi... 

Ca = Corrosion allowance, in Dc = Centerline diameter of eolumns, in E = Modulus of elastieity, psi f = Maximum force in brace. Lbs fa = Axial stress, eompression, psi f, = Tension stress, psi Fa = Allowable axial stress, psi Fb = Allowable stress, bending, psi Fc = Allowable stress, compression, psi Fd = Axial load on column due to dead weight, lbs Fh = Horizontal seismic force. Lbs Fl = Axial load on column due to seismic or wind, lbs Ft = Allowable stress, tension, psi Fv = Vertical seismic force. Lbs Fy = Yield strength of material at temperature, psi g = Acceleration due to gravity, 386 in/sec ... 

Use the required thickness of the bottom ring as determined from axial stress, or the value obtained by the Code formula, whichever is larger, plus the corrosion allowance. 

Bottom Head. When the critical stress is axial, the tangent section of the bottom head must be the same thickness as the shell at the seam because the allowable unit stress has been calculated from an efficiency of the seam weld. If the tangent is upset or if a ring is welded to the tangent, the full v ue of the plate allowable stress may be used for the section below the ring when using a seamless head. 

T = tension load in outer bolt, lb n) = modular ratio, steel to concrete, use 10 Fh = allowable bending stress. p.si Fy = yield stress, psi fh = saddle splitting force, lb fa = axial stress, psi fh = bending stress, psi f = unit force, Ib/in. 

The maximum tensile stress/strength ratios for the reserve shutdown fuel elements, for the in-plane and axial principal stress directions, are 0.35 and 0.30, respectively. These highest values for the stress/strength ratios were found in layer 5. Both the peak in-plane and the peak axial stress/strength ratio are found at the mid-portion of the element s life. These stress levels are within the allowable limits for control fuel elements (see Table 4.2-22). 

Calculate the allowable axial compressive stress using Gc, a modified imperfeetion factor, a, and the appropriate design faetor. 

Additionally, tolerances for cylindrical and conical shells are provided when subjected to external pressure, and uniform axial compression and bending. If the tolerances are exceeded, the allowable buckling stresses must be adjusted. In the case of vessels with large diameter over thickness ratios (approximately 300 or higher), it may be prudent to discuss shell tolerances with the fabricator to ensure that if tolerances cannot be met, the reduced allowable buckhng stresses can be used for checking tlie design of the vessel. 

Step 2 Determine the allowable longitudinal stress due to axial compression. 

Calculate Ac to see if the vessel is subject to column buckling. If it is not then the allowable longitudinal stress due to axial compression is Fxa. 

The thickness ratio obtained by the use of Eflat-plate closure is several times the thickness of the shell for usual values of allowable stress and operating pressure. Some improvement in design proportions may be made pt able by ifuT ising the thickness of the shell to reduce the maximum ih retical combined axial stress in the shell at the jum lion. However, such an increase in shell tlueknesK does not result in a correspon g decrease in the required thickness of the flat-plate closure. (The maximum theoretical combined axial stress in the shel at the junction ala> can Iw decreased by incr sing the thickness of the fiat cover plate.)... 

Column Supports for Lugs. If the column is attached in such a manner that it can be con.sidered as a column under concentric axial load, the allowable fiber stress is given by Eq. 4.18. 

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