Seismic loads

The sway of the tower will produce a maximum velocity as the tower passes through vertical center. Also, the maximum velocity of sway will be at the top of the column with zero velocity at the base. As the column reaches the limit of its deflection, the kinetic energy of motion is transferred to strain enei of the shell, causing reversal of direction. The column will sway back and forth until the energy is dissipated. The total strain energy stored in a tall vertical tower at its point of maximum deflection during sway is given by the equation 

The strain energy given by equation 4-13 may be equated to the kinetic energy of motion as the tower moves through verticsd dead center. The kinetic energy is defined by the equation 

Combining equations 4-13 and 4-14, you can solve for the angular velocity, p, eind express the time factor as the period of vibration, T, by the following  

If you substitute the value of 30,000,000 psi for E, the modulus of elasticity, substitute equation 4-12 for /, the moment of inertia of the shell, and use 32.2 ft./sec. as the gravitational constant, the preceding equation reduces to 

H = Total tower height, ft. (vessel plus skirt) D - Tower diameter, ft. w = Tower weight, lb. /ft. of he ht t = Tower shell thickness, in. 

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Seismic loads shall be as specified PDVSA SPECIFICATION-JA-221 "Diseflo Antisismico de Instalaciones Industriales". 

The four primary coolant pumps are connected to the secondary shield wall by three-link snubbers designed to be flexible under static applied loads (thus, allowing thermal expansion) but become stiff under dynamic loads that might occur during an earthquake. Accordingly, the system is coupled to the wall under seismic loading. 

Category 1. Relea.se of gaseous ammonia primarily from failure of Tank DK-101 by three plant-damage statc.s overpressure, underpressure and seismic load. For all three it was assumed that ... 

Conventional Loads - Load normally considered in structural design such as dead loads, live loads, wind loads, ana seismic loads. 

A dynamic statistical approach is used to predict dynamic stresses in a hyperboloidal cooling tower due to earthquakes. It is shown that the configuration associated with one circumferential wave is the only one which is excitable by earthquake force and that the first mode of such configuration is dominant. An equivalent static load is calculated on this basis. Numerical data presented give coefficients for equivalent static loads, natural frequencies of cooling towers, and static stresses for a seismic load. 21 refs, cited. 

At the very top of the vessel there are no induced stresses introduced by wind or seismic loads the only considerations are the functional design of the vessel and the stress considerations when the vessel is operating either under partial vacuum or under a pressure greater than atmospheric. Furthermore, at the very top of the vessel, there is usually little static dead weight to consider in the stress analysis except when condensers, heat exchangers or other auxiliary apparatus are attached to the top. 

We will now consider the special problems in tall tower design which are not described in the ASME Code for Unfired Pressure Vessels. As discussed previously, circumferential stresses control the design of cylindrical vessels if external loads are of small magnitude. In tall vertical vessels, four major factors (wind load, seismic loads, dead weight and vibration) may contribute to axial stresses — in addition to axial stress produced by the operating pressure or vacuum of the vessel. 

Seismic forces have effects somewhat similar to wind loads in that the vertical tower is loaded as a cantilever beam standing on end and fixed at the base. There is a difference in the distribution of wind loads compared to seismic loads, but in both instances the vertical column is exposed to bending which produces axial tensile stresses on one side and axial compressive stresses on the other side. These must be combined with the axial stresses from the operating pressures for both vacuum and pressure operation. 

In addition to bending stresses caused by a wind load or a seismic load, the weight of the tower and its contents will produce a cumulative axial compressive stress on the shell which increases with distance X from the top of the tower. In a vessel with uniformly distributed compressive loads from the dead weight, this compressive stress is simply the summation of the total weight of the tower above the plane X divided by the cross-sectional... 

The maximum compressive loading will usually be obtained with a vacuum tower operating under full vacuum with a maximum load of liquid in the column. Here, the axial compressive stress from vacuum plus the axial stress from dead weight and the axial bending stress either from the wind load or the seismic load will be additive. 

Equating the appropriate stress equation from equations 4-17 to 4-20 to the allowable stress, a solution for distance X may be obtained for a selected shell thickness. Because the stresses from both wind loads and seismic loads increase with X, the resulting equation is a binomial. 

However, the bending stresses from wind and seismic loads increase with X. Therefore, the shell thickness must be increased more frequently or in greater degrees in progressing down the column. For example, the second increase in shell thickness may require 1/8 in. increment and may be satisfactory for two or three more courses down. The calculations are continued in this manner until you reach the junction of the vessel with the supporting skirt. 

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. 

Seismic Loads, by Victor Lyatkher, ISBN 9781118946244. Combining mathematical and physical modeling, the author of this groundbreaking new volume explores the theories and applications of seismic loads and how to mitigate the risks of seismic activity in buildings and other structures. NOW AVAILABLE ... 

The procedures outlined in this chapter are static-force procedures, which assume that the entire seismic force due to ground motion is applied instantaneously. This assumption is conserv ative but greatly simplifies the calculation procedure. In reality earth quakes are time-dependent events and the full force is not realized instantaneously. The UBC allows, and in some cases requires, that a dynamic analysis be performed in lieu of the static force method. Although much more sophisticated, often the seismic loadings are retluced significantly. 

This procedure is used for calculating the distribution of vertical and horizontal forces due to wind or seismic loadings for vessels, spheres, elevated tanks, and bins supported on cross-braced legs or columns. 

Table 4 shows the results of the seismic margin evaluations and the seismic capacity of KALIMER reactor internal structures including the reactor vessel and containment vessel. From the results, the containment vessel, reactor vessel, inlet plenum, and core support have large seismic stress margins but the reactor vessel liner, support barrel, separation plate, and baffle plate have small margins. The maximum stress occurs in reactor vessel liner parts coimected with the separation plate due to the vertical seismic loads. 

Thiers, R.G., and Seed, H.B. 1969. Strength and stress-strain characteristics of clays subjected to seismic loading conditions. Vibration Effects of Earthquakes on Soils and Foundations, ASTM STP 450. 

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