Overturning Moment

Two major considerations are required to design a foundation for a self-supporting tower soil loading and tower stability. The load on the soil below the tower must not exceed the maximum load the soil will support. The foundation must keep the tower in a vertical position so it will not be overturned by the maximum forces acting on it. 

Foundation sizing is done by a trial and error method. (Explanations of each tower load and example calculations follow.) 

Soil Loading. Use the following equation to find the soil loading  

Si = the total unit soil loading exerted by the dead load, psf. 

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Foundations must be designed to take the weight loads and overturning moments without transmitting vibration to other equipment and buildings. 

The overturning load, Sj, is caused by an overturning moment. Usually, wind pressure is the only force trying to overturn the tower. Because wind pressure is a function of wind velocity and barometric pressure, it is readily calculated using the following equation ... 

Figure 11-1 shows a cylindrical tower on which the wind pressure, P, tends to rotate the tower and its foundation around point A. This produces an overturning moment that is calculated as follows ... 

The stress, or load, on the soil from the overturning moment varies from point to point. Calculate the maximum load, Sj, as follows ... 

The overturning moment is positive at point F and negative at point E as shown in Figure 11-1. Because the soil has no strength in tension, the sum of the stresses at any point must be positive. 

MfIZ = 200,000/250 = 800 psf = maximum soil load from the overturning moment. 

The steel shell is required to withstand the stresses resulting from, (a) the internal pressure (b) the dead load, and (c) the overturning moment from wind pressure. This discussion will be confined to the stress resulting from the wind pressure. 

It was shown by equation (11-1) that the total soil loading, to be considered in the design of tower foundations, is the sum of Si, the dead load, and S2, the load caused by the overturning or wind moment. There is no overturning moment on guyed towers however, the wind pressure does have an important effect on the foundation, as the soil is required to resist the vertical component of the pull on the guy wires. 

Ss = maximum unit shearing load due to overturning moment (lbs. per lineal foot of pedestal perimeter)... 

Calculate shearing stress due to overturning moment, Sg, by equation (11-37). 

Intermittent loading from overturning moment produced by winds... 

The critical line in the skirt support is the weld attaching the vessel to the skirt. This weld, in addition to transmitting the overall weight and overturning moments, must also resist the thermal and bending stresses due to the temperature drop in the skirt. The thinner the sldrt, the better it is able to adjust to temperature variations. A hot box design is... 

Gy=gust response factor for flexible vessels h = height of vessel, ft I = importance factor, see Table 3-1 Iz = the intensity of turbulence at height z Kz = velocity pressure exposure coefficient from Table 3-3a, dimensionless Kct = topographic factor, use 1.0 unless vessel is located near or on isolated hills. See ASCE for specific requirements M = overturning moment at base, ft-lb Ni,Nh,Nb,Na = calculation factors... 

This section outlines the wind design procedures for both of these standards. Wind design is used to determine the forces and moments at each elevation to check if the calculated shell thicknesses are adequate. The overturning moment at tlie base is used to determine all of the anchorage and support details. These details include the number and size of anchor bolts, thickness of skirt, size of legs, and thickness of base plates. 

V = base shear, kips Vx = shear at plane x, kips Mx - moment at plane x, ft-kips Mb = overturning moment at base, ft-ldps D = mean shell diameter of each section, ft or in. E = modulus of elasticity at design temperature, 10 psi... 

M = bending moment, or overturning moment, in.-lb I = moment of inertia, in. ... 

Mb = overturning moment at base, in.-lb M[ = overturning moment at tangent line, in.-lb M, = unit bending moment in base plate, circumferential, in.-Ib/in. 

R, = torsional resistance factor Q = equivalent vertical force at each support due to dead weight and overturning moment, lb q = uniform vertical load on ring beam, Ib/in. q< = tangential shear, Ib/in. 

M = overturning moment of vessel at base of ring beam, in.-lb... 

Ip = importance factor, 1.0-1.5 L = overall length of vessel, ft Ml = overturning moment due to force Fl, ft-lb Ms = overturning moment due to seismic, ft-lb Mr = resultant moment, ft-lb Mw = overturning moment due to wind, ft-lb MwD = modified wind moment, ft-lb qH =wind velocity pressure, psf, per NBC q = external wind pressure, psf per ASME STS-1 S = Strouhal number, use 0.2 T = period of vibration, sec t = shell thickness, in. 

Several of the above analyses have to be carried out for different load combinations at different times in order to find the critical safety factor. For example, local contact stresses between the base and soil may be predominant in installation phase before the voids have been grouted. Similarly, the shear strength of the soil reduces after several years of production owing to cyclic loading to lower than it was shortly after the installation. Typical loads and overturning moments for a foimdation stability analysis is shown in Figure 10.33. 

V is the vertical load H is the horizontal load M is the overturning moment E and p. are the elastic properties... 

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