Buckling pressure

The analysis should include the modulus of soil reaction, because in a buried RTR piping system the elastic medium surrounding the pipe helps increase the pipe s resistance to buckling. The formula into which all these factors can be inserted to determine the critical buckling pressure of the pipe is called the Luscher Hoeg formula (44,56). 

For short closed vessels, and long vessels with stiffening rings, the critical buckling pressure will be higher than that predicted by equation 13.51. The effect of stiffening can be taken into account by introducing a collapse coefficient , Kc, into equation 13.51. 

Any stiffening rings used must be spaced closer than Lc. Equation 13.52 can be used to determine the critical buckling pressure and hence the thickness required to resist a given external pressure see Example 13.2. A factor of safety of at least 3 should be applied to the values predicted using equation 13.52. 

The critical buckling pressure for a sphere subject to external pressure is given by (see Timoshenko, 1936) ... 

Any out-of-roundness in a shell after fabrication will significantly reduce the ability of the vessel to resist external pressure. A deviation from a true circular cross-section equal to the shell thickness will reduce the critical buckling pressure by about 50 per cent. The... 

To meet the designed deflection of no more than 5% the pipe wall structure could be either a straight wall pipe with a thickness of about 1.3 cm (0.50 in.) or a rib wall pipe that provides the same stiffiiess. It has to be determined if the wall structure selected is of sufficient stiffiiess to resist the buckling pressures of burial or superimposed longitudinal loads. The ASME Standard of a 4/1 safety factor on... 

From the preliminary analysis, the increase of the quasi-steady-state pressure of the cover gas in the secondary vessel is about 0 13 MPa and 0 2MPa for a DBL and a BDBL, respectively These values are much less than the external buckling pressure of the primary vessel (0 56MPa), thus the structural integrity of the primary vessel can be secured... 

Sato and Patel (2007) proposed an analytical solution for calculating the buckling capacity by simplifying the problem and determining the buckling pressure of a ring, supported internally by an elastic foundation. They proposed the following equation ... 

Sato M, Patel M H (2007) Exact and simplified estimations for elastic buckling pressures... 

Suppose that this Luscher Hoeg equation says we will require a pipe stiffness of 0.123(10) lbs.-in.V(lineal in.) to meet a four-to-one critical buckling pressure safety factor. This is a straight-wall thickness of approximately 1.9 cm (0.75 in.). But remember that we earlier calculated that a 0.50-in.-thick wall would be sufficient to withstand the anticipated deflection pressure. Which of these two wall thicknesses is correct ... 

For suspensions, Minoshima et al. (2001, 2002) proposed a model based on the buckling behavior of the crust. According to this model, a particle is allowed to shrink as long as the buckling pressure is larger than the permeation pressure of the evaporating fluid. The buckling pressure depends on the shell thickness as... 

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