Safety factor, buckling

In many cases, a product fails when the material begins to yield plastically. In a few cases, one may tolerate a small dimensional change and permit a static load that exceeds the yield strength. Actual fracture at the ultimate strength of the material would then constitute failure. The criterion for failure may be based on normal or shear stress in either case. Impact, creep and fatigue failures are the most common mode of failures. Other modes of failure include excessive elastic deflection or buckling. The actual failure mechanism may be quite complicated each failure theory is only an attempt to explain the failure mechanism for a given class of materials. In each case a safety factor is employed to eliminate failure. 

The allowable buckling stress is the critical buckling stre.ss multiplied by some factor of safety. The safety factor for buckling ranges from 1.5 1 to. 3 1. In addition, certain upper boundaries are specified, such as one-half the yield strength. 

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... 

Effective area Design compressive force Design compression resistance of the cross section Buckling resistance of member Partial safety factor for material resistance... 

Creep-buckling is an issue when the cylindrical component operates in the creep range. The protection against buckling is determined by calculating a critical stress or failure point and applying a safety factor. This safety factor is a variable in the design of such components. 

For these structures, R may be taken as a value of 3, however, additional instructions apply in these cases. If huckUng of the support is determined to be the governing mode of failure, or if the structure is in Risk Category IV, then the seismic response coefficient must be determined using a value of VR =1.0 and checked against the critical buckling resistance (safety factor equal to 1.0). 

Hence safety factor for buckling lies between 0.517 0.459... 

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 ... 

Cladding collapse has been excluded in LWR fuel rod design. However, in the Super FR, pressure difference between internal gas and coolant is higher than that of PWRs. Collapse of cladding is kept as one possible cladding failure mode in the Super FR design. The pressure difference is limited by the buckling collapse pressure with a safety factor of 3 as in the Super LWR (see Chap. 2). 

When the required cladding thickness against buckling collapse is calculated, the safety factor of 1/3 is applied and 110% of the system pressure of 27.5 MPa and the cladding temperature of 800°C are considered. 

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. 

By applying a suitable factor of safety, equation 13.72 can be used to predict the maximum allowable compressive stress to avoid failure by buckling. A large factor of safety is required, as experimental work has shown that cylindrical vessels will buckle at values well below that given by equation 13.72. For steels at ambient temperature E = 200,000 N/mm2, and equation 13.72 with a factor of safety of 12 gives ... 

On the other hand, the 1977 Summer Addendum of the ASME Code permits three alternate methods, but requires a factor of safety between 2 and 3 against buckling, depending upon applicable service limits. 

ASME uses a factor of safety of 3.0 for buckling of cylindrical shells subjected to lateral and end external pressures. Hence, for elastic region (D<,/r s 10),... 

For D /r values less than 10, ASME uses a variable factor of safety that ranges from 3.0 for values of Do/t = 10 to a factor of safety of 2.0 for values of DJt = 4.0. This reduction occurs because for very thick cylinders, buckling ceases to be a consideration and the allowable values in tension and compression are about the same. Hence, for Do/t < 10 the allowable value of P is the lower of die quantities P and Pi given below. 

The rules for this case are based on the axial buckling of a cylindrical shell as given by Eq. 5.28. With E = 30,000,000 psi and a factor of safety 10, this equation becomes... 

Vessels of noncircular cross section may be subjected to external pressure Membrane and bending stresses are considered the same as for internal pressure unless the resulting stresses are compressive where stability may be a possible mode of failure. Interaction equations are used to examine die various plates for stability. Calculated stresses are compared with critical buckling stresses with ii factor of safety applied. This is described in Article 13-14 of the ASME Code,... 

In the plastic region, ASME uses quasi-stress-strain curves similar to those in Fig. 8.11 to determine plastic buckling. These curves are plotted on log-log graphs with a factor of safety of two for stress. Because the stress-strain curves differ for different temperatures, a number of curves for different temperatures are plotted in Fig. 8.11. Hence, allowable stress is given by... 

The governing equation is obtained from Eq. 6.35 for the buckling of a spherical shell with a factor of safety of four. Using E = 30,000,000 psi, the equation becomes... 

Bhattacharya (2006) discusses the deterministic approach to determine the factor of safety of pile foundations against the buckling instability failure. Bhattacharya and Goda (2013) developed a probabilistic procedure for determining the occurrence of a buckling failure of existing piled foundations due to a scenario earthquake. 

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