Design & Analysis of ASME Boiler and Pressure Vessel Components in the Creep Range
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Jawad, Maan H., and Jetter, Robert I. "Axially Loaded Members." Design & Analysis of ASME Boiler and Pressure Vessel Components in the Creep Range. Ed. Maan H. Jawad, and Robert I. Jetter. ASME Press, 2009.
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Axially loaded members subjected to elevated temperatures are encountered in many structures such as internal cyclone hangers in process equipment, structural supports for internal trays, and supports of pressure vessels. It is assumed that buckling, which is discussed in Chapter 7, is not a consideration in this chapter. Theoretically, the analysis of uniaxially loaded members operating in the creep range follow Norton's relationship, correlating stress and strain rate in the creep regime given by
where k′ = constant n = creep exponent, which is a function of material property and temperature dε∕dT = strain rate σ = stress
This equation, however, is impractical to use for most problems encountered by the engineer. Its complexity arises from the non-linear relationship between stress and strain rate. In addition, the equation has to be integrated to obtain strain, and thus deflections. A simpler method is normally used to solve uniaxially loaded members. This method, referred to as the “stationary stress method” or the “elastic analog method,” consists of using a viscoelastic stress-strain equation to evaluate stress due to creep rather than the more complicated creep equation, which relates strain rate to stress. The viscoelastic equation is given by
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