Secondary stress

In the stress analysis of pressure vessels and pressure vessel components stresses are classified as primary or secondary. Primary stresses can be defined as those stresses that are necessary to satisfy the conditions of static equilibrium. The membrane stresses induced by the applied pressure and the bending stresses due to wind loads are examples of primary stresses. Primary stresses are not self-limiting if they exceed the yield point of the material, gross distortion, and in the extreme situation, failure of the vessel will occur. 

Other sources of secondary stresses are the constraints arising at flanges, supports, and the change of section due to reinforcement at a nozzle or opening (see Section 13.6). 

Though secondary stresses do not affect the bursting strength of the vessel, they are an important consideration when the vessel is subject to repeated pressure loading. If local yielding has occurred, residual stress will remain when the pressure load is removed, and repeated pressure cycling can lead to fatigue failure. 

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The stress field corresponding to this regime is shown in Figure 6.18. As this figure shows the measuring surface of the cone is affected by these secondary stresses and hence not all of the measured torque is spent on generation of the primary (i.e, viscometric) flow in the circumferential direction. 

When constmction is complete, the pipeline must be tested for leaks and strength before being put into service industry code specifies the test procedures. Water is the test fluid of choice for natural gas pipelines, and hydrostatic testing is often carried out beyond the yield strength in order to reHeve secondary stresses added during constmction or to ensure that all defects are found. Industry code limits on the hoop stress control the test pressures, which are also limited by location classification based on population. Hoop stress is calculated from the formula, S = PD/2t, where S is the hoop stress in kPa (psig) P is the internal pressure in kPa (psig), and D and T are the outside pipe diameter and nominal wall thickness, respectively, in mm (in.). 

From a constitutive relation of the form t = t(D, ri) (here t is stress not time) it can be readily shown that, since there is no change in electric displacement in an open-circuit, thick-sample configuration, there are no secondary stresses due to electromechanical coupling. Nevertheless, the wavespeed is that of a piezoelectrically stiffened wave. 

For purposes of this specification, stresses in the individual members of a latticed or trussed structure resulting from elastic deformation and rigidity of joints are defined as secondary stresses. These secondary stresses may be taken to be the difference between stresses from an analysis assuming fully rigid joints, with loads applied only at the joints, and stresses from a similar analysis with pinned joints. Stresses arising from eccentric joint connections, or from transverse loading of members between joints, or from applied moments, must be considered primary stresses. 

Allowable unit stresses may be increased 20% from the basic allowable stress when secondary stresses are computed and added to the primary stresses in individual members. However, primary stresses shall not exceed the basic allowable stresses. 

Other Systemic Effects. Endocrine lesions related to 1,2-dibromoethane exposure were reported in the NCI (1978) gavage bioassay. These consisted of adrenal cortical cell degeneration in a small number of exposed male and female Osborne-Mendel rats. The possibility exists that this adrenal change represents a secondary (stress-related) effect rather than a primary effect of 1,2-dibromoethane exposure. 

The cone-plate rheometer. The cone-plate rheometer is often used when measuring the viscosity and the primary and secondary normal stress coefficient functions as a function of shear rate and temperature. The geometry of a cone-plate rheometer is shown in Fig. 2.47. Since the angle Oo is very small, typically < 5°, the shear rate can be considered constant throughout the material confined within the cone and plate. Although it is also possible to determine the secondary stress coefficient function from the normal stress distribution across the plate, it is very difficult to get accurate data. 

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