Proceedings of the Institution of Mechanical Engineers,Conference Proceedings

A method is given in this paper for calculating the mean hoop and meridional bending stresses in a rotating toroidal shell. The rotational stresses in a wheel, consisting of a portion of a toroidal shell, built in at one edge to the hub, have been calculated and are compared with the stresses determined experimentally with electrical resistance strain gauges.

Information available for the calculation of stresses in and flexibility of mitred pipe bends (including lobster- back bends) under elastic conditions, for internal pressure loading, and in-plane and out-of-plane bending loading, is assessed. The results of Owen and Emmerson (4) for single mitre bends under internal pressure loading and their application to lobster-back bends are discussed. The stiffening effect of a ring of varying degrees of stiffness at the joint is considered in the light of some experimental results. The results of in-plane bending tests on two separate single mitre bends of different mitre angles are compared and a further comparison is made with published results on lobster-back bends. It is concluded that the results for single mitre bends under in-plane bending cannot be applied to lobster-back bends, which are more closely approximated by smooth-bend theory. Out-of-plane bending loading is briefly discussed.

The fuel elements in the uranium-magnox carbon-dioxide-cooled reactors, which are currently operating and under erection in the United Kingdom and other countries, are required to maintain their physical shape and dimensions virtually unchanged during a lifetime which may be as long as five years.

During its life in the reactor, the fuel element is subject to forces arising from various causes, e.g. its own weight, because of swelling of the fuel by irradiation, the flow of cooling gas over the element, thermal stresses resulting from charging, load changes and reactor shut-downs and changes in the dimensions of the graphite core which may lead to jamming of the element in the core channel during discharge.

Because of the need to economize in neutron-absorbing material the uranium fuel rod itself becomes the major structural member in the element. The effects of these forces on this and the other component parts of the fuel element are examined, out-of-pile testing is described and the changes in design resulting from this prototype testing are indicated.

In a short theoretical section, means of predicting fuel-element deformation in the light of creep data are given and probable limits of accuracy noted.

The paper describes the first of a series of three tests designed to obtain information about the nozzle assemblies on reactor pressure vessels under a variety of loading conditions, with a view to predicting their behaviour in service. This first test is concerned with the effect of loadings which cause yielding in the nozzle region, and while overloads as severe as those described cannot occur in practice, the results enable a quantitative assessment to be made of the margins between operating pressure and failure pressure as far as shortterm yielding is concerned. They also provide data which will be of interest when improved design methods, involving higher working stresses, are considered.

The test was carried out on a spherical vessel containing a small group of oblique nozzles, manufactured to represent a nozzle layout typical of reactor vessels, at scale size. The vessel was hydraulically pressurized up to 1670 1b/in² gauge when failure occurred through the heat-affected zones of the nozzle to shell welds. The basic shell stress at failure was approximately equal to the ultimate tensile strength of the material.

Strain readings recorded during the tests, and the results of the metrological surveys, carried out on the vessel before and after testing, are discussed in the report.

Thin cylindrical shells subjected to high bending loads normally buckle by forming a number of diamond- shaped panels on part of their compressed surfaces. The values of the buckling loads show considerable scatter but are in general substantially less than those predicted by simple linear theory.

This paper describes an attempt made a few years ago to improve the buckling strength and to reduce the scatter in the buckling loads of such shells by means of internal pressure. It was expected and confirmed that internal pressure would increase the buckling loads, but little improvement was obtained in the amount of scatter. Considerable modifications of the buckling deformations were observed; at sufficiently high pressures the diamond pattern disappeared entirely and was replaced by a single ridge of deformation extending circumferentially around the compressed side of the shell.

An account is given of the experimental investigation together with some excerpts from the theoretical work. Most of the shells were formed from thin steel sheets bent into the shape of a cylinder then soldered down a generator. They were filled with water, plugged at their ends and put under pressure by means of a hand-pump. Observations made during bending included load, pressure, strain, deflections and mode of buckling. These are discussed and compared with the results of other investigations.

This paper summarizes very briefly the history of the use in Germany and elsewhere of design stresses for vessels which are higher by up to 50 per cent than those allowed by British Standard 1500 and the American Society of Mechanical Engineers' Code, and of the approach of Imperial Chemical Industries to this problem.

On the technical side the criteria which should govern local stresses in pressure vessels and their permissible values were then considered, an aspect of design which has received less public discussion than the estimation of stresses due to local loads. The conclusions reached have formed the basis of recommendations submitted in collaboration with other interested organizations to the British Standards Institution.

The use of higher design stresses implies that there is a smaller margin for errors in design or shortcomings in quality of materials or manufacture. The administration of the pressure vessel code in Germany is reviewed and comparisons are drawn with the bodies available for similar purposes in Britain.

Investigations into the effect of temperature and pressure cycling on a pre-loaded model main steam line of 0·5% Cr-0·5% Mo-0·25% V steel have shown that a relatively large increase in length occurred over a few cycles at 100 per cent cold pull, and a decrease in length occurred at 50 per cent cold pull. Using high temperature platinum-tungsten strain gauges, it has been found that large changes in strain occur round an expansion loop in the model pipeline. It is suggested that large changes in the design stress distribution in a main steam line occur during the commissioning stages of a generating unit, making creep behaviour of the line during base loading difficult to predict. It is further suggested that failure in pipelines when a unit is working under a twoshift system is due to low cycle fatigue, as the strain changes occurring do not appear to approach an equilibrium minimum under cycling conditions.

It would appear that strain changes, and hence the effect of low cycle fatigue, can be minimized by choosing a level of cold pull between 50 and 100 per cent, the actual level depending upon the physical characteristics of the pipe material, the more important ones being thermal expansion and the change of yield stress with temperature.

Using the plastic strain range measured in the test a prediction can be made regarding the time to failure.

The results presented in this paper indicate the conditions under which oscillations of large amplitude occur in systems which embody couplings having periodically varying velocity ratios. Experimental results relating to one- and two-degree-of-freedom Hooke's joint systems are given and are compared with theoretical predictions.

A back-to-back gear rig (12 000 ft/min maximum pitch-line velocity) was used to demonstrate various causes of high-speed gear vibrations with either straight spur or helical teeth, the transducers being four strain gauges mounted on the gear shaft. The primary cause of excitation is shown to be transmission errors in the straight spur case, but with helical teeth a variation in contact length is the prominent factor, with lateral movement of the resultant load as possibly the chief cause where the contact length is constant. Noticeable temperature effects were only experienced at the highest speeds; here the thickness of the oil film on the tooth face has a considerable effect on the tip relief, the modification becoming less as the temperature rose. Damping varied considerably (0·004 to 0·042 critical) between modes, and slightly with change in load, and therefore no overall damping factor could be taken for the rig; the average damping factor for the specific mode was used in each amplitude calculation. Calculation of the natural frequencies of the gear system was performed with the use of receptance theory with considerable success; the amplitude predictions were not quite so favourable but were generally of the right order.

An experimental study has been made of the elastic stress distributions arising in the vicinity of two transition rings of the type used to connect cylindrical ducts with large spherical pressure vessels. The effect of bending moments on the duct was considered and theoretical estimates of the stresses were made by modifying certain well-known analyses. Two of these methods gave results close to the experimental values in a region which included the position of maximum stress. This occurred near the weld between the spherical shell and the transition ring.

In a further investigation it was found that, for the order of loads applied, the principle of superposition may be used to calculate the combined effect of a local bending moment and an internal pressure.

When allowable bending moments at design pressure are calculated using a limiting stress concentration factor, the heavier transition piece is slightly superior to the other.