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Although investigations have shown that the theory of limit design applies to beams and some frames made of mild steel, it is not certain whether it applies in the same way to the light alloys. Steel frames satisfy the limit design prediction of a failure mechanism not only because steel is very ductile but also because steel exhibits strain hardening. Light alloys such as high-strength aluminum alloy exhibit very little strain hardening. Two load tests were carried out on redundant beams made of the aluminum alloy to see if the mechanism condition of limit design was reached before failure took place in the beam. Measurements of beam deflections and moments are compared to the deflections and moments predicted by the theory of inelastic bending. The theory of inelastic bending is based on the stress-strain diagram and takes account of strain hardening and a failure strain. Tables of unit functions derived from the stress-strain diagram of the aluminum alloy are presented for use with the inelastic bending theory. In both tests, the mechanism condition of limit design was reached before failure took place. Shortly after the mechanism condition was reached, a fracture occurred in the flange on the tension side of the beam. Thus the type of failure indicates that not all structural configurations will achieve the mechanism condition. Beyond the limit of elastic deformation (17 kips load) and up to a load of about 27 kips, the beam moments were similar to those predicted by the inelastic bending theory. From 27 kips load to failure at 32 kips, the moments were distributed in the beam differently than the predicted moments due to the presence of high shear force. The load-deflection curves are the same as the curves from the theory, although measured deflections were always greater. The ultimate curvature at the section of failure was greater than predicted from the theory. There were some shortcomings of the tests. The tests were originally set up to be unfavourable towards the limit design theory. However, stiffeners were added at the plastic hinge locations to prevent web failure, and the presence of the stiffeners was helpful in allowing redistribution of moments to take place in much the same way as strain hardening does in steel beams. Also the presence of the stiffeners and stiffener holes made interpretation with the inelastic bending theory uncertain. Finally there were some errors in measuring the moments by means of strain gauges. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

The theory of limit design originally was developed for structural steel construction. Tests carried out on mild steel beams and frames are in agreement with the theory. Unfortunately a limited number of tests have been carried out on other ductile materials such as light alloys. Therefore more tests are required in order to investigate whether the theory of limit design is also applicable, with or without modification to aluminum alloys. The failure mechanism predicted in limit design materializes in steel frames not only because steel is very ductile but also because steel has strain hardening. Aluminum alloys exhibit very little strain hardening. In the research described here there were two objects. The first object was to investigate the applicability of limit design to aluminum alloys. The second object was to check experimentally the theory of inelastic bending. Three load tests were carried on continuous beams made of aluminum alloy to see if the mechanism condition was attained before failure of the beam. Moments and deflections predicted by the theory of inelastic bending were compared against measurement of beam moments and deflections. The theory of inelastic bending considers the effect of strain hardening. Tables of unit function derived from the stress-strain diagram of aluminum alloy (65S-T6) are presented so that they may he used when the theory of inelastic bending is applied. The first test failed prematurely due to crippling of the compression flanges. In the second and the third test the mechanism condition of limit design was reached shortly before failure of the tension side of the beam under the load point by fracture. Thus the type of failure indicates that not all structures will achieve the mechanism condition. The failure load and the ratio of moments at failure, as predicted by the theory of inelastic bending was equal to 15.53 Kips and 1.13 respectively. Test results indicated a failure load of 16 Kips and a ratio of moments at failure equal to 1.1. The load-deflection curves were the same as the curves from the theory. At failure the deflection under the load was 5.57 inches compared to computed theoretical deflection of 5.46 inches. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

Isothermal transformations in eutectoid zirconium-niobium alloys have been studied by resistometric techniques at high temperature, and by room-temperature hardness measurements, metallography, and X-ray methods, Room-temperature measurements were performed on specimens which had been heat-treated in evacuated vycor capsules. The resistometric method gave data which were not in agreement with data obtained by room-temperature measurements. A T-T-T curve established by room-temperature hardness and metallography was found to be similar to one obtained by a previous investigator. The lack of agreement between measurements made at high temperature and those made at room temperature suggests that a structural change is occurring in these alloys during the quench from the transformation temperature. For this reason, room temperature metallography is unsatisfactory for following transformations in these alloys. The analysis of micro-structure is complicated by the presence of a needle-like ' phase' which was not identifiable by the X-ray techniques employed. It is shown that the resistometric technique is a sensitive method for observing transformations in zirconium-niobium alloys. / Applied Science, Faculty of / Materials Engineering, Department of / Graduate

The thermodynamic properties of the copper-manganese system were determined by the measurement of the vapour pressure of manganese tagged with Mn⁵⁴, using the Knudsen effusion method. Manganese shows a positive deviation from Raoult's law over the entire composition range. Copper, although showing a strong positive departure from Raoult's law at low copper content, shows a slight negative departure in copper-rich compositions. The negative departure, which can be associated with an affinity of copper for manganese is greatest at compositions of about 35% manganese. The behavior of both copper and manganese is much more ideal at lower manganese compositions. The ideal behaviour of the manganese in the alloys of low manganese content and the affinity of copper for manganese at about 35% manganese appear to corroborate Myers interpretation of the electronic configurations of copper and manganese in this system. / Applied Science, Faculty of / Materials Engineering, Department of / Graduate

An investigation of the zirconium-rich corner of the zirconium-titanium-niobium constitutional diagram is described. X-ray techniques and metallography were used. A high-temperature x-ray goniometer attachment was employed to construct ternary isopleths. Isothermal sections and lattice parameter measurements are also outlined. The occurrence of a transitional ω -phase identified tentatively as tetragonal, is noted. The ternary constitutional data presented represent essentially a survey of the zirconium-rich corner and more detailed results must await further work. / Applied Science, Faculty of / Materials Engineering, Department of / Graduate