Cable-stayed bridges are one of the most popular types of long-span bridges. The structural behaviour of cable-stayed bridges is sensitive to the load distribution between the girder, pylons, and cables. The determination of pretensioning cable stresses is critical in the cable-stayed bridge design procedure. By finding the optimum stresses in cables, the load and moment distribution of the bridge can be improved. In recent years, different research works have studied iterative and modern methods to find optimum stresses of cables. However, most of the proposed methods have limitations in optimising the structural performance of cable-stayed bridges. This paper presents a multiconstraint optimisation method to specify the optimum cable forces in cable-stayed bridges. The proposed optimisation method produces less bending moments and stresses in the bridge members and requires shorter simulation time than other proposed methods. The results of comparative study show that the proposed method is more successful in restricting the deck and pylon displacements and providing uniform deck moment distribution than unit load method (ULM). The final design of cable-stayed bridges can be optimised considerably through proposed multiconstraint optimisation method.
Since the use of the most stable Pb-based materials in the electronic industry has been banned due to human health concerns, numerous research studies have focused on Pb-free materials such as pure tin and its alloys for electronic applications. Pure tin, however, suffers from tin whiskers' formation, which tends to endanger the efficiency of electronic circuits, and even worse, may cause short circuits to the electronic components. This research aims to investigate the effects of stress on tin whiskers' formation and growth and the mitigation method for the immersion of the tin surface's finish deposited on a copper substrate. The coated surface was subjected to external stress by micro-hardness indenters with a 2N load in order to simulate external stress applied to the coating layer, prior to storage in the humidity chamber with environmental conditions of 30 °C/60% RH up to 52 weeks. A nickel underlayer was deposited between the tin surface finish and copper substrate to mitigate the formation and growth of tin whiskers. FESEM was used to observe the whiskers and EDX was used for measuring the chemical composition of the surface finish, tin whiskers, and oxides formed after a certain period of storage. An image analyzer was used to measure the whiskers' length using the JEDEC Standard (JESD22-A121A). The results showed that the tin whiskers increased directly proportional to the storage time, and they formed and grew longer on the thicker tin coating (2.3 μm) than the thin coating (1.5 μm). This is due to greater internal stress being generated by the thicker intermetallic compounds identified as the Cu5Sn6 phase, formed on a thicker tin coating. In addition, the formation and growth of CuO flowers on the 1.5 μm-thick tin coating suppressed the growth of tin whiskers. However, the addition of external stress by an indentation on the tin coating surface showed that the tin whiskers' growth discontinued after week 4 in the indented area. Instead, the whiskers that formed were greater and longer at a distance farther from the indented area due to Sn atom migration from a high stress concentration to a lower stress concentration. Nonetheless, the length of the whisker for the indented surface was shorter than the non-indented surface because the whiskers' growth was suppressed by the formation of CuO flowers. On the other hand, a nickel underlayer successfully mitigated the formation of tin whiskers upon the immersion of a tin surface finish.