To predict loading limits for structures and structural elements is one of the oldest and most important tasks of engineers. Among the theoretical and numericalmethodsavailableforthispurpose,so-called“DirectMethods”,- bracing Limit- and Shakedown Analysis, play an eminent role due to the fact that they allow rapid access to the requested information in mathematically constructive manners. The collection of papers in this book is the outcome of a workshop held at Aachen University of Technology in November 2007. The individual contributions stem in particular from the areas of new numerical developments renderingthemethodsmoreattractive forindustrialdesign,extensionsof the general methodology to new horizons of application, probabilistic approaches and concrete technological applications. The papers are arranged according to the order of the presentations in the workshop and give an excellent insight into state-of-the-art developments in this broad and growing field of research. The editors warmly thank all the scientists, who have contributed by their outstanding papers to the quality of this edition. Special thanks go to Jaan Simon for his great help in putting together the manuscript to its—nal shape.