Analytical Methods in Bin Load Analysis

The storage and handling of bulk materials is a cross-disciplinary field of technology with applications in several branches of engineering, including civil, chemical, mechanical, agricultural and materials processing. Accordingly, the experimental findings and the theoretical backgrounds for the design and operation of storage facilities such as bins and hoppers are dispersed among books and journals of various disciplines. This book provides a comprehensive and systematic review of some of the analytical methods used in the study of loads that bulk materials exert on the walls of bins or hoppers. Methods for shaping their geometry to provide an adequate operational function are also discussed. Emphasis is placed on the theoretical basis for methods that apply to those handling operations that involve a slow or moderate motion of bulk material and that allow solid mechanics to be applied successfully. Three groups of analytical methods that have found application in the study of bin-loads and bin/hopper geometry design are presented in detail: the limit state methods, the methods of differential slices, and the methods of plastic limit analysis. All are approximate methods with various degrees of simplification. The limit state methods involve least approximations, thus being regarded as the most accurate. However, the simplicity and flexibility of the less accurate methods of differential slices makes them the primary tool in bin-load analysis in engineering practice. The methods of plastic limit analysis are located somewhere in between the other two methods with respect to approximations involved. This volume will provide a useful reference on the implications of the latest analytical methods in the study of bin-loads, and will help to initiate and guide future research in this area.

Table of Contents:
1. Mechanics of Storage and Flow of Bulk Solids. 2. Mechanical Properties of Bulk Solids. Introduction. Stress-strain response of bulk solids. The rigid hardening/softening plastic model. The rigid perfectly plastic model. Yield conditions and flow rules. Determination of flow parameters of bulk solids. 3. Analytical Methods of Solution for the Rigid-Perfectly Plastic Model. Problem formulation. Limit state methods. Limit state in plane-strain. Limit state in axisymmetry. Differential slice methods. The direct method of slices. The indirect method of slices. Limit analysis methods. Limit load in bins and hoppers. Theorems of limit analysis. The statical method. The kinematical method. Energy balance. Velocity field for a non-associative material. Closing remarks. 4. Bin-Loads in Quasi-Static Mass Flow. Limit state methods solutions. Stresses in bins. Stresses in hoppers. Direct method of slices solutions. Stresses in bins. Stresses in hoppers. Determination of constant K for bins. Determination of constant K for hoppers. Distribution of wall stresses. Stresses in non-symmetric hoppers. Indirect method of slices solutions. Stresses in bins. Stresses in hoppers. Kinematical method of limit analysis solutions. Stresses in bins. Stresses in hoppers. 5. Bin-Loads in Steady Inertial Mass Flow. Direct method of slices solutions. Stresses in bins for incompressible flow. Stresses in hoppers for incmpressible flow. Stresses in dilating/contracting flow. Rate of flow. 6. Bin-Loads in Unsteady Inertial Mass Flow. Direct method of slices solutions. Stresses and rate of incompressible flow in bins. Stresses and rate of incompressible flow in hoppers. 7. Arching. Structural mechanics approach. Continuum mechanics approach. Direct method of slices. Kinematical method of limit analysis. 8. Channeling. Kinematical method of limit analysis approach. Partial collapse. Axisymmetric collapse. References. Appendices. Glossary of symbols. Author index. Subject index.