Advanced Plastic Analysis of Framed Structures

Introduction to the plastic design of structures. Redistribution of forces. Ductility. Relation with the Codes of Practice. Step-by-step 1st order elastoplastic analysis of frames. Principle of virtual work. Lower and upper bound theorems of plastic collapse. Safe moment distribution. Collapse mechanisms. Holonomic and non-holonomic behaviour. Mathematical programming. Kuhn-Tucker conditions. Linear programming. Simplex method. Mesh and nodal description. Static-kinematic duality. Flow rule. Stable materials. Rigid plastic behaviour. Alternative linear programs of limit analysis. Uniqueness of limit load. Automatic limit load evaluation. Optimal plastic design. Automatic optimal plastic design using linear programming. Variable loading. Alternating plasticity. Incremental collapse. Shakedown. Residual stress. Melan’s theorem. Mesh-unsafe shakedown linear program and automatic shakedown load evaluation. Relation between limit and shakedown load. Elastoplastic analysis with 2nd order effects. Large displacements. Geometric non-linear elasto-plastic stiffness matrix. Arc-length method. Comparison of limit loads with and without 2nd order effects. Merchant-Rankine formula. Inelastic dynamic analysis of MDOF systems. Seismic response of buildings. Ductility ratios. Pounding of buildings. Reference to approximate static methods (pushover, etc.). Practice with commercial packages (SAP, Abaqus, etc.).

Scope

The course aims to the in-depth understanding of the inelastic behaviour of framed structures since plasticity is the basis of all today’s Codes of Practice. Emphasis is also put on the mathematical framework and the computational techniques of plastic analysis. In this way the course addresses both the practicing engineer and the researcher.