Nonlinear Structural Analysis

Prerequisite Knowledge

All courses in Mechanics (Solid and Dynamics of the Solid Body, Mechanics of the Deformable Body), Determinate Structures, Indeterminate Structures, Matrix Theory of Structures, Structural Dynamics, Numerical Analysis.

Course Units

#	Title	Description	Hours
1	Importance of the plastic consideration	Advantages of plastic versus elastic structural analysis. Force redistribution. Ductility. Impact of the plastic approach on the Steel, Concrete and Earthquake Codes.	4
2	Pure plastic bending	Plastic bending. Rectangular Cross section. Steel and concrete cross sections. Beam of a general cross section.	4
3	Plastic bending with axial loading	Influence of the axial loading. Interaction surfaces. Unloading.	4
4	Influence of shear on the plastic behavior	Plastic bending with shear.	4
5	Step by step elastoplastic analysis	Zero length plastic hinges. Step-by-step elastoplastic analysis of determinate and indeterminate structural systems using classical structural analysis. Estimation of the displacements prior to collapse.	4
6	PVW in the elastoplastic analysis	Formulation of the principle of virtual work (PVW) in the elastoplastic analysis. Statically admissible distribution of moments. Kinematically admissible mechanisms.	4
7	Plastic limit analysis theorems	Proportional loading. Lower and upper bound theorems of limit analysis. Significance of the lower limit in the design of structures. Connection with concrete and steel Codes. Theorem of uniqueness. Properties of the collapse load.	4
8	Estimation of the collapse load Independent mechanisms	Independent mechanisms. Method of superposition of mechanisms. Evaluation of the collapse load in framed structures.	4
9	Optimum plastic design	Optimum plastic design. Graphical solution.	4
10	Computational step by step elastoplastic analysis	Material nonlinear analysis. Development of the method-computational steps. Elastoplastic stiffness matrix (Plastic Flow Rule). Semester Project. Different simulations (concentrated, distributed plasticity).	4
11	Concentrated plasticity approach	Basic concepts. Simple and generalized yield criteria.	4
12	Distributed plasticity approach	Distributed plasticity. Introduction, difference with concentrated plasticity. Calculation of member forces.	4
13	Numerical and programming techniques in nonlinear analysis	Numerical techniques in computational elastoplastic analysis. Calculation of the tangent stiffness matrix. Newton-Raphson Method.	2
14	Dynamic plastic analysis	Plastic shear beam model. Formulation and solution of the equations of motion. Presentation of results and annotations for the case of seismic loading.	2

Learning Objectives

Upon successful completion of the course, students will be able to:

1. know the basic principles of plastic behavior of frame structures
2. understand the concept of collapse and the basic static behavior principles that govern it
3. construct the collapse mechanisms in frame structures
4. calculate manually, but also computationally, the collapse load of frame structures.

Teaching Methods

Teaching methods	Class lectures and workshops.
Teaching media	Theory-Applications and Exercises from the Black-Board. Calculations on PC using Excel and source codes.
Computer and software use	Students solve the questions of the semester project using EXCEL on PCs. Use of commercial software (eg. Seismostruct http://goo.gl/UqUqmE) for non-linear static analysis based on the consideration of concentrated and distributed plasticity.
Problems - Applications	Yes
Assignments (projects, reports)	Yes

Student Assessment

• Final written exam: 70%
• Assignments (projects, reports): 20%
• Problems - Applications: 10%

Textbooks - Bibliography

1. Επίλυση και Σχεδιασμός των Γραμμικών Φορέων με την Μέθοδο της Πλαστικότητας Βαρκαράκης Κ.Ι. Εκδόσεις Ε.Μ.Π. 1988 Αθήνα.
2. Σημειώσεις Στατικής V. Πλαστική ανάλυση ραβδωτών φορέων. Σύγχρονες μέθοδοι. Παπαδρακάκης Μ. Εκδόσεις Τσότρας 2013 Αθήνα.

Lecture Time - Place:

• Monday, 12:45 – 14:30,
  Rooms:
  • Ζ. Κτ. 1 Πολ., Αιθ. 7
• Tuesday, 12:45 – 14:30,
  Rooms:
  • Ζ. Κτ. 1 Πολ., Αιθ. 12