72758 - Advanced Structural Mechanics

Learning outcomes

The course is an extension and intensification of Mechanics of Solids and Structures. The goal of the course is to advance students' understanding of structural behavior and enhance their ability to apply structural analysis methods to civil engineering structures. Students will acquire knowledge in the following areas: Structural Matrix Analysis, i.e., techniques for analyzing 2D truss and frame structures using the Direct Stiffness Method and FEM software. Buckling Analysis, i.e., methods for buckling and post-buckling analysis of discrete and continuous systems, with FEM applications. Plastic Analysis, i.e., concepts of plasticity, incremental and limit analysis for truss and beam systems, also using FEM tools. The main skills developed during this course include: Proficiency in matrix analysis and the Finite Element Method (FEM) for analyzing truss and frame structures. Ability to evaluate buckling and post-buckling behavior of rigid and continuous systems, using equilibrium and energy methods. Competence in conducting plastic analysis of structural systems, including an understanding of plastic hinges. Software Proficiency: hands-on experience with FEM-based software for solving structural, buckling, and elasto-plastic problems. Analytical and critical thinking: enhanced ability to approach complex structural issues with theoretical and computational tools. The course contributes to the objectives of the master’s program related to the application of mathematical tools for interpreting, describing, and modeling structural problems.

Course contents

Requirements/Prior knowledge

The course is a continuation and intensification of Mechanics of Solids and Structures. Thus a prior knowledge and understanding of the static behaviour of planar truss and beam structures is recommended. All lectures, tutorials and office hours are in English. The course includes theoretical lectures (module 1), exercises and laboratory sessions (module 2). The latter will cover some practical aspects of the lectures. The instructors will supervise students during the exercises and laboratory activities.

Course Contents

1. Structural matrix analysis

1. Truss element: mathematical and discrete models

2. Structural matrix analysis for truss structures in 2D

3. Basic concepts of the Finite Element Method

4. Beam element: mathematical and discrete models

5. Structural matrix analysis for frame structures in 2D

6. Use of a FEM based software for the solution of truss and beam problems

2. Buckling analysis

1. Equilibrium and energy method for buckling and post-buckling analysis of single and multi-degree-of-freedom rigid systems

2. Equilibrium approach for buckling of continuous systems (beams, trusses and frames)

3. Buckling analysis via stiffness matrix method: the geometric stiffness matrix

4. Use of a FEM based software for the solution of buckling problems in discrete and continuous problems

3. Plastic analysis

1. Fundamentals theorems of plasticity

2. Plastic moment, plastic hinge, and interaction diagrams

3. Incremental plastic analysis of truss and beam systems

4. Limit analysis Plastic analysis of beams

5. Use of a FEM based software for the solution of elasto-plastic problems of truss and beam systems

Readings/Bibliography

Learning Resource

• Instructors’ notes.
• Problem sets with solutions.
• Exams with solutions.

Class/lab notes, solved exercises, solved exams, manual of the software, are available to download in Virtuale: https://virtuale.unibo.it/

Suggested readings

• Matrix Structural Analysis, W. McGuire, R.H. Gallagher, R.D. Ziemian, John Wiley & Sons, 2000.

• Fundamentals of Structural Stability, G.J. Simitses, D.H. Hodges, Elsevier, 2006.

• Advanced Structural Mechanics. A. Carpinteri, Taylor & Francis, 1997.

Teaching methods

The course content will be entirely covered by lectures. The course includes laboratory sessions, which will cover some practical aspects of the lectures. The instructors will supervise students during the laboratory activities.

In consideration of the type of activity and the teaching methods adopted, the attendance of this training activity requires the prior participation of all students in the training modules 1 and 2 on safety in the study places, in e-learning mode.

Assessment methods

The assessment of the "expected learning outcomes" is composed of:

• written test: 3 exercises, 3 hour (30 points)
• oral test: 3 questions on the topics of the course including the discussion of the homework*, 1 hour (30 points)

Written and oral tests are closed-book and closed-note. For the written test, calculators and one page of cheat sheets are permitted.

The final grade is the average of the written and oral tests.

*Homework (to be discussed at the oral exam)

• Homework 1: small project focused on structural matrix analysis (topic 1)
• Homework 2: small project focused on structural buckling analysis (topic 2)
• Homework 3: small project focused on structural plastic analysis (topic 3)

To obtain a passing grade (minimum is 18 points) students are required to demonstrate a knowledge of the key concepts of the subject, some ability for critical application, and a comprehensible use of technical language.

Higher grades (maximum is 30 points, cum laude) will be awarded to students who demonstrate an organic understanding of the subject, a high ability for critical application, and a clear and concise presentation of the contents.

In case of failure students can take any next final term, generally there are 6 final terms per academic year.

Teaching tools

The teaching tools are overhead projector, projector and tablet. The course includes some laboratory sessions in which a finite element based software for structural analysis is used.

Office hours

See the website of Alessandro Marzani

See the website of Antonio Palermo

See the website of Stefano Mariani