ID: 1573
Course type: vocational and applied
Course coordinator: Buljak V. Vladimir
Lecturers: Anđelić M. Nina, Balać M. Igor, Buljak V. Vladimir, Milošević-Mitić O. Vesna, Petrović S. Ana
Contact: Buljak V. Vladimir
Level of studies: B.Sc. (undergraduate) Academic Studies – Mechanical Engineering
ECTS: 6
Final exam type: oral
Department: Department of Strength of Structures
The main scope of this course is to make students become familiar with tonsorial calculus with detailed applications within stress and strain analysis. Students will learn how to formulate and solve structural problems with elastic and inelastic material mechanical behavior. The main experimental techniques employed within stress and stain analysis will be presented within the course. Practical part of the course will contain exercises and demonstrations of the use of different types of extensometers. Finally, the main concept of full-field measurements of displacement field by the use of digital image correlation will be outlined to the students with practical demonstrations in the laboratory.
Upon fulfilling the course the students will be able to: 1. Perform detail stress and strain analysis for complex loading scenarios. 2. Describe constitutive equations for different elastic behaviors and understand foundation of formulating constitutive equations for diverse inelastic material behaviors. 3. Apply displacement method for solving structural problems. 4. Understand and apply strain measuring technique based on the employment of different types of extensometers.
1. Stress analysis. Definition of stress as tensorial quantity. Cauchy equations of equilibrium. Introduction to tensorial calculus. Change in stress components with rotation of reference axis. Principal stresses and principal planes. 2. Strain analysis. Definition of strain tensors. Principal stretches. Kinematic equations and compatibility conditions. 3. Constitutive equations. Formulation of relationship between stress components and strain components within elastic material response. Inelastic material behaviors. Formulation of constitutive equations for elasto-plastic material behavior for simple 1-dimensional case. Equivalent stresses for complex load cases. 4. Solution strategies for stress and strain analysis. Formulation of boundary value problem. Prescribing boundary conditions. Energy principles. Virtual work principle. Theoretical foundation of displacement method. 5. Outline of existing experimental methods applied within stress and strain analysis. Extensometers. Electro resistance strain gauges. Interfering methods and Moire method. 6. Different types of extensometers and strain gauges. Appropriate selection of strain gauges for different applications. Temperature correction. 7. Assessment of strain components in the case when principal stretches are known and in the case when they are unknown. Assessment of residual stresses by employing appropriate strain gauges. 8. Continuum displacement field measuring techniques based on digital image correlation.
1. Numerical examples of tesnorial calculus applied to the stress and strain analysis. Calculation of principal stresses and principal planes for given stress state in a point. Calculation of extreme values of shear stresses identification of their reference panes. 2. Calculation of principal stretches and their directions for given strain tensor components in a point. Calculation of extreme values of shearing strain. 3. Numerical examples of changing of stress and strain tensor component changes with rotation of coordinate system. 4. Examples of constitutive equations for elastic material behavior. Formulation of constitutive equations for inelastic material behavior in 1D. 5. Practical examples of displacement method. 6. Numerical examples of calculations of collapse load for beams and truss structures. 7. Practical examples of calculations of stress components on the basis of assessed strain components by employing strain gauges.
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“Constitutive modeling of engineering materials”, V.Buljak and G.Ranzi, Elsevier, 2021. ISBN: 978-0-12-814696-5 “Inelastic analysis of structures”, M. Jirasek, Z. Bazant, J. Wiley, 2002. ISBN: 0-471-98716-6 “Eksperimentalne metode u projektovanju konstrukcija”, V. Brčić, R. Čukić, Građevinska knjiga, 1988. ISBN: 86-395-0033-9
Total assigned hours: 75
New material: 20
Elaboration and examples (recapitulation): 10
Auditory exercises: 25
Laboratory exercises: 5
Calculation tasks: 0
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0
Review and grading of calculation tasks: 5
Review and grading of lab reports: 5
Review and grading of seminar papers: 0
Review and grading of the project: 0
Test: 0
Test: 3
Final exam: 2
Activity during lectures: 0
Test/test: 0
Laboratory practice: 5
Calculation tasks: 10
Seminar paper: 5
Project: 30
Final exam: 50
Requirement for taking the exam (required number of points): 0
“Constitutive modeling of engineering materials”, V.Buljak and G.Ranzi, Elsevier, 2021. ISBN: 978-0-12-814696-5; “Inelastic analysis of structures”, M. Jirasek, Z. Bazant, J. Wiley, 2002. ISBN: 0-471-98716-6; “Eksperimentalne metode u projektovanju konstrukcija”, V. Brčić, R. Čukić, Građevinska knjiga, 1988. ISBN: 86-395-0033-9