Topic outline

  • Course name:  Stability of Structures

    Schedule for exercise (homework guided sessions):



    In short: In this course, we study the elastic stability structures.

    The primary question, even an engineering design question, is under which conditions an equilibrium becomes unstable.

    The content is conceptually very short having only three fundamental concepts to study: 1) equilibrium, 2) its stability properties and 3) sensitivity of such equilibrium to imperfections

    Many applications of structural stability of typical structural elements commonly used in civil engineering will be studied.


    This course have a very dense and demanding content and six weeks is short.

    The weekly homework topics and the associated readings will be the 'GPS' guiding the student through the necessary material to learn.

    The lectures will concentrate on the key topics and on the invariant fundaments while illustrating all that through examples.   

    Therefore, first we address the physics (mechanics) of instability phenomena (observation) then we try to find the minimum number of degrees of freedom to describe mathematically the problem using first principles (posing or setting the problem) and thirdly, we try to find practical solutions of importance for understanding and doing quality structural design.
    We will not hide the phenomena behind unnecessary complexe mathematics: First comes the physics then the mathematics follows as an instrument of thoughts (ajattekuväline) to obtain handels which gives us the buckling equations. (our mathematics will be the theorem: at a STABLE equilibrium the total potential energy has a local minimum for a conservative system) ,
    and the universal  virtual work principle for both conservative and non-conservative systems

    The student is encouraged to prepare for lectures and homework cessions, at least, by doing the reading assignments on time from references [1] and [2], below. You are working for yourself. Doing actively homework assignments will guide you through te readings and help you to deepen and consolidate what you have learnt.

    Please, do not concentrate to much on subjective workload-concept only since “workload” is just the amount of personal time each one invests in studying new skills and knowledge. Think that you are training to be among the best ... engineers. "What we can gain?" is the correct question not the price in hours. (of course, the work should be doable in six-seven week… and it is)

    D.B, 2021


    Djebar BAROUDI, DR.
    h. 229


    1.    Flexural buckling (nurjahdus)
    2.    Lateral-torsional buckling (kiepahdus)
    3.   Torsional buckling (vääntönurjahdus)
    4.   Buckling of thin plates (levyjen lommahdus)
    5.   Buckling of shells (kuorien lommahdus)


    • CHAI H. YOO &  SUNG C. LE .    STABILITY OF STRUCTURES - Principles and Applications, 2011 Elsevier e-textbook (our course main textbook)
    • Lecturer own pdf-material ---> weeks 1 ... 6 (will be provided weekly)
    • Solutions of homewok
    Additinal reading: (not compulsory)
    • S.P. Timoshenko & J.M. Gere.   Theory of Elastic Stability.  2nd Ed., 1985.  (Classical textbook)
    • Juha Paavola. Structural Stability.   Lecture note - 2018 (pdf in MyCourses) .       (This is a 'must-read' for those interrested in general and systematic energetic approach for elastic stability. .. by Emer. prof. J. Paavola)
    • Markku TUOMALA's Lectures notes: Elastic Stability of structures (lecture notes in Finnish: Rakenteiden stabiilisuusteoria, luentomoniste). 

     (A masterpiece by  M. Tuomala following the long Finnish tradition of mechanics masters to cite some of them like A. Ylinen, M. Mikkola, P. Jumppanen,  E-M. Salonen, J. Aalto, J. Paavola, R. Kouhia, T. Salmi  and many others. This material provides  theorethical basis together with plenty of solved application examples:

    • Lecture's own material: Stability of structures (D. Baroudi) 
    • [they are in given in ...]
    A short review article: Fundaments of stability of structures with examples:

    The course:

    This course is rich in various applications of structural stability. Despite this variety of applications, it is conceptually short having only three fundamental concepts to study: 1) equilibrium, 2) its stability properties and 3) sensitivity of such equilibrium to imperfections

    Please invest actively time wisely to achieve these intended learning goals by doing responsibly the weekly given readings together with the homework. Participating actively to lectures will, for sure, shorten the learning process by minimising unnecessary dissipation.

    Bellow the learning outcomes are recalled in details:

    •  Recognising the key importance of stability of structures as a primary requirement for

    engineering load-bearing structures

    •  Understand thetheoretical foundations of the concept of Equilibrium and Stability of an


    • Understand the meaning of equilibrium paths and post-buckling
    • Understand the physics and mathematics of equilibrium transition from stable to unstable
    • Ability to apply  the energy-based stability analysis 
    • knows how to address the effect of initial imperfections on stability behaviour
    • Ability  to systematically apply the above fundamental energy concept to study the stability of various structures of importance of Civil Engineering, for instance,  frame structures, warping torsion and Saint-Venant torsion of thin-walled members, plane buckling of plane frames and arches, torsional and lateral buckling of thin-walled members and  buckling of plates and cylindrical shells


    • Teacher: Djebar Baroudi, Dr.,
    • Language: English - Finnish terminology will be also provided during the lectures
    •  Credits: 5 cr (op)

    Teaching methods
    • Lectures: 2h x (2 x week) := 4h/week – contact teaching – lecturing and demonstration with

    physical and computer models

    • Guided exercises/homework solving: 2h x (3 x week) – contact teaching – with the re-

    sponsible teacher and an assistant from the industry (a professional) 

    • Self-studies in small groups or alone: at least 2h/day x6weeks x7days = 84 h – not Contact

    teaching: preparing, doing the reading assignments, assimilating the course subjects and
    given readings 
    Assignments + doing the homework outside the guiding hours

    • Examination: 3x3h – three times during the academic year– student personal performance in a written examination
    • Grade 0-1, 0 := fail, 1-5 := pass

    •  Independent studying 50%: (reading and preparation 26%, home assignments 27%),
    • Contact teaching 50% - covers the smaller complement (lectures 22%, exercise sessions

    26%, examination 2%).
    For instance,  ~nominal hours (total 132) should guarantee for a student with average pre-requi-
    sites (grade 3, good) middle range learning outcomes (with the average grade 3, good).