2. The continuum and its coherence Stability analysis of a retaining wall

3. The continuum and its coherence Stability analysis of a retaining wall

4. The continuum and its coherence Stability analysis of a retaining wall

5. The continuum and its coherence Elementary surface forces Stability analysis of a retaining wall

6. The continuum and its coherence

7. Augustin CAUCHY 1789 -1857 Exercices de mathématiques (1829)

15. Linearity

19. Symmetry Equations of dynamics

20. Linearity Symmetry Equations of dynamics Cauchy stress TENSOR Classical presentation of the for modelling INTERNAL FORCES

21. Linearity Symmetry Equations of dynamics Cauchy stress TENSOR Classical presentation of the does not refer to any Stability or Rupture analysis

22. Potential collapse mechanisms Rotation about B Rigid body motion

23. Physical feeling of the Mathematical duality between internal forces and deformation of matter

24. The virtual work method

25. Geometrical Model The virtual work method

26. PRINCIPLE of virtual work Appropriate choice of virtual motions Geometrical Model The virtual work method DUALITY

27. PRINCIPLE of virtual work Appropriate choice of virtual motions Geometrical Model The virtual work method DUALITY

28. PRINCIPLE of virtual work Geometrical Model Representation of FORCES Appropriate choice of virtual motions The virtual work method DUALITY

29. Dimensional analysis The continuum and its coherence Yield design

30. Dimensional analysis The continuum and its coherence Yield design

31. Galileo

32. Yield design Galileo

33. Yield design considers that the beam acts as a lever with fulcrum in B. Galileo

34. Yield design resistance for the wood fibers on the other hand, assuming that they are in their limit state of tension. writes the balance equation for the moments at point B for the active load on the one hand Galileo

35. Yield design Coulomb

36. Yield design Coulomb resistance and the resistance of the material along Beg writes the balance equation between the active forces should look for the most unfavourable partition

37. The Theory of Yield design Galileo Coulomb Geometry of the system Multi-parameter loading process Resistance of the constituent materials a CONVEX domain is assigned to the STRESS state at any point of the system

38. The Theory of Yield design Galileo Coulomb Geometry of the system Multi-parameter loading process Resistance of the constituent materials What loads can be sustained by the system under these conditions

39. The Theory of Yield design Galileo Coulomb What loads can be sustained by the system under these conditions Equilibrium of the system Resistance of the materials must be mathematically compatible

40. The Theory of Yield design Galileo Coulomb for the loads that can be sustained by the system under these conditions Equilibrium of the system Resistance of the materials must be mathematically compatible

41. The Theory of Yield design for the loads that can be sustained by the system under these conditions Equilibrium of the system Resistance of the materials must be mathematically compatible

42. The Theory of Yield design Equilibrium of the system Resistance of the materials are mathematically compatible The domain of potentially safe loads is convex

43. The Theory of Yield design Equilibrium of the system Resistance of the materials are mathematically compatible The domain of potentially safe loads is convex Interior estimate

44. The Theory of Yield design Equilibrium of the system Resistance of the materials are mathematically compatible The domain of potentially safe loads is convex Exterior estimate?

45. must be mathematically compatible The Theory of Yield design Equilibrium of the system Resistance of the materials a CONVEX domain is assigned to the STRESS state at any point of the system

46. The Theory of Yield design Equilibrium of the system Resistance of the materials must be mathematically compatible a CONVEX domain is assigned to the STRESS state at any point of the system the CONVEX domain is defined by DUALITY at any point of the system through its SUPPORT FUNCTION on the VIRTUAL STRAIN RATES

47. The Theory of Yield design Equilibrium of the system Resistance of the materials must be mathematically compatible DUAL DEFINITION of the convex domain of potentially safe loads the CONVEX domain is defined by DUALITY at any point of the system through its SUPPORT FUNCTION on the VIRTUAL STRAIN RATES

48. The Theory of Yield design DUAL DEFINITION of the convex domain of potentially safe loads Constructing virtual velocity fields

49. The Theory of Yield design DUAL DEFINITION of the convex domain of potentially safe loads Constructing virtual velocity fields Writing the balance

50. The Theory of Yield design Constructing virtual velocity fields Writing the balance between the external forces rate of work DUAL DEFINITION of the convex domain of potentially safe loads

51. The Theory of Yield design Constructing virtual velocity fields Writing the balance between the external forces rate of work and the maximum resisting rate of work DUAL DEFINITION of the convex domain of potentially safe loads

52. The Theory of Yield design Constructing virtual velocity fields Writing the balance between the external forces rate of work and the maximum resisting rate of work DUAL DEFINITION of the convex domain of potentially safe loads Exterior estimate

53. The Theory of Yield design Constructing virtual velocity fields Writing the balance between the external forces rate of work and the maximum resisting rate of work DUAL DEFINITION of the convex domain of potentially safe loads Exterior estimate Support function defined by duality

54. Galileo The Theory of Yield design The virtual collapse mechanism is a rotation about fulcrum B.

55. Galileo Exterior estimate The Theory of Yield design

56. Coulomb The virtual collapse mechanism is a rigid body motion of BegC. Exterior estimate of the stability of the wall The Theory of Yield design

57. Ultimate Limit State Design The Theory of Yield design

58. According to the principle of Limit States Design, the design criterion is simply to design for equilibrium in the design limit state of failure. The design criterion could be expressed in the following way: R d ≥ S d S d is the design load effect calculated on the basis of the principles … The design resistance effect R d which in the case of the design of a footing is the design ultimate bearing capacity … N.K. OVESEN

59. According to the principle of Limit States Design, the design criterion is simply to design for equilibrium in the design limit state of failure. The design criterion could be expressed in the following way: R d ≥ S d S d is the design load effect calculated on the basis of the principles … The design resistance effect R d which in the case of the design of a footing is the design ultimate bearing capacity … N.K. OVESEN

60. According to the principle of Limit States Design, the design criterion is simply to design for equilibrium in the design limit state of failure. The design criterion could be expressed in the following way: R d ≥ S d S d is the design load effect calculated on the basis of the principles … The design resistance effect R d which in the case of the design of a footing is the design ultimate bearing capacity … N.K. OVESEN

61. According to the principle of Limit States Design, the design criterion is simply to design for equilibrium in the design limit state of failure. The design criterion could be expressed in the following way: R d ≥ S d S d is the design load effect calculated on the basis of the principles … The design resistance effect R d which in the case of the design of a footing is the design ultimate bearing capacity … N.K. OVESEN

62. For practical implementation to the design of structures this symbolical inequality must be given a quantitative significance Design RESISTANCE Effect Design LOAD Effect

63. For practical implementation to the design of structures this symbolical inequality is given a quantitative significance Design RESISTANCE Effect Design LOAD Effect through the dual approach within the theory of yield design.

64. Dimensional analysis The continuum and its coherence Yield design

65. Dimensional analysis The continuum and its coherence Yield design