Text of The continuum and its coherence Stability analysis of a retaining wall
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The continuum and its coherence Stability analysis of a
retaining wall
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The continuum and its coherence Stability analysis of a
retaining wall
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The continuum and its coherence Stability analysis of a
retaining wall
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The continuum and its coherence Elementary surface forces
Stability analysis of a retaining wall
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The continuum and its coherence
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Augustin CAUCHY 1789 -1857 Exercices de mathmatiques
(1829)
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Linearity
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Symmetry Equations of dynamics
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Linearity Symmetry Equations of dynamics Cauchy stress TENSOR
Classical presentation of the for modelling INTERNAL FORCES
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Linearity Symmetry Equations of dynamics Cauchy stress TENSOR
Classical presentation of the does not refer to any Stability or
Rupture analysis
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Potential collapse mechanisms Rotation about B Rigid body
motion
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Physical feeling of the Mathematical duality between internal
forces and deformation of matter
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The virtual work method
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Geometrical Model The virtual work method
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PRINCIPLE of virtual work Appropriate choice of virtual motions
Geometrical Model The virtual work method DUALITY
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PRINCIPLE of virtual work Appropriate choice of virtual motions
Geometrical Model The virtual work method DUALITY
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PRINCIPLE of virtual work Geometrical Model Representation of
FORCES Appropriate choice of virtual motions The virtual work
method DUALITY
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Dimensional analysis The continuum and its coherence Yield
design
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Dimensional analysis The continuum and its coherence Yield
design
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Galileo
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Yield design Galileo
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Yield design considers that the beam acts as a lever with
fulcrum in B. Galileo
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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
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Yield design Coulomb
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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
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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
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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
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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
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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
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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
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The Theory of Yield design Equilibrium of the system Resistance
of the materials are mathematically compatible The domain of
potentially safe loads is convex
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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
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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?
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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
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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
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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
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The Theory of Yield design DUAL DEFINITION of the convex domain
of potentially safe loads Constructing virtual velocity fields
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The Theory of Yield design DUAL DEFINITION of the convex domain
of potentially safe loads Constructing virtual velocity fields
Writing the balance
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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
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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
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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
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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
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Galileo The Theory of Yield design The virtual collapse
mechanism is a rotation about fulcrum B.
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Galileo Exterior estimate The Theory of Yield design
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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
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Ultimate Limit State Design The Theory of Yield design
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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
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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
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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
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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
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For practical implementation to the design of structures this
symbolical inequality must be given a quantitative significance
Design RESISTANCE Effect Design LOAD Effect
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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.
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Dimensional analysis The continuum and its coherence Yield
design
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Dimensional analysis The continuum and its coherence Yield
design