summary analysis of slender structures dereviations for the standard des
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7/25/2019 Summary Analysis of Slender Structures Dereviations for the Standard Des
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Summary Analysis of Slender Structures: Dereviations for thestandard DEs
Analysis of Slender Structures (Technische Universiteit Delft)
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7/25/2019 Summary Analysis of Slender Structures Dereviations for the Standard Des
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Chapter 1 Axial forces and deformation
Geometric considerations
( hooke's law)
Boundary conditions
-Dirichlet (essential) value of solution u(o)=o
-Neumann ( natural) value of derivative N(L)=F
Solving strategy
Specifiy q as q0
or 0 and integrate
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7/25/2019 Summary Analysis of Slender Structures Dereviations for the Standard Des
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Geometric considerations
Solving strategy
Matching conditions
Sign convention
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7/25/2019 Summary Analysis of Slender Structures Dereviations for the Standard Des
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Chapter 2. Bending beams.
Geometric considerations
Considering ds as a straight line because dx is infinitesimal
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Relationships between load, shearforce and bending moment.
Vertical equilibrium
Moment equilibrium
Hooke's law
with
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7/25/2019 Summary Analysis of Slender Structures Dereviations for the Standard Des
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Solving strategy
Taking q as q0Boundary conditions the same as in chapter 1.
or 0 and integrate.
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7/25/2019 Summary Analysis of Slender Structures Dereviations for the Standard Des
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Chapter 3, shear beams
Geometric considerations
Small deformations so:
Hooke's law
Solving strategy
Taking q as q0Boundary conditions the same as in chapter 1.
or 0 and integrate.
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Chapter 4. Bending and shear.
(chapter 3)
(Hooke's law)
(chapter 2)
Solving strategy
If q=0 then:
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7/25/2019 Summary Analysis of Slender Structures Dereviations for the Standard Des
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Chapter 5, beams on elastic foundations
Shear beam
(Chapter 3)
Particular solutions
Bending beam
(chapter 2)
Particular solutions
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Solving strategy
Check the limit case v(infinite)=0, the term
is zero
with a symmetric load
Easy integrating:
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7/25/2019 Summary Analysis of Slender Structures Dereviations for the Standard Des
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Chapter 6, transverse cable systems
Cable under selfweight
since the effect of loads affect the overall geometry of the
cables. Superposition does not hold!
Moment equilibrium around point A, neglecting second order terms
Cable under distributed load
with u=Weight per unit length
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Horizontal component
Sag to span
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Chapter 7, combined systems
Parallel systems
( triangles)
(eliminate tan a)
Serie systems
Combined system
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Beam cable systems
Assumptions :
homogenous solution suspended bridge
(homogenous solution)
Particular solution suspended bridge
solution suspended bridge
( is eliminated)
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Shear beam-bending beam systems
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