Summary Analysis of Slender Structures Dereviations for the Standard Des

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)

Verspreiden niet toegestaan | Gedownload door Johan de boon ([email protected])

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http://www.studeersnel.nl/nl/course/technische-universiteit-delft/analysis-of-slender-structures/14365?auth=1&auth_prem=1&em=0http://www.studeersnel.nl/nl/document/technische-universiteit-delft/analysis-of-slender-structures/summaries/summary-analysis-of-slender-structures-dereviations-for-the-standard-des/89826?auth=1&auth_prem=1&prem_doc=1&testVersion=http://www.studeersnel.nl/nl


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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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Solving strategy

Matching conditions

Sign convention


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Chapter 2. Bending beams.


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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Solving strategy

Taking q as q0Boundary conditions the same as in chapter 1.

or 0 and integrate.


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Chapter 3, shear beams


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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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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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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Summary Analysis of Slender Structures Dereviations for the Standard Des

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