Grinda Pe Mediu Elastic - PPT

8/12/2019 Grinda Pe Mediu Elastic - PPT

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La ce se foloseste calculul grinzii pe mediu elastic

Radier baraj deversor

Radier ecluze de navigatie

Radier centrale hidroelectrice

Radier rezervor apa

Radier desnisipator *

Coca vapoarelor, etc


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Calcul radier pe mediu deformabil

Radierul&

Terenul de fundare

Stare de deformatie planat=ct

q=ct

Toate sectiunile* au aceleasi deformatii calcul pe fasie de 1 m

Stare dedeformatie plana

Lradier = (teoretic)

Lradier > 3 x B (practic)

( capete)

det. reactiunilorterenului

NN

M

M


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Modele de calcul


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Modele de calcul Ecuatii matematice

Ecuatiilematematice(Interactiune

constructie teren)

modul de comportare al terenului

fibra medie deformata a radierului

= + ()

p = k

p = + 1 + 22 + 33 + +

Winkler

Gurbonov-Posadov

p = +2

2 +

(

2)2+

8

( 2)3

Simvulidi


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Winkler Model

=

=

Reactiunea fundatiei este proportionala cu deplasarea grinzii in acel punct

Ipoteza introdusa de E. Winkler in 1867

Se recomanda aplicarea acestui model pentru calculul fundatiilor in fazele de predimensionare

include rigiditatea grinzii sielasticitatea fundatiei =

4

Caracteristica sistemului

N

mcoeficientul de pat


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Rigiditatea grinzii

Caracterizeaza rigiditatea relativa a grinzii in raport cu mediul elastic

< 0.5 ( 4 )

> 5 ()

0.5 4 < < 5 ()

Short beam

Medium beam

Long beam

The beam deformation can beneglected beams absolutely rigid computed using statics

Loads applied at one end have afinite and not negligible effect onthe other end no approximationsare possible

The effect of a Load applied at oneend can be neglected at the otherend computations are greatlysimplified

A(l)=B(l)=C(l)=D(l)=0


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Mathematical expressions for y M T

= 1() +1

2()

1

3()

1

()

1

3(( )) +

1

(( )) +

1

(( ))

= 1 1 2() 1

3() 4() 1 2(( )) + 1

3(( )) + 1

3(( ))

= 1 +1

2 +

3() +

() +1(( ))

1

2(( )) -

1

2(( ))

= 1 +

2 +

3() 4() 4(( )) 1(( )) -

1(( ))

= = 2

2 =

1 = cosh() cos()

2() =1

2 cosh sin + sinh() cos()

3 =1

2 sinh() sin()

() = 12 cosh sin sinh() cos()


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Winkler model advantages and disadvantages

Dezavantaje:

k nu are sens fizic. Este determinat din testele realizate pe teren (cu placa).

exista o serie de formule pentru k (functie de E,) dar dau valori diferite

nu se poate determina k din aceste formule.

k depinde de: proprietatile fizice ale fundatiei

forma si dimensiunile placii cu care se realizeaza testeleforta concentrata aplicata in timpul testelor

modelul nu considera efectul incarcarilor si deplasarilor laterale

o incarcare uniform distribuita nu produce moment incovoietor, in realitate estefals

Avantaje:

pentru fundatii granulare metoda ofera rezultate bune

Foarte folosit deoarece este un model usor de inteles


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Winkler Example

k=50000 K=kPaLg=15mhg=2m

a = 1.5 mc = 3 mconcrete beam

P=500 kNM = 150 kNmq = 10 kN/m

s = - 20 kN/m

Ansys beam54 elements


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Gurbonov Posadov Method

it is based on Boussinesq/ Flamandmodels (elastic half-space/ half-plane model)

the soil is replaced by a solid body with the following characteristics:

extends laterally and down elastic linear deformable homogeneous and isotropic

Disadvantages:

overestimate the settlements

settlements at the ends tend to infinite

overestimates the moments

the model doesnt consider the lateral loadings

Boussinesq spatial problem

Flamand - plane problem


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Gurbonov Posadov Method

= + ()

= + 1 + 22 + 33 + + Exponential series

polynomial equation (n degree)

, 1, 2, - unknowns

n = 10 (practical reasons)

In order to calculate y, M, T G.P. realized tables for unitary loadings

The tables are realized for half of the slab foundation (because the loadingsare symmetrical).

This half is divided in 10 parts where the efforts, moments and shear forceare calculated.


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N NT TM MPa

S

gr

p

N* N*

M* M*

Equivalent loadings on the floor


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Gurbonov Posadov Tables


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flexibility index

t < 1 short beam (absolutely rigid)1


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Gurbonov Posadov Example

Grinda Pe Mediu Elastic - PPT

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