nm405_12b

23
0 ( ) tan 45 tan 45 2 2 a z L H d d φ φ = + - + +

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L H d d φ φ ( ) tan 45 tan 45 2 2 ′ ′ = + ⋅ − + ⋅ + 0 ANKRAJ LEM D free earth < D fixed earth Serbest Toprak Destei Yönteminde minimum gömme derinlii Ankrajlı Palplan Perdede ekil Deitirme ve Moment Diyagramı b) Optimum position of plate or block ΣM=0 at C PALPLAN PERDEDE GÖÇME (AKSARAY) KUMDA SERBEST TOPRAK DESTE LE ÇÖZÜM

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Page 1: NM405_12b

������

0( ) tan 45 tan 452 2a zL H d dφ φ′ ′� � � �= + ⋅ − + ⋅ +� � � �

� � � �

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ANKRAJ ��LEM�

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Ankrajlı Palplan� Perdede �ekil De�i�tirme ve Moment Diyagramı

a) Serbest Toprak Deste�i Yöntemi b) Ankastre Durum

Dfree earth < Dfixed earth

Serbest Toprak Deste�i Yönteminde minimum gömme derinli�i

Page 9: NM405_12b

Appropriate anchor zone: Place block/root beyond intersection ofactive and passive areas .

b) Optimum position of plate or block

ΣM=0 at C

Page 10: NM405_12b

PALPLAN� PERDEDE GÖÇME (AKSARAY)

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KUMDA SERBEST TOPRAK DESTE�� �LE ÇÖZÜM

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KUMDA SERBEST TOPRAK DESTE�� �LE ÇÖZÜM

= → = ⋅ ⋅� � ��������� � � � �ρ

′= + → = ⋅ + ⋅ ⋅� � � � ��������� � � � � � � � �ρ ρ

( )ρ=

′ ⋅ −�

� �

= + +� � �� � � �Kazı tabanı altında

= + + +� � � �� � � � � derinli�inde net gerilme ρ ′= ⋅ − ⋅� �� � � � �

DEF çizgisinin e�imi 1 dü�eye, yatayρ ′ ⋅ −� � � �

derinli�inde net gerilme = 0

Page 13: NM405_12b

Denge için Fx=0ΣMO’=0

ΣMO’=0

ρ′� �− ⋅ + + − + + ⋅ ⋅ − ⋅ ⋅ + + + ⋅ =� � �

� � � � � � � � �

� �� � � � � � � � �

� � � � � � � � � � � � � � �

ρ⋅ ⋅ + + − +� � � + ⋅ ⋅ + + − =

′ ⋅ −� � � � � �

� � � � �

� � � � ���� � � �

� �

� � � � � �� � � � �

� �

E�itlik deneme-yanılma yöntemiyle çözülerek L bulunur

ΣFx=0 � AACDE-AEBF-T=0

− ⋅ ⋅ − =� �

��

�� � �

ρ ′� �= − ⋅ ⋅ − ⋅ �

�� �

� � � � � �

E�itlik deneme-yanılma yöntemiyle çözülerek L4 bulunur

Dteorik=L3+L4 Dgerçek=1.3 to 1.4 Dteorik

E�er Kp* kullanılırsa, teorik derinli�i 30%-40% arttırmaya gerek yok

Page 14: NM405_12b

Max. teorik moment z=L1 and z=L1+L2 derinlikleri arasında olu�acak.

Kesme kuvvetinin 0, momentin maksimum oldu�u derinlik,

ρ ′⋅ ⋅ − + ⋅ − + ⋅ ⋅ ⋅ − =�

� � � � �

� �� � � � �

� � � � � � � � �

z-L1=x olsun ρ ′⋅ ⋅ − + ⋅ + ⋅ ⋅ ⋅ =�

� � �

� ��

� � � � � � �

Maksimum moment, 0 kesme kuvvetinin Maksimum moment, 0 kesme kuvvetinin oldu�u yerde moment alınarak bulunabilir.

Page 15: NM405_12b

ANKRAJLI ÇEL�K PERDE DUVARDA MOMENT AZALTMA YÖNTEM� (ROWE)

PALPLAN� R�J�TL���

′ = + +� � ���� � � �

1. Uygun kesitte palplan� seç

ρ − � �′= ⋅ ⋅ � ⋅

������� ��

� �

MN/m2 m4/m

1. Uygun kesitte palplan� seç2. Bu kesitin kesit modülünü (S) bul ve atalet momentini (I) hesapla.3. ρ yu hesapla4. Kesitin direnç momentini hesapla5. Kesit için e�risini noktala.

6. 1−5 i�lemlerini birkaç kesit için tekrarla. E�rinin altında kalan kesitler güvensizdir. E�rinin üstündekilerden seçim yap. (Md<Mmax)

σ= ⋅ ��! "

ρ −#�

�$% !

!

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Problem: L1=3.05 m, L2=6.1 m, l1=1.53 m, l2=1.52 m, c=0, φ=30�, ρ=16 kN/m3, ve ρsat=19.5 kN/m3.

a)Teorik ve gerçek gömme derinliklerini bulunuz.b) Ankraj kuvvetini hesaplayınız..c) Maksimum momenti hesaplayınız, Mmax.d) Rowe Moment Azaltma Yöntemiyle uygun palplan� kesitini bulunuz.

(σall=172500 kN/m2, E=207000 MN/m2)

φ� � � �= − = − =� � � �� � � �

� � �� �&� �� &� ��

� � ��

φ� � � �= + = + =� � � �� � ��

&� �� &� �� �� �

� = + = + =� � � �� � � �

&� �� &� �� �� �

− = − =� ����� ��''� � �

ρ ρ ρ′ = − = − = ����� ���� ��'� ()& * �+ #

ρ= ⋅ ⋅ = ⋅ ⋅ = �

� �

��'���� �'��� (

� � � �+ #

ρ ρ ′= ⋅ + ⋅ ⋅ = ⋅ + ⋅ ⋅ = �

� � �

�� � ��'���� ��'�'��� ����� (

� � � � �+ #

ρ= = =

′ ⋅ − ⋅�

���������

� � ��'���''�

� #

� �

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= ⋅ ⋅ + ⋅ + ⋅ − ⋅ + ⋅ ⋅� � � � � � � � �

� � �� �

� � �� � � � �

= ⋅ ⋅ + ⋅ + ⋅ − ⋅ + ⋅ ⋅� � ��'��� ���� �'��� '��� ������ �'����'��� ����� ����

� � ��

= + + + =����� ����� '���� ���� ������ (� �+ #

� �⋅� � � � � � � �= = ⋅ + + + ⋅ + + ⋅ + + ⋅ ⋅ =� � � � � � � � � � � � � � � � �

� ���� '��� '��� � ���� ������ ���� '��� ����� ���� '���� ���� ���� ����

� � � � ������

�!� #

ΣMO’=0ρ

⋅ ⋅ + + − +� � � + ⋅ ⋅ + + − =′ ⋅ −

� � � �� �� � � � �

� � � � ���� � � �

� �

� � � � � �� � � � �

� �ΣMO’=0

ρ� + ⋅ ⋅ + + − =

′ ⋅ −� � � � ���� � � �� �

� � � � �� �

⋅ ⋅ + + − +� � � + ⋅ ⋅ + + − =⋅

� �

� �

� ������ ����� '��� ����� ����� �������� ����� '��� ����� �

��'����''��� �

� =� ���� # � = + = + = ≈� � ���� ��� ���� ����&,�$�-� � � # #

� = ⋅ = ⋅ =��� ��� ��� ����.&/� &,�$�-� � #

( )ρ ′= − ⋅ ⋅ − ⋅ �

� � � � � �

= − ⋅ ⋅ ⋅ = ≈�������� ��'���''� ��� ������ ( ��� (

�� �+ # �+ #

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ρ ′⋅ ⋅ − + ⋅ − + ⋅ ⋅ ⋅ − =�

� � � � �

� �� � � � �

� � � � � � � � �

z-L1=x olsun ρ ′⋅ ⋅ − + ⋅ + ⋅ ⋅ ⋅ =�� � �

� ��

� � � � � � �

⋅ ⋅ − + ⋅ + ⋅ ⋅ ⋅ =�� � ��'��� ���� ��� �'��� ��'� �

� � �� �

� + ⋅ − = � =� ����� ����� � �� � � #

Max. teorik moment z=L1 and z=L1+L2 derinlikleri arasında olu�acak.

Kesme kuvvetinin 0, momentin maksimum oldu�u derinlik (z),

� + ⋅ − = � =� ����� ����� � �� � � #

� = + = + =� � ���� ����� � � #

ρ� � ′= − ⋅ ⋅ ⋅ + + ⋅ + − ⋅ − ⋅ ⋅ ⋅ ⋅� �� �

��

#� � � �

� ���� �� �����

� � � � �

� �! � � � � � �

� �= − ⋅ ⋅ ⋅ + + ⋅ + − ⋅ − ⋅ ⋅ ⋅ ⋅� �� �

��

#�

� ���� � � � ��'��� ���� � ����� ����� �'��� ��'��

� � � � � �!

= ����� (�+# #

Maksimum moment, 0 kesme kuvvetinin oldu�u yerde moment alınarak

Page 20: NM405_12b

′ = + + = + + =� � ���� '�� ���� �����.&/�� � � � #

σ= ⋅ ��! "

Section I (m4/m) H’ (m) ρ log ρ S (m3/m) Md (kNm/m)

Md/Mma

x

PZ-22 115.2*10-6 14.48 20.11*10-4 -2.7 97*10-5 167.33 0.485

σall=172500 kN/m2, E=207000 MN/m2ρ − � �′= ⋅ ⋅ � ⋅

������� ��

� �

MN/m2 m4/m

PZ-22 115.2*10-6 14.48 20.11*10-4 -2.7 97*10-5 167.33 0.485

PZ-27 251.5*10-

614.48 9.21*10-4 -3.04 162.3*10-

5284.84 0.826

PZ-27 yeterli

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FREE EARTH SUPPORT METHOD FOR PENETRATION OF CLAY (having a granular soil backfill)

ρ ρ ′= ⋅ − ⋅ + ⋅' � �� � � . � �

= � − ⋅ =� � '��0 � � �

P1= area of the pressure diagram ACDT= anchor force per unit length of the sheet pile

′ =� �1!

� �⋅ + − − − ⋅ ⋅ + + =� �� �

� � � � � ' � �� � ��

�� � � � � � � �

( )� ⋅ + ⋅ ⋅ ⋅ + − − ⋅ ⋅ + − − =�

' ' � � � � � � � �� � � � � � � � � � � � � � �

This equation gives theoretical depth of penetration, D

Maximum moment occurs at depth L1<z<L1+L2. The depth of zero shear (and thus the maximum moment) may be determined from:

ρ ′⋅ ⋅ − + ⋅ − + ⋅ ⋅ ⋅ − =�� � � � �

� �� � � � �

� � � � � � � � �

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Various types of anchoring for sheet pile walls: a) anchor plate or beam b) tie back c) vertical anchor pile d) anchor beam with batter piles

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ULTIMATE RESISTANCE OF TIE BACKS

π σ φ′= ⋅ ⋅ ⋅ ⋅ ⋅&�/ 2� � �

σ ρ′ = ⋅2 �

�� � 3)4�5�4��6��)�-$�

��#�&� �& φ≈ −� �� "��

Kumda Ankraj Kapasitesi

��#�&� �& φ≈ −� �� "��

Kilde Ankraj Kapasitesi

π α= ⋅ ⋅ ⋅ ⋅/ /� � . α = >���� ��/. ��