La = ( H 0 + d ) ⋅ tan 45 −
φ′ 2
+ d z ⋅ tan 45 +
φ′ 2
ANKRAJ
LEM
Ankrajlı Palplan Perdede ekil De i tirme ve Moment Diyagramı
a) Serbest Toprak Deste i Yöntemi
b) Ankastre Durum
Serbest Toprak Deste i Yönteminde minimum gömme derinli i
Dfree earth < Dfixed earth
b) Optimum position of plate or block Appropriate anchor zone: Place block/root beyond intersection of active and passive areas .
ÎŁM=0 at C
PALPLAN PERDEDE GÖÇME (AKSARAY)
KUMDA SERBEST TOPRAK DESTE LE ÇÖZÜM
KUMDA SERBEST TOPRAK DESTE
= =
=ρ⋅
→ +
=
Kazı tabanı altında
= =
+
+
+
⋅ + ρ′ ⋅
= ρ⋅
→
LE ÇÖZÜM
+
ρ′ ⋅ (
+ −
⋅
derinli inde net gerilme = 0
)
derinli inde net gerilme
DEF çizgisinin e imi 1 dü eye,
ρ′ ⋅
−
= ρ′ ⋅ yatay
−
⋅
Fx=0
Denge için
ΣMO’=0
ΣMO’=0
− ⋅
+
+ +
− ⋅
+ ⋅
⋅ ρ′ ⋅
+ +
+
−
− ⋅
⋅
⋅ + 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 ΣFx=0
AACDE-AEBF-T=0
=
−
⋅ ρ′ ⋅
−
⋅
⋅
−
− =
⋅
⋅ +
+ −
−
+ +
+ =
⋅
=
Max. teorik moment z=L1 and z=L1+L2 derinlikleri arasında olu acak. Kesme kuvvetinin 0, momentin maksimum oldu u derinlik,
⋅
⋅
z-L1=x olsun
−
+
⋅
⋅
⋅
− −
+ +
⋅ ⋅
Maksimum moment, 0 kesme kuvvetinin oldu u yerde moment alınarak bulunabilir.
+
⋅ ρ′ ⋅
−
=
⋅
⋅ ρ′ ⋅
=
ANKRAJLI ÇEL K PERDE DUVARDA MOMENT AZALTMA YÖNTEM (ROWE) PALPLAN R J TL ′=
+
ρ=
⋅
−
⋅
′ ⋅
+
MN/m2
m4/m
1. Uygun kesitte palplan seç 2. Bu kesitin kesit modülünü (S) bul ve atalet momentini (I) hesapla. 3. ρ yu hesapla 4. Kesitin direnç momentini hesapla ! = σ ⋅" 5. Kesit için e risini noktala.
! $%ρ − !#
6. 1−5 i lemlerini birkaç kesit için tekrarla. E rinin altında kalan kesitler güvensizdir. E rinin üstündekilerden seçim yap. (Md<Mmax)
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′ ⋅
−
''
⋅ =
= ⋅ =
' + (#
= ' '⋅
' ⋅ ''
+ (# +
=
' ⋅' ⋅
#
=
+ (#
= =
⋅
⋅
⋅ '
= =
+
⋅
⋅
+
!
=
⋅
ΣMO’=0
+
=
⋅
⋅
+
+'
+
=
+
⋅
+
⋅
+'
#
=
−
+
−
−
⋅
+
⋅ − '
⋅'
+
⋅
+
⋅
⋅
+ (# +
+
−
−
⋅
⋅
⋅
+
& , $-
⋅ ρ′ ⋅ (
⋅
⋅'
. & /
=
−
+ '
+'
+ ⋅
+
'
+'
⋅
⋅
⋅
⋅
+
+ ρ′ ⋅
+
⋅
'
−
+
=
=
⋅
& , $-
+ =
+'
= ⋅
+
+
=
−
''
#≈
#
#
)⋅
' ⋅ '' ⋅
=
+ (# ≈
⋅
=
#
=
− '⋅
=
⋅
+ (#
+
=
Max. teorik moment z=L1 and z=L1+L2 derinlikleri arasında olu acak. Kesme kuvvetinin 0, momentin maksimum oldu u derinlik (z),
⋅
⋅
−
+
⋅
z-L1=x olsun
⋅ '
⋅
−
⋅
−
⋅
−
+
+
⋅ ρ′ ⋅
−
=
+
⋅
⋅ ρ′ ⋅
=
⋅
+
⋅
⋅
⋅
+ '
+
⋅
−
=
+
=
⋅
=
'⋅
+
=
=
#
=
#
Maksimum moment, 0 kesme kuvvetinin oldu u yerde moment alınarak
!# = − ⋅ !# = − ⋅ '
⋅
⋅ ⋅
+ ⋅
+ +
+
⋅
+ ⋅
− +
⋅
− '
− ⋅
⋅ ρ′ ⋅
⋅ −
=
⋅
⋅
'⋅
⋅ ⋅
+# (#
′= ρ=
+
+ −
⋅
=
.& /
⋅
′ ⋅
MN/m2
Section
I (m4/m)
+' +
=
σall=172500 kN/m2, E=207000 MN/m2
251.5*106
! =σ
⋅"
m4/m
H’ (m)
ρ
log ρ
PZ-22 115.2*10-6 14.48 20.11*10-4 -2.7 PZ-27
#
14.48
S (m3/m) 97*10-5
9.21*10-4 -3.04 162.3*105
Md (kNm/m)
Md/Mma
167.33
0.485
284.84
0.826
PZ-27 yeterli
x
FREE EARTH SUPPORT METHOD FOR PENETRATION OF CLAY (having a granular soil backfill) '
+ ρ′ ⋅
⋅ .− ρ ⋅
=
0=
−
'
⋅
=
P1= area of the pressure diagram ACD T= anchor force per unit length of the sheet pile
!1 ′ = ⋅ '
⋅
+ ⋅
'
⋅
⋅
+
+
−
−
−
− ⋅
−
⋅(
'
+
⋅
⋅
−
+
−
+
)=
This equation gives theoretical depth of penetration, D Maximum moment occurs at depth L1<z<L1+L2. The depth of zero shear (and thus the maximum moment) may be determined from: ⋅
⋅
−
+
⋅
−
+
⋅
⋅ ρ′ ⋅
−
=
=
Various types of anchoring for sheet pile walls: a) anchor plate or beam b) tie back c) vertical anchor pile d) anchor beam with batter piles
ULTIMATE RESISTANCE OF TIE BACKS Kumda Ankraj Kapasitesi /
=π ⋅
⋅ ⋅ σ2′ ⋅
⋅& φ
σ2′ = ρ ⋅ 3) 454 6 )-$ & #&
≈ −" φ
Kilde Ankraj Kapasitesi /
=π ⋅
⋅ ⋅ α ⋅ ./
α=
./ >