betonarme kalin temellerde kesme ve kesme surtunmesi hesabi · gİrİŞ 3 kesme ve kesme...

BETONARME KALIN TEMELLERDE KESME VE KESME SÜRTÜNMESİ HESABI

BALKAR İNŞAAT MÜHENDİLİĞİ VE MÜŞAVİRLİK LTD. ŞTİİNŞ. YÜK. MÜH. İRFAN BALIOĞLU

İNŞ. YÜK. MÜH. ÖZCAN KEÇELİOĞLUİNŞ. YÜK. MÜH. COŞKUN KUZUŞ Ş

İÇERİKÇ

2

GİRİŞ•KESME HESABI•KESME SÜRTÜNMESİ HESABI

KESME HESABIKESME HESABI•KALIN TEMELLERDE KESME HESABI•ACI 318’ E GÖRE KESME HESABI•TS 500’ E GÖRE KESME HESABI

Ü Ü İKESME SÜRTÜNMESİ HESABI•KESME SÜRTÜNMESİ NEDİR?•ACI 318’ E GÖRE KESME SÜRTÜNMESİ HESABI•ACI 318’ E GÖRE GELİŞTİRİLMİŞ KESME SÜRTÜNMESİ HESABI

’ Ö İ İ İ İ İ İ Ü Ü İ•ACI 318’ E GÖRE KOMPOZİT BETONARME KİRİŞ ANALOJİSİ İLE KESME SÜRTÜNMESİ HESABI•AASHTO’ YA GÖRE KESME SÜRTÜNMESİ HESABI

ÖZET VE SONUÇLAR

PROJELENDİRME VE SAHA UYGULAMALARIPROJELENDİRME VE SAHA UYGULAMALARI•ÇİZİM DETAYLARI•SAHA UYGULAMALARI

SORULAR

18.06.2015BETONARME KALIN TEMELLERDE KESME VE KESME SÜRTÜNMESİ HESABI

GİRİŞŞ

3

KESME VE KESME SÜRTÜNMESİ

TEMEL KALINLIĞININ TAYİNİTEMEL KALINLIĞININ TAYİNİZIMBALAMA KONTROLÜKALIN TEMELLERHİDRATASYON ISISIKADEMELİ BETON DÖKÜMÜTEMEL ALTI GERİLMELER


KESME HESABI

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KESME HESABIKESME HESABI


KESME HESABI

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KESME HESABI

ACI 318’ e göre Kesme HesabıKesme KontrolüTasarım LimitleriMinimum DonatıMaksimum Kesme KapasitesiÖrnekler

TS500’ ö K H bTS500’ e göre Kesme HesabıKesme KontrolüTasarım LimitleriMinimum DonatıMaksimum Kesme KapasitesiÖrneklerÖrnekler


KESME HESABI: ACI 318’ E GÖRE KESME HESABI

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KESME KONTROLÜ

u cV 0.5 V φ≤ ⋅ ⋅ ⇒ Kesme Donatısına Gerek YokturDurum 1:

u c u cV > 0.5 V and V V φ φ⋅ ⋅ ≤ ⋅ ⇒ Minimum Kesme DonatısıDurum 2:

Kesme Donatısı Hesabı Yapılmalıu cV > V and φ ⋅ ⇒Durum 3:



7

KESME DONATISI HESABI

/ uetn u w

VV V bφ= = ⋅

( )0.17 '

/ 0 17 '

n u w

c c wV f d b

V V V V f d b

φφ

λ

φ λ

= ⋅ ⋅ ⋅ ⋅

( )( )

/ 0.17 '

/ 0.17 '

s n c uet c w

uet c wv s

V V V V f d b

V f d bA Vs f d f d

φ λ

φ λ

= − = − ⋅ ⋅ ⋅ ⋅

− ⋅ ⋅ ⋅ ⋅= =

0.17 '/

yt yt

cv uetv

t t

s f d f d

fA Vb s f d f

λφμ

⋅ ⋅

⋅ ⋅= = −

⋅ ⋅

0.17 'w yt yt

uet v yt c

b s f d f

V f d f dφ μ φ λ= ⋅ ⋅ ⋅ − ⋅ ⋅ ⋅ ⋅



8

MİNİMUM KESME DONATISI

min '0 062 ' 0 062v cw A fb sA f ⋅ ,min

,min ,min

,minmin min

0.062 ' 0.062

0.350.35

v cwv c v

yt w yt

vwv v

fA f

f b s f

Ab sAf b f

μ

μ

= ⋅ ⋅ ⇒ = = ⋅⋅

⋅= ⋅ ⇒ = =,min ,minv v

yt w ytf b s fμ

⋅

İ İ İMAKSİMUM KESME KAPASİTESİ (DONATI)

,max 0.66 's c wV f d b= ⋅ ⋅ ⋅



9

ÖRNEK 1: c

y

Concrete : C50 f ' =50MPaSteel : S420 f = 420MPa

uet

h= 2.50m foundation d= 250-0.05-0.30/2=2.30V = 450 t/m =4500 kN/m= 4500000 N /m (obtained from Etabs)

BETONUN KESME DAYANIMINA KATKISI:

0.17 '

0 17 1 00 50 1000 2300c c wV f b d

V

λ= ⋅ ⋅ ⋅ ⋅

0.17 1.00 50 1000 23002765000

c

c

VV N

= ⋅ ⋅ ⋅ ⋅=

0 5 0 5 0 75 2765000 1040000V Nφ0.5 0.5 0.75 2765000 10400000.75 2765000 2075000

c

c

V NV Nφ

φ⋅ ⋅ = ⋅ ⋅ =

⋅ = ⋅ =

V Vφ≥ olduğundan kesme donatısı gereklidir.


u cV Vφ≥ olduğundan kesme donatısı gereklidir.


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KESME DONATISI:

0.17 '/ cv uet fA V λφμ⋅ ⋅

= = −

4 500 / 0.75 0.17 1.00 50420 2300 420

vw yt ytb s f d f

μ⋅ ⋅

⋅ ⋅= −

⋅0.006211 0.0028620.003350

= −=

2

0.003350 80 80

21.44v v w

v

A b s

A cm

μ= ⋅ ⋅ = ⋅ ⋅

=

Kesme donatılarının 80‐80cm karelajla yerleştirilmesi durumunda:

v



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MAKSİMUM KESME KAPASİTESİ (DONATI):

,max 0.66 's c wV f b d= ⋅ ⋅

,max

0.66 50 1000 230010734 000

10734s

NV kN

= ⋅ ⋅ ⋅==

,max3235 10734s sV kN V kN= ≤

MİNİMUM KESME DONATISI PURSANTAJI:

,min,min

' 500.062 0.062 0.001044420

0 35 0 35

v cv

w yt

A fb s f

A

μ = = ⋅ = ⋅ =⋅

,min,min

0.35 0.35 0.000833420

vv

w yt

Ab s f

μ = = = =⋅



12

ÖRNEK 2: c

y


h 2 50 f d i d 250 0 05 0 30/2 2 30

KESME DONATISI:

uet

h= 2.50mfoundation d= 250-0.05-0.30/2=2.30V =300 t/m =3000 kN/m=3000000 N /m (obtained from Etabs)

0.17 '/

3000 / 0 75 0 17 1 00 50

cv uetv

w yt yt

fA Vb s f d f

λφμ⋅ ⋅

= = −⋅ ⋅

⋅ ⋅3000 / 0.75 0.17 1.00 50420 2300 420

0.004141 0.0028620.001279

⋅ ⋅= −

⋅= −=

2

0.001279 80 80

8.19v v w

v

A b s

A cm

μ= ⋅ ⋅ = ⋅ ⋅

=



v

KESME HESABI: TS 500’ E GÖRE KESME HESABI

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KESME KONTROLÜ

Kesme Donatısına Gerek Yoktur.

Durum 1:d ctd wV 0.65 f d b≤ ⋅ ⋅ ⋅

K D t H b Mi i D t K t lü Y l l d

Durum 2: d ctd w d cd wV > 0.65 f d b V 0.22 f d b ve⋅ ⋅ ⋅ ≤ ⋅ ⋅ ⋅ ⇒

Kesme Donatısı Hesabı ve Minimum Donatı Kontrolü Yapılmalıdır.

Durum 3: d cd wV 0.22 f d b ≥ ⋅ ⋅ ⋅Temel Kalınlığı Artırılmalıdır.



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KESME DONATISI HESABI

d c s

d det w

c ctd w

V < V + VV = V b (Design force)V = k 0.65 f d b (Concrete part of theshear strength)

A

⋅⋅ ⋅ ⋅ ⋅

vs yd

AV = f d (Reinforcement part of theshear strength)s⋅ ⋅

0 65A V V V b k f d bdet

det

0.65

0.65

v d c w ctd w

yd yd

v ctdv

A V V V b k f d bs f d f d

A V k fs b f d f

μ

− ⋅ − ⋅ ⋅ ⋅ ⋅= =

⋅ ⋅

⋅ ⋅= = −

⋅ ⋅

det 0.65w yd yd

v yd ctd

s b f d f

V f d k f dμ= ⋅ ⋅ + ⋅ ⋅ ⋅



15

MİNİMUM KESME DONATISI

A ,min,min ,min

0.3 0.3vctd ctdv w v

ywd w ywd

Af fA b sf b s f

μ⋅ ⋅= ⋅ ⋅ ⇒ = =

⋅

İ İ İMAKSİMUM KESME KAPASİTESİ

,max 0.22d cd wV f d b= ⋅ ⋅ ⋅



16

ÖRNEK 1: c

y


uet

h= 2.50m foundation d= 250-0.05-0.30/2=2.30V = 450 t/m =4500 kN/m= 4500000 N /m (obtained from Etabs)

BETONUN KESME DAYANIMINA KATKISI:

V = k 0 65 f d b⋅ ⋅ ⋅ ⋅c ctd wV k 0.65 f d b

cV = 0.8 0.65 1.65 1000 1000 = 858000 N⋅ ⋅ ⋅ ⋅



17

KESME DONATISI:

det 0.65 4500 0.8 065 1.65ctdV k fAs ⋅ ⋅ ⋅ ⋅det

365 2300 365

0.005360 0.002350 0.003010

ctdv

w yd yd

v

fs b f d f

μ

μ

= = − = −⋅ ⋅ ⋅

= − =


0.003010 80 80v v wA b sμ= ⋅ ⋅ = ⋅ ⋅219.26

v v w

vA cm=



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MAKSİMUM KESME KAPASİTESİ:

'f d b0.22 '4500000 0.22 50 2300 1000 25300000

d c wV f d bN N

≤ ⋅ ⋅ ⋅≤ ⋅ ⋅ ⋅ =

MİNİMUM KESME DONATISI PURSANTAJI:

,min 0.3v ctdv

A fμ = = ⋅

,min

1.65 365

1650 3 0 001356

vw ywd

ctd ywd

v

s b f

f MPa f MPa

A

μ⋅

= =

⇒ , 0.3 0.001356365v

ws bμ⇒ = = ⋅ =

⋅



19

ÖRNEK 2: c

y


h 2 50 f d i d 250 0 05 0 30/2 2 30

KESME DONATISI

uet

h= 2.50mfoundation d= 250-0.05-0.30/2=2.30V =300 t/m =3000 kN/m=3000000 N /m (obtained from Etabs)

KESME DONATISI:

det 0.65 3000 0.5 065 1.65365 2300 365

ctdv

w yd yd

V k fAss b f d f

μ ⋅ ⋅ ⋅ ⋅= = − = −

⋅ ⋅ ⋅


0.003574 0.001469 0.002105vμ = − =

2

0.002105 80 80

13.47v v w

v

A b s

A cm

μ= ⋅ ⋅ = ⋅ ⋅

=


KESME SÜRTÜNMESİ HESABI

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KESME SÜRTÜNMESİ HESABIKESME SÜRTÜNMESİ HESABI


KESME SÜRTÜNMESİ HESABI

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KESME SÜRTÜNMESİ HESABIKesme Sürtünmesi Nedir?Yöntem 1: ACI 318’ e göre Kesme Sürtünmesi Hesabı

Kesme Sürtünmesi HesabıMaksimum Kesme KuvvetiMinimum Kesme Sürtünmesi DonatısıÖrnekler

Yöntem 2: ACI 318’ e göre Geliştirilmiş Kesme Sürtünmesi HesabıKesme Sürtünmesi HesabıMaksimum Kesme KuvvetiMinimum Kesme Sürtünmesi DonatısıÖrnekler

Yö t 3 ACI 318’ ö K it B t Ki i A l ji i il K Sü tü i H bYöntem 3: ACI 318’ e göre Kompozit Betonarme Kiriş Analojisi ile Kesme Sürtünmesi HesabıKesme Sürtünmesi HesabıMaksimum Kesme KuvvetiMinimum Kesme Sürtünmesi DonatısıÖrneklerÖrnekler

Yöntem 4: AASHTO’ ya göre Kesme Sürtünmesi HesabıKesme Sürtünmesi HesabıMaksimum Kesme KuvvetiMinimum Kesme Sürtünmesi DonatısıÖrnekler


KESME SÜRTÜNMESİ HESABI: KESME SÜRTÜNMESİ NEDİR?KESME SÜRTÜNMESİ NEDİR?

22

EĞİLME ELEMANINDA YÜZEY KESME KUVVETİNİN HESABI

M M V l= + ⋅Δ2 1 1

2 2

1 12

/u

u u v

u

M M V lC M d

M V lCd d

= + ⋅Δ

=⋅Δ

= +2

1 1 /

uv v

v

d dC M d=

2 1

1

1

//

h u

h v

hi v

V C CV V dV V d

= −

= ⋅Δ= 1hi v



23

Kesme Kuvveti:

PLAK ELEMANLARDA KESME SÜRTÜNMESİ

uV uet w uetu

V b VSd b d⋅

= = uetu u w w

VV S s b s bd

⎛ ⎞= ⋅ ⋅ = ⋅ ⋅⎜ ⎟

⎝ ⎠uwd b d⋅ d⎝ ⎠



24

SONLU ELEMANLARDA KESME KUVVETİ VE KAYMA GERİLMELERİ



25

KESME SÜRTÜNMESİNE ETKİ EDEN FAKTÖRLER NELERDİR?

•Sürtünme Katsayısı

•Agrega Kenetlenmesi

•Yüzeyler Arası Kesme Transferi

•Pürüzlülük Etkisi

•Donatı Takoz Etkisi (Dowel Action)

•Eksenel Kuvvet

Yöntemler arası farklılıklar, bu faktörlerin göz önünü alınıp alınmamasına göre değişiklik göstermektedir. Aynı zamanda göz önüne alınan parametrelerin büyüklükleri de değişmektedir.


g y g p y ğ ş

KESME SÜRTÜNMESİ HESABI: ACI 318’ E GÖRE KESME SÜRTÜNMESİ HESABIACI 318’ E GÖRE KESME SÜRTÜNMESİ HESABI

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Kesme Sürtünmesi Kontrolü:

KESME SÜRTÜNMESİ KONTROLÜ

n uV Vφ ≥ =0.75φ

Kesme Sürtünmesi Kapasitesi

n vf yV A f μ= ⋅ ⋅

Donatının Açılı Olması Durumunda Kesme Sürtünmesi Kapasitesi:

n vf yf μ

( sin cos )n vf yV A f μ α α= ⋅ ⋅ +



27

SÜRTÜNME KATSAYISI

n vf yV A f μ= ⋅ ⋅n vf yf μ

1.000.85

for normal weight concretefor lightweight concrete

λλ==

1.41.0 int0 6

Concrete placed monolithicallyConcrete placed against hardened concrete with surface entionally roughenedC l d i h

μ λμ λ

λ

= ⇐= ⇐

id d i ll h d0.6 Concrete placed against harμ λ= ⇐ int0.7 inf

dened concrete not entionally roughenedConcrete archared to as rolled structural steel by headed studs or by re orcing barsμ λ= ⇐ −

Note: According to ACI 318M‐11 Section11.6.9, when concrete is placed against previously harden concrete, the interface for shear transfer shall be clean and free of laitance. If µ is assumed equal to 1.0λ, interface shall be roughened to a full amplitude of approximately 6mm.



28

KESME SÜRTÜNMESİ DONATISI

V⎛ ⎞uetvf y w

vf t

VA f s bd

A V

φ μ⎛ ⎞

⋅ ⋅ ⋅ = = ⋅ ⋅⎜ ⎟⎝ ⎠

/

vf uet

w y

vf uet

Vs b f d

A V

φ μ

φμ

=⋅ ⋅ ⋅ ⋅

f uetvf

w y

uet v y

s b f d

V f d

μμ

φ μ μ

= =⋅ ⋅ ⋅

= ⋅ ⋅ ⋅ ⋅



29

Durum 1: Monolitik Döküm veya Kontrollü Pürüzlü Yüzey

MAKSİMUM KESME KUVVETİ

Durum 1: Monolitik Döküm veya Kontrollü Pürüzlü Yüzey

0.2 'min (3.3 0.08 ' ) 1.4 1.0

c c

n c c

f AV f A If andμ λ μ λ

⋅ ⋅⎧⎪≤ ⇒ + ⋅ ⋅ ⇐ = =⎨⎪11 cA⎪ ⋅⎩

Durum 2: Kontrolsüz Pürüzlü Yüzey veya Özel Kesme Sürtünmesi Donatısı Kullanılması

0.2 'min

5.5c c

nc

f A For all other casesV

A⋅ ⋅ ⇐⎧

≤ ⎨ ⋅⎩

seccwhere A Area of concrete tion resisting shear transfer=



30

ÖRNEK 1: c

y


uet

h= 2.50m foundation d= 0.8 h=2.00V = 450 t/m =4500 kN/m= 4500000 N /m (obtained from Etabs)

⋅

Kesme Kuvveti:Kesme Kuvveti:

0.75 2 2500003000000

n u

n

V VV N

V N

φ ≥⋅ ≥

≥

w

u uet w

b = 1.00 m V = V b /d= 4500000 1.00 /2.00= 2250000 N

⇒⋅ ⋅

0.2 50 1000000 10000000N⋅ ⋅ =⎧⎪

3000000nV N≥

Maksimum Kesme Kuvveti:

min (3.3 0.08 50) 1000000 700000011 1000000 11000000

nV NN

⎪≤ + ⋅ ⋅ =⎨⎪ ⋅ =⎩

3000000 7000000nV N= ≤


n


31

Durum 1: Monolitik Döküm


80‐80cm Karelaj

1.4 1.4/ 4500 / 0.75 0.005102

1.4 420 2000vf uet

vfw y

A Vs b f d

μ λφμ

μ

= =

= = = =⋅ ⋅ ⋅ ⋅ ⋅

2

0.005102 80 80

32.65vf vf w

vf

A b s

A cm

μ= ⋅ ⋅ = ⋅ ⋅

=

Durum 2: Kontrollü Pürüzlendirilmiş Yüzey1.0 1.0

/ 4500 / 0.75 0 007142vf uetA Vμ λ

φ= =

2

0.007142 80 80

45 71vf vf wA b s

A

μ= ⋅ ⋅ = ⋅ ⋅

80‐80cm Karelaj

0.0071421.0 420 2000

vf uetv

w ys b f dφμ

μ= = = =

⋅ ⋅ ⋅ ⋅ ⋅

Durum 3: Kontrolsüz Pürüzlendirilmiş Yüzey

245.71vfA cm=

80‐80cm Karelaj0.6 0.6

/ 4500 / 0.75 0.0119050.6 420 2000

vf uetv

w y

A Vs b f d

μ λφμ

μ

= =

= = = =⋅ ⋅ ⋅ ⋅ ⋅

2

0.011905 80 80

76.19vf vf w

vf

A b s

A cm

μ= ⋅ ⋅ = ⋅ ⋅

=



32

ÖRNEK 2: c

y

Concrete : C50 f ' =50MPaSteel : S420 f = 420 MPa

uet

h= 2.50m foundation d= 0.8 h=2.00V =300 t/m =3000 kN/m=3000000 N /m (obtained from Etabs)

⋅


0.75 1 5000002000000

n u

n

V VV N

V N

φ ≥⋅ ≥

≥

w

u uet w

b = 1.00 m V = V b /d= 3000000 1.00 /2.00=1500000 N

⇒⋅ ⋅

0.2 50 1000000 10000000N⋅ ⋅ =⎧⎪

2000000nV N≥


min (3.3 0.08 50) 1000000 700000011 1000000 11000000

nV NN

⎪≤ + ⋅ ⋅ =⎨⎪ ⋅ =⎩

2000000 7000000nV N= ≤


n


33

Durum 1: Monolitik Döküm


80‐80cm Karelaj

1.4 1.4/ 3000 / 0.75 0.003401

1.4 420 2000vf uet

vfw y

A Vs b f d

μ λφμ

μ

= ⋅ =

= = = =⋅ ⋅ ⋅ ⋅ ⋅

2

0.003401 80 80

21.77vf vf w

vf

A b s

A cm

μ= ⋅ ⋅ = ⋅ ⋅

=

Durum 2: Kontrollü Pürüzlendirilmiş Yüzey

1.0 1.0/ 3000 / 0A V

μ λφ

= =2

0.004762 80 80vf vf wA b sμ= ⋅ ⋅ = ⋅ ⋅

80‐80cm Karelaj

Durum 3: Kontrolsüz Pürüzlendirilmiş Yüzey

/ 3000 / 0.75 0.0047621.0 420 2000

vf uetvf

w y

A Vs b f d

φμμ

= = = =⋅ ⋅ ⋅ ⋅ ⋅

230.48vfA cm=

80‐80cm Karelaj

0.6 0.6/ 3000 / 0.75 0.007936

0.6 420 2000vf uet

vfw y

A Vs b f d

μ λφμ

μ

= =

= = = =⋅ ⋅ ⋅ ⋅ ⋅

2

0.007936 80 80

50.79vf vf w

vf

A b s

A cm

μ= ⋅ ⋅ = ⋅ ⋅

=


KESME SÜRTÜNMESİ HESABI: ACI 318’ E GÖRE GELİŞTİRİLMİŞ KESME SÜRTÜNMESİ HESABIACI 318 E GÖRE GELİŞTİRİLMİŞ KESME SÜRTÜNMESİ HESABI

34




n uV Vφ ≥ =0.75φ

10.8n vf y cV A f A K

frictioncomponent cohesion likecomponent

= ⋅ ⋅ + ⋅

−

1

0.82.80

secc

f p pis coefficent of friction

where K MPa for rough surfaceA Area of concrete tion

⎧⎪ =⎨⎪ =⎩

Donatının Açılı Olması Durumunda Kesme Sürtünmesi Kapasitesi:

c f⎩

21(0.8 cos )n vf y cV A f sin A K sinα α α= ⋅ ⋅ ⋅ + + ⋅ ⋅


1( )n vf y cf


35


( )0 8 uetVA f A K s bφ +( )1

1

0.8

/0.8

uetvf y c w

uetvf y c w

A f A K s bd

VA f A K s bd

φ

φ

⋅ ⋅ ⋅ + ⋅ = ⋅ ⋅

⋅ ⋅ + ⋅ = ⋅ ⋅

1/0.8 uet

vf y w wVA f s b K s b

dφ

⋅ ⋅ = ⋅ ⋅ − ⋅ ⋅

A V / Kφvf uet 1

w y y

vf uet 1vf

A V / K= -s b 0.8 f d 0.8 f

A V / Kμ = = -b 0 8 f d 0 8 f

φ

φ

⋅ ⋅ ⋅ ⋅

vfw y y

uet vf y 1

s b 0.8 f d 0.8 f

V =μ 0.8 f d K dφ φ

⋅ ⋅ ⋅ ⋅

⋅ ⋅ ⋅ ⋅ + ⋅ ⋅



36

MİNİMUM KESME SÜRTÜNMESİ DONATISI

vf,min y

c

A f>1.40MPa

A⋅

vf,min vf,minvf,min

w c y

A A 1.40μ = = =s b A f

1 40

⋅

y vf,min1.40Example: f =420MPa μ = = 0.0033420

⇒



37

ÖRNEK 1: c

y


h= 2.50m foundation d= 0.8 h=2.00⋅

uetV = 450 t/m =4500 kN/m= 4500000 N /m (obtained from Etabs)

n vf y c 1

1

V = 0.8 A f + A K

K = 2.80MPa for normal weight concrete

⋅ ⋅ ⋅

Kesme Kuvveti: V Vφ ≥

1

c

0.8 Cofficient of frictionA = Area of concrete section resisting shear transfer

⇒

0.75 2 2500003000000

n u

n

n

V VV N

V N

φ ≥

⋅ ≥≥


w

u uet w

b = 1.00 m V = V b /d= 4500000 1.00 /2.00= 2250000 N

⇒

⋅ ⋅

0.2 50 1000000 10000000min (3.3 0.08 50) 1000000 7000000

11 1000000 11000000n

NV N

N

⋅ ⋅ =⎧⎪≤ + ⋅ ⋅ =⎨⎪ =⎩

3000000 7000000nV N= ≤



11 1000000 11000000 N⎪ ⋅ =⎩


38

Gerekli Donatı:


80‐80cm Karelaj

4500 / 0.75 2.800.8 420 2000 0.8 420

0.000595

vfvf

w

vf

As b

μ

μ

= = −⋅ ⋅ ⋅ ⋅

=2

0.000595 80 80

3.81vf vf w

vf

A b s

A cm

μ= ⋅ ⋅ = ⋅ ⋅

=


Minimum Donatı:1.40 1.4 0.003333f iμ = = = ,min ,min 0.003333 80 80vf vf wA b sμ= ⋅ ⋅ = ⋅ ⋅

80‐80cm Karelaj


, 1.4 0.003333vf minyf

μ2

,min 21.33vfA cm=



39

ÖRNEK 2: c

y


h= 2.50m foundation d= 0.8 h=2.00⋅

uetV =300 t/m =3000 kN/m=3000000 N /m (obtained from Etabs)

n vf y c 1

1

V = 0.8 A f + A K

K = 2.80MPa for normal weight concrete

⋅ ⋅ ⋅

Kesme Kuvveti: V Vφ ≥

1

c

0.8 Cofficient of frictionA = Area of concrete section resisting shear transfer

⇒

0.75 1 5000002000000

n u

n

n

V VV N

V N

φ ≥⋅ ≥

≥


w

u uet w

b = 1.00 m V = V b /d= 3000000 1.00 /2.00=1500000 N

⇒

⋅ ⋅

0.2 50 1000000 10000000min (3.3 0.08 50) 1000000 7000000

11 1000000 11000000n

NV N

N

⋅ ⋅ =⎧⎪≤ + ⋅ ⋅ =⎨⎪ =⎩

2000000 7000000nV N= ≤



11 1000000 11000000 N⎪ ⋅ =⎩


40

Gerekli Donatı:


80‐80cm Karelaj

2

0.00 80 80

0.00vf vf w

vf

A b s

A cm

μ= ⋅ ⋅ = ⋅ ⋅

=

3000 / 0.75 2.800.8 420 2000 0.8 420

0.00

vfv

w

v

As b

μ

μ

= = −⋅ ⋅ ⋅ ⋅

≤


Minimum Donatı:1.40 1.4 0.003333f iμ = = = ,min ,min 0.003333 80 80vf vf wA b sμ= ⋅ ⋅ = ⋅ ⋅

80‐80cm Karelaj


, 1.4 0.003333vf minyf

μ2

,min 21.33vfA cm=


KESME SÜRTÜNMESİ HESABI: ACI 318’ E GÖRE KOMPOZİT BETONARME KİRİŞ ANALOJİSİACI 318 E GÖRE KOMPOZİT BETONARME KİRİŞ ANALOJİSİ

41



n uV Vφ ≥

=0.75φ

Kesme Sürtünmesi KapasitesiKesme Sürtünmesi Kapasitesivf

nh v y w vw

AV = (1.8(MPa)+0.6 ρ f ) λ b d ρ =b s

dV 1 8(MP ) b d + 0 6 A f

where⋅ ⋅ ⋅ ⋅ ⋅⋅

nh v vf yV =1.8(MPa) b d + 0.6 A fs

cohesion-likecomponent friction component

⋅ ⋅ ⋅ ⋅ ⋅



42


d( ) b d fnh v vf ydV =1.8(MPa) b d + 0.6 A fs

1.8 0.6 uet ww vf y

V bdb d A fφ

⋅ ⋅ ⋅ ⋅ ⋅

⋅⋅ ⋅ + ⋅ ⋅ ⋅ >

( / 1.8 )0.6

f y

vf uet w w

y

sA V b b ds f d

φφ ⋅ − ⋅ ⋅

=⋅ ⋅

/ 1.8( )0.6 0.6

y

vf uetvf

w y y

A V MPas b f d f

φμ = = −⋅ ⋅ ⋅ ⋅

uet vf yV =μ 0.6 f d 1.80 dφ φ⋅ ⋅ ⋅ ⋅ + ⋅ ⋅

Note: The method is valid only if contact surface should be intentionally roughened.


y y g


43


nh wV =3.50(MPa) b d⋅ ⋅nh w( )


,min,min ,min

'0.062 ' 0.062vf cw

vf c vfyt w y

A fb sA ff b s f

μ⋅= ⋅ ⋅ ⇔ = = ⋅

⋅

,min,min ,min

0.350.35 /

600

y y

vfvf w yt vf

w y

AA b s f

b s f

s mm

μ= ⋅ ⋅ ⇔ = =⋅

≤ 6004

s mms thickness of foundation layer≤≤ ⋅



44

ÖRNEK 1: c

y


h= 2 50m foundation d= 0 8 h=2 00⋅

uet

h 2.50m foundation d 0.8 h 2.00V = 450 t/m =4500 kN/m= 4500000 N /m (obtained from Etabs)

⋅


w

u uet w

b = 1.00 m V = V b = 4500000 1.00= 4500000 N

⇒

⋅ ⋅


nh,max wV =3.50(MPa).b .d

nh,max

u nh,max

V =3.50 1000 2000 7000000V =4500000 V 7000000

NN N

⋅ ⋅ =

≤ =



45

Ü Ü İ

Gerekli Donatı:


80‐80cm Karelaj

/ 1.8( )vf uetA V MPaφμ0.004763 80 80vf vf wA b sμ= ⋅ ⋅ = ⋅ ⋅( )

0.6 0.6

4500 / 0.75 1.80.6 420 2000 0.6 420

f uetvf

w y y

vf

s b f d fφμ

μ

= = −⋅ ⋅ ⋅ ⋅

= −⋅ ⋅ ⋅

230.48vf vf w

vfA cm=


0.011905 0.007142

0.004763vf

vf

μ

μ

= −

=

Minimum Donatı: 80‐80cm Karelaj


min ' 500 062 0 062 0 001044vf cA f 0 001044 80 80A b sμ= ⋅ ⋅ = ⋅ ⋅,min,min

,min,min

500.062 0.062 0.001044420

0.35 0.35 0.000833420

vf cvf

w y

vfvf

w y

fb s f

Ab s f

μ

μ

= = ⋅ = ⋅ =⋅

= = = =⋅

,min ,min

2,min

0.001044 80 80

6.68vf vf w

vf

A b s

A cm

μ= ⋅ ⋅ = ⋅ ⋅

=



46

ÖRNEK 2: c

y



uet

h 2.50m foundation d 0.8 h 2.00V =300 t/m =3000 kN/m=3000000 N /m (obtained from Etabs)

⋅


w

u uet w

b = 1.00 m V = V b = 3000000 1.00= 3000000 N

⇒

⋅ ⋅


nh,max wV =3.50(MPa).b .d

nh,max

u nh,max

V =3.50 1000 2000 7000000V =3000000 V 7000000

NN N⋅ ⋅ =

≤ =



47

Ü Ü İ

Gerekli Donatı:


80‐80cm Karelaj

/ 1.8( )vf uetA V MPaφμ0.000795 80 80vf vf wA b sμ= ⋅ ⋅ = ⋅ ⋅( )

0.6 0.6

3000 / 0.75 1.80.6 420 2000 0.6 420

f uetvf

w y y

vf

s b f d fφμ

μ

= = −⋅ ⋅ ⋅ ⋅

= −⋅ ⋅ ⋅

25.09vf vf w

vfA cm=


0.007937 0.007142

0.000795vf

vf

μ

μ

= −

=

Minimum Donatı: 80‐80cm Karelaj


min ' 500 062 0 062 0 001044vf cA f 0 001044 80 80A b sμ= ⋅ ⋅ = ⋅ ⋅,min,min

,min,min

500.062 0.062 0.001044420

0.35 0.35 0.000833420

vf cvf

w y

vfvf

w y

fb s f

Ab s f

μ

μ

= = ⋅ = ⋅ =⋅

= = = =⋅

,min ,min

2,min

0.001044 80 80

6.68vf vf w

vf

A b s

A cm

μ= ⋅ ⋅ = ⋅ ⋅

=


KESME SÜRTÜNMESİ HESABI: AASHTO’ YA GÖRE KESME SÜRTÜNMESİ HESABIAASHTO YA GÖRE KESME SÜRTÜNMESİ HESABI

48



n uV Vφ ≥ =0.75φ

Kesme Kuvveti:⎛ ⎞


uet w uetu

w

V b VSd b d⋅

= =⋅

uetu u w w

VV S s b s bd

⎛ ⎞= ⋅ ⋅ = ⋅ ⋅⎜ ⎟

⎝ ⎠


( )ni vf vf y cV c A A f Pμ= ⋅ + ⋅ ⋅ +

↓ ↓1 21.70 1.00 0.25 10.30c MPa K K MPaμ= = = =

Kontrollü Pürüzlendirilmiş Yüzey (6 mm)

contributionof contributionof contributionofcohesion shear friction permanent axial compression

↓ ↓

1 20.52 0.60 0.20 5.50c MPa K K MPaμ= = = =

Kontrolsüz Pürüzlendirilmiş Yüzey



49


ni uV Vφ ≥ ni vf y cV A f A cμ= ⋅ ⋅ + ⋅ uetu w

VV s b= ⋅ ⋅ni uφ ni vf y c u wd

( )/

uetvf y cv w

VA f A c s bd

V

φ μ

φ

⋅ ⋅ ⋅ + ⋅ = ⋅ ⋅

/uetvf y cv w

VA f A c s bdφμ ⋅ ⋅ + ⋅ = ⋅ ⋅

/uetvf y w w

VA f s b c s bφμ ⋅ ⋅ = ⋅ ⋅ − ⋅ ⋅

/

vf y w w

vf uet

w y y

fd

A V cs b f d f

μ

φμ μ

= −⋅ ⋅ ⋅ ⋅

2 1 1

2 2

1 12

/u

u u v

u

M M V lC M d

M V lCd d

= + ⋅ Δ=

⋅ Δ= +

uet vf y

/

V = f d d

vf uetvf

w y y

A V cs b f d f

c

φμμ μ

μ μ φ φ

= = −⋅ ⋅ ⋅ ⋅

⋅ ⋅ ⋅ ⋅ + ⋅ ⋅

1 1

2 1

1

/

//

v v

v

h u

h v

d dC M dV C CV V dV V d

== −= ⋅ Δ


y1 /h i vV V d=


50


Kontrollü Pürüzlendirilmiş Yüzey (6 mm)

1

2

'min c vf

nivf

K f AV

K A

⋅ ⋅⎧⎪≤ ⎨ ⋅⎪⎩1 20.25 10.30K K MPa= =

0 20 5 50K K MP

ş y ( )

Kontrolsüz Pürüzlendirilmiş Yüzey


1 20.20 5.50K K MPa= =


,min,min ,min

0.350.35 /

0 35

vfvf w y vf

w y

AA b s f

b s fμ= ⋅ ⋅ ⇔ = =

⋅

,min0.35: 420 0.00083420y vfExample f MPa μ= ⇒ = =



51

ÖRNEK 1: c

y



uet

h 2.50m foundation d 0.8 h 2.00V = 450 t/m =4500 kN/m= 4500000 N /m (obtained from Etabs)

⋅

Kesme Kuvveti:

w

ui uet w

For b = 1.00 mV = V b /d = 4500000 1.00/2.00= 2 250000 N⋅ ⋅

(a) Kontrollü Pürüzlendirilmiş Yüzey (6 mm)

1 21.70 1.00 0.25 10.30c MPa K K MPaμ= = = =

(b) Kontrolsüz Pürüzlendirilmiş Yüzey

1 20.52 0.60 0.20 5.50c MPa K K MPaμ= = = =



52

( ) K t llü Pü ü l di il i Yü (6 )(a) Kontrollü Pürüzlendirilmiş Yüzey (6 mm)


⎧ 2 250000V V N1

2

' 0.25 50 1000000 12500000min

10.30 1000000 10300000c cv

nicv

K f A NV

K A N⋅ ⋅ = ⋅ ⋅ =⎧

≤ ⇒ ⎨ ⋅ = ⋅ =⎩

2 2

2 250000

2250000 0.75

3000000 / 10300000 /

ri ui

ri ni

ni

ni

V V NV V

V

V N m N m

φ≥ =

=

=

= ≤10300000 10300niV N kN⇒ ≤ =

⇒

Gerekli Kesme Sürtünmesi Donatısı

ni

80‐80cm Karelaj

A

80 80cm Karelaj

/ 4500 / 0.75 1.701.00 420 2000 1.00 420

0.007143 0.004048 0.003095

vf uetv

w y y

v

A V cs b f d f

φμμ μ

μ

= = − = −⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅

= − =

2

0.003095 80 80

19.81vf vf w

vf

A b s

A cm

μ= ⋅ ⋅ = ⋅ ⋅

=

min

min

0.35 0.35 0.00083420

vv

w y

Ab s f

μ = = = =⋅

,min ,min

2,min

0.00083 80 80

5.31vf vf w

vf

A b s

A cm

μ= ⋅ ⋅ = ⋅ ⋅

=

Minimum Kesme Sürtünmesi Donatısı: 80‐80cm Karelaj



53

(b) K t l ü Pü ü l di il i Yü(b) Kontrolsüz Pürüzlendirilmiş Yüzey


⎧ 2250000V V N1

2

' 0.20 50 1000000 10000000min

5.50 1000000 5500000c cv

nicv

K f A NV

K A N⋅ ⋅ = ⋅ ⋅ =⎧

≤ ⇒ ⎨ ⋅ = ⋅ =⎩

2 2

2250000

2250000 0.75

3000000 / 5500000 /

ri ui

ri ni

ni

ni

V V NV V

V

V N m N m

φ≥ ==

=

= ≤5500000 5500niV N kN⇒ ≤ =

⇒


ni

A

80‐80cm Karelaj

/ 4500 / 0.75 0.520.60 420 2000 0.60 420

0.011905 0.002063 0.009841

vf uetv

w y y

v

A V cs b f d f

φμμ μ

μ

= = − = −⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅

= − =2

0.009841 80 80

62.98vf vf w

vf

A b s

A cm

μ= ⋅ ⋅ = ⋅ ⋅

=

80 80cm Karelaj

min

min

0.35 0.35 0.00083420

vv

w y

Ab s f

μ = = = =⋅

,min ,min

2,min

0.00083 80 80

5.31vf vf w

vf

A b s

A cm

μ= ⋅ ⋅ = ⋅ ⋅

=




54

ÖRNEK 2: c

y



uet

h 2.50m foundation d 0.8 h 2.00V =300 t/m =3000 kN/m=3000000 N /m (obtained from Etabs)

⋅

Kesme Kuvveti:

w

ui uet w

For b = 1.00 mV = V b /d = 3000000 1.00/2.00=1500000 N⋅ ⋅

(a) Kontrollü Pürüzlendirilmiş Yüzey (6 mm)

1 21.70 1.00 0.25 10.30c MPa K K MPaμ= = = =

(b) Kontrolsüz Pürüzlendirilmiş Yüzey

1 20.52 0.60 0.20 5.50c MPa K K MPaμ= = = =



55

( ) K t llü Pü ü l di il i Yü (6 )(a) Kontrollü Pürüzlendirilmiş Yüzey (6 mm)


⎧ 1500000V V N1

2

' 0.25 50 1000000 12500000min

10.30 1000000 10300000c cv

nicv

K f A NV

K A N⋅ ⋅ = ⋅ ⋅ =⎧

≤ ⇒ ⎨ ⋅ = ⋅ =⎩

2 2

1500000

1500000 0.75

2000000 / 10300000 /

ri ui

ri ni

ni

ni

V V NV V

V

V N m N m

φ≥ =

=

=

= ≤10300000 10300niV N kN⇒ ≤ =

⇒


ni

80‐80cm Karelaj

A

80 80cm Karelaj

/ 3000 / 0.75 1.701.00 420 2000 1.00 420

0.004762 0.004048 0.000714

vf uetv

w y y

v

A V cs b f d f

φμμ μ

μ

= = − = −⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅

= − =

2

0.000714 80 80

4.57vf vf w

vf

A b s

A cm

μ= ⋅ ⋅ = ⋅ ⋅

=

min

min

0.35 0.35 0.00083420

vv

w y

Ab s f

μ = = = =⋅

,min ,min

2,min

0.00083 80 80

5.31vf vf w

vf

A b s

A cm

μ= ⋅ ⋅ = ⋅ ⋅

=




56

(b) K t l ü Pü ü l di il i Yü(b) Kontrolsüz Pürüzlendirilmiş Yüzey


⎧ 1500000V V N1

2

' 0.20 50 1000000 10000000min

5.50 1000000 5500000c cv

nicv

K f A NV

K A N⋅ ⋅ = ⋅ ⋅ =⎧

≤ ⇒ ⎨ ⋅ = ⋅ =⎩

2 2

1500000

1500000 0.75

2000000 / 5500000 /

ri ui

ri ni

ni

ni

V V NV V

V

V N m N m

φ≥ ==

=

= ≤5500000 5500niV N kN⇒ ≤ =

⇒


ni

A

80‐80cm Karelaj

/ 3000 / 0.75 0.520.60 420 2000 0.60 420

0.007936 0.002063 0.005873

vf uetv

w y y

v

A V cs b f d f

φμμ μ

μ

= = − = −⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅

= − =2

0.005873 80 80

37.59vf vf w

vf

A b s

A cm

μ= ⋅ ⋅ = ⋅ ⋅

=

80 80cm Karelaj

min

min

0.35 0.35 0.00083420

vv

w y

Ab s f

μ = = = =⋅

,min ,min

2,min

0.00083 80 80

5.31vf vf w

vf

A b s

A cm

μ= ⋅ ⋅ = ⋅ ⋅

=



ÖZET VE SONUÇLARÇ

57

ÖZET VE SONUÇLARÖZET VE SONUÇLAR



58

V = 4500kN/mvμ ,minvμShear Design

ACI 318M 11 Sh D i 0 0033 0 0 001044•ACI 318M-11 Shear Design 0.003350 0.001044

•TS-500 Shear Design 0.003010 0.001356

Shear Friction Design vμ ,minvμg

•ACI 318M-11 11.6.4. Shear friction (Concrete placed monolithically) 0.005102 -

•ACI 318M-11 11.6.4. Shear friction (Intentionally roughened) 0.007142 -

•ACI 318M-11 11.6.4. Shear friction (Not intentionally roughened) 0.011905 -

•ACI 318M-11 11.6.3. Modified shear friction 0.005950 0.003333

ACI 318M 11 11 6 3 C it b 0 004761 0 001044•ACI 318M-11 11.6.3. Composite beam 0.004761 0.001044

•AASHTO 5.8.4. Interface shear transfer (Intentionally roughened) 0.003095 0.000833

•AASHTO 5.8.4. Interface shear transfer (Not intentionally roughened) 0.009841 0.000833



59

V = 3000kN/mvμ ,minvμShear Design

ACI 318M 11 Sh D i 0 001 96 0 001044•ACI 318M-11 Shear Design 0.001796 0.001044

•TS-500 Shear Design 0.001224 0.001356

Shear Friction Design vμ ,minvμg

•ACI 318M-11 11.6.4. Shear friction (Concrete placed monolithically) 0.003401 -

•ACI 318M-11 11.6.4. Shear friction (Intentionally roughened) 0.004762 -

•ACI 318M-11 11.6.4. Shear friction (Not intentionally roughened) 0.007936 -

•ACI 318M-11 11.6.3. Modified shear friction - 0.003333

ACI 318M 11 11 6 3 C it b 0 000794 0 001044•ACI 318M-11 11.6.3. Composite beam 0.000794 0.001044

•AASHTO 5.8.4. Interface shear transfer (Intentionally roughened) 0.000714 0.000833

•AASHTO 5.8.4. Interface shear transfer (Not intentionally roughened) 0.005873 0.000833



SONUÇLAR60

SONUÇLAR• Kalın temellerde kesme ve kesme sürtünmesi hesaplarının her ikisi de yapılmalıdır.

• Seçilen kesme donatısı her iki hesaptan elde edilen değerleri sağlamalıdır.

• Kesme hesabında ACI 318 ve TS 500 benzer sonuçlar vermektedir.

• Kohezyon, sürtünme ve eksenel kuvvet etkisi parametrelerinin tamamını göz önüne alması dolayısıyla, AASHTO kesme sürtünmesi

hesabı daha kapsamlıdır.

• AASHTO da yer alan parametreler yüzeylerin pürüzlülüğüne göre de değişmektedir.

• Kesme sürtünmesi esas faydalı yükseklik d= 0.80 ~ 0.90 alınabilir. Faydalı yükseklik temel alt ve üst eğilme donatısı katmanlarının

kalınlıklarına bağlı olarak değişmektedir.

• Gerekli donatı alanı hesabında en önemli parametre, sürtünme katsayıdır. Bu katsayı, yüzeyin pürüzlülüğüne bağlı olarak 0.6 ile 1.4

arasında değişmektedir. Kontrollü pürüzlendirme yapılması durumunda (6 mm), gerekli donatı miktarları önemli ölçüde azalmaktadır.

• Sehpa donatısı, uygun şekilde teşkil edilmesi durumunda, kesme ve kesme sürtünmesi donatısı olarak göz önüne alınabilir. Bunun

için en önemli kriter, sehpa donatının köşelerinde en az bir donatı teşkil edilmelidir.


PROJELENDİRME VE SAHA UYGULAMALARI

61

PROJELENDİRME VE

SAHA UYGULAMALARI



62



63



64



65



66



67


SORULAR

68

GİRİŞ•KESME HESABI•KESME SÜRTÜNMESİ HESABI

KESME HESABIKESME HESABI•KALIN TEMELLERDE KESME HESABI•ACI 318’ E GÖRE KESME HESABI•TS 500’ E GÖRE KESME HESABI

Ü Ü İKESME SÜRTÜNMESİ HESABI•KESME SÜRTÜNMESİ NEDİR?•ACI 318’ E GÖRE KESME SÜRTÜNMESİ HESABI•ACI 318’ E GÖRE GELİŞTİRİLMİŞ KESME SÜRTÜNMESİ HESABI

’ Ö İ İ İ İ İ İ Ü Ü İ•ACI 318’ E GÖRE KOMPOZİT BETONARME KİRİŞ ANALOJİSİ İLE KESME SÜRTÜNMESİ HESABI•AASHTO’ YA GÖRE KESME SÜRTÜNMESİ HESABI

ÖZET VE SONUÇLAR

PROJELENDİRME VE SAHA UYGULAMALARIPROJELENDİRME VE SAHA UYGULAMALARI•ÇİZİM DETAYLARI•SAHA UYGULAMALARI

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