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DÖŞEME KALINLI ĞI HESABI
hf ≥
−×+ 4
120
15
ssn
m
l α
lsn = döşemenin kısa kenarının temiz açıklığı αs = döşemenin uyduğu tip αs = Σ sürekli kenar uzunluğu / Σ kenar uzunluğu
m = s
l
l
l < 2 çift yönde çalışma şartı
D101 DÖŞEMESĐ Tip No 2 : Bir Kenar Süreksiz
m = 035,1462
478 = < 2 ⇒ döşeme çift doğrultuda çalışıyor
αs = ( ) 746,04784622
4784622 =+×+×
lsn = 462 - 25 = 437 cm
hf ≥
−×+ 4
746,01
035,1
2015
437 ⇒ hf ≥ 9.535 cm
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D102 DÖŞEMESĐ Tip No 2 :Bir Kenar Süreksiz
m = 195,1400
478 = < 2 ⇒ döşeme çift doğrultuda çalışıyor
αs = ( ) 772,04004782
4004782 =+×+×
lsn = 400-25 = 375 cm
hf ≥
−×+ 4
772,01
195,1
2015
375 ⇒ hf ≥ 9,535 cm
D103 DÖŞEMESĐ Tip No 2 : Bir Kenar Süreksiz
m = 079,1428
462 = < 2 ⇒ döşeme çift doğrultuda çalışıyor
αs = ( ) 80,04284622
4284622 =+×+×
lsn = 428-25 = 403 cm
hf ≥
−×+ 4
80,01
079,1
2015
403 ⇒ hf ≥ 9,61 cm
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D105 DÖŞEMESĐ Tip No 2 : Bir Kenar Süreksiz
m = 07,1400
428 = < 2 ⇒ döşeme çift doğrultuda çalışıyor
αs = ( ) 742,04284002
4284002 =+×+×
lsn = 400-25 = 375 cm
hf ≥
−×+ 4
742,01
07,1
2015
375 ⇒ hf ≥ 9,07 cm
D106 DÖŞEMESĐ Tip No 1 : Dört kenar sürekli
m = 079,1428
462 = < 2 ⇒ döşeme çift doğrultuda çalışıyor
αs = ( ) 14284622
)428462(2 =+×+×
lsn = 428-25 = 403 cm
hf ≥
−×+ 4
11
079,1
2015
403 ⇒ hf ≥ 9,01 cm
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D102A DÖŞEMESĐ Tip No 4 : Đki Kısa Kenar Süreksiz
m = 079,1400
478 = < 2 ⇒ döşeme çift doğrultuda çalışıyor
αs = ( ) 544,04784002
4782 =+×
×
lsn = 400-25 = 375 cm
hf ≥
−×+ 4
479,01
088,1
2015
397 ⇒ hf ≥ 10,47 cm
D104 DÖŞEMESĐ
hf ≥ 12
160
12=snl
⇒ hf ≥ 13,33 cm
D107 – D108 DÖŞEMESĐ
hf ≥ 12
5,147
12=snl
⇒ hf ≥ 12,29 cm
balkon ve sahanlıkta ⇒⇒⇒⇒ hf = 13 cm seçildi. odalarda ⇒⇒⇒⇒ hf = 13 cm
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DÖŞEME YÜKLER ĐNĐN (Pd) HESABI
ODALARDA Betonarme plak ağırlığı = 25,32513,0 =×=× bfh γ kN/m2
Sıva ve kaplama ağırlığı =..............................= 1,5 kN/m2 Σg =4,75 kN/m2 q = 2 kN/m2 Pd = 1,4.g + 1,6.q = 26,175,44,1 ×+× ⇒ Pd = 9,85 kN/m2 BALKON VE SAHANLIKTA Betonarme plak ağırlığı = 25,32513,0 =×=× bfh γ kN/m2
Sıva ve kaplama ağırlığı =..............................= 1,5 kN/m2 Σg =4,75 kN/m2 q = 3,5 kN/m2 Pd = 1,4.g + 1,6.q = 5,36,175,44,1 ×+× ⇒ Pd = 12,25 kN/m2
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DÖŞEMELERDE MOMENT HESABI açıklıkta ⇒ Mx = αx.Pd.lsn
2 My = αy.Pd.lsn2
mesnetlerde ⇒ X = -αx.Pd.lsn
2 Y = -αy.Pd.lsn2
lsn = kısa temiz açıklık D101 DÖŞEMESĐ m = 1,035 ⇒ α tablodan seçilir Mx = 0,0324 . 9,85 . ( 4,37 ) 2 = 6,09 kNm/m
X = - 0,0438 . 9,85 . ( 4,37 ) 2 = - 8,24 kNm/m
My = 0,031 . 9,85 . ( 4,37 ) 2 = 5,83 kNm/m
Y = - 0,042 . 9,85 . ( 4,37 ) 2 = - 7,90 kNm/m D102 DÖŞEMESĐ m = 1,195 ⇒ α tablodan seçilir Mx = 0,0398 . 9,85 . ( 3,75 ) 2 = 5,51 kNm/m
X = - 0,0527 . 9,85 . ( 3,75 ) 2 = - 7,30 kNm/m
My = 0,031 . 9,85 . ( 3,75 ) 2 = 5,166 kNm/m
Y = - 0,042 . 9,85 . ( 3,75 ) 2 = - 5,82 kNm/m D103 DÖŞEMESĐ m = 1,079 ⇒ α tablodan seçilir Mx = 0,031 . 9,85 . ( 4,03 ) 2 = 4,96 kNm/m
X = - 0,042 . 9,85 . ( 4,03 ) 2 = - 6,72 kNm/m
My = 0,0342 . 9,85 . ( 4,03 ) 2 = 5,41 kNm/m
Y = - 0,046 . 9,85 . ( 4,03 ) 2 = - 7,36 kNm/m D105 DÖŞEMESĐ m = 1,07 ⇒ α tablodan seçilir Mx = 0,0338 . 9,85 . ( 3,75 ) 2 = 4,68 kNm/m
X = - 0,0455 . 9,85 . ( 3,75 ) 2 = - 6,30 kNm/m
My = 0,031 . 9,85 . ( 3,75 ) 2 = 4,29 kNm/m
Y = - 0,042 . 9,85 . ( 3,75 ) 2 = - 5,82 kNm/m
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D106 DÖŞEMESĐ m = 1,08 ⇒ α tablodan seçilir Mx = 0,025 . 9,85 . ( 4,03 ) 2 = 4,00 kNm/m
X = - 0,033 . 9,85 . ( 4,03 ) 2 = - 5,28 kNm/m
My = 0,029 . 9,85 . ( 4,03 ) 2 = 4,64 kNm/m
Y = - 0,0386 . 9,85 . ( 4,03 ) 2 = - 6,17 kNm/m D102A DÖŞEMESĐ m = 1,195 ⇒ α tablodan seçilir Mx = 0,049 . 9,85 . ( 3,75 ) 2 = 6,79 kNm/m
X = - 0,065 . 9,85 . ( 3,75 ) 2 = - 9,00 kNm/m
My = 0,044 . 9,85 . ( 3,75 ) 2 = 6,09 kNm/m
Y = 0 D104 DÖŞEMESĐ
Y = =−=−2
)6,1.(25,12
2
. 22snd lP
- 15,68 kNm/m
D107 – D108 DÖŞEMESĐ
Y = =−=−2
)475,1.(25,12
2
. 22snd lP
- 13,33 kNm/m
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AÇIKLIK DONATISI HESABI
D101 DÖŞEMESĐ Mx = 6,09 kNm/m > My = 5,83 kNm/m
x-x yönü
d1 = hf – d´ = 13 – 2 =11 cm
k m =2
6
2 110.1000
10.09,6
.=
db
M
w
d = 0,50 ⇒ kz = 0,976 ⇒
A s=191.110.976,0
10.09,6
..
6
=ydz
d
fdk
M = 297 mm 2 / m
A s,min = 0,0015 . b . d = 0,0015 . 1000 .110 = 165 mm2 / m
A s = 297 mm 2 / m ⇒ ∅∅∅∅8 / 16,50 seçildi. ⇒ s ≤ 1,5.hf = 19,5 cm ve s ≤ 20 cm
∅∅∅∅8 / 33 düz + ∅∅∅∅8 / 33 pilye
y-y yönü
k m =2
6
2 102.1000
10.83,5
.=
db
M
w
d = 0,56 ⇒ kz = 0,975 ⇒
A s=191.102.975,0
10.09,6
..
6
=ydz
d
fdk
M = 285 mm 2 / m
A s,min = 0,0015 . b . d = 0,0015 . 1000 .102 = 153 mm2 / m
A s = 285 mm 2 / m ⇒ ∅∅∅∅8 / 17,50 seçildi. ⇒ s ≤ 1,5.hf = 19,5 cm ve s ≤ 25 cm ∅∅∅∅8 / 35 düz + ∅∅∅∅8 / 35 pilye r t = ( 305 + 287 ) / ( 1000 . 110 ) = 0,0054 ≥ 0,004 D102 DÖŞEMESĐ Mx = 5,51 kNm/m > My = 4,29 kNm/m
x-x yönü
d1 = hf – d´ = 13 – 2 =11 cm
k m =2
6
2 110.1000
10.51,5
.=
db
M
w
d = 0,46 ⇒ kz = 0,979 ⇒
A s=191.110.979,0
10.51,5
..
6
=ydz
d
fdk
M = 268 mm 2 / m
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A s,min = 0,0015 . b . d = 0,0015 . 1000 .110 = 165 mm2 / m
A s = 268 mm 2 / m ⇒ ∅∅∅∅8 / 18,50 seçildi. ⇒ s ≤ 1,5.hf = 19,5 cm ve s ≤ 20 cm
∅∅∅∅8 / 37 düz + ∅∅∅∅8 / 37 pilye
y-y yönü
k m =2
6
2 102.1000
10.29,4
.=
db
M
w
d = 0,41 ⇒ kz = 0,981 ⇒
A s=191.102.981,0
10.29,4
..
6
=ydz
d
fdk
M = 225 mm 2 / m
A s,min = 0,0015 . b . d = 0,0015 . 1000 .102 = 153 mm2 / m
A s = 225 mm 2 / m ⇒ ∅∅∅∅8 / 19,50 seçildi. ⇒ s ≤ 1,5.hf = 19,5 cm ve s ≤ 25 cm ∅∅∅∅8 / 39 düz + ∅∅∅∅8 / 39 pilye r t = ( 272 + 258 ) / ( 1000 . 110 ) = 0,0048 ≥ 0,004 D103 DÖŞEMESĐ My = 5,41 kNm/m > Mx = 4,96 kNm/m
y-y yönü
d1 = hf – d´ = 13 – 2 =11 cm
k m =2
6
2 110.1000
10.41,5
.=
db
M
w
d = 0,45 ⇒ kz = 0,979 ⇒
A s=191.110.979,0
10.41,5
..
6
=ydz
d
fdk
M = 263 mm 2 / m
A s,min = 0,0015 . b . d = 0,0015 . 1000 .110 = 165 mm2 / m
A s = 263 mm 2 / m ⇒ ∅∅∅∅8 / 19 seçildi. ⇒ s ≤ 1,5.hf = 19,5 cm ve s ≤ 20 cm
∅∅∅∅8 / 38 düz + ∅∅∅∅8 / 38 pilye
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x-x yönü
k m =2
6
2 102.1000
10.96,4
.=
db
M
w
d = 0,52 ⇒ kz = 0,976 ⇒
A s=191.102.976,0
10.96,4
..
6
=ydz
d
fdk
M = 285 mm 2 / m
A s,min = 0,0015 . b . d = 0,0015 . 1000 .102 = 153 mm2 / m
A s = 285 mm 2 / m ⇒ ∅∅∅∅8 / 17,50 seçildi. ⇒ s ≤ 1,5.hf = 19,5 cm ve s ≤ 25 cm ∅∅∅∅8 / 35 düz + ∅∅∅∅8 / 35 pilye r t = ( 287 + 265 ) / ( 1000 . 110 ) = 0,005 ≥ 0,004 D105 DÖŞEMESĐ Mx = 4,68 kNm/m > My = 4,29 kNm/m
x-x yönü
d1 = hf – d´ = 13 – 2 =11 cm
k m =2
6
2 110.1000
10.68,4
.=
db
M
w
d = 0,39 ⇒ kz = 0,982 ⇒
A s=191.110.982,0
10.68,4
..
6
=ydz
d
fdk
M = 227 mm 2 / m
A s,min = 0,0015 . b . d = 0,0015 . 1000 .110 = 165 mm2 / m
A s = 227 mm 2 / m ⇒ ∅∅∅∅8 / 19,50 seçildi. ⇒ s ≤ 1,5.hf = 19,5 cm ve s ≤ 20 cm
∅∅∅∅8 / 39 düz + ∅∅∅∅8 / 39 pilye
y-y yönü
k m =2
6
2 102.1000
10.29,4
.=
db
M
w
d = 0,41 ⇒ kz = 0,981 ⇒
A s=191.102.981,0
10.29,4
..
6
=ydz
d
fdk
M = 225 mm 2 / m
A s,min = 0,0015 . b . d = 0,0015 . 1000 .102 = 153 mm2 / m
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A s = 225 mm 2 / m ⇒ ∅∅∅∅8 / 19,50 seçildi. ⇒ s ≤ 1,5.hf = 19,5 cm ve s ≤ 25 cm ∅∅∅∅8 / 39 düz + ∅∅∅∅8 / 39 pilye r t = ( 258 + 258 ) / ( 1000 . 110 ) = 0,0047 ≥ 0,004 D106 DÖŞEMESĐ My = 4,64 kNm/m > Mx = 4,00 kNm/m
y-y yönü
d1 = hf – d´ = 13 – 2 =11 cm
k m =2
6
2 110.1000
10.64,4
.=
db
M
w
d = 0,38 ⇒ kz = 0,982 ⇒
A s=191.110.982,0
10.64,4
..
6
=ydz
d
fdk
M = 225 mm 2 / m
A s,min = 0,0015 . b . d = 0,0015 . 1000 .110 = 165 mm2 / m
A s = 225 mm 2 / m ⇒ ∅∅∅∅8 / 19,5 seçildi. ⇒ s ≤ 1,5.hf = 19,5 cm ve s ≤ 20 cm
∅∅∅∅8 / 39 düz + ∅∅∅∅8 / 39 pilye
x-x yönü
k m =2
6
2 102.1000
10.00,4
.=
db
M
w
d = 0,38 ⇒ kz = 0,982 ⇒
A s=191.102.982,0
10.00,4
..
6
=ydz
d
fdk
M = 209 mm 2 / m
A s,min = 0,0015 . b . d = 0,0015 . 1000 .102 = 153 mm2 / m
A s = 209 mm 2 / m ⇒ ∅∅∅∅8 / 19,50 seçildi. ⇒ s ≤ 1,5.hf = 19,5 cm ve s ≤ 25 cm ∅∅∅∅8 / 39 düz + ∅∅∅∅8 / 39 pilye
r t = ( 258 + 258 ) / ( 1000 . 110 ) = 0,0047 ≥ 0,004
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D102A DÖŞEMESĐ Mx = 6,79 kNm/m > My = 5,41 kNm/m
x-x yönü
d1 = hf – d´ = 13 – 2 =11 cm
k m =2
6
2 110.1000
10.79,6
.=
db
M
w
d = 0,56 ⇒ kz = 0,975 ⇒
A s=191.110.975,0
10.79,6
..
6
=ydz
d
fdk
M = 332 mm 2 / m
A s,min = 0,0015 . b . d = 0,0015 . 1000 .110 = 165 mm2 / m
A s = 332 mm 2 / m ⇒ ∅∅∅∅8 / 15 seçildi. ⇒ s ≤ 1,5.hf = 19,5 cm ve s ≤ 20 cm
∅∅∅∅8 / 30 düz + ∅∅∅∅8 / 30 pilye
y-y yönü
k m =2
6
2 102.1000
10.09,6
.=
db
M
w
d = 0,59 ⇒ kz = 0,973 ⇒
A s=191.102.973,0
10.09,6
..
6
=ydz
d
fdk
M = 321 mm 2 / m
A s,min = 0,0015 . b . d = 0,0015 . 1000 .102 = 153 mm2 / m
A s = 321 mm 2 / m ⇒ ∅∅∅∅8 / 15,50 seçildi. ⇒ s ≤ 1,5.hf = 19,5 cm ve s ≤ 25 cm ∅∅∅∅8 / 31 düz + ∅∅∅∅8 / 31 pilye r t = ( 324 + 335 ) / ( 1000 . 110 ) = 0,006 ≥ 0,004
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DÖŞEME MESNET DONATILARI HESABI
D101 - D102
24,8
30,7=b
k
X
X = 0,89 > 0,8 ⇒ Md = Xb = 8,24 kNm / m
k m =2
6
2 110.1000
10.24,8
.=
db
M
w
d = 0,68 ⇒ kz = 0,969
As,gerekli =191.110.969,0
10.24,8
..
6
=ydz
d
fdk
M = 405 mm 2 / m
As,mevcut = ∅8 / 33 + ∅8 / 37 = 288 mm2 / m As,ek = 405 – 288 = 117 mm2 / m ⇒⇒⇒⇒ ∅∅∅∅8 / 33 D101 – D106
9,7
17,6=b
k
X
X = 0,78 < 0,8 ⇒ moment dengelemesi yapılacak !
r21 r23
r21 =
28,4
..4
78,4
..478,4
..4
IEIE
IE
+ = 0,47 r23 =
28,4
..4
78,4
..428,4
..4
IEIE
IE
+ = 0,53
B1 = ( ) ( ) 47,0.17,690,7.3
290,7..
3
21
−−=
−− rXXX kbb = 7,36 Md = 7,36 kNm / m
B2 = ( ) ( ) 53,0.17,690,7.3
217,6..
3
22
−+=
−+ rXXX kbk = 6,78
k m =2
6
2 110.1000
10.36,7
.=
db
M
w
d = 0,61 ⇒ kz = 0,972
As,gerekli =191.110.972,0
10.36,7
..
6
=ydz
d
fdk
M = 360 mm 2 / m
As,mevcut = ∅8 / 35 + ∅8 / 39 = 273 mm2 / m As,ek = 360 – 273 = 87 mm2 / m ⇒⇒⇒⇒ ∅∅∅∅8 / 33
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D102A – D102
00,9
30,7=b
k
X
X = 0,81 > 0,8 ⇒ Md = Xb = 9,00 kNm / m
k m =2
6
2 110.1000
10.00,9
.=
db
M
w
d = 0,74 ⇒ kz = 0,967
As,gerekli =191.110.967,0
10.00,9
..
6
=ydz
d
fdk
M = 443 mm 2 / m
As,mevcut = ∅8 / 30 + ∅8 / 37 = 304 mm2 / m As,ek = 443 – 304 = 139 mm2 / m ⇒⇒⇒⇒ ∅∅∅∅8 / 33 D101 – D103
90,7
36,7=b
k
X
X = 0,93 > 0,8 ⇒ Md = Xb = 7,90 kNm / m
k m =2
6
2 110.1000
10.90,7
.=
db
M
w
d = 0,65 ⇒ kz = 0,971
As,gerekli =191.110.971,0
10.90,7
..
6
=ydz
d
fdk
M = 387 mm 2 / m
As,mevcut = ∅8 / 35 + ∅8 / 38 = 276 mm2 / m As,ek = 387 – 276 = 111 mm2 / m ⇒⇒⇒⇒ ∅∅∅∅8 / 33 D102 – D105 ( simetrik )
82,5
82,5=b
k
X
X = 1 > 0,8 ⇒ Md = Xb = 5,82 kNm / m
k m =2
6
2 110.1000
10.82,5
.=
db
M
w
d = 0,48 ⇒ kz = 0,978
As,gerekli =191.110.978,0
10.82,5
..
6
=ydz
d
fdk
M = 283 mm 2 / m
As,mevcut = ∅8 / 39 + ∅8 / 39 = 258 mm2 / m As,ek = 283 – 258 = 25 mm2 / m ⇒⇒⇒⇒ ∅∅∅∅8 / 33
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D105 – D106
30,6
28,5=b
k
X
X = 0.84 > 0,8 ⇒ Md = Xb = 6,30 kNm / m
k m =2
6
2 110.1000
10.30,6
.=
db
M
w
d = 0,52 ⇒ kz = 0,976
As,gerekli =191.110.976,0
10.30,6
..
6
=ydz
d
fdk
M = 307 mm 2 / m
As,mevcut = ∅8 / 39 + ∅8 / 39 = 258 mm2 / m As,ek = 307 – 258 = 49 mm2 / m ⇒⇒⇒⇒ ∅∅∅∅8 / 33 D101 – D102A
00,9
24,8=b
k
X
X = 0.92 > 0,8 ⇒ Md = Xb = 9,00 kNm / m
k m =2
6
2 110.1000
10.00,9
.=
db
M
w
d = 0,74 ⇒ kz = 0,967
As,gerekli =191.110.967,0
10.00,9
..
6
=ydz
d
fdk
M = 443 mm 2 / m
As,mevcut = ∅8 / 33 + ∅8 / 30 = 320 mm2 / m As,ek = 443 – 320 = 123 mm2 / m ⇒⇒⇒⇒ ∅∅∅∅8 / 33 D102 – D102
30,7
30,7=b
k
X
X = 1 > 0,8 ⇒ Md = Xb = 7,30 kNm / m
k m =2
6
2 110.1000
10.30,7
.=
db
M
w
d = 0,60 ⇒ kz = 0,973
As,gerekli =191.110.973,0
10.30,7
..
6
=ydz
d
fdk
M = 357 mm 2 / m
As,mevcut = ∅8 / 37 + ∅8 / 37 = 272 mm2 / m As,ek = 357 – 272 = 85 mm2 / m ⇒⇒⇒⇒ ∅∅∅∅8 / 33
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D101 – D107
Md = 13,13 kNm / m
k m =2
6
2 110.1000
10.33,13
.=
db
M
w
d = 1,10 ⇒ kz = 0,949
As,gerekli =191.110.949,0
10.33,13
..
6
=ydz
d
fdk
M = 667 mm 2 / m
As,mevcut = ∅8 / 35 = 144 mm2 / m As,ek = 667 – 144 = 523 mm2 / m ⇒⇒⇒⇒ ∅∅∅∅8 / 9,5
D102 – D104
Md = 15,68 kNm / m
k m =2
6
2 110.1000
10.68,15
.=
db
M
w
d = 1,30 ⇒ kz = 0,938
As,gerekli =191.110.938,0
10.68,15
..
6
=ydz
d
fdk
M = 796 mm 2 / m
As,mevcut = ∅8 / 39 = 129 mm2 / m As,ek = 796 – 129 = 667 mm2 / m ⇒⇒⇒⇒ ∅∅∅∅8 / 7,5
D103 – D108
Md = 13,13 kNm / m
k m =2
6
2 110.1000
10.33,13
.=
db
M
w
d = 1,10 ⇒ kz = 0,949
As,gerekli =191.110.949,0
10.33,13
..
6
=ydz
d
fdk
M = 667 mm 2 / m
As,mevcut = ∅8 / 35 = 144 mm2 / m As,ek = 667 – 144 = 523 mm2 / m ⇒⇒⇒⇒ ∅∅∅∅8 / 9,5
D106 – D108
Md = 13,13 kNm / m
k m =2
6
2 110.1000
10.33,13
.=
db
M
w
d = 1,10 ⇒ kz = 0,949
As,gerekli =191.110.949,0
10.33,13
..
6
=ydz
d
fdk
M = 667 mm 2 / m
As,mevcut = ∅8 / 39 = 129 mm2 / m As,ek = 667 – 129 = 538 mm2 / m ⇒⇒⇒⇒ ∅∅∅∅8 / 9
• Balkoan ve sahanlıkta dağıtma donatısı :
D107 , D108 , D104 döşemelerinde ∅∅∅∅8 / 25 dağıtma donatısı kullanılmıştır .
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KĐRĐŞ ÖN BOYUT HESABI
b w = 250 mm ve h kiri ş = 600 mm olarak alındı .
KOLON ÖN BOYUT HESABI
S1 Kolonuna Gelen Yük c/2 D107/14
a = 4,78 m S1 K101
c = 4,62 m
a/2 D101 K 113
SABĐT YÜKLER
* Döşeme Yükü = D101 + D107 75,4.60,1.2
62,475,4.
2
62,4.
2
78,4 += = 43,78 kN
* Kiri ş Yükü = K101 + K113 25.2
78,4.6,0.25,025.
2
62,4).13,06,0.(25,0 +−= = 15,75 kN
* Duvar Yükü = Dış Duvarlar 2,4.1.2
62,4
2
78,4
+= = 19,74 kN
* Kolon Kendi A ğırlı ğı = 0,4 . 0,4 . 2,94 . 25 = 11,76 kN G = 91,03 kN HAREKETLĐ YÜKLER
* Döşeme Yükü = D101 + D107 5,3.6,1.2
62,42.
2
62,4.
2
78,4 += = 23,98 kN =Q
Pd = 1,4.G + 1,6.Q = 1,4 . ( 91,03 ) + 1,6 . ( 23.98 ) ⇒ Pd = 165,81 kN P = G + Q = 91,03 + 23,98 ⇒ P = 115,01 kN
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S2 Kolonuna Gelen Yük c/2 D107/14 d/2 K101 K102 a = 4,78 m S2 D101 D102 c = 4,62 m a/2 d = 4,00 m K 115
SABĐT YÜKLER
* Döşeme Yükü = (D101 + D107 ) + D102
++=2
62,4.6,12.
2
78,4
2
62,4.
2
78,4.75,4 = 66,49 kN
* Kiri ş Yükü = K101 + K115 + K102 =
+−+−2
4.6,0
2
78,4).13,06,0(
2
62,4).13,06,0(.25.25,0
= 21,31 kN
* Duvar Yükü = Dış + Đç ( ) 25.60,094,2.2
78,472,4.1.
2
00,4
2
62,4 −+
+= = 34,32 kN
* Kolon Kendi A ğırlı ğı = 0,3 . 0,6 . 2,94 . 25 = 13,23 kN G = 135,35 kN HAREKETLĐ YÜKLER
* Döşeme Yükü = (D101 + D107) + D102 2
62,4.6,1.5,360,20 += = 33,54 kN =Q
Pd = 1,4.G + 1,6.Q = 1,4 . ( 135,35 ) + 1,6 . ( 33,54 ) ⇒ Pd = 243,15 kN P = G + Q = 135,35 + 33,54 ⇒ P = 168,89 kN
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S3 Kolonuna Gelen Yük d/2 d/2 K102 K103 a = 4,22 m S3 D102 D102 d = 4,78 m a/2 K 117
SABĐT YÜKLER
* Döşeme Yükü = D102 + D102
= 75,4.2
00,4.
2
78,4.2 = 45,42 kN
* Kiri ş Yükü= K102 + K103 + K117 25).13,06,0.(2
78,4.25,025.6,0.2.25,0.2 −+ = 22,02 kN
* Duvar Yükü = Dış + Đç ( ) 5,2.60,094,2.2
78,42,4.1.
2
00,4
2
00,4 −+
+= = 30,78 kN
* Kolon Kendi A ğırlı ğı = = 13,23 kN G = 111,450 kN HAREKETLĐ YÜKLER
* Döşeme Yükü = D102 + D102
= 2.2
00,4.
2
00,4.2 = 16,00 kN =Q
Pd = 1,4.G + 1,6.Q = 1,4 . ( 111,450 ) + 1,6 . ( 16,00 ) ⇒ Pd = 181,63 kN P = G + Q = 111,450 + 16,00 ⇒ P = 127,45 kN
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S4 Kolonuna Gelen Yük
c/2
K D101 a = 4,78 m a/2 113 b = 4,28 m c = 4,62 m S4 K105 D103 K b/2 114 SABĐT YÜKLER * Döşeme Yükü = D101 + D103 + D108 = 26,22 + 23,48 + 16,26 = 65,96 kN * Kiri ş Yükü= K113 + K114 + K105 = 8,96 + 6,29 + 6,79 = 22,04 kN
* Duvar Yükü = Dış + Đç ( ) 5,2.60,094,2.2
62,42,4.1.
2
28,5
2
78,4 −+
+= = 34,64kN
* Kolon Kendi A ğırlı ğı = = 13,23 kN G = 135,87 kN HAREKETLĐ YÜKLER * Döşeme Yükü = D101 + D103 + D108 = 11,04 + 9,89 + 11,98 = 32,91 kN =Q Pd = 1,4.G + 1,6.Q = 1,4 . ( 135,87 ) + 1,6 . ( 32,91 ) ⇒ Pd = 242,87 kN P = G + Q = 135,87 + 32,91 ⇒ P = 168,78 kN
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S5 Kolonuna Gelen Yük
c/2 d/2 D101 D102 K a = 4,78 m 115 a/2 b = 4,28 m c = 4,62 m K105 S5 K106 d = 4,00 m D103 D104 K b/2 116 SABĐT YÜKLER *DöşemeYükü=D101+D102+D103+D104
= 75,4.2
00,4.
2
28,4
2
62,4.
2
28,4
2
00,4.
2
78,4
2
62,4.
2
78,4
+++ = 92,74 kN
* Kiri ş Yükü= K115 + K116 + K105 + K106
−+−++−2
4).13,06,0(
2
62,4).13,06,0(
2
28,4.6,0
2
78,4).13,06,0(.25.25,0 = 27,72 kN
* Duvar Yükü = Đç = ( )
+−+−
+2
28,4
2
4).6,094,2.(2,55,2.60,094,2
2
78,4
2
62,4= 77,88 kN
* Kolon Kendi A ğırlı ğı = 0,5 . 0,5 . 2,94 . 25 = 18,38 kN G = 216,72 kN HAREKETLĐ YÜKLER *DöşemeYükü=D101+D102+D103+D104
=2
28,4.
2
4.5,32.
2
28,4.
2
62,4
2
78,4.
2
00,4
2
78,4.
2
62,4 +
++ = 45,47 kN = Q
Pd = 1,4.G + 1,6.Q = 1,4 . ( 216,72 ) + 1,6 . ( 45,47 ) ⇒ Pd = 376,16 kN P = G + Q = 216,72 + 45,47 ⇒ P = 262,19 kN
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S6 Kolonuna Gelen Yük
d/2 d/2 D102 D102 K a = 4,78 m 117 a/2 b = 4,28 m d = 4,00 m K106 S6 K107 D104 D105 K b/2 118 SABĐT YÜKLER *DöşemeYükü=D102+D102+D104+D105
= 75,4.2
28,4.
2
00,4
2
28,4.
2
00,4
2
78,4.
2
00,4.2
++ = 86,07 kN
* Kiri ş Yükü= K117 + K118 + K106 + K107
25.2
4).13,06,0.(25,0.225.
2
28,4.6,0.25,025.
2
78,4).13,06,0.(25,0 −++− = 26,81 kN
* Duvar Yükü = Đç + Merdiven Yakını
= ( ) ( ) 2,5.60,094,2.2
28,4.
2
00,45,2.60,094,2
2
78,4
2
00,4 −
+−
+ = 76,06 kN
* Kolon Kendi A ğırlı ğı = 0,5 . 0,5 . 2,94 . 25 = 18,38 kN G = 207,32 kN HAREKETLĐ YÜKLER *DöşemeYükü=D102+D102+D104+D105
=2
28,4.
2
4.2
2
28,4.
2
4.5,3
2
78,4.
2
4
2
4.2 ++
+ = 42,66 kN = Q
Pd = 1,4.G + 1,6.Q = 1,4 . ( 207,32 ) + 1,6 . ( 42,66 ) ⇒ Pd = 358,504 kN P = G + Q = 207,32 + 42,66 ⇒ P = 249,98 kN
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KOLON ENKES ĐT ALANLARI
Kolon No
Kat No
G Q G + Q 1,4G + 1,6Q N d ( kN )
Ac=Nd/(0.5fck) ( mm 2 )
KESĐT
4 91,03 23,98 115,01 165,81 16581 30 / 30 3 182,06 47,96 230,02 331,62 33162 30 / 30 2 273,09 71,94 345,03 497,43 49743 30 / 30 1 364,12 95,92 460,04 663,24 66324 30 / 30
Zemin 455,15 119,90 575,05 829,05 82905 30 / 30
S 1
4 135,35 33,54 168,89 243,15 24315 30 / 40 3 270,70 67,08 304,24 432,64 43264 30 / 40 2 406,05 100,62 506,67 729,46 72946 30 / 40 1 541,40 134,16 675,56 972,62 97262 30 / 40
Zemin 676,75 167,70 844,45 1215,77 121577 30 / 45
S 2
4 111,45 16 127,45 181,63 18162 30 / 40 3 222,90 32 254,90 363,26 36326 30 / 40 2 334,35 48 382,35 544,89 54489 30 / 40 1 445,80 64 509,80 726,52 72652 30 / 40
Zemin 557,25 80 637,25 908,15 90815 30 / 40
S 3
4 135,87 32,91 168,78 242,87 24287 40 / 30 3 271,74 65,82 337,56 485,75 48575 40 / 30 2 407,61 98,73 506,34 728,62 72862 40 / 30 1 543,48 131,64 675,12 971,50 97150 40 / 30
Zemin 649,35 164,55 843,90 1214,37 121437 45 / 30
S 4
4 216,72 45,47 262,19 376,16 37616 30 / 30 3 433,44 90,94 524,38 752,32 75232 30 / 30 2 650,16 136,41 786,57 1128,48 112848 35 / 35 1 866,88 181,88 1048,76 1504,64 150464 40 / 40
Zemin 1083,60 227,35 1310,95 1880,80 188080 45 / 45
S 5
4 207,32 42,66 249,98 358,504 35850,40 30 / 30 3 414,64 85,32 499,96 717,01 71701 30 / 30 2 621,96 127,98 749,94 1075,51 107551 35 / 35 1 829,28 170,64 999,92 1434,02 143402 40 / 40
Zemin 1036,60 213,30 1249,90 1792,52 179252 45 / 45
S 6
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Ix = 12
. 3bh Iy =
12
. 3hb
KOLON ATALET MOMENTLER Đ
KOLON KAT hkat b h I x Iy kx=(Ix/hkat) ky=(Iy/hkat)
NO NO (m) (dm) (dm) (dm 4) (dm 4) (dm 4/m) (dm 4/m) 4 2,94 3 3 6,75 6,75 2,296 2,296 3 2,94 3 3 6,75 6,75 2,296 2,296 2 2,94 3 3 6,75 6,75 2,296 2,296 1 2,94 3 3 6,75 6,75 2,296 2,296
Zemin 2,94 3 3 6,75 6,75 2,296 2,296
S 1
4 2,94 3 4 9 16 3,061 5,442 3 2,94 3 4 9 16 3,061 5,442 2 2,94 3 4 9 16 3,061 5,442 1 2,94 3 4 9 16 3,061 5,442
Zemin 2,94 3 4,5 10,125 22,781 3,444 7,749
S 2
4 2,94 3 4 9 16 3,061 5,442 3 2,94 3 4 9 16 3,061 5,442 2 2,94 3 4 9 16 3,061 5,442 1 2,94 3 4 9 16 3,061 5,442
Zemin 2,94 3 4 9 16 3,061 5,442
S 3
4 2,94 4 3 16 9 5,442 3,061 3 2,94 4 3 16 9 5,442 3,061 2 2,94 4 3 16 9 5,442 3,061 1 2,94 4 3 16 9 5,442 3,061
Zemin 2,94 4,5 3 22,781 10,125 7,749 3,444
S 4
4 2,94 3 3 6,75 6,75 2,296 2,296 3 2,94 3 3 6,75 6,75 2,296 2,296 2 2,94 3,5 3,5 12,505 12,505 4,253 4,253 1 2,94 4 4 21,333 21,333 7,256 7,256
Zemin 2,94 4,5 4,5 34,172 34,172 11,623 11,623
S 5
4 2,94 3 3 6,75 6,75 2,296 2,296 3 2,94 3 3 6,75 6,75 2,296 2,296 2 2,94 3,5 3,5 12,505 12,505 4,253 4,253 1 2,94 4 4 21,333 21,333 7,256 7,256
Zemin 2,94 4,5 4,5 34,172 34,172 11,623 11,623
S 6
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KĐRĐŞ YÜKLER Đ 1-1 AKSI ** K101 K ĐRĐŞĐ ** 1) SABĐT YÜKLER * Kiri ş Ağırlığı : ( ) ( ) 25.25,0.13,060,0.. −=− bwf bhh γ = 2,938 kN/m
* Duvar Ağırlığı : 2,4.1. =duvduvh γ = 4,2 kN/m
* D107 Döşemesi : 75,4.6,1. 107 =gls = 7,6 kN/m
g1 = 14,738 kN/m ( uniform yayılı )
* D101 Döşemesi : 75,4.2
62,4.
2 101 =gls ⇒ g2 = 10,973 kN/m ( üçgen yayılı )
2) HAREKETLĐ YÜKLER * D107 Döşemesi : 5,3.6,1. 107 =qls ⇒ q1 = 5,6 kN/m ( uniform yayılı )
* D101 Döşemesi : 2.2
62,4.
2 101 =qls ⇒ q2 =4,62 kn/m ( üçgen yayılı )
** K102 K ĐRĐŞĐ ** 1) SABĐT YÜKLER * Kiri ş Ağırlığı : ( ) ( ) 25.25,0.13,060,0.. −=− bwf bhh γ = 2,938 kN / m
* Duvar Ağırlığı : 2,4.1. =duvduvh γ = 4,2 kN / m
g1 = 6,575 kN / m ( uniform yayılı )
* D102 Döşemesi : 75,4.2
00,4.
2 102 =gls ⇒ g2 = 9,50 kN / m ( üçgen yayılı )
2) HAREKETLĐ YÜKLER
* D102 Döşemesi : 2.2
00,4.
2 102 =qls ⇒ q2 =4,00 kN / m ( üçgen yayılı )
K103 ve K104 kirişlerindeki yükler de K101 ve K102 kirişlerinin ki gibidir .
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C - C AKSI ** K117 K ĐRĐŞĐ ** 1) SABĐT YÜKLER * Kiri ş Ağırlığı : ( ) ( ) 25.25,0.12,050,0.. −=− bwf bhh γ = 2,938 kN / m
* Duvar Ağırlığı : ( ) ( ) 5,2.60,094,2. −=− duvkirkat hh γ = 5,85 kN / m
g1 = 8,788 kN / m ( uniform yayılı )
* D102 Döşemesi : 75,4.2
00,4.2.
2.2 102 =gls ⇒ g2 = 19 kN / m ( trapez yayılı )
2) HAREKETLĐ YÜKLER
* D102 Döşemesi : 2.2
00,4.2.
2.2 102 =qls ⇒ q1 =8,00 kN / m ( trapez yayılı )
** K118 K ĐRĐŞĐ ** 1) SABĐT YÜKLER * Kiri ş Ağırlığı : ( ) ( ) 25.25,0.13,060,0.. −=− bwf bhh γ = 2,938 kN / m
* Duvar Ağırlığı : ( ) ( ) 2,5.60,094,2. −=− duvkirkat hh γ = 12,168 kN / m
g1 = 15,106 kN / m ( uniform yayılı )
* D104 Döşemesi : 75,4.2
00,4.
2 104 =gls ⇒ g2 = 9,50 kN / m ( trapez yayılı )
* D105 Döşemesi : 75,4.2
00,4.
2 105 =gls ⇒ g3 = 9,50 kN / m ( trapez yayılı )
2) HAREKETLĐ YÜKLER
* D104 Döşemesi : 5,3.2
00,4.
2 104 =qls ⇒ q1 = 7,00 kN / m ( trapez yayılı )
* D105 Döşemesi : 2.2
00,4.
2 105 =qls ⇒ q2 =4,00 kN / m ( trapez yayılı )
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KĐRĐŞ YÜKLER Đ
KĐRĐŞ YÜKLER Đ ANKASTREL ĐK MOMENTLER Đ KESME KUVVETLER Đ
Mg Mq Vog Voq M(kNm) Vo(kN)
KĐRĐŞ NO L(m) YÜK NO YÜK g q P Pd 0,9g
i j i j i j Đ j
YÜKLEME
i j i j
1 uniform 14,738 5,60 20,338 29,593 13,264 26,21 -26,21 9,96 -9,96 34,04 -34,04 12,94 -12,94 G 38,41 -38,41 46,71 -46,71
2 üçgen 10,973 4,62 15,593 22,754 9,878 12,20 -12,20 5,14 -5,14 12,67 -12,67 5,34 -5,34 G+Q 53,51 -53,51 64,99 -64,99
1,4G+1,6Q 77,93 -77,93 94,64 -94,64 K101 4,62
TOPLAM 38,41 -38,41 15,10 -15,10 46,71 -46,71 18,28 -18,28 0,9G 34,57 -34,57 42,04 -42,04
1 uniform 7,138 0 7,138 9,993 6,424 9,52 -9,52 0 0 14,28 -14,28 0 0 G 17,44 -17,44 23,78 -23,78
2 üçgen 9,5 4,00 13,50 19,70 8,55 7,92 -7,92 3,33 -3,33 9,50 -9,50 4,00 -4,00 G+Q 20,77 -20,77 27,78 -27,78
1,4G+1,6Q 29,74 -29,74 39,69 -39,69 K102 4,00
TOPLAM 17,44 -17,44 3,33 -3,33 23,78 -23,78 4,00 -4,00 0,9G 15,70 -15,70 21,40 -21,40
1 uniform 8,788 0 8,788 12,303 7,909 16,73 -16,73 0 0 21,00 -21,00 0 0 G 42,89 -42,89 47,41 -47,41
2 trapez 19 8 27 39,40 17,10 26,16 -26,16 11,01 -11,01 26,41 -26,41 11,12 -11,12 G+Q 53,90 -53,90 58,53 -58,53
1,4G+1,6Q 77,66 -77,66 84,17 -84,17 K117 4,78
TOPLAM 42,89 -42,89 11,01 -11,01 47,41 -47,41 11,12 -11,12 0,9G 38,60 -38,60 42,67 -42,67
1 uniform 15,106 0 15,106 21,15 13,595 23,06 -23,06 0 0 32,33 -32,33 0 0 G 42,36 -42,36 53,99 -53,99
2 trapez 19 11 30 44,20 17,10 19,30 -19,30 11,17 -11,17 21,66 -21,66 12,54 -12,54 G+Q 53,53 -53,53 66,53 -66,53
1,4G+1,6Q 77,18 -77,18 95,65 -95,65 K118 4,28
TOPLAM 42,36 -42,36 11,17 -11,17 53,99 -53,99 12,54 -12,54 0,9G 38,12 -38,12 48,59 -48,59
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KĐRĐŞ KESĐTLER Đ Y-Y YÖNÜ 4,78 m 4,28 m 4,78 m
Lp =0,7 L1 Lp =0,6 L2 Lp =0,7 L1
= 3,346 m = 2,568 m = 3,346 m **K115-K117-K119 K ĐRĐŞLERĐ**
b = bw + 0,2.Lp l = 4,78 m 0,13 0,13 ( Dış Açıklık ) ⇒ Lp = 3,346 m Lp/10 h = 0,60 b = 0,25 + 0,2 . ( 3,346 ) = 0,9192 m A = 2,5 . 6 + 2 . 30346 . 1,3 = 23,6996 dm2 0,25
y0 =6996,23
35,5.3,1.346,3.23.6.5,2 + = 3,86 dm
I =
+++ 2
32
3
49,1.346,3.3,112
346,3.3,1.286,0.6.5,2
12
6.5,2 = 76,633 dm4
K =78,4
633,76=L
I = 16,032 dm4/m
**K116-K118 KiRi ŞLERi**
b = bw + 0,1.Lp l = 4,28 m 0,13 ( Đç Açıklık ) ⇒ Lp = 2,568 m Lp/10 h = 0,60 b = 0,25 + 0,1 . ( 2,568 ) = 0,5068 m A = 2,5 . 6 + 2,568 . 1,3 = 18,3384 dm2 0,25
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y0 =3384,18
35,5.3,1.568,23.6.5,2 + = 3,4278 dm
I =
+++ 2
32
3
9222,1.568,2.3,112
568,2.3,14278,0.6.5,2
12
6.5,2 = 60,55 dm4
K =28,4
55,60=L
I = 14,147 dm4/m
X-X YÖNÜ 4,62 m 4,00 m 4,00 m 4,62 m Lp = 0,7.L Lp = 0,6.L Lp = 0,6.L Lp = 0,7.L = 3,234 m = 2,40 m = 2,40 m = 3,234 m **K101-K104 K ĐRĐŞLERĐ**
b = bw + 0,2.Lp l = 4,62 m 0,13 0,13 ( Dış Açıklık ) ⇒ Lp = 3,234 m Lp/10 h = 0,60 b = 0,25 + 0,2 . ( 3,234 ) = 0,8968 m A = 2,5 . 6 + 2 . ( 3,234 . 1,3 ) = 23,4084 dm2 0,25
y0 =4084,23
35,5.3,1.234,3.23.6.5,2 + = 3,84 dm
I =
+++ 2
32
3
51,1.234,3.3,112
234,3.3,1.284,0.6.5,2
12
6.5,2 = 75,94 dm4
K =62,4
94,75=L
I = 16,437 dm4/m
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**K102-K103 K ĐRĐŞLERĐ**
b = bw + 0,1.Lp l = 4,00 m 0,13 ( Đç Açıklık ) ⇒ Lp = 2,40 m Lp/10 h = 0,60 b = 0,25 + 0,1 . (2,40) = 0,49 m A = 2,5 . 6 + 2,40 . 1,3 = 18,12 dm2 0,25
y0 =12,18
35,5.3,1.4,23.6.5,2 + = 3,40 dm
I =
+++ 2
32
3
95,1.40,2.3,112
4,2.3,140,0.6.5,2
12
6.5,2 = 59,70 dm4
K =00,4
70,59=L
I = 14,925 dm4/m
Bütün kiri şlerin atalet momentleri ve redörleri : Kiri ş No
L ( m )
I ( dm 4 )
k (dm 4 )
K101 4,62 75,94 16,437 K102 4,00 59,70 14,925 K103 4,00 59,70 14,925 K104 4,62 75,94 16,437 K105 4,62 75,94 16,437 K106 4,00 70,22 17,555 K107 4,00 70,22 17,555 K108 4,62 75,94 16,437 K109 4,62 75,94 16,437 K110 4,00 59,70 14,925 K111 4,00 70,22 17,555 K112 4,62 75,94 16,437 K113 4,78 64,23 13,437 K114 4,28 71,46 16,696 K115 4,78 76,633 16,032 K116 4,28 60,55 14,147 K117 4,78 76,633 16,032 K118 4,28 60,55 14,147 K119 4,78 76,633 16,032 K120 4,28 71,46 16,696
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KĐRĐŞLERE ELVER ĐŞSĐZ YÜKLEMELER C-C AKSI 5 7 9 11 2,94 m K117 2 K118 3 K117 4 1 2,94 m 6 8 10 12 S 3 ( 30 / 40 ) S 6 ( 45 / 45 ) S 6 (45 / 45 ) S 3 ( 30 / 40 )
REDÖR HESABI rij = ij
ij
kn
kn
.
.
Σ
* Simetrik Yüklemeler Đçin
r12 =
8,47
633,76.4
4,29
16.4
4,29
16.48,47
633,76.4
++= 0,60
Σr = 0,60 + 2 . ( 0,20 ) = 1
r15 = r16 =
8,47
633,76.4
4,29
16.4
4,29
16.44,29
00,16.4
++= 0,20
r27 =
8,47
633,76.4
4,29
17,34.4
8,42
55,60.2
4,29
33,21.44,29
33,21.4
+++= 0,17
Σr = 0,17 + 0,19 + 0,27 + 0,37 = 1
r23 =
8,47
633,76.4
4,29
17,34.4
8,42
55,60.2
4,29
33,21.480,42
55,60.2
+++= 0,19
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33
r28 =
8,47
633,76.4
4,29
17,34.4
8,42
55,60.2
4,29
33,21.44,29
17,34.4
+++= 0,27
r21 =
8,47
633,76.4
4,29
17,34.4
8,42
55,60.2
4,29
33,21.480,47
633,76.4
+++= 0,37
1. GRUP 1. YÜKLEME ( Pd – G – Pd )
Bu yüklemede max MK117 , V12 ve X12 bulunur . Pd = 39,40 kN / m Pd = 12,303 kN / m 35,65 kNm 81,46 kNm 74,59 kN 4,78m 93,75 kN V12 V21
M i j M j i
K 117 77,66 -77,66 K 118 42,36 -42,36 K 117 77,66 -77,66
D.N 1 2
Ç.N 15 16 12 27 28 23 21
r 0,20 0,20 0,60 0,17 0,27 0,19 0,37
M0 0 0 77,66 0 0 42,36 -77,36
1 -15,53 -15,53 -46,60 -23,30
2 10,84 9,96 15,82 11,13 21,68
1 -2,17 -2,17 -6,51 -3,26
2 0,61 0,55 0,88 0,62 1,21
1 -0,12 -0,12 -0,37 -0,19
2 0,04 0,03 0,05 0,04 0,07
1 -0,01 -0,01 -0,02 -0,01
toplam -17,83 -17,83 35,65 10,54 16,75 54,15 -81,46
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V12 = 78,4
2
78,4.
2
40,39).78,478,0(
2
78,4.303,1246,8165,35
2
+++− = 74,59 kN
V21 = 78,4
2
78,4.
2
40,39).78,478,0(
2
78,4.303,1246,8165,35
2
++++− = 93,75 kN
• Maximum momentin bulunuşu :
)2.(40,3940,39303,1259,74 −−−− xx = 0 ⇒ x = 2,205 m
Mmax = 2
205,0.40,39205,0
3
2.
2
40,39.2
2
205,2.303,12205,2.59,7465,35
22
−
+−−+−
M max = 63,74 kNm 1. GRUP 2. YÜKLEME ( G – Pd – G )
M i j M j i
K 117 42,89 -42,89 K 118 77,18 -77,18 K 117 42,89 -42,89
D.N 1 2 Ç.N 15 16 12 27 28 23 21
r 0,20 0,20 0,60 0,17 0,27 0,19 0,37
M0 42,89 77,18 -42,89
2 -8,58 -8,58 -25,73 -12,87
1 -3,96 -3,64 -5,78 -4,07 -7,93
2 0,79 0,79 2,38 1,19
1 -0,22 -0,20 -0,32 -0,23 -0,44
2 0,04 0,04 0,13 0,07
1 -0,02 -0,01 -0,02 -0,01 -0,03
2 0,005 0,005 0,01 0,005
toplam -7,745 -7,745 15,48 -3,85 -6,12 72,87 -62,895
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Bu Yüklemede max MK118 Bulunur Pd = 44,20 kN / m Pd = 21,15kN / m 72,87 kNm 72,87 kNm 94,765 kN 4,28m 94,765 kN V23 V32 V23 = V32 = 94,765 kN Yükleme ve Kesit Simetrik ⇒ x = 2,14 m
• Maximum momentin bulunuşu :
Mmax = 2
14,0.14,0.20,4487,72
3
214,0.
2
2.20,44
2
14,2.45,2114,2.765,94
2
−−
+−−
M max = 44,91 kNm
REDÖR HESABI rij = ij
ij
kn
kn
.
.
Σ
* Simetrik Olmayan Yüklemeler Đçin 1. düğüm noktası için simetrik yüklemede hesaplanan redörlerle aynıdır .
r27 =
80,47
633,76.4
4,29
17,34.4
8,42
55,60.4
4,29
33,21.44,29
33,21.4
+++= 0,14
r23 =
80,47
633,76.4
4,29
17,34.4
8,42
55,60.4
4,29
33,21.480,42
55,60.4
+++= 0,32
r25 =
80,47
633,76.4
4,29
17,34.4
8,42
55,60.4
4,29
33,21.440,29
17,34.4
+++= 0,23 Σr = 0,14 + 0,32 + 0,23 + 0,31 = 1
r21 =
80,47
633,76.4
4,29
17,34.4
8,42
55,60.4
4,29
33,21.480,47
633,76.4
+++= 0,31
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r39 =
80,47
633,76.4
4,29
17,34.4
8,42
55,60.4
4,29
33,21.44,29
33,21.4
+++= 0,14
r32 =
80,47
633,76.4
4,29
17,34.4
8,42
55,60.4
4,29
33,21.480,42
55,60.4
+++= 0,32 Σr = 0,14 + 0,32 + 0,23 + 0,31 = 1
r310 =
80,47
633,76.4
4,29
17,34.4
8,42
55,60.4
4,29
33,21.440,29
17,34.4
+++= 0,23
r34 =
80,47
633,76.4
4,29
17,34.4
8,42
55,60.4
4,29
33,21.480,47
633,76.4
+++= 0,31
r43 =
8,47
633,76.4
4,29
16.4
4,29
16.48,47
633,76.4
++= 0,60
Σr = 0,60 + 2 . ( 0,20 ) = 1
r411 = r412 =
8,47
633,76.4
4,29
16.4
4,29
16.44,29
00,16.4
++= 0,20
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1. GRUP 3. YÜKLEME ( Pd – Pd – G )
M i j M j i
K 117 77,16 -77,16 K 118 77,18 -77,18 K 117 42,89 -42,89
D.N 1 2 3 4
Ç.N 15 16 12 21 27 28 23 32 39 310 34 43 412 411
r 0,20 0,20 0,60 0,31 0,14 0,23 0,32 0,32 0,14 0,23 0,31 0,60 0,20 0,20
M 0 77,66 -77,36 77,18 -77,18 42,89 -42,89
1 -15,53 -15,53 -46,60 -23,30
4 12,87 25,73 8,58 8,58
2 3,69 7,37 3,33 5,47 7,61 3,81
3 2,82 5,64 2,47 4,05 5,46 2,73
1 -0,74 -0,74 -2,21 -1,11
4 -0,82 -1,64 -0,55 -0,55
2 -0,27 -0,53 -0,24 -0,39 -0,55 -0,28
3 0,18 0,35 0,15 0,25 0,34 0,17
1 0,05 0,05 0,17 0,09
4 -0,06 -0,11 -0,03 -0,03
2 -0,04 -0,08 -0,04 -0,06 -0,09 -0,05
3 0,02 0,03 0,02 0,03 0,03 0,02
1 0,01 0,01 0,02 0,01
Toplam -16,21 -16,21 32,42 -95,21 3,05 5,02 87,17 -67,68 2,64 4,33 60,71 -15,99 8,00 8,00
Bu yüklemeden max V21 , V23 , X21 ve X23 bulunur
V21 = 78,4
2
78,4.
2
40,39).78,478,0(
2
78,4.303,1221,9542,32
2
++++− = 97,31 kN
V23 = 28,4
2
28,4.
2
20,44).28,428,0(
2
28,4.15,2117,8768,67
2
++++− = 100,20 kN
X 21 = 95,21 kNm X 23 = 87,17 kNm
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2. GRUP 1. YÜKLEME ( P – G – P )
D.N 1 2 Ç.N 15 16 12 27 28 23 21
r 0,20 0,20 0,60 0,17 0,27 0,19 0,37 M0 53,90 42,36 -53,90 1 -10,78 -10,78 -32,34 -16,17 2 5,13 4,71 7,48 5,26 10,25
1 -1,03 -1,03 -3,07 -1,54 2 0,29 0,26 0,42 0,29 0,57 1 -0,06 -0,06 -0,17 -0,09 2 0,02 0,02 0,02 0,02 0,03 1 -0,005 -0,005 -0,01 -0,005
toplam -11,88 -11,88 23,75 4,99 7,92 47,93 -60,86 Bu yüklemede max MK117 , V12 ve X12 bulunur . Pd = 27,00 kN / m Pd = 8,788 kN / m 23,75 kNm 60,86 kNm 50,77 kN 4,78m 66,29 kN V12 V21
V21 = 78,4
2
78,4.
2
00,27).78,478,0(
2
78,4.788,845,2386,60
2
+++− = 66,29 kN
V12 = 78,4
2
78,4.
2
00,27).78,478,0(
2
78,4.788,875,2386,60
2
++++− = 50,77 kN
M i j M j i
K 117 53.90 -53,90 K 118 42,36 -42,36 K 117 53,90 -53,90
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• Maximum momentin bulunuşu :
)2.(00,2700,27788,877,50 −−−− xx = 0 ⇒ x = 2,1731 m
Mmax = 2
1731,0.00,271731,0
3
2.
2
00,27.2
2
1731,2.788,81731,2.77,5075,23
22
−
+−−+−
M max = 42,75 kNm 2. GRUP 2. YÜKLEME ( G – P – G )
Bu Yüklemede max MK118 Bulunur Pd = 30,00 kN / m Pd = 15,106 kN / m 53,87 kNm 53,87 kNm K118 66,53 kN 4,28m 66,53 kN V23 V32 V23 = V32 = 66,53 kN Yükleme ve Kesit Simetrik ⇒ x = 2,14 m
• Maximum momentin bulunuşu :
Mmax = 2
14,0.14,0.00,3087,53
3
214,0.
2
2.00,30
2
14,2.106,1514,2.53,66
2
−−
+−−
M max = 29,42 kNm
D.N 1 2 Ç.N 15 16 12 27 28 23 21
r 0,20 0,20 0,60 0,17 0,27 0,19 0,37 M0 42,89 53,33 -42,89 1 -8,58 -8,58 -25,73 -12,87 2 0,45 0,41 0,66 0,46 0,90 1 -0,09 -0,09 -0,27 -0,14 2 0,03 0,02 0,04 0,03 0,05 1 -0,006 -0,006 -0,02 -0,01
toplam -8,68 -8,68 17,35 0,43 0,70 53,82 -54,96
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40
2. GRUP 3. YÜKLEME ( P – P – G )
M i j M j i
K 117 53,90 -53,90 K 118 53,53 -53,53 K 117 42,89 -42,89
D.N 1 2 3 4
Ç.N 15 16 12 21 27 28 23 32 39 310 34 43 411 412
r 0,20 0,20 0,60 0,31 0,14 0,23 0,32 0,32 0,14 0,23 0,31 0,60 0,20 0,20
M 0 53,90 -53,90 53,53 -53,53 42,89 -42,89
1 -10,78 -10,78 -32,34 -16,17
4 12,87 25,73 8,58 8,58
2 2,57 5,13 2,32 3,80 5,29 2,65
3 -0,78 -1,56 -0,68 -1,12 -1,51 -0,76
1 -0,51 -0,51 -1,55 -0,78
4 0,23 0,46 0,15 0,15
2 0,24 0,48 0,22 0,36 0,50 0,25
3 -0,08 -0,15 -0,07 -0,11 -0,15 -0,08
1 -0,05 -0,05 -0,14 -0,07
4 0,02 0,04 0,02 0,02
2 0,03 0,05 0,02 0,03 0,05 0,03
3 -0,01 -0,02 -0,01 -0,01 -0,01 -0,005
1 -0,005 -0,005 -0,02 -0,01
Toplam -11,35 -11,35 22,69 -65,27 2,56 4,19 58,5 -52,33 -0,76 -1,24 54,34 -17,51 8,75 8,75
Bu yüklemeden max V21 , V23 , X21 ve X23 bulunur
V21 = 78,4
2
78,4.
2
00,27).78,478,0(
2
78,4.788,827,6569,22
2
++++− = 67,44 kN
V23 = 28,4
2
28,4.
2
00,30).28,428,0(
2
28,4.106,1550,5833,52
2
++++− = 67,97 kN
X 21 = 65,27 kNm X 23 = 58,50 kNm
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41
3. GRUP 1. YÜKLEME ( 0,9G – 0,9G – 0,9G )
M i j M j i
K 117 38,60 -38,60 K 118 38,12 -38,12 K 117 38,60 -38,60
D.N 1 2 Ç.N 15 16 12 21 27 28 23
r 0,20 0,20 0,60 0,37 0,17 0,27 0,19 M0 38,60 -38,60 38,12 1 -7,72 -7,72 -23,16 -11,58 2 2,23 4,46 2,05 3,26 2,29 1 -0,45 -0,45 -1,33 -0,67 2 0,13 0,25 0,11 0,18 0,13 1 -0,03 -0,03 -0,07 -0,04 2 0,01 0,02 0,007 0,01 0,008 1 -0,002 -0,002 -0,006
Toplam -8,20 -8,20 16,40 -46,16 2,17 3,45 40,55
• K117 Kiri şi :
Pd = 17,10 kN / m Pd = 7,91 kN / m 16,40 kNm 46,16 kNm 36,45 kN 4,78m 48,90 kN V12 V21
V21 = 78,4
2
78,4.
2
10,17).78,478,0(
2
78,4.91,740,1616,46
2
+++− = 48,90 kN
V12 = 78,4
2
78,4.
2
10,17).78,478,0(
2
78,4.81,740,1616,46
2
++++− = 36,45 kN
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• Maximum momentin bulunuşu :
)2.(10,1710,1791,745,36 −−−− xx = 0 ⇒ x = 2,1411 m
Mmax = 2
1411,0.10,171411,0
3
2.
2
10,17.2
2
1411,2.91,71411,2.45,3640,16
22
−
+−−+−
M max = 48,60kNm
• K118 Kiri şi : Pd = 17,10 kN / m Pd = 13,60 kN / m 40,55 kNm 40,55 kNm K118 48,60 kN 4,28m 48,60 kN V23 V32 V23 = V32 = 48,60 kN Yükleme ve Kesit Simetrik ⇒ x = 2,14 m
• Maximum momentin bulunuşu :
Mmax = 2
14,0.14,0.10,1755,40
3
214,0.
2
2.10,17
2
14,2.60,1314,2.60,48
2
−−
+−−
M max = 18,69 kNm
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C-C AKSI MOMENT DÜZELTMELER Đ
X’ = X - ∆M ⇒ ∆M =3
.aV
1. GRUP YÜKLEME ( P d Yüklemesi )
X’ 12 = 3
40,0.18,7265,35 +− = - 26,026 kNm
X’ 21 = 3
40,0.31,9721,95 +− = - 82,24 kNm
X’ 23 = 3
40,0.20,10017,87 +− = - 73,81 kNm
2. GRUP YÜKLEME ( P Yüklemesi )
X’ 12 = 3
40,0.77,5075,23 +− = - 16,98 kNm
X’ 21 = 3
40,0.44,6727,65 +− = - 56,278 kNm
X’ 23 = 3
40,0.97,6750,58 +− = - 49,44 kNm
3. GRUP YÜKLEME ( 0,9 G Yüklemesi )
X’ 12 = 3
40,0.45,3640,16 +− = -11,54 kNm
X’ 21 = 3
40,0.90,4816,46 +− = - 6,52 kNm
X’ 23 = 3
40,0.60,4855,40 +− = - 34,07 kNm
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C - C AKSI KESME KUVVET Đ DÜZELTMELER Đ 1. GRUP YÜKLEME ( P d Yüklemesi )
S 3 için x = 55,02
40,0
2+=+ d
a= 0,75 m S 6 için x = 55,0
2
40,0
2+=+ d
a= 0,75 m
V ’12 =
2
75,0.745,1675,0.303,1259,74 −− = 59,08 kN
V ’21 =
2
75,0.775,1475,0.303,1231,97 −− = 82,54 kN
V ’23 =
2
75,0.575,1675,0.15,2120,100 −− = 78,12 kN
2. GRUP YÜKLEME ( P Yüklemesi )
S 3 için x = 2
40,0
2=a
= 0,20 m S 6 için x = 2
40,0
2=a
= 0,20 m
V ’12 =
2
20,0.05,420,0.788,877,50 −− = 48,61 kN
V ’21 =
2
20,0.70,220,0.788,844,67 −− = 65,41 kN
V ’23 =
2
20,0.00,320,0.106,1597,67 −− = 64,65 kN
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C - C AKSI ELVER ĐŞSĐZ YÜKLEMELER Đ
1. Grup Moment Grafiği (Pd) ( 73,81 ) ( 73,81 ) ( 26,026 ) ( 82,24 ) 87,17 87,17 ( 82,24 ) ( 26,026 ) 35,65 95,21 95,21 35,65 - - - - - - + + + 69,96 44,91 69,96
2. Grup Moment Grafiği (G+Q) ( 49,44 ) ( 49,44 ) ( 16,98 ) (56,278 ) 58,50 58,50 ( 56,278 ) ( 16,98 ) 23,75 65,27 65,27 23,75 - - - - - - + + + 42,75 29,42 42,75
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3. Grup Moment Grafiği ( 0,9G ) ( 11,54 ) ( 39,64 ) ( 34,07 ) ( 34,07 ) ( 39,64 ) ( 11,54 ) 16,40 46,16 40,55 40,55 46,16 16,40 - - - - - - + + + 29,53 18,69 29,53
1. Grup Kesme Kuvveti Grafiği ( Pd ) 74,59 ( 59,08 ) 100,20 ( 78,12 ) 97,31( 82,54 ) + + + - - - 72,18 97,31 ( 59,08 ) ( 82,54 ) 100,20 ( 78,12 )
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2. Grup Kesme Kuvveti Grafiği ( G+Q ) 50,77 ( 48,61 ) 67,97 ( 64,65 ) 67,44 ( 65,41 ) + + + - - - 50,77 67,44 ( 48,61 ) ( 65,41 ) 67,97 ( 64,65 )
3. Grup Kesme Kuvveti Grafiği ( 0,9G ) 36,45 48,60 48,90 + + + - - - 36,45 48,90 48,60
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1 - 1 AKSI ELVERĐŞSĐZ YÜKLEMELER Đ
1. Grup Moment Grafiği ( Pd ) ( 68,935 ) 79,67 ( 60,111 ) ( 60,111 ) ( 68,935 ) ( 13,643 ) 60,55 ( 21,054 ) ( 21,054 ) 65,55 79,67
22,04 24,64 24,64
22,04 - - - - - - - (13,643) -
+ + + + 18,63 18,63 73,84 73,84
2. Grup Moment Grafiği (G+Q) ( 46,938 ) ( 40,702 ) ( 46,938 ) ( 9,046 ) 54,30 ( 40,702 ) (11,49 ) ( 11,49 ) 44,40 54,30
14,74 44,40 13,74 13,74 14,74 ( 9,046 )
- - - - - - - -
+ + + + 10,21 10,21 49,58 49,58
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3. Grup Moment Grafiği (0,9G)
( 30,942 ) ( 26,987 ) ( 26,987 ) ( 30,942 ) ( 5,599 ) 35,72 29,65 ( 7,113 ) ( 7,113 ) 29,65 35,72
9,23 8,73 8,73 9,23 ( 5,599)
- - - - - - - -
+ + + + 6,00 6,00 31,20 31,20
1. Grup Kesme Kuvveti Grafiği ( Pd )
( 84,22 ) ( 60,84 ) ( 44,98 ) ( 26,45 ) 107,35 83,97 54,39 35,86 + + + + - - - - 35,86 54,39 ( 26,45 ) ( 44,98 ) 83,97 107,35 ( 60,84 ) ( 84,22 )
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2. Grup Kesme Kuvveti Grafiği ( G+Q )
( 70,49 ) ( 53,81 ) ( 35,83 ) ( 21,35 ) 73,62 56,94 36,98 22,50 + + + + - - - - 22,50 36,98 ( 21,35 ) ( 35,83 ) 56,94 73,62 ( 53,81 ) ( 70,49 )
2. Grup Kesme Kuvveti Grafiği ( 0,9G )
47,78 36,31 26,63 16,17 + + + + - - - - 16,17 26,63 36,31 47,78
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DEPREM HESABI KAT VE B ĐNA AĞILI ĞININ BULUNMASI
KOLON BENZER G i ( kN ) Qi ( kN ) S1 4 91,03 23,98 S2 4 135,35 33,54 S3 2 111,45 16,00 S4 4 135,87 32,91 S5 4 216,72 45,47 S6 2 207,32 42,66
n = 0,3 ( hareketli yük azaltma katsayısı ) Wi = Gi + n.Qi ⇒ bir katın ağırlığı W = bina ağılığı Wi = ( ) ( )[ ]++++++++ 47,4591,3254,3398,23.3,072,21687,13535,13503,91.4 ( ) ( )[ ]66,4200,16.3,032,20745,111.2 +++ W i = 3152 kN ⇒⇒⇒⇒ W = 5.Wi =15670 kN
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X-X YÖNÜ KOLON D DEĞERLERĐ
KAT KOLON BNZ kc k1 k2 k3 k4 k' a D ΣΣΣΣD
S1 4 4,225 0,000 10,520 0,000 10,520 2,490 0,555 2,343 S2 4 1,320 10,520 7,625 10,520 7,625 13,746 0,873 1,152 S3 2 1,320 7,625 7,625 7,625 7,625 11,553 0,852 1,125 S4 4 1,900 0,000 10,482 0,000 10,482 5,517 0,734 1,394 S5 2 4,225 10,482 8,976 10,482 8,976 4,605 0,697 2,946
S5A 2 4,225 9,013 10,482 9,013 10,482 4,614 0,698 2,947 S6 1 4,225 8,976 9,013 8,976 9,013 4,258 0,680 2,875
5
S6A 1 4,225 8,976 7,625 8,976 7,625 3,929 0,663 2,800
39,271
S1 4 4,225 0,000 10,520 0,000 10,520 2,490 0,555 2,343 S2 4 1,320 10,520 7,625 10,520 7,625 13,746 0,873 1,152 S3 2 1,320 7,625 7,625 7,625 7,625 11,553 0,852 1,125 S4 4 1,900 0,000 10,482 0,000 10,482 5,517 0,734 1,394 S5 2 4,225 10,482 8,976 10,482 8,976 4,605 0,697 2,946
S5A 2 4,225 9,013 10,482 9,013 10,482 4,614 0,698 2,947 S6 1 4,225 8,976 9,013 8,976 9,013 4,258 0,680 2,875
4
S6A 1 4,225 8,976 7,625 8,976 7,625 3,929 0,663 2,800
39,271
S1 4 7,207 0,000 10,520 0,000 10,520 1,460 0,422 3,041 S2 4 1,540 10,520 7,625 10,520 7,625 11,782 0,855 1,317 S3 2 1,540 7,625 7,625 7,625 7,625 9,903 0,832 1,281 S4 4 3,018 0,000 10,482 0,000 10,482 3,473 0,635 1,915 S5 2 7,207 10,482 8,976 10,482 8,976 2,700 0,574 4,140
S5A 2 7,207 9,013 10,482 9,013 10,482 2,705 0,575 4,143 S6 1 7,207 8,976 9,013 8,976 9,013 2,496 0,555 4,001
3
S6A 1 7,207 8,976 7,625 8,976 7,625 2,303 0,535 3,858
52,078
S1 4 7,207 0,000 10,520 0,000 10,520 1,460 0,422 3,041 S2 4 1,540 10,520 7,625 10,520 7,625 11,782 0,855 1,317 S3 2 1,540 7,625 7,625 7,625 7,625 9,903 0,832 1,281 S4 4 3,018 0,000 10,482 0,000 10,482 3,473 0,635 1,915 S5 2 7,207 10,482 8,976 10,482 8,976 2,700 0,574 4,140
S5A 2 7,207 9,013 10,482 9,013 10,482 2,705 0,575 4,143 S6 1 7,207 8,976 9,013 8,976 9,013 2,496 0,555 4,001
2
S6A 1 7,207 8,976 7,625 8,976 7,625 2,303 0,535 3,858
52,078
S1 4 7,207 0,000 10,520 0,000 10,520 1,460 0,422 3,041 S2 4 2,660 10,520 7,625 10,520 7,625 6,821 0,773 2,057 S3 2 2,660 7,625 7,625 7,625 7,625 5,733 0,741 1,972 S4 4 3,621 0,000 10,482 0,000 10,482 2,895 0,591 2,141 S5 2 11,545 10,482 8,976 10,482 8,976 1,685 0,457 5,280
S5A 2 11,545 9,013 10,482 9,013 10,482 1,689 0,458 5,285 S6 1 11,545 8,976 9,013 8,976 9,013 1,558 0,438 5,056
1
S6A 1 11,545 8,976 7,625 8,976 7,625 1,438 0,418 4,829
63,915
S1 4 7,207 0,000 10,520 0,000 0,000 1,460 0,566 4,082 S2 4 2,660 10,520 7,625 0,000 0,000 6,821 0,830 2,208 S3 2 2,660 7,625 7,625 0,000 0,000 5,733 0,806 2,144 S4 4 3,621 0,000 10,482 0,000 0,000 2,895 0,694 2,511 S5 2 11,545 10,482 8,976 0,000 0,000 1,685 0,593 6,846
S5A 2 11,545 9,013 10,482 0,000 0,000 1,689 0,593 6,850 S6 1 11,545 8,976 9,013 0,000 0,000 1,558 0,578 6,678
ZE
MĐN
S6A 1 11,545 8,976 7,625 0,000 0,000 1,438 0,564 6,508
80,072
k' =(k1+k2+k3+k4) / (2.kc) Zemin Katta ⇒ a = (0,5+k') / (2+k') a = k' / (2+k') k' =( k1+k2 ) / ( kc ) D=a.kc
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X-X YÖNÜ DEPREM HESABI ( 1-1 AKSI )
Vt = 1000 kN için
KATLAR W i ( kN ) Hi ( m ) W iHi VT / Σ Σ Σ Σ WiHi Fi Vi ( kN )
4.KAT 3152 14,70 46334,40 0,00719 333,333 333,333 3.KAT 3152 11,76 37067,52 0,00719 266,667 600 2.KAT 3152 8,82 27800,64 0,00719 200,00 800 1.KAT 3152 5,88 18533,76 0,00719 133,333 913,333
Z KAT 3152 2,94 9266,88 0,00719 66,667 1000
BĐNANIN B ĐRĐNCĐ DOĞAL T ĐTREŞĐM PERYODUNUN BULUNMASI
KAT m i Fi Vi ∑∑∑∑Di.(12E/h2).104 ∆di d fi Fid fi Mid fi2
4.KAT 321,30 333,333 333,333 47,70 6,988 58,374 19457,98 1094837,42 3.KAT 321,30 266,667 600,00 47,70 12,579 51,386 13702,95 848399,40 2.KAT 321,30 200,00 800,00 56,00 14,286 38,807 7761,20 483872,42 1.KAT 321,30 133,333 913,333 66,18 13,801 24,521 3269,46 193191,08
Z KAT 321,30 66,667 1000,00 93,28 10,720 10,720 714,67 36923,28
TOPLAM= 44906,26 2657223,60
ΣΣΣΣfidfi = 44906,26 E= 2,8 * 107 ( kN / m2 )
ΣΣΣΣMidfi2= 2657223,60 h= 2,94 ( m )
w2 = 65,6937 w = 8,1052 (rad/sn) T = 0,7752 (sn)
Zemin Sınıfı Z1 ve 1. Deprem Bölgesi için TA = 0,10 sn TB = 0,30 sn Ra(T1) = R = 8 (süneklik ) A0 = 0,40 ( 1. Deprem bölgesi ) I = 1,00 ( konut ) T = 0,7752 > TB = 0,3
S(T1) =8,08,0
7752,0
3,0.5,2.5,2
=
T
TB = 1,170
A(T1) = A0.I.S(T1) = 0,40 . 1,00 . 1,170 = 0,4679
Vt =8
4679,0.15670
)(
)(.
1
1 =TR
TAW
a
= 917kN
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Vt = 917 kN için
KATLARA ETK ĐYEN TASARIM DEPREM YÜKLER Đ
KATLAR W i ( kN ) Hi ( m ) WiHi VT/ΣΣΣΣWiHi Fi Vi ( kN )
4.KAT 3152 14,70 46334,4 0,006597 305,668 305,668 3.KAT 3152 11,76 37067,52 0,006597 244,534 550,202 2.KAT 3152 8,82 27800,64 0,006597 183,401 733,603 1.KAT 3152 5,88 18533,76 0,006597 122,267 855,870
Z KAT 3152 2,94 9266,88 0,006597 61,134 917,000
305,668 kN Wi =3152 kN 244,534 kN Wi =3152 kN 183,401 kN Wi =3152 kN 122,267 kN Wi =3152 kN 61,134kN Wi =3152 kN
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Y-Y YÖNÜ KOLON D DEĞERLERĐ
KAT KOLON BNZ kC k1 k2 k3 k4 k' a D ΣΣΣΣD
S1 4 4,225 0,000 8,634 0,000 8,634 2,044 0,505 2,135 S2 4 1,900 0,000 10,340 0,000 10,340 5,442 0,731 1,389 S3 2 1,900 0,000 9,013 0,000 9,013 4,744 0,703 1,337 S4 4 1,320 8,634 7,536 8,634 7,536 12,250 0,860 1,135 S5 2 4,225 10,340 8,932 10,340 8,932 4,561 0,695 2,937
S5A 2 4,225 10,340 7,536 10,340 7,536 4,231 0,679 2,869 S6 1 4,225 9,013 7,536 9,013 7,536 3,917 0,662 2,797
5
S6A 1 4,225 9,013 7,536 9,013 7,536 3,917 0,662 2,797
38,516
S1 4 4,225 0,000 8,634 0,000 8,634 2,044 0,505 2,135 S2 4 1,900 0,000 10,340 0,000 10,340 5,442 0,731 1,389 S3 2 1,900 0,000 9,013 0,000 9,013 4,744 0,703 1,337 S4 4 1,320 8,634 7,536 8,634 7,536 12,250 0,860 1,135 S5 2 4,225 10,340 8,932 10,340 8,932 4,561 0,695 2,937
S5A 2 4,225 10,340 7,536 10,340 7,536 4,231 0,679 2,869 S6 1 4,225 9,013 7,536 9,013 7,536 3,917 0,662 2,797
4
S6A 1 4,225 9,013 7,536 9,013 7,536 3,917 0,662 2,797
38,516
S1 4 7,207 0,000 8,634 0,000 8,634 1,198 0,375 2,700 S2 4 3,018 0,000 10,340 0,000 10,340 3,426 0,631 1,906 S3 2 3,018 0,000 9,013 0,000 9,013 2,986 0,599 1,808 S4 4 1,540 8,634 7,536 8,634 7,536 10,500 0,840 1,294 S5 2 7,207 10,340 8,932 10,340 8,932 2,674 0,572 4,123
S5A 2 7,207 10,340 7,536 10,340 7,536 2,480 0,554 3,990 S6 1 7,207 9,013 7,536 9,013 7,536 2,296 0,534 3,852
3
S6A 1 7,207 9,013 7,536 9,013 7,536 2,296 0,534 3,852
51,141
S1 4 7,207 0,000 8,634 0,000 8,634 1,198 0,375 2,700 S2 4 3,018 0,000 10,340 0,000 10,340 3,426 0,631 1,906 S3 2 3,018 0,000 9,013 0,000 9,013 2,986 0,599 1,808 S4 4 1,540 8,634 7,536 8,634 7,536 10,500 0,840 1,294 S5 2 7,207 10,340 8,932 10,340 8,932 2,674 0,572 4,123
S5A 2 7,207 10,340 7,536 10,340 7,536 2,480 0,554 3,990 S6 1 7,207 9,013 7,536 9,013 7,536 2,296 0,534 3,852
2
S6A 1 7,207 9,013 7,536 9,013 7,536 2,296 0,534 3,852
51,141
S1 4 7,207 0,000 8,634 0,000 8,634 1,198 0,375 2,700 S2 4 3,621 0,000 10,340 0,000 10,340 2,856 0,588 2,130 S3 2 3,621 0,000 9,013 0,000 9,013 2,489 0,554 2,008 S4 4 2,660 8,634 7,536 8,634 7,536 6,079 0,752 2,001 S5 2 11,545 10,340 8,932 10,340 8,932 1,669 0,455 5,252
S5A 2 11,545 10,340 7,536 10,340 7,536 1,548 0,436 5,038 S6 1 11,545 9,013 7,536 9,013 7,536 1,433 0,417 4,820
1
S6A 1 11,545 9,013 7,536 9,013 7,536 1,433 0,417 4,820
61,559
S1 4 7,207 0,000 8,634 0,000 0,000 1,198 0,531 3,827 S2 4 3,621 0,000 10,340 0,000 0,000 2,856 0,691 2,502 S3 2 3,621 0,000 9,013 0,000 0,000 2,489 0,666 2,411 S4 4 2,660 8,634 7,536 0,000 0,000 6,079 0,814 2,166 S5 2 11,545 10,340 8,932 0,000 0,000 1,669 0,591 6,825
S5A 2 11,545 10,340 7,536 0,000 0,000 1,548 0,577 6,665 S6 1 11,545 9,013 7,536 0,000 0,000 1,433 0,563 6,501
ZE
MĐN
S6A 1 11,545 9,013 7,536 0,000 0,000 1,433 0,563 6,501
78,785
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Y-Y YÖNÜ DEPREM HESABI ( C - C AKSI )
S(T1) =8,08,0
773696,0
30,0.5,2.5,2
=
T
TB = 1,1716
A(T1) = A0.I.S(T1) = 0,40 . 1,00 . 1,1716 = 0,4686
Vt =8
04686.15670
)(
)(.
1
1 =TR
TAW
a
= 918 kN
Vt = 1000 için
Đ Wi (KN) Hi (m) W iHi VT/ΣΣΣΣWiHi Fi Vi (KN)
4.KAT 3152 14,70 46334,40 0,00719 333,333 333,333 3.KAT 3152 11,76 37067,52 0,00719 266,667 600 2.KAT 3152 8,82 27800,64 0,00719 200,00 800 1.KAT 3152 5,88 18533,76 0,00719 133,333 913,333
Z KAT 3152 2,94 9266,88 0,00719 66,667 1000
BĐNANIN B ĐRĐNCĐ DOĞAL T ĐTREŞĐM PERYODUNUN BULUNMASI
KAT M i Fi Vi Di . (12E/h2) ∆di d fi Fid fi Mid fi2
4.KAT 321,30 333,333 333,333 48,427 6,883 50,034 19344,60631 1082116,19 3.KAT 321,30 266,667 600,00 48,427 12,390 51,151 13640,19607 840646,4848 2.KAT 321,30 200,00 800,00 56,377 14,190 38,761 7752,177751 482723,2075 1.KAT 321,30 133,333 913,333 65,869 13,866 24,571 3276,085785 193975,0866
Z KAT 321,30 66,667 1000,00 93,416 10,705 10,704 713,6571893 36818,67803
TOPLAM= 44726,7231 2636279,647
ΣΣΣΣfidfi = 44726,7231 E= 2,80*107 (kn/m2)
ΣΣΣΣMidfi2= 2636279,647 h= 2,94 (m)
w2 = 65,95 w = 8,121 (rad/sn) T = 0,773696 (sn)
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Vt = 918 kN için
KATLARA ETK ĐYEN TASARIM DEPREM YÜKLER Đ
KATLAR W i ( kN ) Hi ( m ) W iHi VT / ΣΣΣΣWiHi Fi Vi ( kN )
4.KAT 3152 14,70 46334,4 0,0066042 306 306 3.KAT 3152 11,76 37067,52 0,0066042 244,8 550,80 2.KAT 3152 8,82 27800,64 0,0066042 183,6 734,40 1.KAT 3152 5,88 18533,76 0,0066042 122,4 856,80
Z KAT 3152 2,94 9266,88 0,0066042 61,20 918,00
306 kN Wi =3152 kN 244,80 kN Wi =3152 kN 183,60 kN Wi =3152 kN 122,40 kN Wi =3152 kN 61,20 kN Wi =3152 kN
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1-1 AKSI DEPREM YÜKLER Đ DÜZELTMELER Đ S1 S2 S3 S2 S1 34,12 ( 27,16 ) 48,69 ( 38,75 ) 48,29 (38,43 ) 48,69 ( 38,75 ) 34,12 ( 27,16 ) ( 19,31 ) 24,97 ( 19,31 ) 38,74 ( 29,96 ) 34,73 ( 26,85 ) 38,74 ( 29,96 ) 24,97 76,888 52,011 49,685 52,011 76,888 30,52 ( 24,86 ) 47,35 ( 38,57 ) 42,45 ( 34,57 ) 47,35 ( 38,57 ) 30,52 ( 24,86 )
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S1 Kolonu Đçin 34,12 MK101
l = 34,12 + 24,97 = 59,09 kNm 24,97 S2 Kolonu Đçin 48,69 k1 = 16,437 k2 = 14,925 MK101 = 16,437 / ( 16,437 + 14,925 ). 87,43 = 45,82 k 1 k 2 MK101 MK102 MK102 = 14,925 / ( 16,437 + 14,925 ) .87,43 = 41,61 38,74 S3 Kolonu Đçin 48,29 k1 = 14,925 k2 = 14,925 k 1 k 2 MK103 = MK102 = ( 48,29 + 34,73 ) / 2 = 41,51 MK102 MK103 34,73 MOMENT DE ĞERLERĐ MK101
l = 34,12 + 24,97 = 59,09 kNm MK101
r = 16,437 / ( 16,437 + 14,925 ). 87,43 = 45,82 kNm = MK104l
MK102
l =14,925 / ( 16,437 + 14,925 ) .87,43 = 41,61kNm = MK103r
MK102
r =( 48,29 + 34,73 ) / 2 = 41,51 kNm = MK103l
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KESME KUVVET Đ DEĞERLERĐ
VK101 = VK104 =62,4
82,4509,59 + = 22,71 kN
VK102 = VK103 =00,4
51,4161,41 + = 20,78 kN
MOMENT DÜZELTMELER Đ
• Kiri ş Düzeltmeleri :
M = 2
.0
aVM −
MK101l =
2
30,0.71,2209,59 − = 55,68 kNm = MK104
r
MK101r =
2
30,0.71,2282,45 − = 42,41 kNm = MK104
l
MK102l =
2
30,0.78,2061,41 − = 38,49 kNm = MK103
r
MK102r =
2
30,0.78,2051,41 − = 38,39 kNm = MK103
l
• Kolon Düzeltmeleri :
1. Kat S 1 ⇒ M1,S1 = 2
60,0.
94,2
12,3412,3412,34
+− = 27,16 kNm
Z. Kat S 1 ⇒ MZ,S1 = 2
60,0.
94,2
52,3097,2497,24
+− = 19,31 kNm
1. Kat S 2 ⇒ M1,S2 = 2
60,0.
94,2
69,4869,4869,48
+− = 38,75 kNm
Z. Kat S 2 ⇒ MZ,S2 = 2
60,0.
94,2
35,4774,3874,38
+− = 29,96 kNm
1. Kat S 3 ⇒ M1,S3 = 2
60,0.
94,2
29,4829,4829,48
+− = 38,43 kNm
Z. Kat S 3 ⇒ MZ,S3 = 2
60,0.
94,2
45,4273,3473,34
+− = 26,85 kNm
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C - C AKSI DEPREM YÜKLER Đ DÜZELTMELER Đ
S3 S6 S6 S3 61,98 83,69 83,69 61,98 48,97 97,28 97,28 48,97 61,98 93,69 93,69 61,98 60,58 128,95 128,95 60,58
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S3 Kolonu Đçin 61,98 MK117
l 48,97 S6 Kolonu Đçin 93,69 k1 = 14,147 k2 = 16,032 k 1 k 2 MK117 MK118 97,28 MOMENT DE ĞERLERĐ MK117
l = 61,98 + 48,97 = 110,95 kNm
MK117r = ( ) ( )
++
032,16147,14
147,14.28,9769,93 = 89,52 kNm
MK118l = ( ) ( )
++
032,16147,14
032,16.28,9769,93 = 101,45 kNm = MK118
r
KESME KUVVET Đ DEĞERLERĐ
VK117 = 78,4
52,8995,110 + = 41,939 kN
VK118 = 28,4
45,10145,101 + = 23,703 kN
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MOMENT DÜZELTMELER Đ
• Kiri ş Düzeltmesi :
M = 2
.0
aVM −
MK117l =
2
40,0.939,4195,110 − = 102,56 kNm
MK117r =
2
40,0.939,4152,89 − = 81,13 kNm
MK118l =
2
40,0.407,4745,101 − = 96,97 kNm = MK118
r
• Kolon düzeltmesi :
1. Kat S3 ⇒ M1,S2 = 2
40,0.
94,2
98,6198,6198,61
+− = 53,547 kNm
Z. Kat S3 ⇒ MZ,S2 = 2
40,0.
94,2
58,6097,4897,48
+− = 41,518 kNm
1. Kat S6 ⇒ M1,S5 = 2
40,0.
94,2
69,9369,9369,93
+− = 80,943 kNm
Z. Kat S6 ⇒ MZ,S5 = 2
45,0.
94,2
95,12828,9728,97
+− = 79,966 kNm
I – I AKSI D ĐAGRAMLARI :
• KESME KUVVET Đ DĐAGRAMI :
23,21 33,12 32,85 33,12 23,21 22,71 20,78 22,71
18,87 29,28 26,25 29,28 18,87
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• NORMAL KUVVET D ĐAGRAMI :
74,88 6,26 6,26 74,88
97,59 8,19 8,19 97,59
C – C AKSI DĐAGRAMLARI :
• KESME KUVVET Đ DĐAGRAMI : 42,163 63,735 63,735 42,463
41,939 41,939 23,703 37,26 76,946 76,946 37,26
• NORMAL KUVVET D ĐAGRAMI : 110,278 39,227 39,227 110,278 152,217 57,463 57,463 152,217
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KĐRĐŞ DONATI HESABI C – C AKSI EĞĐLME DONATISI HESABI 1 2 3 4
K117 K118 K117
fcd (Mpa) 13,33 13,33 13,33 13,33 13,33 13,33 13,33 13,33 13,33
fyd (Mpa) 191 191 191 191 191 191 191 191 191
b (mm) 919,2 919,2 919,2 506,8 506,8 506,8 919,2 919,2 919,2
bw (mm) 250 250 250 250 250 250 250 250 250
d (mm) 550 550 550 550 550 550 550 550 550
M1,4g+1,6q -260,26 69,96 -82,24 -73,81 44,91 -73,81 -82,24 69,96 -260,26
Mg+q -16,98 -56,28 -49,44 -49,44 -56,28 -16,98
M0,9g -11,54 -39,64 -34,07 -34,07 -39,64 -11,54
Meq ±±±± 102,56 81,13 96,67 96,67 81,13 102,56
Mg+q-eq -119,54 -137,41 -146,11 -146,11 -137,41 -119,54
Mg+q+eq 85,58 24,85 47,23 47,23 24,85 85,58
M0,9g-eq -114,10 -120,77 -130,74 -130,74 -120,77 -114,10
M0,9g+eq 91,02 41,49 62,60 62,60 41,49 69,96 91,02
min M d -119,54 -137,41 -146,11 -146,11 -137,41 -119,54
max M d 91,02 69,96 41,49 62,60 44,91 62,60 41,49 91,02
KĐRĐŞ AÇIKLIK DONATISI
• K117 Kiri şi Açıklık Donatısı: My = ( ) ( ) 610.130.5,0550.130.20,919.33,13.85,0.5,0....85,0 −−=− ffcd hdhbf = 656,665 kNm
My > Md = 69,96 kNm ⇒ Soyut dikdörtgen kesit hesabı M d = 0,85 . f cd . b . a . ( d – 0,5 a ) ⇒ 69,96 . 10 6 = 0,85 . 13,33 . 919,20 . a ( 550 – 0,5 a ) ⇒ a = 13 mm A s . f yd = 0,85 . f cd . b . a ⇒ A s . 191 = 0,85 . 13,33 . 919,20 . 13 ⇒ A s = 709 mm 2 3 ∅∅∅∅ 18 ( 763 mm 2 ) ⇒⇒⇒⇒ 2 ∅∅∅∅ 18 ( DÜZ ) + 1 ∅∅∅∅ 18 ( PĐLYE )
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KONTROL :
ρ b = 038,0191600
600.
191
33,13.85,0
600
600..85,0 22 =
+=
+ ydyd
cd
ff
f
ρ = 310.55,5550.250
763 −= > ρ min = 310.36,4191
04,1.80,0..80,0 −==
yd
ctd
f
f
< ρ max = 0,02 < ρ m = 0,85 . ρ b = 0,85 . 0,038 = 0,0323
• K118 Kiri şi Açıklık Donatısı My = ( ) ( ) 610.130.5,0550.130.80,506.33,13.85,0.5,0....85,0 −−=− ffcd hdhbf = 362,05 kNm
My > Md = 44,91 kNm ⇒ Soyut dikdörtgen kesit hesabı M d = 0,85 . f cd . b . a . ( d – 0,5 a ) ⇒ 44,91 . 10 6 = 0,85 . 13,33 . 506,8 . a ( 550 – 0,5 a ) ⇒ a = 14 mm A s . f yd = 0,85 . f cd . b . a ⇒ A s . 191 = 0,85 . 13,33 . 506,80 . 14 ⇒ A s = 421 mm 2 3 ∅∅∅∅ 14 ( 462 mm 2 ) ⇒⇒⇒⇒ 2 ∅∅∅∅ 14 ( DÜZ ) + 1 ∅∅∅∅ 14 ( PĐLYE ) KONTROL :
ρ b = 038,0191600
600.
191
33,13.85,0
600
600..85,0 22 =
+=
+ ydyd
cd
ff
f
ρ = 00336,0550.250
462 = > ρ min = 310.36,4191
04,1.80,0..80,0 −==
yd
ctd
f
f
< ρ max = 0,02 < ρ m = 0,85 . ρ b = 0,85 . 0,038 = 0,0323
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MESNET DONATI HESABI
• K117 KENAR MESNEDĐ 1. DURUM : ρ1 = 0,40.ρb = 0,0153
M1,s=62
12 10.
33,13
191.0153,0.59,01.191.550.250.0153,0..59,01.... −
−=
−
cd
ydydwb f
ffdb ρρ
=192,41 kNm
77,592
54,119
2==düM
< M1,s = 192,41 ⇒ M1,2 = 2
düM = 59,77 kNm
0,85 . f cd . b w . a = A s1 . f yd ⇒ 0,85 . 13,33 . 250 . a = A s1 . 191 ⇒ a = 0,06743 . A s1 M 1 = A S1 . f yd . ( d – 0,5 a ) ⇒ 59,77 . 10 6 = A S1 . 191 . ( 550 – 0,5 . 0,06743 . A S1 ) A S1 = 590 mm 2 a = 40 mm
A S2 = 266
2 626)50550.(191
10.77,59
).'(
10.mm
fdd
M
yd
=−
=−
As,ü = A S1 + A S2 = 626 + 590 = 1216 mm 2 σ s′ = 600 . ( 1 – 0,85 . d′ / a ) = 600 . ( 1 – 0,85 . 50 / 40 ) = -37,50 σ s′ < f yd ⇒ A s′ = A sü / 2 = 1216 / 2 = 608 mm 2 2. DURUM : My = ( ) ( ) 610.130.5,0550.130.20,919.33,13.85,0.5,0....85,0 −−=− ffcd hdhbf = 656,665 kNm
My > Md = 91,02 kNm ⇒ Soyut dikdörtgen kesit hesabı M d = 0,85 . f cd . b . a . ( d – 0,5 a ) ⇒ 91,02 . 10 6 = 0,85 . 13,33 . 912,20 . a ( 550 – 0,5 a ) ⇒ a = 16 mm A sa . f yd = 0,85 . f cd . b . a ⇒ A sa . 191 = 0,85 . 13,33 . 919,20 . 16 ⇒ A sa = 873 mm 2
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70
Ek Donatı Hesabı :
• Üstte A S,mev = 1 ∅ 18 ( PĐLYE ) + 3 ∅ 12 ( MONTAJ ) = 254 + 339 = 593 mm 2 A S,ek = 1216 – 593 = 623 ⇒⇒⇒⇒ 2 ∅∅∅∅ 20 ( 402 mm 2 )
• Altta A S,mev = 2 ∅ 18 ( DÜZ ) = 509 mm 2 A S,ek = 873 – 509 = 364 ⇒⇒⇒⇒ 2 ∅∅∅∅ 16 ( 402 mm 2 ) KONTROL :
• Üstte
ρ b = 038,0191600
600.
191
33,13.85,0
600
600..85,0 22 =
+=
+ ydyd
cd
ff
f
ρ = 00925,0550.250
1272 = > ρ min = 00544,0191
04,1. ==
yd
ctd
f
f
ρ′ = 006625,0550.250
911 = < ρ max = 0,02
< ρ - ρ′ = 0,002625 ≤ 0,85 . ρ b = 0,85 . 0,038 = 0,0323
• Altta ⇒⇒⇒⇒ A SA ≥ 1272 / 2
• K117 – K118 KĐRĐŞLERĐ ARASINDAK Đ MESNET 1. DURUM : ρ1 = 0,40.ρb = 0,0153
M1,s=62
12 10.
33,13
191.0153,0.59,01.191.550.250.0153,0..59,01.... −
−=
−
cd
ydydwb f
ffdb ρρ
=192,41 kNm
06,732
11,146
2==düM
< M1,s = 192,41 ⇒ M1,2 = 2
düM = 73,06 kNm
0,85 . f cd . b w . a = A S1 . f yd ⇒ 0,85 . 13,33 . 250 . a = A S1 . 191 ⇒ a = 0,06743 . A S1
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M 1 = A S1 . f yd . ( d – 0,5 a ) ⇒ 73,06 . 10 6 = A S1 . 191 . ( 550 – 0,5 . 0,06743 . A S1 ) A S1 = 728 mm 2 a = 49 mm
A S2 = 266
2 765)50550.(191
10.06,73
).'(
10.mm
fdd
M
yd
=−
=−
As,ü = A S1 + A S2 = 728 + 765 = 1493 mm 2 σ s′ = 600 . ( 1 – 0,85 . d′ / a ) = 600 . ( 1 – 0,85 . 50 / 49 ) = 79,59 σ s′ < f yd ⇒ A s′ = A sü / 2 = 1493 / 2 = 747 mm 2 2. DURUM : My = ( ) ( ) 610.130.5,0550.130.80,506.33,13.85,0.5,0....85,0 −−=− ffcd hdhbf = 361,48 kNm
My > Mda = 62,60 kNm ⇒ Soyut dikdörtgen kesit hesabı M d = 0,85 . f cd . b . a . ( d – 0,5 a ) ⇒ 62,60 . 10 6 = 0,85 . 13,33 . 506,80 . a ( 550 – 0,5 a ) ⇒ a = 20 mm A sa . f yd = 0,85 . f cd . b . a ⇒ A sa . 191 = 0,85 . 13,33 . 506,80 . 20 ⇒ A sa = 601 mm 2 Ek Donatı Hesabı :
• Üstte A S,mev = ( 1 ∅ 18 + 1 ∅ 16 ) ( PĐLYE ) + 2 ∅ 16 ( MONTAJ ) = 254 + 201 + 402=857 mm 2 A S,ek = 1493 – 857 = 636 ⇒⇒⇒⇒ 3 ∅∅∅∅ 18 ( 679 mm 2 )
• Altta A S,mev = 2 ∅ 16 ( DÜZ ) = 402 mm 2 A S,ek = 747 – 402 = 345 ⇒⇒⇒⇒ 2 ∅∅∅∅ 16 ( 402 mm 2 )
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KONTROL :
• Üstte
ρ b = 038,0191600
600.
191
33,13.85,0
600
600..85,0 22 =
+=
+ ydyd
cd
ff
f
ρ = 011170,0550.250
1536 = > ρ min = 00544,0191
04,1. ==
yd
ctd
f
f
ρ′ = 00585,0550.250
804 = < ρ max = 0,02
< ρ - ρ′ = 0,00532 ≤ 0,85 . ρ b = 0,85 . 0,038 = 0,0323
• Altta ⇒⇒⇒⇒ A SA ≥ 1536 / 2
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MESNET TAŞIMA GÜCÜ HESABI : K117 KENAR MESNEDĐ :
o M rü ‘nün Hesabı : 0,85 . f cd . b w . a + A s
′ . σ s′ = A s . f yd ⇒
0,85 . 13,33 . 250 . a + 911 . 600 . ( 1 – 0,85 . 50 / a ) = 1272 . 191 2832,625 a 2 + 303648 a – 23230500 = 0 ⇒ a = 52 mm σ s′ = 600 . ( 1 – 0,85 . d′ / a ) = 600 . ( 1 – 0,85 . 50 / 52 ) = 110 Mpa < 191Mpa ⇒ Akmıyor. A s
′ . σ s′ = A S2 . f yd ⇒ 911 . 110 = A S2 . 191 ⇒ A S2 = 525 mm 2 A S1 = A S - A S2 = 1272 – 525 = 747 mm 2 M r = M 1 + M 2 = A S1 . f yd . ( d – 0,5 a ) + A S2 . f yd . ( d - d′ ) M r = 747 . 191 . ( 550 – 0,5 . 52 ) + 525 . 191 . ( 550 – 50 ) ⇒ M rü = 124,90 kNm
o M ra’ın Hesabı : Üst donatıyı ihmal edilerek hesap yapılmıştır . 0,85 . f cd . b w . a = A s . f yd ⇒ 0,85 . 13,33 . 919,20 . a = 911 . 191 ⇒ a = 16,71 mm M r = 0,85 . f cd . b . a . ( d – 0,5 a ) M r = 0,85 . 13,33 . 919,20 . 16,71 . ( 550 – 0,5 . 16,71 ) . 10 -6 ⇒ M ra = 94,265 kNm K117 – K118 MESNEDĐ :
o M rü ‘nün Hesabı : 0,85 . f cd . b w . a + A s
′ . σ s′ = A s . f yd ⇒
0,85 . 13,33 . 250 . a + 804 . 600 . ( 1 – 0,85 . 50 / a ) = 1536 . 191 2832,625 a 2 + 189024 a – 20502000 = 0 ⇒ a = 58 mm σ s′ = 600 . ( 1 – 0,85 . d′ / a ) = 600 . ( 1 – 0,85 . 50 / 58 ) = 160 Mpa < 191Mpa ⇒ Akmıyor.
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A s′ . σ s′ = A S2 . f yd ⇒ 804 . 160 = A S2 . 191 ⇒ A S2 = 674 mm 2
A S1 = A S - A S2 = 1536 – 674 = 862 mm 2 M r = M 1 + M 2 = A S1 . f yd . ( d – 0,5 a ) + A S2 . f yd . ( d - d′ ) M r = 862 . 191 . ( 550 – 0,5 . 58 ) + 674 . 191 . ( 550 – 50 ) ⇒ M rü = 150,145 kNm
o M ra’ın Hesabı : Üst donatıyı ihmal edilerek hesap yapılmıştır . 0,85 . f cd . b w . a = A s . f yd ⇒ 0,85 . 13,33 . 506,80 . a = 804 . 191 ⇒ a = 26,74 mm M r = 0,85 . f cd . b . a . ( d – 0,5 a ) M r = 0,85 . 13,33 . 506,80 . 26,74 . ( 550 – 0,5 . 26,74 ) . 10 -6 ⇒ M ra = 82,40 kNm Pekleşmeli Moment Hesabı :
• K117 Kenar Mesnedi : M pü = 1,4 . M rü = 1,4.124,90=174,86 kNm M pa = 1,4 . M ra = 1,4 . 94,265 =131,971 kNm
• K117 – K118 Mesnedi : M pü = 1,4 . M rü = 1,4.150,145=210,203 kNm M pa=1,4.M ra=1,4. 82,40 =115,36 kNm Max ( M pü + M pa ) / L n ‘nin Hesabı :
• K117 Kenar Mesnedi : V dy = V ( g + q ) 0 = 58,53 kN ∆V 1 = ( 174,86 + 115,36 ) / 4,78 = 60,72 kN V e1 = V dy + ∆V 1 = 58,53 + 60,72 ⇒ V e1 = 119,25 kN
• K117 – K118 Kirişi Solu : V dy = V ( g + q ) 0 = 58,53 kN ∆V 1 = ( 131,971 + 210,203 ) / 4,78 = 71,58 kN V e1 = V dy + ∆V 1 = 58,53 + 71,58 ⇒ V e1 = 130,11 kN
• K117 – K118 Kirişi Sağı : V dy = V ( g + q ) 0 = 53,99 kN ∆V 1 = ( 210,203 + 115,36 ) / 4,28 = 76,07 kN V e1 = V dy + ∆V 1 = 53,99 + 76,07 ⇒ V e1 = 130,06 kN
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C - C AKSI KAYMA DONATISI HESABI i j i j i
K117 K118 K117 V1,4.g+1,6.q (x=d) 59,08 82,54 78,12 78,12 82,54 59,08 Vg+q (x=0) 48,61 65,41 64,65 64,65 65,41 48,61 Veq (x=0) 41,94 41,94 23,70 23,70 41,94 41,94 Vg+q+eg 90,55 107,35 88,35 88,35 107,35 90,55 V(g+q)o 58,53 58,53 53,99 53,99 58,53 58,53 Vcr = 0,65.fctd.bw.d = 0,65 . 1,04 . 250 . 550 . 10 -3 = 92,95 kN Vc = 0,8.Vcr = 0,8 . 92,95 = 74,36 kN Vr,max = 0,22.fcd.bw.d = 0,22 . 13,33 . 250 . 550 . 10 -3 = 403,23 kN MESNETTE HESAP ( D.Y. 1997 )
• K117 KENAR MESNEDĐ : V d = 90,55 kN V dy = V(g+q)o = 58,53 kN Vcr = 92,95 kN V e – V dy = 119,25 – 58,53 = 60,72 kN 0,5 V d = 0,5 . 90,55 = 45,275 kN ( V e – V dy ) ≥ 0,5 V d ⇒ V c = 0 ⇒ V w,et = V d,hesap V d,hesap = max ( V 1,4g+1,6q , V e , V g+q+e ) = V e =119,25 kN ⇒ V w,et = 119,25 kN A sw = ( V w,et . s ) / ( f ywd . d ) ⇒ A sw = ( 119,25 . s . 10 3 ) / ( 191 . 550 ) ∅8 ⇒ A 0 = 50 mm 2 ⇒ s = 88 mm ⇒ ∅∅∅∅8 / 8 s ≤ 600 / 4 = 150 mm ≤ 150 mm
≤ 8 . 12 = 96 mm Vr,max = 403,23 kN > V d,hesap = 119,25 kN ⇒ KESĐT YETERL Đ
• K117 – K118 MESNEDĐ SOL UCU : V d = 107,35 kN V dy = V(g+q)o = 58,53 kN Vcr = 92,95 kN V e – V dy = 130,11 – 58,53 = 71,58 kN 0,5 V d = 0,5 . 107,35 = 53,675 kN ( V e – V dy ) ≥ 0,5 V d ⇒ V c = 0 ⇒ V w,et = V d,hesap V d,hesap = max ( V 1,4g+1,6q , V e , V g+q+e ) = V e =130,11 kN ⇒ V w,et = 130,11 kN
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A sw = ( V w,et . s ) / ( f ywd . d ) ⇒ A sw = ( 130,11 . s . 10 3 ) / ( 191 . 550 ) ∅8 ⇒ A 0 = 50 mm 2 ⇒ s = 81 mm ⇒ ∅∅∅∅8 / 8 s ≤ 600 / 4 = 150 mm ≤ 150 mm
≤ 8 . 12 = 96 mm Vr,max = 403,23 kN > V d,hesap = 130,11 kN ⇒ KESĐT YETERL Đ
• K117 – K118 MESNEDĐ SAĞ UCU : V d = 88,35 kN V dy = V(g+q)o = 53,99 kN Vcr = 92,95 kN V e – V dy = 130,06 – 53,99 = 76,07 kN 0,5 V d = 0,5 . 88,35 = 44,175 kN ( V e – V dy ) ≥ 0,5 V d ⇒ V c = 0 ⇒ V w,et = V d,hesap V d,hesap = max ( V 1,4g+1,6q , V e , V g+q+e ) = V e =130,06 kN ⇒ V w,et = 130,06 kN A sw = ( V w,et . s ) / ( f ywd . d ) ⇒ A sw = ( 130,06 . s . 10 3 ) / ( 191 . 550 ) ∅8 ⇒ A 0 = 50 mm 2 ⇒ s = 80 mm ⇒ ∅∅∅∅8 / 8 s ≤ 600 / 4 = 150 mm ≤ 150 mm
≤ 8 . 12 = 96 mm Vr,max = 403,23 kN > V d,hesap = 130,06 kN ⇒ KESĐT YETERL Đ AÇIKLIKTA HESAP ( TS 500 )
• K117 AÇIKLIK KES ĐTĐ : V d = V pd = 82,54 kN Vr,max = 403,23 kN Vcr = 92,95 kN V d = 82,54 kN < Vcr = 92,95 kN ⇒ min etriye hesabı A s,min = 0,30 . f ctd . b w . s max / f ywd⇒ 2 .50=0,30.1,04.250.s max /191 ⇒ s max = 244 mm s ≤ d / 2 = 550 / 2 = 275 mm ≤ 300 mm ⇒ ∅∅∅∅8 / 24 ≤ b w = 250 mm
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• K118 AÇIKLIK KES ĐTĐ : V d = V pd = 78,12 kN Vr,max = 403,23 kN Vcr = 92,95 kN V d = 78,12 kN < Vcr = 92,95 kN ⇒ min etriye hesabı A s,min = 0,30 . f ctd . b w . s max / f ywd⇒ 2 .50=0,30.1,04.250.s max /191 ⇒ s max = 244 mm s ≤ d / 2 = 550 / 2 = 275 mm ≤ 300 mm ⇒ ∅∅∅∅8 / 24 ≤ b w = 250 mm
C - C AKSI EĞĐLME DONATISI ŞEMASI
2∅20 2∅20 3∅18 3∅18 2∅16 1∅18 1∅18 1∅14 2∅16 2∅16 2∅18 2∅18 2∅14 2∅16 2∅16
C - C AKSI KAYMA DONATISI ŞEMASI
∅8/8 ∅8/24 ∅8/8 ∅8/8 ∅8/24 ∅8/8 ∅8/8 ∅8/24 ∅8/8 K117 K118 K117
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1-1 AKSI EĞĐLME DONATISI HESABI
1 2 3 K101 K102 K103 K104 fcd (Mpa) 13,33 13,33 13,33 13,33 13,33 13,33 13,33 13,33 13,33 13,33 13,33 13,33 fyd (Mpa) 191 191 191 191 191 191 191 191 191 191 191 191 b (mm) 896,80 896,80 896,80 490 490 490 490 490 490 896,80 896,80 896,80 bw (mm) 250 250 250 250 250 250 250 250 250 250 250 250 d (mm) 550 550 550 550 550 550 550 550 550 550 550 550 M1,4g+1,6q -13,64 73,84 -68,94 -60,11 18,63 -21,05 -21,05 18,63 -60,11 -68,94 73,84 -13,64
Mg+q -9,05 -46,94 -40,70 -11,49 -11,49 -40,70 -46,94 -9,05 M0,9g -5,60 -30,94 -26,99 -7,11 -7,11 -26,99 -30,94 -5,60
Meq ±±±± 53,68 42,41 38,49 38,49 38,49 38,49 42,41 53,68 Mg+q-eq -62,73 -89,35 -79,19 -49,98 -49,98 -79,19 -89,35 -62,73 Mg+q+eq 44,63 -4,53 92,21 27 27 92,21 -4,53 44,63 M0,9g-eq -59,28 -73,35 -65,48 -45,60 -45,60 -65,48 -73,35 -59,28 M0,9g+eq 48,08 11,47 11,50 31,38 31,38 11,50 11,47 48,08 min Md -62,73 -89,35 -79,19 -49,98 -49,98 -79,19 -89,35 -62,73 max Md 48,08 73,84 11,47 -11,50 18,63 31,38 31,38 18,63 -11,50 11,47 73,84 48,08
KĐRĐŞ AÇIKLIK DONATISI
• K101 Kiri şi Açıklık Donatısı: My = ( ) ( ) 610.130.5,0550.130.80,896.33,13.85,0.5,0....85,0 −−=− ffcd hdhbf = 640,66 kNm
My > Md = 73,84 kNm ⇒ Soyut dikdörtgen kesit hesabı M d = 0,85 . f cd . b . a . ( d – 0,5 a ) ⇒ 73,84 . 10 6 = 0,85 . 13,33 . 896,80 . a ( 550 – 0,5 a ) ⇒ a = 13 mm A s . f yd = 0,85 . f cd . b . a ⇒ A s . 191 = 0,85 . 13,33 . 896,80 . 13 ⇒ A s = 692 mm 2 3 ∅∅∅∅ 18 ( 763 mm 2 ) ⇒⇒⇒⇒ 2 ∅∅∅∅ 18 ( DÜZ ) + 1 ∅∅∅∅ 18 ( PĐLYE ) KONTROL :
ρ b = 038,0191600
600.
191
33,13.85,0
600
600..85,0 22 =
+=
+ ydyd
cd
ff
f
ρ = 310.55,5550.250
763 −= > ρ min = 310.36,4191
04,1.80,0..80,0 −==
yd
ctd
f
f
< ρ max = 0,02 < ρ m = 0,85 . ρ b = 0,85 . 0,038 = 0,0323
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• K102 Kiri şi Açıklık Donatısı My = ( ) ( ) 610.130.5,0550.130.490.33,13.85,0.5,0....85,0 −−=− ffcd hdhbf = 350 kNm
My > Md = 18,63 kNm ⇒ Soyut dikdörtgen kesit hesabı M d = 0,85 . f cd . b . a . ( d – 0,5 a ) ⇒ 18,63 . 10 6 = 0,85 . 13,33 . 490 . a ( 550 – 0,5 a ) ⇒ a = 6 mm A s . f yd = 0,85 . f cd . b . a ⇒ A s . 191 = 0,85 . 13,33 . 490 . 6 ⇒ A s = 174 mm 2 2 ∅∅∅∅ 12 ( 226 mm 2 ) ⇒⇒⇒⇒ 1 ∅∅∅∅ 12 ( DÜZ ) + 1 ∅∅∅∅ 12 ( PĐLYE ) KONTROL :
ρ b = 038,0191600
600.
191
33,13.85,0
600
600..85,0 22 =
+=
+ ydyd
cd
ff
f
ρ = 001644,0550.250
226 = > ρ min = 310.36,4191
04,1.80,0..80,0 −==
yd
ctd
f
f
< ρ max = 0,02 < ρ m = 0,85 . ρ b = 0,85 . 0,038 = 0,0323 ρ min > ρ ⇒ A s = 0,00436 . 250 . 550 = 600 mm 2 3∅∅∅∅16 ( 603 ) ⇒ 1∅∅∅∅16 ( PĐLYE ) + 2∅∅∅∅16 ( DÜZ )
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MESNET DONATI HESABI
• K101 KENAR MESNEDĐ 1. DURUM : ρ1 = 0,40.ρb = 0,0153
M1,s=62
12 10.
33,13
191.0153,0.59,01.191.550.250.0153,0..59,01.... −
−=
−
cd
ydydwb f
ffdb ρρ
=192,41 kNm
37,312
73,62
2==düM
< M1,s = 192,41 ⇒ M1,2 = 2
düM = 31,37 kNm
0,85 . f cd . b w . a = A s1 . f yd ⇒ 0,85 . 13,33 . 250 . a = A s1 . 191 ⇒ a = 0,06743 . A s1 M 1 = A S1 . f yd . ( d – 0,5 a ) ⇒ 31,37 . 10 6 = A S1 . 191 . ( 550 – 0,5 . 0,06743 . A S1 ) A S1 = 304 mm 2 a = 21 mm
A S2 = 266
2 328)50550.(191
10.37,31
).'(
10.mm
fdd
M
yd
=−
=−
As,ü = A S1 + A S2 = 304 + 328 = 632 mm 2 σ s′ = 600 . ( 1 – 0,85 . d′ / a ) = 600 . ( 1 – 0,85 . 50 / 21 ) = -614,29 σ s′ < f yd ⇒ A s′ = A sü / 2 = 632 / 2 = 316 mm 2 2. DURUM : My = ( ) ( ) 610.130.5,0550.130.80,896.33,13.85,0.5,0....85,0 −−=− ffcd hdhbf = 640,66 kNm
My > Md = 48,08 kNm ⇒ Soyut dikdörtgen kesit hesabı M d = 0,85 . f cd . b . a . ( d – 0,5 a ) ⇒ 48,08 . 10 6 = 0,85 . 13,33 . 896,80 . a ( 550 – 0,5 a ) ⇒ a = 9 mm A sa . f yd = 0,85 . f cd . b . a ⇒ A sa . 191 = 0,85 . 13,33 . 896,80 . 9 ⇒ A sa = 479 mm 2
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Ek Donatı Hesabı :
• Üstte A S,mev = 1 ∅ 18 ( PĐLYE ) + 2 ∅ 14 ( MONTAJ ) = 254 + 308 = 562 mm 2 A S,ek = 748 – 562 = 186 ⇒⇒⇒⇒ 1 ∅∅∅∅ 16 ( 201 mm 2 )
• Altta A S,mev = 2 ∅ 18 ( DÜZ ) = 509 mm 2 A S,mev > A s,alt ⇒⇒⇒⇒ Ek donatıya gerek yok . KONTROL :
• Üstte
ρ b = 038,0191600
600.
191
33,13.85,0
600
600..85,0 22 =
+=
+ ydyd
cd
ff
f
ρ = 005549,0550.250
763 = > ρ min = 00544,0191
04,1. ==
yd
ctd
f
f
ρ′ = 003702,0550.250
509 = < ρ max = 0,02
< ρ - ρ′ = 0,001847 ≤ 0,85 . ρ b = 0,85 . 0,038 = 0,0323
• Altta ⇒⇒⇒⇒ A SA ≥ 763 / 2
• K101 – K102 KĐRĐŞLERĐ ARASINDAK Đ MESNET 1. DURUM : ρ1 = 0,40.ρb = 0,0153
M1,s=62
12 10.
33,13
191.0153,0.59,01.191.550.250.0153,0..59,01.... −
−=
−
cd
ydydwb f
ffdb ρρ
=192,41 kNm
68,442
35,89
2==düM
< M1,s = 192,41 ⇒ M1,2 = 2
düM = 44,68 kNm
0,85 . f cd . b w . a = A S1 . f yd ⇒ 0,85 . 13,33 . 250 . a = A S1 . 191 ⇒ a = 0,06743 . A S1
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M 1 = A S1 . f yd . ( d – 0,5 a ) ⇒ 44,68 . 10 6 = A S1 . 191 . ( 550 – 0,5 . 0,06743 . A S1 ) A S1 = 437 mm 2 a = 30 mm
A S2 = 266
2 468)50550.(191
10.68,44
).'(
10.mm
fdd
M
yd
=−
=−
As,ü = A S1 + A S2 = 468 + 437 = 905 mm 2 σ s′ = 600 . ( 1 – 0,85 . d′ / a ) = 600 . ( 1 – 0,85 . 50 / 30 ) = -250 σ s′ < f yd ⇒ A s′ = A sü / 2 = 905 / 2 = 453 mm 2 2. DURUM : My = ( ) ( ) 610.130.5,0550.130.490.33,13.85,0.5,0....85,0 −−=− ffcd hdhbf = 350 kNm
My > Mda = 11,50 kNm ⇒ Soyut dikdörtgen kesit hesabı M d = 0,85 . f cd . b . a . ( d – 0,5 a ) ⇒ 11,50 . 10 6 = 0,85 . 13,33 . 490 . a ( 550 – 0,5 a ) ⇒ a = 4 mm A sa . f yd = 0,85 . f cd . b . a ⇒ A sa . 191 = 0,85 . 13,33 . 490 . 4 ⇒ A sa = 116 mm 2 Ek Donatı Hesabı :
• Üstte A S,mev = ( 1 ∅ 18 + 1 ∅ 16 ) ( PĐLYE ) + 2 ∅ 14 ( MONTAJ ) = 254 + 201 + 308=763 mm 2 A S,ek = 905 – 763 = 142 ⇒⇒⇒⇒ ∅∅∅∅ 14 ( 154mm 2 )
• Altta A S,mev = 2 ∅ 16 ( DÜZ ) = 402 mm 2 A S,ek = 453 – 402 = 51 ⇒⇒⇒⇒ 1 ∅∅∅∅ 12 ( 113 mm 2 )
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KONTROL :
• Üstte
ρ b = 038,0191600
600.
191
33,13.85,0
600
600..85,0 22 =
+=
+ ydyd
cd
ff
f
ρ = 00667,0550.250
917 = > ρ min = 00544,0191
04,1. ==
yd
ctd
f
f
ρ′ = 00375,0550.250
515 = < ρ max = 0,02
< ρ - ρ′ = 0,00292 ≤ 0,85 . ρ b = 0,85 . 0,038 = 0,0323
• Altta ⇒⇒⇒⇒ A SA ≥ 917 / 2
• K102 – K103 KĐRĐŞLERĐ ARASINDAK Đ MESNET 1. DURUM : ρ1 = 0,40.ρb = 0,0153
M1,s=62
12 10.
33,13
191.0153,0.59,01.191.550.250.0153,0..59,01.... −
−=
−
cd
ydydwb f
ffdb ρρ
=192,41 kNm
99,242
98,49
2==düM
< M1,s = 192,41 ⇒ M1,2 = 2
düM = 24,99 kNm
0,85 . f cd . b w . a = A S1 . f yd ⇒ 0,85 . 13,33 . 250 . a = A S1 . 191 ⇒ a = 0,06743 . A S1 M 1 = A S1 . f yd . ( d – 0,5 a ) ⇒ 24,99 . 10 6 = A S1 . 191 . ( 550 – 0,5 . 0,06743 . A S1 ) A S1 = 241 mm 2 a = 16 mm
A S2 = 266
2 262)50550.(191
10.99,24
).'(
10.mm
fdd
M
yd
=−
=−
As,ü = A S1 + A S2 = 241 + 262 = 503 mm 2 σ s′ = 600 . ( 1 – 0,85 . d′ / a ) = 600 . ( 1 – 0,85 . 50 / 16 ) = -993,75 σ s′ < f yd ⇒ A s′ = A sü / 2 = 503 / 2 = 252 mm 2
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2. DURUM : My = ( ) ( ) 610.130.5,0550.130.490.33,13.85,0.5,0....85,0 −−=− ffcd hdhbf = 350 kNm
My > Mda = 31,38 kNm ⇒ Soyut dikdörtgen kesit hesabı M d = 0,85 . f cd . b . a . ( d – 0,5 a ) ⇒ 31,38 . 10 6 = 0,85 . 13,33 . 490 . a ( 550 – 0,5 a ) ⇒ a = 10 mm A sa . f yd = 0,85 . f cd . b . a ⇒ A sa . 191 = 0,85 . 13,33 . 490 . 10 ⇒ A sa = 291 mm 2 Ek Donatı Hesabı :
• Üstte A S,mev = ( 1 ∅ 16 + 1 ∅ 16 ) ( PĐLYE ) + 2 ∅ 16 ( MONTAJ ) = 804 mm 2 A S,gerekli < A S,mev ⇒⇒⇒⇒ Ek donatıya gerek yok .
• Altta A S,mev = 2 ∅ 16 ( DÜZ ) = 402 mm 2 A S,gerekli < A S,mev ⇒⇒⇒⇒ Ek donatıya gerek yok . KONTROL :
• Üstte
ρ b = 038,0191600
600.
191
33,13.85,0
600
600..85,0 22 =
+=
+ ydyd
cd
ff
f
ρ = 00585,0550.250
804 = > ρ min = 00544,0191
04,1. ==
yd
ctd
f
f
ρ′ = 00292,0550.250
402 = < ρ max = 0,02
< ρ - ρ′ = 0,00293 ≤ 0,85 . ρ b = 0,85 . 0,038 = 0,0323
• Altta ⇒⇒⇒⇒ A SA ≥ 804 / 2 Montaj Donatısı Kontrolü : A S,montaj = 2 ∅ 16 = 402 mm 2 A S,üst(maks) / 4 = 917 / 4 = 229,25 < 402
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85
MESNET TAŞIMA GÜCÜ HESABI : K101 KENAR MESNEDĐ :
o M rü ‘nün Hesabı : 0,85 . f cd . b w . a + A s
′ . σ s′ = A s . f yd ⇒
0,85 . 13,33 . 250 . a + 509 . 600 . ( 1 – 0,85 . 50 / a ) = 763 . 191 2832,625 a 2 + 159667 a – 12979500 = 0 ⇒ a = 45 mm σ s′ = 600 . ( 1 – 0,85 . d′ / a ) = 600.(1 – 0,85 . 50 / 45 ) = 33,33 Mpa < 191Mpa ⇒ Akmıyor. A s
′ . σ s′ = A S2 . f yd ⇒ 509 . 33,33 = A S2 . 191 ⇒ A S2 = 89 mm 2 A S1 = A S - A S2 = 763 – 89 = 674 mm 2 M r = M 1 + M 2 = A S1 . f yd . ( d – 0,5 a ) + A S2 . f yd . ( d - d′ ) M r = 674 . 191 . ( 550 – 0,5 . 45 ) + 89 . 191 . ( 550 – 50 ) ⇒ M rü = 76,407 kNm
o M ra’ın Hesabı : Üst donatıyı ihmal edilerek hesap yapılmıştır . 0,85 . f cd . b w . a = A s . f yd ⇒ 0,85 . 13,33 . 896,80 . a = 509 . 191 ⇒ a = 9,57 mm M r = 0,85 . f cd . b . a . ( d – 0,5 a ) M r = 0,85 . 13,33 . 896,80 . 9,57 . ( 550 – 0,5 . 9,57 ) . 10 -6 ⇒ M ra = 53,018 kNm K101 – K102 MESNEDĐ :
o M rü ‘nün Hesabı : 0,85 . f cd . b w . a + A s
′ . σ s′ = A s . f yd ⇒
0,85 . 13,33 . 250 . a + 515 . 600 . ( 1 – 0,85 . 50 / a ) = 917 . 191 2832,625 a 2 + 133853 a – 13132500 = 0 ⇒ a = 48 mm σ s′ = 600 . ( 1 – 0,85 . d′ / a ) =600.( 1 – 0,85 . 50 / 48 ) = 68,75 Mpa < 191Mpa ⇒ Akmıyor.
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A s′ . σ s′ = A S2 . f yd ⇒ 515 . 68,75 = A S2 . 191 ⇒ A S2 = 185 mm 2
A S1 = A S - A S2 = 917 – 185 = 732 mm 2 M r = M 1 + M 2 = A S1 . f yd . ( d – 0,5 a ) + A S2 . f yd . ( d - d′ ) M r = 732 . 191 . ( 550 – 0,5 . 48 ) + 185 . 191 . ( 550 – 50 ) ⇒ M rü = 91,209 kNm
o M ra’ın Hesabı : Üst donatıyı ihmal edilerek hesap yapılmıştır . 0,85 . f cd . b w . a = A s . f yd ⇒ 0,85 . 13,33 . 490 . a = 515 . 191 ⇒ a = 17,72 mm M r = 0,85 . f cd . b . a . ( d – 0,5 a ) M r = 0,85 . 13,33 . 490 . 17,72 . ( 550 – 0,5 . 17,72 ) . 10 -6 ⇒ M ra = 53,238 kNm K102 – K103 MESNEDĐ :
o M rü ‘nün Hesabı : 0,85 . f cd . b w . a + A s
′ . σ s′ = A s . f yd ⇒
0,85 . 13,33 . 250 . a + 402 . 600 . ( 1 – 0,85 . 50 / a ) = 804 . 191 2832,625 a 2 + 87636 a – 10251000 = 0 ⇒ a = 47 mm σ s′ = 600 . ( 1 – 0,85 . d′ / a ) =600.(1 – 0,85 . 50 / 47) = 57,447 Mpa < 191Mpa ⇒ Akmıyor. A s
′ . σ s′ = A S2 . f yd ⇒ 402 . 57,447 = A S2 . 191 ⇒ A S2 = 121 mm 2 A S1 = A S - A S2 = 804 – 121 = 683 mm 2 M r = M 1 + M 2 = A S1 . f yd . ( d – 0,5 a ) + A S2 . f yd . ( d - d′ ) M r = 683 . 191 . ( 550 – 0,5 . 47 ) + 121 . 191 . ( 550 – 50 ) ⇒ M rü = 80,239 kNm
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o M ra’ın Hesabı :
Üst donatıyı ihmal edilerek hesap yapılmıştır . 0,85 . f cd . b w . a = A s . f yd ⇒ 0,85 . 13,33 . 490 . a = 402 . 191 ⇒ a = 13,83 mm M r = 0,85 . f cd . b . a . ( d – 0,5 a ) M r = 0,85 . 13,33 . 490 . 13,83 . ( 550 – 0,5 . 13,83 ) . 10 -6 ⇒ M ra = 41,70 kNm Pekleşmeli Moment Hesabı :
• K101 Kenar Mesnedi : M pü = 1,4 . M rü = 1,4.76,407=106,97 kNm M pa = 1,4 . M ra = 1,4 . 53,018 =74,225 kNm
• K101 – K102 Mesnedi : M pü = 1,4 . M rü = 1,4.91,209=127,693 kNm M pa=1,4.M ra=1,4. 53,238 =74,533 kNm
• K102 – K103 Mesnedi : M pü = 1,4 . M rü = 1,4.80,239=112,335 kNm M pa=1,4.M ra=1,4. 41,70 =58,38 kNm Max ( M pü + M pa ) / L n ‘nin Hesabı :
• K101 Kenar Mesnedi : V dy = V ( g + q ) 0 = 64,99 kN ∆V 1 = ( 106,97 + 74,533 ) / 4,62 = 39,29 kN V e1 = V dy + ∆V 1 = 64,99 + 39,29 ⇒ V e1 = 104,28 kN
• K101 – K102 Kirişi Solu : V dy = V ( g + q ) 0 = 64,99 kN ∆V 1 = ( 74,225 + 127,693 ) / 4,68 = 43,71 kN V e1 = V dy + ∆V 1 = 64,99 + 43,71 ⇒ V e1 = 108,70 kN
• K101 – K102 Kirişi Sağı : V dy = V ( g + q ) 0 = 27,78 kN ∆V 1 = ( 127,693 + 58,38 ) / 4,00 = 46,52 kN V e1 = V dy + ∆V 1 = 27,78 + 46,52 ⇒ V e1 = 74,30 kN
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• K102 – K103 Kirişi Solu : V dy = V ( g + q ) 0 = 27,78 kN ∆V 1 = ( 74,53 + 112,335 ) / 4,00 = 46,72 kN V e1 = V dy + ∆V 1 = 27,78 + 46,72 ⇒ V e1 = 74,50 kN
• K102 – K103 Kirişi Sağı : V dy = V ( g + q ) 0 = 27,78 kN ∆V 1 = ( 74,533 + 112,235 ) / 4,00 = 46,72 kN V e1 = V dy + ∆V 1 = 27,78 + 46,72 ⇒ V e1 = 74,50 kN
1-1 AKSI KAYMA DONATISI HESABI
K101 K102 K103 K104 V1,4g+1,6g (x=d) 60,84 84,22 44,98 26,45 26,45 44,98 84,22 60,84 Vg+q (x=0) 53,81 70,49 35,83 21,35 21,35 35,83 70,49 53,81 Veq (x=0) 22,71 22,71 20,78 20,78 20,78 20,78 22,71 22,71 Vg+q+eq 76,52 93,20 56,61 42,13 42,13 56,61 93,20 76,52 V(g+q)o 64,99 64,99 27,78 27,78 27,78 27,78 64,99 64,99 Vcr = 0,65.fctd.bw.d = 0,65 . 1,04 . 250 . 550 . 10 -3 = 92,95 kN Vc = 0,8.Vcr = 0,8 . 92,95 = 74,36 kN Vr,max = 0,22.fcd.bw.d = 0,22 . 13,33 . 250 . 550 . 10 -3 = 403,23 kN MESNETTE HESAP ( D.Y. 1997 )
• K101 KENAR MESNEDĐ : V d = 76,52 kN V dy = V(g+q)o = 64,99 kN Vcr = 92,95 kN V e – V dy = 104,28 – 64,99 = 39,29 kN 0,5 V d = 0,5 . 76,52 = 38,26 kN ( V e – V dy ) ≥ 0,5 V d ⇒ V c = 0 ⇒ V w,et = V d,hesap V d,hesap = max ( V 1,4g+1,6q , V e , V g+q+e ) = V e =104,28 kN ⇒ V w,et = 104,28 kN A sw = ( V w,et . s ) / ( f ywd . d ) ⇒ A sw = ( 104,28 . s . 10 3 ) / ( 191 . 550 ) ∅8 ⇒ A 0 = 50 mm 2 ⇒ s = 100 mm ⇒ ∅∅∅∅8 / 9 s ≤ 600 / 4 = 150 mm ≤ 150 mm
≤ 8 . 12 = 96 mm Vr,max = 403,23 kN > V d,hesap = 104,28 kN ⇒ KESĐT YETERL Đ
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• K101 – K102 MESNEDĐ SOL UCU : V d = 93,20 kN V dy = V(g+q)o = 64,99 kN Vcr = 92,95 kN V e – V dy = 108,7 – 64,99 = 43,71 kN 0,5 V d = 0,5 . 93,20 = 46,60 kN ( V e – V dy ) ≤ 0,5 V d ⇒ V c = 74,36 ⇒ V w,et = V d,hesap - V c =34,34 V d,hesap = max ( V 1,4g+1,6q , V e , V g+q+e ) = V e =130,11 kN ⇒ V w,et = 34,34 kN A sw = ( V w,et . s ) / ( f ywd . d ) ⇒ A sw = ( 34,34 . s . 10 3 ) / ( 191 . 550 ) ∅8 ⇒ A 0 = 50 mm 2 ⇒ s 306 mm ⇒ ∅∅∅∅8 / 9 s ≤ 600 / 4 = 150 mm ≤ 150 mm
≤ 8 . 12 = 96 mm Vr,max = 403,23 kN > V d,hesap = 108,27 kN ⇒ KESĐT YETERL Đ
• K101 – K102 MESNEDĐ SAĞ UCU : V d = 56,61 kN V dy = V(g+q)o = 27,78 kN Vcr = 92,95 kN V e – V dy = 74,30 – 27,78 = 46,52 kN 0,5 V d = 0,5 . 56,61 = 28,305 kN ( V e – V dy ) ≥ 0,5 V d ⇒ V c = 0 ⇒ V w,et = V d,hesap V d,hesap = max ( V 1,4g+1,6q , V e , V g+q+e ) = V e =74,30 kN ⇒ V w,et = 74,30 kN A sw = ( V w,et . s ) / ( f ywd . d ) ⇒ A sw = ( 74,30 . s . 10 3 ) / ( 191 . 550 ) ∅8 ⇒ A 0 = 50 mm 2 ⇒ s = 141 mm ⇒ ∅∅∅∅8 / 9 s ≤ 600 / 4 = 150 mm ≤ 150 mm
≤ 8 . 12 = 96 mm Vr,max = 403,23 kN > V d,hesap = 74,30 kN ⇒ KESĐT YETERL Đ
• K102 – K103 MESNEDĐ SOL UCU : V d = 42,13 kN V dy = V(g+q)o = 27,78 kN Vcr = 92,95 kN V e – V dy = 74,50 – 27,78 = 46,72 kN 0,5 V d = 0,5 . 42,13 = 21,065 kN ( V e – V dy ) ≥ 0,5 V d ⇒ V c = 0 ⇒ V w,et = V d,hesap V d,hesap = max ( V 1,4g+1,6q , V e , V g+q+e ) = V e =74,50 kN ⇒ V w,et = 74,50 kN A sw = ( V w,et . s ) / ( f ywd . d ) ⇒ A sw = ( 74,50 . s . 10 3 ) / ( 191 . 550 )
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∅8 ⇒ A 0 = 50 mm 2 ⇒ s = 141 mm ⇒ ∅∅∅∅8 / 9 s ≤ 600 / 4 = 150 mm ≤ 150 mm
≤ 8 . 12 = 96 mm Vr,max = 403,23 kN > V d,hesap = 74,50 kN ⇒ KESĐT YETERL Đ AÇIKLIKTA HESAP ( TS 500 )
• K101 AÇIKLIK KES ĐTĐ : V d = V pd = 84,22 kN Vr,max = 403,23 kN Vcr = 92,95 kN V d = 84,22 kN < Vcr = 92,95 kN ⇒ min etriye hesabı A s,min = 0,30 . f ctd . b w . s max / f ywd⇒ 2 .50=0,30.1,04.250.s max /191 ⇒ s max = 244 mm s ≤ d / 2 = 550 / 2 = 275 mm ≤ 300 mm ⇒ ∅∅∅∅8 / 24 ≤ b w = 250 mm
• K102 AÇIKLIK KES ĐTĐ : V d = V pd = 44,98 kN Vr,max = 403,23 kN Vcr = 92,95 kN V d = 44,98 kN < Vcr = 92,95 kN ⇒ min etriye hesabı A s,min = 0,30 . f ctd . b w . s max / f ywd⇒ 2 .50=0,30.1,04.250.s max /191 ⇒ s max = 244 mm s ≤ d / 2 = 550 / 2 = 275 mm ≤ 300 mm ⇒ ∅∅∅∅8 / 24 ≤ b w = 250 mm
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1 - 1 AKSI EĞĐLME DONATISI ŞEMASI ∅16 2∅16 ∅16 ∅14 (ek) ∅14 (ek) ∅14 (ek) 1∅18 1∅16 1∅16 1∅18 ∅12 (ek ) ∅12 (ek ) ∅12 (ek ) 2∅18 2∅16 2∅16 2∅18
1 - 1 AKSI KAYMA DONATISI ŞEMASI
∅8/9 ∅8/24 ∅8/9 ∅8/9 ∅8/24 ∅8/9
K101 K102
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S3 (30/40) KOLONU BETONARME HESABI C - C AKSI KESĐT TESĐRLERĐ Pd P 0,9G E 8,92 5,94 4,11 61,98 j 0,98 m 0,98 m 0,98 m 1,47 m
17,83 11,88 8,20 48,97 i 17,83 11,88 8,20 61,98 1,96 m 1,96 m 1,96 m 1,31 m j 8,92 5,94 4,11 60,58
98,0
30,098,0.92,81
1
−=M = 6,19 kNm
Pd
96,1
30,096,1.83,171
2
−=M = 15,10 kNm
98,0
30,098,0.11,41
1
−=M = 2,85 kNm
0,9G
96,1
30,096,1.20,81
2
−=M = 6,95 kNm
98,0
30,098,0.94,51
1
−=M = 4,12 kNm
P
96,1
3,096,1.88,111
2
−=M = 10,06 kNm
1.Kat ⇒ 47,1
3,047,1.98,611
1
−=M = 49,33 kNm
E
Zemin Kat ⇒ 31,1
3,031,1.97,481
1
−=M = 37,76 kNm
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ZEM ĐN KAT S3 KOLONU i UCUNDAK Đ MOMENTLER MG+Q = 10,06 kNm M1,4G+1,6Q = 15,10 kNm M0,9G = 6,95 kNm ⇒ MG+Q+E = 70,64 kNm ME = 37,76 kNm ZEM ĐN KAT S3 KOLONU j UCUNDAK Đ MOMENTLER MG+Q = 5,94 kNm M1,4G+1,6Q = 8,92 kNm M0,9G = 4,11 kNm ⇒ MG+Q+E = 66,52 kNm ME = 60,58 kNm Sonuç Kesit Tesirleri M1,4G+1,6Q = 15,10 kNm MG+Q+E = 70,64 kNm 1. KAT S3 KOLONU i UCUNDAK Đ MOMENTLER MG+Q = 10,06 kNm M1,4G+1,6Q = 15,10 kNm M0,9G = 6,95 kNm ⇒ MG+Q+E = 59,39 kNm ME = 49,33 kNm 1. KAT S3 KOLONU j UCUNDAK Đ MOMENTLER MG+Q = 4,12 kNm M1,4G+1,6Q = 6,19 kNm M0,9G = 2,85 kNm ⇒ MG+Q+E = 53,45 kNm ME = 49,33 kNm Sonuç Kesit Tesirleri M1,4G+1,6Q = 15,10 kNm MG+Q+E = 59,39 kNm
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1-1 AKSI KESĐT TESĐRLERĐ Pd P 0,9G E 1,70 3,17 1,10 48,29 j 0,98 m 0,98 m 0,98 m 1,47 m
3,41 6,33 2,20 34,73 i 3,41 6,33 2,20 48,29 1,96 m 1,96 m 1,96 m 1,32 m j 1,70 3,17 1,10 42,45
98,0
30,098,0.70,11
1
−=M = 1,18 kNm
Pd
96,1
30,096,1.41,31
2
−=M = 2,89 kNm
98,0
30,098,0.17,31
1
−=M = 2,20 kNm
P
96,1
30,096,1.33,61
2
−=M = 5,36 kNm
98,0
30,098,0.10,11
1
−=M = 0,76 kNm
0,9G
96,1
30,096,1.20,21
2
−=M = 1,86 kNm
1.Kat ⇒ 47,1
30,047,1.29,481
1
−=M = 33,44 kNm
E
Zemin Kat ⇒ 32,1
30,032,1.73,341
1
−=M = 26,84 kNm
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ZEM ĐN KAT S3 KOLONU i UCUNDAK Đ MOMENTLER MG+Q = 5,36 kNm M1,4G+1,6Q = 2,89 kNm M0,9G = 1,86 kNm ⇒ MG+Q+E = 32,20 kNm ME = 26,84 kNm ZEM ĐN KAT S3 KOLONU j UCUNDAK Đ MOMENTLER MG+Q = 3,17 kNm M1,4G+1,6Q = 1,70 kNm M0,9G = 1,10 kNm ⇒ MG+Q+E = 45,62 kNm ME = 42,45 kNm Sonuç Kesit Tesirleri M1,4G+1,6Q = 2,89 kNm MG+Q+E = 47,81 kNm 1. KAT S3 KOLONU i UCUNDAK Đ MOMENTLER MG+Q = 5,36 kNm M1,4G+1,6Q = 2,89 kNm M0,9G = 1,86 kNm ⇒ MG+Q+E = 38,80 kNm ME = 33,44 kNm 1. KAT S3 KOLONU j UCUNDAK Đ MOMENTLER MG+Q = 2,20 kNm M1,4G+1,6Q = 1,18 kNm M0,9G = 0,76 kNm ⇒ MG+Q+E = 35,64 kNm ME = 33,44 kNm Sonuç Kesit Tesirleri M1,4G+1,6Q = 2,89 kNm MG+Q+E = 38,80 kNm
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KOLON BETONARME HESABI
**ZEM ĐN KAT Y-Y YÖNÜ** 1,4G + 1,6Q YÜKLEMESĐ Nd = 908,15 kN Md = 15,10 kNm d′ = 5 cm ⇒ zs = h – 2.d′ = 40 – 2.5 = 30 cm
40
30=h
zs = 0,75 ⇒ ABAK 2
1. Deprem Bölgesi ⇒ ρmin = 0,0025 ⇒ ωmin =cd
yd
f
f.minρ = 0,036
n =33,13.400.300
10.15,908
..
6
=cd
d
fhb
N = 0,58
ω < ωmin ⇒ minimum hesap yapılır.
m =33,13.400.300
10.10,15
.. 2
6
2=
cd
d
fhb
M = 0,024
ρ′ = ρ = ρmin = 0,0025 ⇒ 400.300.191
33,13.036,0...min
1 === hbf
fwAA
yd
cdss = 302 mm2
G+Q+E YÜKLEMES Đ NG+Q = 637,25 kN N E = 152,217 kN N G+Q+E = 789,467 kN M G+Q = 10,06 kNm M E = 60,58 kNm M G+Q+E = 70,64 kNm
d′ = 5 cm ⇒ zs = h – 2.d′ = 40 – 2.5 = 30 cm 40
30=h
zs = 0,75 ⇒ ABAK 2
n =33,13.300.400
10.467,789
..
3
=cd
d
fhb
N = 0,49
ω =0,015 < ωmin =0,036⇒minimum hesap yapılır.
m =33,13.400.300
10.64,70
.. 2
6
2=
cd
d
fhb
M = 0,11
ρ′ = ρ = ρmin = 0,0025 ⇒ 400.300.191
33,13.036,0...min
1 === hbf
fwAA
yd
cdss = 302 mm2
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0,9G+E YÜKLEMESĐ N 0,9G = 501,525 kN N E = 152,217 kN N 0,9G+E = 653,742 kN M 0,9G = 6,95 kNm M E = 60,58 kNm M 0,9G+E = 67,53 kNm
d′ = 5 cm ⇒ zs = h – 2.d′ = 40 – 2.5 = 30 cm 40
30=h
zs = 0,75 ⇒ ABAK 2
n =33,13.400.300
10.742,653
..
3
=cd
d
fhb
N = 0,41
ω = 0,01 < ωmin = 0,036⇒ minimum hesap yapılır.
m =33,13.400.300
10.53,67
.. 2
6
2=
cd
d
fhb
M = 0,106
ρ′ = ρ = ρmin = 0,0025 ⇒ 400.300.191
33,13.036,0...min
1 === hbf
fwAA
yd
cdss = 302 mm2
• SEÇĐLEN DONATI : A sy = 301 mm 2 ⇒⇒⇒⇒ 3∅∅∅∅16 ( 603 mm 2 )
**ZEM ĐN KAT X-X YÖNÜ** 1,4G + 1,6Q YÜKLEMESĐ Nd = 908,15 kN Md = 2,89 kNm d′ = 5 cm ⇒ zs = h – 2.d′ = 30 – 2.5 = 20 cm
30
20=h
zs = 0,66 ⇒ ABAK 1
1. Deprem Bölgesi ⇒ ρmin = 0,0025 ⇒ ωmin =cd
yd
f
f.minρ = 0,036
n =33,13.400.300
10.15,908
..
6
=cd
d
fhb
N = 0,58
ω < ωmin ⇒ minimum hesap yapılır.
m =33,13.300.400
10.89,2
.. 2
6
2=
cd
d
fhb
M = 0,006
ρ′ = ρ = ρmin = 0,0025 ⇒ 400.300.191
33,13.036,0...min
1 === hbf
fwAA
yd
cdss = 302 mm2
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G+Q+E YÜKLEMES Đ NG+Q = 637,25 kN N E = 0 kN N G+Q+E = 637,25 kN M G+Q = 5,36 kNm M E = 42,45 kNm M G+Q+E = 47,81 kNm
d′ = 5 cm ⇒ zs = h – 2.d′ = 30 – 2.5 = 20 cm 30
20=h
zs = 0,66 ⇒ ABAK 1
n =33,13.300.400
10.25,637
..
3
=cd
d
fhb
N = 0,40
ω < ωmin =0,036⇒minimum hesap yapılır.
m =33,13.300.400
10.81,47
.. 2
6
2=
cd
d
fhb
M = 0,10
ρ′ = ρ = ρmin = 0,0025 ⇒ 400.300.191
33,13.036,0...min
1 === hbf
fwAA
yd
cdss = 302 mm2
0,9G+E YÜKLEMESĐ N 0,9G = 501,525 kN N E = 0 kN N 0,9G+E = 501,525 kN M 0,9G = 1,86 kNm M E = 42,45 kNm M 0,9G+E = 44,31 kNm
d′ = 5 cm ⇒ zs = h – 2.d′ = 30 – 2.5 = 20 cm 30
20=h
zs = 0,66 ⇒ ABAK 1
n =33,13.400.300
10.525,501
..
3
=cd
d
fhb
N = 0,31
ω < ωmin = 0,036⇒ minimum hesap yapılır.
m =33,13.300.400
10.31,44
.. 2
6
2=
cd
d
fhb
M = 0,092
ρ′ = ρ = ρmin = 0,0025 ⇒ 400.300.191
33,13.036,0...min
1 === hbf
fwAA
yd
cdss = 302 mm2
• SEÇĐLEN DONATI : A sy = 301 mm 2 ⇒⇒⇒⇒ 3∅∅∅∅16 ( 603 mm 2 )
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**1. KAT Y-Y YÖNÜ**
1,4G + 1,6Q YÜKLEMESĐ Nd = 726,52 kN Md = 15,10 kNm d′ = 5 cm ⇒ zs = h – 2.d′ = 40 – 2.5 = 30 cm
40
30=h
zs = 0,75 ⇒ ABAK 2
1. Deprem Bölgesi ⇒ ρmin = 0,0025 ⇒ ωmin =cd
yd
f
f.minρ = 0,036
n =33,13.400.300
10.52,726
..
6
=cd
d
fhb
N = 0,45
ω < ωmin ⇒ minimum hesap yapılır.
m =33,13.400.300
10.10,15
.. 2
6
2=
cd
d
fhb
M = 0,024
ρ′ = ρ = ρmin = 0,0025 ⇒ 400.300.191
33,13.036,0...min
1 === hbf
fwAA
yd
cdss = 302 mm2
G+Q+E YÜKLEMES Đ NG+Q = 509,80 kN N E = 110,278 kN N G+Q+E = 620,078 kN M G+Q = 10,06 kNm M E = 49,33 kNm M G+Q+E = 59,39 kNm
d′ = 5 cm ⇒ zs = h – 2.d′ = 40 – 2.5 = 30 cm 40
30=h
zs = 0,75 ⇒ ABAK 2
n =33,13.300.400
10.078,620
..
3
=cd
d
fhb
N = 0,39
ω < ωmin =0,036⇒minimum hesap yapılır.
m =33,13.400.300
10.39,59
.. 2
6
2=
cd
d
fhb
M = 0,093
ρ′ = ρ = ρmin = 0,0025 ⇒ 400.300.191
33,13.036,0...min
1 === hbf
fwAA
yd
cdss = 302 mm2
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0,9G+E YÜKLEMESĐ N 0,9G = 401,22 kN N E = 110,278 kN N 0,9G+E = 511,498 kN M 0,9G = 6,95 kNm M E = 49,33 kNm M 0,9G+E = 56,28 kNm
d′ = 5 cm ⇒ zs = h – 2.d′ = 40 – 2.5 = 30 cm 40
30=h
zs = 0,75 ⇒ ABAK 2
n =33,13.400.300
10.498,511
..
3
=cd
d
fhb
N = 0,32
ω < ωmin = 0,036⇒ minimum hesap yapılır.
m =33,13.400.300
10.28,56
.. 2
6
2=
cd
d
fhb
M = 0,088
ρ′ = ρ = ρmin = 0,0025 ⇒ 400.300.191
33,13.036,0...min
1 === hbf
fwAA
yd
cdss = 302 mm2
• SEÇĐLEN DONATI : A sy = 301 mm 2 ⇒⇒⇒⇒ 3∅∅∅∅16 ( 603 mm 2 )
**1. KAT X-X YÖNÜ** 1,4G + 1,6Q YÜKLEMESĐ Nd = 726,52 kN Md = 2,89 kNm d′ = 5 cm ⇒ zs = h – 2.d′ = 30 – 2.5 = 20 cm
30
20=h
zs = 0,66 ⇒ ABAK 1
1. Deprem Bölgesi ⇒ ρmin = 0,0025 ⇒ ωmin =cd
yd
f
f.minρ = 0,036
n =33,13.400.300
10.52,726
..
6
=cd
d
fhb
N = 0,45
ω < ωmin ⇒ minimum hesap yapılır.
m =33,13.300.400
10.89,2
.. 2
6
2=
cd
d
fhb
M = 0,006
ρ′ = ρ = ρmin = 0,0025 ⇒ 400.300.191
33,13.036,0...min
1 === hbf
fwAA
yd
cdss = 302 mm2
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G+Q+E YÜKLEMES Đ NG+Q = 509,80 kN N E = 0 kN N G+Q+E = 509,80 kN M G+Q = 5,36 kNm M E = 33,44 kNm M G+Q+E = 38,80 kNm
d′ = 5 cm ⇒ zs = h – 2.d′ = 30 – 2.5 = 20 cm 30
20=h
zs = 0,66 ⇒ ABAK 1
n =33,13.300.400
10.80,509
..
3
=cd
d
fhb
N = 0,32
ω < ωmin =0,036⇒minimum hesap yapılır.
m =33,13.300.400
10.80,38
.. 2
6
2=
cd
d
fhb
M = 0,081
ρ′ = ρ = ρmin = 0,0025 ⇒ 400.300.191
33,13.036,0...min
1 === hbf
fwAA
yd
cdss = 302 mm2
0,9G+E YÜKLEMESĐ N 0,9G = 401,22 kN N E = 0 kN N 0,9G+E = 401,22 kN M 0,9G = 1,86 kNm M E = 38,44 kNm M 0,9G+E = 40,30 kNm
d′ = 5 cm ⇒ zs = h – 2.d′ = 30 – 2.5 = 20 cm 30
20=h
zs = 0,66 ⇒ ABAK 1
n =33,13.400.300
10.22,401
..
3
=cd
d
fhb
N = 0,25
ω < ωmin = 0,036⇒ minimum hesap yapılır.
m =33,13.300.400
10.30,40
.. 2
6
2=
cd
d
fhb
M = 0,084
ρ′ = ρ = ρmin = 0,0025 ⇒ 400.300.191
33,13.036,0...min
1 === hbf
fwAA
yd
cdss = 302 mm2
• SEÇĐLEN DONATI : A sy = 301 mm 2 ⇒⇒⇒⇒ 3∅∅∅∅16 ( 603 mm 2 )
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DONATI SEÇĐMĐ VE GÖSTERĐMĐ :
• Zemin Kat : A sx = 302 mm 2 ⇒ 3∅16 ( 603 mm 2 ) A sy = 301 mm 2 ⇒ 3∅16 ( 603 mm 2 ) A s,min = 0,01 . b . h = 0,01 . 300 . 400 = 1200 mm 2 8∅∅∅∅16 A s,maks = 0,04 . b . h = 0,04 . 300 . 400 = 4800 mm 2 (603 mm2) A s,min <<<< A s <<<< A s,maks
• 1. Kat : A sx = 302 mm 2 ⇒ 3∅16 ( 603 mm 2 ) A sy = 301 mm 2 ⇒ 3∅16 ( 603 mm 2 ) A s,min = 0,01 . b . h = 0,01 . 300 . 400 = 1200 mm 2 8∅∅∅∅16 A s,maks = 0,04 . b . h = 0,04 . 300 . 400 = 4800 mm 2 (603 mm2) A s,min <<<< A s <<<< A s,maks
S3 KOLONU SARILMA BÖLGES ĐNDE ETRĐYE HESABI:
• Zemin kat S3 Kolonu : C – C aksında oluşan değerler maksimumudur . M a = 66,52 kNm M ü = 47,82 kNm V E = ( M a + M ü ) / h kat = 114,34 / 2,94 = 38,89 kN 0,22 . f cd . b . h = 0,22 . 13,33 . 300 . 350 . 10 –3 = 307,923 kN
V E = 38,89 kN < 0,22 . f cd . b . h = 307,923 kN V cr = 0,65 . f ctd . b w . d = 0,65 . 1,04 . 300 . ( 400 – 50 ) . 10 –3 = 70,98 kN V d = V E < V cr ⇒ Kesme donatısı hesabına gerek yoktur . Min etriye hesabı yapılır . s < b min / 3 = 300 / 3 = 100 mm ≥ 50 mm ⇒⇒⇒⇒ ∅∅∅∅8 / 10 seçildi . ≥ 100 mm
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• 1. kat S3 Kolonu : C – C aksında oluşan değerler maksimumudur . M a = 59,39 kNm M ü = 53,45 kNm V E = ( M a + M ü ) / h kat = ( 59,39 + 53,45 ) / 2,94 = 38,38 kN 0,22 . f cd . b . h = 0,22 . 13,33 . 300 . 350 . 10 –3 = 307,923 kN
V E = 38,38 kN < 0,22 . f cd . b . h = 307,923 kN V cr = 0,65 . f ctd . b w . d = 0,65 . 1,04 . 300 . ( 400 – 50 ) . 10 –3 = 70,98 kN V d = V E < V cr ⇒ Kesme donatısı hesabına gerek yoktur . Min etriye hesabı yapılır . s < b min / 3 = 300 / 3 = 100 mm ≥ 50 mm ⇒⇒⇒⇒ ∅∅∅∅8 / 10 seçildi . ≥ 100 mm Kolon orta bölgesinde ∅∅∅∅8 / 20 olan etriyenin kullanılması uygun görülmüştür .
KOLON B ĐRLEŞĐM BÖLGESĐNDE KESME GÜVENL ĐĞĐ TAHK ĐKĐ 1 – 1 Aksı :
• 1. Deprem Doğrultusu : ⇒⇒⇒⇒ Deprem Doğrultusu 1
A S1 = 804 A S2 = 804
A′ S1 = 402 A′ S2 = 402
V e = 1,25 . f yk . ( A S1 + A′ S2 ) – V kolon ⇒ V e = 331,65 - V kolon M p1 = 1,4 . f yk . A S1 . k z . d = 1,4 . 220 . 804 . 0,9 . 550 . 10 –6 = 122,58 kNm
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M p2 = 1,4 . f yk . A′ S2 . k z . d = 1,4 . 220 . 402 . 0,9 . 550 . 10 –6 = 61,29 kNm V kolon = ( M p1 + M p2 ) / h kat = ( 122,58 + 61 ,29 ) / 2,94 = 62,54 kN
• 2. Deprem Doğrultusu : ⇐⇐⇐⇐ Deprem Doğrultusu 2
A S1 = 804 A S2 = 804
A′ S1 = 402 A′ S2 = 402
V e = 1,25 . f yk . ( A S2 + A′ S1 ) – V kolon ⇒ V e = 331,65 - V kolon M p1 = 1,4 . f yk . A′ S1 . k z . d = 1,4 . 220 . 402 . 0,9 . 550 . 10 –6 = 61,29 kNm M p2 = 1,4 . f yk . A S2 . k z . d = 1,4 . 220 . 804 . 0,9 . 550 . 10 –6 = 122,58 kNm V kolon = ( M p1 + M p2 ) / h kat = ( 122,58 + 61 ,29 ) / 2,94 = 62,54 kN V e = 331,65 - V kolon = 331,65 – 62,54 = 269,11 kN V e = 269,11 kN V e,max = 0,45 . f yk . b j . h ( Kuşatılmış ) b j = 2 . 12,5 = 25 cm V e,max = 0,45 . 13,33 . 250 . 300 . 10 –3 = 449,89 kN ⇒ V e,max = 449,89 kN V e = 269,11kN < V e,max = 449,89 kN ⇒ Kesit Yeterli C – C Aksı :
• 1. Deprem Doğrultusu : ⇒⇒⇒⇒ Deprem Doğrultusu 1
A S = 1272
A′ S = 911
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V e = 1,25 . f yk . ( A S1 + A′ S2 ) – V kolon ⇒ V e = 250,525 - V kolon M p = 1,4 . f yk . A′ S . k z . d = 1,4 . 220 . 911 . 0,9 . 550 . 10 –6 = 138,89 kNm V kolon = M p / h kat = 138,89 / 2,94 = 47,24 kN
• 2. Deprem Doğrultusu : ⇐⇐⇐⇐ Deprem Doğrultusu 2
A S = 1272
A′ S = 911
V e = 1,25 . f yk . ( A S2 + A′ S1 ) – V kolon ⇒ V e = 349,80 - V kolon M p = 1,4 . f yk . A S . k z . d = 1,4 . 220 . 1272 . 0,9 . 550 . 10 –6 = 193,93 kNm V kolon = M p / h kat = 193,93 / 2,94 = 65,96 kN V e = 349,80 - V kolon = 349,80 – 65,96 = 283,84 kN V e = 283,84 kN V e,max = 0,45 . f yk . b j . h ( Kuşatılmış ) b j = 2 . 12,5 = 25 cm V e,max = 0,45 . 13,33 . 250 . 400 . 10 –3 = 599,85 kN ⇒ V e,max = 599,85 kN V e = 283,84kN < V e,max = 599,85 kN ⇒ Kesit Yeterli
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GÜÇLÜ KOLON – ZAYIF K ĐRĐŞ TAHK ĐKĐ ( S3 KOLONU ĐÇĐN )
X – X YÖNÜ ĐÇĐN ( 1 – 1 AKSI ) :
• Depremin Soldan Sağa Etkimesi Durumu : ⇒⇒⇒⇒ Deprem Doğrultusu M ra
N d,üst = 509,80 kN M rj = 80,229 N d,alt = 637,25 kN
K102 K103 M ri = 41,70
M rü M ra’ın Hesabı :
d′ = 5 cm ⇒ zs = h – 2.d′ = 30 – 2.5 = 20 cm 30
20=h
zs = 0,66 ⇒ ABAK 1
n =33,13.400.300
10.80,509
..
3
=cd
d
fhb
N = 0,32
M ra=m . b . h 2.f cd=0,156 . 400 . 300 2 . 13,33 . 10 -6
w =33,13.300.400
191.603
..
..=
cd
yds
fhb
fA = 0,072 = 74,86 kNm
M rü’nün Hesabı :
d′ = 5 cm ⇒ zs = h – 2.d′ = 30 – 2.5 = 20 cm 30
20=h
zs = 0,66 ⇒ ABAK 1
n =33,13.400.300
10.25,637
..
3
=cd
d
fhb
N = 0,40
M rü=m . b . h 2.f cd=0,160 . 400 . 300 2 . 13,33 . 10 -6
w =33,13.300.400
191.603
..
..=
cd
yds
fhb
fA = 0,072 = 76,78 kNm
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• Depremin Sağdan Sola Etkimesi Durumu : ⇐⇐⇐⇐ Deprem Doğrultusu M ra
N d,üst = 509,80 kN M rj = 41,70 N d,alt = 637,25 kN
K102 K103 M ri = 80,239
M rü M ra’nın Hesabı :
d′ = 5 cm ⇒ zs = h – 2.d′ = 30 – 2.5 = 20 cm 30
20=h
zs = 0,66 ⇒ ABAK 1
n =33,13.400.300
10.80,509
..
3
=cd
d
fhb
N = 0,32
M ra=m . b . h 2.f cd=0,156 . 400 . 300 2 . 13,33 . 10 -6
w =33,13.300.400
191.603
..
..=
cd
yds
fhb
fA = 0,072 = 74,86 kNm
M rü’nün Hesabı :
d′ = 5 cm ⇒ zs = h – 2.d′ = 30 – 2.5 = 20 cm 30
20=h
zs = 0,66 ⇒ ABAK 1
n =33,13.400.300
10.25,637
..
3
=cd
d
fhb
N = 0,40
M rü=m . b . h 2.f cd=0,160 . 400 . 300 2 . 13,33 . 10 -6
w =33,13.300.400
191.603
..
..=
cd
yds
fhb
fA = 0,072 = 76,78 kNm
SONUÇ : 1,2 . ( M ri + M rü ) = 1,2 . ( 41,70 + 80,239 ) = 146,33 kN M ra + M rü = 74,86 + 76,78 = 151,64 kNm 1,2 . ( M ri + M rü ) < ( M ra + M rü ) ⇒ Güçlü kolon zayıf kiriş şartı S3 kolonu için X doğrultusu için sağlandı .
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Y – Y YÖNÜ ĐÇĐN ( C – C AKSI ) :
• Depremin Soldan Sağa Etkimesi Durumu : ⇒⇒⇒⇒ Deprem Doğrultusu M ra
N d,üst = 620,078 kN N d,alt = 789,467 kN
K117 M ri = 94,265
S3
M rü M ra’nın Hesabı :
d′ = 5 cm ⇒ zs = h – 2.d′ = 40 – 2.5 = 30 cm 40
30=h
zs = 0,75 ⇒ ABAK 2
n =33,13.400.300
10.078,620
..
3
=cd
d
fhb
N = 0,39
M ra=m . b . h 2.f cd=0,160 . 300 . 400 2 . 13,33 . 10 -6
w =33,13.300.400
191.603
..
..=
cd
yds
fhb
fA = 0,072 = 102,37 kNm
M rü’nün Hesabı :
d′ = 5 cm ⇒ zs = h – 2.d′ = 40 – 2.5 = 30 cm 40
30=h
zs = 0,75 ⇒ ABAK 2
n =33,13.400.300
10.467,789
..
3
=cd
d
fhb
N = 0,49
M rü=m . b . h 2.f cd=0,160 . 300 . 400 2 . 13,33 . 10 -6
w =33,13.300.400
191.603
..
..=
cd
yds
fhb
fA = 0,072 = 102,37 kNm
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• Depremin Sağdan Sola Etkimesi Durumu : ⇐⇐⇐⇐ Deprem Doğrultusu M ra
N d,üst = 620,078kN N d,alt = 7893467 kN
K117 M ri = 124,90 kNm
M rü M ra’nın Hesabı :
d′ = 5 cm ⇒ zs = h – 2.d′ = 40 – 2.5 = 30 cm 40
30=h
zs = 0,75 ⇒ ABAK 2
n =33,13.400.300
10.078,620
..
3
=cd
d
fhb
N = 0,39
M ra=m . b . h 2.f cd=0,160 . 300 . 400 2 . 13,33 . 10 -6
w =33,13.300.400
191.603
..
..=
cd
yds
fhb
fA = 0,072 = 102,37 kNm
M rü’nün Hesabı :
d′ = 5 cm ⇒ zs = h – 2.d′ = 40 – 2.5 = 30 cm 40
30=h
zs = 0,75 ⇒ ABAK 2
n =33,13.400.300
10.467,789
..
3
=cd
d
fhb
N = 0,49
M rü=m . b . h 2.f cd=0,160 . 300 . 400 2 . 13,33 . 10 -6
w =33,13.300.400
191.603
..
..=
cd
yds
fhb
fA = 0,072 = 102,37 kNm
SONUÇ : 1,2 . ( M ri + M rü ) = 1,2 . ( 124,90 + 0 ) = 149,88 kN M ra + M rü = 102,37 + 102,37 = 204,74 kNm 1,2 . ( M ri + M rü ) < ( M ra + M rü ) ⇒ Güçlü kolon zayıf kiriş şartı S3 kolonu için Y doğrultusu için sağlandı . KOLON – K ĐRĐŞ BĐRLEŞĐM BÖLGESĐ ĐÇĐN ETRĐYE HESABI : s < b min / 3 = 300 / 3 =100 mm ≥ 50 mm ⇒⇒⇒⇒ ∅∅∅∅8 / 10 seçildi . ≤ 100 mm
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TEMEL ÖNBOYUT HESABI
Zemin Sınıfı = Z1 σz,em = 229 kN/m2 σz,net = σz,em – 0,25.0,50 = 216,50 kN/m2 T1 TEMEL Đ S1( 30 / 30 ) Ng+q = 575,05 kN N1,4g+1,6q = 829,05 kN ax = ay = 0,3 m ax / ay = 1
AT = bx.by ≥50,216
05,575=z
iN
σ ⇒ bx = by = 1,70 m
Zımbalama Tahkiki ve Temel Yüksekliğinin Bulunması Vpr ≥ Vpd
Vpd = Vpr ⇒ ( )( )
dUfbb
dadaN pctd
yx
yxd ...
.
.1. γ=
++−
Up = 2.(ax + ay + 2.d )
( )[ ] ( )( )
++−=+1700.1700
300.3001.05,829..2600.2.04,1.1
dddd ⇒ d ≅ 29,5 cm
h = d + 5 = 34,50 cm < 50 cm ⇒ h = 50 cm seçildi . h min < h ⇒ h = 50 cm uygudur . T2 TEMEL Đ S2 ( 30 / 45 ) Ng+q = 844,45 kN N1,4g+1,6q = 1215,77 kN ax = 0,3 m ay = 0,45 m ax / ay = 2 / 3 ⇒ bx = 2 .by / 3
AT = bx.by ≥5,216
45,844=z
iN
σ = 3,90 m2 ⇒ bx = 1,65 m by = 2,45 m
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Zımbalama Tahkiki ve Temel Yüksekliğinin Bulunması Vpr ≥ Vpd
Vpd = Vpr ⇒ ( )( )
dUfbb
dadaN pctd
yx
yxd ...
.
.1. γ=
++−
Up = 2.(ax + ay + 2.d )
( )[ ] ( )( )
++−=+2450.1650
450.3001.77,1215..2750.2.04,1.1
dddd ⇒ d ≅ 35,10 cm
h = d + 5 = 40,10 cm < 50 cm ⇒ h = 50 cm seçildi h min < h ⇒ h = 50 cm uygudur . T3 TEMEL Đ S3 ( 30 / 40 ) Ng+q = 637,25 kN N1,4g+1,6q = 908,15 kN ax = 0,3 m ay = 0,40 m ax / ay = 3 / 4 ⇒ bx = 3 .by / 4
AT = bx.by ≥5,216
25,637=z
iN
σ = 2,9434 m2 ⇒ bx = 1,65 m by = 2,20 m
Zımbalama Tahkiki ve Temel Yüksekliğinin Bulunması Vpr ≥ Vpd
Vpd = Vpr ⇒ ( )( )
dUfbb
dadaN pctd
yx
yxd ...
.
.1. γ=
++−
Up = 2.(ax + ay + 2.d )
( )[ ] ( )( )
++−=+2200.1650
400.3001.15,908..2700.2.04,1.1
dddd ⇒ d ≅ 29,90 cm
h = d + 5 = 34,90 cm < 50 cm ⇒ h = 50 cm seçildi h min < h ⇒ h = 50 cm uygudur .
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T4 TEMEL Đ S3 ( 45 / 30 ) Ng+q = 843,90 kN N1,4g+1,6q = 1214,37 kN ax = 0,45 m ay = 0,30 m ax / ay = 3 / 2 ⇒ bx = 3 .by / 2
AT = bx.by ≥50,216
90,843=z
iN
σ = 3,898 m2 ⇒ bx = 2,45 m by = 1,65 m
Zımbalama Tahkiki ve Temel Yüksekliğinin Bulunması Vpr ≥ Vpd
Vpd = Vpr ⇒ ( )( )
dUfbb
dadaN pctd
yx
yxd ...
.
.1. γ=
++−
Up = 2.(ax + ay + 2.d )
( )[ ] ( )( )
++−=+2450.1650
300.4501.37,1214..2750.2.04,1.1
dddd ⇒ d ≅ 35,10 cm
h = d + 5 = 40,10 cm < 50 cm ⇒ h = 50 cm seçildi h min < h ⇒ h = 50 cm uygudur . T5 TEMEL Đ S4 ( 45 / 45 ) Ng+q = 1310,95 kN N1,4g+1,6q = 1880,80 kN ax = 0,45 m ay = 0,45m ax / ay = 1 ⇒ bx = by
AT = bx.by ≥50,216
95,1310=z
iN
σ = 6,0552 m2 ⇒ bx = 2,50 m by = 2,50 m
Zımbalama Tahkiki ve Temel Yüksekliğinin Bulunması Vpr ≥ Vpd
Vpd = Vpr ⇒ ( )( )
dUfbb
dadaN pctd
yx
yxd ...
.
.1. γ=
++−
Up = 2.(ax + ay + 2.d )
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( )[ ] ( )( )
++−=+2500.2500
450.4501.08,1880..2900.2.04,1.1
dddd ⇒ d ≅ 44,30 cm
h = d + 5 = 49,30 cm < 50 cm ⇒ h = 50 cm seçildi h min < h ⇒ h = 50 cm uygudur . T6 TEMEL Đ S5 ( 45 / 45 ) Ng+q = 1249,90 kN N1,4g+1,6q = 1792,52 kN ax = ay = 0,45 m ax / ay = 1 ⇒ bx = by
AT = bx.by ≥50,216
90,1249=z
iN
σ = 5,77321 m2 ⇒ bx = by = 2,45 m
Zımbalama Tahkiki ve Temel Yüksekliğinin Bulunması Vpr ≥ Vpd
Vpd = Vpr ⇒ ( )( )
dUfbb
dadaN pctd
yx
yxd ...
.
.1. γ=
++−
Up = 2.(ax + ay + 2.d )
( )[ ] ( )( )
++−=+2450.2450
450.4501.80,1880..2900.2.04,1.1
dddd ⇒ d ≅ 42,80 cm
h = d + 5 = 47,80 cm < 50 cm ⇒ h = 50 cm seçildi h min < h ⇒ h = 50 cm uygudur .
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T3 TEMEL Đ BOYUT KONTROLÜ **DEPREM + ĐŞLETME YÜKLER Đ ETK ĐSĐNE GÖRE BOYUT TAHK ĐKĐ** 1) X-X YÖNÜ ( 1 – 1 AKSI ) g+q E 5,36 26,84 3,17 42,45
H =( ) ( )
94,2
45,4273,34
94,2
17,333,6 +++=+∑
kat
üstalt
h
MM= 29,48 kNm
ΣMalt = 3,17 + 42,45 = 42,62 kNm M0 = ΣMalt + H.h = 45,62 + 29,48 . 0,50 = 60,36 kN Ng = γ.h.bx.by = 25 . 0,5 . 1,65 . 2,20 = 45,375 kN
e =375,4525,637
36,600
+=
+ Gi NN
M= 0,0884 < m
bx 275,06
=
σ0 =20,2.65,1
375,4525,637
.
+=+
yx
Gi
bb
NN= 188 kN / m 2 < σz,em = 229 kN/m2 √
σ1,2 =
=
65,1
0884,0.61.188
.61.0 µµ
xb
eσ ⇒ σ1 = 248,43 < 1,5.σz √
σ2 = 127,57 > 0 √ SONUÇ : X doğrultusunda temel genişliği uygundur .
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2) Y-Y YÖNÜ g+q E 11,88 48,97 5,94 60,58
H =( ) ( )
94,2
58,6097,48
94,2
94,588,11 +++=+∑
kat
üstalt
h
MM= 43,32 kNm
ΣMalt = 5,94 + 60,58 = 66,52 kNm M0 = ΣMalt + H.h = 66,52 + 43,32 . 0,50 = 193,88 kN Ng = γ.h.bx.by = 25 . 0,5 . 1,65 . 2,20 = 45,375 kN
e =375,4525,637
88,1930
+=
+ Gi NN
M= 0,2840 < m
by333,0
6=
σ0 =20,2.65,1
375,4525,637
.
+=+
yx
Gi
bb
NN= 188 kN / m 2 < σz,em = 229 kN/m2 √
σ1,2 =
=
20,2
2840,0.61.188
.61.0 µµ
xb
eσ ⇒ σ1 = 333,70 < 1,5.σz = 343,50√
σ2 = 42,40 > 0 √ SONUÇ : Y doğrultusunda temel genişliği uygundur .
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KESĐT TESĐRLERĐ a ) Yalnız Düşey Yükler Đçin ( Hesap Yükleri ) Nd = 908,15 kN
Mx =( ) ( )
65,1
30,065,1.
8
15,908.
8
22 −=−
x
xxd
b
abN = 125,39 kNm
My =( ) ( )
20,2
40,020,2.
8
15,908.
8
22 −=−
y
yyd
b
abN = 167,18 kNm
Vx =( ) ( )
65,1
30,065,1.
2
15,908.
2
−=−
x
xxd
b
abN = 371,52 kN
Vy =( ) ( )
20,2
40,020,2.
2
15,908.
2
−=−
y
yyd
b
abN = 371,52 kN
b ) Düşey Yük + Deprem ( G + Q + E ) x-x yönü Nd = 637,25 kN Md = 45,62 kN H = 29,48 kN
σ0 =20,2.65,1
25,637
.=
yx
d
bb
N = 175,55 < σz = 229 kN/m2
e =375,4525,637
36,600
+=
+ Gi NN
M= 0,0884 < m
bx275,0
6=
σ1 =
+=
+
65,1
0884,0.61.55,175
.61.0
xb
eσ = 236,02 kN/m2 < 1,5.σz = 343,50 √
σ2 =
−=
−
65,1
0884,0.61.55,175
.61.0
xb
eσ = 115,09 kN/m2 > 0 √
93,12065,1
975,0 a= ⇒ a = 71,46 kN/m2
Mx = 2,2.3
2.
2
675,0.47,49
2
675,0.55,186
22
+ = 110,03 kNm
Vx = 2,2.2
675,0.47,49675,0.55,186
2
+ = 313,76 kN
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y-y yönü Nd = 789,467 kN Md = 66,52 kN H = 43,32 kN M0 = 88,18 kN
e =467,789
18,880 =dN
M = 0,11170 <
6yb
= 0,36667
σ0 =20,2.65,1
467,789
.=
yx
d
bb
N = 217,484 kN / m2 < σz = 229 kN / m2
σ1 =
+=
+
20,2
11170,0.61.484,217
.61.0
yb
eσ = 283,79 kN/m2 < 1,5.σz = 343,50 √
σ2 =
−=
−
20,2
11170,0.61.484,217
.61.0
yb
eσ = 151,29 kN/m2 > 0 √
50,13220,2
30,1 a= ⇒ a = 78,30 kN/m2
My = 65,1.3
2.
2
90,0.20,54
2
90,0.59,229
22
+ = 117,57 kNm
Vy = 65,1.2
90,0.20,5490,0.59,229
2
+ = 381,18 kN
SONUÇ KESĐT TESĐRLERĐ : Vx = 371,52 kN Vy = 381,18 kN M x = 125,39 kNm My = 177,57 kNm
TEMEL DONATILARININ HESABI
Mx = 125,39 kNm < My = 177,57 kNm ⇒ Y doğrultusunda hesaba başlanır . Y - Y yönü My = 177,57 kNm b = 1650 mm d = 500 – 50 = 450 mm
k m =2
6
2 450.1650
10.57,177
.=
db
M y = 0,53 ⇒ ks = 0,976
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As =191.450.976,0
10.57,177
..
6
=ydz
d
fdk
M = 2117 mm2
A s,min = 0,002 . b . d = 0,002 . 1650 . 450 = 1485 mm 2 seçilen donatı 11∅∅∅∅16 ( 2211 mm2 ) X – X yönü Mx = 125,39 kNm b = 2200 mm d = 450 – 16 = 434 mm
k m =2
6
2 434.2200
10.39,125
.=
db
M y = 0,30 ⇒ ks = 0,986
As =191.434.986,0
10.39,125
..
6
=ydz
d
fdk
M = 1534 mm2
A s,min = 0,002 . b . d = 0,002 . 2200 . 434 = 1910 mm 2 seçilen donatı 10∅∅∅∅16 ( 2010 mm2 ) 11∅16 10∅16
KESME GÜVENL ĐĞĐ Vcr,x = 0,65.fctd . b . d1 = 0,65 . 1,04 . 2200 . 450 . 10 -3 = 669,24 kN > 371,52 kN Vcr,y = 0,65 . fctd . b . d2 = 0,65 . 1,04 . 1650 . 434 . 10 –3 = 484,08 kN > 381,18 kN Böylece kesme güvenliği hem X hem de Y doğrultusunda sağlanmış oldu .
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BAĞ KĐRĐŞĐ BOYUTLANDIRMASI
Zemin Sınıfı ⇒ Z1 ⇒ A zemin grubu Min. En Kesit Alanı = 625 cm2 Enkesit Boyutu = 25 / 25 min 4∅∅∅∅14 boyuna donatı olarak seçildi Etriye ⇒ ∅∅∅∅8/20 seçildi ( 1997 Deprem Yönetmeliği )