Laporan Struktur Parkir d9

BAB 1 PERHITUNGAN PEMBEBANAN A. Kombinasi Pembebanan

Gambar Rencana Struktur

Kombinasi pembebanan yang digunakan adalah sebagai berikut: Kombinasi 1 : 1.4 D Kombinasi 2 : 1.2 D + 1.6 L + 0.5 H Kombinasi 3 : 1.2 D + 1.6 H + 0.5 L Kombinasi 4 : 1.2 D + 1.3 W + 0.5 L + 0.5 H Kombinasi 5 : 1.2 D + 1.0 E + 0.5 L Kombinasi 6 : 0.9 D + 1.0 E B. Beban Mati 1. Beban Mati Balok, Kolom Dan Plat Untuk beban mati Balok, Kolom dan Plat di input denggan menggunakan Self Weight pada STAAD Pro 2004

2. Beban Mati Atap Jara Antara Kuda-Kuda Baja =

Berat Atap

Lebar m 1.20

Panjang m 4.50

4.50 Tebal m 0.002

m Berat Jumlah Total Berat Jenis 7135.00 1 77.058 kg TOTAL 77.058 kg Aksesoris 10% 7.7058 kg TOTAL BERAT 84.7638 kg TOTAL BERAT 0.847638 kN TOTAL BERAT 0.19 kN/m

3. Beban Mati Sandaran Berat Dinding Tinggi 1 meter Bj Dinding : Tinggi :

0.2 kN/m2 0.80 m

Bera Beratt dind inding ing per-m adalah

0.16 .16 KN/m KN/m

4. Beban Mati Rangka Lantai

4.50 L 60.60.6

4.00 L 60.60.6 UNP 125.65.6.8

PEMBEBANAN SUMBU -Z P BJ (m) (kN/m) 4.00 0.05

JML (bh) 9

Berat Total (kN) 1.95 kN

PEMBEBANAN SUMBU -X P BJ JML (m) (kN/m) (bh) 4.50 0.05 4 4.50 0.13 4 TOTAL PEMBEBANAN BEBAN RANGKA LANTAI

Berat Total (kN) 0.98 kN 2.61 kN 5.54 kN

0.31

C. Beban Hidup 1. Menurut Peraturan Pembebanan Berat Beban Hidup Lantai adalah :

500 kg/ kg /m2 5.00 5.00 K N/m N/m2

2. Beban Hidup Atap Menurut Peraturan Pembebanan Berat Beban Hidup Atap adalah : D. Beban Hujan Beban hidup terbagi rata hujan(Sudut 0°) = 40 kg/m2

H= Beban hidup terbagi rata hujan(Sudut 25°) =

H= H=

1.00 1.0 0 kN

0.4 kN /m2

20 kg/m2 24.0 24.00 0 kg/m kg/m

0.24 kN /m

kN /m /m2

x

1.20

m

E. Beban Angin

1. Pembebanan Angin Pada Atap Untuk Sudut 25° : K1 = 0,02 × 25 – 0,4 = K2 = -0,4 =

0.10 -0.4

H atap tekan = H atap Hisap =

0.0054 kN/m -0.0192 kN/m

F. Beban Gempa

AREA 1 AREA 2 AREA 3 AREA 4

Gambar Pembagian Area Bidang Gempa

Tabel Berat Area - 1

Berat Penutup Atap Double L 75.75.6 Double L 65.65.6 Double L 50.50.5 H 200 x 100 x 5.5 Gording C 150 H 400 x 200 x 8

b m 4.50 35.86 14.92 16.76 4.50 4.50 1.50

h m

t m

BJ n (kN/m) bh 1.00 0.19 2.00 0.07 2.00 0.06 2.00 0.04 2.00 0.21 18.00 0.08 2.00 0.66 TOTAL Wt-1

Wt-1 kN 0.85 4.91 1.76 1.49 1.92 6.08 1.98 18.99

b m 2.75 16.00 4.50 4.50 16.00 4.50

h m

t m

4.50 16.00

0.006

BJ n (kN/m) bh 2.00 0.66 1.00 0.50 3.00 0.30 2.00 0.21 1.00 78.50 1.00 0.31 TOTAL Wt-2

Wt-1 kN 3.63 7.94 4.00 1.92 33.91 22.16 73.55

h m

t m

4.50 16.00

0.006

BJ n (kN/m) bh 2.00 0.66 1.00 0.50 3.00 0.30 2.00 0.21 1.00 78.50 1.00 0.31 TOTAL Wt-3

Wt-1 kN 3.47 7.94 4.00 1.92 33.91 22.16 73.39

h m

t m

0.60

1.00

BJ n (kN/m) bh 2.00 0.66 2.00 24.00 TOTAL Wt-4

Wt-1 kN 0.50 11.52 12.02


H 400 x 200 x 8 H 350 x 175 x 7 H 250 x 125 x 6 H 200 x 100 x 5.5 Pelat Lantai Rangka Lantai Tabel Berat Area - 3

H 400 x 200 x 8 H 350 x 175 x 7 H 250 x 125 x 6 H 200 x 100 x 5.5 Pelat Lantai Rangka Lantai

b m 2.63 16.00 4.50 4.50 16.00 4.50


H 400 x 200 x 8 Kolom 40/60

b m 0.38 0.40

Wilayah gempa di Indonesia dibagi menjadi 6 zona berdasarkan percepatan puncak batuan dasarnya, pembagian zona ini dapat dilihat pada gambar dibawah ini.

Berdasarkan pembagian wilayah gempa pada gambar diatas terlihat bahwa lokasi bangunan termasuk dalam zona gempa 4. Nilai faktor respon gempa bisa ditentukan berdasarkan grafik berikut ini.

Jenis tanah lokasi adalah tanah sedang berdasarkan nilai rata-rata N-SPT pada tiap kedalaman. kedalaman. Nilai waktu waktu getar bangunan Tx=Ty= Tx=Ty= 0,06 H ¾ dengan dengan tinggi bangunan adalah 12.10 m. Tinggi Bangunan = 12.1 m Tx=Ty= 0,06 H^¾ = 0.389 detik Dari pembacaan grafik diatas, maka untuk perencanaan diambil nilai koefisien gempa dasar Ci sebesar 0,7 untuk struktur gedung. Berdasarkan “SNI-1726-2002 Tata cara perencanaan perencanaan ketahanan gempa gempa untuk bangunan gedung” gaya gaya geser dasar nominal nominal sebagai respon ragam ragam yang pertama terhadap terhadap pengaruh gempa rencana menurut persamaan persamaan :

i C Rt Wt

= = = =

Faktor keutamaan Faktor respon gempa Faktor daktilitas Berat total struktur

= = = =

1 0.7 5.6 177.94 kN

Maka : V = Ci*Wt/Rt = 22.2 kN Tabel Perhitungan Beban Gempa W WxH H Area kN (kN.m) (m) 1 18.99 171.85 9.05 2 73.55 444.98 6.05 3 73.39 260.52 3.55 4 12.02 9.61 0.80

Total

177.94

886.96

Fix kN 17.24 29.76 17.42 0.64

Fiy kN 17.24 29.76 17.42 0.64

BAB 2 GORDING, TREKSTANG DAN IKATAN ANGIN A. PERHITUNGAN GORDING 1. PERHITUNGAN GORDING Data Perencanaan : Rencana jarak antar gording Rencana jarak antar kapstang Berat penutup atap Tekanan angin ( PBI ’83 hal 24 ) Kemiringan atap

= = = = =

Profil rencana [ 150 x 65 x 20 x 3.2 ] q= 7.51 kg/m Wx = 44.3 cm3 Ix = 332 cm4

A = Wy = Iy =

2. PERHITUNGAN PEMBEBANAN GORDING

Jarak Gording (a)= Panjang 1 sisi miring kuda-kuda(b) = Jumlah gording(a/b) = Dibulatkan(c) = Jarak Aktual(b/c) = Total Gording(b/(b/c)+1) =

1.20 m 9.9304 m 8.28 bh 9 bh 1.10 m 10 bh

120 450 22 25 25

cm cm kg/m2 kg/m °

9.567 cm2 12.2 cm3 53.8 cm4

1. Akibat Beban Mati (DL) Rencana memakai gording C 150 x 65 x 20 x 3,2 Berat sendiri gording =

7.51 kg/m

2

Berat atap (1,30x 12 kg/m ) = Berat plafond + penggantung =

24.27431111 kg/m 18.00 kg/m

2

((1,30m x cos 15°) x 18 kg/m ) WD = Berat alat sambung + acsesories(10%) = Berat Total Beban Mati(q total) = Peninjauan searah sumbu X-X qx = q tot x sin α =

23.14 kg/m

Peninjauan searah sumbu Y-Y qy = q tot x cos α =

49.63 kg/m

49.78 kg/m 4.98 kg/m 54.76 kg/m

Momen akibat beban Mati

Mx = My =

1/8 . qy . L

2=

125.63 kg.m

1/8 . qx . L

2=

58.58 kg.m

2. Akibat Beban Hidup (LL) Menurut PBI ’83 hal 13, beban atap minimal 100 kg. Diasumsikan beban hidupnya Satu orang pekerja dan per alatannya sebesar Py = 150 kg x sin α = 42.26 kg Px = 150 kg x cos α = 90.63 kg Momen akibat beban Hidup Mx = 1/4 . Py . L = My = 1/4 . Px . L =

47.54 kg.m 101.96 kg.m

3. Akibat Beban Angin (W) angin tiup (w1)

= 0.02 α - 0,4

angin hisap (w2)

= - 0,4

W1 tiup = W2 hisap =

-2.5 kg/m -10 kg/m

100 kg

Q angin tiup = W1 tiup . L.gording = -2.758444444 kg/m Q angin hisap = = W2 hisap . L. gording =

11.03377778 kg/m

Momen akibat beban angin

Mx tiup = 1/8 . Q angin tiup . L2 = -6.98 kg.m 3. Kombinasi Pembebanan Kombinasi beban sementara (beban mati +beban hidup+ beban angin) Mx = Mx1 + Mpx + Mx tiup = 170.42 kg.m My = My1 + Mpy = 100.84 kg.m

3. KONTROL TEGANGAN

=

1211.28 kg/cm2

4. KONTROL TEGANGAN GESER qy = 49.63 kg/m qy dijadikan beban terpusat, maka (qy x L gording) = Q angin tiup = -2.758444444 kg/m Q angin tiup dijadikan beban terpusat, maka (Q x L gording) =

D=

(qy + py + Qangin tiup)/2=

<

1600 kg/cm2 OK

223.34 kg -12.413 kg

126.60 kg 19.85 cm2

=

1211.77 kg/cm2

<

1600 kg/cm2 OK

10.65 cm3

<

44.3 cm3 OK

5. KONTROL MOMEN TAHANAN

6. KONTROL LENDUTAN f max(ijin) = 1/250.L =

1.8 cm

Perhitungan lendutan gording :

=

0.34 cm

< f ijin = 1,8

cm

OK

7. KONTROL STABILITAS KIP Berdasarkan PPBBI ’87 Hal: 43 46.88 <75

h/tb <75 =

Maka :

L/h < 1,25 x b/ts L/h = 30

1,25 x b/ts = 20.83 Karena, L/h > 1,25 x b/ts Maka, gording tersebut di beri pengaku pada tengah jarak antara kedua kuda-kuda sehingga = L dibuat sebesar = 150 cm = 1,5m

10.00 20.83 Maka gording tidak berubah bentuk

L/h =

1,25 x b/ts = Karena,

L/h < 1,25 x b/ts

=

1081.73

=

826.88

Dari (PPBI’84 pasal 5.1 ayat 3 hal 41) Jika C1≥C2, Maka: =

856.128 kg/cm2

Dari (PPBI’84 pasal 5.1 ayat 4 hal 42)

856.128 kg/cm2

>

583.5854769 kg/cm2

Sehingga dimensi gording yang digunakan adalah C 100 x 50 x 20 x 2.3

OK

B. PERHITUNGAN TREKSTANG

=

94.34 kg

Jumlah Medan =

2 medan

R = (m x Pmax)/sin 15°= Luas dimensi trekstang yang digunakan :

446.43 kg

F= d = (4 x F/3,14)^0,5

Maka dimensi trekstang yang digunakan yaitu tulangan Ø 12 mm

0.279 cm2 d= 0.5961877 cm d= 12 mm (Tulangan Praktis Ø 12 mm)

C. PERHITUNGAN IKATAN ANGIN

Gaya P’ diambil dar i hubungan gording dan ikatan angin yang arahnya sejajar sumbu gording ( PPBBI ’84 hal. 64 ). P’ = ( 0,01 x Pkuda-kuda ) + ( 0,05 x n x q x dk x dg )

l=

19.8608 m

=

=

2.33 m

=

2.55 m

37.23 kg

P’ = ( 0,01 x Pkuda-kuda ) + ( 0,05 x n x q x dk x dg ) = =

5.34 kg 2.70 m2

2234.34 kg =

0.45

≥

0.0099335 (OK)

d= d=

0.6518878 cm 12 mm

0.334 cm2 d = (4 x F/3,14)^0,5 Maka dimensi ikatan angin yang digunakan yaitu tulangan Ø 12 mm

BAB 3 PERHITUNGAN KUDA-KUDA RANGKA BATANG A. PERHITUNGAN BATANG TARIK 1. PERHITUNGAN KAPASITAS PENANPANG BATANG -1 (L 75.75.7) Data Perencanaan : Pu = kN 71.59 fy = mPa = 24 240.00 fu = mPa = 37 370.00 Jumlah Penampang = bh 2.00 Diameter Baut = cm 1.60 Jumlah Baut = cm 3.00

Dimensi Profil : b1 = b2 = d= Ix = Iy = Wx = Wy = ix = iy = A= ɸ Leleh = ɸ Retak =

7.50 7.50 0.70 52.40 9.67 2.28 10.10 0.90 0.75

cm cm cm cm4 cm3 cm cm2

Perhitungan : Ag = 20.2 cm2 A lubang = 3.36 cm2 An = Ag - Alubang An = 16.84 cm2 An = Ae Ae ≠ An , Jika Lebih Dari Satu Baris Lubang Baut Ae = 16.84 cm2 Kondisi Leleh : ɸ Pn = fy . Ag 436.32 kN ɸ Pn = ɸ Pn ≥ Pu --->

(OK)

Kondisi Retak : ɸ Pn = fu . Ae 467.31 kN ɸ Pn = ɸ Pn ≥ Pu --->

(OK)

kN/cm2 kN/cm3

2. PERHITUNGAN SAMBUNGAN BAUT BATANG -1 (L 75.75.7) Hasil Perhitungan Gaya : N = 7158.50 kg D= 370.8 kg Data Perencanaan : Sudut Atap =

25

°

Tebal Plat Penyambung = Diameter baut (d) =

0.5 cm 1.6 cm

Rencana jumlah baut (n) =

3.00 bh

Jarak baut dengan tepi (S): ≤ 1,5d ≤

2.4

S

≤

S

≤

Dipakai S =

3d 4.8 30

mm

Jarak antar baut (U) P : 2,5d

≤

U

≤

4

≤

U

≤

Dipakai U =

7d 11.2 50 mm

Kontrol Perhitungan Baut :

σ tarik baut = σ tarik baut =

N/( n . 0.25. 22/7 . D^2) 1186.304451 kg/cm2

≤ 0.75 x 1600 =

1200

kg/cm2 OK

Akibat Gaya Lintang dan Gaya Normal Kombinasi tegangan geser dan tegangan tarik yang diijinkan adalah :

τ = 1/12 x D / (n x 1/4 x 22/7 x d^2) τ = 5.120738636 kg/cm2

≤ 0.58 x 1600 =

928

kg/cm2 OK

σ ideal = σ ideal =

((σ^2)+1.56(τ^2))^0.5 1186.321692 kg/cm2

≤ 0.75 x 1600 =

1200

kg/cm2 OK

B. PERHITUNGAN BATANG TEKAN 1. PERHITUNGAN KAPASITAS PENANPANG BATANG -1 (L 75.75.7) Data Perencanaan : Pu = kN 71.59 fy = mPa = 24 240.00 fu = mPa = 37 370.00 E = 200000.00 mPa = 20000 Jumlah Penampang = bh 2.00 Diameter Baut = cm 1.60 Jumlah Baut = bh 1.00 Batang sendi - sendi maka K: K= 1.00 L= cm 220.00 KL = 220.00

Dimensi Profil : b1 = b2 = d= w= Ix = Iy = Wx = Wy = ix = iy = A= ɸ Leleh = ɸ Retak = ɸ kritis =

7.50 7.50 0.70 7.94 52.40 9.67 2.28 10.10 0.90 0.75 0.85

cm cm cm kg/m cm4 cm3 cm cm2

Rasio Kelangsingan : KL/rx =

96.49122807 < 200

----->

OK

KL/ry =

96.49122807 < 200

----->

OK

λc = (KL/r π) x (fy/E)^0.5 λc = 1.06353997

Fcr = fy (0.658^(λc^2) Fcr = 14.94869948 kN/cm2 Kontrol Kapasitas Penampang : ɸ Pn = Fcr .A ɸ Pn = 256.6691702 kN ɸ Pn ≥ Pu --->

(OK)

kN/cm2 kN/cm2 kN/cm2

2. PERHITUNGAN SAMBUNGAN BAUT BATANG - 1 (L 75.75.7) Hasil Perhitungan Gaya : N = 7158.50 kg D= 370.80 kg Data Perencanaan : Sudut Atap =

25

°


0.5 cm 1.6 cm


3 bh


2.4

S

≤

S

≤

Dipakai S =

3d 4.8 30

mm


≤

U

≤

4

≤

U

≤

Dipakai U =

7d 11.2 75 mm



N/( n . 0.25. 22/7 . D^2) 1186.304451 kg/cm2

≤ 0.75 x 1600 =

1200

kg/cm2 OK


τ = 1/12 x D / (n x 1/4 x 22/7 x d^2) τ = 5.120738636 kg/cm2

≤ 0.58 x 1600 =

928

kg/cm2 OK


((σ^2)+1.56(τ^2))^0.5 1186.321692 kg/cm2

≤ 0.75 x 1600 =

1200

kg/cm2 OK

C. PERHITUNGAN BATANG TARIK 1. PERHITUNGAN KAPASITAS PENANPANG BATANG -2 (L 65.65.6) Data Perencanaan : Pu = kN 27.60 fy = mPa = 24 240.00 fu = mPa = 37 370.00 Jumlah Penampang = bh 2.00 Diameter Baut = cm 1.60 Jumlah Baut = cm 3.00


6.50 6.50 0.60 33.40 7.18 1.96 8.70 0.90 0.75



(OK)


(OK)

kN/cm2 kN/cm3


25

°


0.5 cm 1.2 cm


3.00 bh


1.8

S

≤

S

≤

Dipakai S =

3d 3.6 30

mm


≤

U

≤

3

≤

U

≤

Dipakai U =

7d 8.4 50 mm



N/( n . 0.25. 22/7 . D^2) 813.219697

kg/cm2

≤ 0.75 x 1600 =

1200

kg/cm2 OK


τ = 1/12 x D / (n x 1/4 x 22/7 x d^2) τ = 9.103535354 kg/cm2

≤ 0.58 x 1600 =

928

kg/cm2 OK


((σ^2)+1.56(τ^2))^0.5 813.2991821 kg/cm2

≤ 0.75 x 1600 =

1200

kg/cm2 OK

D. PERHITUNGAN BATANG TEKAN 1. PERHITUNGAN KAPASITAS PENANPANG BATANG -2 (L 65.65.6) Data Perencanaan : Pu = kN 27.60 fy = mPa = 24 240.00 fu = mPa = 37 370.00 E = 200000.00 mPa = 20000 Jumlah Penampang = bh 2.00 Diameter Baut = cm 1.60 Jumlah Baut = bh 1.00 Batang sendi - sendi maka K: K= 1.00 L= cm 373.05 KL = 373.05


6.50 6.50 0.60 6.83 33.40 7.18 1.96 8.70 0.90 0.75 0.85



190.3316327 < 200

----->

OK

KL/ry =

190.3316327 < 200

----->

OK

λc = (KL/r π) x (fy/E)^0.5 λc = 2.097862188


(OK)


2. PERHITUNGAN SAMBUNGAN BAUT BATANG - 2 ((L 65.65.6)) Hasil Perhitungan Gaya : N = 2760.30 kg D= 370.80 kg Data Perencanaan : Sudut Atap =

25

°


0.5 cm 1.2 cm


3 bh


1.8

S

≤

S

≤

Dipakai S =

3d 3.6 30

mm


≤

U

≤

3

≤

U

≤

Dipakai U =

7d 8.4 75 mm



N/( n . 0.25. 22/7 . D^2) 813.219697

kg/cm2

≤ 0.75 x 1600 =

1200

kg/cm2 OK


τ = 1/12 x D / (n x 1/4 x 22/7 x d^2) τ = 9.103535354 kg/cm2

≤ 0.58 x 1600 =

928

kg/cm2 OK


((σ^2)+1.56(τ^2))^0.5 813.2991821 kg/cm2

≤ 0.75 x 1600 =

1200

kg/cm2 OK

E. PERHITUNGAN BATANG TARIK 1. PERHITUNGAN KAPASITAS PENANPANG BATANG -3 (L 60.60.6) Data Perencanaan : Pu = kN 16.31 fy = mPa = 24 240.00 fu = mPa = 37 370.00 Jumlah Penampang = bh 2.00 Diameter Baut = cm 1.60 Jumlah Baut = cm 3.00


6.00 6.00 0.60 22.80 5.29 1.82 6.91 0.90 0.75



(OK)


(OK)

kN/cm2 kN/cm3


25

°


0.5 cm 1.2 cm


2.00 bh


1.8

S

≤

S

≤

Dipakai S =

3d 3.6 30

mm


≤

U

≤

3

≤

U

≤

Dipakai U =

7d 8.4 50 mm



N/( n . 0.25. 22/7 . D^2) 720.8585859 kg/cm2

≤ 0.75 x 1600 =

1200

kg/cm2 OK


τ = 1/12 x D / (n x 1/4 x 22/7 x d^2) τ = 13.65530303 kg/cm2

≤ 0.58 x 1600 =

928

kg/cm2 OK


((σ^2)+1.56(τ^2))^0.5 721.0603233 kg/cm2

≤ 0.75 x 1600 =

1200

kg/cm2 OK

F. PERHITUNGAN BATANG TEKAN 1. PERHITUNGAN KAPASITAS PENANPANG BATANG -3 (L 60.60.6) Data Perencanaan : Pu = kN 16.31 fy = mPa = 24 240.00 fu = mPa = 37 370.00 E = 200000.00 mPa = 20000 Jumlah Penampang = bh 2.00 Diameter Baut = cm 1.60 Jumlah Baut = bh 1.00 Batang sendi - sendi maka K: K= 1.00 L= cm 343.91 KL = 343.91


6.00 6.00 0.60 5.42 22.80 5.29 1.82 6.91 0.90 0.75 0.85



188.9615385 < 200

----->

OK

KL/ry =

188.9615385 < 200

----->

OK

λc = (KL/r π) x (fy/E)^0.5 λc = 2.082760815


(OK)


2. PERHITUNGAN SAMBUNGAN BAUT BATANG - 3 ((L 60.60.6)) Hasil Perhitungan Gaya : N = 1631.20 kg D= 370.80 kg Data Perencanaan : Sudut Atap =

25

°


0.5 cm 1.2 cm


2 bh


1.8

S

≤

S

≤

Dipakai S =

3d 3.6 30

mm


≤

U

≤

3

≤

U

≤

Dipakai U =

7d 8.4 75 mm



N/( n . 0.25. 22/7 . D^2) 720.8585859 kg/cm2

≤ 0.75 x 1600 =

1200

kg/cm2 OK


τ = 1/12 x D / (n x 1/4 x 22/7 x d^2) τ = 13.65530303 kg/cm2

≤ 0.58 x 1600 =

928

kg/cm2 OK


((σ^2)+1.56(τ^2))^0.5 721.0603233 kg/cm2

≤ 0.75 x 1600 =

1200

kg/cm2 OK

4 PERHITUNGAN BALOKBAB KOLOM ( B E AM COLUMN ) R-1 IWF 150 x 75 x 5 PADA ELEMEN STRUKTUR RAFTER DENGAN PENGAKU BADAN

[C]2011 : M. Noer Ilham

A. DATA BAHAN Tegangan leleh baja (yield stress ), Tegangan sisa (residual stress ), Modulus elastik baja (modulus of elasticity ), Angka Poisson (Poisson's ratio ),

f y = f r =

240

MPa

70

MPa

E= u =

200000

MPa

0.3

B. DATA PROFIL BAJA Profil : IWF 150 X 75 X 5

t f

h

tw

h2

ht

r

h1 b f

BEAM COLUMN (RAFTER)

ht = bf = tw = tf =

150

mm

75

mm

5

mm

7

mm

r= A = Ix = Iy = r x = r y = Sx = Sy =

8

mm

1785

2

6660000

mm mm

495000

mm

4

61.1

mm

16.6

mm

88800

mm

13200

mm

C. DATA BALOK KOLOM (RAFTER) Panjang elemen thd.sb. x, Panjang elemen thd.sb. y (jarak dukungan lateral), Jarak antara pengaku vertikal pada badan, Tebal plat pengaku vertikal pada badan, Momen maksimum akibat beban terfaktor, Momen pada 1/4 bentang, Momen di tengah bentang, Momen pada 3/4 bentang, Gaya aksial akibat beban terfaktor, Gaya geser akibat beban terfaktor, Faktor reduksi kekuatan untuk aksial tekan, Faktor reduksi kekuatan untuk lentur, Faktor reduksi kekuatan untuk geser,

Lx = Ly =

4500

mm

4500

mm

a= ts = Mu = M A = MB = MC = Nu = Vu = fn = fb = ff =

2250

mm

5

mm

1348000

Nmm

1348000

Nmm

1348000

Nmm

1348000

Nmm

817

N

1773

N

0.80 0.80 0.75

D. SECTION PROPERTIES G = E / [2*(1 + u)] = 76923 MPa 15.00 mm h1 = tf + r = 120.00 mm h2 = ht - 2 * h1 = 143.00 mm h = ht - tf = 3 3 3 J = S [ b * t /3 ] = 2 * 1/3 * bf * tf + 1/3 * (ht - 2 * tf ) * tw = 22816.7 mm 6 2 Iw = Iy * h / 4 = 2.531E+09 mm X1 = p / Sx * √ [ E * G * J * A / 2 ] = 19802.1 MPa X2 = 4 * [ Sx / (G * J) ] * Iw / Iy = 0.0000523 mm /N 3 2 Zx = tw * ht / 4 + ( bf - tw ) * ( ht - tf ) * tf = 98195.0 mm 2 2 Zy = tf * bf / 2 + ( ht - 2 * tf ) * tw / 4 = 20537.5 mm G = modulus geser, J = Konstanta puntir torsi, Iw = konstanta putir lengkung, h = tinggi bersih badan, Zx = Zy = X1 = X2 =

t f

h

tw

h2

modulus penampang plastis thd. sb. x, modulus penampang plastis thd. sb. y, koefisien momen tekuk torsi lateral, koefisien momen tekuk torsi lateral,

r

h1 b f

ht

E. PERHITUNGAN KEKUATAN a / h ≤ 3.0

Syarat yg harus dipenuhi untuk balok dengan pengaku, maka nilai :

a / h = 15.734

3.00 > tidak berlaku r umus balok dg pengaku

Ketebalan plat badan dengan pengaku vertikal tanpa pengaku memanjang harus memenuhi : h / tw 7.07 * √ ( E / f y ) 28.600

<

tebal plat badan memenuhi (OK )

204.09

1. MOMEN NOMINAL PENGARUH LOCAL BUCK LING 1.1. Pengaruh tekuk lokal (local buckling ) pada sayap

l = bf / tf =

10.714

lp = 500 / √ f y =

32.275

Kelangsingan penampang sayap, Batas kelangsingan maksimum untuk penampang compact ,

Batas kelangsingan maksimum untuk penampang non-compact ,

lr = 625 / √ f y = Mp = f y * Zx = Mr = Sx * ( f y - f r ) =

Momen plastis, Momen batas tekuk, Momen nominal penampang untuk : a. Penampang compact , →

b. Penampang non-compact , →

c. Penampang langsing , →

l

<

lp

40.344 23566800

Nmm

15096000

Nmm

l  lp Mn = Mp lp < l  lr Mn = Mp - (Mp - Mr ) * ( l - lp) / ( lr - lp) l > lr 2 Mn = Mr * ( lr / l ) dan

l

<

Berdasarkan nilai kelangsingan sayap, maka termasuk penampang Momen nominal penampang dihitung sebagai berikut : compact :

Mn = Mp = non-compact : Mn = Mp - (Mp - Mr ) * ( l - lp) / ( lr - lp) = 2 langsing : Mn = Mr * ( lr / l ) = compact Momen nominal untuk penampang : Mn =

lr compact 23566800

Nmm

-

Nmm

-

Nmm

23566800

Nmm

1.2. Pengaruh tekuk lokal (local buckling ) pada badan

l = h / tw =

28.600

lp = 1680 / √ f y =

108.444

Kelangsingan penampang badan, Batas kelangsingan maksimum untuk penampang compact ,


l

lp

<

dan

lr = 2550 / √ f y = l <

164.602

lr compact

Berdasarkan nilai kelangsingan badan, maka termasuk penampang Momen nominal penampang dihitung sebagai berikut : compact :


23566800

Nmm

-

Nmm

-

Nmm

23566800

Nmm

2. MOMEN NOMINAL BALOK PLAT BERDINDING PENUH

l = h / t w =

Kelangsingan penampang badan,

h / tw

Untuk penampang yang mempunyai ukuran :

28.600 maka momen nominal komponen struktur,

> <

28.600

lr 40.344

tidak harus dihitung dengan rumus :

Mn = Kg * S * f cr dengan, Kg = 1 - [ ar / (1200 + 300 * a r ) ] * [ h / tw - 2550 /  f cr ] a. Untuk kelangsingan : lG ≤ lp f cr = f y → b. Untuk kelangsingan : lp < lG ≤ lr →

c. Untuk kelangsingan : Untuk tekuk torsi lateral : Untuk tekuk lokal :

f cr = Cb * f y * [ 1 - ( lG - lp ) / ( 2 * ( lr - lp ) ) ] 2 → lG > lr f cr = f c * ( lr / lG ) f c = Cb * f y / 2 → ≤ f y → f c = f y / 2

≤ ≤

f y f y

Koefisien momen tekuk torsi lateral,

Cb = 12.5 * Mu / ( 2.5*Mu + 3*M A + 4*MB + 3*MC ) = diambil, Cb =

1.00

< 2.3

1.00

Perbandingan luas plat badan terhadap luas plat sayap, Momen inersia,

ar = h * tw / ( bf * tf ) = 3 I1 = Iy / 2 - 1/12 * tw * 1/3 * h2 =

1.362 247083

mm

A1 = A / 2 - 1/3 * tw * h2 =

Luas penampang,

693

mm

Jari-jari girasi daerah plat sayap ditambah sepertiga bagian plat badan yang mengalami

r 1 =  ( I1 / A1 ) =

tekan,

19

mm

4500

mm

2.1. Momen nominal berdasarkan tekuk torsi lateral L = Ly = lG = L / r 1 =

Jarak antara pengekang lateral, Angka kelangsingan,

238.232

Batas kelangsingan maksimum untuk penampang compact ,

lp = 1.76 * √ ( E / f y ) =

50.807


lr = 4.40 * √ ( E / f y ) =

127.017

Tegangan acuan untuk momen kritis tekuk torsi lateral,

f c

lG

< >

f y

lp

f c = Cb * f y / 2 = maka diambil, f c = dan lG >

120.00

MPa

120.00

MPa

lr

Tegangan kritis penampang dihitung sebagai berikut :

lG ≤ lp lp ≤ lG ≤ lr lG > lr

f cr = f y = f cr = Cb* f y*[ 1 - ( lG - lp) / ( 2*( lr - lp)) ] = 2 f cr = f c * ( lr / lG ) = Tegangan kritis penampang, f cr = maka diambil, f cr < f y f cr = Modulus penampang elastis, S = Sx =

-

MPa

-

MPa

34.11

MPa

34.11

MPa

34.11

MPa

88800

mm

3

Koefisien balok plat berdinding penuh,

Kg = 1 - [ ar / (1200 + 300 * ar ) ] * [ h / tw - 2550 /  f cr ] = Momen nominal penampang, Mn = Kg * S * f cr =

1.345 4075501

Nmm

2.2. Momen nominal berdasarkan local buck ling pada sayap Kelangsingan penampang sayap, Faktor kelangsingan plat badan,

lG = bf / ( 2 * t f ) = ke = 4 /  ( h / tw ) =

0.748

ke =

0.748

lp = 0.38 * √ ( E / f y ) =

10.97

diambil,

5.36


< 0.763


lr = 1.35 * √ ( ke * E / f y ) =

33.70

f c = f y / 2 = <

120.00

f cr = f y = f cr = Cb* f y*[ 1 - ( lG - lp) / ( 2*( lr - lp)) ] = f cr = f c * ( lr / lG ) = Tegangan kritis penampang, f cr = maka diambil, f cr < f y f cr = Modulus penampang elastis, S = Sx =

240.00

MPa

-

MPa

-

MPa

240.00

MPa

240.00

MPa

88800

mm

Tegangan acuan untuk momen kritis tekuk lokal,

lG

<

lp

dan

lG

MPa

lr





1.115 23766004

Nmm

3. MOMEN NOMINAL PENGARUH LATERA L BUCKLING Momen nominal komponen struktur dengan pengaruh tekuk lateral, untuk : a. Bentang pendek : L  Lp

Mn = Mp = f y * Zx b. Bentang sedang : Lp  L  Lr → Mn = Cb * [ Mr + ( Mp - Mr ) * ( Lr - L ) / ( Lr - Lp ) ] c. Bentang panjang : L > Lr 2 Mn = Cb * p / L*√ [ E * Iy * G * J + ( p * E / L ) * Iy * Iw ] → →

 Mp  Mp

Panjang bentang maksimum balok yang mampu menahan momen plastis, Tegangan leleh dikurangi tegangan sisa,

Lp = 1.76 * r y * √ ( E / f y ) = f L = f y - f r =

843

mm

170

MPa

Panjang bentang minimum balok yang tahanannya ditentukan oleh momen kritis tekuk torsi lateral,

2

Lr = r y * X1 / f L * √ [ 1 + √ ( 1 + X2 * f L ) ] =

3109

mm


Cb = 12.5 * Mu / ( 2.5*Mu + 3*M A + 4*MB + 3*MC ) = Momen plastis, Mp = f y * Zx = Momen batas tekuk, Mr = Sx * ( f y - f r ) =

1.00 23566800

Nmm

15096000

Nmm

Panjang bentang thd.sb. y (jarak dukungan lateral), L

>

Lp

dan

4500 mm L = Ly = L > Lr bentang ng panja panjang ng Termasuk kategori : benta

Momen nominal dihitung sebagai berikut : Nmm Mn = Mp = f y * Zx = Nmm Mn = Cb * [ Mr + ( Mp - Mr ) * ( Lr - L ) / ( L r - Lp ) ] = 2 Mn = Cb * p / L*√ [ E * Iy * G * J + ( p * E / L ) * Iy * Iw ] = 9828007 Nmm bentang benta ng panja panjang ng Momen nominal balok untuk kategori : Mn = 9828007 Nmm < Mn Mp Momen nominal yang digunakan, 98280 9828006 06.9 .9 Nmm Nmm Mn =

LING PADA BADAN 4. MOMEN NOMINAL PENGARUH LOCAL B UK LING

l = h / t w =

28.600

Ny = A * f y = Nu / ( fb * Ny ) =

428400

N

0.002

N

Kelangsingan penampang badan, Gaya aksial leleh,

a. Batas kelangsingan maksimum untuk penampang compact : Untuk nilai, →

Untuk nilai, →

Nu / ( fb * Ny ) ≤ 0.125 lp = 1680 / √ f y * [ ( 1 - 2.75 * Nu / ( fb * Ny ) ] Nu / ( fb * Ny ) > 0.125 lp = 500 / √ f y * [ ( 2.33 - Nu / ( fb * Ny ) ]  665 / √ f y

b. Batas kelangsingan maksimum untuk penampang non-compact : →

lr = 2550 / √ f y * [ ( 1 - 0.74 * N u / ( fb * Ny ) ]

Nu / ( fb * Ny ) < lp = 1680 / √ f y * [ ( 1 - 2.75 * Nu / ( fb * Ny ) ] = lp = 500 / √ f y * [ ( 2.33 - Nu / ( fb * Ny ) ] = lp = 665 / √ f y = Batas kelangsingan maksimum penampang compact , compact , lp =

Untuk nilai :

0.125 107.733 107.733

Batas kelangsingan maksimum penampang non-compact , non-compact ,

l

lr = 2550 / √ f y * [ ( 1 - 0.74 * Nu / ( fb * Ny ) ] = l lp dan < <

Berdasarkan nilai kelangsingan badan, maka termasuk penampang

164.311

lr compact

Momen nominal dihitung sebagai berikut :

Mn = Mp = non-compact : Mn = Mp - (Mp - Mr ) * ( l - lp) / ( lr - lp) = 2 langsing : Mn = Mr * ( lr / l ) = Momen nominal untuk penampang : compact Mn = compact :

23566800

Nmm

-

Nmm

-

Nmm

23566800

Nmm

Mn = Mn =

23566800

Nmm

23566800

Nmm

Mn = Mn = Mn = Mn = Mn = fb * Mn =

4075501

Nmm

23766004

Nmm

9828007

Nmm

23566800

Nmm

4075501

Nmm

3260400

Nmm

5. TAHANAN MOMEN LENTUR a. Momen nominal pengaruh local buckling : buckling : Momen nominal pengaruh local buckling pada buckling pada sayap, Momen nominal pengaruh local buckling pada buckling pada badan, b. Momen nominal balok plat berdinding penuh : Momen nominal pengaruh tekuk torsi lateral, Momen nominal pengaruh local buckling pd. buckling pd. sayap, c. Momen nominal pengaruh lateral buckling , buckling , d. Momen nominal pengaruh local buckling pada badan, Momen nominal (terkecil) yang menentukan, Tahanan momen lentur,

6. TAHANAN AKSIAL TEKAN Faktor tekuk kolom dihitung dengan rumus sebagai berikut :

lc  0.25 maka termasuk kolom pendek : pendek : w = 1 → b. Untuk nilai 0.25 < lc ≤ 1.20 maka termasuk kolom sedang : sedang : → w = 1.43 / ( 1.6 - 0.67 * lc ) c. Untuk nilai lc > 1.20 maka termasuk kolom langsing : langsing : → w = 1.25 * lc2 a. Untuk nilai

Faktor panjang tekuk efektif terhadap sumbu x, Faktor panjang tekuk efektif terhadap sumbu y,

kx = ky =

1.00

Lx = Lkx = kx * Lx =

4500

mm

4500

mm

1.00

Panjang tekuk efektif dihitung sebagai berikut : Panjang kolom terhadap sumbu x : Panjang tekuk efektif terhadap sumbu x,

Ly = Lky = ky * Ly =

Panjang kolom terhadap sumbu y : Panjang tekuk efektif terhadap sumbu y,

4500

mm

4500

mm

Parameter kelangsingan terhadap sumbu x :

lcx = 1 /p * Lkx / r x * √ ( f y / E ) =

0.8121

Parameter kelangsingan terhadap sumbu y :

lcy = 1 / p * Lky / r y * √ ( f y / E ) =

2.9891

Menentukan nilai faktor tekuk terhadap sumbu x :

lcx = w = w = 1.43 / ( 1.6 - 0.67 * lc ) = w = 1.25 * lc2 = wx =

Untuk parameter kelangsingan terhadap sumbu x, a. Kolom pendek Kolom pendek : : b. Kolom sedang : sedang : c. Kolom langsing : langsing : Faktor tekuk thd.sb. x,

0.8121 1.3543 1.3543

Menentukan nilai faktor tekuk terhadap sumbu y :

lcy = w = w = 1.43 / ( 1.6 - 0.67 * lc ) = w = 1.25 * lc2 = wy = f crx = f y / wx = f cry = f y / wy =

Untuk parameter kelangsingan terhadap sumbu y, a. Kolom pendek Kolom pendek : : b. Kolom sedang : sedang : c. Kolom langsing : langsing : Faktor tekuk thd.sb. y, Tegangan tekuk thd.sb. x, Tegangan tekuk thd.sb. y,

2.9891 11.1686 11.1686 177.212

MPa

21.489

MPa

316324

N

38357

N

38357

N

30686

N

817

N

Tahanan aksial tekan : Tahanan aksial tekan nominal thd.sb. x, Tahanan aksial tekan nominal thd.sb. y, Tahanan aksial tekan nominal terkecil, Tahanan aksial tekan,

Nnx = A * f crx = Nny = A * f cry = Nn = fn * Nn =

7. INTERAKSI AKSIAL TEKAN DAN MOMEN LENTUR Gaya aksial akibat beban terfaktor, Momen akibat beban terfaktor, Tahanan aksial tekan, Tahanan momen lentur,

Nu = Mu = fn * Nn = fb * Mn =

1348000 30686 3260400

Nmm N Nmm

Elemen yang menahan gaya aksial tekan dan momen lentur harus memenuhi persamaan interaksi aksial tekan dan momen lentur sbb :

Nu / ( fn * Nn ) > 0.20 Nu / ( fn * Nn ) + 8 / 9 * [ Mu / ( fb * Mn ) ] Nu / ( fn * Nn ) ≤ 0.20 Nu / ( 2 * fn * Nn ) + [ Mu / ( fb * Mn ) ]

Untuk nilai, →

Untuk nilai, →

Nu / ( fn * Nn ) =

0.0266

<

 1.0  1.0 0.2

Nu / ( fn * Nn ) + 8 / 9 * [ Mu / ( fb * Mn ) ] = Nu / ( 2 * fn * Nn ) + [ Mu / ( fb * Mn ) ] =

0.4268

Nila Nilaii inte intera raks ksii aks aksia iall teka tekan n dan dan momen momen lentu lenturr =

0.426 0.4268 8

0.4268

<

1.0

-

AMAN (OK)

8. TAHANAN GESER Tahanan geser nominal plat badan dengan pengaku dihitung sebagai berikut :

h / tw

Untuk nilai,

≤

1.10 *  ( kn * E / f y )

Tahanan geser plastis : plastis : →

Untuk nilai,

Vn = 0.60 * f y * Aw 1.10 *  ( kn * E / f y )

≤

h / tw

≤

1.37 *  ( kn * E / f y )

Tahanan geser elasto plastis : plastis : →

Untuk nilai,

Vn = 0.60 * f y * Aw * [ 1.10*  ( kn * E / f y ) ] / ( h / t w ) h / tw > 1.37 *  ( kn * E / f y )

Tahanan geser elastis : elastis : →

2

Vn = 0.90 * A w * kn * E / ( h / t w )

Luas penampang badan, Perbandingan tinggi terhadap tebal badan,

Aw = tw * ht = 2 kn = 5 + 5 / ( a / h ) = h / tw = 1.10 *  ( kn * E / f y ) = 1.37 *  ( kn * E / f y ) =

750 5.0202 28.600 71.148 88.612

mm

h / tw

1.10* ( kn*E / f y )

<

1.37* ( kn*E / f y ) plasti s Tahanan geser plasti

h / tw

dan

<

Tahanan geser nominal dihitung sebagai berikut : 108000 Vn = 0.60 * f y * Aw = Vn = 0.60 * f y * Aw * [ 1.10* ( kn * E / f y ) ] / ( h / t w ) = 2 Vn = 0.90 * Aw * kn * E / ( h / t w ) = plastis plas tis Tahana geser nominal untuk geser : 108000 Vn = Tahanan gaya geser, ff * Vn = 81000 Gaya geser akibat beban terfaktor, 1773 Vu = Syarat yg harus dipenuhi : ff * Vn Vu 1773 81000 AMAN (OK) < 0.0219 < 1.0 (OK) Vu / ( ff * Vn ) = 9. INTERAKSI GESER DAN LENTUR

N N N N N N

Elemen yang memikul kombinasi geser dan lentur harus dilakukan kontrol sbb. : Syarat yang harus dipenuhi untuk interakasi geser dan lentur : 1.375 Mu / ( fb * Mn ) + 0.625 * Vu / ( ff * Vn ) 0.4134 Mu / ( fb * Mn ) = 0.0219 Vu / ( ff * Vn ) = 0.4271 Mu / ( fb * Mn ) + 0.625 * Vu / ( ff * Vn ) = 0.4271

<

1.375 AMA AMAN N (OK)

10. PENGAKU VERTIKAL PADA BADAN Luas penampang plat pengaku vertikal harus memenuhi, 2

2

0.5 * D * Aw * (1 + Cv) * [ a / h - (a / h) /  (1 + (a / h) ) ] Tebal plat pengaku vertikal pada badan (stiffner (stiffner ), ), 5 ts = Tinggi plat pengaku, 136 hs = ht - 2 * tf = Luas penampang plat pengaku, 680 As = hs * ts = Untuk sepasang pengaku, 1 D= 7.6718 Cv = 1.5 * kn * E / f y * 1 / ( h /t w ) = 2 2 103 0.5 * D * Aw * (1 + Cv) * [ a / h - (a / h) /  (1 + (a / h) ) ] = As

≥

mm mm mm

mm

Syarat yang harus dipenuhi :

As

≥

2

2

0.5 * D * Aw * (1 + Cv) * [ a / h - (a / h) /  (1 + (a / h) ) ]

>

680

103

(OK)

Pengaku vertikal pada plat badan harus mempunyai momen inersia :

Is Is

≥

3

0.75 * h * t w 3 3 2 1.5 * h * tw / a ≥

untuk untuk

a/h a/h

≤ >

3

Is = 2/3 * hs * ts = a/h=

15.734

2 2 11333

mm

 2

>

Batasan momen inersia pengaku vertikal dihitung sebagai berikut : 3

0.75 * h * t w = 3 3 2 1.5 * h * tw / a = Kontrol momen inersia plat pengaku, 11333 Is =

-

mm

108

mm 4

>

Momen inersia minimum = 108 mm 108 AMAN (OK)

BAB 5 SAMBUNGAN BAUT BALOK R-1 Dipakai

IWF 150 X 75 X 5

Hasil Perhitungan Dengan Staad Pro 2004 M= 1.348 kNm = 13480 kg.cm Q= 177.3 kg N = 81.7 kg D= 177.3 kg Sudut Balok= Tebal Plat Penyambung = Diameter baut =

0

°

5 mm 12 mm

Jarak baut dengan tepi (S): ≤ ≤3d 1,5d S ≤ ≤ 18 S Dipakai S = 25 mm Jarak antar baut (U) ≤ ≤ 2,5d U ≤ ≤ 30 U Dipakai U = 50 mm Y= 15 cm Y1 = 25 ^2 = Y2 = 75 ^2 = Y3 = 125 ^2 = = ΣY =

36

7d 84

625 5625 15625 21875 218.75

mm2 mm2 mm2 mm2 cm2

462.1714 kg

= 408.8565

<

0,75 x 1600 =

1200 OK

kg/cm2


13.07059 kg/cm2

<

= 409.1823 kg/cm2

928 kg/cm2

<

OK

1200 kg/cm2

OK

6 PERHITUNGAN BALOKBAB KOLOM ( B E AM COLUMN ) B-1 IWF 400 x 200 x 8 PADA ELEMEN STRUKTUR RAFTER DENGAN PENGAKU BADAN



f y = f r =

240

MPa

70

MPa

E= u =

200000

MPa

0.3


ht = bf = tw = tf =

t f

h

tw

h2

ht

r

h1 b f


400

mm

200

mm

8

mm

13

mm

13 mm r= 2 mm 8412 A = Ix = 237000000 mm 4 Iy = 17400000 mm 147 mm r x = 45.4 mm r y = Sx = 1190000 mm mm 174000 Sy =


Lx = Ly =

8000

mm

4000

mm


2000

mm

8

mm

177964000 Nmm 177964000 Nmm 177964000 Nmm 177964000 Nmm 14748

N

90442

N

0.80 0.80 0.75


t f

h

tw

h2


r

h1 b f

ht



a/h=

5.168

3.00 > tidakk berlaku tida berlaku r umus balok balok dg pengaku


<

tebal plat bada badan n memenuhi (OK ( OK )

204.09

LING 1. MOMEN NOMINAL PENGARUH LOCAL BUCK LING 1.1. Pengaruh tekuk lokal (local local buckling ) pada sayap

l = bf / tf =

15.385

lp = 500 / √ f y =

32.275

Kelangsingan penampang sayap, Batas kelangsingan maksimum untuk penampang compact , compact ,

Batas kelangsingan maksimum untuk penampang non-compact , non-compact ,

lr = 625 / √ f y =

30862848 8480 Nmm Mp = f y * Zx = 308 20230000 0000 Nmm Mr = Sx * ( f y - f r ) = 202




l

40.344

<

lp


l


<

lr compact

30862848 8480 Mn = Mp = 308 non-compact : Mn = Mp - (Mp - Mr ) * ( l - lp) / ( lr - lp) = 2 langsing : Mn = Mr * ( lr / l ) = compact Momen nominal untuk penampang : 30862848 8480 Mn = 308

Nmm Nmm Nmm Nmm

local buckling ) pada badan 1.2. Pengaruh tekuk lokal (local

l = h / tw =

48.375

lp = 1680 / √ f y =

108.444

Kelangsingan penampang badan, Batas kelangsingan maksimum untuk penampang compact , compact ,


l

lp

<

dan

lr = 2550 / √ f y = l <

164.602

lr compact


30862848 8480 Mn = Mp = 308 non-compact : Mn = Mp - (Mp - Mr ) * ( l - lp) / ( lr - lp) = 2 langsing : Mn = Mr * ( lr / l ) = compact Momen nominal untuk penampang : 30862848 8480 Mn = 308

Nmm Nmm Nmm Nmm


l = h / t w =


h / tw



harus

> >

48.375

lr 40.344

dihitung dengan rumus :

Mn = Kg * S * f cr dengan, Kg = 1 - [ ar / (1200 + 300 * a r ) ] * [ h / t w - 2550 /  f cr ] a. Untuk kelangsingan : lG ≤ lp f cr = f y → b. Untuk kelangsingan : lp < lG ≤ lr →



≤ ≤

f y f y


Cb = 12.5 * M u / ( 2.5*Mu + 3*M A + 4*MB + 3*MC ) = diambil, Cb =

1.00

< 2.3

1.00



1.191 8695051

mm

A1 = A / 2 - 1/3 * t w * h2 =

Luas penampang,

3278

mm


r 1 =  ( I1 / A1 ) =

tekan,

52

mm

4000

mm



77.666

Batas kelangsingan maksimum untuk penampang compact , compact ,

lp = 1.76 * √ ( E / f y ) =

50.807


lr = 4.40 * √ ( E / f y ) =

127.017


f c

lG

< >

f y

lp

f c = Cb * f y / 2 = maka diambil, f c = dan lG <

120.00

MPa

120.00

MPa

lr




-

MPa

197.71

MPa

-

MPa

197.71

MPa

197.71

MPa

1190000

mm

3

Koefisien balok plat berdinding penuh, 1.102 Kg = 1 - [ ar / (1200 + 300 * a r ) ] * [ h / t w - 2550 /  f cr ] = Momen nominal penampang, 25919690 6907 Nmm Mn = Kg * S * f cr = 259

local buck ling pada sayap 2.2. Momen nominal berdasarkan local Kelangsingan penampang sayap, Faktor kelangsingan plat badan,

lG = bf / ( 2 * t f ) = ke = 4 /  ( h / tw ) =

0.575

ke =

0.575

lp = 0.38 * √ ( E / f y ) =

10.97

diambil,

7.69


< 0.763


lr = 1.35 * √ ( ke * E / f y ) =

29.55

f c = f y / 2 = <

120.00


240.00

MPa

-

MPa

-

MPa

240.00

MPa

240.00

MPa

1190000

mm


lG

<

lp

dan

lG

MPa

lr



Koefisien balok plat berdinding penuh, 1.089 Kg = 1 - [ ar / (1200 + 300 * a r ) ] * [ h / t w - 2550 /  f cr ] = Momen nominal penampang, 31098277 2774 Nmm Mn = Kg * S * f cr = 310

BUCKLING 3. MOMEN NOMINAL PENGARUH LATERA L BUCKLING Momen nominal komponen struktur dengan pengaruh tekuk lateral, untuk : a. Bentang pendek : pendek : L  Lp

Mn = Mp = f y * Zx b. Bentang sedang : sedang : Lp  L  Lr → Mn = Cb * [ Mr + ( Mp - Mr ) * ( Lr - L ) / ( L r - Lp ) ] c. Bentang panjang : panjang : L > Lr 2 Mn = Cb * p / L*√ [ E * Iy * G * J + ( p * E / L ) * Iy * Iw ] → →

 Mp  Mp


Lp = 1.76 * r y * √ ( E / f y ) = f L = f y - f r =

2307

mm

170

MPa


2

Lr = r y * X1 / f L * √ [ 1 + √ ( 1 + X2 * f L ) ] =

6794

mm

Koefisien momen tekuk torsi lateral, 1.00 Cb = 12.5 * M u / ( 2.5*Mu + 3*M A + 4*MB + 3*MC ) = Momen plastis, 30862848 8480 Nmm Mp = f y * Zx = 308 Momen batas tekuk, 20230000 0000 Nmm Mr = Sx * ( f y - f r ) = 202


>

Lp

dan

4000 mm L = Ly = L < Lr benta ang s eda edang ng Termasuk kategori : bent

Momen nominal dihitung sebagai berikut : Nmm Mn = Mp = f y * Zx = 26850765 7653 Nmm Mn = Cb * [ Mr + ( Mp - Mr ) * ( Lr - L ) / ( L r - Lp ) ] = 268 2 Nmm Mn = Cb * p / L*√ [ E * Iy * G * J + ( p * E / L ) * Iy * Iw ] = bentan bent angg s eda edang ng Momen nominal balok untuk kategori : 26850765 7653 Nmm Mn = 268 < Mn Mp Momen nominal yang digunakan, 2685076 07653 53 Nmm Nmm Mn = 2685


l = h / t w =


Ny = A * f y = Nu / ( fb * Ny ) =

48.375 2018880

N

0.009

N


Untuk nilai, →



lr = 2550 / √ f y * [ ( 1 - 0.74 * N u / ( fb * Ny ) ]


Untuk nilai :

0.125 105.720 105.720


l



163.490

lr compact


Mn = Mp = 308628480 Nmm non-compact : Nmm Mn = Mp - (Mp - Mr ) * ( l - lp) / ( lr - lp) = 2 langsing : Nmm Mn = Mr * ( lr / l ) = Momen nominal untuk penampang : compact Mn = 308628480 Nmm compact :

5. TAHANAN MOMEN LENTUR a. Momen nominal pengaruh local buckling :

Mn = 308628480 Nmm Mn = 308628480 Nmm

Momen nominal pengaruh local buckling pada sayap, Momen nominal pengaruh local buckling pada badan, b. Momen nominal balok plat berdinding penuh :


Momen nominal pengaruh tekuk torsi lateral, Momen nominal pengaruh local buckling pd. sayap, c. Momen nominal pengaruh lateral buckling , d. Momen nominal pengaruh local buckling pada badan, Momen nominal (terkecil) yang menentukan, Tahanan momen lentur,

259196907 Nmm 310982774 Nmm 268507653 Nmm 308628480 Nmm 259196907 Nmm 207357525 Nmm


lc  0.25 maka termasuk kolom pendek : w = 1 → b. Untuk nilai 0.25 < lc ≤ 1.20 maka termasuk kolom sedang : → w = 1.43 / ( 1.6 - 0.67 * lc ) c. Untuk nilai lc > 1.20 maka termasuk kolom langsing : → w = 1.25 * lc2 a. Untuk nilai


kx = ky =

1.00


8000

mm

8000

mm

1.00




4000

mm

4000

mm


lcx = 1 /p * Lkx / r x * √ ( f y / E ) =

0.6001


lcy = 1 / p * Lky / r y * √ ( f y / E ) =

0.9715


lcx = w = w = 1.43 / ( 1.6 - 0.67 * lc ) = w = 1.25 * lc2 = wx =

Untuk parameter kelangsingan terhadap sumbu x, a. Kolom pendek : b. Kolom sedang : c. Kolom langsing : Faktor tekuk thd.sb. x,

0.6001 1.1937 1.1937



Untuk parameter kelangsingan terhadap sumbu y, a. Kolom pendek : b. Kolom sedang : c. Kolom langsing : Faktor tekuk thd.sb. y, Tegangan tekuk thd.sb. x, Tegangan tekuk thd.sb. y,

0.9715 1.5067 1.5067 201.053

MPa

159.288

MPa

1691260

N

1339932

N

1339932

N

1071946

N




14748 N Nu = Mu = 177964000 Nmm fn * Nn = 1071946 N fb * Mn = 207357525 Nmm



Untuk nilai, →

Untuk nilai, →

Nu / ( fn * Nn ) =

0.0138

<

 1.0  1.0 0.2


0.8651

Nilai interaksi aksial tekan dan momen lentur =

0.8651

0.8651

<

1.0

-

AMAN (OK)


h / tw

Untuk nilai,

≤

1.10 *  ( kn * E / f y )

Tahanan geser plastis : →

Untuk nilai,

Vn = 0.60 * f y * Aw 1.10 *  ( kn * E / f y )

≤

h / tw

≤

1.37 *  ( kn * E / f y )

Tahanan geser elasto plastis : →

Untuk nilai,


Tahanan geser elastis : →

2

Vn = 0.90 * A w * kn * E / ( h / tw )



3200 5.1872 48.375 72.322 90.073

mm

h / tw

1.10* ( kn*E / f y )

<

1.37* ( kn*E / f y ) Tahanan geser plasti s

h / tw

dan

<

Tahanan geser nominal dihitung sebagai berikut : 460800 Vn = 0.60 * f y * Aw = Vn = 0.60 * f y * Aw * [ 1.10* ( kn * E / f y ) ] / ( h / t w ) = 2 Vn = 0.90 * Aw * kn * E / ( h / t w ) = plastis Tahana geser nominal untuk geser : 460800 Vn = Tahanan gaya geser, ff * Vn = 345600 Gaya geser akibat beban terfaktor, 90442 Vu = Syarat yg harus dipenuhi : ff * Vn Vu 90442 345600 AMAN (OK) < 0.2617 < 1.0 (OK) Vu / ( ff * Vn ) = 9. INTERAKSI GESER DAN LENTUR

N N N N N N


<

1.375 AMAN (OK)


2

0.5 * D * Aw * (1 + Cv) * [ a / h - (a / h) /  (1 + (a / h) ) ] Tebal plat pengaku vertikal pada badan (stiffner ), 8 ts = Tinggi plat pengaku, 374 hs = ht - 2 * tf = Luas penampang plat pengaku, 2992 As = hs * ts = Untuk sepasang pengaku, 1 D= 2.7708 Cv = 1.5 * kn * E / f y * 1 / ( h /tw ) = 2 2 568 0.5 * D * Aw * (1 + Cv) * [ a / h - (a / h) /  (1 + (a / h) ) ] = As

≥

mm mm mm

mm


As

≥

2

2

0.5 * D * Aw * (1 + Cv) * [ a / h - (a / h) /  (1 + (a / h) ) ]

>

2992

568

(OK)


Is Is

≥

3

0.75 * h * t w 3 3 2 1.5 * h * tw / a ≥

untuk untuk

a/h a/h

≤ >

3

Is = 2/3 * hs * ts = a/h=

5.168

2 2 127659

mm

 2

>


0.75 * h * t w = 3 3 2 1.5 * h * tw / a = Kontrol momen inersia plat pengaku, Is = 127659

-

mm

11128

mm 4

>


BAB 7 SAMBUNGAN BAUT BALOK B-1 Dipakai

IWF 400 X 200 X 8


0

°

8 mm 19 mm

Jarak baut dengan tepi (S): ≤ ≤3d 1,5d S ≤ ≤ 28.5 S Dipakai S = 30 mm

57

Jarak antar baut (U) ≤ ≤ 2,5d U ≤ ≤ 47.5 U Dipakai U = 105 mm Y= 90 cm Y1 = 30 ^2 = Y2 = 135 ^2 = Y3 = 240 ^2 = Y4 = 345 ^2 = Y5 = 450 ^2 = Y6 = 555 ^2 = Y7 = 660 ^2 = Y8 = 765 ^2 = Y9 = 870 ^2 = = ΣY =

7d 133

900 18225 57600 119025 202500 308025 435600 585225 756900 2484000 24840

mm2 mm2 mm2 mm2 mm2 mm2 mm2 mm2 mm2 mm2 cm2

3223.986 kg

=

1137.67

<

0,75 x 1600 =

1200 OK

kg/cm2


265.9574 kg/cm2

<

= 1185.174 kg/cm2

928 kg/cm2

<

OK

1200 kg/cm2

OK

8 PERHITUNGAN BALOKBAB KOLOM ( B E AM COLUMN ) B-2 IWF 250 x 125 x 6 PADA ELEMEN STRUKTUR RAFTER DENGAN PENGAKU BADAN



f y = f r =

240

MPa

70

MPa

E= u =

200000

MPa

0.3


t f

h

tw

h2

ht

r

h1 b f


ht = bf = tw = tf =

250

mm

125

mm

6

mm

9

mm

r= A = Ix = Iy = r x = r y = Sx = Sy =

12

mm

3766

2

40500000

mm mm

2940000

mm

4

104

mm

27.9

mm

324000

mm

47000

mm


Lx = Ly =

4500

mm

4500

mm


2250

mm

6

mm

17911000

Nmm

17911000

Nmm

17911000

Nmm

17911000

Nmm

27586

N

12028

N

0.80 0.80 0.75


t f

h

tw

h2


r

h1 b f

ht



a/h=

9.336



<


204.09


l = bf / tf =

13.889

lp = 500 / √ f y =

32.275







l

<

lp

40.344 84446640

Nmm

55080000

Nmm


l

<



lr compact 84446640

Nmm

-

Nmm

-

Nmm

84446640

Nmm


l = h / tw =

40.167

lp = 1680 / √ f y =

108.444



l

lp

<

dan

lr = 2550 / √ f y = l <

164.602

lr compact



84446640

Nmm

-

Nmm

-

Nmm

84446640

Nmm


l = h / t w =


h / tw



> <

40.167

lr 40.344





≤ ≤

f y f y



1.00

< 2.3

1.00



1.285 1468752

mm

A1 = A / 2 - 1/3 * tw * h2 =

Luas penampang,

1467

mm


r 1 =  ( I1 / A1 ) =

tekan,

32

mm

4500

mm



142.218


lp = 1.76 * √ ( E / f y ) =

50.807


lr = 4.40 * √ ( E / f y ) =

127.017


f c

lG

< >

f y

lp


120.00

MPa

120.00

MPa

lr




-

MPa

-

MPa

95.72

MPa

95.72

MPa

95.72

MPa

324000

mm

3



1.179 36555697

Nmm


lG = bf / ( 2 * t f ) = ke = 4 /  ( h / tw ) =

0.631

ke =

0.631

lp = 0.38 * √ ( E / f y ) =

10.97

diambil,

6.94


< 0.763


lr = 1.35 * √ ( ke * E / f y ) =

30.96

f c = f y / 2 = <

120.00


240.00

MPa

-

MPa

-

MPa

240.00

MPa

240.00

MPa

324000

mm


lG

<

lp

dan

lG

MPa

lr





1.101 85603707

Nmm



 Mp  Mp


Lp = 1.76 * r y * √ ( E / f y ) = f L = f y - f r =

1418

mm

170

MPa


2

Lr = r y * X1 / f L * √ [ 1 + √ ( 1 + X2 * f L ) ] =

4422

mm



1.00 84446640

Nmm

55080000

Nmm


>

Lp

dan

4500 mm L = Ly = L > Lr Termasuk kategori : bentang panjang

Momen nominal dihitung sebagai berikut : Nmm Mn = Mp = f y * Zx = Nmm Mn = Cb * [ Mr + ( Mp - Mr ) * ( Lr - L ) / ( Lr - Lp ) ] = 2 Mn = Cb * p / L*√ [ E * Iy * G * J + ( p * E / L ) * Iy * Iw ] = 53851854 Nmm bentang panjang Momen nominal balok untuk kategori : Mn = 53851854 Nmm < Mn Mp Momen nominal yang digunakan, Mn = 53851854.5 Nmm

4. MOMEN NOMINAL PENGARUH LOCAL B UK LING PADA BADAN

l = h / t w =

40.167

Ny = A * f y = Nu / ( fb * Ny ) =

903840

N

0.038

N



Untuk nilai, →



lr = 2550 / √ f y * [ ( 1 - 0.74 * Nu / ( fb * Ny ) ]

Nu / ( fb * Ny ) < lp = 1680 / √ f y * [ ( 1 - 2.75 * Nu / ( fb * Ny ) ] = lp = 500 / √ f y * [ ( 2.33 - Nu / ( fb * Ny ) ] = lp = 665 / √ f y = Batas kelangsingan maksimum penampang compact , lp = Untuk nilai :

0.125 97.066 97.066

Batas kelangsingan maksimum penampang non-compact ,

l



159.955

lr compact



84446640

Nmm

-

Nmm

-

Nmm

84446640

Nmm

Mn = Mn =

84446640

Nmm

84446640

Nmm


36555697

Nmm

85603707

Nmm

53851854

Nmm

84446640

Nmm

36555697

Nmm

29244558

Nmm

5. TAHANAN MOMEN LENTUR a. Momen nominal pengaruh local buckling : Momen nominal pengaruh local buckling pada sayap, Momen nominal pengaruh local buckling pada badan, b. Momen nominal balok plat berdinding penuh : Momen nominal pengaruh tekuk torsi lateral, Momen nominal pengaruh local buckling pd. sayap, c. Momen nominal pengaruh lateral buckling , d. Momen nominal pengaruh local buckling pada badan, Momen nominal (terkecil) yang menentukan, Tahanan momen lentur,




kx = ky =

1.00


4500

mm

4500

mm

1.00




4500

mm

4500

mm


lcx = 1 /p * Lkx / r x * √ ( f y / E ) =

0.4771


lcy = 1 / p * Lky / r y * √ ( f y / E ) =

1.7785


lcx = w = w = 1.43 / ( 1.6 - 0.67 * lc ) = w = 1.25 * lc2 = wx =


0.4771 1.1169 1.1169




1.7785 3.9537 3.9537 214.881

MPa

60.702

MPa

809244

N

228604

N

228604

N

182883

N

27586

N





17911000 182883 29244558

Nmm N Nmm



Untuk nilai, →

Untuk nilai, →

Nu / ( fn * Nn ) =

0.1508

<

 1.0  1.0 0.2


0.6879


0.6879

0.6879

<

1.0

-

AMAN (OK)


h / tw

Untuk nilai,

≤

1.10 *  ( kn * E / f y )


Untuk nilai,

Vn = 0.60 * f y * Aw 1.10 *  ( kn * E / f y )

≤

h / tw

≤

1.37 *  ( kn * E / f y )


Untuk nilai,



2

Vn = 0.90 * A w * kn * E / ( h / tw )



1500 5.0574 40.167 71.411 88.939

mm

h / tw

1.10* ( kn*E / f y )

<


h / tw

dan

<


N N N N N N


<

1.375 AMAN (OK)


2


≥

mm mm mm

mm


As

≥

2

2

0.5 * D * Aw * (1 + Cv) * [ a / h - (a / h) /  (1 + (a / h) ) ]

>

1392

196

(OK)


Is Is

≥

3

0.75 * h * t w 3 3 2 1.5 * h * tw / a ≥

untuk untuk

a/h a/h

≤ >

3

Is = 2/3 * hs * ts = a/h=

9.336

2 2 33408

mm

 2

>



-

mm

896

mm 4

>



IWF 250 X 125 X 6


0

°

8 mm 16 mm

Jarak baut dengan tepi (S): ≤ ≤3d 1,5d S ≤ ≤ 24 S Dipakai S = 30 mm Jarak antar baut (U) ≤ ≤ 2,5d U ≤ ≤ 40 U Dipakai U = 80 mm Y= 30 cm Y1 = 30 ^2 = Y2 = 110 ^2 = Y3 = 190 ^2 = Y4 = 270 ^2 = = ΣY =

48

7d 112

900 12100 36100 72900 122000 1220

mm2 mm2 mm2 mm2 mm2 cm2

2202.172 kg

= 1095.826

<

0,75 x 1600 =

1200 OK

kg/cm2


49.87726 kg/cm2

<

= 1097.595 kg/cm2

928 kg/cm2

<

OK

1200 kg/cm2

OK

BAB 10 PERHITUNGAN BALOK KOLOM ( B E AM COLUMN ) B-3 IWF 200 x 100 x 5.5 PADA ELEMEN STRUKTUR RAFTER DENGAN PENGAKU BADAN



f y = f r =

240

MPa

70

MPa

E= u =

200000

MPa

0.3

B. DATA PROFIL BAJA Profil : IWF 200 X 100 X 5.5

t f

h

tw

h2

ht

r

h1 b f


ht = bf = tw = tf =

200

mm

100

mm

5.5

mm

8

mm

r= A = Ix = Iy = r x = r y = Sx = Sy =

11

mm

2316

2

18400000

mm mm

1340000

mm

4

82.4

mm

22.2

mm

184000

mm

26800

mm


Lx = Ly =

4500

mm

4500

mm


2250

mm

5.5

mm

1739000

Nmm

1739000

Nmm

1739000

Nmm

1739000

Nmm

1508

N

2598

N

0.80 0.80 0.75


t f

h

tw

h2


r

h1 b f

ht



a / h = 11.719



<


204.09


l = bf / tf =

12.500

lp = 500 / √ f y =

32.275







l

<

lp

40.344 48036480

Nmm

31280000

Nmm


l

<



lr compact 48036480

Nmm

-

Nmm

-

Nmm

48036480

Nmm


l = h / tw =

34.909

lp = 1680 / √ f y =

108.444



l

lp

<

dan

lr = 2550 / √ f y = l <

164.602

lr compact



48036480

Nmm

-

Nmm

-

Nmm

48036480

Nmm


l = h / t w =


h / tw



> <

34.909

lr 40.344





≤ ≤

f y f y



1.00

< 2.3

1.00



1.320 669251

mm

A1 = A / 2 - 1/3 * t w * h2 =

Luas penampang,

861

mm


r 1 =  ( I1 / A1 ) =

tekan,

28

mm

4500

mm



161.406


lp = 1.76 * √ ( E / f y ) =

50.807


lr = 4.40 * √ ( E / f y ) =

127.017


f c

lG

< >

f y

lp


120.00

MPa

120.00

MPa

lr




-

MPa

-

MPa

74.31

MPa

74.31

MPa

74.31

MPa

184000

mm

3


Kg = 1 - [ ar / (1200 + 300 * a r ) ] * [ h / t w - 2550 /  f cr ] = Momen nominal penampang, Mn = Kg * S * f cr =

1.216 16624133

Nmm

local buck ling pada sayap 2.2. Momen nominal berdasarkan local Kelangsingan penampang sayap, Faktor kelangsingan plat badan,

lG = bf / ( 2 * t f ) = ke = 4 /  ( h / tw ) =

0.677

ke =

0.677

lp = 0.38 * √ ( E / f y ) =

10.97

diambil,

6.25


< 0.763


lr = 1.35 * √ ( ke * E / f y ) =

32.07

f c = f y / 2 = <

120.00


240.00

MPa

-

MPa

-

MPa

240.00

MPa

240.00

MPa

184000

mm


lG

<

lp

dan

lG

MPa

lr




Kg = 1 - [ ar / (1200 + 300 * a r ) ] * [ h / t w - 2550 /  f cr ] = Momen nominal penampang, Mn = Kg * S * f cr =

1.107 48896807

Nmm

BUCKLING 3. MOMEN NOMINAL PENGARUH LATERA L BUCKLING Momen nominal komponen struktur dengan pengaruh tekuk lateral, untuk : a. Bentang pendek : pendek : L  Lp

Mn = Mp = f y * Zx b. Bentang sedang : sedang : Lp  L  Lr → Mn = Cb * [ Mr + ( Mp - Mr ) * ( Lr - L ) / ( L r - Lp ) ] c. Bentang panjang : panjang : L > Lr 2 Mn = Cb * p / L*√ [ E * Iy * G * J + ( p * E / L ) * Iy * Iw ] → →

 Mp  Mp


Lp = 1.76 * r y * √ ( E / f y ) = f L = f y - f r =

1128

mm

170

MPa


2

Lr = r y * X1 / f L * √ [ 1 + √ ( 1 + X2 * f L ) ] =

3447

mm


Cb = 12.5 * M u / ( 2.5*Mu + 3*M A + 4*MB + 3*MC ) = Momen plastis, Mp = f y * Zx = Momen batas tekuk, Mr = Sx * ( f y - f r ) =

1.00 48036480

Nmm

31280000

Nmm


>

Lp

dan

4500 mm L = Ly = L > Lr bentang ng panja panjang ng Termasuk kategori : benta

Momen nominal dihitung sebagai berikut : Nmm Mn = Mp = f y * Zx = Nmm Mn = Cb * [ Mr + ( Mp - Mr ) * ( Lr - L ) / ( L r - Lp ) ] = 2 Mn = Cb * p / L*√ [ E * Iy * G * J + ( p * E / L ) * Iy * Iw ] = 24550570 Nmm bentang benta ng panja panjang ng Momen nominal balok untuk kategori : Mn = 24550570 Nmm < Mn Mp Momen nominal yang digunakan, 24550570 70.3 .3 Nmm Nmm Mn = 245505


l = h / t w =

34.909

Ny = A * f y = Nu / ( fb * Ny ) =

555840

N

0.003

N



Untuk nilai, →



lr = 2550 / √ f y * [ ( 1 - 0.74 * N u / ( fb * Ny ) ]


Untuk nilai :

0.125 107.432 107.432


l



164.189

lr compact



48036480

Nmm

-

Nmm

-

Nmm

48036480

Nmm

Mn = Mn =

48036480

Nmm

48036480

Nmm


16624133

Nmm

48896807

Nmm

24550570

Nmm

48036480

Nmm

16624133

Nmm

13299307

Nmm

5. TAHANAN MOMEN LENTUR a. Momen nominal pengaruh local buckling : buckling : Momen nominal pengaruh local buckling pada buckling pada sayap, Momen nominal pengaruh local buckling pada buckling pada badan, b. Momen nominal balok plat berdinding penuh : Momen nominal pengaruh tekuk torsi lateral, Momen nominal pengaruh local buckling pd. buckling pd. sayap, c. Momen nominal pengaruh lateral buckling , buckling , d. Momen nominal pengaruh local buckling pada badan, Momen nominal (terkecil) yang menentukan, Tahanan momen lentur,


lc  0.25 maka termasuk kolom pendek : pendek : w = 1 → b. Untuk nilai 0.25 < lc ≤ 1.20 maka termasuk kolom sedang : sedang : → w = 1.43 / ( 1.6 - 0.67 * lc ) c. Untuk nilai lc > 1.20 maka termasuk kolom langsing : langsing : → w = 1.25 * lc2 a. Untuk nilai


kx = ky =

1.00


4500

mm

4500

mm

1.00




4500

mm

4500

mm


lcx = 1 /p * Lkx / r x * √ ( f y / E ) =

0.6022


lcy = 1 / p * Lky / r y * √ ( f y / E ) =

2.2351


lcx = w = w = 1.43 / ( 1.6 - 0.67 * lc ) = w = 1.25 * lc2 = wx =

Untuk parameter kelangsingan terhadap sumbu x, a. Kolom pendek Kolom pendek : : b. Kolom sedang : sedang : c. Kolom langsing : langsing : Faktor tekuk thd.sb. x,

0.6022 1.1951 1.1951



Untuk parameter kelangsingan terhadap sumbu y, a. Kolom pendek Kolom pendek : : b. Kolom sedang : sedang : c. Kolom langsing : langsing : Faktor tekuk thd.sb. y, Tegangan tekuk thd.sb. x, Tegangan tekuk thd.sb. y,

2.2351 6.2447 6.2447 200.818

MPa

38.433

MPa

465094

N

89010

N

89010

N

71208

N

1508

N





1739000 71208 13299307

Nmm N Nmm



Untuk nilai, →

Untuk nilai, →

Nu / ( fn * Nn ) =

0.0212

<

 1.0  1.0 0.2


0.1413


0.1413

0.1413

<

1.0

-

AMAN (OK)


h / tw

Untuk nilai,

≤

1.10 *  ( kn * E / f y )


Untuk nilai,

Vn = 0.60 * f y * Aw 1.10 *  ( kn * E / f y )

≤

h / tw

≤

1.37 *  ( kn * E / f y )


Untuk nilai,



2

Vn = 0.90 * A w * kn * E / ( h / tw )



1100 5.0364 34.909 71.263 88.755

mm

h / tw

1.10* ( kn*E / f y )

<


h / tw

dan

<


N N N N N N


<

1.375 AMAN (OK)


2

0.5 * D * Aw * (1 + Cv) * [ a / h - (a / h) /  (1 + (a / h) ) ] Tebal plat pengaku vertikal pada badan (stiffner ), 5.5 ts = Tinggi plat pengaku, 184 hs = ht - 2 * tf = Luas penampang plat pengaku, 1012 As = hs * ts = Untuk sepasang pengaku, 1 D= 5.1660 Cv = 1.5 * kn * E / f y * 1 / ( h /tw ) = 2 2 144 0.5 * D * Aw * (1 + Cv) * [ a / h - (a / h) /  (1 + (a / h) ) ] = As

≥

mm mm mm

mm


As

≥

2

2

0.5 * D * Aw * (1 + Cv) * [ a / h - (a / h) /  (1 + (a / h) ) ]

>

1012

144

(OK)


Is Is

≥

3

0.75 * h * t w 3 3 2 1.5 * h * tw / a ≥

untuk untuk

a/h a/h

≤ >

3

Is = 2/3 * hs * ts = a/h=

11.719

2 2 20409

mm

 2

>



-

mm

349

mm 4

>



IWF 200 X 100 X 5.5


0

°

8 mm 12 mm


36

7d 84

625 10000 30625 41250 412.5

mm2 mm2 mm2 mm2 cm2

421.5758 kg

= 372.9439

<

0,75 x 1600 =

1200 OK

kg/cm2


11.11701 kg/cm2

<

= 373.2023 kg/cm2

928 kg/cm2

<

OK

1200 kg/cm2

OK

BAB 12 PERHITUNGAN BALOK KOLOM ( B E AM COLUMN ) BALOK RAMP B-4 IWF 300 x 150 x 6.5 PADA ELEMEN STRUKTUR RAFTER DENGAN PENGAKU BADAN



f y = f r =

240

MPa

70

MPa

E= u =

200000

MPa

0.3


t f

h

tw

h2

ht

r

h1 b f


ht = bf = tw = tf =

300

mm

150

mm

6.5

mm

9

mm

r= A = Ix = Iy = r x = r y = Sx = Sy =

13

mm

4678

2

72100000

mm mm

5080000

mm

4

124

mm

32.9

mm

481000

mm

67700

mm


Lx = Ly =

4500

mm

4500

mm


2250

mm

6.5

mm

30438000

Nmm

30438000

Nmm

30438000

Nmm

30438000

Nmm

25169

N

27621

N

0.80 0.80 0.75


t f

h

tw

h2


r

h1 b f

ht



a/h=

7.732



<


204.09


l = bf / tf =

16.667

lp = 500 / √ f y =

32.275



lr = 625 / √ f y =

Mp = f y * Zx = 125298360 Nmm Mr = Sx * ( f y - f r ) = 81770000 Nmm




l

40.344

<

lp


l


<

lr compact

Mn = Mp = 125298360 Nmm non-compact : Nmm Mn = Mp - (Mp - Mr ) * ( l - lp) / ( lr - lp) = 2 langsing : Nmm Mn = Mr * ( lr / l ) = compact Momen nominal untuk penampang : Mn = 125298360 Nmm


l = h / tw =

44.769

lp = 1680 / √ f y =

108.444



l

lp

<

dan

lr = 2550 / √ f y = l <

164.602

lr compact


Mn = Mp = 125298360 Nmm non-compact : Nmm Mn = Mp - (Mp - Mr ) * ( l - lp) / ( lr - lp) = 2 langsing : Nmm Mn = Mr * ( lr / l ) = compact Momen nominal untuk penampang : Mn = 125298360 Nmm 2. MOMEN NOMINAL BALOK PLAT BERDINDING PENUH

l = h / t w =


h / tw



harus

> >

44.769

lr 40.344





≤ ≤

f y f y



1.00

< 2.3

1.00



1.401 2538047

mm

A1 = A / 2 - 1/3 * tw * h2 =

Luas penampang,

1784

mm


r 1 =  ( I1 / A1 ) =

tekan,

38

mm

4500

mm



119.317


lp = 1.76 * √ ( E / f y ) =

50.807


lr = 4.40 * √ ( E / f y ) =

127.017


f c

lG

< >

f y

lp


120.00

MPa

120.00

MPa

lr




-

MPa

132.13

MPa

-

MPa

132.13

MPa

132.13

MPa

481000

mm

3



1.153 73283153

Nmm


lG = bf / ( 2 * t f ) = ke = 4 /  ( h / tw ) =

0.598

ke =

0.598

lp = 0.38 * √ ( E / f y ) =

10.97

diambil,

8.33


< 0.763


lr = 1.35 * √ ( ke * E / f y ) =

30.13

f c = f y / 2 = <

120.00


240.00

MPa

-

MPa

-

MPa

240.00

MPa

240.00

MPa

481000

mm


lG

<

lp

dan

lG

MPa

lr



Koefisien balok plat berdinding penuh, 1.104 Kg = 1 - [ ar / (1200 + 300 * ar ) ] * [ h / tw - 2550 /  f cr ] = Momen nominal penampang, Mn = Kg * S * f cr = 127401878 Nmm



 Mp  Mp


Lp = 1.76 * r y * √ ( E / f y ) = f L = f y - f r =

1672

mm

170

MPa


2

Lr = r y * X1 / f L * √ [ 1 + √ ( 1 + X2 * f L ) ] =

4934

mm

Koefisien momen tekuk torsi lateral, 1.00 Cb = 12.5 * Mu / ( 2.5*Mu + 3*M A + 4*MB + 3*MC ) = Momen plastis, Mp = f y * Zx = 125298360 Nmm Momen batas tekuk, Mr = Sx * ( f y - f r ) = 81770000 Nmm


>

Lp

dan

4500 mm L = Ly = L < Lr Termasuk kategori : bentang s edang

Momen nominal dihitung sebagai berikut : Nmm Mn = Mp = f y * Zx = Mn = Cb * [ Mr + ( Mp - Mr ) * ( Lr - L ) / ( Lr - Lp ) ] = 87560070 Nmm 2 Nmm Mn = Cb * p / L*√ [ E * Iy * G * J + ( p * E / L ) * Iy * Iw ] = bentang s edang Momen nominal balok untuk kategori : Mn = 87560070 Nmm < Mn Mp Momen nominal yang digunakan, Mn = 87560070.5 Nmm


l = h / t w =


Ny = A * f y = Nu / ( fb * Ny ) =

44.769 1122720

N

0.028

N


Untuk nilai, →



lr = 2550 / √ f y * [ ( 1 - 0.74 * Nu / ( fb * Ny ) ]


0.125 100.087 100.087


l



161.189

lr compact




Mn = 125298360 Nmm Mn = 125298360 Nmm


Mn = 73283153 Nmm Mn = 127401878 Nmm Mn = 87560070 Nmm Mn = 125298360 Nmm Mn = 73283153 Nmm fb * Mn = 58626522 Nmm





kx = ky =

1.00


4500

mm

4500

mm

1.00




4500

mm

4500

mm


lcx = 1 /p * Lkx / r x * √ ( f y / E ) =

0.4002


lcy = 1 / p * Lky / r y * √ ( f y / E ) =

1.5082


lcx = w = w = 1.43 / ( 1.6 - 0.67 * lc ) = w = 1.25 * lc2 = wx =


0.4002 1.0737 1.0737




1.5082 2.8433 2.8433 223.535

MPa

84.409

MPa



1045695

N

394863

N

394863

N

315891

N

25169

N



30438000 315891 58626522

Nmm N Nmm



Untuk nilai, →

Untuk nilai, →

Nu / ( fn * Nn ) =

0.0797

<

 1.0  1.0 0.2


0.5590


0.5590

0.5590

<

1.0

-

AMAN (OK)


h / tw

Untuk nilai,

≤

1.10 *  ( kn * E / f y )


Untuk nilai,

Vn = 0.60 * f y * Aw 1.10 *  ( kn * E / f y )

≤

h / tw

≤

1.37 *  ( kn * E / f y )


Untuk nilai,



2

Vn = 0.90 * A w * kn * E / ( h / tw )



1950 5.0836 44.769 71.596 89.170

mm

h / tw

1.10* ( kn*E / f y )

<


h / tw

dan

<


N N N N N N


<

1.375 AMAN (OK)


2


≥

mm mm mm

mm


As

≥

2

2

0.5 * D * Aw * (1 + Cv) * [ a / h - (a / h) /  (1 + (a / h) ) ]

>

1833

260

(OK)


Is Is

≥

3

0.75 * h * t w 3 3 2 1.5 * h * tw / a ≥

untuk untuk

a/h a/h

≤ >

3

Is = 2/3 * hs * ts = a/h=

7.732

2 2 51630

mm

 2

>



-

mm

2005

mm 4

>



IWF 300 X 150 X 6.5


0

°

8 mm 16 mm

Jarak baut dengan tepi (S): ≤ ≤3d 1,5d S ≤ ≤ 24 S Dipakai S = 25 mm Jarak antar baut (U) ≤ ≤ 2,5d U ≤ ≤ 40 U Dipakai U = 100 mm Y= 45 cm Y1 = 25 ^2 = Y2 = 125 ^2 = Y3 = 225 ^2 = Y4 = 325 ^2 = Y5 = 425 ^2 = = ΣY =

48

7d 112

625 15625 50625 105625 180625 353125 3531.25

mm2 mm2 mm2 mm2 mm2 mm2 cm2

1939.412 kg

= 965.0738

<

0,75 x 1600 =

1200 OK

kg/cm2


114.5377 kg/cm2

<

= 975.6193 kg/cm2

928 kg/cm2

<

OK

1200 kg/cm2

OK

BAB 14 PERHITUNGAN BALOK KOLOM ( B E AM COLUMN ) B-5 IWF 150 x 75 x 5 PADA ELEMEN STRUKTUR RAFTER DENGAN PENGAKU BADAN



f y = f r =

240

MPa

70

MPa

E= u =

200000

MPa

0.3


t f

h

tw

h2

ht

r

h1 b f


ht = bf = tw = tf =

150

mm

75

mm

5

mm

7

mm

r= A = Ix = Iy = r x = r y = Sx = Sy =

8

mm

1785

2

6660000

mm mm

495000

mm

4

61.1

mm

16.6

mm

88800

mm

13200

mm


Lx = Ly =

2000

mm

2000

mm


2000

mm

5

mm

4741000

Nmm

4741000

Nmm

4741000

Nmm

4741000

Nmm

8114

N

3972

N

0.80 0.80 0.75


t f

h

tw

h2


r

h1 b f

ht



a / h = 13.986



<


204.09


l = bf / tf =

10.714

lp = 500 / √ f y =

32.275







l

<

lp

40.344 23566800

Nmm

15096000

Nmm


l

<



lr compact 23566800

Nmm

-

Nmm

-

Nmm

23566800

Nmm


l = h / tw =

28.600

lp = 1680 / √ f y =

108.444



l

lp

<

dan

lr = 2550 / √ f y = l <

164.602

lr compact



23566800

Nmm

-

Nmm

-

Nmm

23566800

Nmm


l = h / t w =


h / tw



> <

28.600

lr 40.344





≤ ≤

f y f y



1.00

< 2.3

1.00



1.362 247083

mm

A1 = A / 2 - 1/3 * tw * h2 =

Luas penampang,

693

mm


r 1 =  ( I1 / A1 ) =

tekan,

19

mm

2000

mm



105.881


lp = 1.76 * √ ( E / f y ) =

50.807


lr = 4.40 * √ ( E / f y ) =

127.017


f c

lG

< >

f y

lp


120.00

MPa

120.00

MPa

lr




-

MPa

153.28

MPa

-

MPa

153.28

MPa

153.28

MPa

88800

mm

3



1.150 15655306

Nmm


lG = bf / ( 2 * t f ) = ke = 4 /  ( h / tw ) =

0.748

ke =

0.748

lp = 0.38 * √ ( E / f y ) =

10.97

diambil,

5.36


< 0.763


lr = 1.35 * √ ( ke * E / f y ) =

33.70

f c = f y / 2 = <

120.00


240.00

MPa

-

MPa

-

MPa

240.00

MPa

240.00

MPa

88800

mm


lG

<

lp

dan

lG

MPa

lr





1.115 23766004

Nmm



 Mp  Mp


Lp = 1.76 * r y * √ ( E / f y ) = f L = f y - f r =

843

mm

170

MPa


2

Lr = r y * X1 / f L * √ [ 1 + √ ( 1 + X2 * f L ) ] =

3109

mm



1.00 23566800

Nmm

15096000

Nmm


>

Lp

dan


Momen nominal dihitung sebagai berikut : Nmm Mn = Mp = f y * Zx = Mn = Cb * [ Mr + ( Mp - Mr ) * ( Lr - L ) / ( Lr - Lp ) ] = 19242322 Nmm 2 Nmm Mn = Cb * p / L*√ [ E * Iy * G * J + ( p * E / L ) * Iy * Iw ] = bentang s edang Momen nominal balok untuk kategori : Mn = 19242322 Nmm < Mn Mp Momen nominal yang digunakan, Mn = 19242321.6 Nmm


l = h / t w =

28.600

Ny = A * f y = Nu / ( fb * Ny ) =

428400

N

0.024

N



Untuk nilai, →



lr = 2550 / √ f y * [ ( 1 - 0.74 * Nu / ( fb * Ny ) ]


0.125 101.383 101.383


l



161.718

lr compact



23566800

Nmm

-

Nmm

-

Nmm

23566800

Nmm

Mn = Mn =

23566800

Nmm

23566800

Nmm


15655306

Nmm

23766004

Nmm

19242322

Nmm

23566800

Nmm

15655306

Nmm

12524245

Nmm





kx = ky =

1.00


2000

mm

2000

mm

1.00




2000

mm

2000

mm


lcx = 1 /p * Lkx / r x * √ ( f y / E ) =

0.3609


lcy = 1 / p * Lky / r y * √ ( f y / E ) =

1.3285


lcx = w = w = 1.43 / ( 1.6 - 0.67 * lc ) = w = 1.25 * lc2 = wx =


0.3609 1.0529 1.0529




1.3285 2.2062 2.2062 227.945

MPa

108.787

MPa

406882

N

194184

N

194184

N

155347

N

8114

N





4741000

Nmm

155347

N

12524245

Nmm



Untuk nilai, →

Untuk nilai, →

Nu / ( fn * Nn ) =

0.0522

<

 1.0  1.0 0.2


0.4047


0.4047

0.4047

<

1.0

-

AMAN (OK)


h / tw

Untuk nilai,

≤

1.10 *  ( kn * E / f y )


Untuk nilai,

Vn = 0.60 * f y * Aw 1.10 *  ( kn * E / f y )

≤

h / tw

≤

1.37 *  ( kn * E / f y )


Untuk nilai,



2

Vn = 0.90 * A w * kn * E / ( h / tw )



750 5.0256 28.600 71.186 88.659

mm

h / tw

1.10* ( kn*E / f y )

<


h / tw

dan

<


N N N N N N


<

1.375 AMAN (OK)


2


≥

mm mm mm

mm


As

≥

2

2

0.5 * D * Aw * (1 + Cv) * [ a / h - (a / h) /  (1 + (a / h) ) ]

>

680

116

(OK)


Is Is

≥

3

0.75 * h * t w 3 3 2 1.5 * h * tw / a ≥

untuk untuk

a/h a/h

≤ >

3

Is = 2/3 * hs * ts = a/h=

13.986

2 2 11333

mm

 2

>



-

mm

137

mm 4

>



IWF 150 X 75 X 5


0

°

8 mm 16 mm


48

7d 112

625 5625 15625 21875 218.75

mm2 mm2 mm2 mm2 cm2

1625.486 kg

= 808.8603

<

0,75 x 1600 =

1200 OK

kg/cm2


16.47094 kg/cm2

<

= 809.1219 kg/cm2

928 kg/cm2

<

OK

1200 kg/cm2

OK

BAB 16 PERHITUNGAN BALOK KOLOM ( B E AM COLUMN ) K-1 LANTAI 1 DAN 2 ( IWF 400 x 200 x 8)

PADA ELEMEN STRUKTUR RAFTER DENGAN PENGAKU BADAN [C]2011 : M. Noer Ilham


f y = f r =

240

MPa

70

MPa

E= u =

200000

MPa

0.3


ht = bf = tw = tf =

t f

h

tw

h2

ht

r

h1 b f


400

mm

200

mm

8

mm

13

mm

13 mm r= 2 mm 8412 A = Ix = 237000000 mm 4 Iy = 17400000 mm 147 mm r x = 45.4 mm r y = Sx = 1190000 mm mm 174000 Sy =


Lx = Ly =

2500

mm

2500

mm


1250

mm

8

mm

89324000

Nmm

89324000

Nmm

89324000

Nmm

89324000

Nmm

680426

N

78428

N

0.80 0.80 0.75


t f

h

tw

h2


r

h1 b f

ht



a/h=

3.230



<


204.09


l = bf / tf =

15.385

lp = 500 / √ f y =

32.275



lr = 625 / √ f y =





l

40.344

<

lp


l


<

lr compact



l = h / tw =

48.375

lp = 1680 / √ f y =

108.444



l

lp

<

dan

lr = 2550 / √ f y = l <

164.602

lr compact



l = h / t w =


h / tw



harus

> >

48.375

lr 40.344





≤ ≤

f y f y



1.00

< 2.3

1.00



1.191 8695051

mm

A1 = A / 2 - 1/3 * tw * h2 =

Luas penampang,

3278

mm


r 1 =  ( I1 / A1 ) =

tekan,

52

mm

2500

mm



48.541


lp = 1.76 * √ ( E / f y ) =

50.807


lr = 4.40 * √ ( E / f y ) =

127.017


f c

lG

< <

f y

lp


120.00

MPa

120.00

MPa

lr




240.00

MPa

-

MPa

-

MPa

240.00

MPa

240.00

MPa

1190000

mm

3



lG = bf / ( 2 * t f ) = ke = 4 /  ( h / tw ) =

0.575

ke =

0.575

lp = 0.38 * √ ( E / f y ) =

10.97

diambil,

7.69


< 0.763


lr = 1.35 * √ ( ke * E / f y ) =

29.55

f c = f y / 2 = <

120.00


240.00

MPa

-

MPa

-

MPa

240.00

MPa

240.00

MPa

1190000

mm


lG

<

lp

dan

lG

MPa

lr






 Mp  Mp


Lp = 1.76 * r y * √ ( E / f y ) = f L = f y - f r =

2307

mm

170

MPa


2

Lr = r y * X1 / f L * √ [ 1 + √ ( 1 + X2 * f L ) ] =

6794

mm



>

Lp

dan


Momen nominal dihitung sebagai berikut : Nmm Mn = Mp = f y * Zx = Mn = Cb * [ Mr + ( Mp - Mr ) * ( Lr - L ) / ( Lr - Lp ) ] = 304046982 Nmm 2 Nmm Mn = Cb * p / L*√ [ E * Iy * G * J + ( p * E / L ) * Iy * Iw ] = bentang s edang Momen nominal balok untuk kategori : Mn = 304046982 Nmm < Mn Mp Momen nominal yang digunakan, Mn = 304046982 Nmm


l = h / t w =


Ny = A * f y = Nu / ( fb * Ny ) =

48.375 2018880

N

0.421

N


Untuk nilai, →



lr = 2550 / √ f y * [ ( 1 - 0.74 * Nu / ( fb * Ny ) ]

Nu / ( fb * Ny ) > lp = 1680 / √ f y * [ ( 1 - 2.75 * Nu / ( fb * Ny ) ] = lp = 500 / √ f y * [ ( 2.33 - Nu / ( fb * Ny ) ] = lp = 665 / √ f y = Batas kelangsingan maksimum penampang compact , lp = Untuk nilai :

0.125 61.603 42.926 61.603


l



113.287

lr compact




Mn = 308628480 Nmm Mn = 308628480 Nmm




310982774 Nmm 310982774 Nmm 304046982 Nmm 308628480 Nmm 304046982 Nmm 243237585 Nmm




kx = ky =

1.00


2500

mm

2500

mm

1.00




2500

mm

2500

mm


lcx = 1 /p * Lkx / r x * √ ( f y / E ) =

0.1875


lcy = 1 / p * Lky / r y * √ ( f y / E ) =

0.6072


lcx = w = w = 1.43 / ( 1.6 - 0.67 * lc ) = w = 1.25 * lc2 = wx =

Untuk parameter kelangsingan terhadap sumbu x,

0.1875

a. Kolom pendek : b. Kolom sedang :

1.0000

c. Kolom langsing : Faktor tekuk thd.sb. x,

1.0000




0.6072 1.1985 1.1985 240.000

MPa

200.254

MPa

2018880

N

1684540

N

1684540

N

1347632

N




680426 Nu = Mu = 89324000 fn * Nn = 1347632 fb * Mn = 243237585

N Nmm N Nmm



Untuk nilai, →

Untuk nilai, →

Nu / ( fn * Nn ) =

0.5049

>

 1.0  1.0 0.2


0.8313


0.8313

0.8313

<

1.0

AMAN (OK)


h / tw

Untuk nilai,

≤

1.10 *  ( kn * E / f y )


Untuk nilai,

Vn = 0.60 * f y * Aw 1.10 *  ( kn * E / f y )

≤

h / tw

≤

1.37 *  ( kn * E / f y )


Untuk nilai,



2

Vn = 0.90 * A w * kn * E / ( h / tw )



3200 5.4793 48.375 74.330 92.574

mm

h / tw

1.10* ( kn*E / f y )

<


h / tw

dan

<


N N N N N N


<

1.375 AMAN (OK)


2


≥

mm mm mm

mm


As

≥

2

2

0.5 * D * Aw * (1 + Cv) * [ a / h - (a / h) /  (1 + (a / h) ) ]

>

2992

908

(OK)


Is Is

≥

3

0.75 * h * t w 3 3 2 1.5 * h * tw / a ≥

untuk untuk

a/h a/h

≤ >

3

Is = 2/3 * hs * ts = a/h=

3.230

2 2 127659

mm

 2

>


0.75 * h * t w = 3 3 2 1.5 * h * tw / a = Kontrol momen inersia plat pengaku, Is = 127659

-

mm

28489

mm 4

>


BAB 17 PERHITUNGAN PLAT PLENDES K-1 Dipakai IWF 400 x 200 x 8 Hasil Perhitungan Dengan Staad Pro 2004 M= 89.324 kNm = 893240 kg.cm Q= 7842.8 kg N = 68042.6 kg D= 7842.8 kg

x

13

KONTROL TEGANGAN

b = h=

40 cm 60 cm 1600 kg/cm2 1120 kg/cm2 30 mPa

=

300 kg/cm2

KONTROL TEGANGAN BETON

= 28.35481 kg/cm2

<

300

DIMENSI PLAT KAKI KOLOM

b = h=

40 cm 60 cm

28.35480517 kg/cm2

28.35481 kg/cm2

(+)

28.34736 kg/cm2

(-)

kg/cm2

(OK)

a=

10 cm 1417.740258 kg.cm 0.17 1417.740258 : 1600 =

1417.740258 0.17

1600 =

8506.44155

= s=

5.316526 cm2 2.305759 cm

0.17

Dibulatkan =

Dipakai Plat Plendes Dengan Dimensi

2.5 cm 60

cm x

40

cm x

2.5


x/y = y= x+y= x=

0.999737 1.000263

=

x + 29.99606 cm

1.000263 x 1.000263 x =

T= 18000 kg Gaya tarik yang dipikul baut angker = n Baut = 4 bh Gaya yang dipikul 1 Baut Sebesar =

4.017857074 cm2

2.000263 x =

18000 kg

4500 kg

60 cm

cm

d= =

5.118289 cm2 2.262364 cm 22.62364 mm

Dibulatkan =

22 mm

Maka, dipakai angker Ø 4 22 mm pada sisi kiri dan untuk kanan dipakai dengan jumlah baut dan diameter yang sama dengan sisi kiri.

PERHITUNGAN PANJANG ANGKUR

Data angkur yang digunakan :  Mutu baja angkur U 24 

Diameter angkur A= 379.94 mm2 =

Ø

22 mm

416.2034 mm

= Maka Panjang angkur yang dipakai =

400 mm

396 mm

BAB 18 PERHITUNGAN BALOK KOLOM ( B E AM COLUMN ) K-2 LANTAI 3( IWF 250 x 125 x 6)



f y = f r =

240

MPa

70

MPa

E= u =

200000

MPa

0.3


t f

h

tw

h2

ht

r

h1 b f


ht = bf = tw = tf =

250

mm

125

mm

6

mm

9

mm

r= A = Ix = Iy = r x = r y = Sx = Sy =

12

mm

3766

2

40500000

mm mm

2940000

mm

4

104

mm

27.9

mm

324000

mm

47000

mm


Lx = Ly =

3000

mm

3000

mm


1500

mm

6

mm

36325000

Nmm

36325000

Nmm

36325000

Nmm

36325000

Nmm

42481

N

5126

N

0.80 0.80 0.75


t f

h

tw

h2


r

h1 b f

ht



a/h=

6.224



<


204.09


l = bf / tf =

13.889

lp = 500 / √ f y =

32.275







l

<

lp

40.344 84446640

Nmm

55080000

Nmm


l

<



lr compact 84446640

Nmm

-

Nmm

-

Nmm

84446640

Nmm


l = h / tw =

40.167

lp = 1680 / √ f y =

108.444



l

lp

<

dan

lr = 2550 / √ f y = l <

164.602

lr compact



84446640

Nmm

-

Nmm

-

Nmm

84446640

Nmm


l = h / t w =


h / tw



> <

40.167

lr 40.344





≤ ≤

f y f y



1.00

< 2.3

1.00



1.285 1468752

mm

A1 = A / 2 - 1/3 * tw * h2 =

Luas penampang,

1467

mm


r 1 =  ( I1 / A1 ) =

tekan,

32

mm

3000

mm



94.812


lp = 1.76 * √ ( E / f y ) =

50.807


lr = 4.40 * √ ( E / f y ) =

127.017


f c

lG

< >

f y

lp


120.00

MPa

120.00

MPa

lr




-

MPa

170.71

MPa

-

MPa

170.71

MPa

170.71

MPa

324000

mm

3



1.126 62259791

Nmm


lG = bf / ( 2 * t f ) = ke = 4 /  ( h / tw ) =

0.631

ke =

0.631

lp = 0.38 * √ ( E / f y ) =

10.97

diambil,

6.94


< 0.763


lr = 1.35 * √ ( ke * E / f y ) =

30.96

f c = f y / 2 = <

120.00


240.00

MPa

-

MPa

-

MPa

240.00

MPa

240.00

MPa

324000

mm


lG

<

lp

dan

lG

MPa

lr





1.101 85603707

Nmm



 Mp  Mp


Lp = 1.76 * r y * √ ( E / f y ) = f L = f y - f r =

1418

mm

170

MPa


2

Lr = r y * X1 / f L * √ [ 1 + √ ( 1 + X2 * f L ) ] =

4422

mm



1.00 84446640

Nmm

55080000

Nmm


>

Lp

dan


Momen nominal dihitung sebagai berikut : Mn = Mp = f y * Zx = Mn = Cb * [ Mr + ( Mp - Mr ) * ( Lr - L ) / ( Lr - Lp ) ] = 68981286 2 Mn = Cb * p / L*√ [ E * Iy * G * J + ( p * E / L ) * Iy * Iw ] = bentang s edang Momen nominal balok untuk kategori : Mn = 68981286 < Mn Mp Momen nominal yang digunakan, 68981286 Mn =

Nmm Nmm Nmm Nmm Nmm


l = h / t w =

40.167

Ny = A * f y = Nu / ( fb * Ny ) =

903840

N

0.059

N



Untuk nilai, →



lr = 2550 / √ f y * [ ( 1 - 0.74 * Nu / ( fb * Ny ) ]


0.125 90.923 90.923


l



157.446

lr compact



84446640

Nmm

-

Nmm

-

Nmm

84446640

Nmm

Mn = Mn =

84446640

Nmm

84446640

Nmm


62259791

Nmm

85603707

Nmm

68981286

Nmm

84446640

Nmm

62259791

Nmm

49807833

Nmm





kx = ky =

1.00


3000

mm

3000

mm

1.00




3000

mm

3000

mm


lcx = 1 /p * Lkx / r x * √ ( f y / E ) =

0.3181


lcy = 1 / p * Lky / r y * √ ( f y / E ) =

1.1857


lcx = w = w = 1.43 / ( 1.6 - 0.67 * lc ) = w = 1.25 * lc2 = wx =


0.3181 1.0311 1.0311




1.1857 1.7750 1.7750 232.765

MPa

135.208

MPa

876592

N

509192

N

509192

N

407354

N

42481

N





36325000 407354 49807833

Nmm N Nmm



Untuk nilai, →

Untuk nilai, →

Nu / ( fn * Nn ) =

0.1043

<

 1.0  1.0 0.2


0.7814


0.7814

0.7814

<

1.0

-

AMAN (OK)


h / tw

Untuk nilai,

≤

1.10 *  ( kn * E / f y )


Untuk nilai,

Vn = 0.60 * f y * Aw 1.10 *  ( kn * E / f y )

≤

h / tw

≤

1.37 *  ( kn * E / f y )


Untuk nilai,



2

Vn = 0.90 * A w * kn * E / ( h / tw )



1500 5.1291 40.167 71.915 89.567

mm

h / tw

1.10* ( kn*E / f y )

<


h / tw

dan

<


N N N N N N


<

1.375 AMAN (OK)


2


≥

mm mm mm

mm


As

≥

2

2

0.5 * D * Aw * (1 + Cv) * [ a / h - (a / h) /  (1 + (a / h) ) ]

>

1392

294

(OK)


Is Is

≥

3

0.75 * h * t w 3 3 2 1.5 * h * tw / a ≥

untuk untuk

a/h a/h

≤ >

3

Is = 2/3 * hs * ts = a/h=

6.224

2 2 33408

mm

 2

>



-

mm

2016

mm 4

>


BAB 17 PERHITUNGAN PLAT PLENDES KOLOM LT-3 Dipakai IWF 250 x 125 x 6 Hasil Perhitungan Dengan Staad Pro 2004 M= 36.325 kNm = 363250 kg.cm Q= 512.6 kg N = 4248.1 kg D= 512.6 kg

x

9

KONTROL TEGANGAN

b = h=


=

300 kg/cm2


= 5.316936 kg/cm2

<

300


b = h=

20 cm 40 cm

5.316935938 kg/cm2

5.316936 kg/cm2

(+)

5.303314 kg/cm2

(-)

kg/cm2

(OK)

a=

7.5 cm 149.5388232 kg.cm 0.17 149.5388232 : 1600 =

149.5388232 0.17

1600 =

897.2329395

= s=

0.560771 cm2 0.748846 cm

0.17

Dibulatkan =


1 cm 40

cm x

20

cm x

1


x/y = y= x+y= x=

0.997438 1.002569

=

x + 19.97435 cm

1.002569 x 1.002569 x =

T= 3999.993 kg Gaya tarik yang dipikul baut angker = n Baut = 3 bh Gaya yang dipikul 1 Baut Sebesar =

2.002569 x =

3999.993 kg

1333.331 kg

1.190474232 cm2

40 cm

cm

d= =

1.516528 cm2 1.231474 cm 12.31474 mm

Dibulatkan =

16 mm

Maka, dipakai baut Ø 3 16 mm pada sisi kiri dan untuk kanan dipakai dengan jumlah baut dan diameter yang sama dengan sisi kiri.

BAB 20 PERHITUNGAN BALOK KOLOM ( B E AM COLUMN ) K-3 KOLOM RAMP ( IWF 300 x 150 x 6.5)



f y = f r =

240

MPa

70

MPa

E= u =

200000

MPa

0.3


t f

h

tw

h2

ht

r

h1 b f


ht = bf = tw = tf =

300

mm

150

mm

6.5

mm

9

mm

r= A = Ix = Iy = r x = r y = Sx = Sy =

13

mm

4678

2

72100000

mm mm

5080000

mm

4

124

mm

32.9

mm

481000

mm

67700

mm


Lx = Ly =

2500

mm

2500

mm


1250

mm

6.5

mm

40001000

Nmm

40001000

Nmm

40001000

Nmm

40001000

Nmm

99709

N

11516

N

0.80 0.80 0.75


t f

h

tw

h2


r

h1 b f

ht



a/h=

4.296



<


204.09


l = bf / tf =

16.667

lp = 500 / √ f y =

32.275



lr = 625 / √ f y =





l

40.344

<

lp


l


<

lr compact



l = h / tw =

44.769

lp = 1680 / √ f y =

108.444



l

lp

<

dan

lr = 2550 / √ f y = l <

164.602

lr compact



l = h / t w =


h / tw



harus

> >

44.769

lr 40.344





≤ ≤

f y f y



1.00

< 2.3

1.00



1.401 2538047

mm

A1 = A / 2 - 1/3 * tw * h2 =

Luas penampang,

1784

mm


r 1 =  ( I1 / A1 ) =

tekan,

38

mm

2500

mm



66.287


lp = 1.76 * √ ( E / f y ) =

50.807


lr = 4.40 * √ ( E / f y ) =

127.017


f c

lG

< >

f y

lp


120.00

MPa

120.00

MPa

lr




-

MPa

215.63

MPa

-

MPa

215.63

MPa

215.63

MPa

481000

mm

3



lG = bf / ( 2 * t f ) = ke = 4 /  ( h / tw ) =

0.598

ke =

0.598

lp = 0.38 * √ ( E / f y ) =

10.97

diambil,

8.33


< 0.763


lr = 1.35 * √ ( ke * E / f y ) =

30.13

f c = f y / 2 = <

120.00


240.00

MPa

-

MPa

-

MPa

240.00

MPa

240.00

MPa

481000

mm


lG

<

lp

dan

lG

MPa

lr






 Mp  Mp


Lp = 1.76 * r y * √ ( E / f y ) = f L = f y - f r =

1672

mm

170

MPa


2

Lr = r y * X1 / f L * √ [ 1 + √ ( 1 + X2 * f L ) ] =

4934

mm



>

Lp

dan


Momen nominal dihitung sebagai berikut : Nmm Mn = Mp = f y * Zx = Mn = Cb * [ Mr + ( Mp - Mr ) * ( Lr - L ) / ( Lr - Lp ) ] = 114244803 Nmm 2 Nmm Mn = Cb * p / L*√ [ E * Iy * G * J + ( p * E / L ) * Iy * Iw ] = bentang s edang Momen nominal balok untuk kategori : Mn = 114244803 Nmm < Mn Mp Momen nominal yang digunakan, Mn = 114244803 Nmm


l = h / t w =


Ny = A * f y = Nu / ( fb * Ny ) =

44.769 1122720

N

0.111

N


Untuk nilai, →



lr = 2550 / √ f y * [ ( 1 - 0.74 * Nu / ( fb * Ny ) ]


0.125 75.337 75.337


l



151.080

lr compact




Mn = 125298360 Nmm Mn = 125298360 Nmm




115274713 Nmm 127401878 Nmm 114244803 Nmm 125298360 Nmm 114244803 Nmm 91395843

Nmm




kx = ky =

1.00


2500

mm

2500

mm

1.00




2500

mm

2500

mm


lcx = 1 /p * Lkx / r x * √ ( f y / E ) =

0.2223


lcy = 1 / p * Lky / r y * √ ( f y / E ) =

0.8379


lcx = w = w = 1.43 / ( 1.6 - 0.67 * lc ) = w = 1.25 * lc2 = wx =

Untuk parameter kelangsingan terhadap sumbu x,

0.2223

a. Kolom pendek : b. Kolom sedang :

1.0000

c. Kolom langsing : Faktor tekuk thd.sb. x,

1.0000




0.8379 1.3768 1.3768 240.000

MPa

174.313

MPa

1122720

N

815437

N

815437

N

652350

N

99709

N





40001000 652350 91395843

Nmm N Nmm



Untuk nilai, →

Untuk nilai, →

Nu / ( fn * Nn ) =

0.1528

<

 1.0  1.0 0.2


0.5141


0.5141

0.5141

<

1.0

-

AMAN (OK)


h / tw

Untuk nilai,

≤

1.10 *  ( kn * E / f y )


Untuk nilai,

Vn = 0.60 * f y * Aw 1.10 *  ( kn * E / f y )

≤

h / tw

≤

1.37 *  ( kn * E / f y )


Untuk nilai,



2

Vn = 0.90 * A w * kn * E / ( h / tw )



1950 5.2710 44.769 72.903 90.798

mm

h / tw

1.10* ( kn*E / f y )

<


h / tw

dan

<


N N N N N N


<

1.375 AMAN (OK)


2


≥

mm mm mm

mm


As

≥

2

2

0.5 * D * Aw * (1 + Cv) * [ a / h - (a / h) /  (1 + (a / h) ) ]

>

1833

468

(OK)


Is Is

≥

3

0.75 * h * t w 3 3 2 1.5 * h * tw / a ≥

untuk untuk

a/h a/h

≤ >

3

Is = 2/3 * hs * ts = a/h=

4.296

2 2 51630

mm

 2

>



-

mm

6497

mm 4

>


BAB 21 PERHITUNGAN PLAT PLENDES K-3 Dipakai IWF 300 x 150 x 6.5 Hasil Perhitungan Dengan Staad Pro 2004 M= 40.001 kNm = 400010 kg.cm Q= 1151.6 kg N = 9970.9 kg D= 1151.6 kg

x

9

KONTROL TEGANGAN

b = h=


=

300 kg/cm2


= 6.650467 kg/cm2

<

300


b = h=

30 cm 50 cm

6.650466747 kg/cm2

6.650467 kg/cm2

(+)

6.644067 kg/cm2

(-)

kg/cm2

(OK)

a=

10 cm 332.5233373 kg.cm 0.17 332.5233373 : 1600 =

332.5233373 0.17

1600 =

1995.140024

= s=

1.246963 cm2 1.116675 cm

0.17

Dibulatkan =


1.5 cm 50

cm x

30

cm x

1.5


x/y = y= x+y= x=

0.999038 1.000963

=

x + 24.98796 cm

1.000963 x 1.000963 x =

T= 9374.998 kg Gaya tarik yang dipikul baut angker = n Baut = 3 bh Gaya yang dipikul 1 Baut Sebesar =

2.000963 x =

9374.998 kg

3124.999 kg

2.790177925 cm2

50 cm

cm

d= =

3.554367 cm2 1.885303 cm 18.85303 mm

Dibulatkan =

19 mm

Maka, dipakai angker Ø 3 19 mm pada sisi kiri dan untuk kanan dipakai dengan jumlah baut dan diameter yang sama dengan sisi kiri.

PERHITUNGAN PANJANG ANGKUR

Data angkur yang digunakan :  Mutu baja angkur U 24 

Diameter angkur A= 283.385 mm2 =

Ø

19 mm

310.4327 mm

= Maka Panjang angkur yang dipakai =

340 mm

342 mm

Analisis Kekuatan Kolom Beton Bertulang Dengan Diagram Interaksi

ANALISIS KEKUATAN KOLOM BETON BERTULANG BAB 22 DENGAN DIAGRAM INTERAKSI

KP-1 40/60

[C ]2010 : M. N oer Ilham

KODE KOLOM

K7

INPUT DATA KOLOM

f c' = f y =

Kuat tekan beton, Tegangan leleh baja, Lebar kolom, Tinggi kolom, Tebal brutto selimut beton, Jumlah tulangan, Diameter tulangan,

b= h= ds = n= D=

30

MPa

240

MPa

400

mm

600

mm

40

mm

6 buah 16

mm

PERHITUNGAN DIAGRAM INTERAKSI Es =

Modulus elastis baja,

2.E+05

MPa

β1 = 0.85

untuk f c'  30 MPa

β1 = 0.85 - 0.008 (f c' - 30)

untuk fc ' > 30 MPa

Faktor distribusi tegangan,

β1 = 0.85

Luas tulangan total,

2 As = n * p / 4 * D = 1206 mm

Jarak tulangan,

x = ( h - 2*ds ) / 6 = 86.67 mm

Rasio tulangan,

r = As / Ag = 0.50%

Faktor reduksi kekuatan, f = 0.65 untuk Pn ≥ 0.1 * f c' * b * h f = 0.80

untuk Pn = 0

Untuk : 0

≤

Pn ≤ 0.1 * f c' * b * h

f = 0.65 + 0.15 * ( Pno - Pn ) / Pno


6000

b

5500

5000

h

4500

4000

b=

400

mm

h=

600

mm

3500 ) N k ( n P .

6

3000

f

2500

2000

1000

500

0 -100

-50

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

750

f.Mn (kNm)

ANALISIS KOLOM DENGAN DIAGRAM INTERAKSI

800

850

900

950 1000

16

f c' = 30

MPa

f y = 240

MPa

Pu

Mu

(kN)

(kNm)

727.81 1500

D

11.83



No

Luas masing-masing tulangan

Jarak tulangan thd. sisi beton

1

As1 = 7/24 * As =

352

mm

2

As2 = 2/24 * As =

101

mm

2

101

mm

2 2

3

As3 = 2/24 * As =

4

As4 = 2/24 * As =

101

mm

5

As5 = 2/24 * As =

101

mm

6

As6 = 2/24 * As =

101

mm

7

As7 = 7/24 * As =

352

As = 1206

mm

2

mm

2

Pada kondisi tekan aksial sentris (Mno = 0) :

d1 = 6*x + ds =

560 mm

d2 = 5*x + ds =

473 mm

d3 = 4*x + ds =

387 mm

d4 = 3*x + ds =

300 m m

Pada kond isi balance :

d5 = 2*x + ds =

213 mm

c = cb = 600 / (600 + f y) * d1 =

d6 =

x + ds =

127 mm

d7 =

ds =

40 mm

Regangan pada masing-masing baja tulangan :

Pno = 0.80*[ 0.85*f c' *b*h + As*(f y - 0.85*f c')]*10

-3

Pno = 5103 kN -3

0.1 * f c' * b * h *10 =

720

kN

400.00 mm

εsi = 0.003 * ( c - di ) / c

Tegangan pada masing-masing baja tulangan : Untuk Untuk

| εsi | < f y / Es | εsi |  f y / Es

maka : f si = esi* Es

Gaya-gaya internal pada masing-masing baja tulangan : Resultan gaya internal baja tulangan : Momen akibat gaya internal masing-masing baja tulangan : Momen total akibat gaya internal baja tulangan : Tinggi blok tegangan tekan beton, Gaya internal pada beton tekan : Momen akibat gaya internal tekan beton : Momen nominal : Gaya aksial rencana : Momen rencana :

105

→

Dc = 5.7143

maka : f si =| εsi | / esi* f y

URAIAN PERHITUNGAN

Gaya aksial nominal :

Jumlah interval jarak garis netral = PERSAMAAN

UNIT -3

Fsi = Asi * f si * 10 -3 Cs = [ S Fsi ]*10 Msi = Fsi*(h/2 - di) Ms = S Msi a = β1 * c -3 Cc = 0.85 * f c' * b * a * 10 Mc = Cc * (h - a) / 2 Pn = Cs + Cc -3 Mn = (Mc + Ms)*10 Pu = f * Pn Mu = f * Mn

kN kN

kNmm

kNmm mm kN

kNmm kN kNm kN kNm


6000

b

5500

5000

4500

h

4000

b=

400

mm

h=

600

mm

3500

6

) N k ( n P .

3000

f

2500

2000

1500

1000

500

D

f c' = 30

MPa

f y = 240

MPa

Pu

Mu

(kN)

(kNm)

727.81

11.83

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0 -100

-50

0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

750

f.Mn (kNm)


800

850

900

950 1000

16



c

εs1

εs2

εs3

εs4

εs5

εs6

εs7

mm KONDISI TEKAN AKSIAL SENTRIS

f s1

f s2

f s3

f s4

f s5

f s6

f s7

Fs1

Fs2

Fs3

Fs4

Fs5

MPa

MPa

MPa

MPa

MPa

MPa

MPa

kN

kN

kN

kN

kN

72 0. 0

0. 000 67

0 .0 010 3

0. 00 13 9

0. 00 17 5

0. 00 211

0. 00 24 7

0. 00 28 3

1 33 .33

2 05 .5 6

2 40 .0 0

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

4 6. 91

20 .66

2 4. 13

2 4. 13

24 .1 3

71 4. 3

0. 000 65

0 .0 010 1

0. 00 13 8

0. 00 17 4

0. 00 210

0. 00 24 7

0. 00 28 3

1 29 .60

2 02 .4 0

2 40 .0 0

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

4 5. 60

20 .35

2 4. 13

2 4. 13

24 .1 3

70 8. 6

0. 000 63

0 .0 010 0

0. 00 13 6

0. 00 17 3

0. 00 210

0. 00 24 6

0. 00 28 3

1 25 .81

1 99 .1 9

2 40 .0 0

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

4 4. 27

20 .03

2 4. 13

2 4. 13

24 .1 3

70 2. 9 69 7. 1

0. 000 61 0. 000 59

0 .0 009 8 0 .0 009 6

0. 00 13 5 0. 00 13 4

0. 00 17 2 0. 00 17 1

0. 00 209 0. 00 208

0. 00 24 6 0. 00 24 5

0. 00 28 3 0. 00 28 3

1 21 .95 1 18 .03

1 95 .9 3 1 92 .6 2

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .00 2 40 .00

24 0. 00 24 0. 00

4 2. 91 4 1. 53

19 .70 19 .36

2 4. 13 2 4. 13

2 4. 13 2 4. 13

24 .1 3 24 .1 3

69 1. 4

0. 000 57

0 .0 009 5

0. 00 13 2

0. 00 17 0

0. 00 207

0. 00 24 5

0. 00 28 3

1 14 .05

1 89 .2 6

2 40 .0 0

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

4 0. 13

19 .03

2 4. 13

2 4. 13

24 .1 3

68 5. 7

0. 000 55

0 .0 009 3

0. 00 13 1

0. 00 16 9

0. 00 207

0. 00 24 5

0. 00 28 3

1 10 .00

1 85 .8 3

2 40 .0 0

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

3 8. 70

18 .68

2 4. 13

2 4. 13

24 .1 3

68 0. 0

0. 000 53

0 .0 009 1

0. 00 12 9

0. 00 16 8

0. 00 206

0. 00 24 4

0. 00 28 2

1 05 .88

1 82 .3 5

2 40 .0 0

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

3 7. 26

18 .33

2 4. 13

2 4. 13

24 .1 3

67 4. 3 66 8. 6

0. 000 51 0. 000 49

0 .0 008 9 0 .0 008 8

0. 00 12 8 0. 00 12 6

0. 00 16 7 0. 00 16 5

0. 00 205 0. 00 204

0. 00 24 4 0. 00 24 3

0. 00 28 2 0. 00 28 2

1 01 .69 97 .44

1 78 .8 1 1 75 .2 1

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .00 2 40 .00

24 0. 00 24 0. 00

3 5. 78 3 4. 28

17 .98 17 .61

2 4. 13 2 4. 13

2 4. 13 2 4. 13

24 .1 3 24 .1 3

66 2. 9

0. 000 47

0 .0 008 6

0. 00 12 5

0. 00 16 4

0. 00 203

0. 00 24 3

0. 00 28 2

93 .10

1 71 .5 5

2 40 .0 0

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

3 2. 76

17 .25

2 4. 13

2 4. 13

24 .1 3

65 7. 1

0. 000 44

0 .0 008 4

0. 00 12 3

0. 00 16 3

0. 00 203

0. 00 24 2

0. 00 28 2

88 .70

1 67 .8 3

2 40 .0 0

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

3 1. 21

16 .87

2 4. 13

2 4. 13

24 .1 3

65 1. 4 64 5. 7

0. 000 42 0. 000 40

0 .0 008 2 0 .0 008 0

0. 00 12 2 0. 00 12 0

0. 00 16 2 0. 00 16 1

0. 00 202 0. 00 201

0. 00 24 2 0. 00 24 1

0. 00 28 2 0. 00 28 1

84 .21 79 .65

1 64 .0 4 1 60 .1 8

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .00 2 40 .00

24 0. 00 24 0. 00

2 9. 63 2 8. 02

16 .49 16 .10

2 4. 13 2 4. 13

2 4. 13 2 4. 13

24 .1 3 24 .1 3

64 0. 0

0. 000 38

0 .0 007 8

0. 00 11 9

0. 00 15 9

0. 00 200

0. 00 24 1

0. 00 28 1

75 .00

1 56 .2 5

2 37 .5 0

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

2 6. 39

15 .71

2 3. 88

2 4. 13

24 .1 3

63 4. 3

0. 000 35

0 .0 007 6

0. 00 11 7

0. 00 15 8

0. 00 199

0. 00 24 0

0. 00 28 1

70 .27

1 52 .2 5

2 34 .2 3

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

2 4. 73

15 .31

2 3. 55

2 4. 13

24 .1 3

62 8. 6 62 2. 9

0. 000 33 0. 000 30

0 .0 007 4 0 .0 007 2

0. 00 11 5 0. 00 11 4

0. 00 15 7 0. 00 15 6

0. 00 198 0. 00 197

0. 00 24 0 0. 00 23 9

0. 00 28 1 0. 00 28 1

65 .45 60 .55

1 48 .1 8 1 44 .0 4

2 30 .9 1 2 27 .5 2

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .00 2 40 .00

24 0. 00 24 0. 00

2 3. 03 2 1. 31

14 .90 14 .48

2 3. 21 2 2. 87

2 4. 13 2 4. 13

24 .1 3 24 .1 3

61 7. 1

0. 000 28

0 .0 007 0

0. 00 11 2

0. 00 15 4

0. 00 196

0. 00 23 8

0. 00 28 1

55 .56

1 39 .8 1

2 24 .0 7

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

1 9. 55

14 .06

2 2. 53

2 4. 13

24 .1 3

61 1. 4

0. 000 25

0 .0 006 8

0. 00 11 0

0. 00 15 3

0. 00 195

0. 00 23 8

0. 00 28 0

50 .47

1 35 .5 1

2 20 .5 6

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

1 7. 76

13 .62

2 2. 17

2 4. 13

24 .1 3

60 5. 7

0. 000 23

0 .0 006 6

0. 00 10 8

0. 00 15 1

0. 00 194

0. 00 23 7

0. 00 28 0

45 .28

1 31 .1 3

2 16 .9 8

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

1 5. 93

13 .18

2 1. 81

2 4. 13

24 .1 3

60 0. 0 59 4. 3

0. 000 20 0. 000 17

0 .0 006 3 0 .0 006 1

0. 00 10 7 0. 00 10 5

0. 00 15 0 0. 00 14 9

0. 00 193 0. 00 192

0. 00 23 7 0. 00 23 6

0. 00 28 0 0. 00 28 0

40 .00 34 .62

1 26 .6 7 1 22 .1 2

2 13 .3 3 2 09 .6 2

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .00 2 40 .00

24 0. 00 24 0. 00

1 4. 07 1 2. 18

12 .73 12 .28

2 1. 45 2 1. 07

2 4. 13 2 4. 13

24 .1 3 24 .1 3

58 8. 6

0. 000 15

0 .0 005 9

0. 00 10 3

0. 00 14 7

0. 00 191

0. 00 23 5

0. 00 28 0

29 .13

1 17 .4 8

2 05 .8 3

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

1 0. 25

11 .81

2 0. 69

2 4. 13

24 .1 3

58 2. 9

0. 000 12

0 .0 005 6

0. 00 10 1

0. 00 14 6

0. 00 190

0. 00 23 5

0. 00 27 9

23 .53

1 12 .7 5

2 01 .9 6

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

8. 28

11 .33

2 0. 30

2 4. 13

24 .1 3

57 7. 1 57 1. 4

0. 000 09 0. 000 06

0 .0 005 4 0 .0 005 2

0. 00 09 9 0. 00 09 7

0. 00 14 4 0. 00 14 3

0. 00 189 0. 00 188

0. 00 23 4 0. 00 23 4

0. 00 27 9 0. 00 27 9

17 .82 12 .00

1 07 .9 2 1 03 .0 0

1 98 .0 2 1 94 .0 0

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .00 2 40 .00

24 0. 00 24 0. 00

6. 27 4. 22

10 .85 10 .35

1 9. 91 1 9. 50

2 4. 13 2 4. 13

24 .1 3 24 .1 3

56 5. 7

0. 000 03

0 .0 004 9

0 .00 09 5

0. 00 14 1

0. 00 187

0. 00 23 3

0. 00 27 9

6 .06

97 .9 8

1 89 .9 0

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

2. 13

9 .85

1 9. 09

2 4. 13

24 .1 3

56 0. 0

0. 000 00

0 .0 004 6

0 .00 09 3

0. 00 13 9

0. 00 186

0. 00 23 2

0. 00 27 9

0 .00

92 .8 6

1 85 .7 1

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

0. 00

9 .34

1 8. 67

2 4. 13

24 .1 3

55 4. 3

- 0. 00 003

0 .0 004 4

0. 00 09 1

0. 00 13 8

0. 00 185

0. 00 23 1

0. 00 27 8

-6 .19

87 .6 3

1 81 .4 4

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

- 2. 18

8 .81

1 8. 24

2 4. 13

24 .1 3

54 8. 6 54 2. 9

- 0. 00 006 - 0. 00 009

0 .0 004 1 0 .0 003 8

0. 00 08 9 0. 00 08 6

0. 00 13 6 0. 00 13 4

0. 00 183 0. 00 182

0. 00 23 1 0. 00 23 0

0. 00 27 8 0. 00 27 8

- 12 .50 - 18 .95

82 .2 9 76 .8 4

1 77 .0 8 1 72 .6 3

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .00 2 40 .00

24 0. 00 24 0. 00

- 4. 40 - 6. 67

8 .27 7 .73

1 7. 80 1 7. 35

2 4. 13 2 4. 13

24 .1 3 24 .1 3

53 7. 1

- 0. 00 013

0 .0 003 6

0. 00 08 4

0. 00 13 2

0. 00 181

0. 00 22 9

0. 00 27 8

- 25 .53

71 .2 8

1 68 .0 9

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

- 8. 98

7 .17

1 6. 90

2 4. 13

24 .1 3

53 1. 4

- 0. 00 016

0 .0 003 3

0. 00 08 2

0. 00 13 1

0. 00 180

0. 00 22 8

0. 00 27 7

- 32 .26

65 .5 9

1 63 .4 4

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

-1 1. 35

6 .59

1 6. 43

2 4. 13

24 .1 3

52 5. 7

- 0. 00 020

0 .0 003 0

0. 00 07 9

0. 00 12 9

0. 00 178

0. 00 22 8

0. 00 27 7

- 39 .13

59 .7 8

1 58 .7 0

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

-1 3. 77

6 .01

1 5. 95

2 4. 13

24 .1 3

52 0. 0 51 4. 3

- 0. 00 023 - 0. 00 027

0 .0 002 7 0 .0 002 4

0. 00 07 7 0. 00 07 4

0. 00 12 7 0. 00 12 5

0. 00 177 0. 00 176

0. 00 22 7 0. 00 22 6

0. 00 27 7 0. 00 27 7

- 46 .15 - 53 .33

53 .8 5 47 .7 8

1 53 .8 5 1 48 .8 9

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .00 2 40 .00

24 0. 00 24 0. 00

-1 6. 24 -1 8. 77

5 .41 4 .80

1 5. 47 1 4. 97

2 4. 13 2 4. 13

24 .1 3 24 .1 3

50 8. 6

- 0. 00 030

0 .0 002 1

0. 00 07 2

0. 00 12 3

0. 00 174

0. 00 22 5

0. 00 27 6

- 60 .67

41 .5 7

1 43 .8 2

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

-2 1. 35

4 .18

1 4. 46

2 4. 13

24 .1 3

50 2. 9

- 0. 00 034

0 .0 001 8

0. 00 06 9

0. 00 12 1

0. 00 173

0. 00 22 4

0. 00 27 6

- 68 .18

35 .2 3

1 38 .6 4

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

-2 3. 99

3 .54

1 3. 94

2 4. 13

24 .1 3


Fs6

Fs7

Cs

Ms1

Ms2

Ms3

Ms4

Ms5

Ms6

Ms7

kN

kN

kN

kNmm

kNmm

k Nmm

kNmm

kNmm

kNmm

k Nmm

Ms kNmm

a mm

Cc kN

Mc kNmm

Pn

Mn

kN 5103.01

kNm 0.00

Ф.Pn

Ф.Mn

0.65

kN 3316.96

kNm 0.00

Ф

2 4.1 3

84 .45

2 48 .5 3

-12 19 7.7 6

-3 58 1.8 8

- 20 91 .04

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

1 03 58 .41

6 12 .0 0

62 42 .4 0

- 374 54 .4 0

5 10 3. 01

-2 7. 10

0. 65

33 16 .9 6

-1 7. 61

2 4.1 3

84 .45

2 46 .9 0

-11 85 6.2 2

-3 52 6.8 9

- 20 91 .04

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

1 07 54 .94

6 07 .1 4

61 92 .8 6

- 221 17 .3 5

51 03. 01

-1 1. 36

0. 65

33 16 .9 6

- 7. 39

2 4.1 3

84 .45

2 45 .2 5

- 11 50 9.1 7

-3 47 1.0 2

- 20 91 .04

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

1 11 57 .86

6 02 .2 9

61 43 .3 1

- 70 20 .9 3

51 03. 01

4 .1 4

0. 65

33 16 .9 6

2. 69

2 4.1 3 2 4.1 3

84 .45 84 .45

2 43 .5 6 2 41 .8 5

- 11 15 6.4 9 -10 79 8.0 1

-3 41 4.2 4 -3 35 6.5 3

- 20 91 .04 - 20 91 .04

0. 00 0. 00

2 09 1.0 4 2 09 1.0 4

41 82 .09 41 82 .09

2 19 55 .9 6 2 19 55 .9 6

1 15 67 .33 1 19 83 .51

5 97 .4 3 5 92 .5 7

60 93 .7 7 60 44 .2 3

78 34 .8 5 2 24 49 .9 9

51 03. 01 51 03. 01

1 9.4 0 3 4.4 3

0. 65 0. 65

33 16 .9 6 33 16 .9 6

1 2. 61 2 2. 38

2 4.1 3

84 .45

2 40 .1 1

-10 43 3.6 2

-3 29 7.8 6

- 20 91 .04

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

1 24 06 .57

5 87 .7 1

59 94 .6 9

3 68 24 .5 0

51 03. 01

4 9.2 3

0. 65

33 16 .9 6

3 2. 00

2 4.1 3

84 .45

2 38 .3 4

-10 06 3.1 5

-3 23 8.2 1

- 20 91 .04

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

1 28 36 .69

5 82 .8 6

59 45 .1 4

5 09 58 .3 7

51 03. 01

6 3.8 0

0. 65

33 16 .9 6

4 1. 47

2 4.1 3

84 .45

2 36 .5 4

-9 68 6.4 5

-3 17 7.5 7

- 20 91 .04

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

1 32 74 .03

5 78 .0 0

58 95 .6 0

6 48 51 .6 0

51 03. 01

7 8.1 3

0. 65

33 16 .9 6

5 0. 78

2 4.1 3 2 4.1 3

84 .45 84 .45

2 34 .7 1 2 32 .8 5

-9 30 3.3 7 -8 91 3.7 5

-3 11 5.8 9 -3 05 3.1 6

- 20 91 .04 - 20 91 .04

0. 00 0. 00

2 09 1.0 4 2 09 1.0 4

41 82 .09 41 82 .09

2 19 55 .9 6 2 19 55 .9 6

1 37 18 .78 1 41 71 .14

5 73 .1 4 5 68 .2 9

58 46 .0 6 57 96 .5 1

7 85 04 .2 0 9 19 16 .1 6

51 03. 01 51 03. 01

9 2.2 2 10 6.0 9

0. 65 0. 65

33 16 .9 6 33 16 .9 6

5 9. 94 6 8. 96

2 4.1 3

84 .45

2 30 .9 6

-8 51 7.4 0

-2 98 9.3 5

- 20 91 .04

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

1 46 31 .30

5 63 .4 3

57 46 .9 7 1 050 87 .4 8

51 03. 01

11 9.7 2

0. 65

33 16 .9 6

7 7. 82

2 4.1 3

84 .45

2 29 .0 4

-8 11 4.1 6

-2 92 4.4 3

- 20 91 .04

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

1 50 99 .46

5 58 .5 7

56 97 .4 3 1 180 18 .1 6

51 03. 01

13 3.1 2

0. 65

33 16 .9 6

8 6. 53

2 4.1 3 2 4.1 3

84 .45 84 .45

2 27 .0 8 2 25 .0 8

-7 70 3.8 5 -7 28 6.2 7

-2 85 8.3 7 -2 79 1.1 4

- 20 91 .04 - 20 91 .04

0. 00 0. 00

2 09 1.0 4 2 09 1.0 4

41 82 .09 41 82 .09

2 19 55 .9 6 2 19 55 .9 6

1 55 75 .83 1 60 60 .64

5 53 .7 1 5 48 .8 6

56 47 .8 9 1 307 08 .2 1 55 98 .3 4 1 431 57 .6 2

51 03. 01 5 10 3. 01

14 6.2 8 15 9.2 2

0. 65 0. 65

33 16 .9 6 33 16 .9 6

9 5. 08 10 3. 49

2 4.1 3

84 .45

2 22 .8 0

-6 86 1.2 4

-2 72 2.7 1

- 20 69 .26

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

1 65 75 .88

5 44 .0 0

55 48 .8 0 1 553 66 .4 0

5 10 3. 01

17 1.9 4

0. 65

33 16 .9 6

11 1. 76

2 4.1 3

84 .45

2 20 .4 1

-6 42 8.5 5

-2 65 3.0 5

- 20 40 .81

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

1 71 06 .69

5 39 .1 4

54 99 .2 6 1 673 34 .5 4

5 10 3. 01

18 4.4 4

0. 65

33 16 .9 6

11 9. 89

2 4.1 3 2 4.1 3

84 .45 84 .45

2 17 .9 7 2 15 .4 9

-5 98 7.9 9 -5 53 9.3 5

-2 58 2.1 2 -2 50 9.8 9

- 20 11 .84 - 19 82 .34

0. 00 0. 00

2 09 1.0 4 2 09 1.0 4

41 82 .09 41 82 .09

2 19 55 .9 6 2 19 55 .9 6

1 76 47 .14 1 81 97 .52

5 34 .2 9 5 29 .4 3

54 49 .7 1 1 790 62 .0 4 54 00 .1 7 1 905 48 .9 1

5 10 3. 01 5 10 3. 01

19 6.7 1 20 8.7 5

0. 65 0. 65

33 16 .9 6 33 16 .9 6

12 7. 86 13 5. 69

2 4.1 3

84 .45

2 12 .9 6

-5 08 2.4 0

-2 43 6.3 2

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0. 00

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41 82 .09

2 19 55 .9 6

1 87 58 .09

5 24 .5 7

53 50 .6 3 2 017 95 .1 3

5 10 3. 01

22 0.5 5

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14 3. 36

2 4.1 3

84 .45

2 10 .3 8

-4 61 6.9 1

-2 36 1.3 8

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0. 00

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2 19 55 .9 6

1 93 29 .13

5 19 .7 1

53 01 .0 9 2 128 00 .7 3

5 10 3. 01

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15 0. 88

2 4.1 3

84 .45

2 07 .7 6

-4 14 2.6 3

-2 28 5.0 2

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0. 00

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2 19 55 .9 6

1 99 10 .95

5 14 .8 6

52 51 .5 4 2 235 65 .6 8

5 10 3. 01

24 3.4 8

0. 65

33 16 .9 6

15 8. 26

2 4.1 3 2 4.1 3

84 .45 84 .45

2 05 .0 8 2 02 .3 6

-3 65 9.3 3 -3 16 6.7 3

-2 20 7.2 1 -2 12 7.9 1

- 18 58 .71 - 18 26 .31

0. 00 0. 00

2 09 1.0 4 2 09 1.0 4

41 82 .09 41 82 .09

2 19 55 .9 6 2 19 55 .9 6

2 05 03 .85 2 11 08 .15

5 10 .0 0 5 05 .1 4

52 02 .0 0 2 340 90 .0 0 51 52 .4 6 2 443 73 .6 8

5 10 3. 01 5 10 3. 01

25 4.5 9 26 5.4 8

0. 65 0. 65

33 16 .9 6 33 16 .9 6

16 5. 49 17 2. 56

2 4.1 3

84 .45

1 99 .5 8

-2 66 4.5 6

-2 04 7.0 6

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0. 00

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2 19 55 .9 6

2 17 24 .19

5 00 .2 9

51 02 .9 1 2 544 16 .7 3

5 10 3. 01

27 6.1 4

0. 65

33 16 .9 6

17 9. 49

2 4.1 3

84 .45

1 96 .7 5

-2 15 2.5 5

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0. 00

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41 82 .09

2 19 55 .9 6

2 23 52 .30

4 95 .4 3

50 53 .3 7 2 642 19 .1 3

5 10 3. 01

28 6.5 7

0. 65

33 16 .9 6

18 6. 27

2 4.1 3 2 4.1 3

84 .45 84 .45

1 93 .8 6 1 90 .9 1

-1 63 0.3 9 -1 09 7.8 0

-1 88 0.5 6 -1 79 4.8 1

- 17 25 .28 - 16 90 .26

0. 00 0. 00

2 09 1.0 4 2 09 1.0 4

41 82 .09 41 82 .09

2 19 55 .9 6 2 19 55 .9 6

2 29 92 .86 2 36 46 .22

4 90 .5 7 4 85 .7 1

50 03 .8 3 2 737 80 .9 1 49 54 .2 9 2 831 02 .0 4

5 10 3. 01 5 10 3. 01

29 6.7 7 30 6.7 5

0. 65 0. 65

33 16 .9 6 33 16 .9 6

19 2. 90 19 9. 39

2 4.1 3

84 .45

1 87 .9 0

- 55 4.4 4

-1 70 7.3 3

- 16 54 .53

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

2 43 12 .79

4 80 .8 6

49 04 .7 4 2 921 82 .5 4

50 92. 64

31 6.5 0

0. 65

33 10 .2 2

20 5. 72

2 4.1 3

84 .45

1 84 .8 3

0 .0 0

-1 61 8.0 7

- 16 18 .07

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

2 49 92 .96

4 76 .0 0

48 55 .2 0 3 010 22 .4 0

50 40. 03

32 6.0 2

0. 65

32 76 .0 2

21 1. 91

2 4.1 3

84 .45

1 81 .7 0

56 5.8 8

-1 52 6.9 7

- 15 80 .86

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

2 56 87 .15

4 71 .1 4

48 05 .6 6 3 096 21 .6 2

49 87. 36

33 5.3 1

0. 65

32 41 .7 8

21 7. 95

2 4.1 3 2 4.1 3

84 .45 84 .45

1 78 .5 1 1 75 .2 4

1 14 3.5 4 1 73 3.3 7

-1 43 3.9 6 -1 33 9.0 0

- 15 42 .87 - 15 04 .08

0. 00 0. 00

2 09 1.0 4 2 09 1.0 4

41 82 .09 41 82 .09

2 19 55 .9 6 2 19 55 .9 6

2 63 95 .80 2 71 19 .37

4 66 .2 9 4 61 .4 3

47 56 .1 1 3 179 80 .2 1 47 06 .5 7 3 260 98 .1 6

49 34. 62 48 81. 81

34 4.3 8 35 3.2 2

0. 65 0. 65

32 07 .5 0 31 73 .1 8

22 3. 84 22 9. 59

2 4.1 3

84 .45

1 71 .9 1

2 33 5.7 4

-1 24 2.0 2

- 14 64 .47

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

2 78 58 .34

4 56 .5 7

46 57 .0 3 3 339 75 .4 8

48 28. 94

36 1.8 3

0. 65

31 38 .8 1

23 5. 19

2 4.1 3

84 .45

1 68 .5 0

2 95 1.0 7

-1 14 2.9 5

- 14 24 .01

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

2 86 13 .20

4 51 .7 1

46 07 .4 9 3 416 12 .1 6

47 75. 99

37 0.2 3

0. 65

31 04 .3 9

24 0. 65

2 4.1 3

84 .45

1 65 .0 2

3 57 9.7 8

-1 04 1.7 3

- 13 82 .67

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

2 93 84 .47

4 46 .8 6

45 57 .9 4 3 490 08 .2 0

47 22. 97

37 8.3 9

0. 65

30 69 .9 3

24 5. 96

2 4.1 3 2 4.1 3

84 .45 84 .45

1 61 .4 7 1 57 .8 3

4 22 2.3 0 4 87 9.1 0

- 93 8.2 9 - 83 2.5 5

- 13 40 .41 - 12 97 .22

0. 00 0. 00

2 09 1.0 4 2 09 1.0 4

41 82 .09 41 82 .09

2 19 55 .9 6 2 19 55 .9 6

3 01 72 .69 3 09 78 .43

4 42 .0 0 4 37 .1 4

45 08 .4 0 3 561 63 .6 0 44 58 .8 6 3 630 78 .3 7

46 69. 87 46 16. 69

38 6.3 4 39 4.0 6

0. 65 0. 65

30 35 .4 1 30 00 .8 5

25 1. 12 25 6. 14

2 4.1 3

84 .45

1 54 .1 2

5 55 0.6 6

- 72 4.4 3

- 12 53 .06

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

3 18 02 .27

4 32 .2 9

44 09 .3 1 3 697 52 .5 0

45 63. 43

40 1.5 5

0. 65

29 66 .2 3

26 1. 01

2 4.1 3

84 .45

1 50 .3 2

6 23 7.4 9

- 61 3.8 5

- 12 07 .89

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

3 26 44 .84

4 27 .4 3

43 59 .7 7 3 761 85 .9 9

45 10. 09

40 8.8 3

0. 65

29 31 .5 6

26 5. 74



Fs1

Fs2

Fs3

Fs4

Fs5

0. 00 27 6

MPa - 75 .86

MPa 28 .7 4

MPa 1 33 .3 3

MPa 2 37 .9 3

MPa 2 40 .0 0

MPa 2 40 .00

MPa 24 0. 00

kN -2 6. 69

kN 2 .89

kN 1 3. 40

kN 2 3. 92

kN 24 .1 3

0. 00 27 6

- 83 .72

22 .0 9

1 27 .9 1

2 33 .7 2

2 40 .0 0

2 40 .00

24 0. 00

-2 9. 46

2 .22

1 2. 86

2 3. 50

24 .1 3

0. 00 27 5

- 91 .76

15 .2 9

1 22 .3 5

2 29 .4 1

2 40 .0 0

2 40 .00

24 0. 00

-3 2. 29

1 .54

1 2. 30

2 3. 06

24 .1 3

0. 00 22 1

0. 00 27 5

- 100 .00

8 .3 3

1 16 .6 7

2 25 .0 0

2 40 .0 0

2 40 .00

24 0. 00

-3 5. 19

0 .84

1 1. 73

2 2. 62

24 .1 3

0. 00 165 0. 00 16 3

0. 00 22 0 0 .0 02 19

0. 00 27 5 0. 00 27 4

- 108 .43 - 11 7. 07

1 .2 0 - 6. 10

1 10 .8 4 1 04 .8 8

2 20 .4 8 2 15 .8 5

2 40 .0 0 2 40 .0 0

2 40 .00 2 40 .0 0

24 0. 00 2 40 .0 0

-3 8. 15 - 41 .1 9

0 .12 - 0. 61

1 1. 14 1 0. 54

2 2. 17 2 1. 70

24 .1 3 2 4. 13

0. 00 10 6

0. 00 162

0. 00 21 8

0. 00 27 4

- 125 .93

- 13 .5 8

98 .7 7

2 11 .1 1

2 40 .0 0

2 40 .00

24 0. 00

-4 4. 31

-1 .37

9. 93

2 1. 22

24 .1 3

0. 00 10 3

0. 00 160

0. 00 21 7

0. 00 27 4

- 135 .00

- 21 .2 5

92 .5 0

2 06 .2 5

2 40 .0 0

2 40 .00

24 0. 00

-4 7. 50

-2 .14

9. 30

2 0. 73

24 .1 3

0. 00 04 3

0. 00 10 1

0. 00 158

0. 00 21 6

0. 00 27 3

- 144 .30

- 29 .1 1

86 .0 8

2 01 .2 7

2 40 .0 0

2 40 .00

24 0. 00

-5 0. 77

-2 .93

8. 65

2 0. 23

24 .1 3

-0 .0 001 9 -0 .0 002 3

0. 00 04 0 0. 00 03 6

0. 00 09 8 0. 00 09 5

0. 00 156 0. 00 155

0. 00 21 5 0. 00 21 4

0. 00 27 3 0. 00 27 3

- 153 .85 - 163 .64

- 37 .1 8 - 45 .4 5

79 .4 9 72 .7 3

1 96 .1 5 1 90 .9 1

2 40 .0 0 2 40 .0 0

2 40 .00 2 40 .00

24 0. 00 24 0. 00

-5 4. 13 -5 7. 58

-3 .74 -4 .57

7. 99 7. 31

1 9. 72 1 9. 19

24 .1 3 24 .1 3

- 0. 00 087

-0 .0 002 7

0. 00 03 3

0. 00 09 3

0. 00 153

0. 00 21 3

0. 00 27 2

- 173 .68

- 53 .9 5

65 .7 9

1 85 .5 3

2 40 .0 0

2 40 .00

24 0. 00

-6 1. 11

-5 .42

6. 61

1 8. 65

24 .1 3

- 0. 00 092

-0 .0 003 1

0. 00 02 9

0. 00 09 0

0. 00 151

0. 00 21 1

0. 00 27 2

- 184 .00

- 62 .6 7

58 .6 7

1 80 .0 0

2 40 .0 0

2 40 .00

24 0. 00

-6 4. 74

-6 .30

5. 90

1 8. 10

24 .1 3

42 2. 9 41 7. 1

- 0. 00 097 - 0. 00 103

-0 .0 003 6 -0 .0 004 0

0. 00 02 6 0. 00 02 2

0. 00 08 7 0. 00 08 4

0. 00 149 0. 00 147

0. 00 21 0 0. 00 20 9

0. 00 27 2 0. 00 27 1

- 194 .59 - 205 .48

- 71 .6 2 - 80 .8 2

51 .3 5 43 .8 4

1 74 .3 2 1 68 .4 9

2 40 .0 0 2 40 .0 0

2 40 .00 2 40 .00

24 0. 00 24 0. 00

-6 8. 47 -7 2. 30

-7 .20 -8 .13

5. 16 4. 41

1 7. 52 1 6. 94

24 .1 3 24 .1 3

41 1. 4

- 0. 00 108

-0 .0 004 5

0. 00 01 8

0. 00 08 1

0. 00 144

0. 00 20 8

0. 00 27 1

- 216 .67

- 90 .2 8

36 .1 1

1 62 .5 0

2 40 .0 0

2 40 .00

24 0. 00

-7 6. 24

-9 .08

3. 63

1 6. 34

24 .1 3

4 05 .7

- 0. 00 11 4

- 0. 00 05 0

0. 00 01 4

0. 00 07 8

0. 00 14 2

0 .0 02 06

0. 00 27 0

- 2 28 .1 7

-1 00 .0 0

2 8. 17

1 56 .3 4

2 40 .0 0

2 40 .0 0

2 40 .0 0

- 80 .2 8

- 10 .0 5

2 .8 3

1 5. 72

2 4. 13

4 00 .0 3 94 .3

- 0. 00 12 0 - 0. 00 12 6

- 0. 00 05 5 - 0. 00 06 0

0. 00 01 0 0. 00 00 6

0. 00 07 5 0. 00 07 2

0. 00 14 0 0. 00 13 8

0 .0 02 05 0 .0 02 04

0. 00 27 0 0. 00 27 0

- 2 40 .0 0 - 2 40 .0 0

-1 10 .0 0 -1 20 .2 9

2 0. 00 1 1. 59

1 50 .0 0 1 43 .4 8

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

- 84 .4 5 - 84 .4 5

- 11 .0 6 - 12 .0 9

2 .0 1 1 .1 7

1 5. 08 1 4. 42

2 4. 13 2 4. 13

3 88 .6

- 0. 00 13 2

- 0. 00 06 5

0. 00 00 1

0. 00 06 8

0. 00 13 5

0 .0 02 02

0. 00 26 9

- 24 0. 00

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2 .9 4

1 36 .7 6

2 40 .0 0

2 40 .0 0

2 40 .0 0

- 84 .4 5

- 13 .1 6

0 .3 0

1 3. 75

2 4. 13

3 82 .9

- 0. 00 13 9

- 0. 00 07 1 - 0. 00 00 3

0 .0 00 65

0 . 00 13 3

0 .0 02 01

0 .0 02 69

- 24 0. 00

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- 5. 97

1 29 .8 5

2 40 .0 0

2 40 .0 0

2 40 .0 0

- 84 .4 5

- 14 .2 5

- 0. 60

1 3. 05

2 4. 13

3 77 .1

- 0. 00 14 5

-0 .0 00 77 - 0. 00 00 8

0 .0 00 61

0 . 00 13 0

0 .0 01 99

0 .0 02 68

- 24 0. 00

- 15 3. 03

- 15 .1 5

1 22 .7 3

2 40 .0 0

2 40 .0 0

2 40 .0 0

- 84 .4 5

- 15 .3 8

- 1. 52

1 2. 34

2 4. 13

3 71 .4 3 65 .7

- 0. 00 15 2 - 0. 00 15 9

-0 .0 00 82 - 0. 00 01 2 -0 .0 00 88 - 0. 00 01 7

0 .0 00 58 0 .0 00 54

0 . 00 12 8 0 . 00 12 5

0 .0 01 98 0 .0 01 96

0 .0 02 68 0 .0 02 67

- 24 0. 00 - 24 0. 00

- 16 4. 62 - 17 6. 56

- 24 .6 2 - 34 .3 7

1 15 .3 8 1 07 .8 1

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

- 84 .4 5 - 84 .4 5

- 16 .5 5 - 17 .7 5

- 2. 47 - 3. 46

1 1. 60 1 0. 84

2 4. 13 2 4. 13

3 60 .0

- 0. 00 16 7

-0 .0 00 94 - 0. 00 02 2

0 .0 00 50

0 . 00 12 2

0 .0 01 94

0 .0 02 67

- 24 0. 00

- 18 8. 89

- 44 .4 4

1 00 .0 0

2 40 .0 0

2 40 .0 0

2 40 .0 0

- 84 .4 5

- 18 .9 9

- 4. 47

1 0. 05

2 4. 13

3 54 .3

- 0. 00 17 4

- 0. 00 10 1 - 0. 00 02 7

0. 00 04 6

0. 00 11 9

0 .0 01 93

0. 00 26 6

- 2 40 .0 0

-2 01 .6 1

- 54 .8 4

9 1. 94

2 38 .7 1

2 40 .0 0

2 40 .0 0

- 84 .4 5

- 20 .2 7

- 5. 51

9 .2 4

2 4. 00

3 48 .6 3 42 .9

- 0. 00 18 2 - 0. 00 19 0

- 0. 00 10 7 - 0. 00 03 3 - 0. 00 11 4 - 0. 00 03 8

0. 00 04 2 0. 00 03 8

0. 00 11 6 0. 00 11 3

0 .0 01 91 0 .0 01 89

0. 00 26 6 0. 00 26 5

- 2 40 .0 0 - 2 40 .0 0

-2 14 .7 5 -2 28 .3 3

- 65 .5 7 - 76 .6 7

8 3. 61 7 5. 00

2 32 .7 9 2 26 .6 7

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

- 84 .4 5 - 84 .4 5

- 21 .5 9 - 22 .9 5

- 6. 59 - 7. 71

8 .4 1 7 .5 4

2 3. 40 2 2. 79

3 37 .1

- 0. 00 19 8

- 0. 00 12 1 - 0. 00 04 4

0. 00 03 3

0. 00 11 0

0 .0 01 87

0. 00 26 4

- 2 40 .0 0

-2 40 .0 0

- 88 .1 4

6 6. 10

2 20 .3 4

2 40 .0 0

2 40 .0 0

- 84 .4 5

- 24 .1 3

- 8. 86

6 .6 5

2 2. 15

3 31 .4

- 0. 00 20 7

-0 .0 01 28 - 0. 00 05 0

0 .0 00 28

0 . 00 10 7

0 .0 01 85

0 .0 02 64

- 24 0. 00

- 24 0. 00

- 10 0. 00

5 6. 90

2 13 .7 9

2 40 .0 0

2 40 .0 0

- 84 .4 5

- 24 .1 3

- 10 .0 5

5 .7 2

2 1. 49

3 25 .7

- 0. 00 21 6

-0 .0 01 36 - 0. 00 05 6

0 .0 00 24

0 . 00 10 4

0 .0 01 83

0 .0 02 63

- 24 0. 00

- 24 0. 00

- 11 2. 28

4 7. 37

2 07 .0 2

2 40 .0 0

2 40 .0 0

- 84 .4 5

- 24 .1 3

- 11 .2 9

4 .7 6

2 0. 81

3 20 .0 3 14 .3

- 0. 00 22 5 - 0. 00 23 5

-0 .0 01 44 - 0. 00 06 2 -0 .0 01 52 - 0. 00 06 9

0 .0 00 19 0 .0 00 14

0 . 00 10 0 0 . 00 09 6

0 .0 01 81 0 .0 01 79

0 .0 02 63 0 .0 02 62

- 24 0. 00 - 24 0. 00

- 24 0. 00 - 24 0. 00

- 12 5. 00 - 13 8. 18

3 7. 50 2 7. 27

2 00 .0 0 1 92 .7 3

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

- 84 .4 5 - 84 .4 5

- 24 .1 3 - 24 .1 3

- 12 .5 7 - 13 .8 9

3 .7 7 2 .7 4

2 0. 11 1 9. 38

3 08 .6

- 0. 00 24 4

-0 .0 01 60 - 0. 00 07 6

0 .0 00 08

0 . 00 09 3

0 .0 01 77

0 .0 02 61

- 24 0. 00

- 24 0. 00

- 15 1. 85

1 6. 67

1 85 .1 9

2 40 .0 0

2 40 .0 0

- 84 .4 5

- 24 .1 3

- 15 .2 7

1 .6 8

1 8. 62

3 02 .9

- 0. 00 25 5

- 0. 00 16 9 - 0. 00 08 3

0 .0 00 03

0 . 00 08 9

0 .0 01 75

0 .0 02 60

- 24 0. 00

- 24 0. 00

- 16 6. 04

5 .6 6

1 77 .3 6

2 40 .0 0

2 40 .0 0

- 84 .4 5

- 24 .1 3

- 16 .6 9

0 .5 7

1 7. 83

2 97 .1

- 0. 00 26 5

-0 .0 01 78 - 0. 00 09 0 - 0. 00 00 3

0 .0 00 85

0 .0 01 72

0 .0 02 60

- 24 0. 00

- 2 40 .0 0

- 18 0. 77

- 5. 77

1 69 .2 3

2 40 .0 0

2 40 .0 0

- 84 .4 5

- 24 .1 3

- 18 .1 7

- 0. 58

1 7. 01

2 91 .4 2 85 .7

- 0. 00 27 6 - 0. 00 28 8

-0 .0 01 87 - 0. 00 09 8 - 0. 00 00 9 -0 .0 01 97 - 0. 00 10 6 - 0. 00 01 5

0 . 00 08 0 0 . 00 07 6

0 .0 01 70 0 .0 01 67

0 . 00 25 9 0 . 00 25 8

- 24 0. 00 - 24 0. 00

- 2 40 .0 0 - 2 40 .0 0

- 19 6. 08 - 21 2. 00

- 17 .6 5 - 30 .0 0

1 60 .7 8 1 52 .0 0

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

- 84 .4 5 - 84 .4 5

- 24 .1 3 - 24 .1 3

- 19 .7 1 - 21 .3 1

- 1. 77 - 3. 02

1 6. 16 1 5. 28

2 80 .0

- 0. 00 30 0

-0 .0 02 07 - 0. 00 11 4 - 0. 00 02 1

0 . 00 07 1

0 .0 01 64

0 . 00 25 7

- 24 0. 00

- 2 40 .0 0

- 22 8. 57

- 42 .8 6

1 42 .8 6

2 40 .0 0

2 40 .0 0

- 84 .4 5

- 24 .1 3

- 22 .9 8

- 4. 31

1 4. 36

2 74 .3

- 0. 00 31 2

-0 .0 02 18 - 0. 00 12 3 - 0. 00 02 8

0 . 00 06 7

0 .0 01 61

0 . 00 25 6

- 24 0. 00

- 2 40 .0 0

- 24 0. 00

- 56 .2 5

1 33 .3 3

2 40 .0 0

2 40 .0 0

- 84 .4 5

- 24 .1 3

- 24 .1 3

- 5. 65

1 3. 40

c

εs1

εs2

εs3

εs4

εs5

εs6

mm 49 7. 1

- 0. 00 038

0 .0 001 4

0. 00 06 7

0. 00 11 9

0. 00 171

0. 00 22 4

49 1. 4

- 0. 00 042

0 .0 001 1

0. 00 06 4

0. 00 11 7

0. 00 170

0. 00 22 3

48 5. 7

- 0. 00 046

0 .0 000 8

0. 00 06 1

0. 00 11 5

0. 00 168

0. 00 22 2

48 0. 0

- 0. 00 050

0 .0 000 4

0. 00 05 8

0. 00 11 3

0. 00 167

47 4. 3 4 68 .6

- 0. 00 054 - 0. 00 05 9

0 .0 000 1 - 0. 00 00 3

0. 00 05 5 0. 00 05 2

0. 00 11 0 0. 00 10 8

46 2. 9

- 0. 00 063

-0 .0 000 7

0. 00 04 9

45 7. 1

- 0. 00 067

-0 .0 001 1

0. 00 04 6

45 1. 4

- 0. 00 072

-0 .0 001 5

44 5. 7 44 0. 0

- 0. 00 077 - 0. 00 082

43 4. 3 42 8. 6

εs7

f s1

f s2

f s3

f s4

f s5

f s6

f s7


Fs6

Fs7

Cs

kN 2 4.1 3

kN 84 .45

kN 1 46 .2 2

kNmm 6 94 0.1 0

Ms1

kNmm - 50 0.7 3

Ms2

k Nmm - 11 61 .69

Ms3

kNmm 0. 00

Ms4

kNmm 2 09 1.0 4

Ms5

kNmm 41 82 .09

Ms6

k Nmm 2 19 55 .9 6

Ms7

kNmm 3 35 06 .78

Ms

mm 4 22 .5 7

kN kNmm 43 10 .2 3 3 823 78 .8 5

kN 44 56. 45

kNm 41 5.8 9

Cc

Mc

2 4.1 3

84 .45

1 41 .8 2

7 65 9.0 6

- 38 4.9 8

- 11 14 .41

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

3 43 88 .76

4 17 .7 1

42 60 .6 9 3 883 31 .0 7

44 02. 50

2 4.1 3

84 .45

1 37 .3 1

8 39 4.9 3

- 26 6.5 1

- 10 66 .02

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

3 52 91 .49

4 12 .8 6

42 11 .1 4 3 940 42 .6 5

43 48. 46

2 4.1 3

84 .45

1 32 .7 0

9 14 8.3 2

- 14 5.2 1

- 10 16 .48

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

3 62 15 .72

4 08 .0 0

41 61 .6 0 3 995 13 .6 0

2 4.1 3 2 4.1 3

84 .45 84 .45

1 27 .9 8 1 23 .1 4

9 91 9.8 6 10 71 0.2 3

-2 0.9 9 10 6.2 5

-9 65 .74 -9 13 .77

0. 00 0. 00

2 09 1.0 4 2 09 1.0 4

41 82 .09 41 82 .09

2 19 55 .9 6 2 19 55 .9 6

3 71 62 .22 3 81 31 .80

4 03 .1 4 3 98 .2 9

2 4.1 3

84 .45

1 18 .1 8

11 52 0.1 0

23 6.6 4

-8 60 .51

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

3 91 25 .33

2 4.1 3

84 .45

1 13 .1 0

12 35 0.2 3

37 0.2 9

-8 05 .92

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

4 01 43 .69

2 4.1 3

84 .45

1 07 .8 9

13 20 1.3 7

50 7.3 2

-7 49 .95

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

2 4.1 3 2 4.1 3

84 .45 84 .45

1 02 .5 4 97 .0 6

14 07 4.3 4 14 96 9.9 7

64 7.8 7 79 2.0 6

-6 92 .55 -6 33 .65

0. 00 0. 00

2 09 1.0 4 2 09 1.0 4

41 82 .09 41 82 .09

2 19 55 .9 6 2 19 55 .9 6

2 4.1 3

84 .45

91 .4 3

15 88 9.1 8

94 0.0 5

-5 73 .20

0. 00

2 09 1.0 4

41 82 .09

2 4.1 3

84 .45

85 .6 5

16 83 2.9 0

1 09 1.9 9

-5 11 .14

0. 00

2 09 1.0 4

41 82 .09

2 4.1 3 2 4.1 3

84 .45 84 .45

79 .7 2 73 .6 2

17 80 2.1 3 18 79 7.9 1

1 24 8.0 3 1 40 8.3 5

-4 47 .41 -3 81 .93

0. 00 0. 00

2 09 1.0 4 2 09 1.0 4

2 4.1 3

84 .45

67 .3 6

19 82 1.3 6

1 57 3.1 2

-3 14 .62

0. 00

2 4.1 3

84 .45

60 .9 1

20 87 3.6 3

1 74 2.5 4

-2 45 .43

0. 00

2 4.1 3 2 4.1 3

84 .45 84 .45

54 .2 9 51 .7 5

21 95 5.9 6 21 95 5.9 6

1 91 6.7 9 2 09 6.0 9

-1 74 .25 -1 01 .02

2 4.1 3

84 .45

49 .1 4

21 95 5.9 6

2 28 0.6 7

2 4.1 3

84 .45

46 .4 5

21 95 5.9 6

2 47 0.7 6

2 4.1 3

84 .45

43 .6 9

21 95 5.9 6

2 4.1 3 2 4.1 3

84 .45 84 .45

40 .8 3 37 .8 9

2 4.1 3

84 .45

2 4.1 3

84 .45

2 4.1 3 2 4.1 3

Ф.Pn

Ф.Mn

0. 65

kN 28 96 .6 9

kNm 27 0. 33

42 2.7 2

0. 65

28 61 .6 3

27 4. 77

42 9.3 3

0. 65

28 26 .5 0

27 9. 07

42 94. 30

43 5.7 3

0. 65

27 91 .3 0

28 3. 22

41 12 .0 6 4 047 43 .9 1 40 62 .5 1 4 097 33 .5 8

42 40. 03 41 85. 65

44 1.9 1 44 7.8 7

0. 65 0. 65

27 56 .0 2 27 20 .6 7

28 7. 24 29 1. 11

3 93 .4 3

40 12 .9 7 4 144 82 .6 2

41 31. 15

45 3.6 1

0. 65

26 85 .2 5

29 4. 85

3 88 .5 7

39 63 .4 3 4 189 91 .0 2

40 76. 53

45 9.1 3

0. 65

26 49 .7 4

29 8. 44

4 11 87 .83

3 83 .7 1

39 13 .8 9 4 232 58 .7 8

40 21. 77

46 4.4 5

0. 65

26 14 .1 5

30 1. 89

4 22 58 .75 4 33 57 .48

3 78 .8 6 3 74 .0 0

38 64 .3 4 4 272 85 .9 1 38 14 .8 0 4 310 72 .4 0

39 66. 88 39 11. 86

46 9.5 4 47 4.4 3

0. 65 0. 65

25 78 .4 7 25 42 .7 1

30 5. 20 30 8. 38

2 19 55 .9 6

4 44 85 .13

3 69 .1 4

37 65 .2 6 4 346 18 .2 5

38 56. 69

47 9.1 0

0. 65

25 06 .8 5

31 1. 42

2 19 55 .9 6

4 56 42 .85

3 64 .2 9

37 15 .7 1 4 379 23 .4 7

38 01. 37

48 3.5 7

0. 65

24 70 .8 9

31 4. 32

41 82 .09 41 82 .09

2 19 55 .9 6 2 19 55 .9 6

4 68 31 .85 4 80 53 .43

3 59 .4 3 3 54 .5 7

36 66 .1 7 4 409 88 .0 5 36 16 .6 3 4 438 11 .9 9

37 45. 89 36 90. 25

48 7.8 2 49 1.8 7

0. 65 0. 65

24 34 .8 3 23 98 .6 6

31 7. 08 31 9. 71

2 09 1.0 4

41 82 .09

2 19 55 .9 6

4 93 08 .95

3 49 .7 1

35 67 .0 9 4 463 95 .3 0

36 34. 44

49 5.7 0

0. 65

23 62 .3 9

32 2. 21

2 09 1.0 4

41 82 .09

2 19 55 .9 6

5 05 99 .83

3 44 .8 6

35 17 .5 4 4 487 37 .9 7

35 78. 46

49 9.3 4

0. 65

23 26 .0 0

32 4. 57

0. 00 0. 00

2 09 1.0 4 2 09 1.0 4

41 82 .09 41 82 .09

2 19 55 .9 6 2 19 55 .9 6

5 19 27 .59 5 21 80 .14

3 40 .0 0 3 35 .1 4

34 68 .0 0 4 508 40 .0 0 34 18 .4 6 4 527 01 .4 0

35 22. 29 34 70. 21

50 2.7 7 50 4.8 8

0. 65 0. 65

22 89 .4 9 22 55 .6 4

32 6. 80 32 8. 17

- 25 .63

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

5 24 40 .11

3 30 .2 9

33 68 .9 1 4 543 22 .1 6

34 18. 06

50 6.7 6

0. 65

22 21 .7 4

32 9. 40

5 2. 02

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

5 27 07 .83

3 25 .4 3

33 19 .3 7 4 557 02 .2 8

33 65. 83

50 8.4 1

0. 65

21 87 .7 9

33 0. 47

2 66 6.6 1

1 32 .01

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

5 29 83 .68

3 20 .5 7

32 69 .8 3 4 568 41 .7 6

33 13. 51

50 9.8 3

0. 65

21 53 .7 8

33 1. 39

21 95 5.9 6 21 95 5.9 6

2 86 8.4 8 3 07 6.6 7

2 14 .47 2 99 .50

0. 00 0. 00

2 09 1.0 4 2 09 1.0 4

41 82 .09 41 82 .09

2 19 55 .9 6 2 19 55 .9 6

5 32 68 .01 5 35 61 .22

3 15 .7 1 3 10 .8 6

32 20 .2 9 4 577 40 .6 1 31 70 .7 4 4 583 98 .8 2

32 61. 12 32 08. 63

51 1.0 1 51 1.9 6

0. 65 0. 65

21 19 .7 3 20 85 .6 1

33 2. 16 33 2. 77

34 .8 5

21 95 5.9 6

3 29 1.4 6

3 87 .23

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

5 38 63 .75

3 06 .0 0

31 21 .2 0 4 588 16 .4 0

31 56. 05

51 2.6 8

0. 65

20 51 .4 3

33 3. 24

31 .5 9

21 95 5.9 6

3 51 3.1 8

4 77 .79

0. 00

2 07 9.8 0

41 82 .09

2 19 55 .9 6

5 41 64 .79

3 01 .1 4

30 71 .6 6 4 589 93 .3 4

31 03. 24

51 3.1 6

0. 65

20 17 .1 1

33 3. 55

84 .45 84 .45

27 .7 5 23 .7 9

21 95 5.9 6 21 95 5.9 6

3 74 2.1 7 3 97 8.7 9

5 71 .32 6 67 .97

0. 00 0. 00

2 02 8.2 0 1 97 4.8 7

41 82 .09 41 82 .09

2 19 55 .9 6 2 19 55 .9 6

5 44 35 .70 5 47 15 .65

2 96 .2 9 2 91 .4 3

30 22 .1 1 4 589 29 .6 4 29 72 .5 7 4 586 25 .3 1

30 49. 87 29 96. 36

51 3.3 7 51 3.3 4

0. 65 0. 65

19 82 .4 1 19 47 .6 4

33 3. 69 33 3. 67

2 4.1 3

84 .45

19 .9 4

21 95 5.9 6

4 18 2.0 9

7 67 .90

0. 00

1 91 9.7 4

41 82 .09

2 19 55 .9 6

5 49 63 .74

2 86 .5 7

29 23 .0 3 4 580 80 .3 3

29 42. 96

51 3.0 4

0. 65

19 12 .9 3

33 3. 48

2 4.1 3

84 .45

17 .1 6

21 95 5.9 6

4 18 2.0 9

8 71 .27

0. 00

1 86 2.7 1

41 82 .09

2 19 55 .9 6

5 50 10 .08

2 81 .7 1

28 73 .4 9 4 572 94 .7 3

28 90. 65

51 2.3 0

0. 65

18 78 .9 2

33 3. 00

2 4.1 3

84 .45

14 .2 9

21 95 5.9 6

4 18 2.0 9

9 78 .27

0. 00

1 80 3.6 8

41 82 .09

2 19 55 .9 6

5 50 58 .05

2 76 .8 6

28 23 .9 4 4 562 68 .4 8

28 38. 23

51 1.3 3

0. 65

18 44 .8 5

33 2. 36

2 4.1 3 2 4.1 3

84 .45 84 .45

11 .3 1 8 .2 3

21 95 5.9 6 21 95 5.9 6

4 18 2.0 9 4 18 2.0 9

10 89 .09 12 03 .93

0. 00 0. 00

1 74 2.5 4 1 67 9.1 7

41 82 .09 41 82 .09

2 19 55 .9 6 2 19 55 .9 6

5 51 07 .72 5 51 59 .21

2 72 .0 0 2 67 .1 4

27 74 .4 0 4 550 01 .6 0 27 24 .8 6 4 534 94 .0 8

27 85. 71 27 33. 08

51 0.1 1 50 8.6 5

0. 65 0. 65

18 10 .7 1 17 76 .5 0

33 1. 57 33 0. 62

2 4.1 3

84 .45

5 .0 3

21 95 5.9 6

4 18 2.0 9

13 23 .04

0. 00

1 61 3.4 6

41 82 .09

2 19 55 .9 6

5 52 12 .60

2 62 .2 9

26 75 .3 1 4 517 45 .9 3

26 80. 34

50 6.9 6

0. 65

17 42 .2 2

32 9. 52

2 4.1 3

84 .45

1 .7 1

21 95 5.9 6

4 18 2.0 9

14 46 .63

0. 00

1 54 5.2 7

41 82 .09

2 19 55 .9 6

5 52 68 .00

2 57 .4 3

26 25 .7 7 4 497 57 .1 3

26 27. 48

50 5.0 3

0. 65

17 07 .8 6

32 8. 27

2 4.1 3

84 .45

-1 .7 4

21 95 5.9 6

4 18 2.0 9

15 74 .99

0. 00

1 47 4.4 5

41 82 .09

2 19 55 .9 6

5 53 25 .54

2 52 .5 7

25 76 .2 3 4 475 27 .7 1

25 74. 49

50 2.8 5

0. 65

16 73 .4 2

32 6. 85

2 4.1 3 2 4.1 3

84 .45 84 .45

-5 .3 2 -9 .0 5

21 95 5.9 6 21 95 5.9 6

4 18 2.0 9 4 18 2.0 9

17 08 .37 18 47 .09

0. 00 0. 00

1 40 0.8 6 1 32 4.3 3

41 82 .09 41 82 .09

2 19 55 .9 6 2 19 55 .9 6

5 53 85 .33 5 54 47 .52

2 47 .7 1 2 42 .8 6

25 26 .6 9 4 450 57 .6 4 24 77 .1 4 4 423 46 .9 4

25 21. 36 24 68. 10

50 0.4 4 49 7.7 9

0. 65 0. 65

16 38 .8 9 16 04 .2 6

32 5. 29 32 3. 57

2 4.1 3

84 .45

- 12 .9 3

21 95 5.9 6

4 18 2.0 9

19 91 .47

0. 00

1 24 4.6 7

41 82 .09

2 19 55 .9 6

5 55 12 .24

2 38 .0 0

24 27 .6 0 4 393 95 .6 0

24 14. 67

49 4.9 1

0. 65

15 69 .5 4

32 1. 69

2 4.1 3

84 .45

- 16 .3 8

21 95 5.9 6

4 18 2.0 9

20 91 .04

0. 00

1 16 1.6 9

41 82 .09

2 19 55 .9 6

5 55 28 .84

2 33 .1 4

23 78 .0 6 4 362 03 .6 2

23 61. 68

49 1.7 3

0. 65

15 35 .0 9

31 9. 63

a

Pn

Mn

Ф



εs7

f s1

f s2

f s3

0 .0 01 59

0 . 00 25 5

MPa - 24 0. 00

MPa - 2 40 .0 0

MPa - 24 0. 00

Fs1

Fs2

Fs3

Fs4

Fs5

MPa - 70 .2 1

MPa 1 23 .4 0

MPa 2 40 .0 0

MPa 2 40 .0 0

kN - 84 .4 5

kN - 24 .1 3

kN - 24 .1 3

kN - 7. 06

kN 1 2. 41

0 .0 01 55

0 . 00 25 4

- 24 0. 00

- 2 40 .0 0

0 .0 00 51

0 .0 01 52

0 .0 02 53

- 24 0. 00

- 24 0. 00

- 24 0. 00

- 84 .7 8

1 13 .0 4

2 40 .0 0

2 40 .0 0

- 84 .4 5

- 24 .1 3

- 24 .1 3

- 8. 52

1 1. 36

- 24 0. 00

- 10 0. 00

1 02 .2 2

2 40 .0 0

2 40 .0 0

- 84 .4 5

- 24 .1 3

- 24 .1 3

- 10 .0 5

-0 .0 02 65 - 0. 00 16 1 - 0. 00 05 8

0 . 00 04 5

0 .0 01 49

0 . 00 25 2

- 24 0. 00

1 0. 28

- 2 40 .0 0

- 24 0. 00

- 11 5. 91

9 0. 91

2 40 .0 0

2 40 .0 0

- 84 .4 5

- 24 .1 3

- 24 .1 3

- 11 .6 5

- 0. 00 38 4 - 0. 00 40 0

-0 .0 02 78 - 0. 00 17 2 - 0. 00 06 6 -0 .0 02 92 - 0. 00 18 3 - 0. 00 07 5

0 . 00 04 0 0 . 00 03 3

0 .0 01 45 0 .0 01 42

0 . 00 25 1 0 . 00 25 0

9 .1 4

- 24 0. 00 - 24 0. 00

- 2 40 .0 0 - 2 40 .0 0

- 24 0. 00 - 24 0. 00

- 13 2. 56 - 15 0. 00

7 9. 07 6 6. 67

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

- 84 .4 5 - 84 .4 5

- 24 .1 3 - 24 .1 3

- 24 .1 3 - 24 .1 3

- 13 .3 3 - 15 .0 8

7 .9 5 6 .7 0

2 34 .3

- 0. 00 41 7

-0 .0 03 06 - 0. 00 19 5 - 0. 00 08 4

0 . 00 02 7

0 .0 01 38

2 28 .6

- 0. 00 43 5

-0 .0 03 21 - 0. 00 20 7 - 0. 00 09 4

0 . 00 02 0

0 .0 01 34

0 . 00 24 9

- 24 0. 00

- 2 40 .0 0

- 24 0. 00

- 16 8. 29

5 3. 66

2 40 .0 0

2 40 .0 0

- 84 .4 5

- 24 .1 3

- 24 .1 3

- 16 .9 2

5 .3 9

0 . 00 24 8

- 24 0. 00

- 2 40 .0 0

- 24 0. 00

- 18 7. 50

4 0. 00

2 40 .0 0

2 40 .0 0

- 84 .4 5

- 24 .1 3

- 24 .1 3

- 18 .8 5

2 22 .9

- 0. 00 45 4

-0 .0 03 37 - 0. 00 22 1 - 0. 00 10 4

0 . 00 01 3

4 .0 2

0 .0 01 29

0 . 00 24 6

- 24 0. 00

- 2 40 .0 0

- 24 0. 00

- 20 7. 69

2 5. 64

2 40 .0 0

2 40 .0 0

- 84 .4 5

- 24 .1 3

- 24 .1 3

- 20 .8 8

2 17 .1 2 11 .4

- 0. 00 47 4 - 0. 00 49 5

2 .5 8

-0 .0 03 54 - 0. 00 23 4 - 0. 00 11 4 0 . 00 00 5 - 0. 00 37 2 - 0. 00 24 9 - 0. 00 12 6 - 0. 00 00 3

0 .0 01 25 0 .0 01 20

0 . 00 24 5 0 .0 02 43

- 24 0. 00 - 24 0. 00

- 2 40 .0 0 - 24 0. 00

- 24 0. 00 - 24 0. 00

- 22 8. 95 - 24 0. 00

1 0. 53 - 5. 41

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

- 84 .4 5 - 84 .4 5

- 24 .1 3 - 24 .1 3

- 24 .1 3 - 24 .1 3

- 23 .0 2 - 24 .1 3

1 .0 6 - 0. 54

2 05 .7 2 00 .0

- 0. 00 51 7

- 0. 00 39 0 - 0. 00 26 4 - 0. 00 13 7 - 0. 00 01 1

0 .0 01 15

0 .0 02 42

- 24 0. 00

- 24 0. 00

- 24 0. 00

- 24 0. 00

- 22 .2 2

2 30 .5 6

2 40 .0 0

- 84 .4 5

- 24 .1 3

- 24 .1 3

- 24 .1 3

- 2. 23

- 0. 00 54 0

- 0. 00 41 0 - 0. 00 28 0 - 0. 00 15 0 - 0. 00 02 0

0 .0 01 10

0 .0 02 40

- 24 0. 00

- 24 0. 00

- 24 0. 00

- 24 0. 00

- 40 .0 0

2 20 .0 0

2 40 .0 0

- 84 .4 5

- 24 .1 3

- 24 .1 3

- 24 .1 3

- 4. 02

1 94 .3 1 88 .6

- 0. 00 56 5 - 0. 00 59 1

- 0. 00 43 1 - 0. 00 29 7 - 0. 00 16 3 - 0. 00 02 9 - 0. 00 45 3 - 0. 00 31 5 - 0. 00 17 7 - 0. 00 03 9

0 .0 01 04 0 .0 00 98

0 .0 02 38 0 .0 02 36

- 24 0. 00 - 24 0. 00

- 24 0. 00 - 24 0. 00

- 24 0. 00 - 24 0. 00

- 24 0. 00 - 24 0. 00

- 58 .8 2 - 78 .7 9

2 08 .8 2 1 96 .9 7

2 40 .0 0 2 40 .0 0

- 84 .4 5 - 84 .4 5

- 24 .1 3 - 24 .1 3

- 24 .1 3 - 24 .1 3

- 24 .1 3 - 24 .1 3

- 5. 91 - 7. 92

182.9

-0.00619

-0.00477 -0.00334 -0.00192 -0.00050

0.00092

0.00234

-240.00

-240.00

-240.00

-240.00

-100.00

184.38

240.00

-84.45

-24.13

-24.13

-24.13

-10.05

177.1

-0.00648

-0.00502 -0.00355 -0.00208 -0.00061

0.00085

0.00232

-240.00

-240.00

-240.00

-240.00

-122.58

170.97

240.00

-84.45

-24.13

-24.13

-24.13

-12.32

171.4 165.7

-0.00680 -0.00714

-0.00528 -0.00377 -0.00225 -0.00073 -0.00557 -0.00400 -0.00243 -0.00086

0.00078 0.00071

0.00230 0.00228

-240.00 -240.00

-240.00 -240.00

-240.00 -240.00

-240.00 -240.00

-146.67 -172.41

156.67 141.38

240.00 240.00

-84.45 -84.45

-24.13 -24.13

-24.13 -24.13

-24.13 -24.13

-14.74 -17.33

160.0

-0.00750

-0.00587 -0.00425 -0.00262 -0.00100

0.00063

0.00225

-240.00

-240.00

-240.00

-240.00

-200.00

125.00

240.00

-84.45

-24.13

-24.13

-24.13

-20.11

154.3

-0.00789

-0.00620 -0.00452 -0.00283 -0.00115

0.00054

0.00222

-240.00

-240.00

-240.00

-240.00

-229.63

107.41

240.00

-84.45

-24.13

-24.13

-24.13

-23.08

148.6

-0.00831

-0.00656 -0.00481 -0.00306 -0.00131

0.00044

0.00219

-240.00

-240.00

-240.00

-240.00

-240.00

88.46

240.00

-84.45

-24.13

-24.13

-24.13

-24.13

142.9 137.1

-0.00876 -0.00925

-0.00694 -0.00512 -0.00330 -0.00148 -0.00735 -0.00546 -0.00356 -0.00167

0.00034 0.00023

0.00216 0.00213

-240.00 -240.00

-240.00 -240.00

-240.00 -240.00

-240.00 -240.00

-240.00 -240.00

68.00 45.83

240.00 240.00

-84.45 -84.45

-24.13 -24.13

-24.13 -24.13

-24.13 -24.13

-24.13 -24.13

136.2

-0.00933

-0.00743 -0.00552 -0.00361 -0.00170

0.00021

0.00212

-240.00

-240.00

-240.00

-240.00

-240.00

42.00

240.00

-84.45

-24.13

-24.13

-24.13

-24.13

0 .0 02 05

0. 00 27 0

- 2 40 .0 0

-1 10 .0 0

2 0. 00

1 50 .0 0

2 40 .0 0

2 40 .0 0

2 40 .0 0

- 84 .4 5

- 11 .0 6

2 .0 1

1 5. 08

2 4. 13

c

εs1

εs2

εs3

εs4

εs5

mm 2 68 .6

- 0. 00 32 6

-0 .0 02 29 - 0. 00 13 2 - 0. 00 03 5

0 . 00 06 2

2 62 .9

- 0. 00 33 9

-0 .0 02 40 - 0. 00 14 1 - 0. 00 04 2

0 . 00 05 7

2 57 .1

- 0. 00 35 3

- 0. 00 25 2 - 0. 00 15 1 - 0. 00 05 0

2 51 .4

- 0. 00 36 8

2 45 .7 2 40 .0

εs6

f s4

f s5

f s6

f s7

KONDISI TEKAN AKSIAL KECIL : Pn = 0.1 * fc' * b * h KONDISI BALANCE 4 00 .0

- 0. 00 12 0

- 0. 00 05 5

0. 00 01 0

0. 00 07 5

0. 00 14 0


Fs6

Fs7

Cs

kN 2 4.1 3

kN 84 .45

kN - 18 .7 8

kNmm 21 95 5.9 6

Ms1

kNmm 4 18 2.0 9

Ms2

k Nmm 20 91 .04

Ms3

kNmm 0. 00

Ms4

kNmm 1 07 5.1 8

Ms5

kNmm 41 82 .09

Ms6

k Nmm 2 19 55 .9 6

Ms7

kNmm 5 54 42 .33

Ms

mm 2 28 .2 9

kN kNmm 23 28 .5 1 4 327 71 .0 1

kN 23 09. 73

kNm 48 8.2 1

Cc

Mc

2 4.1 3

84 .45

- 21 .2 9

21 95 5.9 6

4 18 2.0 9

20 91 .04

0. 00

98 4.9 1

41 82 .09

2 19 55 .9 6

5 53 52 .06

2 23 .4 3

22 78 .9 7 4 290 97 .7 6

22 57. 69

2 4.1 3

84 .45

- 23 .9 0

21 95 5.9 6

4 18 2.0 9

20 91 .04

0. 00

89 0.6 3

41 82 .09

2 19 55 .9 6

5 52 57 .78

2 18 .5 7

22 29 .4 3 4 251 83 .8 8

22 05. 52

2 4.1 3

84 .45

- 26 .6 4

21 95 5.9 6

4 18 2.0 9

20 91 .04

0. 00

79 2.0 6

41 82 .09

2 19 55 .9 6

5 51 59 .21

2 13 .7 1

21 79 .8 9 4 210 29 .3 6

2 4.1 3 2 4.1 3

84 .45 84 .45

- 29 .5 0 - 32 .5 1

21 95 5.9 6 21 95 5.9 6

4 18 2.0 9 4 18 2.0 9

20 91 .04 20 91 .04

0. 00 0. 00

68 8.9 1 58 0.8 5

41 82 .09 41 82 .09

2 19 55 .9 6 2 19 55 .9 6

5 50 56 .06 5 49 47 .99

2 08 .8 6 2 04 .0 0

2 4.1 3

84 .45

- 35 .6 5

21 95 5.9 6

4 18 2.0 9

20 91 .04

0. 00

46 7.5 1

41 82 .09

2 19 55 .9 6

5 48 34 .66

2 4.1 3

84 .45

- 38 .9 6

21 95 5.9 6

4 18 2.0 9

20 91 .04

0. 00

34 8.5 1

41 82 .09

2 19 55 .9 6

5 47 15 .65

2 4.1 3

84 .45

- 42 .4 3

21 95 5.9 6

4 18 2.0 9

20 91 .04

0. 00

22 3.4 0

41 82 .09

2 19 55 .9 6

2 4.1 3 2 4.1 3

84 .45 84 .45

- 46 .0 9 - 48 .8 0

21 95 5.9 6 21 95 5.9 6

4 18 2.0 9 4 18 2.0 9

20 91 .04 20 91 .04

0. 00 0. 00

9 1.7 1 -4 7. 10

41 82 .09 41 82 .09

2 3.1 8

84 .45

- 51 .4 4

21 95 5.9 6

4 18 2.0 9

20 91 .04

0. 00

- 19 3. 62

2 2.1 2

84 .45

- 54 .2 9

21 95 5.9 6

4 18 2.0 9

20 91 .04

0. 00

- 34 8. 51

2 0.9 9 1 9.8 0

84 .45 84 .45

- 57 .3 0 - 60 .5 0

21 95 5.9 6 21 95 5.9 6

4 18 2.0 9 4 18 2.0 9

20 91 .04 20 91 .04

0. 00 0. 00

1 8.5 4

84 .45

- 63 .9 0

21 95 5.9 6

4 18 2.0 9

20 91 .04

1 7.1 9

84 .45

- 67 .5 2

21 95 5.9 6

4 18 2.0 9

20 91 .04

1 5.7 5 1 4.2 1

84 .45 84 .45

- 71 .3 8 - 75 .5 0

21 95 5.9 6 21 95 5.9 6

4 18 2.0 9 4 18 2.0 9

1 2.5 7

84 .45

- 79 .9 2

21 95 5.9 6

1 0.8 0

84 .45

- 84 .6 7

21 95 5.9 6

8 .8 9

84 .45

- 87 .6 2

6 .8 4 4 .6 1

84 .45 84 .45

4 .2 2

84 .45

Ф.Pn

Ф.Mn

0. 65

kN 15 01 .3 3

kNm 31 7. 34

48 4.4 5

0. 65

14 67 .5 0

31 4. 89

48 0.4 4

0. 65

14 33 .5 9

31 2. 29

21 53. 25

47 6.1 9

0. 65

13 99 .6 1

30 9. 52

21 30 .3 4 4 166 34 .2 0 20 80 .8 0 4 119 98 .4 0

21 00. 84 20 48. 29

47 1.6 9 46 6.9 5

0. 65 0. 65

13 65 .5 4 13 31 .3 9

30 6. 60 30 3. 52

1 99 .1 4

20 31 .2 6 4 071 21 .9 7

19 95. 61

46 1.9 6

0. 65

12 97 .1 4

30 0. 27

1 94 .2 9

19 81 .7 1 4 020 04 .9 0

19 42. 76

45 6.7 2

0. 65

12 62 .7 9

29 6. 87

5 45 90 .55

1 89 .4 3

19 32 .1 7 3 966 47 .1 9

18 89. 74

45 1.2 4

0. 65

12 28 .3 3

29 3. 30

2 19 55 .9 6 2 19 55 .9 6

5 44 58 .86 5 43 20 .05

1 84 .5 7 1 79 .7 1

18 82 .6 3 3 910 48 .8 5 18 33 .0 9 3 852 09 .8 7

18 36. 54 17 84. 29

44 5.5 1 43 9.5 3

0. 65 0. 65

11 93 .7 5 11 59 .7 9

28 9. 58 28 5. 69

40 17 .52

2 19 55 .9 6

5 40 08 .96

1 74 .8 6

17 83 .5 4 3 791 30 .2 5

17 32. 10

43 3.1 4

0. 65

11 25 .8 7

28 1. 54

38 33 .58

2 19 55 .9 6

5 36 70 .13

1 70 .0 0

17 34 .0 0 3 728 10 .0 0

16 79. 71

42 6.4 8

0. 65

10 91 .8 1

27 7. 21

- 51 2. 51 - 68 6. 45

36 38 .83 34 32 .27

2 19 55 .9 6 2 19 55 .9 6

5 33 11 .37 5 29 30 .87

1 65 .1 4 1 60 .2 9

16 84 .4 6 3 662 49 .1 1 16 34 .9 1 3 594 47 .5 8

16 27. 15 15 74. 41

41 9.5 6 41 2.3 8

0. 65 0. 65

10 57 .6 5 10 23 .3 7

27 2. 71 26 8. 05

0. 00

- 87 1. 27

32 12 .80

2 19 55 .9 6

5 25 26 .59

1 55 .4 3

15 85 .3 7 3 524 05 .4 2

15 21. 47

40 4.9 3

0. 65

9 88 .9 6

26 3. 21

0. 00

-1 06 8. 01

29 79 .18

2 19 55 .9 6

5 20 96 .23

1 50 .5 7

15 35 .8 3 3 451 22 .6 2

14 68. 31

39 7.2 2

0. 65

9 54 .4 0

25 8. 19

20 91 .04 20 91 .04

0. 00 0. 00

-1 27 7. 86 -1 50 2. 19

27 29 .97 24 63 .59

2 19 55 .9 6 2 19 55 .9 6

5 16 37 .17 5 11 46 .46

1 45 .7 1 1 40 .8 6

14 86 .2 9 3 375 99 .1 8 14 36 .7 4 3 298 35 .1 1

14 14. 91 13 61. 24

38 9.2 4 38 0.9 8

0. 65 0. 65

9 19 .6 9 8 84 .8 1

25 3. 00 24 7. 64

4 18 2.0 9

20 91 .04

0. 00

-1 74 2. 54

21 78 .17

2 19 55 .9 6

5 06 20 .69

1 36 .0 0

13 87 .2 0 3 218 30 .4 0

13 07. 28

37 2.4 5

0. 65

8 49 .7 3

24 2. 09

4 18 2.0 9

20 91 .04

0. 00

-2 00 0. 69

18 71 .61

2 19 55 .9 6

5 00 55 .98

1 31 .1 4

13 37 .6 6 3 135 85 .0 5

12 52. 99

36 3.6 4

0. 65

8 14 .4 4

23 6. 37

21 95 5.9 6

4 18 2.0 9

20 91 .04

0. 00

-2 09 1. 04

15 41 .47

2 19 55 .9 6

4 96 35 .49

1 26 .2 9

12 88 .1 1 3 050 99 .0 7

12 00. 50

35 4.7 3

0. 65

7 80 .3 2

23 0. 58

- 89 .6 7 - 91 .9 0

21 95 5.9 6 21 95 5.9 6

4 18 2.0 9 4 18 2.0 9

20 91 .04 20 91 .04

0. 00 0. 00

-2 09 1. 04 -2 09 1. 04

11 84 .92 7 98 .66

2 19 55 .9 6 2 19 55 .9 6

4 92 78 .94 4 88 92 .68

1 21 .4 3 1 16 .5 7

12 38 .5 7 2 963 72 .4 5 11 89 .0 3 2 874 05 .1 9

11 48. 90 10 97. 13

34 5.6 5 33 6.3 0

0. 65 0. 65

7 46 .7 8 7 13 .1 3

22 4. 67 21 8. 59

- 92 .2 9

21 95 5.9 6

4 18 2.0 9

20 91 .04

0. 00

-2 09 1. 04

7 31 .81

2 19 55 .9 6

4 88 25 .83

1 15 .7 7

11 80 .8 5 2 859 02 .4 7

10 88. 57

33 4.7 3

0. 65

7 07 .5 7

21 7. 57

a

Pn

Mn

Ф

468.00 0.00 468.00 1000.00

2 4.1 3

84 .45

54 .2 9

21 95 5.9 6

1 91 6.7 9

-1 74 .25

0. 00

2 09 1.0 4

41 82 .09

2 19 55 .9 6

5 19 27 .59

3 40 .0 0

34 68 .0 0 4 508 40 .0 0

35 22. 29

50 2.7 7

0. 65

0.00

0.00

22 89 .4 9

32 6. 80


SENGKANG KP-1 40/60 BAHAN STRUKTUR

Kuat tekan beton,

fc' =

30

MPa

Tegangan leleh baja (deform) untuk tulangan lentur,

fy =

350

MPa

Tegangan leleh baja (polos) untuk tulangan geser,

fy =

240

MPa

b= h= D= P= ts =

400 600 16 10 30

mm mm mm mm mm

31.030

kN

DIMENSI BALOK

Lebar balok Tinggi balok Diameter tulangan (deform) yang digunakan, Diameter sengkang (polos) yang digunakan, Tebal bersih selimut beton, MOMEN DAN GAYA GESER RENCANA

Gaya geser rencana akibat beban terfaktor,

Vu-tump =

1. TULANGAN GESER

Vu =

Gaya geser ultimit rencana, Faktor reduksi kekuatan geser, Tegangan leleh tulangan geser, Kuat geser beton,

31.030 0.60 240

MPa

Vc = (√ fc') / 6 * b * d * 10 =

208.135

kN

f * Vc =

124.881

kN

f= fy = -3

Tahanan geser beton,

Hanya perlu tul.geser min

→

f * Vs = Vu - f * Vc =

Tahanan geser sengkang,

-

kN

31.030

kN

78.54

mm

s = Av * fy * d / ( Vs * 10 ) =

346.25

mm

smax = d / 2 =

276.00

mm

smax =

276.00 276.00 200 200

mm mm mm

Vs =

Kuat geser sengkang, Digunakan sengkang berpenampang :

1

10 2

3

Jarak sengkang maksimum, Jarak sengkang maksimum, Jarak sengkang yang harus digunakan, Diambil jarak sengkang : Digunakan sengkang,

P

Av = ns * p / 4 * P =

Luas tulangan geser sengkang, Jarak sengkang yang diperlukan :

kN

s= s=

→

1

P

10

2



KP-2 30/50


KODE KOLOM

K7

INPUT DATA KOLOM

f c' = f y =


b= h= ds = n= D=

30

MPa

240

MPa

300

mm

500

mm

40

mm

4 buah 16

mm



2.E+05

MPa

β1 = 0.85


β1 = 0.85 - 0.008 (f c' - 30)

untuk fc ' > 30 MPa


β1 = 0.85 2

mm


As = n * p / 4 * D =

Jarak tulangan,

x = ( h - 2*ds ) / 6 = 70.00 mm

Rasio tulangan,

r = As / Ag = 0.54%


untuk Pn = 0

804

Untuk : 0

≤

Pn ≤ 0.1 * f c' * b * h

f = 0.65 + 0.15 * ( Pno - Pn ) / Pno


6000

b

5500

5000

h

4500

4000

b=

300

mm

h=

500

mm

3500 ) N k ( n P .

4

3000

f

2500

2000

1000

500

0 -1 00

-5 0

0

50

10 0 1 50

20 0 2 50

30 0 3 50

40 0 4 50

50 0 5 50

60 0 6 50

70 0 7 50

f.Mn (kNm)


80 0 8 50

90 0 9 50 10 00

16

f c' = 30

MPa

f y = 240

MPa

Pu

Mu

(kN)

(kNm)

595.08 1500

D

47.97



No



1

As1 = 7/24 * As =

235

mm

2

As2 = 2/24 * As =

67

mm

2

67

mm

2 2

3

As3 = 2/24 * As =

4

As4 = 2/24 * As =

67

mm

5

As5 = 2/24 * As =

67

mm

6

As6 = 2/24 * As =

67

mm

7

As7 = 7/24 * As = As =

235 804

mm

2

mm

2


d1 = 6*x + ds =

460 mm

d2 = 5*x + ds =

390 mm

d3 = 4*x + ds =

320 mm

d4 = 3*x + ds =

250 m m


d5 = 2*x + ds =

180 mm

c = cb = 600 / (600 + f y) * d1 =

d6 =

x + ds =

110 mm

d7 =

ds =

40 mm


Pno = 0.80*[ 0.85*f c' *b*h + As*(f y - 0.85*f c')]*10

-3

Pno = 3198 kN -3

0.1 * f c' * b * h *10 =

450

kN

328.57 mm

εsi = 0.003 * ( c - di ) / c


| εsi | < f y / Es | εsi |  f y / Es



105

→

Dc = 4.7619


URAIAN PERHITUNGAN



UNIT -3


kN kN

kNmm

kNmm mm kN

kNmm kN kNm kN kNm


6000

b

5500

5000

4500

h

4000

b=

300

mm

h=

500

mm

3500 ) N k ( n P .

4 3000

f

2500

2000

1500

1000

500

D

f c' = 30

MPa

f y = 240

MPa

Pu

Mu

(kN)

(kNm)

595.08

47.97

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0 - 10 0 - 50

0

50

1 00

1 50

2 00

2 50

30 0 3 50

40 0 4 50

50 0 5 50

60 0 6 50

7 00

7 50

f.Mn (kNm)


8 00

8 50

9 00

9 50 10 00

16



c

εs1

εs2

εs3

εs4

εs5

εs6

εs7


f s1

f s2

f s3

f s4

f s5

f s6

f s7

Fs1

Fs2

Fs3

Fs4

Fs5

MPa

MPa

MPa

MPa

MPa

MPa

MPa

kN

kN

kN

kN

kN

60 0. 0

0. 000 70

0 .0 010 5

0. 00 14 0

0. 00 17 5

0. 00 210

0. 00 24 5

0. 00 28 0

1 40 .00

2 10 .0 0

2 40 .0 0

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

3 2. 84

14 .07

1 6. 08

1 6. 08

16 .0 8

59 5. 2

0. 000 68

0 .0 010 3

0. 00 13 9

0. 00 17 4

0. 00 209

0. 00 24 5

0. 00 28 0

1 36 .32

2 06 .8 8

2 40 .0 0

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

3 1. 98

13 .87

1 6. 08

1 6. 08

16 .0 8

59 0. 5

0. 000 66

0 .0 010 2

0. 00 13 7

0. 00 17 3

0. 00 209

0. 00 24 4

0. 00 28 0

1 32 .58

2 03 .7 1

2 40 .0 0

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

3 1. 10

13 .65

1 6. 08

1 6. 08

16 .0 8

58 5. 7 58 1. 0

0. 000 64 0. 000 62

0 .0 010 0 0 .0 009 9

0. 00 13 6 0. 00 13 5

0. 00 17 2 0. 00 17 1

0. 00 208 0. 00 207

0. 00 24 4 0. 00 24 3

0. 00 28 0 0. 00 27 9

1 28 .78 1 24 .92

2 00 .4 9 1 97 .2 1

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .00 2 40 .00

24 0. 00 24 0. 00

3 0. 21 2 9. 30

13 .44 13 .22

1 6. 08 1 6. 08

1 6. 08 1 6. 08

16 .0 8 16 .0 8

57 6. 2

0. 000 60

0 .0 009 7

0. 00 13 3

0. 00 17 0

0. 00 206

0. 00 24 3

0. 00 27 9

1 20 .99

1 93 .8 8

2 40 .0 0

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

2 8. 38

12 .99

1 6. 08

1 6. 08

16 .0 8

57 1. 4

0. 000 58

0 .0 009 5

0. 00 13 2

0. 00 16 9

0. 00 206

0. 00 24 2

0. 00 27 9

1 17 .00

1 90 .5 0

2 40 .0 0

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

2 7. 44

12 .77

1 6. 08

1 6. 08

16 .0 8

56 6. 7

0. 000 56

0 .0 009 4

0. 00 13 1

0. 00 16 8

0. 00 205

0. 00 24 2

0. 00 27 9

1 12 .94

1 87 .0 6

2 40 .0 0

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

2 6. 49

12 .54

1 6. 08

1 6. 08

16 .0 8

56 1. 9 55 7. 1

0. 000 54 0. 000 52

0 .0 009 2 0 .0 009 0

0. 00 12 9 0. 00 12 8

0. 00 16 7 0. 00 16 5

0. 00 204 0. 00 203

0. 00 24 1 0. 00 24 1

0. 00 27 9 0. 00 27 8

1 08 .81 1 04 .62

1 83 .5 6 1 80 .0 0

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .00 2 40 .00

24 0. 00 24 0. 00

2 5. 52 2 4. 54

12 .30 12 .06

1 6. 08 1 6. 08

1 6. 08 1 6. 08

16 .0 8 16 .0 8

55 2. 4

0. 000 50

0 .0 008 8

0. 00 12 6

0. 00 16 4

0. 00 202

0. 00 24 0

0. 00 27 8

1 00 .34

1 76 .3 8

2 40 .0 0

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

2 3. 54

11 .82

1 6. 08

1 6. 08

16 .0 8

54 7. 6

0. 000 48

0 .0 008 6

0. 00 12 5

0. 00 16 3

0. 00 201

0. 00 24 0

0. 00 27 8

96 .00

1 72 .7 0

2 40 .0 0

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

2 2. 52

11 .57

1 6. 08

1 6. 08

16 .0 8

54 2. 9 53 8. 1

0. 000 46 0. 000 44

0 .0 008 4 0 .0 008 3

0. 00 12 3 0. 00 12 2

0. 00 16 2 0. 00 16 1

0. 00 201 0. 00 200

0. 00 23 9 0. 00 23 9

0. 00 27 8 0. 00 27 8

91 .58 87 .08

1 68 .9 5 1 65 .1 3

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .00 2 40 .00

24 0. 00 24 0. 00

2 1. 48 2 0. 43

11 .32 11 .07

1 6. 08 1 6. 08

1 6. 08 1 6. 08

16 .0 8 16 .0 8

53 3. 3

0. 000 41

0 .0 008 1

0. 00 12 0

0. 00 15 9

0. 00 199

0. 00 23 8

0. 00 27 8

82 .50

1 61 .2 5

2 40 .0 0

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

1 9. 35

10 .81

1 6. 08

1 6. 08

16 .0 8

52 8. 6

0. 000 39

0 .0 007 9

0. 00 11 8

0. 00 15 8

0. 00 198

0. 00 23 8

0. 00 27 7

77 .84

1 57 .3 0

2 36 .7 6

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

1 8. 26

10 .54

1 5. 87

1 6. 08

16 .0 8

52 3. 8 51 9. 0

0. 000 37 0. 000 34

0 .0 007 7 0 .0 007 5

0. 00 11 7 0. 00 11 5

0. 00 15 7 0. 00 15 6

0. 00 197 0. 00 196

0. 00 23 7 0. 00 23 6

0. 00 27 7 0. 00 27 7

73 .09 68 .26

1 53 .2 7 1 49 .1 7

2 33 .4 5 2 30 .0 9

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .00 2 40 .00

24 0. 00 24 0. 00

1 7. 15 1 6. 01

10 .27 10 .00

1 5. 65 1 5. 42

1 6. 08 1 6. 08

16 .0 8 16 .0 8

51 4. 3

0. 000 32

0 .0 007 2

0. 00 11 3

0. 00 15 4

0. 00 195

0. 00 23 6

0. 00 27 7

63 .33

1 45 .0 0

2 26 .6 7

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

1 4. 86

9 .72

1 5. 19

1 6. 08

16 .0 8

50 9. 5

0. 000 29

0 .0 007 0

0. 00 11 2

0. 00 15 3

0. 00 194

0. 00 23 5

0. 00 27 6

58 .32

1 40 .7 5

2 23 .1 8

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

1 3. 68

9 .43

1 4. 96

1 6. 08

16 .0 8

50 4. 8

0. 000 27

0 .0 006 8

0. 00 11 0

0. 00 15 1

0. 00 193

0. 00 23 5

0. 00 27 6

53 .21

1 36 .4 2

2 19 .6 2

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

1 2. 48

9 .14

1 4. 72

1 6. 08

16 .0 8

50 0. 0 49 5. 2

0. 000 24 0. 000 21

0 .0 006 6 0 .0 006 4

0. 00 10 8 0. 00 10 6

0. 00 15 0 0. 00 14 9

0. 00 192 0. 00 191

0. 00 23 4 0. 00 23 3

0. 00 27 6 0. 00 27 6

48 .00 42 .69

1 32 .0 0 1 27 .5 0

2 16 .0 0 2 12 .3 1

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .00 2 40 .00

24 0. 00 24 0. 00

1 1. 26 1 0. 01

8 .85 8 .55

1 4. 48 1 4. 23

1 6. 08 1 6. 08

16 .0 8 16 .0 8

49 0. 5

0. 000 19

0 .0 006 1

0. 00 10 4

0. 00 14 7

0. 00 190

0. 00 23 3

0. 00 27 6

37 .28

1 22 .9 1

2 08 .5 4

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

8. 75

8 .24

1 3. 98

1 6. 08

16 .0 8

48 5. 7

0. 000 16

0 .0 005 9

0. 00 10 2

0. 00 14 6

0. 00 189

0. 00 23 2

0. 00 27 5

31 .76

1 18 .2 4

2 04 .7 1

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

7. 45

7 .92

1 3. 72

1 6. 08

16 .0 8

48 1. 0 47 6. 2

0. 000 13 0. 000 10

0 .0 005 7 0 .0 005 4

0. 00 10 0 0. 00 09 8

0. 00 14 4 0. 00 14 3

0. 00 188 0. 00 187

0. 00 23 1 0. 00 23 1

0. 00 27 5 0. 00 27 5

26 .14 20 .40

1 13 .4 7 1 08 .6 0

2 00 .7 9 1 96 .8 0

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .00 2 40 .00

24 0. 00 24 0. 00

6. 13 4. 79

7 .60 7 .28

1 3. 46 1 3. 19

1 6. 08 1 6. 08

16 .0 8 16 .0 8

47 1. 4

0. 000 07

0 .0 005 2

0. 00 09 6

0. 00 14 1

0. 00 185

0. 00 23 0

0. 00 27 5

14 .55

1 03 .6 4

1 92 .7 3

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

3. 41

6 .95

1 2. 92

1 6. 08

16 .0 8

46 6. 7

0. 000 04

0 .0 004 9

0 .00 09 4

0. 00 13 9

0. 00 184

0. 00 22 9

0. 00 27 4

8 .57

98 .5 7

1 88 .5 7

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

2. 01

6 .61

1 2. 64

1 6. 08

16 .0 8

46 1. 9

0. 000 01

0 .0 004 7

0 .00 09 2

0. 00 13 8

0. 00 183

0. 00 22 9

0. 00 27 4

2 .47

93 .4 0

1 84 .3 3

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

0. 58

6 .26

1 2. 35

1 6. 08

16 .0 8

45 7. 1 45 2. 4

- 0. 00 002 - 0. 00 005

0 .0 004 4 0 .0 004 1

0. 00 09 0 0. 00 08 8

0. 00 13 6 0. 00 13 4

0. 00 182 0. 00 181

0. 00 22 8 0. 00 22 7

0. 00 27 4 0. 00 27 3

-3 .75 - 10 .11

88 .1 2 82 .7 4

1 80 .0 0 1 75 .5 8

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .00 2 40 .00

24 0. 00 24 0. 00

- 0. 88 - 2. 37

5 .91 5 .55

1 2. 06 1 1. 77

1 6. 08 1 6. 08

16 .0 8 16 .0 8

44 7. 6

- 0. 00 008

0 .0 003 9

0. 00 08 6

0. 00 13 2

0. 00 179

0. 00 22 6

0. 00 27 3

- 16 .60

77 .2 3

1 71 .0 6

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

- 3. 89

5 .18

1 1. 46

1 6. 08

16 .0 8

44 2. 9

- 0. 00 012

0 .0 003 6

0. 00 08 3

0. 00 13 1

0. 00 178

0. 00 22 5

0. 00 27 3

- 23 .23

71 .6 1

1 66 .4 5

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

- 5. 45

4 .80

1 1. 16

1 6. 08

16 .0 8

43 8. 1

- 0. 00 015

0 .0 003 3

0. 00 08 1

0. 00 12 9

0. 00 177

0. 00 22 5

0. 00 27 3

- 30 .00

65 .8 7

1 61 .7 4

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

- 7. 04

4 .41

1 0. 84

1 6. 08

16 .0 8

43 3. 3 42 8. 6

- 0. 00 018 - 0. 00 022

0 .0 003 0 0 .0 002 7

0. 00 07 8 0. 00 07 6

0. 00 12 7 0. 00 12 5

0. 00 175 0. 00 174

0. 00 22 4 0. 00 22 3

0. 00 27 2 0. 00 27 2

- 36 .92 - 44 .00

60 .0 0 54 .0 0

1 56 .9 2 1 52 .0 0

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .00 2 40 .00

24 0. 00 24 0. 00

- 8. 66 -1 0. 32

4 .02 3 .62

1 0. 52 1 0. 19

1 6. 08 1 6. 08

16 .0 8 16 .0 8

42 3. 8

- 0. 00 026

0 .0 002 4

0. 00 07 3

0. 00 12 3

0. 00 173

0. 00 22 2

0. 00 27 2

- 51 .24

47 .8 7

1 46 .9 7

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

-1 2. 02

3 .21

9. 85

1 6. 08

16 .0 8

41 9. 0

- 0. 00 029

0 .0 002 1

0. 00 07 1

0. 00 12 1

0. 00 171

0. 00 22 1

0. 00 27 1

- 58 .64

41 .5 9

1 41 .8 2

2 40 .0 0

2 40 .0 0

2 40 .00

24 0. 00

-1 3. 75

2 .79

9. 50

1 6. 08

16 .0 8


Fs6

Fs7

Cs

Ms1

Ms2

Ms3

Ms4

Ms5

Ms6

Ms7

kN

kN

kN

kNmm

kNmm

k Nmm

kNmm

kNmm

kNmm

k Nmm

Ms kNmm

a mm

Cc kN

Mc kNmm

Pn

Mn

kN 3198.01

kNm 0.00

Ф 0.65

Ф.Pn

Ф.Mn

kN 2078.71

kNm 0.00

1 6.0 8

56 .30

1 67 .5 5

-6 89 6.4 2

-1 97 0.4 1

- 11 25 .95

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

52 07 .50

5 10 .0 0

39 01 .5 0

- 195 07 .5 0

31 98. 01

-1 4. 30

0. 65

20 78 .7 1

- 9. 29

1 6.0 8

56 .30

1 66 .4 8

-6 71 5.1 5

-1 94 1.1 3

- 11 25 .95

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

54 18 .06

5 05 .9 5

38 70 .5 4

- 115 19 .4 5

31 98. 01

- 6. 10

0. 65

20 78 .7 1

- 3. 97

16.08

56.30

165.39

-6530.95

-1911.39

-1125.95

0.00

1125.95

2251.89

11822.44

5632.00

501.90

3839.57

-3656.73

3 198.01

1.98

0.65

2078.71

1.28

16.08 1 6.0 8

56.30 56 .30

164.28 1 63 .1 6

-6343.75 -6 15 3.4 8

-1881.16 -1 85 0.4 3

-1125.95 - 11 25 .95

0.00 0. 00

1125.95 1 12 5.9 5

2251.89 22 51 .89

11822.44 1 18 22 .4 4

5849.43 60 70 .42

497.86 4 93 .8 1

3808.61 37 77 .6 4

4080.65 1 16 92 .7 0

3198.01 31 98. 01

9.93 1 7.7 6

0.65 0. 65

2078.71 20 78 .7 1

6.45 1 1. 55

1 6.0 8

56 .30

1 62 .0 1

-5 96 0.0 7

-1 81 9.2 0

- 11 25 .95

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

62 95 .07

4 89 .7 6

37 46 .6 8

1 91 79 .4 3

31 98. 01

2 5.4 7

0. 65

20 78 .7 1

1 6. 56

1 6.0 8

56 .30

1 60 .8 5

-5 76 3.4 4

-1 78 7.4 4

- 11 25 .95

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

65 23 .45

4 85 .7 1

37 15 .7 1

2 65 40 .8 2

31 98. 01

3 3.0 6

0. 65

20 78 .7 1

2 1. 49

1 6.0 8

56 .30

1 59 .6 7

-5 56 3.5 0

-1 75 5.1 5

- 11 25 .95

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

67 55 .68

4 81 .6 7

36 84 .7 5

3 37 76 .8 8

31 98. 01

4 0.5 3

0. 65

20 78 .7 1

2 6. 35

1 6.0 8 1 6.0 8

56 .30 56 .30

1 58 .4 6 1 57 .2 4

-5 36 0.1 7 -5 15 3.3 7

-1 72 2.3 2 -1 68 8.9 2

- 11 25 .95 - 11 25 .95

0. 00 0. 00

1 12 5.9 5 1 12 5.9 5

22 51 .89 22 51 .89

1 18 22 .4 4 1 18 22 .4 4

69 91 .84 72 32 .04

4 77 .6 2 4 73 .5 7

36 53 .7 9 36 22 .8 2

4 08 87 .6 0 4 78 73 .0 0

31 98. 01 31 98. 01

4 7.8 8 5 5.1 1

0. 65 0. 65

20 78 .7 1 20 78 .7 1

3 1. 12 3 5. 82

1 6.0 8

56 .30

1 56 .0 0

-4 94 3.0 0

-1 65 4.9 5

- 11 25 .95

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

74 76 .38

4 69 .5 2

35 91 .8 6

5 47 33 .0 6

31 98. 01

6 2.2 1

0. 65

20 78 .7 1

4 0. 44

1 6.0 8

56 .30

1 54 .7 3

-4 72 8.9 8

-1 62 0.3 8

- 11 25 .95

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

77 24 .97

4 65 .4 8

35 60 .8 9

6 14 67 .7 9

31 98. 01

6 9.1 9

0. 65

20 78 .7 1

4 4. 98

1 6.0 8 1 6.0 8

56 .30 56 .30

1 53 .4 4 1 52 .1 3

-4 51 1.1 9 -4 28 9.5 6

-1 58 5.2 1 -1 54 9.4 2

- 11 25 .95 - 11 25 .95

0. 00 0. 00

1 12 5.9 5 1 12 5.9 5

22 51 .89 22 51 .89

1 18 22 .4 4 1 18 22 .4 4

79 77 .93 82 35 .35

4 61 .4 3 4 57 .3 8

35 29 .9 3 34 98 .9 6

6 80 77 .1 9 7 45 61 .2 6

31 98. 01 31 98. 01

7 6.0 6 8 2.8 0

0. 65 0. 65

20 78 .7 1 20 78 .7 1

4 9. 44 5 3. 82

1 6.0 8

56 .30

1 50 .8 0

-4 06 3.9 6

-1 51 2.9 9

- 11 25 .95

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

84 97 .38

4 53 .3 3

34 68 .0 0

8 09 20 .0 0

31 98. 01

8 9.4 2

0. 65

20 78 .7 1

5 8. 12

1 6.0 8

56 .30

1 49 .2 2

-3 83 4.3 1

-1 47 5.9 0

- 11 10 .73

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

87 79 .34

4 49 .2 9

34 37 .0 4

8 71 53 .4 1

31 98. 01

9 5.9 3

0. 65

20 78 .7 1

6 2. 36

1 6.0 8 1 6.0 8

56 .30 56 .30

1 47 .6 2 1 45 .9 8

-3 60 0.4 7 -3 36 2.3 5

-1 43 8.1 4 -1 39 9.6 9

- 10 95 .24 - 10 79 .46

0. 00 0. 00

1 12 5.9 5 1 12 5.9 5

22 51 .89 22 51 .89

1 18 22 .4 4 1 18 22 .4 4

90 66 .43 93 58 .79

4 45 .2 4 4 41 .1 9

34 06 .0 7 33 75 .1 1

9 32 61 .4 8 9 92 44 .2 2

31 98. 01 31 98. 01

10 2.3 3 10 8.6 0

0. 65 0. 65

20 78 .7 1 20 78 .7 1

6 6. 51 7 0. 59

1 6.0 8

56 .30

1 44 .3 2

-3 11 9.8 1

-1 36 0.5 2

- 10 63 .39

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

96 56 .56

4 37 .1 4

33 44 .1 4 1 051 01 .6 3

31 98. 01

11 4.7 6

0. 65

20 78 .7 1

7 4. 59

1 6.0 8

56 .30

1 42 .6 2

-2 87 2.7 4

-1 32 0.6 2

- 10 47 .03

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

99 59 .89

4 33 .1 0

33 13 .1 8 1 108 33 .7 1

31 98. 01

12 0.7 9

0. 65

20 78 .7 1

7 8. 52

1 6.0 8

56 .30

1 40 .9 0

-2 62 1.0 1

-1 27 9.9 7

- 10 30 .35

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

1 02 68 .95

4 29 .0 5

32 82 .2 1 1 164 40 .4 6

31 98. 01

12 6.7 1

0. 65

20 78 .7 1

8 2. 36

1 6.0 8 1 6.0 8

56 .30 56 .30

1 39 .1 3 1 37 .3 4

-2 36 4.4 9 -2 10 3.0 3

-1 23 8.5 4 -1 19 6.3 2

- 10 13 .35 -9 96 .03

0. 00 0. 00

1 12 5.9 5 1 12 5.9 5

22 51 .89 22 51 .89

1 18 22 .4 4 1 18 22 .4 4

1 05 83 .90 1 09 04 .90

4 25 .0 0 4 20 .9 5

32 51 .2 5 1 219 21 .8 8 32 20 .2 9 1 272 77 .9 6

31 98. 01 31 98. 01

13 2.5 1 13 8.1 8

0. 65 0. 65

20 78 .7 1 20 78 .7 1

8 6. 13 8 9. 82

1 6.0 8

56 .30

1 35 .5 1

-1 83 6.5 0

-1 15 3.2 8

-9 78 .37

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

1 12 32 .14

4 16 .9 0

31 89 .3 2 1 325 08 .7 1

31 98. 01

14 3.7 4

0. 65

20 78 .7 1

9 3. 43

1 6.0 8

56 .30

1 33 .6 5

-1 56 4.7 3

-1 10 9.3 9

-9 60 .37

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

1 15 65 .79

4 12 .8 6

31 58 .3 6 1 376 14 .1 3

31 98. 01

14 9.1 8

0. 65

20 78 .7 1

9 6. 97

1 6.0 8 1 6.0 8

56 .30 56 .30

1 31 .7 5 1 29 .8 1

-1 28 7.5 9 -1 00 4.9 1

-1 06 4.6 3 -1 01 8.9 8

-9 42 .01 -9 23 .28

0. 00 0. 00

1 12 5.9 5 1 12 5.9 5

22 51 .89 22 51 .89

1 18 22 .4 4 1 18 22 .4 4

1 19 06 .05 1 22 53 .12

4 08 .8 1 4 04 .7 6

31 27 .3 9 1 425 94 .2 2 30 96 .4 3 1 474 48 .9 8

31 98. 01 31 98. 01

15 4.5 0 15 9.7 0

0. 65 0. 65

20 78 .7 1 20 78 .7 1

10 0. 43 10 3. 81

1 6.0 8

56 .30

1 27 .8 3

- 71 6.5 1

- 97 2.4 1

-9 04 .17

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

1 26 07 .19

4 00 .7 1

30 65 .4 6 1 521 78 .4 1

31 93. 29

16 4.7 9

0. 65

20 75 .6 4

10 7. 11

1 6.0 8

56 .30

1 25 .8 1

- 42 2.2 3

- 92 4.8 8

-8 84 .67

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

1 29 68 .49

3 96 .6 7

30 34 .5 0 1 567 82 .5 0

31 60. 31

16 9.7 5

0. 65

20 54 .2 0

11 0. 34

1 6.0 8

56 .30

1 23 .7 5

- 12 1.8 8

- 87 6.3 8

-8 64 .77

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

1 33 37 .25

3 92 .6 2

30 03 .5 4 1 612 61 .2 6

31 27. 28

17 4.6 0

0. 65

20 32 .7 3

11 3. 49

1 6.0 8 1 6.0 8

56 .30 56 .30

1 21 .6 4 1 19 .4 9

18 4.7 3 49 7.7 9

- 82 6.8 7 - 77 6.3 1

-8 44 .46 -8 23 .72

0. 00 0. 00

1 12 5.9 5 1 12 5.9 5

22 51 .89 22 51 .89

1 18 22 .4 4 1 18 22 .4 4

1 37 13 .68 1 40 98 .04

3 88 .5 7 3 84 .5 2

29 72 .5 7 1 656 14 .6 9 29 41 .6 1 1 698 42 .7 9

30 94. 21 30 61. 10

17 9.3 3 18 3.9 4

0. 65 0. 65

20 11 .2 4 19 89 .7 2

11 6. 56 11 9. 56

1 6.0 8

56 .30

1 17 .3 0

81 7.5 1

- 72 4.6 8

-8 02 .54

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

1 44 90 .58

3 80 .4 8

29 10 .6 4 1 739 45 .5 6

30 27. 94

18 8.4 4

0. 65

19 68 .1 6

12 2. 48

1 6.0 8

56 .30

1 15 .0 6

1 14 4.1 1

- 67 1.9 4

-7 80 .90

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

1 48 91 .55

3 76 .4 3

28 79 .6 8 1 779 23 .0 0

29 94. 74

19 2.8 1

0. 65

19 46 .5 8

12 5. 33

1 6.0 8

56 .30

1 12 .7 7

1 47 7.8 1

- 61 8.0 5

-7 58 .79

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

1 53 01 .25

3 72 .3 8

28 48 .7 1 1 817 75 .1 0

29 61. 48

19 7.0 8

0. 65

19 24 .9 6

12 8. 10

1 6.0 8 1 6.0 8

56 .30 56 .30

1 10 .4 3 1 08 .0 4

1 81 8.8 4 2 16 7.4 5

- 56 2.9 7 - 50 6.6 8

-7 36 .20 -7 13 .10

0. 00 0. 00

1 12 5.9 5 1 12 5.9 5

22 51 .89 22 51 .89

1 18 22 .4 4 1 18 22 .4 4

1 57 19 .95 1 61 47 .95

3 68 .3 3 3 64 .2 9

28 17 .7 5 1 855 01 .8 8 27 86 .7 9 1 891 03 .3 2

29 28. 18 28 94. 82

20 1.2 2 20 5.2 5

0. 65 0. 65

19 03 .3 2 18 81 .6 3

13 0. 79 13 3. 41

1 6.0 8

56 .30

1 05 .5 9

2 52 3.8 9

- 44 9.1 1

-6 89 .48

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

1 65 85 .58

3 60 .2 4

27 55 .8 2 1 925 79 .4 3

28 61. 41

20 9.1 7

0. 65

18 59 .9 2

13 5. 96

1 6.0 8

56 .30

1 03 .0 9

2 88 8.4 4

- 39 0.2 4

-6 65 .33

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

1 70 33 .14

3 56 .1 9

27 24 .8 6 1 959 30 .2 0

28 27. 95

21 2.9 6

0. 65

18 38 .1 7

13 8. 43



Fs1

Fs2

Fs3

Fs4

Fs5

0. 00 27 1

MPa - 66 .21

MPa 35 .1 7

MPa 1 36 .5 5

MPa 2 37 .9 3

MPa 2 40 .0 0

MPa 2 40 .00

MPa 24 0. 00

kN -1 5. 53

kN 2 .36

kN 9. 15

kN 1 5. 95

kN 16 .0 8

0. 00 27 1

- 73 .95

28 .6 0

1 31 .1 6

2 33 .7 2

2 40 .0 0

2 40 .00

24 0. 00

-1 7. 35

1 .92

8. 79

1 5. 66

16 .0 8

0. 00 27 0

- 81 .88

21 .8 8

1 25 .6 5

2 29 .4 1

2 40 .0 0

2 40 .00

24 0. 00

-1 9. 21

1 .47

8. 42

1 5. 38

16 .0 8

0. 00 21 8

0. 00 27 0

- 90 .00

15 .0 0

1 20 .0 0

2 25 .0 0

2 40 .0 0

2 40 .00

24 0. 00

-2 1. 11

1 .01

8. 04

1 5. 08

16 .0 8

0. 00 163 0. 00 162

0. 00 21 7 0. 00 21 5

0. 00 27 0 0. 00 26 9

- 98 .31 - 106 .83

7 .9 5 0 .7 3

1 14 .2 2 1 08 .2 9

2 20 .4 8 2 15 .8 5

2 40 .0 0 2 40 .0 0

2 40 .00 2 40 .00

24 0. 00 24 0. 00

-2 3. 06 -2 5. 06

0 .53 0 .05

7. 65 7. 26

1 4. 78 1 4. 47

16 .0 8 16 .0 8

0. 00 10 6

0. 00 160

0. 00 21 4

0. 00 26 9

- 115 .56

-6 .6 7

1 02 .2 2

2 11 .1 1

2 40 .0 0

2 40 .00

24 0. 00

-2 7. 11

-0 .45

6. 85

1 4. 15

16 .0 8

0. 00 10 3

0. 00 158

0. 00 21 3

0. 00 26 9

- 124 .50

- 14 .2 5

96 .0 0

2 06 .2 5

2 40 .0 0

2 40 .00

24 0. 00

-2 9. 20

-0 .96

6. 43

1 3. 82

16 .0 8

0. 00 04 5

0. 00 10 1

0. 00 156

0. 00 21 2

0. 00 26 8

- 133 .67

- 22 .0 3

89 .6 2

2 01 .2 7

2 40 .0 0

2 40 .00

24 0. 00

-3 1. 36

-1 .48

6. 01

1 3. 49

16 .0 8

-0 .0 001 5 -0 .0 001 9

0. 00 04 2 0. 00 03 8

0. 00 09 8 0. 00 09 5

0. 00 155 0. 00 153

0. 00 21 1 0. 00 21 0

0. 00 26 8 0. 00 26 7

- 143 .08 - 152 .73

- 30 .0 0 - 38 .1 8

83 .0 8 76 .3 6

1 96 .1 5 1 90 .9 1

2 40 .0 0 2 40 .0 0

2 40 .00 2 40 .00

24 0. 00 24 0. 00

-3 3. 56 -3 5. 83

-2 .01 -2 .56

5. 57 5. 12

1 3. 15 1 2. 79

16 .0 8 16 .0 8

- 0. 00 081

-0 .0 002 3

0. 00 03 5

0. 00 09 3

0. 00 151

0. 00 20 9

0. 00 26 7

- 162 .63

- 46 .5 8

69 .4 7

1 85 .5 3

2 40 .0 0

2 40 .00

24 0. 00

-3 8. 15

-3 .12

4. 66

1 2. 43

16 .0 8

- 0. 00 086

-0 .0 002 8

0. 00 03 1

0. 00 09 0

0. 00 149

0. 00 20 8

0. 00 26 6

- 172 .80

- 55 .2 0

62 .4 0

1 80 .0 0

2 40 .0 0

2 40 .00

24 0. 00

-4 0. 53

-3 .70

4. 18

1 2. 06

16 .0 8

35 2. 4 34 7. 6

- 0. 00 092 - 0. 00 097

-0 .0 003 2 -0 .0 003 7

0. 00 02 8 0. 00 02 4

0. 00 08 7 0. 00 08 4

0. 00 147 0. 00 145

0. 00 20 6 0. 00 20 5

0. 00 26 6 0. 00 26 5

- 183 .24 - 193 .97

- 64 .0 5 - 73 .1 5

55 .1 4 47 .6 7

1 74 .3 2 1 68 .4 9

2 40 .0 0 2 40 .0 0

2 40 .00 2 40 .00

24 0. 00 24 0. 00

-4 2. 98 -4 5. 50

-4 .29 -4 .90

3. 70 3. 19

1 1. 68 1 1. 29

16 .0 8 16 .0 8

34 2. 9

- 0. 00 103

-0 .0 004 1

0. 00 02 0

0. 00 08 1

0. 00 143

0. 00 20 4

0. 00 26 5

- 205 .00

- 82 .5 0

40 .0 0

1 62 .5 0

2 40 .0 0

2 40 .00

24 0. 00

-4 8. 09

-5 .53

2. 68

1 0. 89

16 .0 8

33 8. 1

- 0. 00 108

-0 .0 004 6

0. 00 01 6

0. 00 07 8

0. 00 140

0. 00 20 2

0. 00 26 5

- 216 .34

- 92 .1 1

32 .1 1

1 56 .3 4

2 40 .0 0

2 40 .00

24 0. 00

-5 0. 75

-6 .17

2. 15

1 0. 48

16 .0 8

3 33 .3 32 8. 6

- 0. 00 11 4 - 0. 00 120

- 0. 00 05 1 -0 .0 005 6

0. 00 01 2 0. 00 00 8

0. 00 07 5 0. 00 07 2

0. 00 13 8 0. 00 136

0 .0 02 01 0. 00 20 0

0. 00 26 4 0. 00 26 3

- 22 8. 00 - 240 .00

-1 02 .0 0 - 112 .1 7

2 4. 00 15 .6 5

1 50 .0 0 1 43 .4 8

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .00

2 40 .0 0 24 0. 00

- 53 .4 8 -5 6. 30

- 6. 84 -7 .52

1 .6 1 1. 05

1 0. 05 9. 62

1 6. 08 16 .0 8

32 3. 8

- 0. 00 126

-0 .0 006 1

0. 00 00 4

0. 00 06 8

0. 00 133

0. 00 19 8

0. 00 26 3

- 240 .00

- 122 .6 5

7 .0 6

1 36 .7 6

2 40 .0 0

2 40 .00

24 0. 00

-5 6. 30

-8 .22

0. 47

9. 17

16 .0 8

3 19 .0

- 0. 00 13 3

- 0. 00 06 7 - 0. 00 00 1

0. 00 06 5

0. 00 13 1

0 .0 01 97

0. 00 26 2

- 24 0. 00

-1 33 .4 3

- 1. 79

1 29 .8 5

2 40 .0 0

2 40 .0 0

2 40 .0 0

- 56 .3 0

- 8. 94

- 0. 12

8 .7 0

1 6. 08

3 14 .3

- 0. 00 13 9

- 0. 00 07 2 - 0. 00 00 5

0. 00 06 1

0. 00 12 8

0 .0 01 95

0. 00 26 2

- 2 40 .0 0

-1 44 .5 5

- 10 .9 1

1 22 .7 3

2 40 .0 0

2 40 .0 0

2 40 .0 0

- 56 .3 0

- 9. 69

- 0. 73

8 .2 3

1 6. 08

3 09 .5 3 04 .8

- 0. 00 14 6 - 0. 00 15 3

- 0. 00 07 8 - 0. 00 01 0 - 0. 00 08 4 - 0. 00 01 5

0 .0 00 58 0 .0 00 54

0 . 00 12 6 0 . 00 12 3

0 .0 01 93 0 .0 01 92

0 .0 02 61 0 .0 02 61

- 24 0. 00 - 24 0. 00

- 15 6. 00 - 16 7. 81

- 20 .3 1 - 30 .0 0

1 15 .3 8 1 07 .8 1

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

- 56 .3 0 - 56 .3 0

- 10 .4 6 - 11 .2 5

- 1. 36 - 2. 01

7 .7 3 7 .2 3

1 6. 08 1 6. 08

3 00 .0

- 0. 00 16 0

- 0. 00 09 0 - 0. 00 02 0

0 .0 00 50

0 . 00 12 0

0 .0 01 90

0 .0 02 60

- 24 0. 00

- 18 0. 00

- 40 .0 0

1 00 .0 0

2 40 .0 0

2 40 .0 0

2 40 .0 0

- 56 .3 0

- 12 .0 6

- 2. 68

6 .7 0

1 6. 08

2 95 .2

- 0. 00 16 7

- 0. 00 09 6 - 0. 00 02 5

0. 00 04 6

0. 00 11 7

0 .0 01 88

0. 00 25 9

- 2 40 .0 0

-1 92 .5 8

- 50 .3 2

9 1. 94

2 34 .1 9

2 40 .0 0

2 40 .0 0

- 56 .3 0

- 12 .9 1

- 3. 37

6 .1 6

1 5. 70

2 90 .5 2 85 .7

- 0. 00 17 5 - 0. 00 18 3

- 0. 00 10 3 - 0. 00 03 0 - 0. 00 11 0 - 0. 00 03 6

0. 00 04 2 0. 00 03 7

0. 00 11 4 0. 00 11 1

0 .0 01 86 0 .0 01 85

0. 00 25 9 0. 00 25 8

- 2 40 .0 0 - 2 40 .0 0

-2 05 .5 7 -2 19 .0 0

- 60 .9 8 - 72 .0 0

8 3. 61 7 5. 00

2 28 .2 0 2 22 .0 0

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

- 56 .3 0 - 56 .3 0

- 13 .7 8 - 14 .6 8

- 4. 09 - 4. 83

5 .6 0 5 .0 3

1 5. 29 1 4. 88

2 81 .0

- 0. 00 19 1

- 0. 00 11 6 - 0. 00 04 2

0. 00 03 3

0. 00 10 8

0 .0 01 83

0. 00 25 7

- 2 40 .0 0

-2 32 .8 8

- 83 .3 9

6 6. 10

2 15 .5 9

2 40 .0 0

2 40 .0 0

- 56 .3 0

- 15 .6 1

- 5. 59

4 .4 3

1 4. 45

2 76 .2

- 0. 00 20 0

- 0. 00 12 4 - 0. 00 04 8

0. 00 02 8

0. 00 10 4

0 .0 01 81

0. 00 25 7

- 2 40 .0 0

-2 40 .0 0

- 95 .1 7

5 6. 90

2 08 .9 7

2 40 .0 0

2 40 .0 0

- 56 .3 0

- 16 .0 8

- 6. 38

3 .8 1

1 4. 01

2 71 .4

- 0. 00 20 8

- 0. 00 13 1 - 0. 00 05 4

0 .0 00 24

0 . 00 10 1

0 .0 01 78

0 .0 02 56

- 24 0. 00

- 24 0. 00

- 10 7. 37

4 7. 37

2 02 .1 1

2 40 .0 0

2 40 .0 0

- 56 .3 0

- 16 .0 8

- 7. 20

3 .1 7

1 3. 55

2 66 .7 2 61 .9

- 0. 00 21 8 - 0. 00 22 7

- 0. 00 13 9 - 0. 00 06 0 - 0. 00 14 7 - 0. 00 06 7

0 .0 00 19 0 .0 00 14

0 . 00 09 7 0 . 00 09 4

0 .0 01 76 0 .0 01 74

0 .0 02 55 0 .0 02 54

- 24 0. 00 - 24 0. 00

- 24 0. 00 - 24 0. 00

- 12 0. 00 - 13 3. 09

3 7. 50 2 7. 27

1 95 .0 0 1 87 .6 4

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

- 56 .3 0 - 56 .3 0

- 16 .0 8 - 16 .0 8

- 8. 04 - 8. 92

2 .5 1 1 .8 3

1 3. 07 1 2. 58

2 57 .1

- 0. 00 23 7

- 0. 00 15 5 - 0. 00 07 3

0 .0 00 08

0 . 00 09 0

0 .0 01 72

0 .0 02 53

- 24 0. 00

- 24 0. 00

- 14 6. 67

1 6. 67

1 80 .0 0

2 40 .0 0

2 40 .0 0

- 56 .3 0

- 16 .0 8

- 9. 83

1 .1 2

1 2. 06

2 52 .4

- 0. 00 24 7

- 0. 00 16 4 - 0. 00 08 0

0 .0 00 03

0 . 00 08 6

0 .0 01 69

0 .0 02 52

- 24 0. 00

- 24 0. 00

- 16 0. 75

5 .6 6

1 72 .0 8

2 40 .0 0

2 40 .0 0

- 56 .3 0

- 16 .0 8

- 10 .7 7

0 .3 8

1 1. 53

2 47 .6

- 0. 00 25 7

-0 .0 01 73 - 0. 00 08 8 - 0. 00 00 3

0 .0 00 82

0 .0 01 67

0 .0 02 52

- 24 0. 00

- 2 40 .0 0

- 17 5. 38

- 5. 77

1 63 .8 5

2 40 .0 0

2 40 .0 0

- 56 .3 0

- 16 .0 8

- 11 .7 5

- 0. 39

1 0. 98

2 42 .9 2 38 .1

- 0. 00 26 8 - 0. 00 28 0

-0 .0 01 82 - 0. 00 09 5 - 0. 00 00 9 -0 .0 01 91 - 0. 00 10 3 - 0. 00 01 5

0 . 00 07 8 0 .0 00 73

0 .0 01 64 0 .0 01 61

0 . 00 25 1 0 .0 02 50

- 24 0. 00 - 24 0. 00

- 2 40 .0 0 - 2 40 .0 0

- 19 0. 59 - 20 6. 40

- 17 .6 5 - 30 .0 0

1 55 .2 9 1 46 .4 0

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

- 56 .3 0 - 56 .3 0

- 16 .0 8 - 16 .0 8

- 12 .7 7 - 13 .8 3

- 1. 18 - 2. 01

1 0. 41 9 .8 1

2 33 .3

- 0. 00 29 1

-0 .0 02 01 - 0. 00 11 1 - 0. 00 02 1

0 .0 00 69

0 .0 01 59

0 .0 02 49

- 24 0. 00

- 2 40 .0 0

- 22 2. 86

- 42 .8 6

1 37 .1 4

2 40 .0 0

2 40 .0 0

- 56 .3 0

- 16 .0 8

- 14 .9 4

- 2. 87

9 .1 9

2 28 .6

- 0. 00 30 4

-0 .0 02 12 - 0. 00 12 0 - 0. 00 02 8

0 .0 00 64

0 .0 01 56

0 .0 02 48

- 24 0. 00

- 2 40 .0 0

- 24 0. 00

- 56 .2 5

1 27 .5 0

2 40 .0 0

2 40 .0 0

- 56 .3 0

- 16 .0 8

- 16 .0 8

- 3. 77

8 .5 5

c

εs1

εs2

εs3

εs4

εs5

εs6

mm 41 4. 3

- 0. 00 033

0 .0 001 8

0. 00 06 8

0. 00 11 9

0. 00 170

0. 00 22 0

40 9. 5

- 0. 00 037

0 .0 001 4

0. 00 06 6

0. 00 11 7

0. 00 168

0. 00 21 9

40 4. 8

- 0. 00 041

0 .0 001 1

0. 00 06 3

0. 00 11 5

0. 00 167

0. 00 21 8

40 0. 0

- 0. 00 045

0 .0 000 7

0. 00 06 0

0. 00 11 3

0. 00 165

39 5. 2 39 0. 5

- 0. 00 049 - 0. 00 053

0 .0 000 4 0 .0 000 0

0. 00 05 7 0. 00 05 4

0. 00 11 0 0. 00 10 8

38 5. 7

- 0. 00 058

-0 .0 000 3

0. 00 05 1

38 1. 0

- 0. 00 062

-0 .0 000 7

0. 00 04 8

37 6. 2

- 0. 00 067

-0 .0 001 1

37 1. 4 36 6. 7

- 0. 00 072 - 0. 00 076

36 1. 9 35 7. 1

εs7

f s1

f s2

f s3

f s4

f s5

f s6

f s7


Fs6

Fs7

Cs

kN 1 6.0 8

kN 56 .30

kN 1 00 .3 9

kNmm 3 26 1.3 6

Ms1

kNmm - 33 0.0 2

Ms2

k Nmm -6 40 .62

Ms3

kNmm 0. 00

Ms4

kNmm 1 12 5.9 5

Ms5

kNmm 22 51 .89

Ms6

k Nmm 1 18 22 .4 4

Ms7

kNmm 1 74 91 .00

Ms

mm 3 52 .1 4

kN kNmm 26 93 .8 9 1 991 55 .6 5

kN 27 94. 29

kNm 21 6.6 5

Cc

Mc

1 6.0 8

56 .30

97 .4 9

3 64 2.9 6

- 26 8.3 9

-6 15 .34

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

1 79 59 .51

3 48 .1 0

26 62 .9 3 2 022 55 .7 7

27 60. 42

1 6.0 8

56 .30

94 .5 2

4 03 3.5 4

- 20 5.3 2

-5 89 .47

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

1 84 39 .03

3 44 .0 5

26 31 .9 6 2 052 30 .5 5

27 26. 49

1 6.0 8

56 .30

91 .4 8

4 43 3.4 2

- 14 0.7 4

-5 62 .97

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

1 89 29 .98

3 40 .0 0

26 01 .0 0 2 080 80 .0 0

1 6.0 8 1 6.0 8

56 .30 56 .30

88 .3 7 85 .1 8

4 84 2.9 3 5 26 2.4 3

-7 4.6 1 - 6.8 7

-5 35 .84 -5 08 .05

0. 00 0. 00

1 12 5.9 5 1 12 5.9 5

22 51 .89 22 51 .89

1 18 22 .4 4 1 18 22 .4 4

1 94 32 .76 199 47 .80

3 35 .9 5 3 31 .9 0

1 6.0 8

56 .30

81 .9 1

5 69 2.2 9

6 2.5 5

-4 79 .57

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

204 75 .55

1 6.0 8

56 .30

78 .5 6

6 13 2.8 9

13 3.7 1

-4 50 .38

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

2 10 16 .50

1 6.0 8

56 .30

75 .1 3

6 58 4.6 5

20 6.6 6

-4 20 .45

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

2 15 71 .15

1 6.0 8 1 6.0 8

56 .30 56 .30

71 .6 1 68 .0 0

7 04 7.9 9 7 52 3.3 7

28 1.4 9 35 8.2 6

-3 89 .75 -3 58 .26

0. 00 0. 00

1 12 5.9 5 1 12 5.9 5

22 51 .89 22 51 .89

1 18 22 .4 4 1 18 22 .4 4

1 6.0 8

56 .30

64 .2 9

8 01 1.2 6

43 7.0 5

-3 25 .93

0. 00

1 12 5.9 5

22 51 .89

1 6.0 8

56 .30

60 .4 8

8 51 2.1 6

51 7.9 4

-2 92 .75

0. 00

1 12 5.9 5

22 51 .89

1 6.0 8 1 6.0 8

56 .30 56 .30

56 .5 7 52 .5 5

9 02 6.5 9 9 55 5.1 2

60 1.0 1 68 6.3 6

-2 58 .66 -2 23 .65

0. 00 0. 00

1 12 5.9 5 1 12 5.9 5

1 6.0 8

56 .30

48 .4 2

10 09 8.3 4

77 4.0 9

-1 87 .66

0. 00

1 6.0 8

56 .30

44 .1 8

10 65 6.8 5

86 4.2 8

-1 50 .65

0. 00

1 6.0 8 1 6.0 8

56 .30 56 .30

39 .8 1 35 .3 2

11 23 1.3 2 11 82 2.4 4

95 7.0 5 1 05 2.5 2

-1 12 .59 - 73 .43

1 6.0 8

56 .30

33 .5 9

11 82 2.4 4

1 15 0.7 8

1 6.0 8

56 .30

31 .8 1

1 182 2.4 4

1 25 1.9 9

1 6.0 8

56 .30

29 .9 8

11 82 2.4 4

1 6.0 8 1 6.0 8

56 .30 56 .30

28 .0 9 26 .1 4

1 6.0 8

56 .30

1 6.0 8

56 .30

1 6.0 8 1 6.0 8

Ф.Pn

Ф.Mn

0. 65

kN 18 16 .2 9

kNm 14 0. 82

22 0.2 2

0. 65

17 94 .2 7

14 3. 14

22 3.6 7

0. 65

17 72 .2 2

14 5. 39

26 92. 48

22 7.0 1

0. 65

17 50 .1 1

14 7. 56

25 70 .0 4 2 108 04 .1 2 25 39 .0 7 2 134 02 .9 1

26 58. 41 26 24. 25

23 0.2 4 23 3.3 5

0. 65 0. 65

17 27 .9 6 17 05 .7 6

14 9. 65 15 1. 68

3 27 .8 6

25 08 .1 1 2 158 76 .3 6

25 90. 02

23 6.3 5

0. 65

16 83 .5 1

15 3. 63

3 23 .8 1

24 77 .1 4 2 182 24 .4 9

25 55. 71

23 9.2 4

0. 65

16 61 .2 1

15 5. 51

3 19 .7 6

24 46 .1 8 2 204 47 .2 8

25 21. 31

24 2.0 2

0. 65

16 38 .8 5

15 7. 31

2 21 40 .01 2 27 23 .65

3 15 .7 1 3 11 .6 7

24 15 .2 1 2 225 44 .7 4 23 84 .2 5 2 245 16 .8 8

24 86. 82 24 52. 25

24 4.6 8 24 7.2 4

0. 65 0. 65

16 16 .4 4 15 93 .9 6

15 9. 05 16 0. 71

1 18 22 .4 4

2 33 22 .65

3 07 .6 2

23 53 .2 9 2 263 63 .6 7

24 17. 57

24 9.6 9

0. 65

15 71 .4 2

16 2. 30

1 18 22 .4 4

2 39 37 .63

3 03 .5 7

23 22 .3 2 2 280 85 .1 4

23 82. 80

25 2.0 2

0. 65

15 48 .8 2

16 3. 81

22 51 .89 22 51 .89

1 18 22 .4 4 1 18 22 .4 4

2 45 69 .22 2 52 18 .12

2 99 .5 2 2 95 .4 8

22 91 .3 6 2 296 81 .2 8 22 60 .3 9 2 311 52 .0 8

23 47. 93 23 12. 94

25 4.2 5 25 6.3 7

0. 65 0. 65

15 26 .1 5 15 03 .4 1

16 5. 26 16 6. 64

1 12 5.9 5

22 51 .89

1 18 22 .4 4

2 58 85 .05

2 91 .4 3

22 29 .4 3 2 324 97 .5 5

22 77. 85

25 8.3 8

0. 65

14 80 .6 0

16 7. 95

1 12 5.9 5

22 51 .89

1 18 22 .4 4

2 65 70 .76

2 87 .3 8

21 98 .4 6 2 337 17 .6 9

22 42. 64

26 0.2 9

0. 65

14 57 .7 2

16 9. 19

0. 00 0. 00

1 12 5.9 5 1 12 5.9 5

22 51 .89 22 51 .89

1 18 22 .4 4 1 18 22 .4 4

2 72 76 .06 2 80 01 .81

2 83 .3 3 2 79 .2 9

21 67 .5 0 2 348 12 .5 0 21 36 .5 4 2 357 81 .9 8

22 07. 31 21 71. 85

26 2.0 9 26 3.7 8

0. 65 0. 65

14 34 .7 5 14 11 .7 0

17 0. 36 17 1. 46

- 33 .12

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

2 81 40 .39

2 75 .2 4

21 05 .5 7 2 366 26 .1 2

21 39. 16

26 4.7 7

0. 65

13 90 .4 5

17 2. 10

8. 40

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

282 83 .11

2 71 .1 9

20 74 .6 1 2 373 44 .9 4

21 06. 42

26 5.6 3

0. 65

13 69 .1 7

17 2. 66

1 35 6.2 5

5 1. 18

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

2 84 30 .16

2 67 .1 4

20 43 .6 4 2 379 38 .4 2

20 73. 62

26 6.3 7

0. 65

13 47 .8 5

17 3. 14

11 82 2.4 4 11 82 2.4 4

1 46 3.7 3 1 57 4.5 7

9 5. 27 1 40 .74

0. 00 0. 00

1 12 5.9 5 1 12 5.9 5

22 51 .89 22 51 .89

1 18 22 .4 4 1 18 22 .4 4

2 85 81 .73 2 87 38 .03

2 63 .1 0 2 59 .0 5

20 12 .6 8 2 384 06 .5 7 19 81 .7 1 2 387 49 .3 9

20 40. 77 20 07. 85

26 6.9 9 26 7.4 9

0. 65 0. 65

13 26 .5 0 13 05 .1 0

17 3. 54 17 3. 87

24 .1 3

11 82 2.4 4

1 68 8.9 2

1 87 .66

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

2 88 99 .30

2 55 .0 0

19 50 .7 5 2 389 66 .8 8

19 74. 88

26 7.8 7

0. 65

12 83 .6 7

17 4. 11

21 .6 6

11 82 2.4 4

1 80 6.9 6

2 36 .09

0. 00

1 09 8.7 1

22 51 .89

1 18 22 .4 4

2 90 38 .53

2 50 .9 5

19 19 .7 9 2 390 59 .0 3

19 41. 45

26 8.1 0

0. 65

12 61 .9 4

17 4. 26

56 .30 56 .30

19 .1 2 16 .4 9

11 82 2.4 4 11 82 2.4 4

1 92 8.8 8 2 05 4.8 5

2 86 .10 3 37 .78

0. 00 0. 00

1 07 0.5 7 1 04 1.5 0

22 51 .89 22 51 .89

1 18 22 .4 4 1 18 22 .4 4

2 91 82 .33 2 93 30 .91

2 46 .9 0 2 42 .8 6

18 88 .8 2 2 390 25 .8 5 18 57 .8 6 2 388 67 .3 5

19 07. 94 18 74. 34

26 8.2 1 26 8.2 0

0. 65 0. 65

12 40 .1 6 12 18 .3 2

17 4. 34 17 4. 33

1 6.0 8

56 .30

13 .7 7

11 82 2.4 4

2 18 5.1 0

3 91 .22

0. 00

1 01 1.4 4

22 51 .89

1 18 22 .4 4

2 94 84 .54

2 38 .8 1

18 26 .8 9 2 385 83 .5 1

18 40. 66

26 8.0 7

0. 65

11 96 .4 3

17 4. 24

1 6.0 8

56 .30

11 .4 4

11 82 2.4 4

2 25 1.8 9

4 46 .50

0. 00

98 0.3 5

22 51 .89

1 18 22 .4 4

2 95 75 .52

2 34 .7 6

17 95 .9 3 2 381 74 .3 4

18 07. 37

26 7.7 5

0. 65

11 74 .7 9

17 4. 04

1 6.0 8

56 .30

9 .5 2

1 182 2.4 4

2 25 1.8 9

5 03 .71

0. 00

94 8.1 7

22 51 .89

1 18 22 .4 4

296 00 .55

2 30 .7 1

17 64 .9 6 2 376 39 .8 3

17 74. 49

26 7.2 4

0. 65

11 53 .4 2

17 3. 71

1 6.0 8 1 6.0 8

56 .30 56 .30

7 .5 4 5 .4 8

1 182 2.4 4 1 182 2.4 4

2 25 1.8 9 2 25 1.8 9

5 62 .97 6 24 .39

0. 00 0. 00

91 4.8 3 88 0.2 9

22 51 .89 22 51 .89

1 18 22 .4 4 1 18 22 .4 4

296 26 .48 296 53 .34

2 26 .6 7 2 22 .6 2

17 34 .0 0 2 369 80 .0 0 17 03 .0 4 2 361 94 .8 3

17 41. 54 17 08. 52

26 6.6 1 26 5.8 5

0. 65 0. 65

11 32 .0 0 11 10 .5 4

17 3. 29 17 2. 80

1 6.0 8

56 .30

3 .3 5

1 182 2.4 4

2 25 1.8 9

6 88 .08

0. 00

84 4.4 6

22 51 .89

1 18 22 .4 4

296 81 .21

2 18 .5 7

16 72 .0 7 2 352 84 .3 4

16 75. 42

26 4.9 7

0. 65

10 89 .0 2

17 2. 23

1 6.0 8

56 .30

1 .1 4

1 182 2.4 4

2 25 1.8 9

7 54 .17

0. 00

80 7.2 8

22 51 .89

1 18 22 .4 4

297 10 .12

2 14 .5 2

16 41 .1 1 2 342 48 .5 1

16 42. 25

26 3.9 6

0. 65

10 67 .4 6

17 1. 57

1 6.0 8

56 .30

-1 .1 6

1 182 2.4 4

2 25 1.8 9

8 22 .81

0. 00

76 8.6 8

22 51 .89

1 18 22 .4 4

2 97 40 .15

2 10 .4 8

16 10 .1 4 2 330 87 .3 5

16 08. 98

26 2.8 3

0. 65

10 45 .8 4

17 0. 84

1 6.0 8 1 6.0 8

56 .30 56 .30

-3 .5 5 -6 .0 3

1 182 2.4 4 1 182 2.4 4

2 25 1.8 9 2 25 1.8 9

8 94 .13 9 68 .31

0. 00 0. 00

72 8.5 5 68 6.8 3

22 51 .89 22 51 .89

1 18 22 .4 4 1 18 22 .4 4

2 97 71 .36 2 98 03 .81

2 06 .4 3 2 02 .3 8

15 79 .1 8 2 318 00 .8 5 15 48 .2 1 2 303 89 .0 3

15 75. 63 15 42. 18

26 1.5 7 26 0.1 9

0. 65 0. 65

10 24 .1 6 10 02 .4 2

17 0. 02 16 9. 13

1 6.0 8

56 .30

-8 .6 2

1 182 2.4 4

2 25 1.8 9

10 45 .52

0. 00

64 3.4 0

22 51 .89

1 18 22 .4 4

2 98 37 .59

1 98 .3 3

15 17 .2 5 2 288 51 .8 8

15 08. 63

25 8.6 9

0. 65

9 80 .6 1

16 8. 15

1 6.0 8

56 .30

- 11 .3 1

11 82 2.4 4

2 25 1.8 9

11 25 .95

0. 00

59 8.1 6

22 51 .89

1 18 22 .4 4

2 98 72 .78

1 94 .2 9

14 86 .2 9 2 271 89 .3 9

14 74. 98

25 7.0 6

0. 65

9 58 .7 3

16 7. 09

a

Pn

Mn

Ф



εs7

f s1

f s2

f s3

0 .0 01 53

0 .0 02 46

MPa - 24 0. 00

MPa - 2 40 .0 0

MPa - 24 0. 00

Fs1

Fs2

Fs3

Fs4

Fs5

MPa - 70 .2 1

MPa 1 17 .4 5

MPa 2 40 .0 0

MPa 2 40 .0 0

kN - 56 .3 0

kN - 16 .0 8

kN - 16 .0 8

kN - 4. 71

kN 7 .8 7

0 .0 01 49

0 .0 02 45

- 24 0. 00

- 2 40 .0 0

0 .0 00 48

0 .0 01 46

0 .0 02 44

- 24 0. 00

- 2 40 .0 0

- 24 0. 00

- 84 .7 8

1 06 .9 6

2 40 .0 0

2 40 .0 0

- 56 .3 0

- 16 .0 8

- 16 .0 8

- 5. 68

7 .1 7

- 24 0. 00

- 10 0. 00

9 6. 00

2 40 .0 0

2 40 .0 0

- 56 .3 0

- 16 .0 8

- 16 .0 8

- 6. 70

-0 .0 02 58 - 0. 00 15 8 - 0. 00 05 8

0 .0 00 42

0 .0 01 42

0 .0 02 43

- 24 0. 00

6 .4 3

- 2 40 .0 0

- 24 0. 00

- 11 5. 91

8 4. 55

2 40 .0 0

2 40 .0 0

- 56 .3 0

- 16 .0 8

- 16 .0 8

- 7. 77

- 0. 00 37 4 - 0. 00 39 0

-0 .0 02 71 - 0. 00 16 9 - 0. 00 06 6 -0 .0 02 85 - 0. 00 18 0 - 0. 00 07 5

0 .0 00 36 0 . 00 03 0

0 .0 01 39 0 .0 01 35

0 .0 02 41 0 . 00 24 0

5 .6 7

- 24 0. 00 - 24 0. 00

- 2 40 .0 0 - 2 40 .0 0

- 24 0. 00 - 24 0. 00

- 13 2. 56 - 15 0. 00

7 2. 56 6 0. 00

2 40 .0 0 2 40 .0 0

2 40 .0 0 2 40 .0 0

- 56 .3 0 - 56 .3 0

- 16 .0 8 - 16 .0 8

- 16 .0 8 - 16 .0 8

- 8. 88 - 10 .0 5

4 .8 6 4 .0 2

1 95 .2

- 0. 00 40 7

-0 .0 02 99 - 0. 00 19 2 - 0. 00 08 4

0 . 00 02 3

0 .0 01 31

1 90 .5

- 0. 00 42 5

-0 .0 03 14 - 0. 00 20 4 - 0. 00 09 4

0 . 00 01 6

0 .0 01 27

0 . 00 23 9

- 24 0. 00

- 2 40 .0 0

- 24 0. 00

- 16 8. 29

4 6. 83

2 40 .0 0

2 40 .0 0

- 56 .3 0

- 16 .0 8

- 16 .0 8

- 11 .2 8

3 .1 4

0 . 00 23 7

- 24 0. 00

- 2 40 .0 0

- 24 0. 00

- 18 7. 50

3 3. 00

2 40 .0 0

2 40 .0 0

- 56 .3 0

- 16 .0 8

- 16 .0 8

- 12 .5 7

1 85 .7

- 0. 00 44 3

-0 .0 03 30 - 0. 00 21 7 - 0. 00 10 4

0 . 00 00 9

2 .2 1

0 .0 01 22

0 . 00 23 5

- 24 0. 00

- 2 40 .0 0

- 24 0. 00

- 20 7. 69

1 8. 46

2 40 .0 0

2 40 .0 0

- 56 .3 0

- 16 .0 8

- 16 .0 8

- 13 .9 2

1 81 .0 1 76 .2

- 0. 00 46 3 - 0. 00 48 3

1 .2 4

-0 .0 03 47 - 0. 00 23 1 - 0. 00 11 4 0 .0 00 02 - 0. 00 36 4 - 0. 00 24 5 - 0. 00 12 6 - 0. 00 00 6

0 .0 01 18 0 .0 01 13

0 .0 02 34 0 .0 02 32

- 24 0. 00 - 24 0. 00

- 2 40 .0 0 - 24 0. 00

- 24 0. 00 - 24 0. 00

- 22 8. 95 - 24 0. 00

3 .1 6 - 12 .9 7

2 35 .2 6 2 25 .4 1

2 40 .0 0 2 40 .0 0

- 56 .3 0 - 56 .3 0

- 16 .0 8 - 16 .0 8

- 16 .0 8 - 16 .0 8

- 15 .3 4 - 16 .0 8

0 .2 1 - 0. 87

1 71 .4 1 66 .7

- 0. 00 50 5

- 0. 00 38 3 - 0. 00 26 0 - 0. 00 13 8 - 0. 00 01 5

0 .0 01 07

0 .0 02 30

- 24 0. 00

- 24 0. 00

- 24 0. 00

- 24 0. 00

- 30 .0 0

2 15 .0 0

2 40 .0 0

- 56 .3 0

- 16 .0 8

- 16 .0 8

- 16 .0 8

- 2. 01

- 0. 00 52 8

- 0. 00 40 2 - 0. 00 27 6 - 0. 00 15 0 - 0. 00 02 4

0 .0 01 02

0 .0 02 28

- 24 0. 00

- 24 0. 00

- 24 0. 00

- 24 0. 00

- 48 .0 0

2 04 .0 0

2 40 .0 0

- 56 .3 0

- 16 .0 8

- 16 .0 8

- 16 .0 8

- 3. 22

1 61 .9 1 57 .1

- 0. 00 55 2 - 0. 00 57 8

- 0. 00 42 3 - 0. 00 29 3 - 0. 00 16 3 - 0. 00 03 4 - 0. 00 44 5 - 0. 00 31 1 - 0. 00 17 7 - 0. 00 04 4

0 .0 00 96 0 .0 00 90

0 .0 02 26 0 .0 02 24

- 24 0. 00 - 24 0. 00

- 24 0. 00 - 24 0. 00

- 24 0. 00 - 24 0. 00

- 24 0. 00 - 24 0. 00

- 67 .0 6 - 87 .2 7

1 92 .3 5 1 80 .0 0

2 40 .0 0 2 40 .0 0

- 56 .3 0 - 56 .3 0

- 16 .0 8 - 16 .0 8

- 16 .0 8 - 16 .0 8

- 16 .0 8 - 16 .0 8

- 4. 49 - 5. 85

152.4

-0.00606

-0.00468 -0.00330 -0.00192 -0.00054

0.00083

0.00221

-240.00

-240.00

-240.00

-240.00

-108.75

166.87

240.00

-56.30

-16.08

-16.08

-16.08

-7.29

147.6

-0.00635

-0.00493 -0.00350 -0.00208 -0.00066

0.00076

0.00219

-240.00

-240.00

-240.00

-240.00

-131.61

152.90

240.00

-56.30

-16.08

-16.08

-16.08

-8.82

142.9 138.1

-0.00666 -0.00699

-0.00519 -0.00372 -0.00225 -0.00078 -0.00547 -0.00395 -0.00243 -0.00091

0.00069 0.00061

0.00216 0.00213

-240.00 -240.00

-240.00 -240.00

-240.00 -240.00

-240.00 -240.00

-156.00 -182.07

138.00 122.07

240.00 240.00

-56.30 -56.30

-16.08 -16.08

-16.08 -16.08

-16.08 -16.08

-10.46 -12.20

133.3

-0.00735

-0.00578 -0.00420 -0.00263 -0.00105

0.00052

0.00210

-240.00

-240.00

-240.00

-240.00

-210.00

105.00

240.00

-56.30

-16.08

-16.08

-16.08

-14.07

128.6

-0.00773

-0.00610 -0.00447 -0.00283 -0.00120

0.00043

0.00207

-240.00

-240.00

-240.00

-240.00

-240.00

86.67

240.00

-56.30

-16.08

-16.08

-16.08

-16.08

123.8

-0.00815

-0.00645 -0.00475 -0.00306 -0.00136

0.00033

0.00203

-240.00

-240.00

-240.00

-240.00

-240.00

66.92

240.00

-56.30

-16.08

-16.08

-16.08

-16.08

119.0 114.3

-0.00859 -0.00908

-0.00683 -0.00506 -0.00330 -0.00154 -0.00724 -0.00540 -0.00356 -0.00173

0.00023 0.00011

0.00199 0.00195

-240.00 -240.00

-240.00 -240.00

-240.00 -240.00

-240.00 -240.00

-240.00 -240.00

45.60 22.50

240.00 240.00

-56.30 -56.30

-16.08 -16.08

-16.08 -16.08

-16.08 -16.08

-16.08 -16.08

136.2

-0.00713

-0.00559 -0.00405 -0.00251 -0.00096

0.00058

0.00212

-240.00

-240.00

-240.00

-240.00

-192.95

115.42

240.00

-56.30

-16.08

-16.08

-16.08

-12.93

0. 00 20 0

0. 00 26 3

- 240 .00

- 112 .1 7

15 .6 5

1 43 .4 8

2 40 .0 0

2 40 .00

24 0. 00

-5 6. 30

-7 .52

1. 05

9. 62

16 .0 8

c

εs1

εs2

εs3

εs4

εs5

mm 2 23 .8

- 0. 00 31 7

-0 .0 02 23 - 0. 00 12 9 - 0. 00 03 5

0 .0 00 59

2 19 .0

- 0. 00 33 0

-0 .0 02 34 - 0. 00 13 8 - 0. 00 04 2

0 .0 00 53

2 14 .3

- 0. 00 34 4

-0 .0 02 46 - 0. 00 14 8 - 0. 00 05 0

2 09 .5

- 0. 00 35 9

2 04 .8 2 00 .0

εs6

f s4

f s5

f s6

f s7

KONDISI TEKAN AKSIAL KECIL : Pn = 0.1 * fc' * b * h KONDISI BALANCE 32 8. 6

- 0. 00 120

-0 .0 005 6

0. 00 00 8

0. 00 07 2

0. 00 136


Fs6

Fs7

Cs

kN 1 6.0 8

kN 56 .30

kN - 12 .9 2

kNmm 11 82 2.4 4

Ms1

kNmm 2 25 1.8 9

Ms2

k Nmm 11 25 .95

Ms3

kNmm 0. 00

Ms4

kNmm 55 1.0 0

Ms5

kNmm 22 51 .89

Ms6

k Nmm 1 18 22 .4 4

Ms7

kNmm 2 98 25 .61

Ms

mm 1 90 .2 4

kN kNmm 14 55 .3 2 2 254 01 .5 7

kN 14 42. 40

kNm 25 5.2 3

Cc

Mc

1 6.0 8

56 .30

- 14 .6 0

11 82 2.4 4

2 25 1.8 9

11 25 .95

0. 00

50 1.7 8

22 51 .89

1 18 22 .4 4

2 97 76 .40

1 86 .1 9

14 24 .3 6 2 234 88 .4 2

14 09. 76

1 6.0 8

56 .30

- 16 .3 5

11 82 2.4 4

2 25 1.8 9

11 25 .95

0. 00

45 0.3 8

22 51 .89

1 18 22 .4 4

2 97 25 .00

1 82 .1 4

13 93 .3 9 2 214 49 .9 4

13 77. 04

1 6.0 8

56 .30

- 18 .1 9

11 82 2.4 4

2 25 1.8 9

11 25 .95

0. 00

39 6.6 4

22 51 .89

1 18 22 .4 4

2 96 71 .26

1 78 .1 0

13 62 .4 3 2 192 86 .1 2

1 6.0 8 1 6.0 8

56 .30 56 .30

- 20 .1 1 - 22 .1 2

11 82 2.4 4 11 82 2.4 4

2 25 1.8 9 2 25 1.8 9

11 25 .95 11 25 .95

0. 00 0. 00

34 0.4 0 28 1.4 9

22 51 .89 22 51 .89

1 18 22 .4 4 1 18 22 .4 4

2 96 15 .02 2 95 56 .10

1 74 .0 5 1 70 .0 0

1 6.0 8

56 .30

- 24 .2 3

11 82 2.4 4

2 25 1.8 9

11 25 .95

0. 00

21 9.7 0

22 51 .89

1 18 22 .4 4

2 94 94 .31

1 6.0 8

56 .30

- 26 .4 4

11 82 2.4 4

2 25 1.8 9

11 25 .95

0. 00

15 4.8 2

22 51 .89

1 18 22 .4 4

2 94 29 .43

1 6.0 8

56 .30

- 28 .7 7

1 182 2.4 4

2 25 1.8 9

11 25 .95

0. 00

8 6.6 1

22 51 .89

1 18 22 .4 4

1 5.7 7 1 5.1 1

56 .30 56 .30

- 31 .5 3 - 34 .0 2

1 182 2.4 4 11 82 2.4 4

2 25 1.8 9 2 25 1.8 9

11 25 .95 11 25 .95

0. 00 0. 00

1 4.8 2 -6 0. 86

22 07 .45 21 14 .95

1 4.4 1

56 .30

- 35 .8 6

11 82 2.4 4

2 25 1.8 9

11 25 .95

0. 00

- 14 0. 74

1 3.6 7

56 .30

- 37 .8 0

11 82 2.4 4

2 25 1.8 9

11 25 .95

0. 00

- 22 5. 19

1 2.8 9 1 2.0 6

56 .30 56 .30

- 39 .8 6 - 42 .0 4

11 82 2.4 4 11 82 2.4 4

2 25 1.8 9 2 25 1.8 9

11 25 .95 11 25 .95

0. 00 0. 00

1 1.1 8

56 .30

- 44 .3 6

1 182 2.4 4

2 25 1.8 9

11 25 .95

1 0.2 5

56 .30

- 46 .8 3

1 182 2.4 4

2 25 1.8 9

11 25 .95

9 .2 5 8 .1 8

56 .30 56 .30

- 49 .4 6 - 52 .2 8

1 182 2.4 4 1 182 2.4 4

2 25 1.8 9 2 25 1.8 9

7.04

56.30

-55.29

11822.44

5 .8 1

56 .30

- 58 .5 3

1 182 2.4 4

4 .4 9

56 .30

- 59 .8 5

3 .0 6 1.51

56 .30 56.30

7 .7 4

56 .30

Ф.Pn

Ф.Mn

0. 65

kN 9 37 .5 6

kNm 16 5. 90

25 3.2 6

0. 65

9 16 .3 4

16 4. 62

25 1.1 7

0. 65

8 95 .0 8

16 3. 26

13 44. 24

24 8.9 6

0. 65

8 73 .7 6

16 1. 82

13 31 .4 6 2 169 96 .9 8 13 00 .5 0 2 145 82 .5 0

13 11. 36 12 78. 38

24 6.6 1 24 4.1 4

0. 65 0. 65

8 52 .3 8 8 30 .9 5

16 0. 30 15 8. 69

1 65 .9 5

12 69 .5 4 2 120 42 .6 9

12 45. 31

24 1.5 4

0. 65

8 09 .4 5

15 7. 00

1 61 .9 0

12 38 .5 7 2 093 77 .5 5

12 12. 13

23 8.8 1

0. 65

7 87 .8 9

15 5. 22

2 93 61 .23

1 57 .8 6

12 07 .6 1 2 065 87 .0 8

11 78. 84

23 5.9 5

0. 65

7 66 .2 5

15 3. 37

1 18 22 .4 4 1 18 22 .4 4

2 92 44 .99 2 90 76 .82

1 53 .8 1 1 49 .7 6

11 76 .6 4 2 036 71 .2 8 11 45 .6 8 2 006 30 .1 4

11 45. 11 11 11. 66

23 2.9 2 22 9.7 1

0. 65 0. 65

7 44 .3 2 7 22 .5 8

15 1. 40 14 9. 31

20 17 .32

1 18 22 .4 4

2 88 99 .30

1 45 .7 1

11 14 .7 1 1 974 63 .6 7

10 78. 86

22 6.3 6

0. 65

7 01 .2 6

14 7. 14

19 14 .11

1 18 22 .4 4

2 87 11 .64

1 41 .6 7

10 83 .7 5 1 941 71 .8 7

10 45. 95

22 2.8 8

0. 65

6 79 .8 7

14 4. 87

- 31 4. 60 - 40 9. 44

18 04 .83 16 88 .92

1 18 22 .4 4 1 18 22 .4 4

2 85 12 .95 2 83 02 .21

1 37 .6 2 1 33 .5 7

10 52 .7 9 1 907 54 .7 4 10 21 .8 2 1 872 12 .2 8

10 12. 93 97 9. 78

21 9.2 7 21 5.5 1

0. 65 0. 65

6 58 .4 0 6 36 .8 6

14 2. 52 14 0. 08

0. 00

- 51 0. 19

15 65 .77

1 18 22 .4 4

2 80 78 .30

1 29 .5 2

9 90 .8 6 1 835 44 .4 9

94 6. 50

21 1.6 2

0. 65

6 15 .2 2

13 7. 55

0. 00

- 61 7. 45

14 34 .67

1 18 22 .4 4

2 78 39 .94

1 25 .4 8

9 59 .8 9 1 797 51 .3 6

91 3. 06

20 7.5 9

0. 65

5 93 .4 9

13 4. 93

11 25 .95 11 25 .95

0. 00 0. 00

- 73 1. 87 - 85 4. 17

12 94 .84 11 45 .36

1 18 22 .4 4 1 18 22 .4 4

2 75 85 .70 2 73 13 .92

1 21 .4 3 1 17 .3 8

9 28 .9 3 1 758 32 .9 1 8 97 .9 6 1 717 89 .1 2

87 9. 47 84 5. 69

20 3.4 2 19 9.1 0

0. 65 0. 65

5 71 .6 5 5 49 .7 0

13 2. 22 12 9. 42

2251.89

1125.95

0.00

-985.20

985.20

11822.44

27022.72

113.33

867.00 167620.00

811.71

194.64

0.65

527.61

126.52

2 25 1.8 9

11 25 .95

0. 00

-1 12 5. 95

8 13 .18

1 18 22 .4 4

2 67 09 .96

1 09 .2 9

8 36 .0 4 1 633 25 .5 5

77 7. 50

19 0.0 4

0. 65

5 05 .3 8

12 3. 52

1 182 2.4 4

2 25 1.8 9

11 25 .95

0. 00

-1 12 5. 95

6 27 .93

1 18 22 .4 4

2 65 24 .71

1 05 .2 4

8 05 .0 7 1 589 05 .7 7

74 5. 22

18 5.4 3

0. 65

4 84 .3 9

12 0. 53

- 61 .2 8 -62.83

1 182 2.4 4 11822.44

2 25 1.8 9 2251.89

11 25 .95 1125.95

0. 00 0.00

-1 12 5. 95 -1125.95

4 27 .86 211.12

1 18 22 .4 4 11822.44

2 63 24 .64 26107.89

1 01 .1 9 97.14

7 74 .1 1 1 543 60 .6 5 743.14 149690.20

71 2. 82 680.31

18 0.6 9 175.80

0. 65 0.65

4 63 .3 4 442.20

11 7. 45 114.27

- 53 .4 5

1 182 2.4 4

2 25 1.8 9

11 25 .95

0. 00

- 90 5. 22

10 82 .96

1 18 22 .4 4

2 72 00 .46

1 15 .7 7

8 85 .6 4 1 701 44 .8 2

83 2. 19

19 7.3 5

0. 65

5 40 .9 2

12 8. 27

a

Pn

Mn

Ф

292.50 0.00 292.50 1000.00

1 6.0 8

56 .30

35 .3 2

11 82 2.4 4

1 05 2.5 2

- 73 .43

0. 00

1 12 5.9 5

22 51 .89

1 18 22 .4 4

2 80 01 .81

2 79 .2 9

21 36 .5 4 2 357 81 .9 8

21 71. 85

26 3.7 8

0. 65

0.00

0.00

14 11 .7 0

17 1. 46


SENGKANG KP-2 30/50 BAHAN STRUKTUR

Kuat tekan beton,

fc' =

30

MPa


fy =

350

MPa


fy =

240

MPa

b= h= D= P= ts =

300 500 16 10 30

mm mm mm mm mm

17.880

kN

DIMENSI BALOK



Vu-tump =

1. TULANGAN GESER

Vu =


17.880 0.60 240

MPa

Vc = (√ fc') / 6 * b * d * 10 =

128.715

kN

f * Vc =

77.229

kN

f= fy = -3



→

f * Vs = Vu - f * Vc =


-

kN

17.880

kN

78.54

mm

s = Av * fy * d / ( Vs * 10 ) =

495.49

mm

smax = d / 2 =

226.00

mm

smax =

226.00 226.00 200 200

mm mm mm

Vs =


1

10 2

3


P

Av = ns * p / 4 * P =


kN

s= s=

→

1

P

10

2

BAB 24 S-1 20/45

A. DATA BALOK LANTAI BAHAN STRUKTUR

Kuat tekan beton,

fc' =

30

MPa


fy =

350

MPa


fy =

240

MPa

b= h= D= P= ts =

200 400 16 10 30

mm mm mm mm mm

DIMENSI BALOK


Momen rencana positif akibat beban terfaktor,

Mu =

+

16.055

kNm

Momen rencana negatif akibat beban terfaktor,

Mu =

-

16.055

kNm


Vu-tump =

11.960

kN


Vu-lap =

11.960

kN

B. PERHITUNGAN TULANGAN

Untuk : fc'

≤ 30 MPa,

b1 =

Untuk : fc' > 30 MPa,

b1 = 0.85 - 0.05 * ( fc' - 30) / 7 =

b1 = Faktor bentuk distribusi tegangan beton, Rasio tulangan pada kondisi balance , rb = b1* 0.85 * fc’/ fy * 600 / ( 600 + fy ) = →

Faktor tahanan momen maksimum, Rmax = 0.75 * rb * fy * [1 – ½*0.75* rb * fy / ( 0.85 * fc’ Faktor reduksi kekuatan lentur, Jarak tulangan terhadap sisi luar beton,

)] =

f = ds = ts + Æ + D/2 =

0.85 0.85 0.0391 8.2002 0.80 48.00

mm

1. TULANGAN TUMPUAN +

Mn = Mu / f = Momen positif nominal rencana, Diperkirakan jarak pusat tulangan lentur ke sisi beton, d' = Tinggi efektif balok, d = h - d' = 6

20.069 30 370.00

2

Rn = Mn * 10 / ( b * d ) =

Faktor tahanan momen, Rn

<

Rmax

→

kNm mm mm

0.7330 (OK)

Rasio tulangan yang diperlukan : ρ=

0.85 * fc’ / fy * [ 1 - √ [1 – 2 * Rn / ( 0.85 * fc’ ) ] = rmin = √ fc' / ( 4 * fy ) = Rasio tulangan minimum,

0.00213 0.00391

rmin = 1.4 / fy =

0.00400 0.00400

Rasio tulangan minimum, Rasio tulangan yang digunakan,

r=

→

As = r * b * d =

Luas tulangan yang diperlukan,

2

n = As / ( p / 4 * D ) =

Jumlah tulangan yang diperlukan, Digunakan tulangan,

Tul. Tarik

2

D

1.472 2

402 352.00 27.608

mm

Mn = As * fy * ( d - a / 2 ) * 10 =

47.618

kNm

f * Mn =

38.094

kNm

As = n * p / 4 * D =

Luas tulangan terpakai, Tinggi efektif balok,

d = h - d' = a = As * fy / ( 0.85 * fc' * b ) = -6

Tahanan momen balok, f * Mn

Syarat :

2

mm

16 2

Momen nominal,

296

38.094

≥ >

mm mm

+

Mu

16.055

→

AMAN (OK)

2. TULANGAN LAPANGAN -

Mn = Mu / f = Momen negatif nominal rencana, Diperkirakan jarak pusat tulangan lentur ke sisi beton, d' = Tinggi efektif balok, d = h - d' = 6

2

Rn = Mn * 10 / ( b * d ) =


<

Rmax

→

16.055 30 370.00

kNm mm mm

0.5864 (OK)



0.00170 0.00391

r min = 1.4 / fy =

0.00400 0.00400

Rasio tulangan minimum, Rasio tulangan yang digunakan, Luas tulangan yang diperlukan,

→

r=

As = r * b * d =

296

2

mm

2

n = As / ( p / 4 * D ) =


Tul. Tarik

2

D

1.472 16

2

mm

Mn = As * fy * ( d - a / 2 ) * 10 =

50.152

kNm

f * Mn =

40.122

kNm

d = h - d' = a = As * fy / ( 0.85 * fc' * b ) = -6

Momen nominal, Tahanan momen balok, 40.122

mm mm

-

≥

f * Mn

Syarat :

2

402 370.0 27.608

As = n * p / 4 * D =


Mu

>

16.055

AMAN (OK)

→

3. TULANGAN GESER TUMPUAN

Vu =


11.960 0.60 240

MPa

Vc = (√ fc') / 6 * b * d * 10 =

67.552

kN

f * Vc =

40.531

kN

f= fy = -3



→

f * Vs = Vu - f * Vc =


-

kN

11.960

kN

78.54

mm

s = Av * fy * d / ( Vs * 10 ) =

583.14

mm

smax = d / 2 =

176.00

mm

smax =

176.00 176.00 150 150

mm mm mm

Vs =


1

10 2

3


P

Av = ns * p / 4 * P =


kN

s= s=

→

1

P

10

2

4. TULANGAN GESER LAPANGAN

Vu =


11.960 0.60 48

MPa

Vc = (√ fc') / 6 * b * d * 10 =

67.552

kN

f * Vc =

40.531

kN

f= fy = -3



→

f * Vs = Vu - f * Vc =


-

kN

11.960

kN

78.54

mm

s = Av * fy * d / ( Vs * 10 ) =

583.14

mm

smax = d / 2 =

176.00

mm

smax =

176.00 176.00 175 175

mm mm mm

Vs =


1

P

10 2

Av = ns * p / 4 * P =


kN

3


s= s=

→

1

P

5. TABEL RENCANA PENULANGAN

TULANGAN TUMPUAN TUL ATAS 2 D TUL BAWAH 2 D SENGKANG D 10 -

16 16 150

TULANGAN LAPANGAN TUL ATAS 2 D TUL BAWAH 2 D SENGKANG D 10 -

16 16 175

10

2

BAB 25 S-2 15/30

A. DATA BALOK LANTAI BAHAN STRUKTUR

Kuat tekan beton,

fc' =

30

MPa


fy =

350

MPa


fy =

240

MPa

b= h= D= P= ts =

150 300 12 8 30

mm mm mm mm mm

DIMENSI BALOK


Momen rencana positif akibat beban terfaktor,

Mu =

+

3.447

kNm

Momen rencana negatif akibat beban terfaktor,

Mu =

-

3.447

kNm


Vu-tump =

4.518

kN


Vu-lap =

4.518

kN

≤ 30 MPa,

b1 =

0.85

Untuk : fc' > 30 MPa,

b1 = 0.85 - 0.05 * ( fc' - 30) / 7 =

B. PERHITUNGAN TULANGAN

Untuk : fc'

b1 = Faktor bentuk distribusi tegangan beton, Rasio tulangan pada kondisi balance , rb = b1* 0.85 * fc’/ fy * 600 / ( 600 + fy ) = →

Faktor tahanan momen maksimum, Rmax = 0.75 * rb * fy * [1 – ½*0.75* rb * fy / ( 0.85 * fc’ Faktor reduksi kekuatan lentur, Jarak tulangan terhadap sisi luar beton,

)] =

f = ds = ts + Æ + D/2 =

0.85 0.0391 8.2002 0.80 44.00

mm

1. TULANGAN TUMPUAN +

Mn = Mu / f = Momen positif nominal rencana, Diperkirakan jarak pusat tulangan lentur ke sisi beton, d' = Tinggi efektif balok, d = h - d' = 6

4.309 30 270.00

2

Rn = Mn * 10 / ( b * d ) =


<

Rmax

→

kNm mm mm

0.3940 (OK)



0.00113 0.00391

rmin = 1.4 / fy =

0.00400 0.00400

Rasio tulangan minimum, Rasio tulangan yang digunakan,

r=

→

As = r * b * d =

Luas tulangan yang diperlukan,

2

n = As / ( p / 4 * D ) =


Tul. Tarik

2

D

1.432 2

226 237.50 20.706

mm

Mn = As * fy * ( d - a / 2 ) * 10 =

17.990

kNm

f * Mn =

14.392

kNm

As = n * p / 4 * D =


d = h - d' = a = As * fy / ( 0.85 * fc' * b ) = -6

Tahanan momen balok, f * Mn

Syarat :

2

mm

12 2

Momen nominal,

162

14.392

≥ >

mm mm

+

Mu

3.447

→

AMAN (OK)

2. TULANGAN LAPANGAN -

Mn = Mu / f = Momen negatif nominal rencana, Diperkirakan jarak pusat tulangan lentur ke sisi beton, d' = Tinggi efektif balok, d = h - d' = 6

2

Rn = Mn * 10 / ( b * d ) =


<

Rmax

→

3.447 30 270.00

kNm mm mm

0.3152 (OK)



0.00091 0.00391

r min = 1.4 / fy =

0.00400 0.00400

Rasio tulangan minimum, Rasio tulangan yang digunakan, Luas tulangan yang diperlukan,

→

r=

As = r * b * d =

162

2

mm

2

n = As / ( p / 4 * D ) =


Tul. Tarik

2

D

1.432 12

2

mm

Mn = As * fy * ( d - a / 2 ) * 10 =

20.564

kNm

f * Mn =

16.451

kNm

d = h - d' = a = As * fy / ( 0.85 * fc' * b ) = -6

Momen nominal, Tahanan momen balok, 16.451

mm mm

-

≥

f * Mn

Syarat :

2

226 270.0 20.706

As = n * p / 4 * D =


Mu

>

3.447

AMAN (OK)

→

3. TULANGAN GESER TUMPUAN

Vu =


4.518 0.60 240

MPa

Vc = (√ fc') / 6 * b * d * 10 =

36.971

kN

f * Vc =

22.183

kN

f= fy = -3



→

f * Vs = Vu - f * Vc =


-

kN

4.518

kN

50.27

mm

s = Av * fy * d / ( Vs * 10 ) =

720.94

mm

smax = d / 2 =

118.75

mm

smax =

118.75 118.75 100 100

mm mm mm

Vs =


1

8 2

3


P

Av = ns * p / 4 * P =


kN

s= s=

→

1

P

8

2

4. TULANGAN GESER LAPANGAN

Vu =


4.518 0.60 44

MPa

Vc = (√ fc') / 6 * b * d * 10 =

36.971

kN

f * Vc =

22.183

kN

f= fy = -3



→

f * Vs = Vu - f * Vc =


-

kN

4.518

kN

50.27

mm

s = Av * fy * d / ( Vs * 10 ) =

720.94

mm

smax = d / 2 =

118.75

mm

smax =

118.75 118.75 100 100

mm mm mm

Vs =


1

P

8 2

Av = ns * p / 4 * P =


kN

3


s= s=

→

1

P

5. TABEL RENCANA PENULANGAN

TULANGAN TUMPUAN TUL ATAS 2 D TUL BAWAH 2 D SENGKANG D 8 -

12 16 100

TULANGAN LAPANGAN TUL ATAS 2 D TUL BAWAH 2 D SENGKANG D 8 -

12 12 100

8

2

BAB 26 PONDASI (P-1)

A. DATA TANAH DATA HASIL PENGUJIAN

No

Kedalaman z1 (m) 1 2 3 4 5

z2 (m)

0.00 1.25 2.50 3.75 5.00

1.20 2.40 3.60 4.80 6.00

LABORATORIUM (DATA BOR TANAH) Jenis

cu

g

Tanah

(kN/m )

lempung lempung lempung lemp. padat lemp. padat

40.00 40.00 75.00 150.00 250.00

SONDIR

SPT

qf

Nilai SPT

(kN/m )

j ( ... ▫ )

(kN/m )

N

33.33 34.78 68.18 142.86 250.00

0 5 5 10 30

40.00 40.00 75.00 150.00 150.00

5 12 40 75 150

B. DATA BAHAN Jenis tiang pancang :

Beton bertulang tampang lingkaran

Diameter tiang pancang,

D=

0.30

m

Panjang tiang pancang,

L=

5.00

m

f c' =

30

MPa

wc =

24

kN/m

Kuat tekan beton tiang pancang, Berat beton bertulang,

C. TAHANAN AKSIAL TIANG PANCANG 1. BERDASARKAN KEKUATAN BAHAN Luas penampang tiang pancang, Berat tiang pancang, Kuat tekan beton tiang pancang,

2

A = p / 4 * D = Wp = A * L * wc =

0.0707

m

8.48

kN

f c' =

30000

kPa

626

kN

2

Kapasitas dukung nominal tiang pancang, Faktor reduksi kekuatan, Tahanan aksial tiang pancang,

Pn = 0.30 * f c' * A - 1.2 * W p = f = f * Pn =

0.70 438.20

kN

3

2. BERDASARKAN DATA BOR TANAH (SKEMPTON) a. Tahanan ujung Pb = Ab * cb * Nc

Tahanan ujung nominal dihitung dengan rumus : 2

Ab = Luas penampang ujung bawah tiang (m ), 2 cb = Kohesi tanah di bawah dasar tiang (kN/m ),

Nc = Faktor daya dukung. D=


0.30

m

Ab = p / 4 * D =

0.0707

m

Kohesi tanah di sekitar dasar tiang,

cb =

250.00

kN/m

Faktor daya dukung menurut Skempton,

Nc =

9

Tahanan ujung nominal tiang pancang :

Pb = Ab * cb * Nc =

2

Luas tampang tiang pancang,

159.043

2

kN

b. Tahanan gesek Ps = S [ ad * cu * As ]

Tahanan gesek nominal menurut Skempton :

ad = faktor adhesi 2 cu = Kohesi tanah di sepanjang tiang (kN/m ) 2 As = Luas permukaan dinding tiang (m ).

Faktor adhesi untuk jenis tanah lempung pada tiang pancang yang nilainya tergantung dari

ad = 0.2 + [ 0.98 ] 0.300 D=

→

nilai kohesi tanah, menurut Skempton, diambil : Diameter tiang pancang,

cu

m

As = p * D * L1

Luas permukaan dinding segmen tiang,

L1 = panjang segmen tiang pancang yang ditinjau (m). Perhitungan tahanan gesek nominal tiang No

Kedalaman

L1

As 2

cu

ad 2

Ps

z1 (m)

z2 (m)

(m)

(m )

(kN/m )

1

1.25

2.40

1.2

1.0838

40.00

0.65

27.994

2

2.50

3.60

1.1

1.0367

75.00

0.42

32.638

3

3.75

4.80

1.1

0.9896

150.00

0.25

36.857

4

5.00

6.00

1.0

0.9425

250.00

0.21

48.633

(kN)

Tahanan gesek nominal tiang,

146.122

Ps = S ad * cu * As =

146.122

kN

Pn = Pb + Ps = f = f * Pn =

305.17

kN

c. Tahanan aksial tiang pancang Tahanan nominal tiang pancang, Faktor reduksi kekuatan, Tahanan aksial tiang pancang,

0.70 213.62

kN

2

3. BERDASARKAN HASIL UJI SONDIR (BAGEMANN) a. Tahanan ujung Pb = w * Ab * qc

Tahanan ujung nominal dihitung dengan rumus :

w = faktor reduksi nilai tahanan ujung nominal tiang, 2 Ab = luas ujung bawah tiang (m ),

qc = tahanan penetrasi kerucut statis yang merupakan nilai rata-rata dihitung dari 8.D di 2

atas dasar tiang sampai 4.D di bawah dasar tiang (kN/m ),

D=


2

Ab = p / 4 * D =


0.30

m

0.0707

m

Tahanan penetrasi kerucut statis rata-rata dari 8.D di atas dasar s.d. 4.D di bawah dasar 2 kg/cm → tiang pancang, 15000 qc = 150 qc =

w =

Faktor reduksi nilai tahanan ujung nominal tiang,

Pb = w * Ab * qc =


2

kN/m

2

0.50 530.144

kN

b. Tahanan gesek Ps = S [ As * qf ]

Tahanan gesek nominal menurut Skempton dihitung dg rumus : 2 Af = Luas permukaan segmen dinding tiang (m ).

As = p * D * L1

qf = tahanan gesek kerucut statis rata-rata (kN/m). No

Kedalaman

L1

As

qf

Ps

z1 (m)

z2 (m)

(m)

(m )

(kN/m )

(kN)

1

1.25

2.40

1.2

1.0838

40.00

43.35

2

2.50

3.60

1.1

1.0367

40.00

41.47

3

3.75

4.80

1.1

0.9896

75.00

74.22

4

5.00

5.00

1.0

0.9425

19.50

18.38

Ps = S [ As * qf ] =

177.42


Pn = Pb + Ps = f = → f * Pn =

707.57

kN

0.70 495.30

kN

4. BERDASARKAN HASIL UJI SPT (MEYERHOFF) Kapasitas nominal tiang pancang secara empiris dari nilai N hasil pengujian SPT menurut Meyerhoff dinyatakan dengan rumus : dan harus 

Pn = 40 * Nb * Ab + Ň * As

(kN)

Pn = 380 * Ň * Ab

(kN)

Nb = nilai SPT di sekitar dasar tiang, dihitung dari 8.D di atas dasar tiang s.d 4.D di bawah dasar tiang,

Ň = nilai SPT rata-rata di sepanjang tiang, 2 Ab = luas dasar tiang (m ) 2 As = luas selimut tiang (m )

Berdasarkan hasil pengujian SPT diperoleh data sbb. No

Nilai SPT

L1

z2 (m)

N

(m)

Kedalaman z1 (m)

L1 * N

1

0.00

1.20

5

1.2

6.0

2

1.25

2.40

12

1.2

13.8

3

2.50

3.60

40

1.1

44.0

4

3.75

5.00

75

1.3

93.8

4.7

157.6

Ň = S L1*N / S L1 =

Nilai SPT rata-rata di sepanjang tiang,

33.52

Nilai SPT di sekitar dasar tiang (8.D di atas dasar tiang s.d 4.D di bawah dasar tiang),

Nb = D= L=

Diameter tiang pancang, Panjang tiang pancang,

2

75.00 0.30

m

5.00

m 2

Luas dasar tiang pancang,

Ab = p / 4 * D =

0.0707

m

Luas selimut tiang pancang,

As = p * D * L =

4.7124

m

2

Pn = 40 * Nb * Ab + Ň * As = 370.0228 kN Pn

<

Kapasitas nominal tiang pancang, Faktor reduksi kekuatan, Tahanan aksial tiang pancang,

→

380 * Ň * Ab =

900.40

kN

Pn = f = f * Pn =

370.02

kN

0.70 259.02

kN

5. REKAP TAHANAN AKSIAL TIANG PANCANG No 1 2 3 4

f * Pn

Uraian Tahanan Aksial Tiang Pancang Berdasarkan kekuatan bahan Berdasarkan data bor tanah (Skempton) Berdasarkan hasil uji sondir (Bagemann) Berdasarkan hasil uji SPT (Meyerhoff)

438.20 213.62 495.30 259.02

Daya dukung aksial terkecil, Diambil tahanan aksial tiang pancang,

→

f * Pn = f * Pn =

213.62

kN

210.00

kN

D. TAHANAN LATERAL TIANG PANCANG 1. BERDASARKAN DEFLEKSI TIANG MAKSIMUM (BROMS) Tahanan lateral tiang (H) kategori tiang panjang, dapat dihitung dengan persamaan :

H = yo * kh * D / [ 2 * b * ( e * b + 1 ) ] 0.25

dengan, b = [ kh * D / ( 4 * E c * Ic ) ]

D= L= kh =

D = Diameter tiang pancang (m), L = panjang tiang pancang (m), 3 kh = modulus subgrade horisontal (kN/m ), 2 Ec = modulus elastis tiang (kN/m ),

5.00

m 3 kN/m

26720

4

e = Jarak beban lateral terhadap muka tanah (m),

yo = defleksi tiang maksimum (m).

Ic = p / 64 * D = 0.000398 m 0.80 m e= 0.010 m yo =

4

b = [ kh * D / ( 4 * E c * Ic ) ]0.25 = 0.6651906 m

koefisien defleksi tiang,

b*L=

m

2 3 Ec = 4700 *  f c' * 10 = 25742960 kN/m

4 Ic = momen inersia penampang (m ),

b=

0.30

3.33

> 2.5

maka termasuk tiang panjang (OK)

Tahanan lateral nominal tiang pancang,

H = yo * kh * D / [ 2 * b * ( e * b + 1 ) ] = f = f * Hn = →

Faktor reduksi kekuatan, Tahanan lateral tiang pancang,

39.33

kN

0.60 23.60

kN

12000

kN/m

2. BERDASARKAN MOMEN MAKSIMUM (BRINCH HANSEN) 3

f b = 0.40 * f c' * 10 =

Kuat lentur beton tiang pancang,

W = Ic / (D/2) =

Tahanan momen,

My = f b * W =

Momen maksimum, Kohesi tanah rata-rata di sepanjang tiang No

L1

cu

(m) 1.2 1.2 1.1 2.3

(kN/m )

Kedalaman 1 2 3 4

z1 (m)

z2 (m)

0.00 1.25 2.50 3.75

1.20 2.40 3.60 6.00

S L1 =

40.00 40.00 75.00 250.00

5.7

Kohesi tanah rata-rata,

2

My = 9 / 4 * D * ču * g Dari pers.(1) :

f = 0.00285671 * Hn

31.81

m

3

kNm

cu * L1 48.00 46.00 82.50 562.50

Scu*L1 = 739.00 ču = S [ cu * L1 ] / S L1 =

f = Hn / [ 9 * ču * D ] g = L - ( f + 1.5 * D ) My = Hn * ( e + 1.5 * D + 0.5 * f )

0.00265

2

pers.(1) pers.(2) pers.(3) pers.(4)

129.64912 kN/m

2

Dari pers.(2) :

g= 2

g = Dari pers.(3) :

Dari pers.(4) :

-0.00285671 * Hn

4.55

2

* Hn

0.000008

My =

Hn * (

My =

0.00143

* Hu

My = 0.00071418

* Hu

Pers.kuadrat :

0=

1.250 2

* Hn

20.70

9 / 4 * D * cu =

87.513

0.00143

* Hn )

1.25000

* Hn

2

-2.2750 * Hn

1811.741

2

3.5250 * Hn

-1811.741

* Hu

0.00071

+

-0.0259961

Hn =

Dari pers. kuadrat, diperoleh tahanan lateral nominal,

kN m

Mmax = Hn * ( e + 1.5 * D + 0.5 * f ) =

901.312

kNm

>

Mmax Dari pers.(3) :

f=

469.340 1.341

My =

My

Hn * (

→

1.250

Pers.kuadrat :

0.00143 * Hn

0=

2

0.00143 * Hn ) 2

=

31.81

Termasuk tiang panjang (OK)

0.00143 * Hn

+

1.25000 * Hn

Dari pers. kuadrat, diperoleh tahanan lateral nominal, Faktor reduksi kekuatan, →

Tahanan lateral tiang pancang,

1.25000 * Hu -31.81

Hn = f = f * Hn =

24.747

kN

0.60 14.85

kN

3. REKAP TAHANAN LATERAL TIANG No

f * Hn

Uraian Tahanan Lateral Tiang Pancang 1 Berdasarkan defleksi tiang maksimum (Broms) 2 Berdasarkan momen maksimum (Brinch Hansen)

23.60 14.85

Tahanan lateral tiang terkecil, →

Diambil tahanan lateral tiang pancang,

f * Hn = f * Hn =

14.85

kN

10.00

kN

PERHITUNGAN KEKUATAN FONDASI KODE FONDASI :

F4

DATA BAHAN PILECAP Kuat tekan beton,

f c' =

30

MPa

Kuat leleh baja tulangan deform (  > 12 mm ),

f y =

350

MPa

Kuat leleh baja tulangan polos ( 

f y =

240

MPa

wc =

24

kN/m

Berat beton bertulang,

≤ 12

mm ),

3

DATA DIMENSI FONDASI Lebar kolom arah x,

bx =

0.40

m

Lebar kolom arah y,

0.60

m

0.30

m

0.30

m

0.80

Berat volume tanah di atas pilecap,

by = a= h= z= ws =

18.00

m 3 kN/m

Posisi kolom (dalam = 40, tepi = 30, sudut = 20)

as =

40

Gaya aksial kolom akibat beban terfaktor,

Puk =

727.81

kN

Momen arah x akibat beban terfaktor.

Mux =

11.83

kNm

Momen arah y akibat beban terfaktor.

Muy =

5.92

kNm

Gaya lateral arah x akibat beban terfaktor,

Hux =

31.03

kN

Gaya lateral arah y akibat beban terfaktor,

Huy =

15.52

kN

210.00

kN

10.00

kN

Jarak tiang pancang tepi terhadap sisi luar beton, Tebal pilecap, Tebal tanah di atas pilecap,

DATA BEBAN FONDASI

f * Pn = f * Hn =

Tahanan aksial tiang pancang, Tahanan lateral tiang pancang, DATA SUSUNAN TIANG PANCANG Susunan tiang pancang arah x : 2

No.

Jumlah

x

n*x

1 2

n 2 2

(m) 0.50 0.50

(m ) 0.50 0.50

4

S x2 =

1.00

Susunan tiang pancang arah y : 2

No.

Jumlah

y

n*y

1 2

n 2 2

(m) 0.50 0.50

(m ) 0.50 0.50

4

S y2 =

1.00

Lebar pilecap arah x,

Lx =

1.60

m

Lebar pilecap arah y,

Ly =

1.60

m

n=

2

n=

2

1. GAYA AKSIAL PADA TIANG PANCANG Berat tanah di atas pilecap,

Ws = Lx * Ly * z * ws =

36.86

kN

Berat pilecap,

Wc = Lx * Ly * h * wc =

18.43

kN

Pu = Puk + 1.2 * W s + 1.2 * W c =

794.17

kN

Total gaya aksial terfaktor,

Lengan maksimum tiang pancang arah x thd. pusat,

xmax =

0.50

m

Lengan maksimum tiang pancang arah y thd. pusat,

ymax =

0.50

m

Lengan minimum tiang pancang arah x thd. pusat,

xmin =

0.50

m

Lengan minimum tiang pancang arah y thd. pusat, Gaya aksial maksimum dan minimum pada tiang pancang,

ymin =

0.50

m

207.42

kN

207.42

kN

2

2

pumax = Pu / n + Mux* xmax / Sx + Muy* ymax / Sy = 2

pumin = Pu / n + Mux* xmin / Sx pumax

Syarat :

207.42

2

+ Muy* ymin / Sy =

f * Pn

≤

<

→

210.00

AMAN (OK)

2. GAYA LATERAL PADA TIANG PANCANG Gaya lateral arah x pada tiang,

hux = Hux / n =

7.76

kN

Gaya lateral arah y pada tiang,

huy = Huy / n =

3.88

kN

8.67

kN

2

Syarat :

2

humax =  ( hux + huy ) =

Gaya lateral kombinasi dua arah,

humax 8.67

3. TINJAUAN GESER ARAH X

≤

<

f * Hn 10.00

→

AMAN (OK)

0.100

m

0.200

m

Jarak bid. kritis terhadap sisi luar,

d' = d = h - d' = cx = ( Lx - bx - d ) / 2 =

0.500

m

Berat beton,

W1 = cx * Ly * h * wc =

5.760

kN

Berat tanah,

W2 = cx * Ly * z * ws =

11.520

kN

397.554

kN

1600

mm

200

mm

Jarak pusat tulangan terhadap sisi luar beton, Tebal efektif pilecap,

Vux = 2 * pumax - W1 - W2 =

Gaya geser arah x,

b = Ly = d= bc = bx / by =

Lebar bidang geser untuk tinjauan arah x, Tebal efektif pilecap, Rasio sisi panjang thd. sisi pendek kolom,

0.6667

Kuat geser pilecap arah x, diambil nilai terkecil dari Vc yang diperoleh dari pers.sbb. : -3

Vc = [ 1 + 2 / bc ] * √ f c' * b * d / 6 * 10 = 1168.475 kN -3

Vc = [ as * d / b + 2 ] * √ f c' * b * d / 12 * 10 = 1022.415 kN -3

Vc = 1 / 3 * √ f c' * b * d * 10 =

584.237

kN

Vc = f = f * Vc =

584.237

kN

Diambil, kuat geser pilecap, Faktor reduksi kekuatan geser, Kuat geser pilecap,

0.75 438.178

Syarat yang harus dipenuhi,

f * Vc 438.178

4. TINJAUAN GESER ARAH Y

≥

>

Vux 397.554

AMAN (OK)

kN

0.100

m

0.200

m


d' = d = h - d' = cy = ( Ly - by - d ) / 2 =

0.400

m

Berat beton,

W1 = cy * Lx * h * wc =

4.608

kN

Berat tanah,

W2 = cy * Lx * z * ws =

9.216

kN

401.010

kN

1600

mm

200

mm


Vuy = 2 * pumax - W1 - W2 =

Gaya geser arah y,

b = Lx = d= bc = bx / by =

Lebar bidang geser untuk tinjauan arah y, Tebal efektif pilecap, Rasio sisi panjang thd. sisi pendek kolom,

0.6667

Kuat geser pilecap arah y, diambil nilai terkecil dari V c yang diperoleh dari pers.sbb. : -3

Vc = [ 1 + 2 / bc ] * √ f c' * b * d / 6 * 10 = 1168.475 kN -3

Vc = [ as * d / b + 2 ] * √ f c' * b * d / 12 * 10 = 1022.415 kN -3

Vc = 1 / 3 * √ f c' * b * d * 10 =

584.237

kN

Vc = f = f * Vc =

584.237

kN


0.75 438.178


f * Vc 438.178

≥

>

5. TINJAUAN GESER DUA ARAH (PONS)

Vux 401.010

AMAN (OK)

kN

0.100

m

0.200

m

Lebar bidang geser pons arah x,

d' = d = h - d' = Bx = bx + d =

0.600

m

Lebar bidang geser pons arah y,

By = by + d =

0.800

m

727.810

kN

Ap = 2 * ( Bx + By ) * d =

0.560

m

bp = 2 * ( Bx + By ) =

2.800

m

bc = bx / by =

0.6667


Puk =

Gaya geser pons akibat beban terfaktor pada kolom, Luas bidang geser pons, Lebar bidang geser pons, Rasio sisi panjang thd. sisi pendek kolom,

2

Tegangan geser pons, diambil nilai terkecil dari f p yang diperoleh dari pers.sbb. :

f p = [ 1 + 2 / bc ] * √ f c' / 6 =

3.651

MPa

f p = [ as * d / bp + 2 ] * √ f c' / 12 =

2.217

MPa

f p = 1 / 3 * √ f c' =

1.826

MPa

f p = f =

1.826

MPa

f * Vnp = f * Ap * f p * 103 =

766.81

Tegangan geser pons yang disyaratkan, Faktor reduksi kekuatan geser pons, Kuat geser pons, Syarat :

f * Vnp 766.812

6. PEMBESIAN PILECAP 6.1. TULANGAN LENTUR ARAH X

≥

>

0.75

Puk 727.810

AMAN (OK)

kN

cx = ( Lx - bx ) / 2 =

0.600

m

ex = cx - a =

0.300

m

Berat beton,

W1 = cx * Ly * h * wc =

6.912

kN

Berat tanah, Momen yang terjadi pada pilecap,

W2 = cx * Ly * z * ws =

13.824

kN

Jarak tepi kolom terhadap sisi luar pilecap, Jarak tiang thd. sisi kolom,

Mux = 2 * pumax * ex - W1 * cx / 2 - W 2 * cx / 2 = Lebar pilecap yang ditinjau, Tebal pilecap, Jarak pusat tulangan thd. sisi luar beton, Tebal efektif plat, Kuat tekan beton,

118.229

kNm

b = Ly = h= d' = d = h - d' = f c' =

1600

mm

300

mm

100

mm

200

mm

30

MPa

f y =

350

MPa

Kuat leleh baja tulangan, Modulus elastis baja,

Es = 2.00E+05 MPa

Faktor distribusi teg. beton,

b1 =

rb = b1* 0.85 * f c’/ f y * 600 / ( 600 + f y ) = Faktor reduksi kekuatan lentur, f = Rmax = 0.75 * rb * f y * [1-½*0.75* rb * f y / ( 0.85 * f c’ ) ] = Mn = Mux / f = 6

2

Rn = Mn * 10 / ( b * d ) = Rn

<

Rmax

0.85 0.0391128 0.80 8.200 147.787

kNm

2.30917

(OK)

Rasio tulangan yang diperlukan,

r = 0.85 * f c’ / f y * [ 1 -  {1 – 2 * Rn / ( 0.85 * f c’ ) } ] = Rasio tulangan minimum, rmin = r= Rasio tulangan yang digunakan, Luas tulangan yang diperlukan, As = r * b * d =

0.0025 0.0069 2216.61

D 16

Diameter tulangan yang digunakan, Jarak tulangan yang diperlukan,

0.0069

2

mm

2

mm

s = p / 4 * D * b / As =

145

mm

smax =

200

mm

s=

145

mm

Jarak tulangan maksimum, Jarak tulangan yang digunakan, Digunakan tulangan,

D 16

Luas tulangan terpakai,

As = p / 4 * D * b / s =

2

140 2297.85

mm

2

6.2. TULANGAN LENTUR ARAH Y

cy = ( Ly - by ) / 2 =

0.500

m

ey = cy - a =

0.200

m

Berat beton,

W1 = cy * Lx * h * wc =

5.760

kN


W2 = cy * Lx * z * ws =

11.520

kN

Muy = 2 * pumax * ey - W1 * cy / 2 - W2 * cy / 2 =

78.647

kNm

b = Lx = h= d' = d = h - d' = f c' =

1600

mm

300

mm

100

mm

200

mm

30

MPa

f y =

350

MPa

Jarak tepi kolom terhadap sisi luar pilecap, Jarak tiang thd. sisi kolom,

Lebar pilecap yang ditinjau, Tebal pilecap, Jarak pusat tulangan thd. sisi luar beton, Tebal efektif plat, Kuat tekan beton, Kuat leleh baja tulangan, Modulus elastis baja,

Es = 2.00E+05 MPa


b1 =

rb = b1* 0.85 * f c’/ f y * 600 / ( 600 + f y ) = Faktor reduksi kekuatan lentur, f = Rmax = 0.75 * rb * f y * [1-½*0.75* rb * f y / ( 0.85 * f c’ ) ] = Mn = Muy / f = 6

2

Rn = Mn * 10 / ( b * d ) = Rn

<

Rmax

0.85 0.0391128 0.80 8.200 98.308

kNm

1.53607

(OK)



0.0045 0.0025 0.0045 1449.46

mm

2

D 16


2

s = p / 4 * D * b / As =

222

mm

smax =

200

mm

s=

200

mm

Jarak tulangan maksimum, Jarak tulangan yang digunakan, Digunakan tulangan, Luas tulangan terpakai,

mm

D 16

200

2

As = p / 4 * D * b / s =

1608.50

rsmin =

0.0014

mm

2

3. TULANGAN SUSUT Rasio tulangan susut minimum, Luas tulangan susut arah x,

Asx = rsmin* b * d =

448

mm

2

Luas tulangan susut arah y,

Asy = rsmin* b * d =

448

mm

2

Diameter tulangan yang digunakan, Jarak tulangan susut arah x,

12 2

sx = p / 4 *  * b / Asx =

404

mm

sx,max =

200

mm

sx =

200

mm

sy = p / 4 *  * b / Asy =

404

mm

sy,max =

200

mm

sy =

200

mm

Jarak tulangan susut maksimum arah x, Jarak tulangan susut arah x yang digunakan, Jarak tulangan susut arah y,

2

Jarak tulangan susut maksimum arah y, Jarak tulangan susut arah y yang digunakan, Digunakan tulangan susut arah x, Digunakan tulangan susut arah y,

mm

 12  12

-

200 200

BAB 27 PONDASI (P-2)

A. DATA TANAH DATA HASIL PENGUJIAN

No

Kedalaman z1 (m) 1 2 3 4 5

z2 (m)

0.00 1.25 2.50 3.75 5.00

1.20 2.40 3.60 4.80 6.00

LABORATORIUM (DATA BOR TANAH) Jenis

cu

g

Tanah

(kN/m )

lempung lempung lempung lemp. padat lemp. padat

40.00 40.00 75.00 150.00 250.00

SONDIR

SPT

qf

Nilai SPT

(kN/m )

j ( ... ▫ )

(kN/m )

N

33.33 34.78 68.18 142.86 250.00

0 5 5 10 30

40.00 40.00 75.00 150.00 150.00

5 12 40 75 150

B. DATA BAHAN Jenis tiang pancang :

Beton bertulang tampang lingkaran


D=

0.30

m

Panjang tiang pancang,

L=

5.00

m

f c' =

30

MPa

wc =

24

kN/m

Kuat tekan beton tiang pancang, Berat beton bertulang,

C. TAHANAN AKSIAL TIANG PANCANG 1. BERDASARKAN KEKUATAN BAHAN Luas penampang tiang pancang, Berat tiang pancang, Kuat tekan beton tiang pancang,

2

A = p / 4 * D = Wp = A * L * wc =

0.0707

m

8.48

kN

f c' =

30000

kPa

626

kN

2

Kapasitas dukung nominal tiang pancang, Faktor reduksi kekuatan, Tahanan aksial tiang pancang,

Pn = 0.30 * f c' * A - 1.2 * W p = f = f * Pn =

0.70 438.20

kN

3

2. BERDASARKAN DATA BOR TANAH (SKEMPTON) a. Tahanan ujung Pb = Ab * cb * Nc

Tahanan ujung nominal dihitung dengan rumus : 2

Ab = Luas penampang ujung bawah tiang (m ), 2 cb = Kohesi tanah di bawah dasar tiang (kN/m ),

Nc = Faktor daya dukung. D=


0.30

m

Ab = p / 4 * D =

0.0707

m

Kohesi tanah di sekitar dasar tiang,

cb =

250.00

kN/m

Faktor daya dukung menurut Skempton,

Nc =

9


Pb = Ab * cb * Nc =

2


159.043

2

kN

b. Tahanan gesek Ps = S [ ad * cu * As ]

Tahanan gesek nominal menurut Skempton :

ad = faktor adhesi 2 cu = Kohesi tanah di sepanjang tiang (kN/m ) 2 As = Luas permukaan dinding tiang (m ).

Faktor adhesi untuk jenis tanah lempung pada tiang pancang yang nilainya tergantung dari

ad = 0.2 + [ 0.98 ] 0.300 D=

→

nilai kohesi tanah, menurut Skempton, diambil : Diameter tiang pancang,

cu

m

As = p * D * L1

Luas permukaan dinding segmen tiang,

L1 = panjang segmen tiang pancang yang ditinjau (m). Perhitungan tahanan gesek nominal tiang No

Kedalaman

L1

As 2

cu

ad 2

Ps

z1 (m)

z2 (m)

(m)

(m )

(kN/m )

1

1.25

2.40

1.2

1.0838

40.00

0.65

27.994

2

2.50

3.60

1.1

1.0367

75.00

0.42

32.638

3

3.75

4.80

1.1

0.9896

150.00

0.25

36.857

4

5.00

6.00

1.0

0.9425

250.00

0.21

48.633

(kN)

Tahanan gesek nominal tiang,

146.122

Ps = S ad * cu * As =

146.122

kN

Pn = Pb + Ps = f = f * Pn =

305.17

kN


0.70 213.62

kN

2

3. BERDASARKAN HASIL UJI SONDIR (BAGEMANN) a. Tahanan ujung Pb = w * Ab * qc

Tahanan ujung nominal dihitung dengan rumus :

w = faktor reduksi nilai tahanan ujung nominal tiang, 2 Ab = luas ujung bawah tiang (m ),

qc = tahanan penetrasi kerucut statis yang merupakan nilai rata-rata dihitung dari 8.D di 2

atas dasar tiang sampai 4.D di bawah dasar tiang (kN/m ),

D=


2

Ab = p / 4 * D =


0.30

m

0.0707

m

Tahanan penetrasi kerucut statis rata-rata dari 8.D di atas dasar s.d. 4.D di bawah dasar 2 kg/cm → tiang pancang, 15000 qc = 150 qc =

w =

Faktor reduksi nilai tahanan ujung nominal tiang,

Pb = w * Ab * qc =


2

kN/m

2

0.50 530.144

kN

b. Tahanan gesek Ps = S [ As * qf ]

Tahanan gesek nominal menurut Skempton dihitung dg rumus : 2 Af = Luas permukaan segmen dinding tiang (m ).

As = p * D * L1

qf = tahanan gesek kerucut statis rata-rata (kN/m). No

Kedalaman

L1

As

qf

Ps

z1 (m)

z2 (m)

(m)

(m )

(kN/m )

(kN)

1

1.25

2.40

1.2

1.0838

40.00

43.35

2

2.50

3.60

1.1

1.0367

40.00

41.47

3

3.75

4.80

1.1

0.9896

75.00

74.22

4

5.00

5.00

1.0

0.9425

19.50

18.38

Ps = S [ As * qf ] =

177.42


Pn = Pb + Ps = f = → f * Pn =

707.57

kN

0.70 495.30

kN

4. BERDASARKAN HASIL UJI SPT (MEYERHOFF) Kapasitas nominal tiang pancang secara empiris dari nilai N hasil pengujian SPT menurut Meyerhoff dinyatakan dengan rumus : dan harus 

Pn = 40 * Nb * Ab + Ň * As

(kN)

Pn = 380 * Ň * Ab

(kN)

Nb = nilai SPT di sekitar dasar tiang, dihitung dari 8.D di atas dasar tiang s.d 4.D di bawah dasar tiang,

Ň = nilai SPT rata-rata di sepanjang tiang, 2 Ab = luas dasar tiang (m ) 2 As = luas selimut tiang (m )

Berdasarkan hasil pengujian SPT diperoleh data sbb. No

Nilai SPT

L1

z2 (m)

N

(m)

Kedalaman z1 (m)

L1 * N

1

0.00

1.20

5

1.2

6.0

2

1.25

2.40

12

1.2

13.8

3

2.50

3.60

40

1.1

44.0

4

3.75

5.00

75

1.3

93.8

4.7

157.6

Ň = S L1*N / S L1 =

Nilai SPT rata-rata di sepanjang tiang,

33.52

Nilai SPT di sekitar dasar tiang (8.D di atas dasar tiang s.d 4.D di bawah dasar tiang),

Nb = D= L=

Diameter tiang pancang, Panjang tiang pancang,

2

75.00 0.30

m

5.00

m 2

Luas dasar tiang pancang,

Ab = p / 4 * D =

0.0707

m

Luas selimut tiang pancang,

As = p * D * L =

4.7124

m

2

Pn = 40 * Nb * Ab + Ň * As = 370.0228 kN Pn

<

Kapasitas nominal tiang pancang, Faktor reduksi kekuatan, Tahanan aksial tiang pancang,

→

380 * Ň * Ab =

900.40

kN

Pn = f = f * Pn =

370.02

kN

0.70 259.02

kN

5. REKAP TAHANAN AKSIAL TIANG PANCANG No 1 2 3 4

f * Pn

Uraian Tahanan Aksial Tiang Pancang Berdasarkan kekuatan bahan Berdasarkan data bor tanah (Skempton) Berdasarkan hasil uji sondir (Bagemann) Berdasarkan hasil uji SPT (Meyerhoff)

438.20 213.62 495.30 259.02

Daya dukung aksial terkecil, Diambil tahanan aksial tiang pancang,

→

f * Pn = f * Pn =

213.62

kN

210.00

kN

D. TAHANAN LATERAL TIANG PANCANG 1. BERDASARKAN DEFLEKSI TIANG MAKSIMUM (BROMS) Tahanan lateral tiang (H) kategori tiang panjang, dapat dihitung dengan persamaan :

H = yo * kh * D / [ 2 * b * ( e * b + 1 ) ] 0.25

dengan, b = [ kh * D / ( 4 * E c * Ic ) ]

D= L= kh =

D = Diameter tiang pancang (m), L = panjang tiang pancang (m), 3 kh = modulus subgrade horisontal (kN/m ), 2 Ec = modulus elastis tiang (kN/m ),

5.00

m 3 kN/m

26720

4

e = Jarak beban lateral terhadap muka tanah (m),

yo = defleksi tiang maksimum (m).

Ic = p / 64 * D = 0.000398 m 0.80 m e= 0.010 m yo =

4

b = [ kh * D / ( 4 * E c * Ic ) ]0.25 = 0.6651906 m

koefisien defleksi tiang,

b*L=

m

2 3 Ec = 4700 *  f c' * 10 = 25742960 kN/m

4 Ic = momen inersia penampang (m ),

b=

0.30

3.33

> 2.5

maka termasuk tiang panjang (OK)

Tahanan lateral nominal tiang pancang,

H = yo * kh * D / [ 2 * b * ( e * b + 1 ) ] = f = f * Hn = →

Faktor reduksi kekuatan, Tahanan lateral tiang pancang,

39.33

kN

0.60 23.60

kN

12000

kN/m

2. BERDASARKAN MOMEN MAKSIMUM (BRINCH HANSEN) 3

f b = 0.40 * f c' * 10 =

Kuat lentur beton tiang pancang,

W = Ic / (D/2) =

Tahanan momen,

My = f b * W =

Momen maksimum, Kohesi tanah rata-rata di sepanjang tiang No

L1

cu

(m) 1.2 1.2 1.1 2.3

(kN/m )

Kedalaman 1 2 3 4

z1 (m)

z2 (m)

0.00 1.25 2.50 3.75

1.20 2.40 3.60 6.00

S L1 =

40.00 40.00 75.00 250.00

5.7

Kohesi tanah rata-rata,

2

My = 9 / 4 * D * ču * g Dari pers.(1) :

f = 0.00285671 * Hn

31.81

m

3

kNm

cu * L1 48.00 46.00 82.50 562.50

Scu*L1 = 739.00 ču = S [ cu * L1 ] / S L1 =

f = Hn / [ 9 * ču * D ] g = L - ( f + 1.5 * D ) My = Hn * ( e + 1.5 * D + 0.5 * f )

0.00265

2

pers.(1) pers.(2) pers.(3) pers.(4)

129.64912 kN/m

2

Dari pers.(2) :

g= 2

g = Dari pers.(3) :

Dari pers.(4) :

-0.00285671 * Hn

4.55

2

* Hn

0.000008

My =

Hn * (

My =

0.00143

* Hu

My = 0.00071418

* Hu

Pers.kuadrat :

0=

1.250 2

* Hn

20.70

9 / 4 * D * cu =

87.513

0.00143

* Hn )

1.25000

* Hn

2

-2.2750 * Hn

1811.741

2

3.5250 * Hn

-1811.741

* Hu

0.00071

+

-0.0259961

Hn =

Dari pers. kuadrat, diperoleh tahanan lateral nominal,

kN m

Mmax = Hn * ( e + 1.5 * D + 0.5 * f ) =

901.312

kNm

>

Mmax Dari pers.(3) :

f=

469.340 1.341

My =

My

Hn * (

→

1.250

Pers.kuadrat :

0.00143 * Hn

0=

2

0.00143 * Hn ) 2

=

31.81

Termasuk tiang panjang (OK)

0.00143 * Hn

+

1.25000 * Hn

Dari pers. kuadrat, diperoleh tahanan lateral nominal, Faktor reduksi kekuatan, →

Tahanan lateral tiang pancang,

1.25000 * Hu -31.81

Hn = f = f * Hn =

24.747

kN

0.60 14.85

kN

3. REKAP TAHANAN LATERAL TIANG No

f * Hn

Uraian Tahanan Lateral Tiang Pancang 1 Berdasarkan defleksi tiang maksimum (Broms) 2 Berdasarkan momen maksimum (Brinch Hansen)

23.60 14.85

Tahanan lateral tiang terkecil, →

Diambil tahanan lateral tiang pancang,

f * Hn = f * Hn =

14.85

kN

10.00

kN

PERHITUNGAN KEKUATAN FONDASI KODE FONDASI :

F2

DATA BAHAN PILECAP Kuat tekan beton,

f c' =

30

MPa

Kuat leleh baja tulangan deform (  > 12 mm ),

f y =

350

MPa

Kuat leleh baja tulangan polos ( 

f y =

240

MPa

wc =

24

kN/m

Berat beton bertulang,

≤ 12

mm ),

3

DATA DIMENSI FONDASI Lebar kolom arah x,

bx =

0.30

m

Lebar kolom arah y,

0.50

m

0.30

m

0.30

m

0.80

Berat volume tanah di atas pilecap,

by = a= h= z= ws =

18.00

m 3 kN/m

Posisi kolom (dalam = 40, tepi = 30, sudut = 20)

as =

40

Gaya aksial kolom akibat beban terfaktor,

Puk =

357.05

Momen arah x akibat beban terfaktor.

Mux =

9.59

kNm

Momen arah y akibat beban terfaktor.

Muy =

0.00

kNm

Gaya lateral arah x akibat beban terfaktor,

Hux =

17.88

kN

Gaya lateral arah y akibat beban terfaktor,

Huy =

8.94

kN

210.00

kN

10.00

kN

Jarak tiang pancang tepi terhadap sisi luar beton, Tebal pilecap, Tebal tanah di atas pilecap,

DATA BEBAN FONDASI

f * Pn = f * Hn =

Tahanan aksial tiang pancang, Tahanan lateral tiang pancang, DATA SUSUNAN TIANG PANCANG Susunan tiang pancang arah x : 2

No.

Jumlah

x

n*x

1 2

n 1 1

(m) 0.50 -0.50

(m ) 0.25 0.25

2

S x2 =

0.50

kN

Susunan tiang pancang arah y : 2

No.

Jumlah

y

n*y

1

n 1

(m) 0.40

(m ) 0.16

1

S y2 =

0.16

Lebar pilecap arah x,

Lx =

1.60

m

Lebar pilecap arah y,

Ly =

1.00

m

n=

2

n=

2

1. GAYA AKSIAL PADA TIANG PANCANG Berat tanah di atas pilecap,

Ws = Lx * Ly * z * ws =

23.04

kN

Berat pilecap,

Wc = Lx * Ly * h * wc =

11.52

kN

Pu = Puk + 1.2 * W s + 1.2 * W c =

398.52

kN

Total gaya aksial terfaktor,

Lengan maksimum tiang pancang arah x thd. pusat,

xmax =

0.50

m

Lengan minimum tiang pancang arah x thd. pusat, Gaya aksial maksimum dan minimum pada tiang pancang,

xmin =

-0.50

m

208.85

kN

189.66

kN

2

pumax = Pu / n + Mux* xmax / Sx = 2

pumin = Pu / n + Mux* xmin / Sx = pumax

Syarat :

208.85

f * Pn

≤

<

→

210.00

AMAN (OK)

2. GAYA LATERAL PADA TIANG PANCANG Gaya lateral arah x pada tiang,

hux = Hux / n =

8.94

kN

Gaya lateral arah y pada tiang,

huy = Huy / n =

4.47

kN

9.995

kN

2

Syarat :

2

humax =  ( hux + huy ) =

Gaya lateral kombinasi dua arah,

humax 9.995

3. TINJAUAN TERHADAP GESER

≤

<

f * Hn 10.00

→

AMAN (OK)

0.100

m

0.200

m


d' = d = h - d' = cx = ( Lx - bx - d ) / 2 =

0.550

m

Berat beton,

W1 = cx * Ly * h * wc =

3.960

kN

Berat tanah,

W2 = cx * Ly * z * ws =

7.920

kN


Vux = pumax - W1 - W2 = 196.9725 kN

Gaya geser arah x,

b = Ly = d= bc = bx / by =

Lebar bidang geser untuk tinjauan arah x, Tebal efektif pilecap, Rasio sisi panjang thd. sisi pendek kolom,

1000

mm

200

mm

0.6000

Kuat geser pilecap arah x, diambil nilai terkecil dari Vc yang diperoleh dari pers.sbb. : -3

Vc = [ 1 + 2 / bc ] * √ f c' * b * d / 6 * 10 =

791.155

kN

912.871

kN

Vc = 1 / 3 * √ f c' * b * d * 10 =

365.148

kN

Vc = f = f * Vc =

365.148

kN

-3

Vc = [ as * d / b + 2 ] * √ f c' * b * d / 12 * 10 = -3


0.75 273.861

kN


f * Vc 273.861

≥

>

Vux 196.973

AMAN (OK)

6. PEMBESIAN PILECAP

Jarak tepi kolom terhadap sisi luar pilecap, Jarak tiang thd. sisi kolom, Berat beton,

cx = ( Lx - bx ) / 2 =

0.650

m

ex = cx - a =

0.350

m

W1 = cx * Ly * h * wc =

4.680

kN

W2 = cx * Ly * z * ws =


Mux = 2 * pumax * ex - W1 * cx / 2 - W 2 * cx / 2 = Lebar pilecap yang ditinjau, Tebal pilecap, Jarak pusat tulangan thd. sisi luar beton, Tebal efektif plat, Kuat tekan beton,

9.360

kN

141.634

kNm

b = Ly = h= d' = d = h - d' = f c' =

1000

mm

300

mm

100

mm

200

mm

30

MPa

f y =

350

MPa

Kuat leleh baja tulangan, Modulus elastis baja,

Es = 2.00E+05 MPa


b1 =

rb = b1* 0.85 * f c’/ f y * 600 / ( 600 + f y ) = Faktor reduksi kekuatan lentur, f = Rmax = 0.75 * rb * f y * [1-½*0.75* rb * f y / ( 0.85 * f c’ ) ] = Mn = Mux / f = 6

2

Rn = Mn * 10 / ( b * d ) = Rn

<

Rmax

0.85 0.0391128 0.80 8.200 177.042

kNm

4.42605

(OK)



mm

2

mm 72

mm

smax =

200

mm

s=

72

mm

As = p / 4 * D * b / s =

2872.31

mm

2

Asb = 50% * As =

1436.16

mm

2

s = p / 4 * D * b / Asb =

140

mm

smax =

200

mm

s=

140

mm

D 16

70

2

Tulangan bagi diambil 50% tulangan pokok, Jarak tulangan bagi yang diperlukan,

2797.76

2

Jarak tulangan yang digunakan, Luas tulangan terpakai,

0.0140

s = p / 4 * D * b / As =

Jarak tulangan maksimum,

Digunakan tulangan,

0.0025

D 16


0.0140

2

Jarak tulangan maksimum, Jarak tulangan yang digunakan, Digunakan tulangan,

D 16

Luas tulangan terpakai,

As = p / 4 * D * b / s =

2

140 1436.16

mm

2

3. TULANGAN SUSUT

rsmin =

Rasio tulangan susut minimum,

As = rsmin* b * d =

Luas tulangan susut, Diameter tulangan yang digunakan, Jarak tulangan susut,

280 12

2

mm

2

mm

s = p / 4 *  * b / As =

404

mm

smax = s=

200

mm

200

mm

Jarak tulangan susut maksimum, Jarak tulangan susut arah x yang digunakan, Digunakan tulangan susut arah x,

0.0014

 12

-

200



STORUS D 30 CM


KODE KOLOM

K7

INPUT DATA KOLOM

f c' = f y =


30

MPa

350

MPa

b = 265.9 h = 265.9 ds = 40 n= 6 D = 16

mm mm mm buah mm



2.E+05

MPa

β1 = 0.85


β1 = 0.85 - 0.008 (f c' - 30)

untuk fc ' > 30 MPa


β1 = 0.85


2 As = n * p / 4 * D = 1206 mm

Jarak tulangan,

x = ( h - 2*ds ) / 6 = 30.98 mm

Rasio tulangan,

r = As / Ag = 1.71%


untuk Pn = 0

Untuk : 0

≤

Pn ≤ 0.1 * f c' * b * h

f = 0.65 + 0.15 * ( Pno - Pn ) / Pno


6000

b

5500

5000

h

4500

b = 265.9 mm

4000

h = 265.9 mm 3500 ) N k ( n P .

6

3000

f

2500

2000

1000

500

0 0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

750

f.Mn (kNm)


800

850

900

950

1 000

16

f c' = 30

MPa

f y = 350

MPa

Pu

Mu

(kN)

(kNm)

181.95 1500

D

11.83



No



1

As1 = 7/24 * As =

352

mm

2

As2 = 2/24 * As =

101

mm

2 2 2

3

As3 = 2/24 * As =

101

mm

4

As4 = 2/24 * As =

101

mm

5

As5 = 2/24 * As =

101

mm

6

As6 = 2/24 * As =

101

mm

7

As7 = 7/24 * As =

352

As = 1206

mm

2

mm

2


226 mm

d2 = 5*x + ds =

195 mm

Pno = 1756 kN

d3 = 4*x + ds =

164 mm

0.1 * f c' * b * h *10 = 212.1 kN

d4 = 3*x + ds =

133 m m


d5 = 2*x + ds =

102 mm

c = cb = 600 / (600 + f y) * d1 =

d6 =

x + ds =

71 mm

d7 =

ds =

40 mm


Pno = 0.80*[ 0.85*f c' *b*h + As*(f y - 0.85*f c')]*10

-3

d1 = 6*x + ds =

-3

142.67 mm

εsi = 0.003 * ( c - di ) / c


| εsi | < f y / Es | εsi |  f y / Es



105

→

Dc = 2.5324


URAIAN PERHITUNGAN



UNIT -3


kN kN

kNmm

kNmm mm kN

kNmm kN kNm kN kNm


6000

b

5500

5000

4500

h

4000

b = 265.9 mm h = 265.9 mm

3500 ) N k ( n P .

6 3000

f

2500

2000

1500

1000

500

D

f c' = 30

MPa

f y = 350

MPa

Pu

Mu

(kN)

(kNm)

181.95

11.83

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0 0

50

100

150

200

250

300

350

400

450

500

550

600

650

700

750

f.Mn (kNm)


800

850

900

950

1000

16



c

εs1

εs2

εs3

εs4

εs5

εs6

εs7


f s1

f s2

f s3

f s4

f s5

f s6

f s7

Fs1

Fs2

Fs3

Fs4

Fs5

MPa

MPa

MPa

MPa

MPa

MPa

MPa

kN

kN

kN

kN

kN

31 9. 1

0. 000 88

0 .0 011 7

0. 00 14 6

0. 00 17 5

0. 00 204

0. 00 23 3

0. 00 26 2

1 75 .22

2 33 .4 8

2 91 .7 4

3 50 .0 0

3 50 .0 0

3 50 .00

35 0. 00

6 1. 65

23 .47

2 9. 33

3 5. 19

35 .1 9

31 6. 5

0. 000 86

0 .0 011 5

0. 00 14 5

0. 00 17 4

0. 00 203

0. 00 23 3

0. 00 26 2

1 71 .82

2 30 .5 5

2 89 .2 7

3 48 .0 0

3 50 .0 0

3 50 .00

35 0. 00

6 0. 46

23 .18

2 9. 08

3 4. 98

35 .1 9

31 4. 0

0. 000 84

0 .0 011 4

0. 00 14 3

0. 00 17 3

0. 00 203

0. 00 23 2

0. 00 26 2

1 68 .36

2 27 .5 7

2 86 .7 7

3 45 .9 7

3 50 .0 0

3 50 .00

35 0. 00

5 9. 24

22 .88

2 8. 83

3 4. 78

35 .1 9

31 1. 5 30 9. 0

0. 000 82 0. 000 81

0 .0 011 2 0 .0 011 1

0. 00 14 2 0. 00 14 1

0. 00 17 2 0. 00 17 1

0. 00 202 0. 00 201

0. 00 23 2 0. 00 23 1

0. 00 26 1 0. 00 26 1

1 64 .86 1 61 .29

2 24 .5 4 2 21 .4 6

2 84 .2 2 2 81 .6 3

3 43 .9 0 3 41 .8 0

3 50 .0 0 3 50 .0 0

3 50 .00 3 50 .00

35 0. 00 35 0. 00

5 8. 01 5 6. 75

22 .57 22 .26

2 8. 57 2 8. 31

3 4. 57 3 4. 36

35 .1 9 35 .1 9

30 6. 4

0. 000 79

0 .0 010 9

0. 00 14 0

0. 00 17 0

0. 00 200

0. 00 23 1

0. 00 26 1

1 57 .66

2 18 .3 3

2 79 .0 0

3 39 .6 7

3 50 .0 0

3 50 .00

35 0. 00

5 5. 48

21 .95

2 8. 05

3 4. 15

35 .1 9

30 3. 9

0. 000 77

0 .0 010 8

0. 00 13 8

0. 00 16 9

0. 00 199

0. 00 23 0

0. 00 26 1

1 53 .98

2 15 .1 5

2 76 .3 3

3 37 .5 0

3 50 .0 0

3 50 .00

35 0. 00

5 4. 18

21 .63

2 7. 78

3 3. 93

35 .1 9

30 1. 4

0. 000 75

0 .0 010 6

0. 00 13 7

0. 00 16 8

0. 00 198

0. 00 22 9

0. 00 26 0

1 50 .23

2 11 .9 2

2 73 .6 1

3 35 .2 9

3 50 .0 0

3 50 .00

35 0. 00

5 2. 86

21 .30

2 7. 51

3 3. 71

35 .1 9

29 8. 8 29 6. 3

0. 000 73 0. 000 71

0 .0 010 4 0 .0 010 3

0. 00 13 5 0. 00 13 4

0. 00 16 7 0. 00 16 5

0. 00 198 0. 00 197

0. 00 22 9 0. 00 22 8

0. 00 26 0 0. 00 25 9

1 46 .42 1 42 .54

2 08 .6 3 2 05 .2 8

2 70 .8 4 2 68 .0 3

3 33 .0 5 3 30 .7 7

3 50 .0 0 3 50 .0 0

3 50 .00 3 50 .00

35 0. 00 35 0. 00

5 1. 52 5 0. 15

20 .97 20 .64

2 7. 23 2 6. 94

3 3. 48 3 3. 25

35 .1 9 35 .1 9

29 3. 8

0. 000 69

0 .0 010 1

0. 00 13 3

0. 00 16 4

0. 00 196

0. 00 22 8

0. 00 25 9

1 38 .60

2 01 .8 8

2 65 .1 6

3 28 .4 5

3 50 .0 0

3 50 .00

35 0. 00

4 8. 77

20 .30

2 6. 66

3 3. 02

35 .1 9

29 1. 2

0. 000 67

0 .0 009 9

0. 00 13 1

0. 00 16 3

0. 00 195

0. 00 22 7

0. 00 25 9

1 34 .58

1 98 .4 2

2 62 .2 5

3 26 .0 9

3 50 .0 0

3 50 .00

35 0. 00

4 7. 35

19 .95

2 6. 36

3 2. 78

35 .1 9

28 8. 7 28 6. 2

0. 000 65 0. 000 63

0 .0 009 7 0 .0 009 6

0. 00 13 0 0. 00 12 8

0. 00 16 2 0. 00 16 1

0. 00 194 0. 00 193

0. 00 22 6 0. 00 22 6

0. 00 25 8 0. 00 25 8

1 30 .50 1 26 .35

1 94 .9 0 1 91 .3 1

2 59 .2 9 2 56 .2 8

3 23 .6 8 3 21 .2 4

3 50 .0 0 3 50 .0 0

3 50 .00 3 50 .00

35 0. 00 35 0. 00

4 5. 92 4 4. 46

19 .59 19 .23

2 6. 07 2 5. 76

3 2. 54 3 2. 29

35 .1 9 35 .1 9

28 3. 6

0. 000 61

0 .0 009 4

0. 00 12 7

0. 00 15 9

0. 00 192

0. 00 22 5

0. 00 25 8

1 22 .12

1 87 .6 6

2 53 .2 1

3 18 .7 5

3 50 .0 0

3 50 .00

35 0. 00

4 2. 97

18 .87

2 5. 46

3 2. 04

35 .1 9

28 1. 1

0. 000 59

0 .0 009 2

0. 00 12 5

0. 00 15 8

0. 00 191

0. 00 22 4

0. 00 25 7

1 17 .81

1 83 .9 5

2 50 .0 8

3 16 .2 2

3 50 .0 0

3 50 .00

35 0. 00

4 1. 45

18 .49

2 5. 14

3 1. 79

35 .1 9

27 8. 6 27 6. 0

0. 000 57 0. 000 54

0 .0 009 0 0 .0 008 8

0. 00 12 3 0. 00 12 2

0. 00 15 7 0. 00 15 6

0. 00 190 0. 00 189

0. 00 22 4 0. 00 22 3

0. 00 25 7 0. 00 25 7

1 13 .43 1 08 .97

1 80 .1 7 1 76 .3 1

2 46 .9 0 2 43 .6 6

3 13 .6 4 3 11 .0 1

3 50 .0 0 3 50 .0 0

3 50 .00 3 50 .00

35 0. 00 35 0. 00

3 9. 91 3 8. 34

18 .11 17 .72

2 4. 82 2 4. 50

3 1. 53 3 1. 27

35 .1 9 35 .1 9

27 3. 5

0. 000 52

0 .0 008 6

0. 00 12 0

0. 00 15 4

0. 00 188

0. 00 22 2

0. 00 25 6

1 04 .42

1 72 .3 9

2 40 .3 6

3 08 .3 3

3 50 .0 0

3 50 .00

35 0. 00

3 6. 74

17 .33

2 4. 16

3 1. 00

35 .1 9

27 1. 0

0. 000 50

0 .0 008 4

0. 00 11 9

0. 00 15 3

0. 00 187

0. 00 22 1

0. 00 25 6

99 .79

1 68 .3 9

2 37 .0 0

3 05 .6 1

3 50 .0 0

3 50 .00

35 0. 00

3 5. 11

16 .93

2 3. 83

3 0. 72

35 .1 9

26 8. 4

0. 000 48

0 .0 008 2

0. 00 11 7

0. 00 15 1

0. 00 186

0. 00 22 1

0. 00 25 5

95 .07

1 64 .3 2

2 33 .5 8

3 02 .8 3

3 50 .0 0

3 50 .00

35 0. 00

3 3. 45

16 .52

2 3. 48

3 0. 44

35 .1 9

26 5. 9 26 3. 4

0. 000 45 0. 000 43

0 .0 008 0 0 .0 007 8

0. 00 11 5 0. 00 11 3

0. 00 15 0 0. 00 14 9

0. 00 185 0. 00 184

0. 00 22 0 0. 00 21 9

0. 00 25 5 0. 00 25 4

90 .26 85 .36

1 60 .1 7 1 55 .9 4

2 30 .0 9 2 26 .5 3

3 00 .0 0 2 97 .1 2

3 50 .0 0 3 50 .0 0

3 50 .00 3 50 .00

35 0. 00 35 0. 00

3 1. 76 3 0. 03

16 .10 15 .68

2 3. 13 2 2. 77

3 0. 16 2 9. 87

35 .1 9 35 .1 9

26 0. 8

0. 000 40

0 .0 007 6

0. 00 11 1

0. 00 14 7

0. 00 183

0. 00 21 8

0. 00 25 4

80 .36

1 51 .6 3

2 22 .9 0

2 94 .1 7

3 50 .0 0

3 50 .00

35 0. 00

2 8. 28

15 .24

2 2. 41

2 9. 57

35 .1 9

25 8. 3

0. 000 38

0 .0 007 4

0. 00 11 0

0. 00 14 6

0. 00 182

0. 00 21 8

0. 00 25 4

75 .27

1 47 .2 4

2 19 .2 1

2 91 .1 8

3 50 .0 0

3 50 .00

35 0. 00

2 6. 48

14 .80

2 2. 04

2 9. 27

35 .1 9

25 5. 8 25 3. 2

0. 000 35 0. 000 32

0 .0 007 1 0 .0 006 9

0. 00 10 8 0. 00 10 6

0. 00 14 4 0. 00 14 3

0. 00 180 0. 00 179

0. 00 21 7 0. 00 21 6

0. 00 25 3 0. 00 25 3

70 .07 64 .77

1 42 .7 5 1 38 .1 8

2 15 .4 4 2 11 .5 9

2 88 .1 2 2 85 .0 0

3 50 .0 0 3 50 .0 0

3 50 .00 3 50 .00

35 0. 00 35 0. 00

2 4. 66 2 2. 79

14 .35 13 .89

2 1. 66 2 1. 27

2 8. 96 2 8. 65

35 .1 9 35 .1 9

25 0. 7

0. 000 30

0 .0 006 7

0. 00 10 4

0. 00 14 1

0. 00 178

0. 00 21 5

0. 00 25 2

59 .37

1 33 .5 2

2 07 .6 7

2 81 .8 2

3 50 .0 0

3 50 .00

35 0. 00

2 0. 89

13 .42

2 0. 88

2 8. 33

35 .1 9

24 8. 2

0. 000 27

0 .0 006 4

0. 00 10 2

0. 00 13 9

0. 00 177

0. 00 21 4

0. 00 25 2

53 .85

1 28 .7 6

2 03 .6 6

2 78 .5 7

3 50 .0 0

3 50 .00

35 0. 00

1 8. 95

12 .94

2 0. 47

2 8. 01

35 .1 9

24 5. 6

0. 000 24

0 .0 006 2

0. 00 10 0

0. 00 13 8

0. 00 175

0. 00 21 3

0. 00 25 1

48 .22

1 23 .9 0

1 99 .5 8

2 75 .2 6

3 50 .0 0

3 50 .00

35 0. 00

1 6. 97

12 .46

2 0. 06

2 7. 67

35 .1 9

24 3. 1 24 0. 6

0. 000 21 0. 000 18

0 .0 005 9 0 .0 005 7

0. 00 09 8 0. 00 09 6

0. 00 13 6 0. 00 13 4

0. 00 174 0. 00 173

0. 00 21 2 0. 00 21 1

0. 00 25 1 0. 00 25 0

42 .47 36 .60

1 18 .9 4 1 13 .8 8

1 95 .4 1 1 91 .1 5

2 71 .8 8 2 68 .4 2

3 48 .3 4 3 45 .6 9

3 50 .00 3 50 .00

35 0. 00 35 0. 00

1 4. 94 1 2. 88

11 .96 11 .45

1 9. 64 1 9. 22

2 7. 33 2 6. 98

35 .0 2 34 .7 5

23 8. 0

0. 000 15

0 .0 005 4

0. 00 09 3

0. 00 13 2

0. 00 171

0. 00 21 1

0. 00 25 0

30 .61

1 08 .7 0

1 86 .8 0

2 64 .8 9

3 42 .9 9

3 50 .00

35 0. 00

1 0. 77

10 .93

1 8. 78

2 6. 63

34 .4 8

23 5. 5

0. 000 12

0 .0 005 2

0. 00 09 1

0. 00 13 1

0. 00 170

0. 00 21 0

0. 00 24 9

24 .49

1 03 .4 2

1 82 .3 6

2 61 .2 9

3 40 .2 2

3 50 .00

35 0. 00

8. 62

10 .40

1 8. 33

2 6. 27

34 .2 0

23 3. 0

0. 000 09

0 .0 004 9

0 .00 08 9

0. 00 12 9

0. 00 169

0. 00 20 9

0. 00 24 8

18 .23

98 .0 2

1 77 .8 2

2 57 .6 1

3 37 .4 0

3 50 .00

35 0. 00

6. 41

9 .85

1 7. 88

2 5. 90

33 .9 2

23 0. 4 22 7. 9

0. 000 06 0. 000 03

0 .0 004 6 0 .0 004 3

0 .00 08 7 0 .00 08 4

0. 00 12 7 0. 00 12 5

0. 00 167 0. 00 166

0. 00 20 8 0. 00 20 7

0. 00 24 8 0. 00 24 7

11 .84 5 .30

92 .5 1 86 .8 7

1 73 .1 8 1 68 .4 3

2 53 .8 5 2 50 .0 0

3 34 .5 2 3 31 .5 7

3 50 .00 3 50 .00

35 0. 00 35 0. 00

4. 17 1. 87

9 .30 8 .73

1 7. 41 1 6. 93

2 5. 52 2 5. 13

33 .6 3 33 .3 3

22 5. 4

- 0. 00 001

0 .0 004 1

0. 00 08 2

0. 00 12 3

0. 00 164

0. 00 20 6

0. 00 24 7

-1 .38

81 .1 0

1 63 .5 9

2 46 .0 7

3 28 .5 5

3 50 .00

35 0. 00

- 0. 49

8 .15

1 6. 45

2 4. 74

33 .0 3

22 2. 8

- 0. 00 004

0 .0 003 8

0. 00 07 9

0. 00 12 1

0. 00 163

0. 00 20 4

0. 00 24 6

-8 .21

75 .2 1

1 58 .6 3

2 42 .0 5

3 25 .4 6

3 50 .00

35 0. 00

- 2. 89

7 .56

1 5. 95

2 4. 33

32 .7 2


Fs6

Fs7

Cs

Ms1

Ms2

Ms3

Ms4

Ms5

Ms6

Ms7

kN

kN

kN

kNmm

kNmm

k Nmm

kNmm

kNmm

kNmm

k Nmm

Ms kNmm

a mm

Cc kN

Mc kNmm

Pn

Mn

kN 1755.51

kNm 0.00

Ф.Pn

Ф.Mn

0.65

kN 1141.08

kNm 0.00 1.13

Ф

35.19

123.15

343.16

-5730.49

-1454.46

-908.70

0.00

1090.17

2180.35

11446.83

6623.70

271.22

1838.98

-4889.85

1 755.51

1.73

0.65

1141.08

35.19

123.15

341.22

-5619.35

-1436.20

-901.02

0.00

1090.17

2180.35

11446.83

6760.79

269.07

1824.39

-2887.52

1 755.51

3.87

0.65

1141.08

2.52

35.19

123.15

339.25

-5506.41

-1417.64

-893.22

0.00

1090.17

2180.35

11446.83

6900.09

266.91

1809.79

-916.62

1755.51

5.98

0.65

1141.08

3.89

35.19 3 5.1 9

123.15 1 23 .15

337.25 3 35 .2 1

-5391.64 -5 27 4.9 9

-1398.77 -1 37 9.6 0

-885.28 -8 77 .22

0.00 0. 00

1090.17 1 09 0.1 7

2180.35 21 80 .35

11446.83 1 14 46 .8 3

7041.65 71 85 .54

264.76 2 62 .6 1

1795.19 17 80 .6 0

1022.88 29 30 .9 5

1755.51 17 55. 51

8.06 1 0.1 2

0.65 0. 65

1141.08 11 41 .0 8

5.24 6. 58

3 5.1 9

1 23 .15

3 33 .1 4

-5 15 6.4 1

-1 36 0.1 1

-8 69 .03

0. 00

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21 80 .35

1 14 46 .8 3

73 31 .80

2 60 .4 6

17 66 .0 0

48 07 .6 1

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1 2.1 4

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11 41 .0 8

7. 89

3 5.1 9

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3 31 .0 4

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0. 00

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1 14 46 .8 3

74 80 .50

2 58 .3 0

17 51 .4 1

66 52 .8 5

17 55. 51

1 4.1 3

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11 41 .0 8

9. 19

3 5.1 9

1 23 .15

3 28 .9 0

-4 91 3.2 7

-1 32 0.1 5

-8 52 .22

0. 00

1 09 0.1 7

21 80 .35

1 14 46 .8 3

76 31 .71

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17 36 .8 1

84 66 .6 8

17 55. 51

1 6.1 0

0. 65

11 41 .0 8

1 0. 46

3 5.1 9 3 5.1 9

1 23 .15 1 23 .15

3 26 .7 2 3 24 .5 1

-4 78 8.6 1 -4 66 1.8 2

-1 29 9.6 7 -1 27 8.8 3

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0. 00 0. 00

1 09 0.1 7 1 09 0.1 7

21 80 .35 21 80 .35

1 14 46 .8 3 1 14 46 .8 3

77 85 .47 79 41 .86

2 54 .0 0 2 51 .8 5

17 22 .2 2 17 07 .6 2

1 02 49 .0 9 1 20 00 .0 9

17 55. 51 17 55. 51

1 8.0 3 1 9.9 4

0. 65 0. 65

11 41 .0 8 11 41 .0 8

1 1. 72 1 2. 96

3 5.1 9

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3 22 .2 6

-4 53 2.8 5

-1 25 7.6 3

-8 25 .93

0. 00

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1 14 46 .8 3

81 00 .95

2 49 .6 9

16 93 .0 3

1 37 19 .6 6

17 55. 51

2 1.8 2

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11 41 .0 8

1 4. 18

3 5.1 9

1 23 .15

3 19 .9 7

-4 40 1.6 3

-1 23 6.0 6

-8 16 .86

0. 00

1 09 0.1 7

21 80 .35

1 14 46 .8 3

82 62 .81

2 47 .5 4

16 78 .4 3

1 54 07 .8 3

17 55. 51

2 3.6 7

0. 65

11 41 .0 8

1 5. 39

3 5.1 9 3 5.1 9

1 23 .15 1 23 .15

3 17 .6 4 3 15 .2 7

-4 26 8.1 0 -4 13 2.2 2

-1 21 4.1 2 -1 19 1.7 9

-8 07 .63 -7 98 .24

0. 00 0. 00

1 09 0.1 7 1 09 0.1 7

21 80 .35 21 80 .35

1 14 46 .8 3 1 14 46 .8 3

84 27 .50 85 95 .11

2 45 .3 9 2 43 .2 4

16 63 .8 4 16 49 .2 4

1 70 64 .5 7 1 86 89 .9 0

17 55. 51 17 55. 51

2 5.4 9 2 7.2 9

0. 65 0. 65

11 41 .0 8 11 41 .0 8

1 6. 57 1 7. 74

3 5.1 9

1 23 .15

3 12 .8 6

-3 99 3.9 1

-1 16 9.0 5

-7 88 .68

0. 00

1 09 0.1 7

21 80 .35

1 14 46 .8 3

87 65 .71

2 41 .0 8

16 34 .6 5

2 02 83 .8 1

17 55. 51

2 9.0 5

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1 8. 88

3 5.1 9

1 23 .15

3 10 .4 0

-3 85 3.1 0

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-7 78 .95

0. 00

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21 80 .35

1 14 46 .8 3

89 39 .39

2 38 .9 3

16 20 .0 5

2 18 46 .3 1

17 55. 51

3 0.7 9

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11 41 .0 8

2 0. 01

3 5.1 9 3 5.1 9

1 23 .15 1 23 .15

3 07 .9 0 3 05 .3 5

-3 70 9.7 4 -3 56 3.7 4

-1 12 2.3 5 -1 09 8.3 6

-7 69 .04 -7 58 .95

0. 00 0. 00

1 09 0.1 7 1 09 0.1 7

21 80 .35 21 80 .35

1 14 46 .8 3 1 14 46 .8 3

91 16 .22 92 96 .30

2 36 .7 8 2 34 .6 3

16 05 .4 6 15 90 .8 6

2 33 77 .3 9 2 48 77 .0 6

17 55. 51 17 55. 51

3 2.4 9 3 4.1 7

0. 65 0. 65

11 41 .0 8 11 41 .0 8

2 1. 12 2 2. 21

3 5.1 9

1 23 .15

3 02 .7 5

-3 41 5.0 5

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-7 48 .68

0. 00

1 09 0.1 7

21 80 .35

1 14 46 .8 3

94 79 .72

2 32 .4 7

15 76 .2 7

2 63 45 .3 0

17 55. 51

3 5.8 3

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11 41 .0 8

2 3. 29

3 5.1 9

1 23 .15

3 00 .1 1

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-7 38 .21

0. 00

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21 80 .35

1 14 46 .8 3

96 66 .56

2 30 .3 2

15 61 .6 7

2 77 82 .1 4

17 55. 51

3 7.4 5

0. 65

11 41 .0 8

2 4. 34

3 5.1 9

1 23 .15

2 97 .4 2

-3 10 9.2 3

-1 02 3.6 6

-7 27 .54

0. 00

1 09 0.1 7

21 80 .35

1 14 46 .8 3

98 56 .93

2 28 .1 7

15 47 .0 8

2 91 87 .5 5

17 55. 51

3 9.0 4

0. 65

11 41 .0 8

2 5. 38

3 5.1 9 3 5.1 9

1 23 .15 1 23 .15

2 94 .6 7 2 91 .8 8

-2 95 1.9 6 -2 79 1.6 6

- 99 7.8 1 - 97 1.4 6

-7 16 .67 -7 05 .59

0. 00 0. 00

1 09 0.1 7 1 09 0.1 7

21 80 .35 21 80 .35

1 14 46 .8 3 1 14 46 .8 3

1 00 50 .92 1 02 48 .64

2 26 .0 2 2 23 .8 6

15 32 .4 8 15 17 .8 9

3 05 61 .5 5 3 19 04 .1 3

17 55. 51 17 55. 51

4 0.6 1 4 2.1 5

0. 65 0. 65

11 41 .0 8 11 41 .0 8

2 6. 40 2 7. 40

3 5.1 9

1 23 .15

2 89 .0 2

-2 62 8.2 5

- 94 4.6 1

-6 94 .30

0. 00

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21 80 .35

1 14 46 .8 3

1 04 50 .21

2 21 .7 1

15 03 .2 9

3 32 15 .3 0

17 55. 51

4 3.6 7

0. 65

11 41 .0 8

2 8. 38

3 5.1 9

1 23 .15

2 86 .1 2

-2 46 1.6 3

- 91 7.2 2

-6 82 .78

0. 00

1 09 0.1 7

21 80 .35

1 14 46 .8 3

1 06 55 .72

2 19 .5 6

14 88 .7 0

3 44 95 .0 5

17 55. 51

4 5.1 5

0. 65

11 41 .0 8

2 9. 35

3 5.1 9 3 5.1 9

1 23 .15 1 23 .15

2 83 .1 5 2 80 .1 3

-2 29 1.7 1 -2 11 8.4 0

- 88 9.3 0 - 86 0.8 1

-6 71 .04 -6 59 .06

0. 00 0. 00

1 09 0.1 7 1 09 0.1 7

21 80 .35 21 80 .35

1 14 46 .8 3 1 14 46 .8 3

1 08 65 .31 1 10 79 .09

2 17 .4 0 2 15 .2 5

14 74 .1 0 14 59 .5 1

3 57 43 .3 8 3 69 60 .3 0

17 55. 51 17 39. 64

4 6.6 1 4 8.0 4

0. 65 0. 65

11 41 .0 8 11 30 .7 6

3 0. 30 3 1. 23

3 5.1 9

1 23 .15

2 77 .0 4

-1 94 1.5 8

- 83 1.7 5

-6 46 .84

0. 00

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21 80 .35

1 14 46 .8 3

1 12 97 .18

2 13 .1 0

14 44 .9 1

3 81 45 .8 0

17 21. 95

4 9.4 4

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3 2. 14

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1 23 .15

2 73 .8 9

-1 76 1.1 6

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0. 00

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21 80 .35

1 14 46 .8 3

1 15 19 .73

2 10 .9 5

14 30 .3 2

3 92 99 .8 9

17 04. 21

5 0.8 2

0. 65

11 07 .7 4

3 3. 03

3 5.1 9

1 23 .15

2 70 .6 8

-1 57 7.0 2

- 77 1.8 3

-6 21 .64

0. 00

1 09 0.1 7

21 80 .35

1 14 46 .8 3

1 17 46 .86

2 08 .7 9

14 15 .7 2

4 04 22 .5 6

16 86. 40

5 2.1 7

0. 65

10 96 .1 6

3 3. 91

3 5.1 9 3 5.1 9

1 23 .15 1 23 .15

2 67 .2 3 2 63 .6 2

-1 38 9.0 3 -1 19 7.1 0

- 74 0.9 4 - 70 9.3 9

-6 08 .65 -5 95 .39

0. 00 0. 00

1 08 5.0 1 1 07 6.7 6

21 80 .35 21 80 .35

1 14 46 .8 3 1 14 46 .8 3

1 19 73 .57 1 22 02 .07

2 06 .6 4 2 04 .4 9

14 01 .1 3 13 86 .5 3

4 15 13 .8 1 4 25 73 .6 5

16 68. 36 16 50. 15

5 3.4 9 5 4.7 8

0. 65 0. 65

10 84 .4 3 10 72 .6 0

3 4. 77 3 5. 60

3 5.1 9

1 23 .15

2 59 .9 2

-1 00 1.0 7

- 67 7.1 8

-5 81 .84

0. 00

1 06 8.3 4

21 80 .35

1 14 46 .8 3

1 24 35 .43

2 02 .3 4

13 71 .9 4

4 36 02 .0 7

16 31. 86

5 6.0 4

0. 65

10 60 .7 1

3 6. 42

3 5.1 9

1 23 .15

2 56 .1 5

- 80 0.8 4

- 64 4.2 7

-5 68 .00

0. 00

1 05 9.7 3

21 80 .35

1 14 46 .8 3

126 73 .80

2 00 .1 8

13 57 .3 4

445 99 .0 7

16 13. 49

5 7.2 7

0. 65

10 48 .7 7

3 7. 23

3 5.1 9

1 23 .15

2 52 .3 0

- 59 6.2 5

- 61 0.6 4

-5 53 .86

0. 00

1 05 0.9 3

21 80 .35

1 14 46 .8 3

129 17 .36

1 98 .0 3

13 42 .7 5

455 64 .6 6

15 95. 05

5 8.4 8

0. 65

10 36 .7 8

3 8. 01

3 5.1 9 3 5.1 9

1 23 .15 1 23 .15

2 48 .3 6 2 44 .3 3

- 38 7.1 6 - 17 3.4 3

- 57 6.2 8 - 54 1.1 5

-5 39 .41 -5 24 .64

0. 00 0. 00

1 04 1.9 4 1 03 2.7 6

21 80 .35 21 80 .35

1 14 46 .8 3 1 14 46 .8 3

131 66 .28 134 20 .72

1 95 .8 8 1 93 .7 3

13 28 .1 5 13 13 .5 6

464 98 .8 3 474 01 .5 9

15 76. 51 15 57. 89

5 9.6 7 6 0.8 2

0. 65 0. 65

10 24 .7 3 10 12 .6 3

3 8. 78 3 9. 53

35.19

123.15

240.22

45.11

-505.24

-509.53

0.00

1023.36

2180.35

11446.83

13680.88

191.57

1298.96

48272.93

1539.18

61.95

0.65

1000.47

40.27

35.19

123.15

236.01

268.61

-468.50

-494.09

0.00

1013.75

2180.35

11446.83

13946.96

189.42

1284.37

49112.85

1520.37

63.06

0.65

988.24

40.99



Fs1

Fs2

Fs3

Fs4

Fs5

kN - 5. 35

kN 6 .95

kN 1 5. 44

kN 2 3. 92

kN 32 .4 0

35 0. 00

- 7. 87

6 .33

1 4. 91

2 3. 50

32 .0 8

35 0. 00

-1 0. 44

5 .70

1 4. 38

2 3. 06

31 .7 5

3 50 .00

35 0. 00

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5 .05

1 3. 83

2 2. 62

31 .4 1

3 08 .9 3 3 05 .3 8

3 50 .00 3 50 .00

35 0. 00 35 0. 00

-1 5. 78 -1 8. 55

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1 3. 27 1 2. 70

2 2. 17 2 1. 70

31 .0 6 30 .7 0

2 11 .1 1

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1 2. 11

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2 06 .2 5

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1 1. 51

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1 08 .3 4

2 01 .2 7

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1 0. 89

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7 .9 3 0 .2 4

1 02 .0 4 95 .5 7

1 96 .1 5 1 90 .9 1

2 90 .2 7 2 86 .2 5

3 50 .00 3 50 .00

35 0. 00 35 0. 00

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1 0. 26 9. 61

1 9. 72 1 9. 19

29 .1 8 28 .7 8

- 104 .25

-7 .6 6

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1 85 .5 3

2 82 .1 2

3 50 .00

35 0. 00

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1 8. 65

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- 113 .64

- 15 .7 6

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1 80 .0 0

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3 50 .00

35 0. 00

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1 8. 10

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- 123 .28 - 133 .19

- 24 .0 8 - 32 .6 3

75 .1 2 67 .9 3

1 74 .3 2 1 68 .4 9

2 73 .5 3 2 69 .0 5

3 50 .00 3 50 .00

35 0. 00 35 0. 00

-4 3. 38 -4 6. 86

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7. 55 6. 83

1 7. 52 1 6. 94

27 .5 0 27 .0 5

0. 00 23 4

- 143 .37

- 41 .4 1

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1 62 .5 0

2 64 .4 6

3 50 .00

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- 153 .84

- 50 .4 5

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1 56 .3 4

2 59 .7 3

3 50 .00

35 0. 00

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5. 32

1 5. 72

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0. 00 18 0 0. 00 17 8

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- 164 .61 - 175 .69

- 59 .7 4 - 69 .3 0

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1 50 .0 0 1 43 .4 8

2 54 .8 7 2 49 .8 7

3 50 .00 3 50 .00

35 0. 00 35 0. 00

-5 7. 92 -6 1. 82

-6 .01 -6 .97

4. 54 3. 73

1 5. 08 1 4. 42

25 .6 2 25 .1 2

0. 00 122

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0. 00 23 0

- 187 .10

- 79 .1 4

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1 36 .7 6

2 44 .7 2

3 50 .00

35 0. 00

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-7 .96

2. 90

1 3. 75

24 .6 0

0. 00 120

0. 00 17 4

0. 00 22 9

- 198 .85

- 89 .2 8

20 .2 8

1 29 .8 5

2 39 .4 2

3 48 .98

35 0. 00

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2. 04

1 3. 05

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0. 00 06 1

0. 00 11 7

0 .0 01 73

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- 21 0. 95

- 99 .7 2

1 1. 50

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2 33 .9 5

3 45 .1 8

3 50 .0 0

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1 .1 6

1 2. 34

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- 0. 00 05 5 0. 00 00 1 - 0. 00 06 1 - 0. 00 00 3

0. 00 05 8 0 .0 00 54

0. 00 11 4 0 . 00 11 1

0 .0 01 71 0 .0 01 69

0. 00 22 7 0 .0 02 26

- 22 3. 43 - 23 6. 29

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1 15 .3 8 1 07 .8 1

2 28 .3 2 2 22 .5 1

3 41 .2 6 3 37 .2 2

3 50 .0 0 3 50 .0 0

- 78 .6 1 - 83 .1 4

- 11 .1 1 - 12 .2 2

0 .2 5 - 0. 69

1 1. 60 1 0. 84

2 2. 95 2 2. 37

- 0. 00 12 5

-0 .0 00 67 - 0. 00 00 8

0 .0 00 50

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1 00 .0 0

2 16 .5 2

3 33 .0 5

3 50 .0 0

- 87 .8 1

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0. 00 04 6

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0 .0 01 64

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- 2 63 .2 7

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9 1. 94

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3 28 .7 4

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- 0. 00 13 9 - 0. 00 14 6

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0. 00 04 2 0 .0 00 38

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0 .0 01 62 0 .0 01 60

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8 3. 61 7 5. 00

2 03 .9 5 1 97 .3 5

3 24 .2 9 3 19 .7 0

3 50 .0 0 3 50 .0 0

- 97 .6 1 - 10 2. 76

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0 .0 00 33

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0 .0 00 24

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4 7. 37

1 76 .1 6

3 04 .9 4

3 50 .0 0

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1 41 .8 1 39 .3

- 0. 00 17 8 - 0. 00 18 7

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0 .0 00 19 0 .0 00 14

0 . 00 08 4 0 .0 00 80

0 .0 01 50 0 .0 01 47

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- 35 0. 00 - 35 0. 00

- 22 4. 68 - 2 39 .6 7

- 93 .5 9 - 10 6. 20

3 7. 50 2 7. 27

1 68 .5 9 1 60 .7 4

2 99 .6 8 2 94 .2 2

3 50 .0 0 3 50 .0 0

- 12 3. 15 - 12 3. 15

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3 .7 7 2 .7 4

1 6. 95 1 6. 16

1 36 .7

- 0. 00 19 6

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0 .0 00 08

0 .0 00 76

0 .0 01 44

0 .0 02 12

- 35 0. 00

- 2 55 .2 2

- 11 9. 28

1 6. 67

1 52 .6 1

2 88 .5 5

3 50 .0 0

- 12 3. 15

- 25 .6 6

- 11 .9 9

1 .6 8

1 5. 34

1 34 .2

- 0. 00 20 5

-0 .0 01 36 - 0. 00 06 6

0 .0 00 03

0 . 00 07 2

0 .0 01 41

0 .0 02 11

- 35 0. 00

- 27 1. 36

- 13 2. 85

5 .6 6

1 44 .1 7

2 82 .6 8

3 50 .0 0

- 12 3. 15

- 27 .2 8

- 13 .3 6

0 .5 7

1 4. 49

1 31 .7

- 0. 00 21 5

-0 .0 01 44 - 0. 00 07 3 - 0. 00 00 3

0 . 00 06 8

0 .0 01 38

0 . 00 20 9

- 35 0. 00

- 2 88 .1 1

- 14 6. 94

- 5. 77

1 35 .4 0

2 76 .5 7

3 50 .0 0

- 12 3. 15

- 28 .9 6

- 14 .7 7

- 0. 58

1 3. 61

1 29 .2 1 26 .6

- 0. 00 22 5 - 0. 00 23 5

- 0. 00 15 3 - 0. 00 08 1 - 0. 00 00 9 - 0. 00 16 2 - 0. 00 08 8 - 0. 00 01 5

0 .0 00 63 0 .0 00 58

0 .0 01 35 0 .0 01 32

0 .0 02 07 0 .0 02 05

- 35 0. 00 - 35 0. 00

- 30 5. 53 - 32 3. 64

- 16 1. 59 - 17 6. 82

- 17 .6 5 - 30 .0 0

1 26 .2 9 1 16 .8 2

2 70 .2 3 2 63 .6 4

3 50 .0 0 3 50 .0 0

- 12 3. 15 - 12 3. 15

- 30 .7 1 - 32 .5 4

- 16 .2 4 - 17 .7 8

- 1. 77 - 3. 02

1 2. 70 1 1. 74

1 24 .1

- 0. 00 24 6

- 0. 00 17 1 - 0. 00 09 6 - 0. 00 02 1

0 .0 00 53

0 .0 01 28

0 .0 02 03

- 35 0. 00

- 34 2. 49

- 19 2. 67

- 42 .8 6

1 06 .9 6

2 56 .7 7

3 50 .0 0

- 12 3. 15

- 34 .4 3

- 19 .3 7

- 4. 31

1 0. 75

1 21 .6

- 0. 00 25 8

-0 .0 01 81 - 0. 00 10 5 - 0. 00 02 8

0 .0 00 48

0 .0 01 25

0 .0 02 01

- 35 0. 00

- 3 50 .0 0

- 20 9. 19

- 56 .2 5

9 6. 69

2 49 .6 2

3 50 .0 0

- 12 3. 15

- 35 .1 9

- 21 .0 3

- 5. 65

9 .7 2

c

εs1

εs2

εs3

εs4

εs5

εs6

mm 22 0. 3

- 0. 00 008

0 .0 003 5

0. 00 07 7

0. 00 11 9

0. 00 161

0. 00 20 3

21 7. 8

- 0. 00 011

0 .0 003 2

0. 00 07 4

0. 00 11 7

0. 00 160

0. 00 20 2

21 5. 3

- 0. 00 015

0 .0 002 8

0. 00 07 2

0. 00 11 5

0. 00 158

0. 00 20 1

21 2. 7

- 0. 00 019

0 .0 002 5

0. 00 06 9

0. 00 11 3

0. 00 156

21 0. 2 20 7. 7

- 0. 00 022 - 0. 00 026

0 .0 002 2 0 .0 001 8

0. 00 06 6 0. 00 06 3

0. 00 11 0 0. 00 10 8

20 5. 1

- 0. 00 030

0 .0 001 5

0. 00 06 0

20 2. 6

- 0. 00 035

0 .0 001 1

0. 00 05 7

20 0. 1

- 0. 00 039

0 .0 000 8

19 7. 5 19 5. 0

- 0. 00 043 - 0. 00 048

0 .0 000 4 0 .0 000 0

19 2. 5

- 0. 00 052

-0 .0 000 4

0. 00 04 4

18 9. 9

- 0. 00 057

-0 .0 000 8

0. 00 04 1

18 7. 4 18 4. 9

- 0. 00 062 - 0. 00 067

-0 .0 001 2 -0 .0 001 6

0. 00 03 8 0. 00 03 4

18 2. 3

- 0. 00 072

-0 .0 002 1

17 9. 8

- 0. 00 077

-0 .0 002 5

17 7. 3 17 4. 7

- 0. 00 082 - 0. 00 088

17 2. 2 16 9. 7

εs7

f s1

f s2

f s3

f s4

f s5

f s6

f s7

0. 00 24 6

MPa - 15 .20

MPa 69 .1 7

MPa 1 53 .5 5

MPa 2 37 .9 3

MPa 3 22 .3 1

MPa 3 50 .00

MPa 35 0. 00

0. 00 24 5

- 22 .36

63 .0 0

1 48 .3 6

2 33 .7 2

3 19 .0 8

3 50 .00

0. 00 24 4

- 29 .68

56 .6 8

1 43 .0 5

2 29 .4 1

3 15 .7 8

3 50 .00

0. 00 20 0

0. 00 24 4

- 37 .18

50 .2 2

1 37 .6 1

2 25 .0 0

3 12 .3 9

0. 00 154 0. 00 153

0. 00 19 9 0. 00 19 7

0. 00 24 3 0. 00 24 2

- 44 .85 - 52 .72

43 .5 9 36 .8 1

1 32 .0 4 1 26 .3 3

2 20 .4 8 2 15 .8 5

0. 00 10 6

0. 00 151

0. 00 19 6

0. 00 24 1

- 60 .77

29 .8 5

1 20 .4 8

0. 00 10 3

0. 00 149

0. 00 19 5

0. 00 24 1

- 69 .03

22 .7 3

1 14 .4 9

0. 00 05 4

0. 00 10 1

0. 00 147

0. 00 19 4

0. 00 24 0

- 77 .50

15 .4 2

0. 00 05 1 0 .00 04 8

0. 00 09 8 0. 00 09 5

0. 00 145 0. 00 143

0. 00 19 2 0. 00 19 1

0. 00 23 9 0. 00 23 8

- 86 .19 - 95 .10

0. 00 09 3

0. 00 141

0. 00 18 9

0. 00 23 8

0. 00 09 0

0. 00 139

0. 00 18 8

0. 00 23 7

0. 00 08 7 0. 00 08 4

0. 00 137 0. 00 135

0. 00 18 6 0. 00 18 5

0. 00 23 6 0. 00 23 5

0. 00 03 0

0. 00 08 1

0. 00 132

0. 00 18 3

0. 00 02 6

0. 00 07 8

0. 00 130

0. 00 18 2

-0 .0 003 0 -0 .0 003 5

0. 00 02 3 0. 00 01 9

0. 00 07 5 0. 00 07 2

0. 00 127 0. 00 125

- 0. 00 094

-0 .0 004 0

0. 00 01 4

0. 00 06 8

- 0. 00 099

-0 .0 004 5

0. 00 01 0

0. 00 06 5

1 67 .1

- 0. 00 10 5

- 0. 00 05 0

0. 00 00 6

1 64 .6 1 62 .1

- 0. 00 11 2 - 0. 00 11 8

1 59 .5 1 57 .0


Fs6

Fs7

Cs

Ms6

Ms7

Mc

Pn

Mn

kN 35.19

kN 123.15

kN 231.70

kNmm 497.25

Ms1

kNmm -430.93

Ms2

k Nmm -478.28

Ms3

kNmm 0.00

Ms4

kNmm 1003.92

Ms5

kNmm 2180.35

k Nmm 11446.83

kNmm 14219.15

Ms

mm 187.27

kN 1269.77

kNmm 49921.36

kN 1501.47

kNm 64.14

Cc

35.19

123.15

227.29

731.21

-392.47

-462.11

0.00

993.87

2180.35

11446.83

14497.67

185.12

1255.18

50698.45

1482.47

35.19

123.15

222.78

970.67

-353.12

-445.56

0.00

983.57

2180.35

11446.83

14782.75

182.96

1240.58

51444.12

1463.36

35.19

123.15

218.16

1215.84

-312.83

-428.62

0.00

973.03

2180.35

11446.83

15074.61

180.81

1225.99

52158.38

35.19 35.19

123.15 123.15

213.43 208.59

1466.91 1724.11

-271.56 -229.29

-411.27 -393.49

0.00 0.00

962.24 951.18

2180.35 2180.35

11446.83 11446.83

15373.50 15679.69

178.66 176.51

1211.39 1196.80

35.19

123.15

203.62

1987.65

-185.98

-375.28

0.00

939.85

2180.35

11446.83

15993.43

174.35

35.19

123.15

198.53

2257.79

-141.58

-356.61

0.00

928.24

2180.35

11446.83

16315.02

172.20

35.19

123.15

193.32

2534.76

-96.06

-337.46

0.00

916.33

2180.35

11446.83

16644.75

35.19 35.19

123.15 123.15

187.97 182.47

2818.84 3110.29

-49.37 -1.47

-317.83 -297.69

0.00 0.00

904.12 891.59

2180.35 2180.35

11446.83 1 1446.83

35.19

123.15

176.84

3409.41

47.69

-277.01

0.00

878.73

2180.35

35.19

123.15

171.05

3716.52

98.16

-255.79

0.00

865.53

2180.35

35.19 35.19

123.15 123.15

165.11 159.01

4031.92 4355.96

150.00 203.26

-233.99 -211.60

0.00 0.00

851.97 838.04

35.19

123.15

152.74

4689.00

257.99

-188.58

0.00

35.19

123.15

146.28

5031.43

314.27

-164.91

0.00

35.19 35.19

123.15 123.15

139.65 132.82

5383.63 5746.05

372.16 431.72

-140.57 -115.52

35.19

123.15

125.79

6119.13

493.04

35.08

123.15

118.45

6503.34

556.18

34.70

123.15

110.62

6899.20

34.31 33.90

123.15 123.15

102.53 94.20

33.48

123.15

33.05

123.15

32.60 32.14

Ф.Pn

Ф.Mn

0.65

kN 975.96

kNm 41.69

65.20

0.65

963.60

42.38

66.23

0.65

951.19

43.05

1444.15

67.23

0.65

938.70

43.70

52841.22 53492.65

1424.82 1405.38

68.21 69.17

0.65 0.65

926.14 913.50

44.34 44.96

1182.20

54112.66

1385.82

70.11

0.65

900.79

45.57

1167.61

54701.25

1366.14

71.02

0.65

887.99

46.16

170.05

1153.01

55258.42

1346.33

71.90

0.65

875.11

46.74

16982.94 1 7329.91

167.90 1 65.74

1138.42 1123.82

55784.18 5 6278.53

1326.38 1306.30

72.77 73.61

0.65 0.65

862.15 849.09

47.30 47.85

1 1446.83

1 7686.01

1 63.59

1109.23

5 6741.46

1286.07

74.43

0.65

835.94

48.38

1 1446.83

1 8051.60

1 61.44

1094.63

5 7172.97

1265.69

75.22

0.65

822.70

48.90

2180.35 2180.35

11446.83 11446.83

18427.08 18812.85

159.29 157.13

1080.04 1065.44

57573.06 57941.74

1245.15 1224.45

76.00 76.75

0.65 0.65

809.35 795.89

49.40 49.89

823.73

2180.35

11446.83

19209.33

154.98

1050.85

58279.01

1203.58

77.49

0.65

782.33

50.37

809.01

2180.35

11446.83

19616.97

152.83

1036.25

58584.85

1182.54

78.20

0.65

768.65

50.83

0.00 0.00

793.87 778.29

2180.35 2180.35

11446.83 11446.83

20036.27 20467.72

150.68 148.52

1021.66 1007.06

58859.28 59102.30

1161.31 1139.88

78.90 79.57

0.65 0.65

754.85 740.92

51.28 51.72

-89.74

0.00

762.25

2180.35

1 1446.83

2 0911.86

1 46.37

992.47

5 9313.89

1118.26

80.23

0.65

726.87

52.15

-63.18

0.00

745.73

2174.01

1 1446.83

2 1362.92

1 44.22

977.87

5 9494.08

1096.32

80.86

0.65

712.61

52.56

621.24

-35.82

0.00

728.71

2150.32

1 1446.83

2 1810.48

1 42.07

963.28

5 9642.84

1073.89

81.45

0.65

698.03

52.94

7307.23 7728.02

688.30 757.46

-7.62 21.46

0.00 0.00

711.17 693.08

2125.90 2100.71

1 1446.83 11446.83

2 2271.81 22747.57

1 39.91 137.76

948.68 934.09

5 9760.19 59846.12

1051.21 1028.29

82.03 82.59

0.65 0.65

683.29 668.39

53.32 53.69

85.60

8162.16

828.81

51.46

0.00

674.42

2074.73

11446.83

23238.42

135.61

919.49

59900.64

1005.09

83.14

0.65

653.31

54.04

76.73

8610.31

902.47

82.44

0.00

655.16

2047.90

11446.83

23745.11

133.46

904.89

59923.74

981.62

83.67

0.65

638.06

54.38

123.15 123.15

67.56 58.09

9073.16 9551.43

978.54 1057.14

114.43 147.48

0.00 0.00

635.26 614.70

2020.20 1991.58

11446.83 1 1446.83

24268.41 2 4809.16

131.30 1 29.15

890.30 875.70

59915.42 5 9875.69

957.86 933.80

84.18 84.68

0.65 0.65

622.61 606.97

54.72 55.05

31.66

123.15

48.30

10045.91

1138.41

181.66

0.00

593.44

1961.98

1 1446.83

2 5368.23

1 27.00

861.11

5 9804.54

909.41

85.17

0.65

591.12

55.36

31.17

123.15

38.17

10557.45

1222.48

217.01

0.00

571.45

1931.36

1 1446.83

2 5946.59

1 24.85

846.51

5 9701.98

884.68

85.65

0.65

575.04

55.67

30.66

123.15

27.68

11086.93

1309.50

253.60

0.00

548.69

1899.67

1 1446.83

2 6545.24

1 22.69

831.92

5 9568.00

859.60

86.11

0.65

558.74

55.97

30.13 29.58

123.15 123.15

18.85 13.71

11446.83 11446.83

1399.63 1493.04

291.51 330.79

0.00 0.00

525.11 500.68

1866.85 1832.83

1 1446.83 1 1446.83

2 6976.77 2 7051.01

1 20.54 1 18.39

817.32 802.73

5 9402.60 5 9205.78

836.17 816.44

86.38 86.26

0.65 0.65

543.51 530.68

56.15 56.07

29.01

123.15

8.38

11446.83

1589.91

371.52

0.00

475.35

1797.56

1 1446.83

2 7127.99

1 16.24

788.13

5 8977.56

796.51

86.11

0.65

517.73

55.97

28.42

123.15

2.85

11446.83

1690.43

413.79

0.00

449.05

1760.95

1 1446.83

2 7207.89

1 14.08

773.54

5 8717.91

776.38

85.93

0.65

504.65

55.85

27.80

123.15

-2.90

11446.83

1794.81

457.69

0.00

421.75

1722.94

1 1446.83

2 7290.85

1 11.93

758.94

5 8426.85

756.04

85.72

0.65

491.43

55.72

27.17 26.50

123.15 123.15

-8.87 -15.08

11446.83 11446.83

1903.30 2016.12

503.31 550.75

0.00 0.00

393.37 363.86

1683.43 1642.34

1 1446.83 1 1446.83

2 7377.07 2 7466.74

1 09.78 1 07.63

744.35 729.75

5 8104.37 5 7750.47

735.48 714.67

85.48 85.22

0.65 0.65

478.06 464.54

55.56 55.39

25.81

123.15

-21.54

11446.83

2133.54

600.13

0.00

333.15

1599.58

1 1446.83

2 7560.07

1 05.47

715.16

5 7365.16

693.62

84.93

0.65

450.85

55.20

25.09

123.15

-27.06

11446.83

2180.35

651.57

0.00

301.16

1555.03

1 1446.83

2 7581.77

1 03.32

700.56

5 6948.43

673.51

84.53

0.65

437.78

54.94

a

Ф


Analisis Kekuatan Kekuatan Kolom Beton Bertulang Bertulang Dengan Diagram Diagram Interaksi

εs7

f s1 s1

f s2 s2

f s3 s3

0 .0 .0 01 01 21 21

0 .0 .0 01 01 99 99

MPa - 35 35 0. 0. 00 00

MPa - 3 50 50 .0 .0 0

MPa - 22 22 6. 6. 40 40

0 .0 .0 01 01 17 17

0 .0 .0 01 01 97 97

- 35 35 0. 0. 00 00

- 3 50 50 .0 .0 0

0 .0 .0 00 00 32 32

0 .0 .0 01 01 13 13

0 .0 .0 01 01 95 95

- 35 35 0. 0. 00 00

- 35 35 0. 0. 00 00

- 0. 0. 00 00 22 22 5 - 0. 0. 00 00 14 14 1 - 0. 0. 00 00 05 05 8

0 .0 .0 00 00 25 25

0 .0 .0 01 01 09 09

0 .0 .0 01 01 92 92

- 35 35 0. 0. 00 00

- 35 35 0. 0. 00 00

- 0. 0. 00 00 23 23 7 - 0. 0. 00 00 15 15 2 - 0. 0. 00 00 06 06 6 - 0. 0. 00 00 25 25 0 - 0. 0. 00 00 16 16 2 - 0. 0. 00 00 07 07 5

0 .0 .0 00 00 19 19 0 .0 .0 00 00 12 12

0 .0 .0 01 01 04 04 0 .0 .0 01 01 00 00

0 .0 .0 01 01 90 90 0 .0 .0 01 01 87 87

- 35 35 0. 0. 00 00 - 35 35 0. 0. 00 00

- 35 35 0. 0. 00 00 - 35 35 0. 0. 00 00

- 0. 0. 00 00 35 35 3

- 0. 0. 00 00 26 26 3 - 0. 0. 00 00 17 17 4 - 0. 0. 00 00 08 08 4

0 .0 .0 00 00 05 05

0 .0 .0 00 00 95 95

0 .0 .0 01 01 84 84

- 35 35 0. 0. 00 00

- 35 35 0. 0. 00 00

- 0. 0. 00 00 36 36 9

- 0. 0. 00 00 27 27 7 - 0. 0. 00 00 18 18 6 - 0. 0. 00 00 09 09 4 - 0. 0. 00 00 00 00 2

0 .0 .0 00 00 90 90

0 .0 .0 01 01 82 82

- 35 35 0. 0. 00 00

- 35 35 0. 0. 00 00

9 8. 8. 8

- 0. 0. 00 00 38 38 6 - 0. 0. 00 00 29 29 2 - 0. 0. 00 00 19 19 8 - 0. 0. 00 00 10 10 4 - 0. 0. 00 00 01 01 0

0 .0 .0 00 00 84 84

0 .0 .0 01 01 78 78

- 35 35 0. 0. 00 00

- 35 35 0. 0. 00 00

9 6. 6. 2 9 3. 3. 7

- 0. 0. 00 00 40 40 4 - 0. 0. 00 00 30 30 8 - 0. 0. 00 00 21 21 1 - 0. 0. 00 00 11 11 4 - 0. 0. 00 00 01 01 8 - 0. 0. 00 00 42 42 3 - 0. 0. 00 00 32 32 4 - 0. 0. 00 00 22 22 5 - 0. 0. 00 00 12 12 6 - 0. 0. 00 00 02 02 6

0 .0 .0 00 00 79 79 0 .0 .0 00 00 73 73

0 .0 .0 01 01 75 75 0 .0 .0 01 01 72 72

- 35 35 0. 0. 00 00 - 35 35 0. 0. 00 00

- 35 35 0. 0. 00 00 - 35 35 0. 0. 00 00

9 1. 1. 2

- 0. 0. 00 00 44 44 3 - 0. 0. 00 00 34 34 1 - 0. 0. 00 00 23 23 9 - 0. 0. 00 00 13 13 7 - 0. 0. 00 00 03 03 6

0 .0 .0 00 00 66 66

0 .0 .0 01 01 68 68

- 35 35 0. 0. 00 00

8 8. 8. 6

- 0. 0. 00 00 46 46 5 - 0. 0. 00 00 36 36 0 - 0. 0. 00 00 25 25 5 - 0. 0. 00 00 15 15 0 - 0. 0. 00 00 04 04 5

0 .0 .0 00 00 60 60

0 .0 .0 01 01 65 65

- 35 35 0. 0. 00 00

86.1 86.1 83.6 83.6

-0.0 -0.004 0487 87 -0.0 -0.005 0511 11

-0.0 -0.003 0379 79 -0.0 -0.002 0271 71 -0.0 -0.001 0163 63 -0.0 -0.000 0055 55 -0.0 -0.004 0400 00 -0.0 -0.002 0288 88 -0.0 -0.001 0177 77 -0.0 -0.000 0066 66

0.00 0.0005 053 3 0.00 0.0004 045 5

0.001 0.00161 61 0.001 0.00156 56

81.0 81.0

-0.0 -0.005 0536 36

-0.0 -0.004 0422 22 -0.0 -0.003 0307 07 -0.0 -0.001 0192 92 -0.0 -0.000 0077 77

0.00 0.0003 037 7

78.5 78.5

-0.0 -0.005 0563 63

-0.0 -0.004 0445 45 -0.0 -0.003 0326 26 -0.0 -0.002 0208 08 -0.0 -0.000 0090 90

0.00 0.0002 029 9

76.0 76.0 73.4 73.4

-0.0 -0.005 0592 92 -0.0 -0.006 0623 23

-0.0 -0.004 0470 70 -0.0 -0.003 0347 47 -0.0 -0.002 0225 25 -0.0 -0.001 0103 03 -0.0 -0.004 0496 96 -0.0 -0.003 0370 70 -0.0 -0.002 0243 43 -0.0 -0.001 0117 17

70.9 70.9

-0.0 -0.006 0656 56

68.4 68.4

-0.0 -0.006 0691 91

65.8 65.8

-0.0 -0.007 0729 29

63.3 63.3 60.8 60.8

-0.0 -0.007 0770 70 -0.0 -0.008 0815 15

1 36 36 .2 .2

- 0. 0. 00 00 19 19 8

-0 -0 .0 .0 01 01 29 29 - 0. 0. 00 00 06 06 1

c

εs1

εs2

εs3

εs4

εs5

Fs2

Fs3

Fs4

Fs5

MPa - 70 70 .2 .2 1

MPa 8 5. 5. 98 98

MPa 2 42 42 .1 .1 7

MPa 3 50 50 .0 .0 0

kN - 12 12 3. 3. 15 15

kN - 35 35 .1 .1 9

kN - 22 22 .7 .7 6

kN kN - 7. 7. 06 06

kN 8 .6 .6 4

- 24 24 4. 4. 37 37

- 84 84 .7 .7 8

7 4. 4. 80 80

2 34 34 .3 .3 9

3 50 50 .0 .0 0

- 12 12 3. 3. 15 15

- 35 35 .1 .1 9

- 24 24 .5 .5 7

- 8. 8. 52 52

7 .5 .5 2

- 26 26 3. 3. 13 13

- 10 10 0. 0. 00 00

6 3. 3. 13 13

2 26 26 .2 .2 6

3 50 50 .0 .0 0

- 12 12 3. 3. 15 15

- 35 35 .1 .1 9

- 26 26 .4 .4 5

- 10 10 .0 .0 5

6 .3 .3 5

- 28 28 2. 2. 75 75

- 11 11 5. 5. 91 91

5 0. 0. 93 93

2 17 17 .7 .7 7

3 50 50 .0 .0 0

- 12 12 3. 3. 15 15

- 35 35 .1 .1 9

- 28 28 .4 .4 2

- 11 11 .6 .6 5

5 .1 .1 2

- 30 30 3. 3. 28 28 - 32 32 4. 4. 78 78

- 13 13 2. 2. 56 56 - 15 15 0. 0. 00 00

3 8. 8. 16 16 2 4. 4. 78 78

2 08 08 .8 .8 8 1 99 99 .5 .5 7

3 50 50 .0 .0 0 3 50 50 .0 .0 0

- 12 12 3. 3. 15 15 - 12 12 3. 3. 15 15

- 35 35 .1 .1 9 - 35 35 .1 .1 9

- 30 30 .4 .4 9 - 32 32 .6 .6 5

- 13 13 .3 .3 3 - 15 15 .0 .0 8

3 .8 .8 4 2 .4 .4 9

- 34 34 7. 7. 34 34

- 16 16 8. 8. 29 29

1 0. 0. 75 75

1 89 89 .8 .8 0

3 50 50 .0 .0 0

- 12 12 3. 3. 15 15

- 35 35 .1 .1 9

- 34 34 .9 .9 2

- 16 16 .9 .9 2

1 .0 .0 8

- 35 35 0. 0. 00 00

- 18 18 7. 7. 50 50

- 3. 3. 98 98

1 79 79 .5 .5 5

3 50 50 .0 .0 0

- 12 12 3. 3. 15 15

- 35 35 .1 .1 9

- 35 35 .1 .1 9

- 18 18 .8 .8 5

- 0. 0. 40 40

- 35 35 0. 0. 00 00

- 20 20 7. 7. 69 69

- 19 19 .4 .4 6

1 68 68 .7 .7 7

3 50 50 .0 .0 0

- 12 12 3. 3. 15 15

- 35 35 .1 .1 9

- 35 35 .1 .1 9

- 20 20 .8 .8 8

- 1. 1. 96 96

- 35 35 0. 0. 00 00 - 35 35 0. 0. 00 00

- 22 22 8. 8. 95 95 - 25 25 1. 1. 35 35

- 35 35 .7 .7 7 - 52 52 .9 .9 5

1 57 57 .4 .4 2 1 45 45 .4 .4 6

3 50 50 .0 .0 0 3 43 43 .8 .8 6

- 12 12 3. 3. 15 15 - 12 12 3. 3. 15 15

- 35 35 .1 .1 9 - 35 35 .1 .1 9

- 35 35 .1 .1 9 - 35 35 .1 .1 9

- 23 23 .0 .0 2 - 25 25 .2 .2 7

- 3. 3. 60 60 - 5. 5. 32 32

- 35 35 0. 0. 00 00

- 35 35 0. 0. 00 00

- 27 27 5. 5. 00 00

- 71 71 .0 .0 9

1 32 32 .8 .8 3

3 36 36 .7 .7 4

- 12 12 3. 3. 15 15

- 35 35 .1 .1 9

- 35 35 .1 .1 9

- 27 27 .6 .6 5

- 7. 7. 15 15

- 35 35 0. 0. 00 00

- 35 35 0. 0. 00 00

- 30 30 0. 0. 00 00

- 90 90 .2 .2 6

1 19 19 .4 .4 8

3 29 29 .2 .2 2

- 12 12 3. 3. 15 15

- 35 35 .1 .1 9

- 35 35 .1 .1 9

- 30 30 .1 .1 6

- 9. 9. 07 07

-350 -350.0 .00 0 -350 -350.0 .00 0

-350 -350.0 .00 0 -350.0 -350.00 0 -350. -350.00 00 -350. -350.00 00

-326 -326.4 .47 7 -350.0 -350.00 0

-110 -110.5 .56 6 -132 -132.0 .09 9

105. 105.35 35 90.3 90.36 6

321. 321.26 26 312. 312.81 81

-123 -123.1 .15 5 -123 -123.1 .15 5

-35. -35.19 19 -35. -35.19 19

-35. -35.19 19 -35. -35.19 19

-32. -32.82 82 -35. -35.19 19

-11. -11.11 11 -13. -13.28 28

0.001 0.00152 52

-350 -350.0 .00 0

-350. -350.00 00

-350. -350.00 00

-350.0 -350.00 0

-154 -154.9 .97 7

74.4 74.43 3

303. 303.84 84

-123 -123.1 .15 5

-35. -35.19 19

-35. -35.19 19

-35. -35.19 19

-15. -15.58 58

0.001 0.00147 47

-350 -350.0 .00 0

-350. -350.00 00

-350. -350.00 00

-350.0 -350.00 0

-179 -179.3 .33 3

57.4 57.48 8

294. 294.28 28

-123 -123.1 .15 5

-35. -35.19 19

-35. -35.19 19

-35. -35.19 19

-18. -18.03 03

0.00 0.0002 020 0 0.00 0.0001 010 0

0.001 0.00142 42 0.001 0.00137 37

-350 -350.0 .00 0 -350 -350.0 .00 0

-350. -350.00 00 -350. -350.00 00

-350. -350.00 00 -350. -350.00 00

-350.0 -350.00 0 -350.0 -350.00 0

-205 -205.3 .30 0 -233 -233.0 .07 7

39.3 39.39 9 20.0 20.06 6

284. 284.09 09 273. 273.20 20

-123 -123.1 .15 5 -123 -123.1 .15 5

-35. -35.19 19 -35. -35.19 19

-35. -35.19 19 -35. -35.19 19

-35. -35.19 19 -35. -35.19 19

-20. -20.64 64 -23. -23.43 43

-0. -0.00 0052 525 5 -0.0 -0.003 0394 94 -0.0 -0.002 0262 62 -0.0 -0.001 0131 31

0.00 0.0000 000 0

0.001 0.00131 31

-350 -350.0 .00 0

-350. -350.00 00

-350 -350.0 .00 0

-350 -350.0 .00 0

-262 -262.8 .82 2

-0.6 -0.65 5

261. 261.53 53

-123 -123.1 .15 5

-35. -35.19 19

-35. -35.19 19

-35. -35.19 19

-26. -26.42 42

-0.0 -0.005 0555 55 -0.0 -0.004 0419 19 -0.0 -0.002 0283 83 -0.0 -0.001 0147 47

-0.0 -0.000 0011 11

0.001 0.00124 24

-350 -350.0 .00 0

-350 -350.0 .00 0

-350.0 -350.00 0

-350 -350.0 .00 0

-294 -294.7 .78 8

-22. -22.89 89

248. 248.99 99

-123 -123.1 .15 5

-35. -35.19 19

-35. -35.19 19

-35. -35.19 19

-29. -29.63 63

-0.0 -0.005 0588 88 -0.0 -0.004 0447 47 -0.0 -0.003 0306 06 -0.0 -0.001 0165 65

-0.0 -0.000 0023 23

0.001 0.00118 18

-350 -350.0 .00 0

-350 -350.0 .00 0

-350.0 -350.00 0

-350 -350.0 .00 0

-329 -329.2 .20 0

-46. -46.85 85

235. 235.49 49

-123 -123.1 .15 5

-35. -35.19 19

-35. -35.19 19

-35. -35.19 19

-33. -33.09 09

-0.0 -0.006 0624 24 -0.0 -0.004 0477 77 -0.0 -0.003 0330 30 -0.0 -0.001 0183 83 -0.00 -0.0066 662 2 -0. -0.00 0050 509 9 -0. -0.00 0035 356 6 -0. -0.00 0020 203 3

-0.0 -0.000 0036 36 -0.0 -0.000 0050 50

0.001 0.00110 10 0.001 0.00103 03

-350 -350.0 .00 0 -350 -350.0 .00 0

-350 -350.0 .00 0 -350 -350.0 .00 0

-350.0 -350.00 0 -350 -350.0 .00 0

-350 -350.0 .00 0 -350 -350.0 .00 0

-350 -350.0 .00 0 -350 -350.0 .00 0

-72. -72.73 73 -100 -100.7 .76 6

220. 220.91 91 205. 205.11 11

-123 -123.1 .15 5 -123 -123.1 .15 5

-35. -35.19 19 -35. -35.19 19

-35. -35.19 19 -35. -35.19 19

-35. -35.19 19 -35. -35.19 19

-35. -35.19 19 -35. -35.19 19

0 .0 .0 00 00 75 75

0 .0 .0 01 01 44 44

0 .0 .0 02 02 12 12

- 35 35 0. 0. 00 00

- 2 58 58 .6 .6 6

- 12 12 2. 2. 17 17

1 4. 4. 32 32

1 50 50 .8 .8 1

2 87 87 .3 .3 0

3 50 50 .0 .0 0

- 12 12 3. 3. 15 15

- 26 26 .0 .0 0

- 12 12 .2 .2 8

1 .4 .4 4

1 5. 5. 16 16

0 . 00 00 08 08 6

0 .0 .0 01 01 51 51

0 .0 .0 02 02 16 16

- 35 35 0. 0. 00 00

- 21 21 9. 9. 70 70

- 89 89 .4 .4 1

4 0. 0. 89 89

1 71 71 .1 .1 9

3 01 01 .4 .4 9

3 50 50 .0 .0 0

- 12 12 3. 3. 15 15

- 22 22 .0 .0 9

- 8. 8. 99 99

4 .1 .1 1

1 7. 7. 21 21

mm 1 19 19 .0 .0

- 0. 0. 00 00 26 26 9

-0 -0 .0 .0 01 01 91 91 - 0. 0. 00 00 11 11 3 - 0. 0. 00 00 03 03 5

0 .0 .0 00 00 43 43

1 16 16 .5 .5

- 0. 0. 00 00 28 28 2

-0 -0 .0 .0 02 02 02 02 - 0. 0. 00 00 12 12 2 - 0. 0. 00 00 04 04 2

0 .0 .0 00 00 37 37

1 14 14 .0 .0

- 0. 0. 00 00 29 29 5

- 0. 0. 00 00 21 21 3 - 0. 0. 00 00 13 13 2 - 0. 0. 00 00 05 05 0

1 11 11 .4 .4

- 0. 0. 00 00 30 30 8

1 08 08 .9 .9 1 06 06 .4 .4

- 0. 0. 00 00 32 32 2 - 0. 0. 00 00 33 33 7

1 03 03 .8 .8 1 01 01 .3 .3

0 .0 .0 00 00 07 07

εs6

f s4 s4

f s5 s5

f s6 s6

f s7 s7

Fs1

KONDISI TEKAN AKSIAL KECIL : Pn = 0.1 * fc' * b * h KONDISI BALANCE 1 42 42 .7 .7

- 0. 0. 00 00 17 17 5

- 0. 0. 00 00 11 11 0 - 0. 0. 00 00 04 04 5

0 .0 .0 00 00 20 20


Fs6

Fs7

Cs

Ms6

Ms7

Ms

a

kN 24.35

kN 123.15

kN -32.02

kNmm 11446.83

Ms1

kNmm 2180.35

Ms2

k Nmm 705.19

Ms3

kN k Nmm 0.00

Ms4

kN k Nmm 267.80

Ms5

kN k Nmm 1508.59

k Nmm 1 14 1446.83

kNmm 2 75 7555.60

mm 1 01 01.17

kN 685.97

Cc

kNmm 5 65 6500.29

Mc

kN 653.95

kNm 84.06

23.56

123.15

-37.19

11446.83

2180.35

761.15

0.00

232.99

1460.13

1 14 1446.83

2 75 7528.30

99.02

671.37

5 60 6020.73

634.18

22.75

123.15

-42.60

11446.83

2180.35

819.60

0.00

196.64

1409.52

1 14 1446.83

2 74 7499.77

96.86

656.78

5 55 5509.75

614.18

21.89

123.15

-48.25

11446.83

2180.35

880.70

0.00

158.64

1356.61

1 14 1446.83

2 74 7469.96

94.71

642.18

5 49 4967.36

21.00 20.06

123.15 123.15

-54.17 -60.36

11446.83 11446.83

2180.35 2180.35

944.64 1011.63

0.00 0.00

118.86 77.20

1301.23 1243.22

1 14 1446.83 1 14 1446.83

2 74 7438.75 2 74 7406.06

92.56 90.41

627.59 612.99

5 43 4393.55 5 37 3788.33

19.08

123.15

-66.86

11446.83

2180.35

1081.89

0.00

33.50

1182.38

1 14 1446.83

2 73 7371.78

88.25

598.40

5 31 3151.69

531.54

80.52

0.65

345.50

52.34

18.05

123.15

-71.57

11446.83

2180.35

1090.17

0.00

-12.39

1118.49

1 14 1446.83

2 72 7270.29

86.10

583.80

5 24 2483.63

512.23

79.75

0.65

332.95

51.84

16.97

123.15

-76.24

11446.83

2180.35

1090.17

0.00

-60.63

1051.33

1 14 1446.83

2 71 7154.90

83.95

569.21

5 17 1784.16

492.97

78.94

0.65

320.43

51.31

15.83 14.62

123.15 120.99

-81.16 -88.50

11446.83 11446.83

2180.35 2180.35

1090.17 1090.17

0.00 0.00

-111.40 -164.92

980.64 906.12

1 14 1446.83 1 12 1245.96

2 70 7033.43 2 67 6704.52

81.80 79.64

554.61 540.02

5 10 1053.27 5 02 0290.96

473.45 451.52

78.09 77.00

0.65 0.65

307.75 293.49

50.76 50.05

13.35

118.49

-96.48

11446.83

2180.35

1090.17

0.00

-221.42

827.47

1 10 1013.26

2 63 6336.67

77.49

525.42

4 94 9497.24

428.95

75.83

0.65

278.82

49.29

12.01

115.84

-104.90

11446.83

2180.35

1090.17

0.00

-281.14

744.32

10767.27

25947.80

75.34

510.83

48672.10

405.92

74.62

0.65

263.85

48.50

10.59 9.08

113.04 110.07

-113.83 -122.84

11446.83 11446.83

2180.35 2180.35

1090.17 1090.17

0.00 0.00

-344.37 -411.44

656.27 562.90

10506.80 1 02 0230.55

25536.06 2 50 5099.36

73.19 71.03

496.23 481.64

47815.54 4 69 6927.57

382.40 358.80

73.35 72.03

0.65 0.65

248.56 233.22

47.68 46.82

7.48

106.91

-129.90

11446.83

2180.35

1090.17

0.00

-482.70

463.68

9937.03

2 46 4635.36

68.88

467.04

4 60 6008.18

337.15

70.64

0.65

219.14

45.92

5.78

103.55

-137.41

11446.83

2180.35

1090.17

0.00

-558.56

358.07

9624.57

2 41 4141.44

66.73

452.45

4 50 5057.38

315.04

69.20

0.65

204.77

44.98

3.96 2.02

99.96 96.13

-145.43 -153.99

11446.83 11446.83

2180.35 2180.35

1090.17 1090.17

0.00 0.00

-639.47 -725.97

245.41 124.99

9291.29 8935.02

2 36 3614.58 2 30 3051.39

64.58 62.42

437.85 423.26

4 40 4075.16 4 30 3061.52

292.43 269.26

67.69 66.11

0.65 0.65

190.08 175.02

44.00 42.97

-0.07

92.02

-163.17

1 14 1446.83

2180.35

1090.17

0.00

-818.64

-4.04

8553.30

22 22447.97

60.27

408.66

42 42016.47

245.49

64.46

0.65

159.57

41.90

-2.30

87.61

-173.03

11446.83

2180.35

1090.17

0.00

-918.18

-142.63

8143.30

2 17 1799.86

58.12

394.07

4 09 0940.00

221.03

62.74

0.65

143.67

40.78

-4.71

82.86

-183.65

11446.83

2180.35

1090.17

0.00

-1025.37

-291.87

7701.77

2 11 1101.88

55.97

379.47

3 98 9832.12

195.82

60.93

0.66

129.54

40.31

-7.31 -10.13

77.73 72.17

-193.48 -201.85

11446.83 11446.83

2180.35 2180.35

1090.17 1090.17

0.00 0.00

-1090.17 -1090.17

-453.06 -627.67

7224.92 6708.32

2 03 0399.04 19707.83

53.81 51.66

364.88 350.28

3 86 8692.82 37522.10

171.40 148.43

59.09 57.23

0.68 0.70

116.34 103.16

40.11 39.78

28.88

123.15

7.20

11446.83

1611.36

380.54

0.00

469.73

1789.74

1 14 1446.83

2 71 7145.05

1 15 15.77

784.97

5 89 8923.98

792.17

86.07

0.65

514.91

55.94

Pn

Mn

Ф.Pn

Ф.Mn

0.65

kN 425.07

kNm 54.64

83.55

0.65

412.22

54.31

83.01

0.65

399.22

53.96

593.93

82.44

0.65

386.06

53.58

573.42 552.63

81.83 81.19

0.65 0.65

372.72 359.21

53.19 52.78

Ф

137.87 0.00 137.87 1000.00

30.31

123.15

20.55

11446.83

1368.65

278.48

0.00

533.22

1878.13

1 14 1446.83

2 69 6952.15

1 21 21.27

822.28

5 94 9462.31

842.84

86.41

0.65

0.00

0.00

547.84

56.17


SENGKANG STROUS D 30 CM BAHAN STRUKTUR

Kuat tekan beton,

fc' =

30

MPa


fy =

350

MPa


fy =

240

MPa

b= h= D= P= ts =

266 266 16 10 30

mm mm mm mm mm

31.030

kN

DIMENSI BALOK



Vu-tump =

1. TULANGAN GESER

Vu =


31.030 0.60 240

MPa

Vc = (√ fc') / 6 * b * d * 10 =

57.261

kN

f * Vc =

34.356

kN

f= fy = -3



→

f * Vs = Vu - f * Vc =


-

kN

31.030

kN

78.54

mm

s = Av * fy * d / ( Vs * 10 ) =

143.30

mm

smax = d / 2 =

108.95

mm

smax =

108.95 108.95 100 100

mm mm mm

Vs =


1

10 2

3


P

Av = ns * p / 4 * P =


kN

s= s=

→

1

P

10

2

BAB 29 PERHITUNGAN BALOK KOLOM ( B E AM COLUMN )

RANGKA LANTAI ( CNP 150 x 75 x 6.5)



f y = f r =

240

MPa

70

MPa

E= u =

200000

MPa

0.3

B. DATA PROFIL BAJA Profil : CNP 150 X 75 X 6.5 X 10


ht = bf = tw = tf =

150

mm

75

mm

6.5

mm

10

mm

r= A = Ix = Iy = r x = r y = Sx = Sy =

13

mm

2371

2

8640000

mm mm

1220000

mm

4

60.4

mm

22.7

mm

115000

mm

23600

mm


Lx = Ly =

4500

mm

600

mm


4500

mm

6.5

mm

21381000

Nmm

21381000

Nmm

21381000

Nmm

21381000

Nmm

0

N

17736

N

0.80 0.80 0.75

D. SECTION PROPERTIES G = E / [2*(1 + u)] = 76923 MPa 23.00 mm h1 = tf + r = 104.00 mm h2 = ht - 2 * h1 = 140.00 mm h = ht - tf = 3 3 3 J = S [ b * t /3 ] = 2 * 1/3 * bf * tf + 1/3 * (ht - 2 * tf ) * tw = 61900.4 mm 6 2 Iw = Iy * h / 4 = 5.978E+09 mm X1 = p / Sx * √ [ E * G * J * A / 2 ] = 29026.4 MPa X2 = 4 * [ Sx / (G * J) ] * Iw / Iy = 0.0000114 mm /N 3 2 Zx = tw * ht / 4 + ( bf - tw ) * ( ht - tf ) * tf = 132462.5 mm 2 2 Zy = tf * bf / 2 + ( ht - 2 * tf ) * tw / 4 = 29498.1 mm G = modulus geser, J = Konstanta puntir torsi, Iw = konstanta putir lengkung, h= Zx = Zy = X1 = X2 =

tinggi bersih badan, modulus penampang plastis thd. sb. x, modulus penampang plastis thd. sb. y, koefisien momen tekuk torsi lateral, koefisien momen tekuk torsi lateral,



a / h = 32.143



<


204.09


l = bf / tf =

7.500

lp = 500 / √ f y =

32.275







l

<

lp

40.344 31791000

Nmm

19550000

Nmm


l

<



lr compact 31791000

Nmm

-

Nmm

-

Nmm

31791000

Nmm


l = h / tw =

21.538

lp = 1680 / √ f y =

108.444



l

lp

<

dan

lr = 2550 / √ f y = l <

164.602

lr compact



31791000

Nmm

-

Nmm

-

Nmm

31791000

Nmm


l = h / t w =


h / tw



> <

21.538

lr 40.344





≤ ≤

f y f y



1.00

< 2.3

1.00



1.213 609207

mm

A1 = A / 2 - 1/3 * tw * h2 =

Luas penampang,

960

mm


r 1 =  ( I1 / A1 ) =

tekan,

25

mm

600

mm



23.820


lp = 1.76 * √ ( E / f y ) =

50.807


lr = 4.40 * √ ( E / f y ) =

127.017


f c

lG

< <

f y

lp


120.00

MPa

120.00

MPa

lr




240.00

MPa

-

MPa

-

MPa

240.00

MPa

240.00

MPa

115000

mm

3



1.111 30663238

Nmm


lG = bf / ( 2 * t f ) = ke = 4 /  ( h / tw ) =

0.862

ke =

0.763

lp = 0.38 * √ ( E / f y ) =

10.97

diambil,

3.75


> 0.763


lr = 1.35 * √ ( ke * E / f y ) =

34.04

f c = f y / 2 = <

120.00


240.00

MPa

-

MPa

-

MPa

240.00

MPa

240.00

MPa

115000

mm


lG

<

lp

dan

lG

MPa

lr





1.111 30663238

Nmm



 Mp  Mp


Lp = 1.76 * r y * √ ( E / f y ) = f L = f y - f r =

1153

mm

170

MPa


2

Lr = r y * X1 / f L * √ [ 1 + √ ( 1 + X2 * f L ) ] =

5688

mm



1.00 31791000

Nmm

19550000

Nmm


<

Lp

dan

600 mm L = Ly = L < Lr Termasuk kategori : bentang pendek


Mn = Mp = f y * Zx = 31791000 Mn = Cb * [ Mr + ( Mp - Mr ) * ( Lr - L ) / ( Lr - Lp ) ] = 2 Mn = Cb * p / L*√ [ E * Iy * G * J + ( p * E / L ) * Iy * Iw ] = bentang pendek Momen nominal balok untuk kategori : Mn = 31791000 > Mn Mp Momen nominal yang digunakan, 31791000 Mn =

Nmm Nmm Nmm Nmm Nmm


l = h / t w =

21.538

Ny = A * f y = Nu / ( fb * Ny ) =

569040

N

0.000

N



Untuk nilai, →



lr = 2550 / √ f y * [ ( 1 - 0.74 * Nu / ( fb * Ny ) ]


0.125 108.444 108.444


l



164.602

lr compact



31791000

Nmm

-

Nmm

-

Nmm

31791000

Nmm

Mn = Mn =

31791000

Nmm

31791000

Nmm


30663238

Nmm

30663238

Nmm

31791000

Nmm

31791000

Nmm

30663238

Nmm

24530591

Nmm





kx = ky =

1.00


4500

mm

4500

mm

1.00




600

mm

600

mm


lcx = 1 /p * Lkx / r x * √ ( f y / E ) =

0.8215


lcy = 1 / p * Lky / r y * √ ( f y / E ) =

0.2915


lcx = w = w = 1.43 / ( 1.6 - 0.67 * lc ) = w = 1.25 * lc2 = wx =


0.8215 1.3624 1.3624




0.2915 1.0180 1.0180 176.154

MPa

235.758

MPa

417661

N

558983

N

417661

N

334129

N

0

N





21381000 334129 24530591

Nmm N Nmm



Untuk nilai, →

Untuk nilai, →

Nu / ( fn * Nn ) =

0.0000

<

 1.0  1.0 0.2


0.8716


0.8716

0.8716

<

1.0

-

AMAN (OK)


h / tw

Untuk nilai,

≤

1.10 *  ( kn * E / f y )


Untuk nilai,

Vn = 0.60 * f y * Aw 1.10 *  ( kn * E / f y )

≤

h / tw

≤

1.37 *  ( kn * E / f y )


Untuk nilai,



2

Vn = 0.90 * A w * kn * E / ( h / tw )



975 5.0048 21.538 71.039 88.476

mm

h / tw

1.10* ( kn*E / f y )

<


h / tw

dan

<


N N N N N N


<

1.375 AMAN (OK)


2

0.5 * D * Aw * (1 + Cv) * [ a / h - (a / h) /  (1 + (a / h) ) ] Tebal plat pengaku vertikal pada badan (stiffner ), 6.5 ts = Tinggi plat pengaku, 130 hs = ht - 2 * tf = Luas penampang plat pengaku, 845 As = hs * ts = Untuk sepasang pengaku, 1 D= Cv = 1.5 * kn * E / f y * 1 / ( h /tw ) = 13.4856 2 2 110 0.5 * D * Aw * (1 + Cv) * [ a / h - (a / h) /  (1 + (a / h) ) ] = As

≥

mm mm mm

mm


As

≥

2

2

0.5 * D * Aw * (1 + Cv) * [ a / h - (a / h) /  (1 + (a / h) ) ]

>

845

110

(OK)


Is Is

≥

3

0.75 * h * t w 3 3 2 1.5 * h * tw / a ≥

untuk untuk

a/h a/h

≤ >

3

Is = 2/3 * hs * ts = a/h=

32.143

2 2 23801

mm

 2

>



-

mm

56

mm 4

>


BAB 30 PERHITUNGAN BALOK KOLOM ( B E AM COLUMN )

RANGKA LANTAI ( L 50.50.5)



f y = f r =

240

MPa

70

MPa

E= u =

200000

MPa

0.3

B. DATA PROFIL BAJA Profil : L 50.50.5


ht = bf = tw = tf =

50

mm

50

mm

5

mm

5

mm

r= A = Ix = Iy = r x = r y = Sx = Sy =

5

mm

480

2

110000

mm mm

110000

mm

4

15.1

mm

15.1

mm

3050

mm

3050

mm


Lx = Ly =

1200

mm

600

mm


4000

mm

5

mm

611000

Nmm

611000

Nmm

611000

Nmm

611000

Nmm

0

N

1157

N

0.80 0.80 0.75

D. SECTION PROPERTIES G = E / [2*(1 + u)] = 76923 MPa 10.00 mm h1 = tf + r = 30.00 mm h2 = ht - 2 * h1 = 45.00 mm h = ht - tf = 3 3 3 mm 5833.3 J = S [ b * t /3 ] = 2 * 1/3 * bf * tf + 1/3 * (ht - 2 * tf ) * tw = 6 2 Iw = Iy * h / 4 = 5.569E+07 mm X1 = p / Sx * √ [ E * G * J * A / 2 ] = 151167.1 MPa X2 = 4 * [ Sx / (G * J) ] * Iw / Iy = 0.0000001 mm /N 3 2 Zx = tw * ht / 4 + ( bf - tw ) * ( ht - tf ) * tf = 13250.0 mm 2 2 mm 6500.0 Zy = tf * bf / 2 + ( ht - 2 * tf ) * tw / 4 = G = modulus geser, J = Konstanta puntir torsi, Iw = konstanta putir lengkung, h= Zx = Zy = X1 = X2 =

tinggi bersih badan, modulus penampang plastis thd. sb. x, modulus penampang plastis thd. sb. y, koefisien momen tekuk torsi lateral, koefisien momen tekuk torsi lateral,



a / h = 88.889



<


204.09


l = bf / tf =

10.000

lp = 500 / √ f y =

32.275







l

<

lp

40.344 3180000

Nmm

518500

Nmm


l

<



lr compact 3180000

Nmm

-

Nmm

-

Nmm

3180000

Nmm


l = h / tw =


9.000


lp = 1680 / √ f y =

108.444


l

lp

<

dan

lr = 2550 / √ f y = l <

164.602

lr compact



3180000

Nmm

-

Nmm

-

Nmm

3180000

Nmm


l = h / t w =


h / tw



> <

9.000

lr 40.344





≤ ≤

f y f y



1.00

< 2.3

1.00



0.900 54896

mm

A1 = A / 2 - 1/3 * tw * h2 =

Luas penampang,

190

mm


r 1 =  ( I1 / A1 ) =

tekan,

17

mm

600

mm



35.299


lp = 1.76 * √ ( E / f y ) =

50.807


lr = 4.40 * √ ( E / f y ) =

127.017


f c

lG

< <

f y

lp


120.00

MPa

120.00

MPa

lr




240.00

MPa

-

MPa

-

MPa

240.00

MPa

240.00

MPa

3050

mm

3



1.095 801735

Nmm


lG = bf / ( 2 * t f ) = ke = 4 /  ( h / tw ) =

1.333

ke =

0.763

lp = 0.38 * √ ( E / f y ) =

10.97

diambil,

5.00


> 0.763


lr = 1.35 * √ ( ke * E / f y ) =

34.04

f c = f y / 2 = <

120.00


240.00

MPa

-

MPa

-

MPa

240.00

MPa

240.00

MPa

3050

mm


lG

<

lp

dan

lG

MPa

lr





1.095 801735

Nmm



 Mp  Mp


Lp = 1.76 * r y * √ ( E / f y ) = f L = f y - f r =

767

mm

170

MPa


2

Lr = r y * X1 / f L * √ [ 1 + √ ( 1 + X2 * f L ) ] =

18995

mm



1.00 3180000

Nmm

518500

Nmm


<

Lp

dan

600 mm L = Ly = L < Lr Termasuk kategori : bentang pendek


Mn = Mp = f y * Zx = 3180000 Nmm Nmm Mn = Cb * [ Mr + ( Mp - Mr ) * ( Lr - L ) / ( Lr - Lp ) ] = 2 Nmm Mn = Cb * p / L*√ [ E * Iy * G * J + ( p * E / L ) * Iy * Iw ] = bentang pendek Momen nominal balok untuk kategori : Mn = 3180000 Nmm > Mn Mp Momen nominal yang digunakan, 3180000 Nmm Mn = 4. MOMEN NOMINAL PENGARUH LOCAL B UK LING PADA BADAN

l = h / t w =


Ny = A * f y = Nu / ( fb * Ny ) =

9.000 115200

N

0.000

N


Untuk nilai, →



lr = 2550 / √ f y * [ ( 1 - 0.74 * Nu / ( fb * Ny ) ]


0.125 108.444 108.444


l



164.602

lr compact



3180000

Nmm

-

Nmm

-

Nmm

3180000

Nmm

Mn = Mn =

3180000

Nmm

3180000

Nmm


801735

Nmm

801735

Nmm

3180000

Nmm

3180000

Nmm

801735

Nmm

641388

Nmm





kx = ky =

1.00


1200

mm

1200

mm

1.00




600

mm

600

mm


lcx = 1 /p * Lkx / r x * √ ( f y / E ) =

0.8763


lcy = 1 / p * Lky / r y * √ ( f y / E ) =

0.4381


lcx = w = w = 1.43 / ( 1.6 - 0.67 * lc ) = w = 1.25 * lc2 = wx =


0.8763 1.4118 1.4118




0.4381 1.0946 1.0946 169.995

MPa

219.263

MPa



81598

N

105246

N

81598

N

65278

N

0

N



611000

Nmm

65278

N

641388

Nmm



Untuk nilai, →

Untuk nilai, →

Nu / ( fn * Nn ) =

0.0000

<

 1.0  1.0 0.2


0.9526


0.9526

0.9526

<

1.0

-

AMAN (OK)


h / tw

Untuk nilai,

≤

1.10 *  ( kn * E / f y )


Untuk nilai,

Vn = 0.60 * f y * Aw 1.10 *  ( kn * E / f y )

≤

h / tw

≤

1.37 *  ( kn * E / f y )


Untuk nilai,



2

Vn = 0.90 * A w * kn * E / ( h / tw )



250 5.0006 9.000 71.009 88.439

mm

h / tw

1.10* ( kn*E / f y )

<


h / tw

dan

<


N N N N N N


<

1.375 AMAN (OK)


2

0.5 * D * Aw * (1 + Cv) * [ a / h - (a / h) /  (1 + (a / h) ) ] Tebal plat pengaku vertikal pada badan (stiffner ), 5 ts = Tinggi plat pengaku, 40 hs = ht - 2 * tf = Luas penampang plat pengaku, 200 As = hs * ts = Untuk sepasang pengaku, 1 D= Cv = 1.5 * kn * E / f y * 1 / ( h /tw ) = 77.1703 2 2 55 0.5 * D * Aw * (1 + Cv) * [ a / h - (a / h) /  (1 + (a / h) ) ] = As

≥

mm mm mm

mm


As

≥

2

2

0.5 * D * Aw * (1 + Cv) * [ a / h - (a / h) /  (1 + (a / h) ) ]

>

200

55

(OK)


Is Is

≥

3

0.75 * h * t w 3 3 2 1.5 * h * tw / a ≥

untuk untuk

a/h a/h

≤ >

3

Is = 2/3 * hs * ts = a/h=

88.889

2 2 3333

mm

 2

>



-

mm

1

mm 4

>


BAB 31 RENCANA PLAT LANTAI ( PLAT BORDES) A. DATA BAHAN STRUKTUR f y =

240

MPa

f y =

24

kN/cm2

f y =

240000

kN/m2

Panjang bentang plat tinjauan arah x,

Lx =

0.60

m

Panjang bentang plat tinjauan arah y,

Ly = h=

0.60

m

Tegangan leleh baja untuk tulangan lentur,

B. DATA PLAT LANTAI

Tebal plat lantai,

6

mm

C. BEBAN PLAT LANTAI 1. BEBAN MATI ( D E A D No

LOAD

)

Jenis Beban Mati 1

3

Berat sendiri plat lantai (kN/m )

2. BEBAN HIDUP (L I V E

LOAD

Tebal (m)

Q (kN/m )

78.5

0.006

0.471

QD =

Total beban mati,

2

Berat satuan

0.471

) 2

500

kg/m

QL =

5.000

kN/m

2

Qu = 1.2 * Q D + 1.6 * Q L =

8.565

kN/m

2

Mu =

0.385

kNm

Beban hidup air pada lantai bangunan =

3. BEBAN RENCANA TERFAKTOR Beban rencana terfaktor,

4. MOMEN PLAT AKIBAT BEBAN TERFAKTOR Momen rencana (maksimum) plat,

Laporan Struktur Parkir d9

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