struktur beton 1: Oktober 2012

Selasa, 23 Oktober 2012

UJIAN ONLINE STRUKTUR BETON 1

Ketentuan Ujian Online Stuktur Beton I :
1. Ujian wajib diikuti peserta mk STRUKTUR BETON I (semester 5)
2. Soal dan dan bahan ujian dapat dilihat pada web : www.strukturbeton1.blogspot.com
3. Ujian online mulai tanggal 24 Oktober 2012 jam 13.00 s/d 25 Oktober 2012 jam 18.00
4. Jawaban lengkap ujian disampaikan pada email : strukturbeton@gmail.com dan sumirinms@gmail.com
5. Jawaban singkat dapat disampaikan pada komentar di bawah ini.

Soal Ujian Online :

Nomor 1.
Hitung secara manual luas tulangan tarik dan jumlah tulangan tarik balok persegi beton bertulang :
fc'=200 kg/cm2 (20 MPa); fy=4000 kg/cm2 (400 MPa)
(a)b=30cm; h=50cm; Mu=20 ton.m
(b)b=30cm; h=50cm; Mu=10 ton.m

(c)b=30cm; h=60cm; Mu=40 ton.m

(d)b=40cm; h=70cm; Mu=40 ton.m

Nomor 2.

Soal nomor 1 dihitung menggunakan program DsgWin

Nomor 3.

(a) Bagaimana menghitung jumlah tulangan minimum balok ?

(b) Berapa luas tulangan maksimum sebuha balok ?

(d) Tuliskan rumus dan prosedur perhitungan tulangan balok T !

Nomor 4.

Hitung secara manual luas tulangan geser sengkang balok persegi beton bertulang :

fc'=150 kg/cm2 (15 MPa); fyv=2400 kg/cm2 (240 MPa)

(a)b=30cm; h=50cm; Vu=30 ton

(b)b=25cm; h=50cm; Vu=20 ton

(c)b=30cm; h=60cm; Vu=40 ton

(d)b=40cm; h=60cm; Vu=40 ton

Nomor 5.

Hitung soal Nomor 4 menggunakan program DsgWin

Nomor 6.

Hitung dan gambar penulangan 4 sisi kolom beton bertulang berikut (D19 mm atau D20 mm):

(a) b=400mm; h=600mm; fc'=15 MPa; fy=400 MPa; P=1000 kN; Mu=250 kN.m

(b) b=500mm; h=500mm; fc'=15 MPa; fy=400 MPa; P=2000 kN; Mu=300 kN.m

Perhitungan dengan 3 cara yaitu :

1)menggunakan Grafik 2)menggunakan Program DsgWin 3) menggunakan PCACOLUMN

Nomor 7.

Kolom persegi b=50cm; h=50cm; fc'=20 MPa' fy=400 MPa; tulangan 4 sisi 20D25

(a) Buatlah diagram interksi menggunakan Program CONBAR dan EXCEL

(b) Buatlah diagram interaksi menggunakan Program PCACOLUMN

Nomor 8.

Buatlah contoh perhitungan kolom bentuk L dan kolom berlubang menggunakan program ACECOMS GEAR

Data-data lain tentukan sendiri

Selamat mengerjakan !

Kalau ada pertanyaan, silahkan tulis komentar di bawah ini !

Perhitungan Kolom Cara Manual ( dengan Rumus)

Beban kolom maksimum, Pu :

dimana : f=0.65; Ag=b*h = luas penampang kolom (cm2)
Ast=m*0.25*3.14*db^2 = luas tulangan total (cm2)
m=jumlah tulangan total
fy=kuat leleh baja rencana (kg/cm2)

Kolom bertulangan simetri 2 sisi dapat didekati dengan rumus :

dimana : e=Mu/Pu; d=0.85*h; d'=0.15*h

Rumus analisis kolom lainnya baca dari :

https://sites.google.com/site/strukturbeton1/rumus-analisis-kolom

Rabu, 17 Oktober 2012

Program ACECOMS GEAR

Silahkan dicoba program ACECOMS GEAR berikut :
https://sites.google.com/site/strukturbeton1/program-gear

Contoh Penggunaan Program ACECOMS-GEAR pada Kolom Berlubang :

; Computing Moment Capacity:

Applied Axial Load, Pu = 3,000.0 kN

Applied Moment, Mux = 200.0 kN-m

Applied Moment, Muy = 100.0 kN-m

Resultsnt Moment, Muxy = 223.6 kN-m

Resultant Moment Angle = 26 Deg.

; Detailed Capacity Calculations:

Neutral axis angle = 32 Deg.

Neutral axis depth = 389 mm

Capacity reduction factor = 0.9

Stress in Rebars:

Bar No, Size, Cord-X , Cord-Y, Area , Stress

1, d 16, -360, -360, 204, -400.0

2, d 16, 360, 360, 204, 378.8

3, d 16, 360, -360, 204, -400.0

4, d 16, -360, 360, 204, -78.6

5, d 16, -360, -240, 204, -400.0

6, d 16, -360, -120, 204, -400.0

7, d 16, -360, 0, 204, -400.0

8, d 16, -360, 120, 204, -374.0

9, d 16, -360, 240, 204, -234.9

10, d 16, -240, 360, 204, 15.7

11, d 16, -120, 360, 204, 98.0

12, d 16, 0, 360, 204, 196.9

13, d 16, 120, 360, 204, 285.8

14, d 16, 240, 360, 204, 367.3

15, d 16, 360, 240, 204, 320.1

16, d 16, 360, 120, 204, 181.2

17, d 16, 360, 0, 204, 33.3

18, d 16, 360, -120, 204, -110.0

19, d 16, 360, -240, 204, -264.3

20, d 16, 240, -360, 204, -400.0

21, d 16, 120, -360, 204, -400.0

22, d 16, 0, -360, 204, -400.0

23, d 16, -120, -360, 204, -400.0

24, d 16, -240, -360, 204, -400.0

; Result Summary:

Axial Compresion, ØPno = 6,750.4 kN

Axial Tension, ØPnt = -1,762.6 kN

Moment Capacity, ØMnx = 1,287.9 kN-m

Moment Capacity, ØMny = 385.0 kN-m

Resultant Capacity, ØMnxy = 1,344.2 kN-m

Resultant Angle = 16 Deg.

Concrete volume = 0.48 m^3

Main Steel weight = 37.92 Kg/m

Steel weight/ volume = 79.00 Kgm^3

RUMUS PERHITUNGAN DISAIN DAN ANALISIS PENAMPANG BALOK

RUMUS PERHITUNGAN

DISAIN DAN ANALISIS PENAMPANG BALOK

1. PERENCANAAN (DISAIN) PENAMPANG BALOK :

( TULANGAN TUNGGAL )

Diketahui :

- Dimensi balok : b; h

- Momen lentur : Mu

- Mutu bahan : fc’; fy

Hitung :

- Luas dan jumlah tulangan balok : As, m

Penyelesaian :

- Koefisien penampang : Rn = Mu/(f.0.85 fc’ b d²); dimana : f=0.80

- Indeks tulangan : w = 1-Ö(1-2*Rn)

- Rasio tulangan : r = w.0,85.fc’/fy

r_min = 14/fy

r_maks = 0,75*0,85*fc’/fy*6000/(6000+fy)

Bila : r < r_min ; As = r_min*b*d

Bila : r_maks r < r_min ; As = r *b*d

Bila : r > r_maks ; Dimensi penampang ( b atau h) diperbesar, hitung ulang.

( alternatif lain dpasang tulangan tekan !)

- Jumlah tulangan : m=As/(0.25*π*d_b²)

dimana : d_b = diameter tulangan (13;16;19;22;25 mm) disesuaikan dimensi balok.

Catatan :

Semua satuan harus kompatibel.

Mu = kg.cm; fc dan fy = kg/cm²; Rn, w, r = tidak bersatuan

As = cm²; d_b = cm; b dan h = cm

2. ANALISIS KAPASITAS PENAMPANG BALOK :

( TULANGAN TUNGGAL )

Diketahui :

- Dimensi balok : b; h

- Tulangan tarik : As=m*0.25*3.14*d_b²

- Mutu bahan : fc’; fy

Hitung :

- Momen yang dapat ditahan : Mu

- Tinggi garis netral, c

- Tinggi blok tegangan beton, a

Penyelesaian :

- Rasio tulangan : ρ=As/(b*d); d≈0.9*h

- Indeks tulangan : w= ρ*fy/(0.85*fc’)

- Koefisien penampang : Rn=w(1-w/2)

- Momen : Mu=Rn*ø*0.85*fc’*b*d² ; dimana : ø=0.80

atau :

- a=As*fy/(0.85*fc'*b);

- Mu=ø*0.85*fc'*b*a*(d-a/2)

Parameter Penampang :

- Tinggi blok tegangan : a=w*d

- Tinggi garis netral : c=a/β₁; dimana : β₁=0.85

- Gaya tekan blok tegangan beton Cc=a*b*0.85*fc’

- Gaya tarik baja tulangan : T=As*fy

3. ANALISIS KAPASITAS PENAMPANG BALOK

TULANGAN RANGKAP

Satuan SI,

Mu (kN.m); As; As' (mm2), b; h(mm); fc'; fy (MPa)

Soal :

Buatlah latihan soal dan jawaban balok untuk kasus 1,2 dan 3 !

Selasa, 16 Oktober 2012

Tanggapan Jawaban Soal tentang Disain Kolom

Saya menerima email dari Mas Muhammad Edwin R.(022103060). Terima kasih sudah menanggapi dan mengerjakan, sehingga saya bisa mengoreksi dan membetulkan bila terjadi kesalahan.

Soal :

Nomor : 1.

Kolom bertulangan 4 sisi, fc'=150 kg/cm2 (15 MPa); fy=4000 kg/cm2 (400 MPa); dimensi b=40cm; h=40cm; Menahan Momen Mu=20 ton.m ; Gaya aksial Pu=100 ton.

Hitung jumlah tulangan (pakai D19) dan gambarkan penampang kolom tersebut.

Komentar saya sbb :

1. Urutan jawaban sudah benar

2. Kesalahan : pada soal diminta kolom bertulangan 4 sisi tetapi grafik menggunakan 2 sisi, gambar penulangan yang disajikan 4 sisi. Jadi tidak konsisten.

3. Apabila digunakan grafik kolom 4 sisi diperoleh sbb :

r=0.07 (ektrapolasi)

beta=0.60 (fc=15 MPa.); maka Rho-t=0.07*0.60=0.042

Ast=0.042*40*40=67.2cm2

dipakai diameter tulangan D19-->As=0.25*3.14*1.9^2=2.83 cm2

Jumlah tulangan nb=67.2/2.83=23.74 dibulatkan 24.

Tulangan yang dipakai : 24D19

Kontrol :
Bila digunakan Program DsgWin -->
https://sites.google.com/site/strukturbeton1/dsgwin-program-disain-beton-bertulang
Diperoleh : Ast=68.04 cm2 dipakai 24D19 !
Hasil mendekati !
Sekian, selamat mencoba soal yang lain.

SANS for Windows V.4.7

Concrete Design Utility

(C) Faheem Ahmad & Nathan Madutujuh, 1999-2004

LICENSEE : Civil Engineering Student

UNIT SYSTEM : Kg, cm

DESIGN CODE : PBI-91

DESIGN TARGET : Rect Column

Min Column Rebar Percent = 1.000 %

DATA:

Column Width, Bw = 40.00 cm

Column Height, Ht = 40.00 cm

Factored Moment, Mu = 20000.00 kg.m

Factored Shear, Vu = 0.00 kg

Factored Normal, Pu = 100000.00 kg

Factored Torsion, Tu = 0.00 kg.m

Concrete Compressive Strength fc1 = 150.00 kg/cm2

Concrete Crack Strength fcr = 150.00 kg/cm2

Concrete Initial Strength fci = 120.00 kg/cm2

Main Rebar Yield Strength fy = 4000.00 kg/cm2

Stirrups Rebar Yield Strength fyv = 2400.00 kg/cm2

Main rebar diameter dbm = 1.90 cm

2nd main rebar diameter dbn = 1.90 cm

Stirrups Rebar diameter dbv = 1.00 cm

Min concrete cover, Cover = 4.00 cm

Min rebar clear space, Minclrspc = 2.50 cm

RESULT:

Flexural Reinforcement: OK

Balanced neutral axis, cbal = 20.5871 cm

Balanced Compr. block, abal = 17.4990 cm

Balanced Moment Capacity, Mnb = 35586.56 kg.m

Balanced Normal Capacity, Pnb = 89490.90 kg

Balanced Eccentricity, ebal = 39.77 cm

Location of neutral axis, c = 23.8331 cm

Length of compression block, a = 20.2582 cm

Total Rebar (incl. side bar) nbt = 24 d19

Total Side Rebar nbs = 0 d19

Total Rebar area, Ast = 68.0469 cm2 = 4.25%

Nominal Moment Capacity, Md = 20409.26 kg.m

Nominal Normal Capacity, Pd = 100006.37 kg

Shear Reinforcement: OK

Av = 2*(0.25*Pi*dbv*dbv) = 0.00 cm2

Ag = bw*h = 0.00 cm2

pw = Ast/(bw*d) = 0.0000

x1 = bw-2*cv-2*dbv = 0.00 cm

y1 = h-2*cv-2*dbv = 0.00 cm

Vn = Vu/phi = 0.00 kg

Tn = Tu/phi = 0.00 kg.m

Vc = = 0.00 kg

Tc = = 0.00 kg.m

Vnc = Vn - Vc = 0.00 kg

Tnc = Tn - Tc = 0.00 kg.m

Avs = Vnc/(fy*d) = 0.00 cm2

Ats = Tnc/(zt*x1*y1*fy) = 0.00 cm2

Atst = Avs + 2*Ats = 0.00 cm2

Additional Longitudinal Rebar, At = 0.00 cm2

Stirrups Spacing, spc = 30.40 cm

Senin, 15 Oktober 2012

Diagram Interaksi Kolom PCAColumn

Program PCAColumn
http://www.structurepoint.org
Untuk menghitung kapasitas / kekuatan kolom dengan diagram interaksi.
https://sites.google.com/site/strukturbeton1/program-pcacolumn
.

General Information:
====================
File Name: D:\PROYEK2\PCA_COL\K70X70.col
Project: RS
Column: K70X70 Engineer: SMR
Code: ACI 318-02 Units: Metric

Run Option: Investigation Slenderness: Not considered
Run Axis: X-axis Column Type: Structural

Material Properties:
====================
f'c = 25 MPa fy = 400 MPa
Ec = 23500 MPa Es = 200000 MPa
Ultimate strain = 0.003 mm/mm
Beta1 = 0.85

Section:
========
Rectangular: Width = 700 mm Depth = 700 mm

Gross section area, Ag = 490000 mm^2
Ix = 2.00083e+010 mm^4 Iy = 2.00083e+010 mm^4
Xo = 0 mm Yo = 0 mm

Reinforcement:
==============
Rebar Database: ASTM A615M
Size Diam (mm) Area (mm^2) Size Diam (mm) Area (mm^2) Size Diam (mm) Area (mm^2)
---- --------- ----------- ---- --------- ----------- ---- --------- -----------
# 10 10 71 # 13 13 129 # 16 16 199
# 19 19 284 # 22 22 387 # 25 25 510
# 29 29 645 # 32 32 819 # 36 36 1006
# 43 43 1452 # 57 57 2581

Confinement: Tied; #10 ties with #22 bars, #10 with larger bars.
phi(a) = 0.8, phi(b) = 0.9, phi(c) = 0.65

Layout: Rectangular
Pattern: All Sides Equal (Cover to transverse reinforcement)
Total steel area, As = 13932 mm^2 at 2.84%
36 #22 Cover = 40 mm

Factored Loads and Moments with Corresponding Capacities: (see user's manual for notation)
=========================================================
Pu Mux fMnx
No. kN kN-m kN-m fMn/Mu
--- ------------ ------------ ------------ --------
1 7000.0 500.0 789.1 1.578
2 8000.0 500.0 578.6 1.157

*** Program completed as requested! ***

Angle = 0.0
Point Load Moment NA depth
1 10915.66 -0.00 1947.00
2 10369.88 141.92 1115.07
3 9824.09 272.86 822.19
4 9278.31 437.81 775.49
5 8732.53 589.36 728.91
6 8186.75 720.14 685.28
7 7640.96 830.17 639.44
8 7095.18 932.99 599.48
9 6549.40 1024.59 560.52
10 6003.61 1106.78 524.40
11 5457.83 1179.00 490.54
12 4912.05 1247.83 458.54
13 4366.26 1311.81 428.41
14 3820.48 1373.09 400.81
15 3274.70 1403.72 367.94
16 2728.92 1399.01 332.16
17 2183.13 1374.52 295.93
18 1637.35 1331.46 260.28
19 1091.57 1315.36 221.23
20 545.78 1383.44 181.65
21 0.00 1400.11 151.55
22 -984.96 1165.16 111.67
23 -1969.92 895.77 77.95
24 -2954.88 608.09 53.01
25 -3939.84 309.78 36.71
26 -4924.80 0.00 0.00

Bahan Bacaan Struktur Beton Bertulang

https://sites.google.com/site/strukturbeton1/teori-dan-rumus-balok-dan-pelat-beton-bertulang

Minggu, 14 Oktober 2012

Program Diagram Interaksi Kolom

Program Diagram Interaksi Kolom
BCOL
https://sites.google.com/site/strukturbeton1/bcol-program-diagram-interaksi-kolomi
Output Program dalam file : CONBAR (bukan *.exe) buka dengan NotePad dan Gambarkan dalam Excel !

Contoh Output :
.

SANS/89 Design Aid
Concrete Design PBI- 91
K7036D22
Column Interaction D iagram
fc1 = 249.0
fy = 4000.0
Es = 2.1e+06
Ag = 4900.0
ecmax = 0.0030
Beta = 0.8300
As = 136.8478
rho = 2.7928 %
Strength Reduction F actor (phi) was corrected for Po < 0.1.fc1.Ag
Bending Moment
Normal Force
1
1
0
20000000
-400000
900000
10
10
0
91
0 -350330.3218 0 -350.3303218
6190901.872 -233553.6641 61.90901872 -233.5536641
9466490.408 -116777.0072 94.66490408 -116.7770072
12420381.06 -0.3498 124.2038106 -0.0003498
12492665.66 116776.3074 124.9266566 116.7763074
12537583.86 126612.3812 125.3758386 126.6123812
12685378.24 136448.4555 126.8537824 136.4484555
12830945.8 146284.5291 128.309458 146.2845291
12974081.1 156120.6035 129.740811 156.1206035
13100782.92 165956.6769 131.0078292 165.9566769
13218098.79 175792.7513 132.1809879 175.7927513
13333633.12 185628.8254 133.3363312 185.6288254
13447215.06 195464.8985 134.4721506 195.4648985
13558673.37 205300.9732 135.5867337 205.3009732
13667836.87 215137.047 136.6783687 215.137047
13774535.13 224973.1205 137.7453513 224.9731205
13859797.59 234809.1948 138.5979759 234.8091948
13941334.25 244645.2683 139.4133425 244.6452683
14020991.64 254481.3423 140.2099164 254.4813423
14098623.33 264317.4166 140.9862333 264.3174166
14174082.69 274153.4905 141.7408269 274.1534905
14247223.22 283989.5645 142.4722322 283.9895645
14305986.71 293825.6385 143.0598671 293.8256385
14353264.93 303661.7128 143.5326493 303.6617128
14398703.01 313497.7865 143.9870301 313.4977865
14442173.01 323333.8599 144.4217301 323.3338599
14483546.67 333169.934 144.8354667 333.169934
14522217.75 343006.0079 145.2221775 343.0060079
14555210.77 352842.0818 145.5521077 352.8420818
14569993.93 362678.1566 145.6999393 362.6781566
14577603.22 372514.2298 145.7760322 372.5142298
14583306.99 382350.3038 145.8330699 382.3503038
14586986.39 392186.3784 145.8698639 392.1863784
14588522.56 402022.4523 145.8852256 402.0224523
14587796.84 411858.5257 145.8779684 411.8585257
14570471.4 421694.5995 145.704714 421.6945995
14467978.82 431530.6739 144.6797882 431.5306739
14381639.83 441366.748 143.8163983 441.366748
14294777.2 451202.8218 142.947772 451.2028218
14207331.3 461038.8958 142.073313 461.0388958
14119241.24 470874.9696 141.1924124 470.8749696
14030444.9 480711.0435 140.304449 480.7110435
13940878.99 490547.1173 139.4087899 490.5471173
13850479.07 500383.1916 138.5047907 500.3831916
13759179.63 510219.2651 137.5917963 510.2192651
13666914.04 520055.3393 136.6691404 520.0553393
13573614.72 529891.4133 135.7361472 529.8914133
13479213.1 539727.4874 134.792131 539.7274874
13383639.7 549563.5613 133.836397 549.5635613
13286824.17 559399.6351 132.8682417 559.3996351
13188695.36 569235.7093 131.8869536 569.2357093
13089181.37 579071.7834 130.8918137 579.0717834
12978249.67 588907.8571 129.7824967 588.9078571
12875523.77 598743.9309 128.7552377 598.7439309
12771182.43 608580.0052 127.7118243 608.5800052
12665151.21 618416.0787 126.6515121 618.4160787
12557355.15 628252.1533 125.5735515 628.2521533
12447718.94 638088.2272 124.4771894 638.0882272
12336166.88 647924.3009 123.3616688 647.9243009
12222622.96 657760.3751 122.2262296 657.7603751
12106357.09 667596.4491 121.0635709 667.5964491
11985055.73 677432.5232 119.8505573 677.4325232
11861523.86 687268.597 118.6152386 687.268597
11735682.73 697104.6703 117.3568273 697.1046703
11607453.61 706940.7445 116.0745361 706.9407445
11476757.91 716776.8186 114.7675791 716.7768186
11337850.02 726612.8923 113.3785002 726.6128923
11201607.69 736448.9664 112.0160769 736.4489664
11062652.99 746285.0406 110.6265299 746.2850406
10920908.27 756121.1144 109.2090827 756.1211144
10776296.21 765957.1885 107.7629621 765.9571885
10628739.95 775793.262 106.2873995 775.793262
10478163.01 785629.336 104.7816301 785.629336
10324489.44 795465.4103 103.2448944 795.4654103
10167643.84 805301.4842 101.6764384 805.3014842
10007551.35 815137.558 100.0755135 815.137558
9844137.721 824973.6325 98.44137721 824.9736325
9677329.377 834809.7061 96.77329377 834.8097061
9505017.211 844645.7799 95.05017211 844.6457799
9330693.653 854481.8543 93.30693653 854.4818543
9152748.699 864317.9275 91.52748699 864.3179275
8971111.693 874154.0022 89.71111693 874.1540022
8785712.85 883990.0763 87.8571285 883.9900763
8596483.161 893826.1502 85.96483161 893.8261502
8403354.453 903662.224 84.03354453 903.662224
8206259.407 913498.2975 82.06259407 913.4982975
8005131.55 923334.3718 80.0513155 923.3343718
7799565.951 933170.4461 77.99565951 933.1704461
7586785.003 943006.5193 75.86785003 943.0065193
7370314.816 952842.5935 73.70314816 952.8425935
7148656.231 962678.6671 71.48656231 962.6786671
6921894.423 972514.7417 69.21894423 972.5147417
6690250.995 982350.8153 66.90250995 982.3508153
0 983607.3955 0 983.6073955

.
Contoh Plot pada Exel dari hasil CONBAR :
Kolom 80x100 cm; fc'=300 kg/cm2; fy=4000 kg/cm2

Tugas :
Gambarkan Diagram Interaksi Setiap Kolom Berikut :
fc'=250 kg/cm2; fy=4000 kg/cm2