Perbandingan Hasil Perhitungan (SK SNI T-15-1991-03)
Diagram Interaksi Kolom Beton Uniaksial dan Biaksial
Program Bantu PCACOL
14/05/03 PCACOL V3.00 - PORTLAND CEMENT ASSOCIATION - Page 2 General Information:
====================
File Name: C:\PROGRA~1\PCACOL\DATA\ALIAP14.COL Project: Ali A., P.14
Column: K400x400 Engineer: syont Code: ACI 318-95 Units: Metric
Run Option: Investigation Slenderness: Not considered Run Axis: X-axis Column Type: Structural Material Properties:
====================
f'c = 20 MPa fy = 300 MPa Ec = 21019 MPa Es = 200000 MPa
fc = 17 MPa Rupture strain = Infinity Ultimate strain = 0.003 mm/mm
Beta1 = 0.85 Section:
========
Gross section area, Ag = 160000 mm^2
Ix = 2.13333e+009 mm^4 Iy = 2.13333e+009 mm^4 Xo = 0 mm Yo = 0 mm
Reinforcement: ==============
Rebar Database: User-defined
Size Diam (mm) Area (mm^2) Size Diam (mm) Area (mm^2) Size Diam (mm) Area (mm^2) ---- --- ---- --- ---- --- # 6 6 28 # 8 8 50 # 10 10 79 # 12 12 113 # 13 13 133 # 14 14 154 # 16 16 201 # 19 19 284 # 20 20 314 # 22 22 380 # 25 25 491 # 28 28 616 # 32 32 801 # 40 40 1256
Confinement: User-defined; #6 ties with #19 bars, #6 with larger bars. phi(a) = 0.8, phi(b) = 0.8, phi(c) = 0.65
Layout: Rectangular
Pattern: Sides Different (Cover to longitudinal reinforcement) Total steel area, As = 3801 mm^2 at 2.38%
Top Bottom Left Right Bars 5 #22 5 #22 0 #22 0 #22 Cover(mm) 49 49 49 49
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 3795.0 0.0 0.0 0.000 2 2467.0 0.0 0.0 0.000 3 3036.0 0.0 0.0 0.000 4 1973.0 0.0 77.1 999.999 5 1398.0 147.0 142.7 0.970 6 853.0 192.0 187.4 0.976 7 601.0 183.0 181.5 0.992 8 0.0 111.0 137.5 1.239 9 0.0 137.0 137.5 1.004
14/05/03 PCACOL V3.00 - PORTLAND CEMENT ASSOCIATION - Page 3 General Information:
====================
File Name: C:\PROGRA~1\PCACOL\DATA\ALIAP17.COL Project: Ali A., P.14
Column: K400x400 Engineer: syont Code: ACI 318-95 Units: Metric
Run Option: Investigation Slenderness: Not considered Run Axis: X-axis Column Type: Structural Material Properties:
====================
f'c = 20 MPa fy = 300 MPa Ec = 21019 MPa Es = 200000 MPa
fc = 17 MPa Rupture strain = Infinity Ultimate strain = 0.003 mm/mm
Beta1 = 0.85 Section:
========
14/05/03 PCACOL V3.00 - PORTLAND CEMENT ASSOCIATION - Page 2 General Information:
====================
File Name: C:\PROGRA~1\PCACOL\DATA\ALIAP17R.COL Project: Ali A., P.17
Column: K400x400 Engineer: syont Code: ACI 318-95 Units: Metric
Run Option: Investigation Slenderness: Not considered Run Axis: X-axis Column Type: Structural Material Properties:
====================
f'c = 20 MPa fy = 300 MPa Ec = 21019 MPa Es = 200000 MPa
fc = 17 MPa Rupture strain = Infinity Ultimate strain = 0.003 mm/mm
Beta1 = 0.85 Section:
========
Rectangular: Width = 400 mm Depth = 400 mm Gross section area, Ag = 160000 mm^2
Ix = 2.13333e+009 mm^4 Iy = 2.13333e+009 mm^4 Xo = 0 mm Yo = 0 mm
Reinforcement: ==============
Rebar Database: User-defined
Size Diam (mm) Area (mm^2) Size Diam (mm) Area (mm^2) Size Diam (mm) Area (mm^2) ---- --- ---- --- ---- --- # 6 6 28 # 8 8 50 # 10 10 79 # 12 12 113 # 13 13 133 # 14 14 154 # 16 16 201 # 19 19 284 # 20 20 314 # 22 22 380 # 25 25 491 # 28 28 616 # 32 32 801 # 40 40 1256
Confinement: User-defined; #6 ties with #19 bars, #6 with larger bars. phi(a) = 0.8, phi(b) = 0.8, phi(c) = 0.65
Pattern: Irregular
Total steel area, As = 3801 mm^2 at 2.38%
Area mm^2 X (mm) Y (mm) Area mm^2 X (mm) Y (mm) Area mm^2 X (mm) Y (mm) - - - 380 -140 140 380 0 140 380 140 140 380 -140 -140 380 0 -140 380 140 -140 380 -140 80 380 -140 -80 380 140 80 380 140 -80
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 2467.0 0.0 0.0 0.000 2 1973.0 0.0 73.5 999.999 3 1458.0 131.4 127.3 0.968 4 923.7 167.3 163.7 0.978 5 527.0 159.4 158.4 0.994 6 0.0 99.2 133.3 1.344 7 0.0 122.1 133.3 1.092 *** Program completed as requested! ***
14/05/03 PCACOL V3.00 - PORTLAND CEMENT ASSOCIATION - Page 2 General Information:
====================
File Name: C:\PROGRA~1\PCACOL\DATA\ALIAP126.COL Project: Ali A., P.126
Column: K400x400 Engineer: syont Code: ACI 318-95 Units: Metric
Run Option: Investigation Slenderness: Not considered Run Axis: Biaxial Column Type: Structural Material Properties:
====================
f'c = 20 MPa fy = 300 MPa Ec = 21019 MPa Es = 200000 MPa
fc = 17 MPa Rupture strain = Infinity Ultimate strain = 0.003 mm/mm
Beta1 = 0.85 Section:
========
Rectangular: Width = 400 mm Depth = 400 mm Gross section area, Ag = 160000 mm^2
Ix = 2.13333e+009 mm^4 Iy = 2.13333e+009 mm^4 Xo = 0 mm Yo = 0 mm
Reinforcement: ==============
Rebar Database: User-defined
Size Diam (mm) Area (mm^2) Size Diam (mm) Area (mm^2) Size Diam (mm) Area (mm^2) ---- --- ---- --- ---- --- # 6 6 28 # 8 8 50 # 10 10 79 # 12 12 113 # 13 13 133 # 14 14 154 # 16 16 201 # 19 19 284 # 20 20 314 # 22 22 380 # 25 25 491 # 28 28 616 # 32 32 801 # 40 40 1256
Confinement: User-defined; #6 ties with #19 bars, #6 with larger bars. phi(a) = 0.8, phi(b) = 0.8, phi(c) = 0.65
Layout: Rectangular
Pattern: Sides Different (Cover to longitudinal reinforcement) Total steel area, As = 3969 mm^2 at 2.48%
Top Bottom Left Right Bars 5 #19 5 #19 2 #19 2 #19 Cover(mm) 49 49 49 49
Factored Loads and Moments with Corresponding Capacities: (see user's manual for notation) =========================================================
Pu Mux Muy fMnx fMny
No. kN kN-m kN-m kN-m kN-m fMn/Mu --- --- --- --- --- --- 1 1998.5 0.0 0.0 0.0 0.0 0.000 2 2498.0 0.0 0.0 0.0 0.0 0.000 3 1184.0 154.0 0.0 150.7 0.0 0.979 4 905.0 170.0 0.0 167.3 0.0 0.984 5 504.0 162.0 0.0 162.2 0.0 1.001 6 0.0 106.0 0.0 143.4 0.0 1.353 7 0.0 130.0 0.0 143.4 0.0 1.103 8 1214.0 0.0 145.0 0.0 142.9 0.986 9 931.0 0.0 159.0 0.0 157.5 0.990
14/05/03 PCACOL V3.00 - PORTLAND CEMENT ASSOCIATION - Page 3 10 586.0 0.0 151.0 0.0 156.2 1.034
11 0.0 0.0 108.0 0.0 139.8 1.294 12 0.0 0.0 133.0 0.0 139.8 1.051 13 800.0 135.0 90.0 120.2 80.4 0.891 *** Program completed as requested! ***
Perbandingan merujuk pada pustaka, titik angka pada point menunjukkan hasil dari perhitungan
manual. Pada persamaan kolom biaksial metode Bresler, adanya suatu konstanta m dan n yang
merupakan fungsi dari bentuk kolom dan konfigurasi tulangan.
a
=
M
uxM
uxo
m
M
uyM
uyo
n1 ...yang berarti aman
dengan,
m = n = 1,5 untuk kolom persegi panjang
m = n = 2,0 untuk kolom bulat / bujur sangkar
Dalam pustaka nilai m = n diambil samadengan 2 yang menghasilkan rasio = 0,97 < 1.0 ... yang berarti
aman.
sedangkan menurut Buyokozturk O. (2004) pada catatan kuliah MIT OpenCourse menyebutkan bahwa:
“Experiments suggest that m = n =
α
depends on column geometry. Typically 1.15 <
α
< 1.55 for most
rectangular columns with uniform reinforcement.
... There is no single value that can be assigned to the exponent to represent the true shape of the load
contour in all cases”
Jika merujuk pada pernyataan diatas, maka nilai m = n diambil misal samadengan 1,55 yang
menghasilkan rasio = 1,13 > 1,0 ... yang berarti tidak aman.
Konstanta tersebut menghasilkan rasio yang lebih mendekati dengan analisa permukaan runtuh 3D
program bantu PCACOL, seperti yang ditunjukkan plot diagram M
nxdan M
nypada beban aksial konstan
Pn
= 800 kN.
Selisih perhitungan diagram kekuatan kolom uniaksial dapat dianggap kecil ini diakibatkan pada
pembulatan angka, sedangkan pada perbandingan diagram kekuatan kolom biaksial terlihat cukup
signifikan karena pengaruh konstanta m dan n.
Berikut perbandingan lain untuk kolom biaksial dengan bentuk tidak beraturan yaitu bentuk L,
perbandingan yang digunakan adalah dari penelitian Hsu (1985) melalui Rodriguez & Dario (1999)
untuk kejelasan satuan dibuat SI.
Dimensi :
Btop
= 3 * 25.4 = 76.2 mm
Bbot
= 6 * 25.4 = 152.4 mm
H = 7.5 * 25.4 = 190.5 mm
Cover
= 0.5 * 25.4 = 12.7 mm
Tulangan,
Ǿ
3/8” = (3/8)*25.4 = 9.525 mm
Atul
= (1/4)*Pi*9.525^2 = 71.25 mm
2Mutu Bahan :
Beton, f'
c= 3.5*6.894757 = 24.13 Mpa
ε
ult= 0.0038 in/in (mm/mm)
Baja, f
y= 51.8* 6.894757 = 357.15 Mpa
Letak garis netral
x'
= ((152.4*76.2*76.2)+(76.2*(190.5-76.2)*38.1))/((152.4*76.2)+(76.2*(190.5-76.2)))
= 59.87 mm
y'
= ((152.4*76.2*(76.2/2))+(76.2*(190.5-76.2)*133.35))/((152.4*76.2)+(76.2*(190.5-76.2)))
= 78.92 mm
Penulis tidak mendapatkan adanya data angka hasil penelitian, hanya plot grafik yang terdapat pada
pustaka sehingga dilakukan skala digital untuk mendapatkan nilai (P
n,M
n) tersebut. Dari hasil skala
pada P
n=120 kips terlihat adanya perbedaan ini kemungkinan besar disebabkan distorsi gambar pada
proses scaning. Namun setidaknya langkah ini dapat menjadikan suatu perbandingan walaupun
nilainya kurang tepat.
Skala Horisontal arah-X (Momen, M
n) = 10 Kip.in
Skala Vertikal arah-Y (Aksial, P
n) = 20 Kips
Point 1
Pn
= 8.58*20*4.448222 = 763.31 kN.
Mn
= ((0.00*10)/12)*1.355818 = 0.00 kN.m
1
2
3
4
5
6
7
8
9
10
Point 2
Pn
= 7.80*20*4.448222 = 693.92 kN.
Mn
= ((1.89*10)/12)*1.355818 = 2.14 kN.m
Point 3
Pn
= 7.07*20*4.448222 = 628.97 kN.
Mn
= ((3.72*10)/12)*1.355818 = 4.20 kN.m
Point 4
Pn
= 6.12*20*4.448222 = 544.46 kN.
Mn
= ((5.49*10)/12)*1.355818 = 6.20 kN.m
Point 5
Pn
= 5.41*20*4.448222 = 481.29 kN.
Mn
= ((7.65*10)/12)*1.355818 = 8.64 kN.m
Point 6
Pn
= 3.69*20*4.448222 = 328.27 kN.
Mn
= ((9.7*10)/12)*1.355818 = 10.96 kN.m
Point 7
Pn
= 2.38*20*4.448222 = 211.73 kN.
Mn
= ((10.35*10)/12)*1.355818 = 11.69 kN.m
Point 8
Pn
= 1.28*20*4.448222 = 113.87 kN.
Mn
= ((10.03*10)/12)*1.355818 = 11.33 kN.m
Point 9
Pn
= 0.46*20*4.448222 = 40.92 kN.
Mn
= ((9.57*10)/12)*1.355818 = 10.81 kN.m
Point 10
Pn
= 0.00*20*4.448222 = 0.00 kN.
Mn
= ((8.75*10)/12)*1.355818 = 9.89 kN.m
Dalam penggunaan program bantu PCACOL tidak dapat dipergunakan input beban (P
n, M
n) pada suatu
sudut putar 45
onamun hanya digunakan input beban pada sudut putar 0
o(M
y) dan 90
o(M
x) sehingga
14/05/03 PCACOL V3.00 - PORTLAND CEMENT ASSOCIATION - Page 2 General Information:
====================
File Name: C:\PROGRA~1\PCACOL\DATA\JSEAD.COL Project: Rodriguez, Dario 1999
Column: L-shaped Engineer: syont Code: ACI 318-95 Units: Metric
Run Option: Investigation Slenderness: Not considered Run Axis: Biaxial Column Type: Structural Material Properties:
====================
f'c = 24.13 MPa fy = 357.15 MPa Ec = 23087.5 MPa Es = 200000 MPa
fc = 20.5105 MPa Rupture strain = Infinity Ultimate strain = 0.0038 mm/mm
Beta1 = 0.85 Section:
========
Exterior Points
No. X (mm) Y (mm) No. X (mm) Y (mm) No. X (mm) Y (mm) --- --- --- 1 -60 112 2 16 112 3 16 -3 4 93 -3 5 93 -79 6 -60 -79 Gross section area, Ag = 20322.5 mm^2
Ix = 6.02551e+007 mm^4 Iy = 3.39154e+007 mm^4 Xo = 0.00142852 mm Yo = 0.00143006 mm Reinforcement:
==============
Rebar Database: prEN 10080
Size Diam (mm) Area (mm^2) Size Diam (mm) Area (mm^2) Size Diam (mm) Area (mm^2) ---- --- ---- --- ---- --- # 6 6 28 # 8 8 50 # 10 10 79 # 12 12 113 # 14 14 154 # 16 16 201 # 20 20 314 # 25 25 491 # 28 28 616 # 32 32 801 # 40 40 1256
Confinement: User-defined; #6 ties with #25 bars, #6 with larger bars. phi(a) = 1, phi(b) = 1, phi(c) = 1
Pattern: Irregular
Total steel area, As = 998 mm^2 at 4.91%
Area mm^2 X (mm) Y (mm) Area mm^2 X (mm) Y (mm) Area mm^2 X (mm) Y (mm) - - - 71 -42 94 71 1 94 71 -42 56 71 1 56 71 -42 -20 71 1 -20 71 -42 18 71 1 18 71 -42 -61 71 1 -61 71 75 -20 71 75 -61 71 37 -61 71 37 -20
14/05/03 PCACOL V3.00 - PORTLAND CEMENT ASSOCIATION - Page 3 Control Points:
===============
Axial Load P X-Moment Y-Moment N.A. depth Bending about kN kN-m kN-m mm --- - - - X @ Pure compression 752.6 -0 0 326 @ Max compression 752.6 -0 0 326 @ fs = 0.0 606.5 12 4 173 @ fs = 0.5*fy 503.3 18 6 140 @ Balanced point 416.9 23 8 118 @ Pure bending -0.0 20 6 45 @ Pure tension -356.3 0 -0 0 Y @ Pure compression 752.6 -0 0 255 @ Max compression 752.6 -0 0 255 @ fs = 0.0 445.5 5 12 135 @ fs = 0.5*fy 253.5 8 15 109 @ Balanced point 80.7 11 17 92 @ Pure bending -0.0 10 16 77 @ Pure tension -356.3 0 -0 0 -X @ Pure compression 752.6 -0 0 326 @ Max compression 752.6 -0 0 326 @ fs = 0.0 469.6 -15 -4 173 @ fs = 0.5*fy 278.7 -20 -7 140 @ Balanced point 143.9 -24 -8 118 @ Pure bending -0.0 -24 -8 90 @ Pure tension -356.3 0 -0 0 -Y @ Pure compression 752.6 -0 0 255 @ Max compression 752.6 -0 0 255 @ fs = 0.0 625.4 -5 -8 135 @ fs = 0.5*fy 540.0 -8 -12 109 @ Balanced point 447.2 -11 -15 92 @ Pure bending 0.0 -6 -16 33 @ Pure tension -356.3 0 -0 0 *** Program completed as requested! ***
Skala Horisontal (Momen, M
n
) = 1 kN.m
Skala Vertikal arah-Y (Aksial, P
n
) = 50 KN
Perbedaan dalam asumsi perhitungan pada program PCACOL menggunakan diagram tegangan persegi
metode Whitney, sedangkan pustaka menggunakan blok tegangan tekan beton motode second degree
parabola. Selain itu asumsi pada pustaka menggunakan hubungan tegangan regangan elastoplastis
multi-linear baja tulangan, sehingga hasil perhitungan lebih mendekati dengan hasil penelitian.
Dari hasil plot diagram interaksi kolom terlihat pada beban aksial yang besar (P > 40% Pn) hasil
PCACOL cukup mendekati dengan hasil penelitian, namun pada keadaan P kecil hasilnya over
Catatan : Kolom bentuk lain seperti bentuk T, Box, Circular-Hollow sedang dalam tahap
akan dibuat tulisannya di kesempatan mendatang.
PUSTAKA
●
Asroni, A., Trinugroho, S., 2001, Struktur Beton II, KMTS Universitas Muhammadiyah
Surakarta
●
Buyokozturk, O., 2004, Mechanics and Design of Concrete Structures, MIT OpenCourse
●
