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 -
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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 Run Axis: X-axis Material Properties: ==================== f'c = 20 MPa Ec = 21019 MPa fc = 17 MPa Ultimate strain = 0.003 mm/mm Beta1 = 0.85 Section: ======== Rectangular: Width = 400 mm
Catatan-catatan kecil - Suyono Nt.
Slenderness: Not considered Column Type: Structural
fy = 300 MPa Es = 200000 MPa Rupture strain = Infinity
Depth = 400 mm
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Gross section area, Ag = Ix = 2.13333e+009 mm^4 Xo = 0 mm
160000 mm^2
Reinforcement: ============== Rebar Database: User-defined Size Diam (mm) Area (mm^2) ---- --------- ----------# 6 6 28 # 12 12 113 # 16 16 201 # 22 22 380 # 32 32 801
Iy = Yo =
2.13333e+009 mm^4 0 mm
Size Diam (mm) Area (mm^2) ---- --------- ----------# 8 8 50 # 13 13 133 # 19 19 284 # 25 25 491 # 40 40 1256
Confinement: User-defined; #6 ties with #19 bars, phi(a) = 0.8, phi(b) = 0.8, phi(c) = 0.65
Size Diam (mm) Area (mm^2) ---- --------- ----------# 10 10 79 # 14 14 154 # 20 20 314 # 28 28 616
#6 with larger bars.
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 -
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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 Run Axis: X-axis Material Properties: ==================== f'c = 20 MPa Ec = 21019 MPa fc = 17 MPa Ultimate strain = 0.003 mm/mm Beta1 = 0.85 Section: ======== Rectangular: Width = 400 mm
Catatan-catatan kecil - Suyono Nt.
Slenderness: Not considered Column Type: Structural
fy = 300 MPa Es = 200000 MPa Rupture strain = Infinity
Depth = 400 mm
Hal. 2 dari 14
14/05/03 PCACOL V3.00 - PORTLAND CEMENT ASSOCIATION -
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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 Run Axis: X-axis
Slenderness: Not considered Column Type: Structural
Material Properties: ==================== f'c = 20 MPa Ec = 21019 MPa fc = 17 MPa Ultimate strain = 0.003 mm/mm Beta1 = 0.85 Section: ======== Rectangular: Width = 400 mm Gross section area, Ag = Ix = 2.13333e+009 mm^4 Xo = 0 mm
Catatan-catatan kecil - Suyono Nt.
fy = 300 MPa Es = 200000 MPa Rupture strain = Infinity
Depth = 400 mm
160000 mm^2 Iy = Yo =
2.13333e+009 mm^4 0 mm
Hal. 3 dari 14
Reinforcement: ============== Rebar Database: User-defined Size Diam (mm) Area (mm^2) ---- --------- ----------# 6 6 28 # 12 12 113 # 16 16 201 # 22 22 380 # 32 32 801
Size Diam (mm) Area (mm^2) ---- --------- ----------# 8 8 50 # 13 13 133 # 19 19 284 # 25 25 491 # 40 40 1256
Confinement: User-defined; #6 ties with #19 bars, phi(a) = 0.8, phi(b) = 0.8, phi(c) = 0.65
Size Diam (mm) Area (mm^2) ---- --------- ----------# 10 10 79 # 14 14 154 # 20 20 314 # 28 28 616
#6 with larger bars.
Pattern: Irregular Total steel area, As = 3801 mm^2 at 2.38% Area mm^2 X (mm) Y (mm) --------- -------- -------380 -140 140 380 -140 -140 380 -140 80 380 140 -80
Area mm^2 X (mm) Y (mm) --------- -------- -------380 0 140 380 0 -140 380 -140 -80
Area mm^2 X (mm) Y (mm) --------- -------- -------380 140 140 380 140 -140 380 140 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! ***
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14/05/03 PCACOL V3.00 - PORTLAND CEMENT ASSOCIATION -
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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 Run Axis: Biaxial
Slenderness: Not considered Column Type: Structural
Material Properties: ==================== f'c = 20 MPa Ec = 21019 MPa fc = 17 MPa Ultimate strain = 0.003 mm/mm Beta1 = 0.85 Section: ======== Rectangular: Width = 400 mm Gross section area, Ag = Ix = 2.13333e+009 mm^4 Xo = 0 mm
fy = 300 MPa Es = 200000 MPa Rupture strain = Infinity
Depth = 400 mm
160000 mm^2
Reinforcement: ============== Rebar Database: User-defined Size Diam (mm) Area (mm^2) ---- --------- ----------# 6 6 28 # 12 12 113 # 16 16 201 # 22 22 380 # 32 32 801
Iy = Yo =
2.13333e+009 mm^4 0 mm
Size Diam (mm) Area (mm^2) ---- --------- ----------# 8 8 50 # 13 13 133 # 19 19 284 # 25 25 491 # 40 40 1256
Confinement: User-defined; #6 ties with #19 bars, phi(a) = 0.8, phi(b) = 0.8, phi(c) = 0.65
Size Diam (mm) Area (mm^2) ---- --------- ----------# 10 10 79 # 14 14 154 # 20 20 314 # 28 28 616
#6 with larger bars.
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
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586.0 0.0 0.0 800.0
0.0 0.0 0.0 135.0
151.0 108.0 133.0 90.0
0.0 0.0 0.0 120.2
Page 156.2 139.8 139.8 80.4
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1.034 1.294 1.051 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. m n M ux M uy a= 1 ...yang berarti aman M uxo M uyo 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.
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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 Mnx dan Mny pada 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 mm2 Mutu Bahan : Beton, f'c = 3.5*6.894757 = 24.13 Mpa εult = 0.0038 in/in (mm/mm) Baja, fy = 51.8* 6.894757 = 357.15 Mpa
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2 3 4 5 6 7 8 9 10
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 (Pn,Mn) tersebut. Dari hasil skala pada Pn=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, Mn) = 10 Kip.in Skala Vertikal arah-Y (Aksial, Pn) = 20 Kips Point 1 Pn = 8.58*20*4.448222 = 763.31 kN. Mn = ((0.00*10)/12)*1.355818 = 0.00 kN.m Catatan-catatan kecil - Suyono Nt.
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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
Penentuan koordinat titik tepi penampang dan koordinat baja tulangan terhadap sumbu netral. Catatan-catatan kecil - Suyono Nt.
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Dalam penggunaan program bantu PCACOL tidak dapat dipergunakan input beban (Pn, Mn) pada suatu sudut putar 45o namun hanya digunakan input beban pada sudut putar 0o (My) dan 90o (Mx) sehingga hasil plot beban dilakukan dengan cara skala digital.
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14/05/03 PCACOL V3.00 - PORTLAND CEMENT ASSOCIATION -
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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 Run Axis: Biaxial
Slenderness: Not considered Column Type: Structural
Material Properties: ==================== f'c = 24.13 MPa Ec = 23087.5 MPa fc = 20.5105 MPa Ultimate strain = 0.0038 mm/mm Beta1 = 0.85 Section: ======== Exterior Points No. X (mm) Y (mm) ----- ---------- ---------1 -60 112 4 93 -3 Gross section area, Ag = Ix = 6.02551e+007 mm^4 Xo = 0.00142852 mm
fy = 357.15 MPa Es = 200000 MPa Rupture strain = Infinity
No. X (mm) Y (mm) ----- ---------- ---------2 16 112 5 93 -79
No. X (mm) Y (mm) ----- ---------- ---------3 16 -3 6 -60 -79
20322.5 mm^2
Reinforcement: ============== Rebar Database: prEN 10080 Size Diam (mm) Area (mm^2) ---- --------- ----------# 6 6 28 # 12 12 113 # 20 20 314 # 32 32 801
Iy = Yo =
3.39154e+007 mm^4 0.00143006 mm
Size Diam (mm) Area (mm^2) ---- --------- ----------# 8 8 50 # 14 14 154 # 25 25 491 # 40 40 1256
Confinement: User-defined; #6 ties with #25 bars, phi(a) = 1, phi(b) = 1, phi(c) = 1
Size Diam (mm) Area (mm^2) ---- --------- ----------# 10 10 79 # 16 16 201 # 28 28 616
#6 with larger bars.
Pattern: Irregular Total steel area, As = 998 mm^2 at 4.91% Area mm^2 X (mm) Y (mm) --------- -------- -------71 -42 94 71 1 56 71 -42 18 71 1 -61 71 37 -61
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Area mm^2 X (mm) Y (mm) --------- -------- -------71 1 94 71 -42 -20 71 1 18 71 75 -20 71 37 -20
Area mm^2 X (mm) Y (mm) --------- -------- -------71 -42 56 71 1 -20 71 -42 -61 71 75 -61
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14/05/03 PCACOL V3.00 - PORTLAND CEMENT ASSOCIATION -
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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 Max compression fs = 0.0 fs = 0.5*fy Balanced point Pure bending Pure tension
752.6 752.6 445.5 253.5 80.7 -0.0 -356.3
-0 -0 5 8 11 10 0
0 0 12 15 17 16 -0
255 255 135 109 92 77 0
-X @ @ @ @ @ @ @
Pure compression Max compression fs = 0.0 fs = 0.5*fy Balanced point Pure bending Pure tension
752.6 752.6 469.6 278.7 143.9 -0.0 -356.3
-0 -0 -15 -20 -24 -24 0
0 0 -4 -7 -8 -8 -0
326 326 173 140 118 90 0
-Y @ @ @ @ @ @ @
Pure compression Max compression fs = 0.0 fs = 0.5*fy Balanced point Pure bending Pure tension
752.6 752.6 625.4 540.0 447.2 0.0 -356.3
-0 -0 -5 -8 -11 -6 0
0 0 -8 -12 -15 -16 -0
255 255 135 109 92 33 0
*** Program completed as requested! ***
Skala Horisontal (Momen, Mn) = 1 kN.m Skala Vertikal arah-Y (Aksial, Pn) = 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 estimated.
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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 ● Rodriguez, J.A., Aristizabal-Ochoa, J.D.,1999, Biaxial Interaction for Short RC Columns of Any Cross Section, Journal of Structural Engineering
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