Perbandingan Hasil Perhitungan (SK SNI T ) Diagram Interaksi Kolom Beton Uniaksial dan Biaksial Program Bantu PCACOL

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1 Perbandingan Hasil Perhitungan (SK SNI T ) Diagram Interaksi Kolom Beton Uniaksial dan Biaksial Program Bantu PCACOL 14/05/03 PCACOL V 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 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 = MPa Es = MPa fc = 17 MPa Rupture strain = Infinity Ultimate strain = mm/mm Beta1 = 0.85 Section: ======== Rectangular: Width = 400 mm Depth = 400 mm Catatan-catatan kecil - Suyono Nt. Hal. 1 dari 14

2 Gross section area, Ag = mm^2 Ix = e+009 mm^4 Xo = 0 mm Iy = e+009 mm^4 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) # # # # # # # # # # # # # # 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) Factored Loads and Moments with Corresponding Capacities: (see user's manual for notation) ================= Pu Mux fmnx No. kn kn-m kn-m fmn/mu /05/03 PCACOL V 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 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 = MPa Es = MPa fc = 17 MPa Rupture strain = Infinity Ultimate strain = mm/mm Beta1 = 0.85 Section: ======== Rectangular: Width = 400 mm Depth = 400 mm Catatan-catatan kecil - Suyono Nt. Hal. 2 dari 14

3 14/05/03 PCACOL V 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 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 = MPa Es = MPa fc = 17 MPa Rupture strain = Infinity Ultimate strain = mm/mm Beta1 = 0.85 Section: ======== Rectangular: Width = 400 mm Gross section area, Ag = mm^2 Ix = e+009 mm^4 Xo = 0 mm Depth = 400 mm Iy = e+009 mm^4 Yo = 0 mm Catatan-catatan kecil - Suyono Nt. Hal. 3 dari 14

4 Reinforcement: ============== Rebar Database: User-defined Size Diam (mm) Area (mm^2) Size Diam (mm) Area (mm^2) Size Diam (mm) Area (mm^2) # # # # # # # # # # # # # # 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) Factored Loads and Moments with Corresponding Capacities: (see user's manual for notation) ================= Pu Mux fmnx No. kn kn-m kn-m fmn/mu *** Program completed as requested! *** Catatan-catatan kecil - Suyono Nt. Hal. 4 dari 14

5 Catatan-catatan kecil - Suyono Nt. Hal. 5 dari 14

6 14/05/03 PCACOL V 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 Units: Metric Run Option: Investigation Slenderness: Not considered Run Axis: Biaxial Column Type: Structural Material Properties: f'c = 20 MPa fy = 300 MPa Ec = MPa Es = MPa fc = 17 MPa Rupture strain = Infinity Ultimate strain = mm/mm Beta1 = 0.85 Section: ======== Rectangular: Width = 400 mm Gross section area, Ag = mm^2 Ix = e+009 mm^4 Xo = 0 mm Depth = 400 mm Iy = e+009 mm^4 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) # # # # # # # # # # # # # # 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) 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 Catatan-catatan kecil - Suyono Nt. Hal. 6 dari 14

7 14/05/03 PCACOL V PORTLAND CEMENT ASSOCIATION - Page *** 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 m n ux 1...yang berarti aman M uxo M uy 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 < yang berarti aman. Catatan-catatan kecil - Suyono Nt. Hal. 7 dari 14

8 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 nx dan M ny pada beban aksial konstan P n = 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 : B top = 3 * 25.4 = 76.2 mm B bot = 6 * 25.4 = mm H = 7.5 * 25.4 = mm C over = 0.5 * 25.4 = 12.7 mm Tulangan, Ǿ 3/8 = (3/8)*25.4 = mm A tul = (1/4)*Pi*9.525^2 = mm 2 Mutu Bahan : Beton, f' c = 3.5* = Mpa ε ult = in/in (mm/mm) Baja, f y = 51.8* = Mpa Catatan-catatan kecil - Suyono Nt. Hal. 8 dari 14

9 Letak garis netral x' = ((152.4*76.2*76.2)+(76.2*( )*38.1))/((152.4*76.2)+(76.2*( ))) = mm y' = ((152.4*76.2*(76.2/2))+(76.2*( )*133.35))/((152.4*76.2)+(76.2*( ))) = 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 P n = 8.58*20* = kn. M n = ((0.00*10)/12)* = 0.00 kn.m Catatan-catatan kecil - Suyono Nt. Hal. 9 dari 14

10 Point 2 P n = 7.80*20* = kn. M n = ((1.89*10)/12)* = 2.14 kn.m Point 3 P n = 7.07*20* = kn. M n = ((3.72*10)/12)* = 4.20 kn.m Point 4 P n = 6.12*20* = kn. M n = ((5.49*10)/12)* = 6.20 kn.m Point 5 P n = 5.41*20* = kn. M n = ((7.65*10)/12)* = 8.64 kn.m Point 6 P n = 3.69*20* = kn. M n = ((9.7*10)/12)* = kn.m Point 7 P n = 2.38*20* = kn. M n = ((10.35*10)/12)* = kn.m Point 8 P n = 1.28*20* = kn. M n = ((10.03*10)/12)* = kn.m Point 9 P n = 0.46*20* = kn. M n = ((9.57*10)/12)* = kn.m Point 10 P n = 0.00*20* = 0.00 kn. M n = ((8.75*10)/12)* = 9.89 kn.m Penentuan koordinat titik tepi penampang dan koordinat baja tulangan terhadap sumbu netral. Catatan-catatan kecil - Suyono Nt. Hal. 10 dari 14

11 Dalam penggunaan program bantu PCACOL tidak dapat dipergunakan input beban (P n, M n ) pada suatu sudut putar 45 o namun hanya digunakan input beban pada sudut putar 0 o (M y ) dan 90 o (M x ) sehingga hasil plot beban dilakukan dengan cara skala digital. Catatan-catatan kecil - Suyono Nt. Hal. 11 dari 14

12 14/05/03 PCACOL V 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 Units: Metric Run Option: Investigation Slenderness: Not considered Run Axis: Biaxial Column Type: Structural Material Properties: f'c = MPa fy = MPa Ec = MPa Es = MPa fc = MPa Rupture strain = Infinity Ultimate strain = mm/mm Beta1 = 0.85 Section: ======== Exterior Points No. X (mm) Y (mm) No. X (mm) Y (mm) No. X (mm) Y (mm) Gross section area, Ag = mm^2 Ix = e+007 mm^4 Xo = mm Iy = e+007 mm^4 Yo = mm Reinforcement: ============== Rebar Database: pren Size Diam (mm) Area (mm^2) Size Diam (mm) Area (mm^2) Size Diam (mm) Area (mm^2) # # # # # # # # # # # 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) Catatan-catatan kecil - Suyono Nt. Hal. 12 dari 14

13 14/05/03 PCACOL V 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 Pure compression Max compression fs = fs = 0.5*fy Balanced point Pure bending Pure tension Pure compression Max compression fs = fs = 0.5*fy Balanced point Pure bending Pure tension Pure compression Max compression fs = fs = 0.5*fy Balanced point Pure bending Pure tension Pure compression Max compression fs = fs = 0.5*fy Balanced point Pure bending Pure tension *** 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% P n ) hasil PCACOL cukup mendekati dengan hasil penelitian, namun pada keadaan P kecil hasilnya over estimated. Catatan-catatan kecil - Suyono Nt. Hal. 13 dari 14

14 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 Catatan-catatan kecil - Suyono Nt. Hal. 14 dari 14